%------------------------------------------------------------------------------
% 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 : n017.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 00:21:08 EDT 2023

% Result   : Theorem 0.73s 0.91s
% Output   : Proof 0.73s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.16  % Problem    : SWW474+1 : TPTP v8.1.2. Released v5.3.0.
% 0.12/0.17  % Command    : do_cvc5 %s %d
% 0.17/0.38  % Computer : n017.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit   : 300
% 0.17/0.38  % WCLimit    : 300
% 0.17/0.38  % DateTime   : Sun Aug 27 21:46:12 EDT 2023
% 0.17/0.38  % CPUTime    : 
% 0.24/0.55  %----Proving TF0_NAR, FOF, or CNF
% 0.73/0.91  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.U7bphOZjUP/cvc5---1.0.5_12470.p...
% 0.73/0.91  ------- get file name : TPTP file name is SWW474+1
% 0.73/0.91  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_12470.smt2...
% 0.73/0.91  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.73/0.91  % SZS status Theorem for SWW474+1
% 0.73/0.91  % SZS output start Proof for SWW474+1
% 0.73/0.91  (
% 0.73/0.91  (let ((_let_1 (tptp.hAPP_c1126217667_state tptp.hoare_Mirabelle_MGT tptp.y))) (let ((_let_2 (tptp.insert1415133716_state _let_1 tptp.bot_bo620288102e_bool))) (let ((_let_3 (tptp.dom_pname_com tptp.body))) (let ((_let_4 (tptp.image_2003357581_state (tptp.cOMBB_699532858_pname tptp.hoare_Mirabelle_MGT tptp.body_1) _let_3))) (let ((_let_5 (tptp.hoare_1598289066_state _let_4))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP_f971112728l_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_165779456gleton))) (let ((_let_11 (forall ((Pn $$unsorted) (B_2 $$unsorted)) (=> (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 $$unsorted)) (=> (tptp.hBOOL tptp.hoare_165779456gleton) (=> (tptp.hBOOL tptp.wT_bodies) (=> (tptp.hBOOL (tptp.wt C_1)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hoare_1598289066_state tptp.bot_bo620288102e_bool) (tptp.insert1415133716_state (tptp.hAPP_c1126217667_state tptp.hoare_Mirabelle_MGT C_1) tptp.bot_bo620288102e_bool))))))))) (let ((_let_13 (forall ((G $$unsorted) (G_1 $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_1598289066_state G))) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hoare_1598289066_state G_1) Ts)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 G_1)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 Ts)))))))) (let ((_let_14 (forall ((G $$unsorted)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hoare_1598289066_state G) tptp.bot_bo620288102e_bool))))) (let ((_let_15 (tptp.fun tptp.pname tptp.bool))) (let ((_let_16 (forall ((G $$unsorted) (G_1 $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_1598289066_state G))) (or (not (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hoare_1598289066_state G_1) Ts))) (not (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 G_1))) (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 Ts))))))) (let ((_let_17 (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_5 tptp.bot_bo620288102e_bool)))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hoare_1598289066_state tptp.bot_bo620288102e_bool) _let_2)))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 _let_18 _let_6))) (let ((_let_22 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_23 (not _let_21))) (let ((_let_24 (tptp.hBOOL (tptp.wt tptp.y)))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_19))) (let ((_let_27 (forall ((C_1 $$unsorted)) (or (not (tptp.hBOOL (tptp.wt C_1))) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hoare_1598289066_state tptp.bot_bo620288102e_bool) (tptp.insert1415133716_state (tptp.hAPP_c1126217667_state tptp.hoare_Mirabelle_MGT C_1) tptp.bot_bo620288102e_bool))))))) (let ((_let_28 (ASSUME :args (_let_9)))) (let ((_let_29 (_let_27))) (let ((_let_30 (not _let_8))) (let ((_let_31 (or _let_30 _let_24))) (let ((_let_32 (forall ((Pn $$unsorted) (B_2 $$unsorted)) (or (not (= (tptp.hAPP_p799580910on_com tptp.body Pn) (tptp.some_com B_2))) (tptp.hBOOL (tptp.wt B_2)))))) (let ((_let_33 (_let_32))) (let ((_let_34 (_let_14))) (let ((_let_35 (ASSUME :args _let_34))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_22 :args (_let_4 tptp.bot_bo620288102e_bool _let_2 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_f971112728l_bool (tptp.hoare_1598289066_state G_1) Ts) (tptp.hoare_1598289066_state G)))) :args (_let_16))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_6 _let_18 _let_20 _let_23))) (ASSUME :args (_let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (_let_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hoare_1598289066_state G)))) :args _let_34)) _let_35 :args (_let_17 false _let_14)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_25 _let_19 (not _let_26)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_30 _let_24 (not _let_31)))) (ASSUME :args (_let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_33) :args (tptp.pn tptp.y QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_p799580910on_com tptp.body Pn) (tptp.some_com B_2)))) :args _let_33)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))) _let_28 :args (_let_32 false _let_9)) :args (_let_31 false _let_32)) :args (_let_24 false _let_8 false _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_29) :args (tptp.y QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP_c1126217667_state tptp.hoare_Mirabelle_MGT C_1)))) :args _let_29)) (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_28 :args (_let_27 false _let_10 false _let_9)) :args (_let_26 false _let_27)) :args (_let_19 false _let_24 false _let_26)) :args (_let_23 true _let_6 false _let_17 false _let_19)) _let_22 :args (false true _let_21 false _let_16)) :args ((forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2_1) (tptp.is_fun_pname_bool (tptp.cOMBB_647938656_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_2_1) (tptp.is_fun1661590463l_bool (tptp.cOMBB_307249310e_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_bool B_1_1) (tptp.is_fun_pname_bool (tptp.cOMBK_bool_pname B_1_1)))) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_bool B_1_1) (tptp.is_fun1661590463l_bool (tptp.cOMBK_1857069011e_bool B_1_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2_1) (tptp.is_fun_pname_bool (tptp.cOMBS_568398431l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_2_1) (tptp.is_fun1661590463l_bool (tptp.cOMBS_350070575l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.wt B_1_1))) (tptp.is_bool tptp.wT_bodies) (tptp.is_fun1661590463l_bool tptp.finite_finite_pname) (tptp.is_pname (tptp.undefined_pname tptp.pname)) (tptp.is_fun_pname_bool (tptp.undefi17486888e_bool _let_15)) (tptp.is_fun1661590463l_bool (tptp.undefi64961550l_bool (tptp.fun _let_15 tptp.bool))) (tptp.is_bool tptp.hoare_165779456gleton) (forall ((B_1_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.dom_pname_com B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_fun1661590463l_bool (tptp.dom_fu2081503504ol_com B_1_1))) (tptp.is_fun_pname_bool tptp.bot_bo844097828e_bool) (tptp.is_fun1661590463l_bool tptp.bot_bo1649642514l_bool) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_1_1) (tptp.is_fun_pname_bool (tptp.collect_pname B_1_1)))) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_1_1) (tptp.is_fun1661590463l_bool (tptp.collec1974731493e_bool B_1_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2_1) (tptp.is_fun_pname_bool (tptp.image_pname_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2_1) (tptp.is_fun1661590463l_bool (tptp.image_47868345e_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.image_54689091_pname B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun1661590463l_bool (tptp.image_2131964411e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_2_1) (tptp.is_fun_pname_bool (tptp.image_1283814551_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.image_187965177_pname B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.image_1705983821_pname B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.image_1619336331_pname B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (and (tptp.is_pname B_1_1) (tptp.is_fun_pname_bool B_2_1)) (tptp.is_fun_pname_bool (tptp.insert_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (and (tptp.is_fun_pname_bool B_1_1) (tptp.is_fun1661590463l_bool B_2_1)) (tptp.is_fun1661590463l_bool (tptp.insert1325755072e_bool B_1_1 B_2_1)))) (tptp.is_bool tptp.fFalse) (tptp.is_bool tptp.fTrue) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_pname B_2_1) (tptp.is_pname (tptp.hAPP_pname_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (and (tptp.is_fun_pname_bool B_1_1) (tptp.is_pname B_2_1)) (tptp.is_bool (tptp.hAPP_pname_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_pname B_2_1) (tptp.is_fun_pname_bool (tptp.hAPP_p61793385e_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_pname B_2_1) (tptp.is_fun1661590463l_bool (tptp.hAPP_p338031245l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_bool B_2_1) (tptp.is_bool (tptp.hAPP_bool_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_pname (tptp.hAPP_H1621176307_pname B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_H78829294e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.hAPP_H356885323e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2_1) (tptp.is_pname (tptp.hAPP_f1297739591_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (and (tptp.is_fun1661590463l_bool B_1_1) (tptp.is_fun_pname_bool B_2_1)) (tptp.is_bool (tptp.hAPP_f1664156314l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2_1) (tptp.is_fun_pname_bool (tptp.hAPP_f759274231e_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2_1) (tptp.is_fun1661590463l_bool (tptp.hAPP_f434788991l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_pname (tptp.hAPP_f560369737_pname B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f971112728l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_2_1) (tptp.is_bool (tptp.hAPP_f1935102916l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_2_1) (tptp.is_fun1661590463l_bool (tptp.hAPP_f559147733l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f166538662l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f389811538l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f468958928l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f595608956l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f1022807134l_bool B_1_1 B_2_1))) (tptp.is_pname tptp.pn) _let_14 (forall ((Ts $$unsorted) (G $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool Ts) G)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hoare_1598289066_state G) Ts)))) (forall ((Ts $$unsorted) (G $$unsorted) (Ts_1 $$unsorted)) (let ((_let_1 (tptp.hoare_1598289066_state G))) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 Ts_1)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool Ts) Ts_1)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 Ts)))))) (forall ((G $$unsorted) (G_1 $$unsorted) (Ts $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hoare_1598289066_state G_1) Ts)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool G_1) G)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hoare_1598289066_state G) Ts))))) _let_13 (forall ((Ts $$unsorted) (G $$unsorted) (T $$unsorted)) (let ((_let_1 (tptp.hoare_1598289066_state G))) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 (tptp.insert1415133716_state T tptp.bot_bo620288102e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 Ts)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 (tptp.insert1415133716_state T Ts))))))) (forall ((G $$unsorted) (T $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_1598289066_state G))) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 (tptp.insert1415133716_state T Ts))) (and (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 (tptp.insert1415133716_state T tptp.bot_bo620288102e_bool))) (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 Ts)))))) (forall ((Pn_1 $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.hAPP_c1126217667_state tptp.hoare_Mirabelle_MGT (tptp.hAPP_pname_com tptp.body_1 Pn_1)))) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hoare_1598289066_state (tptp.insert1415133716_state _let_1 G)) (tptp.insert1415133716_state (tptp.hAPP_c1126217667_state tptp.hoare_Mirabelle_MGT (tptp.hAPP_option_com_com tptp.the_com (tptp.hAPP_p799580910on_com tptp.body Pn_1))) tptp.bot_bo620288102e_bool))) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hoare_1598289066_state G) (tptp.insert1415133716_state _let_1 tptp.bot_bo620288102e_bool)))))) (forall ((A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool tptp.ord_le313189616e_bool) A)))))) (forall ((A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state A)) (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool (tptp.collec1823980261e_bool (tptp.hAPP_f72706945l_bool (tptp.cOMBC_449066458l_bool tptp.ord_le1285840794e_bool) A)))))) (forall ((A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool A)) (tptp.hBOOL (tptp.hAPP_f595608956l_bool tptp.finite1491191519l_bool (tptp.collec792590109l_bool (tptp.hAPP_f1759205631l_bool (tptp.cOMBC_336095980l_bool tptp.ord_le1375671464l_bool) A)))))) (forall ((A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f468958928l_bool tptp.finite796539827l_bool A)) (tptp.hBOOL (tptp.hAPP_f1022807134l_bool tptp.finite34021339l_bool (tptp.collec256567069l_bool (tptp.hAPP_f667366769l_bool (tptp.cOMBC_747715418l_bool tptp.ord_le889598034l_bool) A)))))) (forall ((A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool A)) (tptp.hBOOL (tptp.hAPP_f468958928l_bool tptp.finite796539827l_bool (tptp.collec488126193l_bool (tptp.hAPP_f585161855l_bool (tptp.cOMBC_1691491604l_bool tptp.ord_le287025148l_bool) A)))))) (forall ((A $$unsorted)) (=> (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 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state (tptp.image_2003357581_state H Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (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 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f468958928l_bool tptp.finite796539827l_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_1619336331_pname H Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_187965177_pname H Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_1283814551_pname H Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool Fa)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state (tptp.image_677922117_state H Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f468958928l_bool tptp.finite796539827l_bool Fa)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state (tptp.image_892968839_state H Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state (tptp.image_18964633_state H Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state (tptp.image_516545147_state H Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (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 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f468958928l_bool tptp.finite796539827l_bool (tptp.image_288317893l_bool H Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool (tptp.image_70449425e_bool H Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.image_47868345e_bool H Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state Fa)) (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool (tptp.image_1210605179l_bool H Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state Fa)) (tptp.hBOOL (tptp.hAPP_f468958928l_bool tptp.finite796539827l_bool (tptp.image_1761575943l_bool H Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state Fa)) (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool (tptp.image_1828608335e_bool H Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state Fa)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.image_2131964411e_bool H Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_54689091_pname H Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (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 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool tptp.bot_bo620288102e_bool) A))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool tptp.bot_bo1649642514l_bool) A))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f585161855l_bool tptp.ord_le287025148l_bool tptp.bot_bo535777328l_bool) A))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool tptp.bot_bo844097828e_bool) A))) (forall ((A_2 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state A)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state (tptp.insert1415133716_state A_2 A))))) (forall ((A_2 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f468958928l_bool tptp.finite796539827l_bool A)) (tptp.hBOOL (tptp.hAPP_f468958928l_bool tptp.finite796539827l_bool (tptp.insert203537868l_bool A_2 A))))) (forall ((A_2 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool A)) (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool (tptp.insert1556680138e_bool A_2 A))))) (forall ((A_2 $$unsorted) (A $$unsorted)) (=> (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_f971112728l_bool tptp.finite364844667_state tptp.bot_bo620288102e_bool)) (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool tptp.bot_bo1537088220l_bool)) (tptp.hBOOL (tptp.hAPP_f468958928l_bool tptp.finite796539827l_bool tptp.bot_bo1761158942l_bool)) (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool tptp.bot_bo535777328l_bool)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool tptp.bot_bo1649642514l_bool)) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (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 $$unsorted) (P_1 $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state (tptp.collec307967673_state P_1))) (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state (tptp.collec307967673_state Q_1)))) (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state (tptp.collec307967673_state (tptp.cOMBS_458705923l_bool (tptp.cOMBB_962198420_state tptp.fconj P_1) Q_1)))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (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 $$unsorted) (P_1 $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f468958928l_bool tptp.finite796539827l_bool (tptp.collec488126193l_bool P_1))) (tptp.hBOOL (tptp.hAPP_f468958928l_bool tptp.finite796539827l_bool (tptp.collec488126193l_bool Q_1)))) (tptp.hBOOL (tptp.hAPP_f468958928l_bool tptp.finite796539827l_bool (tptp.collec488126193l_bool (tptp.cOMBS_1358309691l_bool (tptp.cOMBB_404111180l_bool tptp.fconj P_1) Q_1)))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool (tptp.collec1823980261e_bool P_1))) (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool (tptp.collec1823980261e_bool Q_1)))) (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool (tptp.collec1823980261e_bool (tptp.cOMBS_2066081387l_bool (tptp.cOMBB_1585081418e_bool tptp.fconj P_1) Q_1)))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_2003357581_state (tptp.cOMBK_367030522_pname C_1) A))) (let ((_let_2 (= A tptp.bot_bo844097828e_bool))) (=> (tptp.is_fun_pname_bool A) (and (=> _let_2 (= _let_1 tptp.bot_bo620288102e_bool)) (=> (not _let_2) (= _let_1 (tptp.insert1415133716_state C_1 tptp.bot_bo620288102e_bool)))))))) (forall ((C_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_54689091_pname (tptp.cOMBK_168215364_state C_1) A))) (let ((_let_2 (= A tptp.bot_bo620288102e_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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_2131964411e_bool (tptp.cOMBK_2035509764_state C_1) A))) (let ((_let_2 (= A tptp.bot_bo620288102e_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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_1828608335e_bool (tptp.cOMBK_1039769424_state C_1) A))) (let ((_let_2 (= A tptp.bot_bo620288102e_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo535777328l_bool)) (=> (not _let_2) (= _let_1 (tptp.insert1556680138e_bool C_1 tptp.bot_bo535777328l_bool))))))) (forall ((C_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_47868345e_bool (tptp.cOMBK_37193422_pname C_1) A))) (let ((_let_2 (= A tptp.bot_bo844097828e_bool))) (=> (tptp.is_fun_pname_bool A) (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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_70449425e_bool (tptp.cOMBK_1706929794_pname C_1) A))) (let ((_let_2 (= A tptp.bot_bo844097828e_bool))) (=> (tptp.is_fun_pname_bool A) (and (=> _let_2 (= _let_1 tptp.bot_bo535777328l_bool)) (=> (not _let_2) (= _let_1 (tptp.insert1556680138e_bool C_1 tptp.bot_bo535777328l_bool)))))))) (forall ((C_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_pname_pname (tptp.cOMBK_pname_pname C_1) A))) (let ((_let_2 (= A tptp.bot_bo844097828e_bool))) (=> (tptp.is_fun_pname_bool A) (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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_516545147_state (tptp.cOMBK_1503445380e_bool C_1) A))) (let ((_let_2 (= A tptp.bot_bo1649642514l_bool))) (=> (tptp.is_fun1661590463l_bool A) (and (=> _let_2 (= _let_1 tptp.bot_bo620288102e_bool)) (=> (not _let_2) (= _let_1 (tptp.insert1415133716_state C_1 tptp.bot_bo620288102e_bool)))))))) (forall ((C_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_18964633_state (tptp.cOMBK_701929478e_bool C_1) A))) (let ((_let_2 (= A tptp.bot_bo535777328l_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo620288102e_bool)) (=> (not _let_2) (= _let_1 (tptp.insert1415133716_state C_1 tptp.bot_bo620288102e_bool))))))) (forall ((C_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_1283814551_pname (tptp.cOMBK_948730864e_bool C_1) A))) (let ((_let_2 (= A tptp.bot_bo1649642514l_bool))) (=> (tptp.is_fun1661590463l_bool A) (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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_187965177_pname (tptp.cOMBK_1589414042e_bool C_1) A))) (let ((_let_2 (= A tptp.bot_bo535777328l_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 $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (= (tptp.image_2003357581_state (tptp.cOMBK_367030522_pname C_1) A) (tptp.insert1415133716_state C_1 tptp.bot_bo620288102e_bool)))) (forall ((C_1 $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state X_2) A)) (= (tptp.image_54689091_pname (tptp.cOMBK_168215364_state C_1) A) (tptp.insert_pname C_1 tptp.bot_bo844097828e_bool)))) (forall ((C_1 $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state X_2) A)) (= (tptp.image_2131964411e_bool (tptp.cOMBK_2035509764_state C_1) A) (tptp.insert1325755072e_bool C_1 tptp.bot_bo1649642514l_bool)))) (forall ((C_1 $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state X_2) A)) (= (tptp.image_1828608335e_bool (tptp.cOMBK_1039769424_state C_1) A) (tptp.insert1556680138e_bool C_1 tptp.bot_bo535777328l_bool)))) (forall ((C_1 $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (= (tptp.image_47868345e_bool (tptp.cOMBK_37193422_pname C_1) A) (tptp.insert1325755072e_bool C_1 tptp.bot_bo1649642514l_bool)))) (forall ((C_1 $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (= (tptp.image_70449425e_bool (tptp.cOMBK_1706929794_pname C_1) A) (tptp.insert1556680138e_bool C_1 tptp.bot_bo535777328l_bool)))) (forall ((C_1 $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (= (tptp.image_pname_pname (tptp.cOMBK_pname_pname C_1) A) (tptp.insert_pname C_1 tptp.bot_bo844097828e_bool)))) (forall ((C_1 $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) A)) (= (tptp.image_516545147_state (tptp.cOMBK_1503445380e_bool C_1) A) (tptp.insert1415133716_state C_1 tptp.bot_bo620288102e_bool)))) (forall ((C_1 $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f210337421l_bool tptp.member2114907555e_bool X_2) A)) (= (tptp.image_18964633_state (tptp.cOMBK_701929478e_bool C_1) A) (tptp.insert1415133716_state C_1 tptp.bot_bo620288102e_bool)))) (forall ((C_1 $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f210337421l_bool tptp.member2114907555e_bool X_2) A)) (= (tptp.image_187965177_pname (tptp.cOMBK_1589414042e_bool C_1) A) (tptp.insert_pname C_1 tptp.bot_bo844097828e_bool)))) (forall ((F $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted)) (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 $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.dom_fu2081503504ol_com F))) (=> (= (tptp.hAPP_f2138803836on_com F X_2) (tptp.some_com Y_2)) (= (tptp.insert1325755072e_bool X_2 _let_1) _let_1)))) (forall ((F $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.dom_fu1342267980ol_com F))) (=> (= (tptp.hAPP_f2134636538on_com F X_2) (tptp.some_com Y_2)) (= (tptp.insert1556680138e_bool X_2 _let_1) _let_1)))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool B) (tptp.image_2003357581_state F A))) (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f468958928l_bool tptp.finite796539827l_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_1619336331_pname F A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_187965177_pname F A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_1283814551_pname F A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool B) (tptp.image_677922117_state F A))) (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f468958928l_bool tptp.finite796539827l_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool B) (tptp.image_892968839_state F A))) (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool B) (tptp.image_18964633_state F A))) (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool B) (tptp.image_516545147_state F A))) (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f468958928l_bool (tptp.hAPP_f667366769l_bool tptp.ord_le889598034l_bool B) (tptp.image_288317893l_bool F A))) (tptp.hBOOL (tptp.hAPP_f468958928l_bool tptp.finite796539827l_bool B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f585161855l_bool tptp.ord_le287025148l_bool B) (tptp.image_70449425e_bool F A))) (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state A)) (=> (tptp.hBOOL (tptp.hAPP_f389811538l_bool (tptp.hAPP_f1759205631l_bool tptp.ord_le1375671464l_bool B) (tptp.image_1210605179l_bool F A))) (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state A)) (=> (tptp.hBOOL (tptp.hAPP_f468958928l_bool (tptp.hAPP_f667366769l_bool tptp.ord_le889598034l_bool B) (tptp.image_1761575943l_bool F A))) (tptp.hBOOL (tptp.hAPP_f468958928l_bool tptp.finite796539827l_bool B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_54689091_pname F A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state A)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f585161855l_bool tptp.ord_le287025148l_bool B) (tptp.image_1828608335e_bool F A))) (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) (tptp.image_2131964411e_bool F A))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B))))) (forall ((A $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.insert1415133716_state X_2 tptp.bot_bo620288102e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool A) _let_1)) (or (= A tptp.bot_bo620288102e_bool) (= A _let_1))))) (forall ((A $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.insert1325755072e_bool X_2 tptp.bot_bo1649642514l_bool))) (=> (tptp.is_fun1661590463l_bool A) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A) _let_1)) (or (= A tptp.bot_bo1649642514l_bool) (= A _let_1)))))) (forall ((A $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.insert1556680138e_bool X_2 tptp.bot_bo535777328l_bool))) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f585161855l_bool tptp.ord_le287025148l_bool A) _let_1)) (or (= A tptp.bot_bo535777328l_bool) (= A _let_1))))) (forall ((A $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.insert_pname X_2 tptp.bot_bo844097828e_bool))) (=> (tptp.is_fun_pname_bool A) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) _let_1)) (or (= A tptp.bot_bo844097828e_bool) (= A _let_1)))))) _let_12 (forall ((A_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state A_2) tptp.bot_bo620288102e_bool)))) (forall ((A_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool A_2) tptp.bot_bo1649642514l_bool)))) (forall ((A_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f210337421l_bool tptp.member2114907555e_bool A_2) tptp.bot_bo535777328l_bool)))) (forall ((A_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_2) tptp.bot_bo844097828e_bool)))) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H30606679l_bool tptp.member1338687867_state A_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 B))) (= A_2 B_1)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 (tptp.insert1415133716_state B_1 B)))))) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool A_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 B))) (= A_2 B_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 (tptp.insert1325755072e_bool B_1 B)))))) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f210337421l_bool tptp.member2114907555e_bool A_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f166538662l_bool _let_1 B))) (= A_2 B_1)) (tptp.hBOOL (tptp.hAPP_f166538662l_bool _let_1 (tptp.insert1556680138e_bool B_1 B)))))) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))) (= A_2 B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname B_1 B)))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H30606679l_bool tptp.member1338687867_state A_2))) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 (tptp.insert1415133716_state B_1 A))) (=> (not (= A_2 B_1)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 A)))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool A_2))) (=> (and (tptp.is_fun_pname_bool A_2) (tptp.is_fun_pname_bool B_1)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 (tptp.insert1325755072e_bool B_1 A))) (=> (not (= A_2 B_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 A))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f210337421l_bool tptp.member2114907555e_bool A_2))) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool _let_1 (tptp.insert1556680138e_bool B_1 A))) (=> (not (= A_2 B_1)) (tptp.hBOOL (tptp.hAPP_f166538662l_bool _let_1 A)))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_2))) (=> (and (tptp.is_pname A_2) (tptp.is_pname B_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname B_1 A))) (=> (not (= A_2 B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool B) A)) (= A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.is_fun1661590463l_bool A) (tptp.is_fun1661590463l_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) A)) (= A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f585161855l_bool tptp.ord_le287025148l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f585161855l_bool tptp.ord_le287025148l_bool B) A)) (= A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.is_fun_pname_bool A) (tptp.is_fun_pname_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A)) (= A B))))) (forall ((C_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H30606679l_bool tptp.member1338687867_state C_1))) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 B)))))) (forall ((C_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool C_1))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 B)))))) (forall ((C_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f210337421l_bool tptp.member2114907555e_bool C_1))) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f585161855l_bool tptp.ord_le287025148l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f166538662l_bool _let_1 B)))))) (forall ((C_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((A $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_2 $$unsorted)) (=> (= B_1 (tptp.hAPP_H356885323e_bool F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state X_2) A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool B_1) (tptp.image_2131964411e_bool F A)))))) (forall ((A $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_2 $$unsorted)) (=> (= B_1 (tptp.hAPP_H1049623551e_bool F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state X_2) A)) (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f210337421l_bool tptp.member2114907555e_bool B_1) (tptp.image_1828608335e_bool F A)))))) (forall ((A $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_2 $$unsorted)) (=> (= B_1 (tptp.hAPP_p61793385e_bool F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool B_1) (tptp.image_47868345e_bool F A)))))) (forall ((A $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_2 $$unsorted)) (=> (= B_1 (tptp.hAPP_p442853985e_bool F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f210337421l_bool tptp.member2114907555e_bool B_1) (tptp.image_70449425e_bool F A)))))) (forall ((A $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_2 $$unsorted)) (=> (= B_1 (tptp.hAPP_f888949707_state F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state B_1) (tptp.image_516545147_state F A)))))) (forall ((A $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_2 $$unsorted)) (=> (= B_1 (tptp.hAPP_f1387463497_state F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f210337421l_bool tptp.member2114907555e_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state B_1) (tptp.image_18964633_state F A)))))) (forall ((A $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_2 $$unsorted)) (=> (= B_1 (tptp.hAPP_H1621176307_pname F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state X_2) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.image_54689091_pname F A)))))) (forall ((A $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_2 $$unsorted)) (=> (= B_1 (tptp.hAPP_pname_pname F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.image_pname_pname F A)))))) (forall ((A $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_2 $$unsorted)) (=> (= B_1 (tptp.hAPP_f1297739591_pname F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.image_1283814551_pname F A)))))) (forall ((A $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_2 $$unsorted)) (=> (= B_1 (tptp.hAPP_f560369737_pname F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f210337421l_bool tptp.member2114907555e_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.image_187965177_pname F A)))))) (forall ((A $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_2 $$unsorted)) (=> (= B_1 (tptp.hAPP_p1422361149_state F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state B_1) (tptp.image_2003357581_state F A)))))) (forall ((A_2 $$unsorted) (A $$unsorted)) (=> (= A tptp.bot_bo1649642514l_bool) (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool A_2) A))))) (forall ((A_2 $$unsorted) (A $$unsorted)) (=> (= A tptp.bot_bo535777328l_bool) (not (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f210337421l_bool tptp.member2114907555e_bool A_2) A))))) (forall ((A_2 $$unsorted) (A $$unsorted)) (=> (= A tptp.bot_bo620288102e_bool) (not (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state A_2) A))))) (forall ((A_2 $$unsorted) (A $$unsorted)) (=> (= A tptp.bot_bo844097828e_bool) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_2) A))))) (forall ((P_1 $$unsorted)) (= (= (tptp.collec1613912337l_bool P_1) tptp.bot_bo1537088220l_bool) (forall ((X_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool X_1) (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 X_1))))))) (forall ((P_1 $$unsorted)) (= (= (tptp.collec488126193l_bool P_1) tptp.bot_bo1761158942l_bool) (forall ((X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f166538662l_bool P_1 X_1)))))) (forall ((P_1 $$unsorted)) (= (= (tptp.collec1823980261e_bool P_1) tptp.bot_bo535777328l_bool) (forall ((X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f971112728l_bool P_1 X_1)))))) (forall ((P_1 $$unsorted)) (= (= (tptp.collec1974731493e_bool P_1) tptp.bot_bo1649642514l_bool) (forall ((X_1 $$unsorted)) (=> (tptp.is_fun_pname_bool X_1) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 X_1))))))) (forall ((P_1 $$unsorted)) (= (= (tptp.collec307967673_state P_1) tptp.bot_bo620288102e_bool) (forall ((X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_H78829294e_bool P_1 X_1)))))) (forall ((P_1 $$unsorted)) (= (= (tptp.collect_pname P_1) tptp.bot_bo844097828e_bool) (forall ((X_1 $$unsorted)) (=> (tptp.is_pname X_1) (not (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_1))))))) (forall ((C_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool C_1) tptp.bot_bo1649642514l_bool)))) (forall ((C_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f210337421l_bool tptp.member2114907555e_bool C_1) tptp.bot_bo535777328l_bool)))) (forall ((C_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state C_1) tptp.bot_bo620288102e_bool)))) (forall ((C_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname C_1) tptp.bot_bo844097828e_bool)))) (forall ((P_1 $$unsorted)) (= (= tptp.bot_bo1537088220l_bool (tptp.collec1613912337l_bool P_1)) (forall ((X_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool X_1) (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 X_1))))))) (forall ((P_1 $$unsorted)) (= (= tptp.bot_bo1761158942l_bool (tptp.collec488126193l_bool P_1)) (forall ((X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f166538662l_bool P_1 X_1)))))) (forall ((P_1 $$unsorted)) (= (= tptp.bot_bo535777328l_bool (tptp.collec1823980261e_bool P_1)) (forall ((X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f971112728l_bool P_1 X_1)))))) (forall ((P_1 $$unsorted)) (= (= tptp.bot_bo1649642514l_bool (tptp.collec1974731493e_bool P_1)) (forall ((X_1 $$unsorted)) (=> (tptp.is_fun_pname_bool X_1) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 X_1))))))) (forall ((P_1 $$unsorted)) (= (= tptp.bot_bo620288102e_bool (tptp.collec307967673_state P_1)) (forall ((X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_H78829294e_bool P_1 X_1)))))) (forall ((P_1 $$unsorted)) (= (= tptp.bot_bo844097828e_bool (tptp.collect_pname P_1)) (forall ((X_1 $$unsorted)) (=> (tptp.is_pname X_1) (not (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_1))))))) (forall ((A $$unsorted)) (=> (tptp.is_fun1661590463l_bool A) (= (exists ((X_1 $$unsorted)) (and (tptp.is_fun_pname_bool X_1) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1) A)))) (not (= A tptp.bot_bo1649642514l_bool))))) (forall ((A $$unsorted)) (= (exists ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f210337421l_bool tptp.member2114907555e_bool X_1) A))) (not (= A tptp.bot_bo535777328l_bool)))) (forall ((A $$unsorted)) (= (exists ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state X_1) A))) (not (= A tptp.bot_bo620288102e_bool)))) (forall ((A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (= (exists ((X_1 $$unsorted)) (and (tptp.is_pname X_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)))) (not (= A tptp.bot_bo844097828e_bool))))) (forall ((A $$unsorted)) (=> (tptp.is_fun1661590463l_bool A) (= (forall ((X_1 $$unsorted)) (=> (tptp.is_fun_pname_bool X_1) (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1) A))))) (= A tptp.bot_bo1649642514l_bool)))) (forall ((A $$unsorted)) (= (forall ((X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f210337421l_bool tptp.member2114907555e_bool X_1) A)))) (= A tptp.bot_bo535777328l_bool))) (forall ((A $$unsorted)) (= (forall ((X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state X_1) A)))) (= A tptp.bot_bo620288102e_bool))) (forall ((A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (= (forall ((X_1 $$unsorted)) (=> (tptp.is_pname X_1) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A))))) (= A tptp.bot_bo844097828e_bool)))) (= tptp.bot_bo1761158942l_bool (tptp.collec488126193l_bool (tptp.cOMBK_482404831l_bool tptp.fFalse))) (= tptp.bot_bo535777328l_bool (tptp.collec1823980261e_bool (tptp.cOMBK_129401207e_bool tptp.fFalse))) (= tptp.bot_bo1649642514l_bool (tptp.collec1974731493e_bool (tptp.cOMBK_1857069011e_bool tptp.fFalse))) (= tptp.bot_bo620288102e_bool (tptp.collec307967673_state (tptp.cOMBK_659609255_state tptp.fFalse))) (= tptp.bot_bo844097828e_bool (tptp.collect_pname (tptp.cOMBK_bool_pname tptp.fFalse))) (forall ((A_2 $$unsorted) (A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_2) A)) (= (tptp.insert_pname A_2 A) A)))) (forall ((A_2 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state A_2) A)) (= (tptp.insert1415133716_state A_2 A) A))) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (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 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H30606679l_bool tptp.member1338687867_state A_2))) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 (tptp.insert1415133716_state B_1 B)))))) (forall ((B $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_2))) (=> (and (tptp.is_fun_pname_bool B) (tptp.is_fun_pname_bool A)) (=> (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 $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H30606679l_bool tptp.member1338687867_state X_2))) (=> (not (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 B))) (= (= (tptp.insert1415133716_state X_2 A) (tptp.insert1415133716_state X_2 B)) (= A B)))))) (forall ((Y_2 $$unsorted) (A $$unsorted) (X_2 $$unsorted)) (=> (and (tptp.is_pname Y_2) (tptp.is_pname X_2)) (= (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 $$unsorted) (A $$unsorted) (X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H78829294e_bool (tptp.insert1415133716_state Y_2 A) X_2)) (or (= Y_2 X_2) (tptp.hBOOL (tptp.hAPP_H78829294e_bool A X_2))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_2))) (=> (and (tptp.is_pname A_2) (tptp.is_pname B_1)) (= (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 $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H30606679l_bool tptp.member1338687867_state A_2))) (= (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 (tptp.insert1415133716_state B_1 A))) (or (= A_2 B_1) (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 A)))))) (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (A $$unsorted)) (= (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 $$unsorted) (Y_2 $$unsorted) (A $$unsorted)) (= (tptp.insert1415133716_state X_2 (tptp.insert1415133716_state Y_2 A)) (tptp.insert1415133716_state Y_2 (tptp.insert1415133716_state X_2 A)))) (forall ((X_2 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.insert_pname X_2 A))) (= (tptp.insert_pname X_2 _let_1) _let_1))) (forall ((X_2 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.insert1415133716_state X_2 A))) (= (tptp.insert1415133716_state X_2 _let_1) _let_1))) (forall ((A_2 $$unsorted) (P_1 $$unsorted)) (= (tptp.insert_pname A_2 (tptp.collect_pname P_1)) (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fimplies (tptp.cOMBB_647938656_pname tptp.fNot (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_2))) P_1)))) (forall ((A_2 $$unsorted) (P_1 $$unsorted)) (= (tptp.insert1415133716_state A_2 (tptp.collec307967673_state P_1)) (tptp.collec307967673_state (tptp.cOMBS_458705923l_bool (tptp.cOMBB_962198420_state tptp.fimplies (tptp.cOMBB_2144135922_state tptp.fNot (tptp.hAPP_H1049623551e_bool (tptp.cOMBC_654211620e_bool tptp.fequal1111551311_state) A_2))) P_1)))) (forall ((A_2 $$unsorted) (P_1 $$unsorted)) (= (tptp.insert1325755072e_bool A_2 (tptp.collec1974731493e_bool P_1)) (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fimplies (tptp.cOMBB_307249310e_bool tptp.fNot (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_2))) P_1)))) (forall ((A_2 $$unsorted) (P_1 $$unsorted)) (= (tptp.insert1556680138e_bool A_2 (tptp.collec1823980261e_bool P_1)) (tptp.collec1823980261e_bool (tptp.cOMBS_2066081387l_bool (tptp.cOMBB_1585081418e_bool tptp.fimplies (tptp.cOMBB_1522210668e_bool tptp.fNot (tptp.hAPP_f72706945l_bool (tptp.cOMBC_449066458l_bool tptp.fequal1311889615e_bool) A_2))) P_1)))) (forall ((A_2 $$unsorted) (B $$unsorted)) (= (tptp.insert_pname A_2 B) (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fdisj (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_2)) (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool tptp.member_pname) B))))) (forall ((A_2 $$unsorted) (B $$unsorted)) (= (tptp.insert1415133716_state A_2 B) (tptp.collec307967673_state (tptp.cOMBS_458705923l_bool (tptp.cOMBB_962198420_state tptp.fdisj (tptp.hAPP_H1049623551e_bool (tptp.cOMBC_654211620e_bool tptp.fequal1111551311_state) A_2)) (tptp.hAPP_f98417237e_bool (tptp.cOMBC_1734175330l_bool tptp.member1338687867_state) B))))) (forall ((A_2 $$unsorted) (B $$unsorted)) (= (tptp.insert1325755072e_bool A_2 B) (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_2)) (tptp.hAPP_f559147733l_bool (tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) B))))) (forall ((A_2 $$unsorted) (B $$unsorted)) (= (tptp.insert1556680138e_bool A_2 B) (tptp.collec1823980261e_bool (tptp.cOMBS_2066081387l_bool (tptp.cOMBB_1585081418e_bool tptp.fdisj (tptp.hAPP_f72706945l_bool (tptp.cOMBC_449066458l_bool tptp.fequal1311889615e_bool) A_2)) (tptp.hAPP_f1201187855l_bool (tptp.cOMBC_1114453604l_bool tptp.member2114907555e_bool) B))))) (forall ((A_2 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_2) (tptp.insert_pname A_2 B)))) (forall ((A_2 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state A_2) (tptp.insert1415133716_state A_2 B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (not (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (not (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool A) B)) (not (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool B) A))))))) (forall ((C_2 $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool B) C_2)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 C_2)))))) (forall ((X_2 $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H30606679l_bool tptp.member1338687867_state X_2))) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 B)))))) (forall ((B $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (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 $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H30606679l_bool tptp.member1338687867_state X_2))) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 B)))))) (forall ((X_2 $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H30606679l_bool tptp.member1338687867_state X_2))) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool B) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool A) B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.is_fun_pname_bool A) (tptp.is_fun_pname_bool B)) (= (= A B) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool B) A))))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) A))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool A) A))) (forall ((B_1 $$unsorted) (F $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (=> (= B_1 (tptp.hAPP_p1422361149_state F X_2)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state B_1) (tptp.image_2003357581_state F A)))))) (forall ((F $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state (tptp.hAPP_p1422361149_state F X_2)) (tptp.image_2003357581_state F A))))) (forall ((Z $$unsorted) (F $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state Z) (tptp.image_2003357581_state F A))) (exists ((X_1 $$unsorted)) (and (tptp.is_pname X_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (= Z (tptp.hAPP_p1422361149_state F X_1)))))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (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 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state (tptp.collec307967673_state (tptp.cOMBS_458705923l_bool (tptp.cOMBB_962198420_state tptp.fdisj P_1) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state (tptp.collec307967673_state P_1))) (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state (tptp.collec307967673_state Q_1)))))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (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 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool (tptp.collec1823980261e_bool (tptp.cOMBS_2066081387l_bool (tptp.cOMBB_1585081418e_bool tptp.fdisj P_1) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool (tptp.collec1823980261e_bool P_1))) (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool (tptp.collec1823980261e_bool Q_1)))))) (forall ((X_1 $$unsorted) (Xa $$unsorted)) (= (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 $$unsorted) (Xa $$unsorted)) (= (tptp.insert1415133716_state X_1 Xa) (tptp.collec307967673_state (tptp.cOMBS_458705923l_bool (tptp.cOMBB_962198420_state tptp.fdisj (tptp.hAPP_H1049623551e_bool (tptp.cOMBC_654211620e_bool tptp.fequal1111551311_state) X_1)) (tptp.hAPP_f98417237e_bool (tptp.cOMBC_1734175330l_bool tptp.member1338687867_state) Xa))))) (forall ((X_1 $$unsorted) (Xa $$unsorted)) (= (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 $$unsorted) (Xa $$unsorted)) (= (tptp.insert1556680138e_bool X_1 Xa) (tptp.collec1823980261e_bool (tptp.cOMBS_2066081387l_bool (tptp.cOMBB_1585081418e_bool tptp.fdisj (tptp.hAPP_f72706945l_bool (tptp.cOMBC_449066458l_bool tptp.fequal1311889615e_bool) X_1)) (tptp.hAPP_f1201187855l_bool (tptp.cOMBC_1114453604l_bool tptp.member2114907555e_bool) Xa))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (=> (and (tptp.is_pname A_2) (tptp.is_pname B_1)) (=> (= (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 $$unsorted) (B_1 $$unsorted)) (=> (= (tptp.insert1415133716_state A_2 tptp.bot_bo620288102e_bool) (tptp.insert1415133716_state B_1 tptp.bot_bo620288102e_bool)) (= A_2 B_1))) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (=> (and (tptp.is_pname B_1) (tptp.is_pname A_2)) (=> (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 $$unsorted) (A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state B_1) (tptp.insert1415133716_state A_2 tptp.bot_bo620288102e_bool))) (= B_1 A_2))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (=> (and (tptp.is_pname A_2) (tptp.is_pname B_1) (tptp.is_pname C_1) (tptp.is_pname D_1)) (= (= (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 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (= (= (tptp.insert1415133716_state A_2 (tptp.insert1415133716_state B_1 tptp.bot_bo620288102e_bool)) (tptp.insert1415133716_state C_1 (tptp.insert1415133716_state D_1 tptp.bot_bo620288102e_bool))) (or (and (= A_2 C_1) (= B_1 D_1)) (and (= A_2 D_1) (= B_1 C_1))))) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (=> (and (tptp.is_pname B_1) (tptp.is_pname A_2)) (= (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 $$unsorted) (A_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state B_1) (tptp.insert1415133716_state A_2 tptp.bot_bo620288102e_bool))) (= B_1 A_2))) (forall ((A_2 $$unsorted) (A $$unsorted)) (not (= (tptp.insert_pname A_2 A) tptp.bot_bo844097828e_bool))) (forall ((A_2 $$unsorted) (A $$unsorted)) (not (= (tptp.insert1415133716_state A_2 A) tptp.bot_bo620288102e_bool))) (forall ((A_2 $$unsorted) (A $$unsorted)) (not (= tptp.bot_bo844097828e_bool (tptp.insert_pname A_2 A)))) (forall ((A_2 $$unsorted) (A $$unsorted)) (not (= tptp.bot_bo620288102e_bool (tptp.insert1415133716_state A_2 A)))) (forall ((A_2 $$unsorted) (A $$unsorted)) (= (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 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state (tptp.insert1415133716_state A_2 A))) (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state A)))) (forall ((A_2 $$unsorted) (A $$unsorted)) (= (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 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool (tptp.insert1556680138e_bool A_2 A))) (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool A)))) (forall ((A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) tptp.bot_bo844097828e_bool)) (= A tptp.bot_bo844097828e_bool)))) (forall ((A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool A) tptp.bot_bo620288102e_bool)) (= A tptp.bot_bo620288102e_bool))) (forall ((F $$unsorted) (A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (= (= (tptp.image_2003357581_state F A) tptp.bot_bo620288102e_bool) (= A tptp.bot_bo844097828e_bool)))) (forall ((F $$unsorted)) (= (tptp.image_2003357581_state F tptp.bot_bo844097828e_bool) tptp.bot_bo620288102e_bool)) (forall ((F $$unsorted) (A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (= (= tptp.bot_bo620288102e_bool (tptp.image_2003357581_state F A)) (= A tptp.bot_bo844097828e_bool)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f585161855l_bool tptp.ord_le287025148l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool B)) (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state B)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f585161855l_bool tptp.ord_le287025148l_bool A) B)) (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state B)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state A))))) (forall ((A_2 $$unsorted) (C_2 $$unsorted) (D $$unsorted)) (=> (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 $$unsorted) (C_2 $$unsorted) (D $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool C_2) D)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool (tptp.insert1415133716_state A_2 C_2)) (tptp.insert1415133716_state A_2 D))))) (forall ((X_2 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_pname_bool A X_2)))) (forall ((X_2 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state X_2) A)) (tptp.hBOOL (tptp.hAPP_H78829294e_bool A X_2)))) (forall ((P_1 $$unsorted)) (=> (tptp.is_fun_pname_bool P_1) (= (tptp.collect_pname P_1) P_1))) (forall ((P_1 $$unsorted)) (= (tptp.collec307967673_state P_1) P_1)) (forall ((P_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool P_1) (= (tptp.collec1974731493e_bool P_1) P_1))) (forall ((P_1 $$unsorted)) (= (tptp.collec1823980261e_bool P_1) P_1)) (forall ((B_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 (tptp.insert1415133716_state B_1 B)))))) (forall ((B $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (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 $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state X_2) A))) (= (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 (tptp.insert1415133716_state X_2 B))) (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 B)))))) (forall ((X_2 $$unsorted) (A $$unsorted) (B $$unsorted)) (= (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool (tptp.insert1415133716_state X_2 A)) B)) (and (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state X_2) B)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool A) B))))) (forall ((B $$unsorted) (A_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.insert_pname A_2 B)))) (forall ((B $$unsorted) (A_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool B) (tptp.insert1415133716_state A_2 B)))) (forall ((F $$unsorted) (X_2 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_2003357581_state F A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (= (tptp.insert1415133716_state (tptp.hAPP_p1422361149_state F X_2) _let_1) _let_1)))) (forall ((F $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (= (tptp.image_2003357581_state F (tptp.insert_pname A_2 B)) (tptp.insert1415133716_state (tptp.hAPP_p1422361149_state F A_2) (tptp.image_2003357581_state F B)))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool (tptp.image_2003357581_state F A)) (tptp.image_2003357581_state F B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool B) (tptp.image_2003357581_state F A))) (exists ((AA $$unsorted)) (and (tptp.is_fun_pname_bool AA) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool AA) A)) (= B (tptp.image_2003357581_state F AA)))))) (forall ((M $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (=> (= (tptp.hAPP_p799580910on_com M A_2) (tptp.some_com B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_2) (tptp.dom_pname_com M))))) (forall ((P_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fconj (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_2)) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_pname_bool P_1 A_2)))) (and (=> _let_2 (= _let_1 (tptp.insert_pname A_2 tptp.bot_bo844097828e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo844097828e_bool)))))) (forall ((P_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.collec307967673_state (tptp.cOMBS_458705923l_bool (tptp.cOMBB_962198420_state tptp.fconj (tptp.hAPP_H1049623551e_bool (tptp.cOMBC_654211620e_bool tptp.fequal1111551311_state) A_2)) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H78829294e_bool P_1 A_2)))) (and (=> _let_2 (= _let_1 (tptp.insert1415133716_state A_2 tptp.bot_bo620288102e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo620288102e_bool)))))) (forall ((P_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_2)) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 A_2)))) (and (=> _let_2 (= _let_1 (tptp.insert1325755072e_bool A_2 tptp.bot_bo1649642514l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1649642514l_bool)))))) (forall ((P_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.collec1823980261e_bool (tptp.cOMBS_2066081387l_bool (tptp.cOMBB_1585081418e_bool tptp.fconj (tptp.hAPP_f72706945l_bool (tptp.cOMBC_449066458l_bool tptp.fequal1311889615e_bool) A_2)) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f971112728l_bool P_1 A_2)))) (and (=> _let_2 (= _let_1 (tptp.insert1556680138e_bool A_2 tptp.bot_bo535777328l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo535777328l_bool)))))) (forall ((P_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fconj (tptp.hAPP_p61793385e_bool tptp.fequal_pname A_2)) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_pname_bool P_1 A_2)))) (and (=> _let_2 (= _let_1 (tptp.insert_pname A_2 tptp.bot_bo844097828e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo844097828e_bool)))))) (forall ((P_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.collec307967673_state (tptp.cOMBS_458705923l_bool (tptp.cOMBB_962198420_state tptp.fconj (tptp.hAPP_H1049623551e_bool tptp.fequal1111551311_state A_2)) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H78829294e_bool P_1 A_2)))) (and (=> _let_2 (= _let_1 (tptp.insert1415133716_state A_2 tptp.bot_bo620288102e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo620288102e_bool)))))) (forall ((P_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool A_2)) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 A_2)))) (and (=> _let_2 (= _let_1 (tptp.insert1325755072e_bool A_2 tptp.bot_bo1649642514l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1649642514l_bool)))))) (forall ((P_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.collec1823980261e_bool (tptp.cOMBS_2066081387l_bool (tptp.cOMBB_1585081418e_bool tptp.fconj (tptp.hAPP_f72706945l_bool tptp.fequal1311889615e_bool A_2)) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f971112728l_bool P_1 A_2)))) (and (=> _let_2 (= _let_1 (tptp.insert1556680138e_bool A_2 tptp.bot_bo535777328l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo535777328l_bool)))))) (forall ((A_2 $$unsorted)) (= (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 $$unsorted)) (= (tptp.collec307967673_state (tptp.hAPP_H1049623551e_bool (tptp.cOMBC_654211620e_bool tptp.fequal1111551311_state) A_2)) (tptp.insert1415133716_state A_2 tptp.bot_bo620288102e_bool))) (forall ((A_2 $$unsorted)) (= (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 $$unsorted)) (= (tptp.collec1823980261e_bool (tptp.hAPP_f72706945l_bool (tptp.cOMBC_449066458l_bool tptp.fequal1311889615e_bool) A_2)) (tptp.insert1556680138e_bool A_2 tptp.bot_bo535777328l_bool))) (forall ((A_2 $$unsorted)) (= (tptp.collect_pname (tptp.hAPP_p61793385e_bool tptp.fequal_pname A_2)) (tptp.insert_pname A_2 tptp.bot_bo844097828e_bool))) (forall ((A_2 $$unsorted)) (= (tptp.collec307967673_state (tptp.hAPP_H1049623551e_bool tptp.fequal1111551311_state A_2)) (tptp.insert1415133716_state A_2 tptp.bot_bo620288102e_bool))) (forall ((A_2 $$unsorted)) (= (tptp.collec1974731493e_bool (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool A_2)) (tptp.insert1325755072e_bool A_2 tptp.bot_bo1649642514l_bool))) (forall ((A_2 $$unsorted)) (= (tptp.collec1823980261e_bool (tptp.hAPP_f72706945l_bool tptp.fequal1311889615e_bool A_2)) (tptp.insert1556680138e_bool A_2 tptp.bot_bo535777328l_bool))) (forall ((C_1 $$unsorted) (G $$unsorted)) (=> (tptp.hBOOL tptp.hoare_165779456gleton) (=> (forall ((X_1 $$unsorted)) (=> (tptp.is_pname X_1) (=> (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_f971112728l_bool (tptp.hoare_1598289066_state G) (tptp.insert1415133716_state (tptp.hAPP_c1126217667_state tptp.hoare_Mirabelle_MGT (tptp.hAPP_pname_com tptp.body_1 X_1)) tptp.bot_bo620288102e_bool)))))) (=> (tptp.hBOOL (tptp.wt C_1)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hoare_1598289066_state G) (tptp.insert1415133716_state (tptp.hAPP_c1126217667_state tptp.hoare_Mirabelle_MGT C_1) tptp.bot_bo620288102e_bool))))))) _let_11 (forall ((B_1 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state B_1) (tptp.image_2003357581_state F A))) (not (forall ((X_1 $$unsorted)) (=> (tptp.is_pname X_1) (=> (= B_1 (tptp.hAPP_p1422361149_state F X_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A))))))))) (forall ((P_1 $$unsorted) (A $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Fa) A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 tptp.bot_bo844097828e_bool)) (=> (forall ((A_1 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_1))) (=> (and (tptp.is_pname A_1) (tptp.is_fun_pname_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 F_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 (tptp.insert_pname A_1 F_1)))))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 Fa))))))) (forall ((P_1 $$unsorted) (A $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state Fa)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool Fa) A)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool P_1 tptp.bot_bo620288102e_bool)) (=> (forall ((A_1 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H30606679l_bool tptp.member1338687867_state A_1))) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state F_1)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 F_1))) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool P_1 (tptp.insert1415133716_state A_1 F_1))))))))) (tptp.hBOOL (tptp.hAPP_f971112728l_bool P_1 Fa))))))) (forall ((P_1 $$unsorted) (A $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool Fa) A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 tptp.bot_bo1649642514l_bool)) (=> (forall ((A_1 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool A_1))) (=> (and (tptp.is_fun_pname_bool A_1) (tptp.is_fun1661590463l_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 F_1))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 (tptp.insert1325755072e_bool A_1 F_1)))))))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 Fa))))))) (forall ((P_1 $$unsorted) (A $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool (tptp.hAPP_f585161855l_bool tptp.ord_le287025148l_bool Fa) A)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool P_1 tptp.bot_bo535777328l_bool)) (=> (forall ((A_1 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f210337421l_bool tptp.member2114907555e_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool tptp.finite464017571e_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f166538662l_bool _let_1 F_1))) (=> (tptp.hBOOL (tptp.hAPP_f166538662l_bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP_f166538662l_bool P_1 (tptp.insert1556680138e_bool A_1 F_1))))))))) (tptp.hBOOL (tptp.hAPP_f166538662l_bool P_1 Fa))))))) (forall ((P $$unsorted)) (=> (tptp.hBOOL (tptp.wt (tptp.hAPP_pname_com tptp.body_1 P))) (not (forall ((Y_1 $$unsorted)) (not (= (tptp.hAPP_p799580910on_com tptp.body P) (tptp.some_com Y_1))))))) (forall ((B $$unsorted) (A $$unsorted)) (=> (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (=> (tptp.is_pname X_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)))) (forall ((B $$unsorted) (A $$unsorted)) (=> (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H30606679l_bool tptp.member1338687867_state X_1))) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool A) B)))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state B)) (=> (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool B) (tptp.image_2003357581_state F A))) (exists ((C $$unsorted)) (and (tptp.is_fun_pname_bool C) (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_2003357581_state F C))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname _let_3)) (forall ((Pname_1 $$unsorted) (Pname $$unsorted)) (=> (and (tptp.is_pname Pname_1) (tptp.is_pname Pname)) (= (= (tptp.hAPP_pname_com tptp.body_1 Pname_1) (tptp.hAPP_pname_com tptp.body_1 Pname)) (= Pname_1 Pname)))) (forall ((P $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P))) (not (tptp.hBOOL P)))) (forall ((P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P)))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q))) (tptp.hBOOL P) (tptp.hBOOL Q))) (not (tptp.hBOOL tptp.fFalse)) (forall ((P $$unsorted)) (=> (tptp.is_bool P) (or (= P tptp.fTrue) (= P tptp.fFalse)))) (forall ((Q $$unsorted) (P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q))) (not (tptp.hBOOL P)) (tptp.hBOOL Q))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.is_pname X) (tptp.is_pname Y)) (or (not (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool tptp.fequal_pname X) Y))) (= X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool tptp.fequal_pname X) Y)))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_pname_bool (tptp.cOMBK_bool_pname P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_pname P) (= (tptp.hAPP_pname_pname (tptp.cOMBK_pname_pname P) Q) P))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.is_fun_pname_bool X) (tptp.is_fun_pname_bool Y)) (or (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool X) Y))) (= X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool X) Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.cOMBB_647938656_pname P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_pname_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.cOMBS_568398431l_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_p393069232l_bool P R) (tptp.hAPP_pname_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_f1664156314l_bool (tptp.cOMBK_1857069011e_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_pname P) (= (tptp.hAPP_f1297739591_pname (tptp.cOMBK_948730864e_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_fun_pname_bool P) (= (tptp.hAPP_p61793385e_bool (tptp.cOMBK_37193422_pname P) Q) P))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_H78829294e_bool (tptp.hAPP_H1049623551e_bool tptp.fequal1111551311_state X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_H78829294e_bool (tptp.hAPP_H1049623551e_bool tptp.fequal1111551311_state X) Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_com (tptp.cOMBB_923936821_pname P Q) R) (tptp.hAPP_option_com_com P (tptp.hAPP_p799580910on_com Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1664156314l_bool (tptp.cOMBB_307249310e_bool P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_f1664156314l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p393069232l_bool (tptp.cOMBB_675860798_pname P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_pname_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_H78829294e_bool (tptp.cOMBK_659609255_state P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_pname P) (= (tptp.hAPP_H1621176307_pname (tptp.cOMBK_168215364_state P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_p1422361149_state (tptp.cOMBK_367030522_pname P) Q) P)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.fequal1311889615e_bool X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.fequal1311889615e_bool X) Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p1422361149_state (tptp.cOMBB_699532858_pname P Q) R) (tptp.hAPP_c1126217667_state P (tptp.hAPP_pname_com Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H78829294e_bool (tptp.cOMBB_2144135922_state P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_H78829294e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H78829294e_bool (tptp.cOMBS_458705923l_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_H1187982158l_bool P R) (tptp.hAPP_H78829294e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1476298914l_bool (tptp.cOMBB_2095475776e_bool P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f1664156314l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_f971112728l_bool (tptp.cOMBK_129401207e_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_pname P) (= (tptp.hAPP_f560369737_pname (tptp.cOMBK_1589414042e_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_f888949707_state (tptp.cOMBK_1503445380e_bool P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_fun_pname_bool P) (= (tptp.hAPP_H356885323e_bool (tptp.cOMBK_2035509764_state P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_p442853985e_bool (tptp.cOMBK_1706929794_pname P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f971112728l_bool (tptp.cOMBB_1522210668e_bool P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_f971112728l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1187982158l_bool (tptp.cOMBB_962198420_state P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_H78829294e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f971112728l_bool (tptp.cOMBS_2066081387l_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_f637090980l_bool P R) (tptp.hAPP_f971112728l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f32027384l_bool (tptp.cOMBB_689948150l_bool P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f1935102916l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_f166538662l_bool (tptp.cOMBK_482404831l_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H78829294e_bool (tptp.hAPP_H1049623551e_bool (tptp.cOMBC_654211620e_bool P) Q) R) (tptp.hAPP_H78829294e_bool (tptp.hAPP_H1049623551e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f637090980l_bool (tptp.cOMBB_1585081418e_bool P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f971112728l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f166538662l_bool (tptp.cOMBS_1358309691l_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_f2143399574l_bool P R) (tptp.hAPP_f166538662l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_f1387463497_state (tptp.cOMBK_701929478e_bool P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_H1049623551e_bool (tptp.cOMBK_1039769424_state P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H78829294e_bool (tptp.hAPP_f98417237e_bool (tptp.cOMBC_1734175330l_bool P) Q) R) (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f2143399574l_bool (tptp.cOMBB_404111180l_bool P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f166538662l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool (tptp.cOMBC_449066458l_bool P) Q) R) (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f971112728l_bool (tptp.hAPP_f1201187855l_bool (tptp.cOMBC_1114453604l_bool P) Q) R) (tptp.hAPP_f166538662l_bool (tptp.hAPP_f210337421l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f166538662l_bool (tptp.hAPP_f585161855l_bool (tptp.cOMBC_1691491604l_bool P) Q) R) (tptp.hAPP_f166538662l_bool (tptp.hAPP_f585161855l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f468958928l_bool (tptp.hAPP_f667366769l_bool (tptp.cOMBC_747715418l_bool P) Q) R) (tptp.hAPP_f468958928l_bool (tptp.hAPP_f667366769l_bool P R) Q))) _let_10 _let_9 (tptp.hBOOL (tptp.hAPP_f971112728l_bool tptp.finite364844667_state tptp.fa)) (not (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_H30606679l_bool tptp.member1338687867_state _let_1) tptp.fa))) (tptp.hBOOL (tptp.hAPP_f971112728l_bool (tptp.hAPP_f72706945l_bool tptp.ord_le1285840794e_bool tptp.fa) (tptp.image_2003357581_state (tptp.cOMBB_699532858_pname tptp.hoare_Mirabelle_MGT (tptp.cOMBB_923936821_pname tptp.the_com tptp.body)) _let_3))) _let_8 (tptp.hBOOL (tptp.hAPP_f971112728l_bool _let_5 tptp.fa)) _let_7 true))))))))))))))))))))))))))))))))))))))
% 0.73/0.92  )
% 0.73/0.92  % SZS output end Proof for SWW474+1
% 0.73/0.92  % cvc5---1.0.5 exiting
% 0.73/0.92  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------