TSTP Solution File: SWW471^2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW471^2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:20:58 EDT 2023
% Result : Timeout 299.76s 300.17s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.22 % Problem : SWW471^2 : TPTP v8.1.2. Released v5.3.0.
% 0.22/0.23 % Command : do_cvc5 %s %d
% 0.23/0.44 % Computer : n024.cluster.edu
% 0.23/0.44 % Model : x86_64 x86_64
% 0.23/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.44 % Memory : 8042.1875MB
% 0.23/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.23/0.44 % CPULimit : 300
% 0.23/0.44 % WCLimit : 300
% 0.23/0.44 % DateTime : Sun Aug 27 18:20:38 EDT 2023
% 0.23/0.44 % CPUTime :
% 0.29/0.67 %----Proving TH0
% 0.29/0.68 %------------------------------------------------------------------------------
% 0.29/0.68 % File : SWW471^2 : TPTP v8.1.2. Released v5.3.0.
% 0.29/0.68 % Domain : Software Verification
% 0.29/0.68 % Problem : Hoare's Logic with Procedures line 269, 500 axioms selected
% 0.29/0.68 % Version : Especial.
% 0.29/0.68 % English :
% 0.29/0.68
% 0.29/0.68 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.29/0.68 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.29/0.68 % Source : [Bla11]
% 0.29/0.68 % Names : hoare_500_thf_l269 [Bla11]
% 0.29/0.68
% 0.29/0.68 % Status : ContradictoryAxioms
% 0.29/0.68 % Rating : 1.00 v7.2.0, 0.88 v7.1.0, 1.00 v5.3.0
% 0.29/0.68 % Syntax : Number of formulae : 849 ( 298 unt; 135 typ; 0 def)
% 0.29/0.68 % Number of atoms : 3194 ( 697 equ; 48 cnn)
% 0.29/0.68 % Maximal formula atoms : 14 ( 4 avg)
% 0.29/0.68 % Number of connectives : 6398 ( 258 ~; 46 |; 101 &;5209 @)
% 0.29/0.68 % ( 150 <=>; 634 =>; 0 <=; 0 <~>)
% 0.29/0.68 % Maximal formula depth : 19 ( 7 avg)
% 0.29/0.68 % Number of types : 9 ( 8 usr)
% 0.29/0.68 % Number of type conns : 1823 (1823 >; 0 *; 0 +; 0 <<)
% 0.29/0.68 % Number of symbols : 134 ( 127 usr; 12 con; 0-5 aty)
% 0.29/0.68 % Number of variables : 2050 ( 106 ^;1909 !; 35 ?;2050 :)
% 0.29/0.68 % SPC : TH0_CAX_EQU_NAR
% 0.29/0.68
% 0.29/0.68 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.29/0.68 % 2011-08-09 19:25:05
% 0.29/0.68 %------------------------------------------------------------------------------
% 0.29/0.68 %----Should-be-implicit typings (8)
% 0.29/0.68 thf(ty_ty_t__a,type,
% 0.29/0.68 x_a: $tType ).
% 0.29/0.68
% 0.29/0.68 thf(ty_ty_tc__Com__Ocom,type,
% 0.29/0.68 com: $tType ).
% 0.29/0.68
% 0.29/0.68 thf(ty_ty_tc__Com__Opname,type,
% 0.29/0.68 pname: $tType ).
% 0.29/0.68
% 0.29/0.68 thf(ty_ty_tc__Com__Ostate,type,
% 0.29/0.68 state: $tType ).
% 0.29/0.68
% 0.29/0.68 thf(ty_ty_tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J,type,
% 0.29/0.68 hoare_1775062406iple_a: $tType ).
% 0.29/0.68
% 0.29/0.68 thf(ty_ty_tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J,type,
% 0.29/0.68 hoare_1167836817_state: $tType ).
% 0.29/0.68
% 0.29/0.68 thf(ty_ty_tc__Nat__Onat,type,
% 0.29/0.68 nat: $tType ).
% 0.29/0.68
% 0.29/0.68 thf(ty_ty_tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 0.29/0.68 option_com: $tType ).
% 0.29/0.68
% 0.29/0.68 %----Explicit typings (127)
% 0.29/0.68 thf(sy_c_Big__Operators_Olattice__class_OInf__fin_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.68 big_la1126801287name_o: ( ( pname > $o ) > $o ) > pname > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Big__Operators_Olattice__class_OInf__fin_000_062_Itc__Hoare____Mirabelle___,type,
% 0.29/0.68 big_la447547205le_a_o: ( ( hoare_1775062406iple_a > $o ) > $o ) > hoare_1775062406iple_a > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Big__Operators_Olattice__class_OInf__fin_000_062_Itc__Hoare____Mirabelle____001,type,
% 0.29/0.68 big_la831793456tate_o: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Big__Operators_Olattice__class_OInf__fin_000_Eo,type,
% 0.29/0.68 big_la1690136417_fin_o: ( $o > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Big__Operators_Olattice__class_OSup__fin_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.68 big_la1286884090name_o: ( ( pname > $o ) > $o ) > pname > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Big__Operators_Olattice__class_OSup__fin_000_062_Itc__Hoare____Mirabelle___,type,
% 0.29/0.68 big_la1843772984le_a_o: ( ( hoare_1775062406iple_a > $o ) > $o ) > hoare_1775062406iple_a > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Big__Operators_Olattice__class_OSup__fin_000_062_Itc__Hoare____Mirabelle____002,type,
% 0.29/0.68 big_la1138507389tate_o: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Big__Operators_Olattice__class_OSup__fin_000_Eo,type,
% 0.29/0.68 big_la727467310_fin_o: ( $o > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Com_Obody,type,
% 0.29/0.68 body_1: pname > option_com ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Com_Ocom_OBODY,type,
% 0.29/0.68 body: pname > com ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Com_Ocom_OCond,type,
% 0.29/0.68 cond: ( state > $o ) > com > com > com ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Com_Ocom_OSKIP,type,
% 0.29/0.68 skip: com ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Com_Ocom_OSemi,type,
% 0.29/0.68 semi: com > com > com ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Com_Ocom_OWhile,type,
% 0.29/0.68 while: ( state > $o ) > com > com ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Com_Ocom_Ocom__size,type,
% 0.29/0.68 com_size: com > nat ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.68 finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_,type,
% 0.29/0.68 finite789576932le_a_o: ( ( hoare_1775062406iple_a > $o ) > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple__003,type,
% 0.29/0.68 finite1380128977tate_o: ( ( hoare_1167836817_state > $o ) > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Finite__Set_Ofinite_000_Eo,type,
% 0.29/0.68 finite_finite_o: ( $o > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Finite__Set_Ofinite_000tc__Com__Opname,type,
% 0.29/0.68 finite_finite_pname: ( pname > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_,type,
% 0.29/0.68 finite2063573081iple_a: ( hoare_1775062406iple_a > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__C,type,
% 0.29/0.68 finite1084549118_state: ( hoare_1167836817_state > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otr,type,
% 0.29/0.68 finite1805141964_pname: ( ( hoare_1775062406iple_a > $o ) > ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o ) > ( pname > hoare_1775062406iple_a > $o ) > ( hoare_1775062406iple_a > $o ) > ( pname > $o ) > hoare_1775062406iple_a > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otr_004,type,
% 0.29/0.68 finite1068437657_pname: ( ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > ( pname > hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > ( pname > $o ) > hoare_1167836817_state > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Finite__Set_Ofolding__one_000tc__Com__Opname,type,
% 0.29/0.68 finite1282449217_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____srushsumbx__Otriple_,type,
% 0.29/0.68 finite2078349315iple_a: ( hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a ) > ( ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____srushsumbx__Otriple__005,type,
% 0.29/0.68 finite1074406356_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname,type,
% 0.29/0.68 finite89670078_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____srushsumbx__Ot,type,
% 0.29/0.68 finite1358382848iple_a: ( hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a ) > ( ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____srushsumbx__Ot_006,type,
% 0.29/0.68 finite806517911_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.68 minus_minus_pname_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Hoare____Mirabelle____srushsumbx__,type,
% 0.29/0.68 minus_1944206118le_a_o: ( hoare_1775062406iple_a > $o ) > ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Hoare____Mirabelle____srushsumbx___007,type,
% 0.29/0.68 minus_2107060239tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat,type,
% 0.29/0.68 minus_minus_nat: nat > nat > nat ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat,type,
% 0.29/0.68 one_one_nat: nat ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat,type,
% 0.29/0.68 plus_plus_nat: nat > nat > nat ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat,type,
% 0.29/0.68 zero_zero_nat: nat ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_HOL_OThe_000tc__Com__Opname,type,
% 0.29/0.68 the_pname: ( pname > $o ) > pname ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_HOL_OThe_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J,type,
% 0.29/0.68 the_Ho1155011127iple_a: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_HOL_OThe_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_,type,
% 0.29/0.68 the_Ho310147232_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Hoare__Mirabelle__srushsumbx_OMGT,type,
% 0.29/0.68 hoare_Mirabelle_MGT: com > hoare_1167836817_state ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Hoare__Mirabelle__srushsumbx_Ohoare__derivs_000t__a,type,
% 0.29/0.68 hoare_1508237396rivs_a: ( hoare_1775062406iple_a > $o ) > ( hoare_1775062406iple_a > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Hoare__Mirabelle__srushsumbx_Ohoare__derivs_000tc__Com__Ostate,type,
% 0.29/0.68 hoare_123228589_state: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Hoare__Mirabelle__srushsumbx_Ohoare__valids_000t__a,type,
% 0.29/0.68 hoare_1846070742lids_a: ( hoare_1775062406iple_a > $o ) > ( hoare_1775062406iple_a > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Hoare__Mirabelle__srushsumbx_Ohoare__valids_000tc__Com__Ostate,type,
% 0.29/0.68 hoare_529639851_state: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Hoare__Mirabelle__srushsumbx_Otriple_Otriple_000t__a,type,
% 0.29/0.68 hoare_1766022166iple_a: ( x_a > state > $o ) > com > ( x_a > state > $o ) > hoare_1775062406iple_a ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Hoare__Mirabelle__srushsumbx_Otriple_Otriple_000tc__Com__Ostate,type,
% 0.29/0.68 hoare_908217195_state: ( state > state > $o ) > com > ( state > state > $o ) > hoare_1167836817_state ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Hoare__Mirabelle__srushsumbx_Otriple_Otriple__size_000t__a,type,
% 0.29/0.68 hoare_1118907895size_a: ( x_a > nat ) > hoare_1775062406iple_a > nat ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Hoare__Mirabelle__srushsumbx_Otriple_Otriple__size_000tc__Com__Ostate,type,
% 0.29/0.68 hoare_545207370_state: ( state > nat ) > hoare_1167836817_state > nat ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Hoare__Mirabelle__srushsumbx_Otriple__valid_000t__a,type,
% 0.29/0.68 hoare_1462269968alid_a: nat > hoare_1775062406iple_a > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Hoare__Mirabelle__srushsumbx_Otriple__valid_000tc__Com__Ostate,type,
% 0.29/0.68 hoare_56934129_state: nat > hoare_1167836817_state > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J,type,
% 0.29/0.68 if_Hoa1047340790iple_a: $o > hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J,type,
% 0.29/0.68 if_Hoa833675553_state: $o > hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Com__Opname_M_Eo_,type,
% 0.29/0.68 semila2013987940me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Hoare____Mirabell,type,
% 0.29/0.68 semila1691990438_a_o_o: ( ( hoare_1775062406iple_a > $o ) > $o ) > ( ( hoare_1775062406iple_a > $o ) > $o ) > ( hoare_1775062406iple_a > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Hoare____Mirabell_008,type,
% 0.29/0.68 semila1758709489te_o_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_Eo_M_Eo_J,type,
% 0.29/0.68 semila232696320nf_o_o: ( $o > $o ) > ( $o > $o ) > $o > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.68 semila1673364395name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Hoare____Mirabelle____s,type,
% 0.29/0.68 semila966743401le_a_o: ( hoare_1775062406iple_a > $o ) > ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Hoare____Mirabelle____s_009,type,
% 0.29/0.68 semila179895820tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_Eo,type,
% 0.29/0.68 semila854092349_inf_o: $o > $o > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Com__Opname_M_Eo_,type,
% 0.29/0.68 semila181081674me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Hoare____Mirabell,type,
% 0.29/0.68 semila2069193356_a_o_o: ( ( hoare_1775062406iple_a > $o ) > $o ) > ( ( hoare_1775062406iple_a > $o ) > $o ) > ( hoare_1775062406iple_a > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Hoare____Mirabell_010,type,
% 0.29/0.68 semila866907787te_o_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_Eo_M_Eo_J,type,
% 0.29/0.68 semila2062604954up_o_o: ( $o > $o ) > ( $o > $o ) > $o > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.68 semila1780557381name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Hoare____Mirabelle____s,type,
% 0.29/0.68 semila13410563le_a_o: ( hoare_1775062406iple_a > $o ) > ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Hoare____Mirabelle____s_011,type,
% 0.29/0.68 semila1172322802tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_Eo,type,
% 0.29/0.68 semila10642723_sup_o: $o > $o > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Nat_OSuc,type,
% 0.29/0.68 suc: nat > nat ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Nat_Onat_Onat__case_000tc__Nat__Onat,type,
% 0.29/0.68 nat_case_nat: nat > ( nat > nat ) > nat > nat ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Nat_Osize__class_Osize_000tc__Com__Ocom,type,
% 0.29/0.68 size_size_com: com > nat ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Nat_Osize__class_Osize_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It_,type,
% 0.29/0.68 size_s724313756iple_a: hoare_1775062406iple_a > nat ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Nat_Osize__class_Osize_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc,type,
% 0.29/0.68 size_s645941755_state: hoare_1167836817_state > nat ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Natural_Oevalc,type,
% 0.29/0.68 evalc: com > state > state > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Natural_Oevaln,type,
% 0.29/0.68 evaln: com > state > nat > state > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Option_Othe_000tc__Com__Ocom,type,
% 0.29/0.68 the_com: option_com > com ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.29/0.68 bot_bot_pname_o_o: ( pname > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Hoare____Mirabelle____srushsu,type,
% 0.29/0.68 bot_bo1976773294_a_o_o: ( hoare_1775062406iple_a > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Hoare____Mirabelle____srushsu_012,type,
% 0.29/0.68 bot_bo691907561te_o_o: ( hoare_1167836817_state > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_Eo_M_Eo_J,type,
% 0.29/0.68 bot_bot_o_o: $o > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.68 bot_bot_pname_o: pname > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____srushsumbx__O,type,
% 0.29/0.68 bot_bo751897185le_a_o: hoare_1775062406iple_a > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____srushsumbx__O_013,type,
% 0.29/0.68 bot_bo70021908tate_o: hoare_1167836817_state > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Orderings_Obot__class_Obot_000_Eo,type,
% 0.29/0.68 bot_bot_o: $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Orderings_Obot__class_Obot_000tc__Nat__Onat,type,
% 0.29/0.68 bot_bot_nat: nat ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_OCollect_000tc__Com__Opname,type,
% 0.29/0.68 collect_pname: ( pname > $o ) > pname > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_OCollect_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J,type,
% 0.29/0.68 collec676402587iple_a: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_OCollect_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ost,type,
% 0.29/0.68 collec1027672124_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.68 image_1085733413name_o: ( ( pname > $o ) > pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_M,type,
% 0.29/0.68 image_2014247585le_a_o: ( ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o ) > ( ( hoare_1775062406iple_a > $o ) > $o ) > ( hoare_1775062406iple_a > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com_,type,
% 0.29/0.68 image_1488525317tate_o: ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Oimage_000_Eo_000_Eo,type,
% 0.29/0.68 image_o_o: ( $o > $o ) > ( $o > $o ) > $o > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,type,
% 0.29/0.68 image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____srushsumbx__Otri,type,
% 0.29/0.68 image_2063119815iple_a: ( pname > hoare_1775062406iple_a ) > ( pname > $o ) > hoare_1775062406iple_a > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____srushsumbx__Otri_014,type,
% 0.29/0.68 image_575578384_state: ( pname > hoare_1167836817_state ) > ( pname > $o ) > hoare_1167836817_state > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_000tc__,type,
% 0.29/0.68 image_51246659_pname: ( hoare_1775062406iple_a > pname ) > ( hoare_1775062406iple_a > $o ) > pname > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_000tc___015,type,
% 0.29/0.68 image_1170193413iple_a: ( hoare_1775062406iple_a > hoare_1775062406iple_a ) > ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_000tc___016,type,
% 0.29/0.68 image_1021683026_state: ( hoare_1775062406iple_a > hoare_1167836817_state ) > ( hoare_1775062406iple_a > $o ) > hoare_1167836817_state > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat,type,
% 0.29/0.68 image_1802845250iple_a: ( hoare_1167836817_state > hoare_1775062406iple_a ) > ( hoare_1167836817_state > $o ) > hoare_1775062406iple_a > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat_017,type,
% 0.29/0.68 image_31595733_state: ( hoare_1167836817_state > hoare_1167836817_state ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Oinsert_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.68 insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Oinsert_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_,type,
% 0.29/0.68 insert1210049533le_a_o: ( hoare_1775062406iple_a > $o ) > ( ( hoare_1775062406iple_a > $o ) > $o ) > ( hoare_1775062406iple_a > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Oinsert_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com,type,
% 0.29/0.68 insert999278200tate_o: ( hoare_1167836817_state > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Oinsert_000_Eo,type,
% 0.29/0.68 insert_o: $o > ( $o > $o ) > $o > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Oinsert_000tc__Com__Opname,type,
% 0.29/0.68 insert_pname: pname > ( pname > $o ) > pname > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J,type,
% 0.29/0.68 insert1281456128iple_a: hoare_1775062406iple_a > ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Osta,type,
% 0.29/0.68 insert2134838167_state: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Othe__elem_000tc__Com__Opname,type,
% 0.29/0.68 the_elem_pname: ( pname > $o ) > pname ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Othe__elem_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J,type,
% 0.29/0.68 the_el1844711461iple_a: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_Set_Othe__elem_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__O,type,
% 0.29/0.68 the_el323660082_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_fequal_000tc__Com__Opname,type,
% 0.29/0.68 fequal_pname: pname > pname > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_fequal_000tc__Com__Ostate,type,
% 0.29/0.68 fequal_state: state > state > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J,type,
% 0.29/0.68 fequal1288209029iple_a: hoare_1775062406iple_a > hoare_1775062406iple_a > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J,type,
% 0.29/0.68 fequal1831255762_state: hoare_1167836817_state > hoare_1167836817_state > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_member_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.68 member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_member_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_M_Eo_,type,
% 0.29/0.68 member1207314404le_a_o: ( hoare_1775062406iple_a > $o ) > ( ( hoare_1775062406iple_a > $o ) > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_member_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ost,type,
% 0.29/0.68 member864234961tate_o: ( hoare_1167836817_state > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_member_000_Eo,type,
% 0.29/0.68 member_o: $o > ( $o > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_member_000tc__Com__Opname,type,
% 0.29/0.68 member_pname: pname > ( pname > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_member_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J,type,
% 0.29/0.68 member2122167641iple_a: hoare_1775062406iple_a > ( hoare_1775062406iple_a > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_c_member_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J,type,
% 0.29/0.68 member2058392318_state: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_v_G,type,
% 0.29/0.68 g: hoare_1775062406iple_a > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_v_P,type,
% 0.29/0.68 p: pname > x_a > state > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_v_Procs,type,
% 0.29/0.68 procs: pname > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_v_Q,type,
% 0.29/0.68 q: pname > x_a > state > $o ).
% 0.29/0.68
% 0.29/0.68 thf(sy_v_n,type,
% 0.29/0.68 n: nat ).
% 0.29/0.68
% 0.29/0.68 %----Relevant facts (698)
% 0.29/0.68 thf(fact_0_triple_Oinject,axiom,
% 0.29/0.68 ! [Fun1_4: x_a > state > $o,Com: com,Fun2_4: x_a > state > $o,Fun1_3: x_a > state > $o,Com_1: com,Fun2_3: x_a > state > $o] :
% 0.29/0.68 ( ( ( hoare_1766022166iple_a @ Fun1_4 @ Com @ Fun2_4 )
% 0.29/0.68 = ( hoare_1766022166iple_a @ Fun1_3 @ Com_1 @ Fun2_3 ) )
% 0.29/0.68 <=> ( ( Fun1_4 = Fun1_3 )
% 0.29/0.68 & ( Com = Com_1 )
% 0.29/0.68 & ( Fun2_4 = Fun2_3 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_1_triple_Oinject,axiom,
% 0.29/0.68 ! [Fun1_4: state > state > $o,Com: com,Fun2_4: state > state > $o,Fun1_3: state > state > $o,Com_1: com,Fun2_3: state > state > $o] :
% 0.29/0.68 ( ( ( hoare_908217195_state @ Fun1_4 @ Com @ Fun2_4 )
% 0.29/0.68 = ( hoare_908217195_state @ Fun1_3 @ Com_1 @ Fun2_3 ) )
% 0.29/0.68 <=> ( ( Fun1_4 = Fun1_3 )
% 0.29/0.68 & ( Com = Com_1 )
% 0.29/0.68 & ( Fun2_4 = Fun2_3 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_2_hoare__valids__def,axiom,
% 0.29/0.68 ! [G_25: hoare_1167836817_state > $o,Ts_4: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( hoare_529639851_state @ G_25 @ Ts_4 )
% 0.29/0.68 <=> ! [N: nat] :
% 0.29/0.68 ( ! [X: hoare_1167836817_state] :
% 0.29/0.68 ( ( member2058392318_state @ X @ G_25 )
% 0.29/0.68 => ( hoare_56934129_state @ N @ X ) )
% 0.29/0.68 => ! [X: hoare_1167836817_state] :
% 0.29/0.68 ( ( member2058392318_state @ X @ Ts_4 )
% 0.29/0.68 => ( hoare_56934129_state @ N @ X ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_3_hoare__valids__def,axiom,
% 0.29/0.68 ! [G_25: hoare_1775062406iple_a > $o,Ts_4: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( hoare_1846070742lids_a @ G_25 @ Ts_4 )
% 0.29/0.68 <=> ! [N: nat] :
% 0.29/0.68 ( ! [X: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( member2122167641iple_a @ X @ G_25 )
% 0.29/0.68 => ( hoare_1462269968alid_a @ N @ X ) )
% 0.29/0.68 => ! [X: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( member2122167641iple_a @ X @ Ts_4 )
% 0.29/0.68 => ( hoare_1462269968alid_a @ N @ X ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_4_hoare__derivs_OBody,axiom,
% 0.29/0.68 ! [G_24: hoare_1167836817_state > $o,P_37: pname > state > state > $o,Q_20: pname > state > state > $o,Procs_1: pname > $o] :
% 0.29/0.68 ( ( hoare_123228589_state
% 0.29/0.68 @ ( semila1172322802tate_o @ G_24
% 0.29/0.68 @ ( image_575578384_state
% 0.29/0.68 @ ^ [P_10: pname] : ( hoare_908217195_state @ ( P_37 @ P_10 ) @ ( body @ P_10 ) @ ( Q_20 @ P_10 ) )
% 0.29/0.68 @ Procs_1 ) )
% 0.29/0.68 @ ( image_575578384_state
% 0.29/0.68 @ ^ [P_10: pname] : ( hoare_908217195_state @ ( P_37 @ P_10 ) @ ( the_com @ ( body_1 @ P_10 ) ) @ ( Q_20 @ P_10 ) )
% 0.29/0.68 @ Procs_1 ) )
% 0.29/0.68 => ( hoare_123228589_state @ G_24
% 0.29/0.68 @ ( image_575578384_state
% 0.29/0.68 @ ^ [P_10: pname] : ( hoare_908217195_state @ ( P_37 @ P_10 ) @ ( body @ P_10 ) @ ( Q_20 @ P_10 ) )
% 0.29/0.68 @ Procs_1 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_5_hoare__derivs_OBody,axiom,
% 0.29/0.68 ! [G_24: hoare_1775062406iple_a > $o,P_37: pname > x_a > state > $o,Q_20: pname > x_a > state > $o,Procs_1: pname > $o] :
% 0.29/0.68 ( ( hoare_1508237396rivs_a
% 0.29/0.68 @ ( semila13410563le_a_o @ G_24
% 0.29/0.68 @ ( image_2063119815iple_a
% 0.29/0.68 @ ^ [P_10: pname] : ( hoare_1766022166iple_a @ ( P_37 @ P_10 ) @ ( body @ P_10 ) @ ( Q_20 @ P_10 ) )
% 0.29/0.68 @ Procs_1 ) )
% 0.29/0.68 @ ( image_2063119815iple_a
% 0.29/0.68 @ ^ [P_10: pname] : ( hoare_1766022166iple_a @ ( P_37 @ P_10 ) @ ( the_com @ ( body_1 @ P_10 ) ) @ ( Q_20 @ P_10 ) )
% 0.29/0.68 @ Procs_1 ) )
% 0.29/0.68 => ( hoare_1508237396rivs_a @ G_24
% 0.29/0.68 @ ( image_2063119815iple_a
% 0.29/0.68 @ ^ [P_10: pname] : ( hoare_1766022166iple_a @ ( P_37 @ P_10 ) @ ( body @ P_10 ) @ ( Q_20 @ P_10 ) )
% 0.29/0.68 @ Procs_1 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_6_UnE,axiom,
% 0.29/0.68 ! [C_42: hoare_1167836817_state,A_138: hoare_1167836817_state > $o,B_79: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( member2058392318_state @ C_42 @ ( semila1172322802tate_o @ A_138 @ B_79 ) )
% 0.29/0.68 => ( ~ ( member2058392318_state @ C_42 @ A_138 )
% 0.29/0.68 => ( member2058392318_state @ C_42 @ B_79 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_7_UnE,axiom,
% 0.29/0.68 ! [C_42: hoare_1775062406iple_a,A_138: hoare_1775062406iple_a > $o,B_79: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ C_42 @ ( semila13410563le_a_o @ A_138 @ B_79 ) )
% 0.29/0.68 => ( ~ ( member2122167641iple_a @ C_42 @ A_138 )
% 0.29/0.68 => ( member2122167641iple_a @ C_42 @ B_79 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_8_UnE,axiom,
% 0.29/0.68 ! [C_42: pname,A_138: pname > $o,B_79: pname > $o] :
% 0.29/0.68 ( ( member_pname @ C_42 @ ( semila1780557381name_o @ A_138 @ B_79 ) )
% 0.29/0.68 => ( ~ ( member_pname @ C_42 @ A_138 )
% 0.29/0.68 => ( member_pname @ C_42 @ B_79 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_9_sup1E,axiom,
% 0.29/0.68 ! [A_137: hoare_1167836817_state > $o,B_78: hoare_1167836817_state > $o,X_51: hoare_1167836817_state] :
% 0.29/0.68 ( ( semila1172322802tate_o @ A_137 @ B_78 @ X_51 )
% 0.29/0.68 => ( ~ ( A_137 @ X_51 )
% 0.29/0.68 => ( B_78 @ X_51 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_10_sup1E,axiom,
% 0.29/0.68 ! [A_137: pname > $o,B_78: pname > $o,X_51: pname] :
% 0.29/0.68 ( ( semila1780557381name_o @ A_137 @ B_78 @ X_51 )
% 0.29/0.68 => ( ~ ( A_137 @ X_51 )
% 0.29/0.68 => ( B_78 @ X_51 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_11_sup1E,axiom,
% 0.29/0.68 ! [A_137: hoare_1775062406iple_a > $o,B_78: hoare_1775062406iple_a > $o,X_51: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( semila13410563le_a_o @ A_137 @ B_78 @ X_51 )
% 0.29/0.68 => ( ~ ( A_137 @ X_51 )
% 0.29/0.68 => ( B_78 @ X_51 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_12_sup1CI,axiom,
% 0.29/0.68 ! [A_136: hoare_1167836817_state > $o,B_77: hoare_1167836817_state > $o,X_50: hoare_1167836817_state] :
% 0.29/0.68 ( ( ~ ( B_77 @ X_50 )
% 0.29/0.68 => ( A_136 @ X_50 ) )
% 0.29/0.68 => ( semila1172322802tate_o @ A_136 @ B_77 @ X_50 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_13_sup1CI,axiom,
% 0.29/0.68 ! [A_136: pname > $o,B_77: pname > $o,X_50: pname] :
% 0.29/0.68 ( ( ~ ( B_77 @ X_50 )
% 0.29/0.68 => ( A_136 @ X_50 ) )
% 0.29/0.68 => ( semila1780557381name_o @ A_136 @ B_77 @ X_50 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_14_sup1CI,axiom,
% 0.29/0.68 ! [A_136: hoare_1775062406iple_a > $o,B_77: hoare_1775062406iple_a > $o,X_50: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( ~ ( B_77 @ X_50 )
% 0.29/0.68 => ( A_136 @ X_50 ) )
% 0.29/0.68 => ( semila13410563le_a_o @ A_136 @ B_77 @ X_50 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_15_UnCI,axiom,
% 0.29/0.68 ! [A_135: hoare_1167836817_state > $o,C_41: hoare_1167836817_state,B_76: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( ~ ( member2058392318_state @ C_41 @ B_76 )
% 0.29/0.68 => ( member2058392318_state @ C_41 @ A_135 ) )
% 0.29/0.68 => ( member2058392318_state @ C_41 @ ( semila1172322802tate_o @ A_135 @ B_76 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_16_UnCI,axiom,
% 0.29/0.68 ! [A_135: hoare_1775062406iple_a > $o,C_41: hoare_1775062406iple_a,B_76: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( ~ ( member2122167641iple_a @ C_41 @ B_76 )
% 0.29/0.68 => ( member2122167641iple_a @ C_41 @ A_135 ) )
% 0.29/0.68 => ( member2122167641iple_a @ C_41 @ ( semila13410563le_a_o @ A_135 @ B_76 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_17_UnCI,axiom,
% 0.29/0.68 ! [A_135: pname > $o,C_41: pname,B_76: pname > $o] :
% 0.29/0.68 ( ( ~ ( member_pname @ C_41 @ B_76 )
% 0.29/0.68 => ( member_pname @ C_41 @ A_135 ) )
% 0.29/0.68 => ( member_pname @ C_41 @ ( semila1780557381name_o @ A_135 @ B_76 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_18_image__eqI,axiom,
% 0.29/0.68 ! [A_134: pname > $o,B_75: hoare_1167836817_state,F_41: pname > hoare_1167836817_state,X_49: pname] :
% 0.29/0.68 ( ( B_75
% 0.29/0.68 = ( F_41 @ X_49 ) )
% 0.29/0.68 => ( ( member_pname @ X_49 @ A_134 )
% 0.29/0.68 => ( member2058392318_state @ B_75 @ ( image_575578384_state @ F_41 @ A_134 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_19_image__eqI,axiom,
% 0.29/0.68 ! [A_134: hoare_1775062406iple_a > $o,B_75: pname,F_41: hoare_1775062406iple_a > pname,X_49: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( B_75
% 0.29/0.68 = ( F_41 @ X_49 ) )
% 0.29/0.68 => ( ( member2122167641iple_a @ X_49 @ A_134 )
% 0.29/0.68 => ( member_pname @ B_75 @ ( image_51246659_pname @ F_41 @ A_134 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_20_image__eqI,axiom,
% 0.29/0.68 ! [A_134: pname > $o,B_75: hoare_1775062406iple_a,F_41: pname > hoare_1775062406iple_a,X_49: pname] :
% 0.29/0.68 ( ( B_75
% 0.29/0.68 = ( F_41 @ X_49 ) )
% 0.29/0.68 => ( ( member_pname @ X_49 @ A_134 )
% 0.29/0.68 => ( member2122167641iple_a @ B_75 @ ( image_2063119815iple_a @ F_41 @ A_134 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_21_image__Un,axiom,
% 0.29/0.68 ! [F_40: pname > hoare_1167836817_state,A_133: pname > $o,B_74: pname > $o] :
% 0.29/0.68 ( ( image_575578384_state @ F_40 @ ( semila1780557381name_o @ A_133 @ B_74 ) )
% 0.29/0.68 = ( semila1172322802tate_o @ ( image_575578384_state @ F_40 @ A_133 ) @ ( image_575578384_state @ F_40 @ B_74 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_22_image__Un,axiom,
% 0.29/0.68 ! [F_40: hoare_1775062406iple_a > hoare_1167836817_state,A_133: hoare_1775062406iple_a > $o,B_74: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( image_1021683026_state @ F_40 @ ( semila13410563le_a_o @ A_133 @ B_74 ) )
% 0.29/0.68 = ( semila1172322802tate_o @ ( image_1021683026_state @ F_40 @ A_133 ) @ ( image_1021683026_state @ F_40 @ B_74 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_23_image__Un,axiom,
% 0.29/0.68 ! [F_40: hoare_1775062406iple_a > pname,A_133: hoare_1775062406iple_a > $o,B_74: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( image_51246659_pname @ F_40 @ ( semila13410563le_a_o @ A_133 @ B_74 ) )
% 0.29/0.68 = ( semila1780557381name_o @ ( image_51246659_pname @ F_40 @ A_133 ) @ ( image_51246659_pname @ F_40 @ B_74 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_24_image__Un,axiom,
% 0.29/0.68 ! [F_40: hoare_1167836817_state > hoare_1775062406iple_a,A_133: hoare_1167836817_state > $o,B_74: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( image_1802845250iple_a @ F_40 @ ( semila1172322802tate_o @ A_133 @ B_74 ) )
% 0.29/0.68 = ( semila13410563le_a_o @ ( image_1802845250iple_a @ F_40 @ A_133 ) @ ( image_1802845250iple_a @ F_40 @ B_74 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_25_image__Un,axiom,
% 0.29/0.68 ! [F_40: pname > hoare_1775062406iple_a,A_133: pname > $o,B_74: pname > $o] :
% 0.29/0.68 ( ( image_2063119815iple_a @ F_40 @ ( semila1780557381name_o @ A_133 @ B_74 ) )
% 0.29/0.68 = ( semila13410563le_a_o @ ( image_2063119815iple_a @ F_40 @ A_133 ) @ ( image_2063119815iple_a @ F_40 @ B_74 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_26_sup__fun__def,axiom,
% 0.29/0.68 ! [F_39: hoare_1167836817_state > $o,G_23: hoare_1167836817_state > $o,X: hoare_1167836817_state] :
% 0.29/0.68 ( ( semila1172322802tate_o @ F_39 @ G_23 @ X )
% 0.29/0.68 <=> ( semila10642723_sup_o @ ( F_39 @ X ) @ ( G_23 @ X ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_27_sup__fun__def,axiom,
% 0.29/0.68 ! [F_39: pname > $o,G_23: pname > $o,X: pname] :
% 0.29/0.68 ( ( semila1780557381name_o @ F_39 @ G_23 @ X )
% 0.29/0.68 <=> ( semila10642723_sup_o @ ( F_39 @ X ) @ ( G_23 @ X ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_28_sup__fun__def,axiom,
% 0.29/0.68 ! [F_39: hoare_1775062406iple_a > $o,G_23: hoare_1775062406iple_a > $o,X: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( semila13410563le_a_o @ F_39 @ G_23 @ X )
% 0.29/0.68 <=> ( semila10642723_sup_o @ ( F_39 @ X ) @ ( G_23 @ X ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_29_sup__apply,axiom,
% 0.29/0.68 ! [F_38: hoare_1167836817_state > $o,G_22: hoare_1167836817_state > $o,X_48: hoare_1167836817_state] :
% 0.29/0.68 ( ( semila1172322802tate_o @ F_38 @ G_22 @ X_48 )
% 0.29/0.68 <=> ( semila10642723_sup_o @ ( F_38 @ X_48 ) @ ( G_22 @ X_48 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_30_sup__apply,axiom,
% 0.29/0.68 ! [F_38: pname > $o,G_22: pname > $o,X_48: pname] :
% 0.29/0.68 ( ( semila1780557381name_o @ F_38 @ G_22 @ X_48 )
% 0.29/0.68 <=> ( semila10642723_sup_o @ ( F_38 @ X_48 ) @ ( G_22 @ X_48 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_31_sup__apply,axiom,
% 0.29/0.68 ! [F_38: hoare_1775062406iple_a > $o,G_22: hoare_1775062406iple_a > $o,X_48: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( semila13410563le_a_o @ F_38 @ G_22 @ X_48 )
% 0.29/0.68 <=> ( semila10642723_sup_o @ ( F_38 @ X_48 ) @ ( G_22 @ X_48 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_32_cut,axiom,
% 0.29/0.68 ! [G_21: hoare_1167836817_state > $o,G_20: hoare_1167836817_state > $o,Ts_3: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( hoare_123228589_state @ G_20 @ Ts_3 )
% 0.29/0.68 => ( ( hoare_123228589_state @ G_21 @ G_20 )
% 0.29/0.68 => ( hoare_123228589_state @ G_21 @ Ts_3 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_33_cut,axiom,
% 0.29/0.68 ! [G_21: hoare_1775062406iple_a > $o,G_20: hoare_1775062406iple_a > $o,Ts_3: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( hoare_1508237396rivs_a @ G_20 @ Ts_3 )
% 0.29/0.68 => ( ( hoare_1508237396rivs_a @ G_21 @ G_20 )
% 0.29/0.68 => ( hoare_1508237396rivs_a @ G_21 @ Ts_3 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_34_sup__assoc,axiom,
% 0.29/0.68 ! [X_47: hoare_1167836817_state > $o,Y_21: hoare_1167836817_state > $o,Z_14: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ X_47 @ Y_21 ) @ Z_14 )
% 0.29/0.68 = ( semila1172322802tate_o @ X_47 @ ( semila1172322802tate_o @ Y_21 @ Z_14 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_35_sup__assoc,axiom,
% 0.29/0.68 ! [X_47: pname > $o,Y_21: pname > $o,Z_14: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ ( semila1780557381name_o @ X_47 @ Y_21 ) @ Z_14 )
% 0.29/0.68 = ( semila1780557381name_o @ X_47 @ ( semila1780557381name_o @ Y_21 @ Z_14 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_36_sup__assoc,axiom,
% 0.29/0.68 ! [X_47: $o,Y_21: $o,Z_14: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ ( semila10642723_sup_o @ X_47 @ Y_21 ) @ Z_14 )
% 0.29/0.68 <=> ( semila10642723_sup_o @ X_47 @ ( semila10642723_sup_o @ Y_21 @ Z_14 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_37_sup__assoc,axiom,
% 0.29/0.68 ! [X_47: hoare_1775062406iple_a > $o,Y_21: hoare_1775062406iple_a > $o,Z_14: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ ( semila13410563le_a_o @ X_47 @ Y_21 ) @ Z_14 )
% 0.29/0.68 = ( semila13410563le_a_o @ X_47 @ ( semila13410563le_a_o @ Y_21 @ Z_14 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_38_inf__sup__aci_I6_J,axiom,
% 0.29/0.68 ! [X_46: hoare_1167836817_state > $o,Y_20: hoare_1167836817_state > $o,Z_13: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ X_46 @ Y_20 ) @ Z_13 )
% 0.29/0.68 = ( semila1172322802tate_o @ X_46 @ ( semila1172322802tate_o @ Y_20 @ Z_13 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_39_inf__sup__aci_I6_J,axiom,
% 0.29/0.68 ! [X_46: pname > $o,Y_20: pname > $o,Z_13: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ ( semila1780557381name_o @ X_46 @ Y_20 ) @ Z_13 )
% 0.29/0.68 = ( semila1780557381name_o @ X_46 @ ( semila1780557381name_o @ Y_20 @ Z_13 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_40_inf__sup__aci_I6_J,axiom,
% 0.29/0.68 ! [X_46: $o,Y_20: $o,Z_13: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ ( semila10642723_sup_o @ X_46 @ Y_20 ) @ Z_13 )
% 0.29/0.68 <=> ( semila10642723_sup_o @ X_46 @ ( semila10642723_sup_o @ Y_20 @ Z_13 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_41_inf__sup__aci_I6_J,axiom,
% 0.29/0.68 ! [X_46: hoare_1775062406iple_a > $o,Y_20: hoare_1775062406iple_a > $o,Z_13: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ ( semila13410563le_a_o @ X_46 @ Y_20 ) @ Z_13 )
% 0.29/0.68 = ( semila13410563le_a_o @ X_46 @ ( semila13410563le_a_o @ Y_20 @ Z_13 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_42_sup_Oassoc,axiom,
% 0.29/0.68 ! [A_132: hoare_1167836817_state > $o,B_73: hoare_1167836817_state > $o,C_40: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ A_132 @ B_73 ) @ C_40 )
% 0.29/0.68 = ( semila1172322802tate_o @ A_132 @ ( semila1172322802tate_o @ B_73 @ C_40 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_43_sup_Oassoc,axiom,
% 0.29/0.68 ! [A_132: pname > $o,B_73: pname > $o,C_40: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ ( semila1780557381name_o @ A_132 @ B_73 ) @ C_40 )
% 0.29/0.68 = ( semila1780557381name_o @ A_132 @ ( semila1780557381name_o @ B_73 @ C_40 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_44_sup_Oassoc,axiom,
% 0.29/0.68 ! [A_132: $o,B_73: $o,C_40: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ ( semila10642723_sup_o @ A_132 @ B_73 ) @ C_40 )
% 0.29/0.68 <=> ( semila10642723_sup_o @ A_132 @ ( semila10642723_sup_o @ B_73 @ C_40 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_45_sup_Oassoc,axiom,
% 0.29/0.68 ! [A_132: hoare_1775062406iple_a > $o,B_73: hoare_1775062406iple_a > $o,C_40: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ ( semila13410563le_a_o @ A_132 @ B_73 ) @ C_40 )
% 0.29/0.68 = ( semila13410563le_a_o @ A_132 @ ( semila13410563le_a_o @ B_73 @ C_40 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_46_sup__left__commute,axiom,
% 0.29/0.68 ! [X_45: hoare_1167836817_state > $o,Y_19: hoare_1167836817_state > $o,Z_12: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ X_45 @ ( semila1172322802tate_o @ Y_19 @ Z_12 ) )
% 0.29/0.68 = ( semila1172322802tate_o @ Y_19 @ ( semila1172322802tate_o @ X_45 @ Z_12 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_47_sup__left__commute,axiom,
% 0.29/0.68 ! [X_45: pname > $o,Y_19: pname > $o,Z_12: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ X_45 @ ( semila1780557381name_o @ Y_19 @ Z_12 ) )
% 0.29/0.68 = ( semila1780557381name_o @ Y_19 @ ( semila1780557381name_o @ X_45 @ Z_12 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_48_sup__left__commute,axiom,
% 0.29/0.68 ! [X_45: $o,Y_19: $o,Z_12: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ X_45 @ ( semila10642723_sup_o @ Y_19 @ Z_12 ) )
% 0.29/0.68 <=> ( semila10642723_sup_o @ Y_19 @ ( semila10642723_sup_o @ X_45 @ Z_12 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_49_sup__left__commute,axiom,
% 0.29/0.68 ! [X_45: hoare_1775062406iple_a > $o,Y_19: hoare_1775062406iple_a > $o,Z_12: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ X_45 @ ( semila13410563le_a_o @ Y_19 @ Z_12 ) )
% 0.29/0.68 = ( semila13410563le_a_o @ Y_19 @ ( semila13410563le_a_o @ X_45 @ Z_12 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_50_inf__sup__aci_I7_J,axiom,
% 0.29/0.68 ! [X_44: hoare_1167836817_state > $o,Y_18: hoare_1167836817_state > $o,Z_11: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ X_44 @ ( semila1172322802tate_o @ Y_18 @ Z_11 ) )
% 0.29/0.68 = ( semila1172322802tate_o @ Y_18 @ ( semila1172322802tate_o @ X_44 @ Z_11 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_51_inf__sup__aci_I7_J,axiom,
% 0.29/0.68 ! [X_44: pname > $o,Y_18: pname > $o,Z_11: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ X_44 @ ( semila1780557381name_o @ Y_18 @ Z_11 ) )
% 0.29/0.68 = ( semila1780557381name_o @ Y_18 @ ( semila1780557381name_o @ X_44 @ Z_11 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_52_inf__sup__aci_I7_J,axiom,
% 0.29/0.68 ! [X_44: $o,Y_18: $o,Z_11: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ X_44 @ ( semila10642723_sup_o @ Y_18 @ Z_11 ) )
% 0.29/0.68 <=> ( semila10642723_sup_o @ Y_18 @ ( semila10642723_sup_o @ X_44 @ Z_11 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_53_inf__sup__aci_I7_J,axiom,
% 0.29/0.68 ! [X_44: hoare_1775062406iple_a > $o,Y_18: hoare_1775062406iple_a > $o,Z_11: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ X_44 @ ( semila13410563le_a_o @ Y_18 @ Z_11 ) )
% 0.29/0.68 = ( semila13410563le_a_o @ Y_18 @ ( semila13410563le_a_o @ X_44 @ Z_11 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_54_sup_Oleft__commute,axiom,
% 0.29/0.68 ! [B_72: hoare_1167836817_state > $o,A_131: hoare_1167836817_state > $o,C_39: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ B_72 @ ( semila1172322802tate_o @ A_131 @ C_39 ) )
% 0.29/0.68 = ( semila1172322802tate_o @ A_131 @ ( semila1172322802tate_o @ B_72 @ C_39 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_55_sup_Oleft__commute,axiom,
% 0.29/0.68 ! [B_72: pname > $o,A_131: pname > $o,C_39: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ B_72 @ ( semila1780557381name_o @ A_131 @ C_39 ) )
% 0.29/0.68 = ( semila1780557381name_o @ A_131 @ ( semila1780557381name_o @ B_72 @ C_39 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_56_sup_Oleft__commute,axiom,
% 0.29/0.68 ! [B_72: $o,A_131: $o,C_39: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ B_72 @ ( semila10642723_sup_o @ A_131 @ C_39 ) )
% 0.29/0.68 <=> ( semila10642723_sup_o @ A_131 @ ( semila10642723_sup_o @ B_72 @ C_39 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_57_sup_Oleft__commute,axiom,
% 0.29/0.68 ! [B_72: hoare_1775062406iple_a > $o,A_131: hoare_1775062406iple_a > $o,C_39: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ B_72 @ ( semila13410563le_a_o @ A_131 @ C_39 ) )
% 0.29/0.68 = ( semila13410563le_a_o @ A_131 @ ( semila13410563le_a_o @ B_72 @ C_39 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_58_sup__left__idem,axiom,
% 0.29/0.68 ! [X_43: hoare_1167836817_state > $o,Y_17: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ X_43 @ ( semila1172322802tate_o @ X_43 @ Y_17 ) )
% 0.29/0.68 = ( semila1172322802tate_o @ X_43 @ Y_17 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_59_sup__left__idem,axiom,
% 0.29/0.68 ! [X_43: pname > $o,Y_17: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ X_43 @ ( semila1780557381name_o @ X_43 @ Y_17 ) )
% 0.29/0.68 = ( semila1780557381name_o @ X_43 @ Y_17 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_60_sup__left__idem,axiom,
% 0.29/0.68 ! [X_43: $o,Y_17: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ X_43 @ ( semila10642723_sup_o @ X_43 @ Y_17 ) )
% 0.29/0.68 <=> ( semila10642723_sup_o @ X_43 @ Y_17 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_61_sup__left__idem,axiom,
% 0.29/0.68 ! [X_43: hoare_1775062406iple_a > $o,Y_17: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ X_43 @ ( semila13410563le_a_o @ X_43 @ Y_17 ) )
% 0.29/0.68 = ( semila13410563le_a_o @ X_43 @ Y_17 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_62_inf__sup__aci_I8_J,axiom,
% 0.29/0.68 ! [X_42: hoare_1167836817_state > $o,Y_16: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ X_42 @ ( semila1172322802tate_o @ X_42 @ Y_16 ) )
% 0.29/0.68 = ( semila1172322802tate_o @ X_42 @ Y_16 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_63_inf__sup__aci_I8_J,axiom,
% 0.29/0.68 ! [X_42: pname > $o,Y_16: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ X_42 @ ( semila1780557381name_o @ X_42 @ Y_16 ) )
% 0.29/0.68 = ( semila1780557381name_o @ X_42 @ Y_16 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_64_inf__sup__aci_I8_J,axiom,
% 0.29/0.68 ! [X_42: $o,Y_16: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ X_42 @ ( semila10642723_sup_o @ X_42 @ Y_16 ) )
% 0.29/0.68 <=> ( semila10642723_sup_o @ X_42 @ Y_16 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_65_inf__sup__aci_I8_J,axiom,
% 0.29/0.68 ! [X_42: hoare_1775062406iple_a > $o,Y_16: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ X_42 @ ( semila13410563le_a_o @ X_42 @ Y_16 ) )
% 0.29/0.68 = ( semila13410563le_a_o @ X_42 @ Y_16 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_66_sup_Oleft__idem,axiom,
% 0.29/0.68 ! [A_130: hoare_1167836817_state > $o,B_71: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ A_130 @ ( semila1172322802tate_o @ A_130 @ B_71 ) )
% 0.29/0.68 = ( semila1172322802tate_o @ A_130 @ B_71 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_67_sup_Oleft__idem,axiom,
% 0.29/0.68 ! [A_130: pname > $o,B_71: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ A_130 @ ( semila1780557381name_o @ A_130 @ B_71 ) )
% 0.29/0.68 = ( semila1780557381name_o @ A_130 @ B_71 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_68_sup_Oleft__idem,axiom,
% 0.29/0.68 ! [A_130: $o,B_71: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ A_130 @ ( semila10642723_sup_o @ A_130 @ B_71 ) )
% 0.29/0.68 <=> ( semila10642723_sup_o @ A_130 @ B_71 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_69_sup_Oleft__idem,axiom,
% 0.29/0.68 ! [A_130: hoare_1775062406iple_a > $o,B_71: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ A_130 @ ( semila13410563le_a_o @ A_130 @ B_71 ) )
% 0.29/0.68 = ( semila13410563le_a_o @ A_130 @ B_71 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_70_sup__commute,axiom,
% 0.29/0.68 ! [X_41: hoare_1167836817_state > $o,Y_15: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ X_41 @ Y_15 )
% 0.29/0.68 = ( semila1172322802tate_o @ Y_15 @ X_41 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_71_sup__commute,axiom,
% 0.29/0.68 ! [X_41: pname > $o,Y_15: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ X_41 @ Y_15 )
% 0.29/0.68 = ( semila1780557381name_o @ Y_15 @ X_41 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_72_sup__commute,axiom,
% 0.29/0.68 ! [X_41: $o,Y_15: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ X_41 @ Y_15 )
% 0.29/0.68 <=> ( semila10642723_sup_o @ Y_15 @ X_41 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_73_sup__commute,axiom,
% 0.29/0.68 ! [X_41: hoare_1775062406iple_a > $o,Y_15: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ X_41 @ Y_15 )
% 0.29/0.68 = ( semila13410563le_a_o @ Y_15 @ X_41 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_74_inf__sup__aci_I5_J,axiom,
% 0.29/0.68 ! [X_40: hoare_1167836817_state > $o,Y_14: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ X_40 @ Y_14 )
% 0.29/0.68 = ( semila1172322802tate_o @ Y_14 @ X_40 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_75_inf__sup__aci_I5_J,axiom,
% 0.29/0.68 ! [X_40: pname > $o,Y_14: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ X_40 @ Y_14 )
% 0.29/0.68 = ( semila1780557381name_o @ Y_14 @ X_40 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_76_inf__sup__aci_I5_J,axiom,
% 0.29/0.68 ! [X_40: $o,Y_14: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ X_40 @ Y_14 )
% 0.29/0.68 <=> ( semila10642723_sup_o @ Y_14 @ X_40 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_77_inf__sup__aci_I5_J,axiom,
% 0.29/0.68 ! [X_40: hoare_1775062406iple_a > $o,Y_14: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ X_40 @ Y_14 )
% 0.29/0.68 = ( semila13410563le_a_o @ Y_14 @ X_40 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_78_sup_Ocommute,axiom,
% 0.29/0.68 ! [A_129: hoare_1167836817_state > $o,B_70: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ A_129 @ B_70 )
% 0.29/0.68 = ( semila1172322802tate_o @ B_70 @ A_129 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_79_sup_Ocommute,axiom,
% 0.29/0.68 ! [A_129: pname > $o,B_70: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ A_129 @ B_70 )
% 0.29/0.68 = ( semila1780557381name_o @ B_70 @ A_129 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_80_sup_Ocommute,axiom,
% 0.29/0.68 ! [A_129: $o,B_70: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ A_129 @ B_70 )
% 0.29/0.68 <=> ( semila10642723_sup_o @ B_70 @ A_129 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_81_sup_Ocommute,axiom,
% 0.29/0.68 ! [A_129: hoare_1775062406iple_a > $o,B_70: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ A_129 @ B_70 )
% 0.29/0.68 = ( semila13410563le_a_o @ B_70 @ A_129 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_82_sup__idem,axiom,
% 0.29/0.68 ! [X_39: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ X_39 @ X_39 )
% 0.29/0.68 = X_39 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_83_sup__idem,axiom,
% 0.29/0.68 ! [X_39: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ X_39 @ X_39 )
% 0.29/0.68 = X_39 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_84_sup__idem,axiom,
% 0.29/0.68 ! [X_39: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ X_39 @ X_39 )
% 0.29/0.68 <=> X_39 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_85_sup__idem,axiom,
% 0.29/0.68 ! [X_39: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ X_39 @ X_39 )
% 0.29/0.68 = X_39 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_86_sup_Oidem,axiom,
% 0.29/0.68 ! [A_128: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ A_128 @ A_128 )
% 0.29/0.68 = A_128 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_87_sup_Oidem,axiom,
% 0.29/0.68 ! [A_128: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ A_128 @ A_128 )
% 0.29/0.68 = A_128 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_88_sup_Oidem,axiom,
% 0.29/0.68 ! [A_128: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ A_128 @ A_128 )
% 0.29/0.68 <=> A_128 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_89_sup_Oidem,axiom,
% 0.29/0.68 ! [A_128: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ A_128 @ A_128 )
% 0.29/0.68 = A_128 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_90_rev__image__eqI,axiom,
% 0.29/0.68 ! [B_69: hoare_1167836817_state,F_37: pname > hoare_1167836817_state,X_38: pname,A_127: pname > $o] :
% 0.29/0.68 ( ( member_pname @ X_38 @ A_127 )
% 0.29/0.68 => ( ( B_69
% 0.29/0.68 = ( F_37 @ X_38 ) )
% 0.29/0.68 => ( member2058392318_state @ B_69 @ ( image_575578384_state @ F_37 @ A_127 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_91_rev__image__eqI,axiom,
% 0.29/0.68 ! [B_69: pname,F_37: hoare_1775062406iple_a > pname,X_38: hoare_1775062406iple_a,A_127: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ X_38 @ A_127 )
% 0.29/0.68 => ( ( B_69
% 0.29/0.68 = ( F_37 @ X_38 ) )
% 0.29/0.68 => ( member_pname @ B_69 @ ( image_51246659_pname @ F_37 @ A_127 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_92_rev__image__eqI,axiom,
% 0.29/0.68 ! [B_69: hoare_1775062406iple_a,F_37: pname > hoare_1775062406iple_a,X_38: pname,A_127: pname > $o] :
% 0.29/0.68 ( ( member_pname @ X_38 @ A_127 )
% 0.29/0.68 => ( ( B_69
% 0.29/0.68 = ( F_37 @ X_38 ) )
% 0.29/0.68 => ( member2122167641iple_a @ B_69 @ ( image_2063119815iple_a @ F_37 @ A_127 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_93_imageI,axiom,
% 0.29/0.68 ! [F_36: pname > hoare_1167836817_state,X_37: pname,A_126: pname > $o] :
% 0.29/0.68 ( ( member_pname @ X_37 @ A_126 )
% 0.29/0.68 => ( member2058392318_state @ ( F_36 @ X_37 ) @ ( image_575578384_state @ F_36 @ A_126 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_94_imageI,axiom,
% 0.29/0.68 ! [F_36: hoare_1775062406iple_a > pname,X_37: hoare_1775062406iple_a,A_126: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ X_37 @ A_126 )
% 0.29/0.68 => ( member_pname @ ( F_36 @ X_37 ) @ ( image_51246659_pname @ F_36 @ A_126 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_95_imageI,axiom,
% 0.29/0.68 ! [F_36: pname > hoare_1775062406iple_a,X_37: pname,A_126: pname > $o] :
% 0.29/0.68 ( ( member_pname @ X_37 @ A_126 )
% 0.29/0.68 => ( member2122167641iple_a @ ( F_36 @ X_37 ) @ ( image_2063119815iple_a @ F_36 @ A_126 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_96_image__iff,axiom,
% 0.29/0.68 ! [Z_10: hoare_1167836817_state,F_35: pname > hoare_1167836817_state,A_125: pname > $o] :
% 0.29/0.68 ( ( member2058392318_state @ Z_10 @ ( image_575578384_state @ F_35 @ A_125 ) )
% 0.29/0.68 <=> ? [X: pname] :
% 0.29/0.68 ( ( member_pname @ X @ A_125 )
% 0.29/0.68 & ( Z_10
% 0.29/0.68 = ( F_35 @ X ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_97_image__iff,axiom,
% 0.29/0.68 ! [Z_10: hoare_1775062406iple_a,F_35: pname > hoare_1775062406iple_a,A_125: pname > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ Z_10 @ ( image_2063119815iple_a @ F_35 @ A_125 ) )
% 0.29/0.68 <=> ? [X: pname] :
% 0.29/0.68 ( ( member_pname @ X @ A_125 )
% 0.29/0.68 & ( Z_10
% 0.29/0.68 = ( F_35 @ X ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_98_UnI2,axiom,
% 0.29/0.68 ! [A_124: hoare_1167836817_state > $o,C_38: hoare_1167836817_state,B_68: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( member2058392318_state @ C_38 @ B_68 )
% 0.29/0.68 => ( member2058392318_state @ C_38 @ ( semila1172322802tate_o @ A_124 @ B_68 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_99_UnI2,axiom,
% 0.29/0.68 ! [A_124: hoare_1775062406iple_a > $o,C_38: hoare_1775062406iple_a,B_68: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ C_38 @ B_68 )
% 0.29/0.68 => ( member2122167641iple_a @ C_38 @ ( semila13410563le_a_o @ A_124 @ B_68 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_100_UnI2,axiom,
% 0.29/0.68 ! [A_124: pname > $o,C_38: pname,B_68: pname > $o] :
% 0.29/0.68 ( ( member_pname @ C_38 @ B_68 )
% 0.29/0.68 => ( member_pname @ C_38 @ ( semila1780557381name_o @ A_124 @ B_68 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_101_UnI1,axiom,
% 0.29/0.68 ! [B_67: hoare_1167836817_state > $o,C_37: hoare_1167836817_state,A_123: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( member2058392318_state @ C_37 @ A_123 )
% 0.29/0.68 => ( member2058392318_state @ C_37 @ ( semila1172322802tate_o @ A_123 @ B_67 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_102_UnI1,axiom,
% 0.29/0.68 ! [B_67: hoare_1775062406iple_a > $o,C_37: hoare_1775062406iple_a,A_123: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ C_37 @ A_123 )
% 0.29/0.68 => ( member2122167641iple_a @ C_37 @ ( semila13410563le_a_o @ A_123 @ B_67 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_103_UnI1,axiom,
% 0.29/0.68 ! [B_67: pname > $o,C_37: pname,A_123: pname > $o] :
% 0.29/0.68 ( ( member_pname @ C_37 @ A_123 )
% 0.29/0.68 => ( member_pname @ C_37 @ ( semila1780557381name_o @ A_123 @ B_67 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_104_sup1I2,axiom,
% 0.29/0.68 ! [A_122: hoare_1167836817_state > $o,B_66: hoare_1167836817_state > $o,X_36: hoare_1167836817_state] :
% 0.29/0.68 ( ( B_66 @ X_36 )
% 0.29/0.68 => ( semila1172322802tate_o @ A_122 @ B_66 @ X_36 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_105_sup1I2,axiom,
% 0.29/0.68 ! [A_122: pname > $o,B_66: pname > $o,X_36: pname] :
% 0.29/0.68 ( ( B_66 @ X_36 )
% 0.29/0.68 => ( semila1780557381name_o @ A_122 @ B_66 @ X_36 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_106_sup1I2,axiom,
% 0.29/0.68 ! [A_122: hoare_1775062406iple_a > $o,B_66: hoare_1775062406iple_a > $o,X_36: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( B_66 @ X_36 )
% 0.29/0.68 => ( semila13410563le_a_o @ A_122 @ B_66 @ X_36 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_107_sup1I1,axiom,
% 0.29/0.68 ! [B_65: hoare_1167836817_state > $o,A_121: hoare_1167836817_state > $o,X_35: hoare_1167836817_state] :
% 0.29/0.68 ( ( A_121 @ X_35 )
% 0.29/0.68 => ( semila1172322802tate_o @ A_121 @ B_65 @ X_35 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_108_sup1I1,axiom,
% 0.29/0.68 ! [B_65: pname > $o,A_121: pname > $o,X_35: pname] :
% 0.29/0.68 ( ( A_121 @ X_35 )
% 0.29/0.68 => ( semila1780557381name_o @ A_121 @ B_65 @ X_35 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_109_sup1I1,axiom,
% 0.29/0.68 ! [B_65: hoare_1775062406iple_a > $o,A_121: hoare_1775062406iple_a > $o,X_35: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( A_121 @ X_35 )
% 0.29/0.68 => ( semila13410563le_a_o @ A_121 @ B_65 @ X_35 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_110_ball__Un,axiom,
% 0.29/0.68 ! [P_36: hoare_1167836817_state > $o,A_120: hoare_1167836817_state > $o,B_64: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ! [X: hoare_1167836817_state] :
% 0.29/0.68 ( ( member2058392318_state @ X @ ( semila1172322802tate_o @ A_120 @ B_64 ) )
% 0.29/0.68 => ( P_36 @ X ) )
% 0.29/0.68 <=> ( ! [X: hoare_1167836817_state] :
% 0.29/0.68 ( ( member2058392318_state @ X @ A_120 )
% 0.29/0.68 => ( P_36 @ X ) )
% 0.29/0.68 & ! [X: hoare_1167836817_state] :
% 0.29/0.68 ( ( member2058392318_state @ X @ B_64 )
% 0.29/0.68 => ( P_36 @ X ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_111_ball__Un,axiom,
% 0.29/0.68 ! [P_36: pname > $o,A_120: pname > $o,B_64: pname > $o] :
% 0.29/0.68 ( ! [X: pname] :
% 0.29/0.68 ( ( member_pname @ X @ ( semila1780557381name_o @ A_120 @ B_64 ) )
% 0.29/0.68 => ( P_36 @ X ) )
% 0.29/0.68 <=> ( ! [X: pname] :
% 0.29/0.68 ( ( member_pname @ X @ A_120 )
% 0.29/0.68 => ( P_36 @ X ) )
% 0.29/0.68 & ! [X: pname] :
% 0.29/0.68 ( ( member_pname @ X @ B_64 )
% 0.29/0.68 => ( P_36 @ X ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_112_ball__Un,axiom,
% 0.29/0.68 ! [P_36: hoare_1775062406iple_a > $o,A_120: hoare_1775062406iple_a > $o,B_64: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ! [X: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( member2122167641iple_a @ X @ ( semila13410563le_a_o @ A_120 @ B_64 ) )
% 0.29/0.68 => ( P_36 @ X ) )
% 0.29/0.68 <=> ( ! [X: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( member2122167641iple_a @ X @ A_120 )
% 0.29/0.68 => ( P_36 @ X ) )
% 0.29/0.68 & ! [X: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( member2122167641iple_a @ X @ B_64 )
% 0.29/0.68 => ( P_36 @ X ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_113_bex__Un,axiom,
% 0.29/0.68 ! [P_35: hoare_1167836817_state > $o,A_119: hoare_1167836817_state > $o,B_63: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ? [X: hoare_1167836817_state] :
% 0.29/0.68 ( ( member2058392318_state @ X @ ( semila1172322802tate_o @ A_119 @ B_63 ) )
% 0.29/0.68 & ( P_35 @ X ) )
% 0.29/0.68 <=> ( ? [X: hoare_1167836817_state] :
% 0.29/0.68 ( ( member2058392318_state @ X @ A_119 )
% 0.29/0.68 & ( P_35 @ X ) )
% 0.29/0.68 | ? [X: hoare_1167836817_state] :
% 0.29/0.68 ( ( member2058392318_state @ X @ B_63 )
% 0.29/0.68 & ( P_35 @ X ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_114_bex__Un,axiom,
% 0.29/0.68 ! [P_35: pname > $o,A_119: pname > $o,B_63: pname > $o] :
% 0.29/0.68 ( ? [X: pname] :
% 0.29/0.68 ( ( member_pname @ X @ ( semila1780557381name_o @ A_119 @ B_63 ) )
% 0.29/0.68 & ( P_35 @ X ) )
% 0.29/0.68 <=> ( ? [X: pname] :
% 0.29/0.68 ( ( member_pname @ X @ A_119 )
% 0.29/0.68 & ( P_35 @ X ) )
% 0.29/0.68 | ? [X: pname] :
% 0.29/0.68 ( ( member_pname @ X @ B_63 )
% 0.29/0.68 & ( P_35 @ X ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_115_bex__Un,axiom,
% 0.29/0.68 ! [P_35: hoare_1775062406iple_a > $o,A_119: hoare_1775062406iple_a > $o,B_63: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ? [X: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( member2122167641iple_a @ X @ ( semila13410563le_a_o @ A_119 @ B_63 ) )
% 0.29/0.68 & ( P_35 @ X ) )
% 0.29/0.68 <=> ( ? [X: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( member2122167641iple_a @ X @ A_119 )
% 0.29/0.68 & ( P_35 @ X ) )
% 0.29/0.68 | ? [X: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( member2122167641iple_a @ X @ B_63 )
% 0.29/0.68 & ( P_35 @ X ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_116_Un__assoc,axiom,
% 0.29/0.68 ! [A_118: hoare_1167836817_state > $o,B_62: hoare_1167836817_state > $o,C_36: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ A_118 @ B_62 ) @ C_36 )
% 0.29/0.68 = ( semila1172322802tate_o @ A_118 @ ( semila1172322802tate_o @ B_62 @ C_36 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_117_Un__assoc,axiom,
% 0.29/0.68 ! [A_118: pname > $o,B_62: pname > $o,C_36: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ ( semila1780557381name_o @ A_118 @ B_62 ) @ C_36 )
% 0.29/0.68 = ( semila1780557381name_o @ A_118 @ ( semila1780557381name_o @ B_62 @ C_36 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_118_Un__assoc,axiom,
% 0.29/0.68 ! [A_118: hoare_1775062406iple_a > $o,B_62: hoare_1775062406iple_a > $o,C_36: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ ( semila13410563le_a_o @ A_118 @ B_62 ) @ C_36 )
% 0.29/0.68 = ( semila13410563le_a_o @ A_118 @ ( semila13410563le_a_o @ B_62 @ C_36 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_119_Un__iff,axiom,
% 0.29/0.68 ! [C_35: hoare_1167836817_state,A_117: hoare_1167836817_state > $o,B_61: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( member2058392318_state @ C_35 @ ( semila1172322802tate_o @ A_117 @ B_61 ) )
% 0.29/0.68 <=> ( ( member2058392318_state @ C_35 @ A_117 )
% 0.29/0.68 | ( member2058392318_state @ C_35 @ B_61 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_120_Un__iff,axiom,
% 0.29/0.68 ! [C_35: hoare_1775062406iple_a,A_117: hoare_1775062406iple_a > $o,B_61: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ C_35 @ ( semila13410563le_a_o @ A_117 @ B_61 ) )
% 0.29/0.68 <=> ( ( member2122167641iple_a @ C_35 @ A_117 )
% 0.29/0.68 | ( member2122167641iple_a @ C_35 @ B_61 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_121_Un__iff,axiom,
% 0.29/0.68 ! [C_35: pname,A_117: pname > $o,B_61: pname > $o] :
% 0.29/0.68 ( ( member_pname @ C_35 @ ( semila1780557381name_o @ A_117 @ B_61 ) )
% 0.29/0.68 <=> ( ( member_pname @ C_35 @ A_117 )
% 0.29/0.68 | ( member_pname @ C_35 @ B_61 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_122_Un__left__commute,axiom,
% 0.29/0.68 ! [A_116: hoare_1167836817_state > $o,B_60: hoare_1167836817_state > $o,C_34: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ A_116 @ ( semila1172322802tate_o @ B_60 @ C_34 ) )
% 0.29/0.68 = ( semila1172322802tate_o @ B_60 @ ( semila1172322802tate_o @ A_116 @ C_34 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_123_Un__left__commute,axiom,
% 0.29/0.68 ! [A_116: pname > $o,B_60: pname > $o,C_34: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ A_116 @ ( semila1780557381name_o @ B_60 @ C_34 ) )
% 0.29/0.68 = ( semila1780557381name_o @ B_60 @ ( semila1780557381name_o @ A_116 @ C_34 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_124_Un__left__commute,axiom,
% 0.29/0.68 ! [A_116: hoare_1775062406iple_a > $o,B_60: hoare_1775062406iple_a > $o,C_34: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ A_116 @ ( semila13410563le_a_o @ B_60 @ C_34 ) )
% 0.29/0.68 = ( semila13410563le_a_o @ B_60 @ ( semila13410563le_a_o @ A_116 @ C_34 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_125_Un__left__absorb,axiom,
% 0.29/0.68 ! [A_115: hoare_1167836817_state > $o,B_59: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ A_115 @ ( semila1172322802tate_o @ A_115 @ B_59 ) )
% 0.29/0.68 = ( semila1172322802tate_o @ A_115 @ B_59 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_126_Un__left__absorb,axiom,
% 0.29/0.68 ! [A_115: pname > $o,B_59: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ A_115 @ ( semila1780557381name_o @ A_115 @ B_59 ) )
% 0.29/0.68 = ( semila1780557381name_o @ A_115 @ B_59 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_127_Un__left__absorb,axiom,
% 0.29/0.68 ! [A_115: hoare_1775062406iple_a > $o,B_59: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ A_115 @ ( semila13410563le_a_o @ A_115 @ B_59 ) )
% 0.29/0.68 = ( semila13410563le_a_o @ A_115 @ B_59 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_128_Un__commute,axiom,
% 0.29/0.68 ! [A_114: hoare_1167836817_state > $o,B_58: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ A_114 @ B_58 )
% 0.29/0.68 = ( semila1172322802tate_o @ B_58 @ A_114 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_129_Un__commute,axiom,
% 0.29/0.68 ! [A_114: pname > $o,B_58: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ A_114 @ B_58 )
% 0.29/0.68 = ( semila1780557381name_o @ B_58 @ A_114 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_130_Un__commute,axiom,
% 0.29/0.68 ! [A_114: hoare_1775062406iple_a > $o,B_58: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ A_114 @ B_58 )
% 0.29/0.68 = ( semila13410563le_a_o @ B_58 @ A_114 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_131_Un__def,axiom,
% 0.29/0.68 ! [A_113: hoare_1167836817_state > $o,B_57: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ A_113 @ B_57 )
% 0.29/0.68 = ( collec1027672124_state
% 0.29/0.68 @ ^ [X: hoare_1167836817_state] : ( (|) @ ( member2058392318_state @ X @ A_113 ) @ ( member2058392318_state @ X @ B_57 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_132_Un__def,axiom,
% 0.29/0.68 ! [A_113: hoare_1775062406iple_a > $o,B_57: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ A_113 @ B_57 )
% 0.29/0.68 = ( collec676402587iple_a
% 0.29/0.68 @ ^ [X: hoare_1775062406iple_a] : ( (|) @ ( member2122167641iple_a @ X @ A_113 ) @ ( member2122167641iple_a @ X @ B_57 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_133_Un__def,axiom,
% 0.29/0.68 ! [A_113: pname > $o,B_57: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ A_113 @ B_57 )
% 0.29/0.68 = ( collect_pname
% 0.29/0.68 @ ^ [X: pname] : ( (|) @ ( member_pname @ X @ A_113 ) @ ( member_pname @ X @ B_57 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_134_Un__absorb,axiom,
% 0.29/0.68 ! [A_112: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ A_112 @ A_112 )
% 0.29/0.68 = A_112 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_135_Un__absorb,axiom,
% 0.29/0.68 ! [A_112: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ A_112 @ A_112 )
% 0.29/0.68 = A_112 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_136_Un__absorb,axiom,
% 0.29/0.68 ! [A_112: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ A_112 @ A_112 )
% 0.29/0.68 = A_112 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_137_image__image,axiom,
% 0.29/0.68 ! [F_34: hoare_1775062406iple_a > hoare_1167836817_state,G_19: pname > hoare_1775062406iple_a,A_111: pname > $o] :
% 0.29/0.68 ( ( image_1021683026_state @ F_34 @ ( image_2063119815iple_a @ G_19 @ A_111 ) )
% 0.29/0.68 = ( image_575578384_state
% 0.29/0.68 @ ^ [X: pname] : ( F_34 @ ( G_19 @ X ) )
% 0.29/0.68 @ A_111 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_138_image__image,axiom,
% 0.29/0.68 ! [F_34: hoare_1167836817_state > hoare_1775062406iple_a,G_19: pname > hoare_1167836817_state,A_111: pname > $o] :
% 0.29/0.68 ( ( image_1802845250iple_a @ F_34 @ ( image_575578384_state @ G_19 @ A_111 ) )
% 0.29/0.68 = ( image_2063119815iple_a
% 0.29/0.68 @ ^ [X: pname] : ( F_34 @ ( G_19 @ X ) )
% 0.29/0.68 @ A_111 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_139_sup__Un__eq,axiom,
% 0.29/0.68 ! [R_2: hoare_1167836817_state > $o,S_6: hoare_1167836817_state > $o,X: hoare_1167836817_state] :
% 0.29/0.68 ( ( semila1172322802tate_o
% 0.29/0.68 @ ^ [Y_2: hoare_1167836817_state] : ( member2058392318_state @ Y_2 @ R_2 )
% 0.29/0.68 @ ^ [Y_2: hoare_1167836817_state] : ( member2058392318_state @ Y_2 @ S_6 )
% 0.29/0.68 @ X )
% 0.29/0.68 <=> ( member2058392318_state @ X @ ( semila1172322802tate_o @ R_2 @ S_6 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_140_sup__Un__eq,axiom,
% 0.29/0.68 ! [R_2: hoare_1775062406iple_a > $o,S_6: hoare_1775062406iple_a > $o,X: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( semila13410563le_a_o
% 0.29/0.68 @ ^ [Y_2: hoare_1775062406iple_a] : ( member2122167641iple_a @ Y_2 @ R_2 )
% 0.29/0.68 @ ^ [Y_2: hoare_1775062406iple_a] : ( member2122167641iple_a @ Y_2 @ S_6 )
% 0.29/0.68 @ X )
% 0.29/0.68 <=> ( member2122167641iple_a @ X @ ( semila13410563le_a_o @ R_2 @ S_6 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_141_sup__Un__eq,axiom,
% 0.29/0.68 ! [R_2: pname > $o,S_6: pname > $o,X: pname] :
% 0.29/0.68 ( ( semila1780557381name_o
% 0.29/0.68 @ ^ [Y_2: pname] : ( member_pname @ Y_2 @ R_2 )
% 0.29/0.68 @ ^ [Y_2: pname] : ( member_pname @ Y_2 @ S_6 )
% 0.29/0.68 @ X )
% 0.29/0.68 <=> ( member_pname @ X @ ( semila1780557381name_o @ R_2 @ S_6 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_142_Collect__disj__eq,axiom,
% 0.29/0.68 ! [P_34: pname > $o,Q_19: pname > $o] :
% 0.29/0.68 ( ( collect_pname
% 0.29/0.68 @ ^ [X: pname] : ( (|) @ ( P_34 @ X ) @ ( Q_19 @ X ) ) )
% 0.29/0.68 = ( semila1780557381name_o @ ( collect_pname @ P_34 ) @ ( collect_pname @ Q_19 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_143_Collect__disj__eq,axiom,
% 0.29/0.68 ! [P_34: hoare_1167836817_state > $o,Q_19: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( collec1027672124_state
% 0.29/0.68 @ ^ [X: hoare_1167836817_state] : ( (|) @ ( P_34 @ X ) @ ( Q_19 @ X ) ) )
% 0.29/0.68 = ( semila1172322802tate_o @ ( collec1027672124_state @ P_34 ) @ ( collec1027672124_state @ Q_19 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_144_Collect__disj__eq,axiom,
% 0.29/0.68 ! [P_34: hoare_1775062406iple_a > $o,Q_19: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( collec676402587iple_a
% 0.29/0.68 @ ^ [X: hoare_1775062406iple_a] : ( (|) @ ( P_34 @ X ) @ ( Q_19 @ X ) ) )
% 0.29/0.68 = ( semila13410563le_a_o @ ( collec676402587iple_a @ P_34 ) @ ( collec676402587iple_a @ Q_19 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_145_imageE,axiom,
% 0.29/0.68 ! [B_56: pname,F_33: hoare_1775062406iple_a > pname,A_110: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member_pname @ B_56 @ ( image_51246659_pname @ F_33 @ A_110 ) )
% 0.29/0.68 => ~ ! [X: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( B_56
% 0.29/0.68 = ( F_33 @ X ) )
% 0.29/0.68 => ~ ( member2122167641iple_a @ X @ A_110 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_146_imageE,axiom,
% 0.29/0.68 ! [B_56: hoare_1167836817_state,F_33: pname > hoare_1167836817_state,A_110: pname > $o] :
% 0.29/0.68 ( ( member2058392318_state @ B_56 @ ( image_575578384_state @ F_33 @ A_110 ) )
% 0.29/0.68 => ~ ! [X: pname] :
% 0.29/0.68 ( ( B_56
% 0.29/0.68 = ( F_33 @ X ) )
% 0.29/0.68 => ~ ( member_pname @ X @ A_110 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_147_imageE,axiom,
% 0.29/0.68 ! [B_56: hoare_1775062406iple_a,F_33: pname > hoare_1775062406iple_a,A_110: pname > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ B_56 @ ( image_2063119815iple_a @ F_33 @ A_110 ) )
% 0.29/0.68 => ~ ! [X: pname] :
% 0.29/0.68 ( ( B_56
% 0.29/0.68 = ( F_33 @ X ) )
% 0.29/0.68 => ~ ( member_pname @ X @ A_110 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_148_Body__triple__valid__Suc,axiom,
% 0.29/0.68 ! [N_8: nat,P_33: state > state > $o,Pn_6: pname,Q_18: state > state > $o] :
% 0.29/0.68 ( ( hoare_56934129_state @ N_8 @ ( hoare_908217195_state @ P_33 @ ( the_com @ ( body_1 @ Pn_6 ) ) @ Q_18 ) )
% 0.29/0.68 <=> ( hoare_56934129_state @ ( suc @ N_8 ) @ ( hoare_908217195_state @ P_33 @ ( body @ Pn_6 ) @ Q_18 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_149_Body__triple__valid__Suc,axiom,
% 0.29/0.68 ! [N_8: nat,P_33: x_a > state > $o,Pn_6: pname,Q_18: x_a > state > $o] :
% 0.29/0.68 ( ( hoare_1462269968alid_a @ N_8 @ ( hoare_1766022166iple_a @ P_33 @ ( the_com @ ( body_1 @ Pn_6 ) ) @ Q_18 ) )
% 0.29/0.68 <=> ( hoare_1462269968alid_a @ ( suc @ N_8 ) @ ( hoare_1766022166iple_a @ P_33 @ ( body @ Pn_6 ) @ Q_18 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_150_triple_Oexhaust,axiom,
% 0.29/0.68 ! [Y_13: hoare_1775062406iple_a] :
% 0.29/0.68 ~ ! [Fun1_2: x_a > state > $o,Com_4: com,Fun2_2: x_a > state > $o] :
% 0.29/0.68 ( Y_13
% 0.29/0.68 != ( hoare_1766022166iple_a @ Fun1_2 @ Com_4 @ Fun2_2 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_151_triple_Oexhaust,axiom,
% 0.29/0.68 ! [Y_13: hoare_1167836817_state] :
% 0.29/0.68 ~ ! [Fun1_2: state > state > $o,Com_4: com,Fun2_2: state > state > $o] :
% 0.29/0.68 ( Y_13
% 0.29/0.68 != ( hoare_908217195_state @ Fun1_2 @ Com_4 @ Fun2_2 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_152_Body1,axiom,
% 0.29/0.68 ! [Pn_5: pname,G_18: hoare_1167836817_state > $o,P_32: pname > state > state > $o,Q_17: pname > state > state > $o,Procs: pname > $o] :
% 0.29/0.68 ( ( hoare_123228589_state
% 0.29/0.68 @ ( semila1172322802tate_o @ G_18
% 0.29/0.68 @ ( image_575578384_state
% 0.29/0.68 @ ^ [P_10: pname] : ( hoare_908217195_state @ ( P_32 @ P_10 ) @ ( body @ P_10 ) @ ( Q_17 @ P_10 ) )
% 0.29/0.68 @ Procs ) )
% 0.29/0.68 @ ( image_575578384_state
% 0.29/0.68 @ ^ [P_10: pname] : ( hoare_908217195_state @ ( P_32 @ P_10 ) @ ( the_com @ ( body_1 @ P_10 ) ) @ ( Q_17 @ P_10 ) )
% 0.29/0.68 @ Procs ) )
% 0.29/0.68 => ( ( member_pname @ Pn_5 @ Procs )
% 0.29/0.68 => ( hoare_123228589_state @ G_18 @ ( insert2134838167_state @ ( hoare_908217195_state @ ( P_32 @ Pn_5 ) @ ( body @ Pn_5 ) @ ( Q_17 @ Pn_5 ) ) @ bot_bo70021908tate_o ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_153_Body1,axiom,
% 0.29/0.68 ! [Pn_5: pname,G_18: hoare_1775062406iple_a > $o,P_32: pname > x_a > state > $o,Q_17: pname > x_a > state > $o,Procs: pname > $o] :
% 0.29/0.68 ( ( hoare_1508237396rivs_a
% 0.29/0.68 @ ( semila13410563le_a_o @ G_18
% 0.29/0.68 @ ( image_2063119815iple_a
% 0.29/0.68 @ ^ [P_10: pname] : ( hoare_1766022166iple_a @ ( P_32 @ P_10 ) @ ( body @ P_10 ) @ ( Q_17 @ P_10 ) )
% 0.29/0.68 @ Procs ) )
% 0.29/0.68 @ ( image_2063119815iple_a
% 0.29/0.68 @ ^ [P_10: pname] : ( hoare_1766022166iple_a @ ( P_32 @ P_10 ) @ ( the_com @ ( body_1 @ P_10 ) ) @ ( Q_17 @ P_10 ) )
% 0.29/0.68 @ Procs ) )
% 0.29/0.68 => ( ( member_pname @ Pn_5 @ Procs )
% 0.29/0.68 => ( hoare_1508237396rivs_a @ G_18 @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ ( P_32 @ Pn_5 ) @ ( body @ Pn_5 ) @ ( Q_17 @ Pn_5 ) ) @ bot_bo751897185le_a_o ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_154_image__cong,axiom,
% 0.29/0.68 ! [F_32: pname > hoare_1167836817_state,G_17: pname > hoare_1167836817_state,M_2: pname > $o,N_7: pname > $o] :
% 0.29/0.68 ( ( M_2 = N_7 )
% 0.29/0.68 => ( ! [X: pname] :
% 0.29/0.68 ( ( member_pname @ X @ N_7 )
% 0.29/0.68 => ( ( F_32 @ X )
% 0.29/0.68 = ( G_17 @ X ) ) )
% 0.29/0.68 => ( ( image_575578384_state @ F_32 @ M_2 )
% 0.29/0.68 = ( image_575578384_state @ G_17 @ N_7 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_155_image__cong,axiom,
% 0.29/0.68 ! [F_32: pname > hoare_1775062406iple_a,G_17: pname > hoare_1775062406iple_a,M_2: pname > $o,N_7: pname > $o] :
% 0.29/0.68 ( ( M_2 = N_7 )
% 0.29/0.68 => ( ! [X: pname] :
% 0.29/0.68 ( ( member_pname @ X @ N_7 )
% 0.29/0.68 => ( ( F_32 @ X )
% 0.29/0.68 = ( G_17 @ X ) ) )
% 0.29/0.68 => ( ( image_2063119815iple_a @ F_32 @ M_2 )
% 0.29/0.68 = ( image_2063119815iple_a @ G_17 @ N_7 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_156_Body__triple__valid__0,axiom,
% 0.29/0.68 ! [P_31: state > state > $o,Pn_4: pname,Q_16: state > state > $o] : ( hoare_56934129_state @ zero_zero_nat @ ( hoare_908217195_state @ P_31 @ ( body @ Pn_4 ) @ Q_16 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_157_Body__triple__valid__0,axiom,
% 0.29/0.68 ! [P_31: x_a > state > $o,Pn_4: pname,Q_16: x_a > state > $o] : ( hoare_1462269968alid_a @ zero_zero_nat @ ( hoare_1766022166iple_a @ P_31 @ ( body @ Pn_4 ) @ Q_16 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_158_com_Osimps_I6_J,axiom,
% 0.29/0.68 ! [Pname: pname,Pname_1: pname] :
% 0.29/0.68 ( ( ( body @ Pname )
% 0.29/0.68 = ( body @ Pname_1 ) )
% 0.29/0.68 <=> ( Pname = Pname_1 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_159_evalc_OBody,axiom,
% 0.29/0.68 ! [Pn_1: pname,S0: state,S1: state] :
% 0.29/0.68 ( ( evalc @ ( the_com @ ( body_1 @ Pn_1 ) ) @ S0 @ S1 )
% 0.29/0.68 => ( evalc @ ( body @ Pn_1 ) @ S0 @ S1 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_160_evalc__elim__cases_I6_J,axiom,
% 0.29/0.68 ! [P: pname,S: state,S1: state] :
% 0.29/0.68 ( ( evalc @ ( body @ P ) @ S @ S1 )
% 0.29/0.68 => ( evalc @ ( the_com @ ( body_1 @ P ) ) @ S @ S1 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_161_Sup__fin_Oidem,axiom,
% 0.29/0.68 ! [X_34: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ X_34 @ X_34 )
% 0.29/0.68 = X_34 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_162_Sup__fin_Oidem,axiom,
% 0.29/0.68 ! [X_34: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ X_34 @ X_34 )
% 0.29/0.68 = X_34 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_163_Sup__fin_Oidem,axiom,
% 0.29/0.68 ! [X_34: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ X_34 @ X_34 )
% 0.29/0.68 <=> X_34 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_164_Sup__fin_Oidem,axiom,
% 0.29/0.68 ! [X_34: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ X_34 @ X_34 )
% 0.29/0.68 = X_34 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_165_emptyE,axiom,
% 0.29/0.68 ! [A_109: hoare_1775062406iple_a] :
% 0.29/0.68 ~ ( member2122167641iple_a @ A_109 @ bot_bo751897185le_a_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_166_emptyE,axiom,
% 0.29/0.68 ! [A_109: hoare_1167836817_state] :
% 0.29/0.68 ~ ( member2058392318_state @ A_109 @ bot_bo70021908tate_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_167_emptyE,axiom,
% 0.29/0.68 ! [A_109: pname] :
% 0.29/0.68 ~ ( member_pname @ A_109 @ bot_bot_pname_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_168_insertE,axiom,
% 0.29/0.68 ! [A_108: hoare_1167836817_state,B_55: hoare_1167836817_state,A_107: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( member2058392318_state @ A_108 @ ( insert2134838167_state @ B_55 @ A_107 ) )
% 0.29/0.68 => ( ( A_108 != B_55 )
% 0.29/0.68 => ( member2058392318_state @ A_108 @ A_107 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_169_insertE,axiom,
% 0.29/0.68 ! [A_108: hoare_1775062406iple_a,B_55: hoare_1775062406iple_a,A_107: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ A_108 @ ( insert1281456128iple_a @ B_55 @ A_107 ) )
% 0.29/0.68 => ( ( A_108 != B_55 )
% 0.29/0.68 => ( member2122167641iple_a @ A_108 @ A_107 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_170_insertE,axiom,
% 0.29/0.68 ! [A_108: pname,B_55: pname,A_107: pname > $o] :
% 0.29/0.68 ( ( member_pname @ A_108 @ ( insert_pname @ B_55 @ A_107 ) )
% 0.29/0.68 => ( ( A_108 != B_55 )
% 0.29/0.68 => ( member_pname @ A_108 @ A_107 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_171_insertCI,axiom,
% 0.29/0.68 ! [B_54: hoare_1167836817_state,A_106: hoare_1167836817_state,B_53: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( ~ ( member2058392318_state @ A_106 @ B_53 )
% 0.29/0.68 => ( A_106 = B_54 ) )
% 0.29/0.68 => ( member2058392318_state @ A_106 @ ( insert2134838167_state @ B_54 @ B_53 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_172_insertCI,axiom,
% 0.29/0.68 ! [B_54: hoare_1775062406iple_a,A_106: hoare_1775062406iple_a,B_53: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( ~ ( member2122167641iple_a @ A_106 @ B_53 )
% 0.29/0.68 => ( A_106 = B_54 ) )
% 0.29/0.68 => ( member2122167641iple_a @ A_106 @ ( insert1281456128iple_a @ B_54 @ B_53 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_173_insertCI,axiom,
% 0.29/0.68 ! [B_54: pname,A_106: pname,B_53: pname > $o] :
% 0.29/0.68 ( ( ~ ( member_pname @ A_106 @ B_53 )
% 0.29/0.68 => ( A_106 = B_54 ) )
% 0.29/0.68 => ( member_pname @ A_106 @ ( insert_pname @ B_54 @ B_53 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_174_empty__not__insert,axiom,
% 0.29/0.68 ! [A_105: hoare_1167836817_state,A_104: hoare_1167836817_state > $o] :
% 0.29/0.68 ( bot_bo70021908tate_o
% 0.29/0.68 != ( insert2134838167_state @ A_105 @ A_104 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_175_empty__not__insert,axiom,
% 0.29/0.68 ! [A_105: hoare_1775062406iple_a,A_104: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( bot_bo751897185le_a_o
% 0.29/0.68 != ( insert1281456128iple_a @ A_105 @ A_104 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_176_empty__not__insert,axiom,
% 0.29/0.68 ! [A_105: pname,A_104: pname > $o] :
% 0.29/0.68 ( bot_bot_pname_o
% 0.29/0.68 != ( insert_pname @ A_105 @ A_104 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_177_insert__not__empty,axiom,
% 0.29/0.68 ! [A_103: hoare_1167836817_state,A_102: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( insert2134838167_state @ A_103 @ A_102 )
% 0.29/0.68 != bot_bo70021908tate_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_178_insert__not__empty,axiom,
% 0.29/0.68 ! [A_103: hoare_1775062406iple_a,A_102: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( insert1281456128iple_a @ A_103 @ A_102 )
% 0.29/0.68 != bot_bo751897185le_a_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_179_insert__not__empty,axiom,
% 0.29/0.68 ! [A_103: pname,A_102: pname > $o] :
% 0.29/0.68 ( ( insert_pname @ A_103 @ A_102 )
% 0.29/0.68 != bot_bot_pname_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_180_bot__empty__eq,axiom,
% 0.29/0.68 ! [X: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( bot_bo751897185le_a_o @ X )
% 0.29/0.68 <=> ( member2122167641iple_a @ X @ bot_bo751897185le_a_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_181_bot__empty__eq,axiom,
% 0.29/0.68 ! [X: hoare_1167836817_state] :
% 0.29/0.68 ( ( bot_bo70021908tate_o @ X )
% 0.29/0.68 <=> ( member2058392318_state @ X @ bot_bo70021908tate_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_182_bot__empty__eq,axiom,
% 0.29/0.68 ! [X: pname] :
% 0.29/0.68 ( ( bot_bot_pname_o @ X )
% 0.29/0.68 <=> ( member_pname @ X @ bot_bot_pname_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_183_empty__def,axiom,
% 0.29/0.68 ( bot_bo751897185le_a_o
% 0.29/0.68 = ( collec676402587iple_a
% 0.29/0.68 @ ^ [X: hoare_1775062406iple_a] : $false ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_184_empty__def,axiom,
% 0.29/0.68 ( bot_bot_pname_o
% 0.29/0.68 = ( collect_pname
% 0.29/0.68 @ ^ [X: pname] : $false ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_185_empty__def,axiom,
% 0.29/0.68 ( bot_bo70021908tate_o
% 0.29/0.68 = ( collec1027672124_state
% 0.29/0.68 @ ^ [X: hoare_1167836817_state] : $false ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_186_insertI1,axiom,
% 0.29/0.68 ! [A_101: hoare_1167836817_state,B_52: hoare_1167836817_state > $o] : ( member2058392318_state @ A_101 @ ( insert2134838167_state @ A_101 @ B_52 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_187_insertI1,axiom,
% 0.29/0.68 ! [A_101: hoare_1775062406iple_a,B_52: hoare_1775062406iple_a > $o] : ( member2122167641iple_a @ A_101 @ ( insert1281456128iple_a @ A_101 @ B_52 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_188_insertI1,axiom,
% 0.29/0.68 ! [A_101: pname,B_52: pname > $o] : ( member_pname @ A_101 @ ( insert_pname @ A_101 @ B_52 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_189_all__not__in__conv,axiom,
% 0.29/0.68 ! [A_100: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ! [X: hoare_1775062406iple_a] :
% 0.29/0.68 ~ ( member2122167641iple_a @ X @ A_100 )
% 0.29/0.68 <=> ( A_100 = bot_bo751897185le_a_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_190_all__not__in__conv,axiom,
% 0.29/0.68 ! [A_100: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ! [X: hoare_1167836817_state] :
% 0.29/0.68 ~ ( member2058392318_state @ X @ A_100 )
% 0.29/0.68 <=> ( A_100 = bot_bo70021908tate_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_191_all__not__in__conv,axiom,
% 0.29/0.68 ! [A_100: pname > $o] :
% 0.29/0.68 ( ! [X: pname] :
% 0.29/0.68 ~ ( member_pname @ X @ A_100 )
% 0.29/0.68 <=> ( A_100 = bot_bot_pname_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_192_singleton__conv2,axiom,
% 0.29/0.68 ! [A_99: hoare_1167836817_state] :
% 0.29/0.68 ( ( collec1027672124_state @ ( fequal1831255762_state @ A_99 ) )
% 0.29/0.68 = ( insert2134838167_state @ A_99 @ bot_bo70021908tate_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_193_singleton__conv2,axiom,
% 0.29/0.68 ! [A_99: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( collec676402587iple_a @ ( fequal1288209029iple_a @ A_99 ) )
% 0.29/0.68 = ( insert1281456128iple_a @ A_99 @ bot_bo751897185le_a_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_194_singleton__conv2,axiom,
% 0.29/0.68 ! [A_99: pname] :
% 0.29/0.68 ( ( collect_pname @ ( fequal_pname @ A_99 ) )
% 0.29/0.68 = ( insert_pname @ A_99 @ bot_bot_pname_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_195_ex__in__conv,axiom,
% 0.29/0.68 ! [A_98: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ? [X: hoare_1775062406iple_a] : ( member2122167641iple_a @ X @ A_98 )
% 0.29/0.68 <=> ( A_98 != bot_bo751897185le_a_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_196_ex__in__conv,axiom,
% 0.29/0.68 ! [A_98: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ? [X: hoare_1167836817_state] : ( member2058392318_state @ X @ A_98 )
% 0.29/0.68 <=> ( A_98 != bot_bo70021908tate_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_197_ex__in__conv,axiom,
% 0.29/0.68 ! [A_98: pname > $o] :
% 0.29/0.68 ( ? [X: pname] : ( member_pname @ X @ A_98 )
% 0.29/0.68 <=> ( A_98 != bot_bot_pname_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_198_singleton__conv,axiom,
% 0.29/0.68 ! [A_97: hoare_1167836817_state] :
% 0.29/0.68 ( ( collec1027672124_state
% 0.29/0.68 @ ^ [X: hoare_1167836817_state] : ( X = A_97 ) )
% 0.29/0.68 = ( insert2134838167_state @ A_97 @ bot_bo70021908tate_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_199_singleton__conv,axiom,
% 0.29/0.68 ! [A_97: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( collec676402587iple_a
% 0.29/0.68 @ ^ [X: hoare_1775062406iple_a] : ( X = A_97 ) )
% 0.29/0.68 = ( insert1281456128iple_a @ A_97 @ bot_bo751897185le_a_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_200_singleton__conv,axiom,
% 0.29/0.68 ! [A_97: pname] :
% 0.29/0.68 ( ( collect_pname
% 0.29/0.68 @ ^ [X: pname] : ( X = A_97 ) )
% 0.29/0.68 = ( insert_pname @ A_97 @ bot_bot_pname_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_201_Collect__conv__if2,axiom,
% 0.29/0.68 ! [P_30: hoare_1167836817_state > $o,A_96: hoare_1167836817_state] :
% 0.29/0.68 ( ( ( P_30 @ A_96 )
% 0.29/0.68 => ( ( collec1027672124_state
% 0.29/0.68 @ ^ [X: hoare_1167836817_state] : ( (&) @ ( A_96 = X ) @ ( P_30 @ X ) ) )
% 0.29/0.68 = ( insert2134838167_state @ A_96 @ bot_bo70021908tate_o ) ) )
% 0.29/0.68 & ( ~ ( P_30 @ A_96 )
% 0.29/0.68 => ( ( collec1027672124_state
% 0.29/0.68 @ ^ [X: hoare_1167836817_state] : ( (&) @ ( A_96 = X ) @ ( P_30 @ X ) ) )
% 0.29/0.68 = bot_bo70021908tate_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_202_Collect__conv__if2,axiom,
% 0.29/0.68 ! [P_30: hoare_1775062406iple_a > $o,A_96: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( ( P_30 @ A_96 )
% 0.29/0.68 => ( ( collec676402587iple_a
% 0.29/0.68 @ ^ [X: hoare_1775062406iple_a] : ( (&) @ ( A_96 = X ) @ ( P_30 @ X ) ) )
% 0.29/0.68 = ( insert1281456128iple_a @ A_96 @ bot_bo751897185le_a_o ) ) )
% 0.29/0.68 & ( ~ ( P_30 @ A_96 )
% 0.29/0.68 => ( ( collec676402587iple_a
% 0.29/0.68 @ ^ [X: hoare_1775062406iple_a] : ( (&) @ ( A_96 = X ) @ ( P_30 @ X ) ) )
% 0.29/0.68 = bot_bo751897185le_a_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_203_Collect__conv__if2,axiom,
% 0.29/0.68 ! [P_30: pname > $o,A_96: pname] :
% 0.29/0.68 ( ( ( P_30 @ A_96 )
% 0.29/0.68 => ( ( collect_pname
% 0.29/0.68 @ ^ [X: pname] : ( (&) @ ( A_96 = X ) @ ( P_30 @ X ) ) )
% 0.29/0.68 = ( insert_pname @ A_96 @ bot_bot_pname_o ) ) )
% 0.29/0.68 & ( ~ ( P_30 @ A_96 )
% 0.29/0.68 => ( ( collect_pname
% 0.29/0.68 @ ^ [X: pname] : ( (&) @ ( A_96 = X ) @ ( P_30 @ X ) ) )
% 0.29/0.68 = bot_bot_pname_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_204_Collect__conv__if,axiom,
% 0.29/0.68 ! [P_29: hoare_1167836817_state > $o,A_95: hoare_1167836817_state] :
% 0.29/0.68 ( ( ( P_29 @ A_95 )
% 0.29/0.68 => ( ( collec1027672124_state
% 0.29/0.68 @ ^ [X: hoare_1167836817_state] : ( (&) @ ( X = A_95 ) @ ( P_29 @ X ) ) )
% 0.29/0.68 = ( insert2134838167_state @ A_95 @ bot_bo70021908tate_o ) ) )
% 0.29/0.68 & ( ~ ( P_29 @ A_95 )
% 0.29/0.68 => ( ( collec1027672124_state
% 0.29/0.68 @ ^ [X: hoare_1167836817_state] : ( (&) @ ( X = A_95 ) @ ( P_29 @ X ) ) )
% 0.29/0.68 = bot_bo70021908tate_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_205_Collect__conv__if,axiom,
% 0.29/0.68 ! [P_29: hoare_1775062406iple_a > $o,A_95: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( ( P_29 @ A_95 )
% 0.29/0.68 => ( ( collec676402587iple_a
% 0.29/0.68 @ ^ [X: hoare_1775062406iple_a] : ( (&) @ ( X = A_95 ) @ ( P_29 @ X ) ) )
% 0.29/0.68 = ( insert1281456128iple_a @ A_95 @ bot_bo751897185le_a_o ) ) )
% 0.29/0.68 & ( ~ ( P_29 @ A_95 )
% 0.29/0.68 => ( ( collec676402587iple_a
% 0.29/0.68 @ ^ [X: hoare_1775062406iple_a] : ( (&) @ ( X = A_95 ) @ ( P_29 @ X ) ) )
% 0.29/0.68 = bot_bo751897185le_a_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_206_Collect__conv__if,axiom,
% 0.29/0.68 ! [P_29: pname > $o,A_95: pname] :
% 0.29/0.68 ( ( ( P_29 @ A_95 )
% 0.29/0.68 => ( ( collect_pname
% 0.29/0.68 @ ^ [X: pname] : ( (&) @ ( X = A_95 ) @ ( P_29 @ X ) ) )
% 0.29/0.68 = ( insert_pname @ A_95 @ bot_bot_pname_o ) ) )
% 0.29/0.68 & ( ~ ( P_29 @ A_95 )
% 0.29/0.68 => ( ( collect_pname
% 0.29/0.68 @ ^ [X: pname] : ( (&) @ ( X = A_95 ) @ ( P_29 @ X ) ) )
% 0.29/0.68 = bot_bot_pname_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_207_empty__Collect__eq,axiom,
% 0.29/0.68 ! [P_28: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( bot_bo751897185le_a_o
% 0.29/0.68 = ( collec676402587iple_a @ P_28 ) )
% 0.29/0.68 <=> ! [X: hoare_1775062406iple_a] :
% 0.29/0.68 ~ ( P_28 @ X ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_208_empty__Collect__eq,axiom,
% 0.29/0.68 ! [P_28: pname > $o] :
% 0.29/0.68 ( ( bot_bot_pname_o
% 0.29/0.68 = ( collect_pname @ P_28 ) )
% 0.29/0.68 <=> ! [X: pname] :
% 0.29/0.68 ~ ( P_28 @ X ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_209_empty__Collect__eq,axiom,
% 0.29/0.68 ! [P_28: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( bot_bo70021908tate_o
% 0.29/0.68 = ( collec1027672124_state @ P_28 ) )
% 0.29/0.68 <=> ! [X: hoare_1167836817_state] :
% 0.29/0.68 ~ ( P_28 @ X ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_210_mem__def,axiom,
% 0.29/0.68 ! [X_33: hoare_1775062406iple_a,A_94: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ X_33 @ A_94 )
% 0.29/0.68 <=> ( A_94 @ X_33 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_211_mem__def,axiom,
% 0.29/0.68 ! [X_33: pname,A_94: pname > $o] :
% 0.29/0.68 ( ( member_pname @ X_33 @ A_94 )
% 0.29/0.68 <=> ( A_94 @ X_33 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_212_Collect__def,axiom,
% 0.29/0.68 ! [P_27: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( collec676402587iple_a @ P_27 )
% 0.29/0.68 = P_27 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_213_Collect__def,axiom,
% 0.29/0.68 ! [P_27: pname > $o] :
% 0.29/0.68 ( ( collect_pname @ P_27 )
% 0.29/0.68 = P_27 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_214_empty__iff,axiom,
% 0.29/0.68 ! [C_33: hoare_1775062406iple_a] :
% 0.29/0.68 ~ ( member2122167641iple_a @ C_33 @ bot_bo751897185le_a_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_215_empty__iff,axiom,
% 0.29/0.68 ! [C_33: hoare_1167836817_state] :
% 0.29/0.68 ~ ( member2058392318_state @ C_33 @ bot_bo70021908tate_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_216_empty__iff,axiom,
% 0.29/0.68 ! [C_33: pname] :
% 0.29/0.68 ~ ( member_pname @ C_33 @ bot_bot_pname_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_217_insert__compr,axiom,
% 0.29/0.68 ! [A_93: hoare_1167836817_state,B_51: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( insert2134838167_state @ A_93 @ B_51 )
% 0.29/0.68 = ( collec1027672124_state
% 0.29/0.68 @ ^ [X: hoare_1167836817_state] : ( (|) @ ( X = A_93 ) @ ( member2058392318_state @ X @ B_51 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_218_insert__compr,axiom,
% 0.29/0.68 ! [A_93: hoare_1775062406iple_a,B_51: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( insert1281456128iple_a @ A_93 @ B_51 )
% 0.29/0.68 = ( collec676402587iple_a
% 0.29/0.68 @ ^ [X: hoare_1775062406iple_a] : ( (|) @ ( X = A_93 ) @ ( member2122167641iple_a @ X @ B_51 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_219_insert__compr,axiom,
% 0.29/0.68 ! [A_93: pname,B_51: pname > $o] :
% 0.29/0.68 ( ( insert_pname @ A_93 @ B_51 )
% 0.29/0.68 = ( collect_pname
% 0.29/0.68 @ ^ [X: pname] : ( (|) @ ( X = A_93 ) @ ( member_pname @ X @ B_51 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_220_insert__Collect,axiom,
% 0.29/0.68 ! [A_92: hoare_1167836817_state,P_26: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( insert2134838167_state @ A_92 @ ( collec1027672124_state @ P_26 ) )
% 0.29/0.68 = ( collec1027672124_state
% 0.29/0.68 @ ^ [U_2: hoare_1167836817_state] : ( (=>) @ ( (~) @ ( U_2 = A_92 ) ) @ ( P_26 @ U_2 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_221_insert__Collect,axiom,
% 0.29/0.68 ! [A_92: hoare_1775062406iple_a,P_26: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( insert1281456128iple_a @ A_92 @ ( collec676402587iple_a @ P_26 ) )
% 0.29/0.68 = ( collec676402587iple_a
% 0.29/0.68 @ ^ [U_2: hoare_1775062406iple_a] : ( (=>) @ ( (~) @ ( U_2 = A_92 ) ) @ ( P_26 @ U_2 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_222_insert__Collect,axiom,
% 0.29/0.68 ! [A_92: pname,P_26: pname > $o] :
% 0.29/0.68 ( ( insert_pname @ A_92 @ ( collect_pname @ P_26 ) )
% 0.29/0.68 = ( collect_pname
% 0.29/0.68 @ ^ [U_2: pname] : ( (=>) @ ( (~) @ ( U_2 = A_92 ) ) @ ( P_26 @ U_2 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_223_singleton__iff,axiom,
% 0.29/0.68 ! [B_50: hoare_1167836817_state,A_91: hoare_1167836817_state] :
% 0.29/0.68 ( ( member2058392318_state @ B_50 @ ( insert2134838167_state @ A_91 @ bot_bo70021908tate_o ) )
% 0.29/0.68 <=> ( B_50 = A_91 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_224_singleton__iff,axiom,
% 0.29/0.68 ! [B_50: hoare_1775062406iple_a,A_91: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( member2122167641iple_a @ B_50 @ ( insert1281456128iple_a @ A_91 @ bot_bo751897185le_a_o ) )
% 0.29/0.68 <=> ( B_50 = A_91 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_225_singleton__iff,axiom,
% 0.29/0.68 ! [B_50: pname,A_91: pname] :
% 0.29/0.68 ( ( member_pname @ B_50 @ ( insert_pname @ A_91 @ bot_bot_pname_o ) )
% 0.29/0.68 <=> ( B_50 = A_91 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_226_insert__absorb2,axiom,
% 0.29/0.68 ! [X_32: hoare_1167836817_state,A_90: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( insert2134838167_state @ X_32 @ ( insert2134838167_state @ X_32 @ A_90 ) )
% 0.29/0.68 = ( insert2134838167_state @ X_32 @ A_90 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_227_insert__absorb2,axiom,
% 0.29/0.68 ! [X_32: hoare_1775062406iple_a,A_90: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( insert1281456128iple_a @ X_32 @ ( insert1281456128iple_a @ X_32 @ A_90 ) )
% 0.29/0.68 = ( insert1281456128iple_a @ X_32 @ A_90 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_228_insert__absorb2,axiom,
% 0.29/0.68 ! [X_32: pname,A_90: pname > $o] :
% 0.29/0.68 ( ( insert_pname @ X_32 @ ( insert_pname @ X_32 @ A_90 ) )
% 0.29/0.68 = ( insert_pname @ X_32 @ A_90 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_229_insert__commute,axiom,
% 0.29/0.68 ! [X_31: hoare_1167836817_state,Y_12: hoare_1167836817_state,A_89: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( insert2134838167_state @ X_31 @ ( insert2134838167_state @ Y_12 @ A_89 ) )
% 0.29/0.68 = ( insert2134838167_state @ Y_12 @ ( insert2134838167_state @ X_31 @ A_89 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_230_insert__commute,axiom,
% 0.29/0.68 ! [X_31: hoare_1775062406iple_a,Y_12: hoare_1775062406iple_a,A_89: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( insert1281456128iple_a @ X_31 @ ( insert1281456128iple_a @ Y_12 @ A_89 ) )
% 0.29/0.68 = ( insert1281456128iple_a @ Y_12 @ ( insert1281456128iple_a @ X_31 @ A_89 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_231_insert__commute,axiom,
% 0.29/0.68 ! [X_31: pname,Y_12: pname,A_89: pname > $o] :
% 0.29/0.68 ( ( insert_pname @ X_31 @ ( insert_pname @ Y_12 @ A_89 ) )
% 0.29/0.68 = ( insert_pname @ Y_12 @ ( insert_pname @ X_31 @ A_89 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_232_insert__iff,axiom,
% 0.29/0.68 ! [A_88: hoare_1167836817_state,B_49: hoare_1167836817_state,A_87: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( member2058392318_state @ A_88 @ ( insert2134838167_state @ B_49 @ A_87 ) )
% 0.29/0.68 <=> ( ( A_88 = B_49 )
% 0.29/0.68 | ( member2058392318_state @ A_88 @ A_87 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_233_insert__iff,axiom,
% 0.29/0.68 ! [A_88: hoare_1775062406iple_a,B_49: hoare_1775062406iple_a,A_87: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ A_88 @ ( insert1281456128iple_a @ B_49 @ A_87 ) )
% 0.29/0.68 <=> ( ( A_88 = B_49 )
% 0.29/0.68 | ( member2122167641iple_a @ A_88 @ A_87 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_234_insert__iff,axiom,
% 0.29/0.68 ! [A_88: pname,B_49: pname,A_87: pname > $o] :
% 0.29/0.68 ( ( member_pname @ A_88 @ ( insert_pname @ B_49 @ A_87 ) )
% 0.29/0.68 <=> ( ( A_88 = B_49 )
% 0.29/0.68 | ( member_pname @ A_88 @ A_87 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_235_Collect__empty__eq,axiom,
% 0.29/0.68 ! [P_25: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( ( collec676402587iple_a @ P_25 )
% 0.29/0.68 = bot_bo751897185le_a_o )
% 0.29/0.68 <=> ! [X: hoare_1775062406iple_a] :
% 0.29/0.68 ~ ( P_25 @ X ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_236_Collect__empty__eq,axiom,
% 0.29/0.68 ! [P_25: pname > $o] :
% 0.29/0.68 ( ( ( collect_pname @ P_25 )
% 0.29/0.68 = bot_bot_pname_o )
% 0.29/0.68 <=> ! [X: pname] :
% 0.29/0.68 ~ ( P_25 @ X ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_237_Collect__empty__eq,axiom,
% 0.29/0.68 ! [P_25: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( ( collec1027672124_state @ P_25 )
% 0.29/0.68 = bot_bo70021908tate_o )
% 0.29/0.68 <=> ! [X: hoare_1167836817_state] :
% 0.29/0.68 ~ ( P_25 @ X ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_238_doubleton__eq__iff,axiom,
% 0.29/0.68 ! [A_86: hoare_1167836817_state,B_48: hoare_1167836817_state,C_32: hoare_1167836817_state,D_1: hoare_1167836817_state] :
% 0.29/0.68 ( ( ( insert2134838167_state @ A_86 @ ( insert2134838167_state @ B_48 @ bot_bo70021908tate_o ) )
% 0.29/0.68 = ( insert2134838167_state @ C_32 @ ( insert2134838167_state @ D_1 @ bot_bo70021908tate_o ) ) )
% 0.29/0.68 <=> ( ( ( A_86 = C_32 )
% 0.29/0.68 & ( B_48 = D_1 ) )
% 0.29/0.68 | ( ( A_86 = D_1 )
% 0.29/0.68 & ( B_48 = C_32 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_239_doubleton__eq__iff,axiom,
% 0.29/0.68 ! [A_86: hoare_1775062406iple_a,B_48: hoare_1775062406iple_a,C_32: hoare_1775062406iple_a,D_1: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( ( insert1281456128iple_a @ A_86 @ ( insert1281456128iple_a @ B_48 @ bot_bo751897185le_a_o ) )
% 0.29/0.68 = ( insert1281456128iple_a @ C_32 @ ( insert1281456128iple_a @ D_1 @ bot_bo751897185le_a_o ) ) )
% 0.29/0.68 <=> ( ( ( A_86 = C_32 )
% 0.29/0.68 & ( B_48 = D_1 ) )
% 0.29/0.68 | ( ( A_86 = D_1 )
% 0.29/0.68 & ( B_48 = C_32 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_240_doubleton__eq__iff,axiom,
% 0.29/0.68 ! [A_86: pname,B_48: pname,C_32: pname,D_1: pname] :
% 0.29/0.68 ( ( ( insert_pname @ A_86 @ ( insert_pname @ B_48 @ bot_bot_pname_o ) )
% 0.29/0.68 = ( insert_pname @ C_32 @ ( insert_pname @ D_1 @ bot_bot_pname_o ) ) )
% 0.29/0.68 <=> ( ( ( A_86 = C_32 )
% 0.29/0.68 & ( B_48 = D_1 ) )
% 0.29/0.68 | ( ( A_86 = D_1 )
% 0.29/0.68 & ( B_48 = C_32 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_241_insert__code,axiom,
% 0.29/0.68 ! [Y_11: hoare_1167836817_state,A_85: hoare_1167836817_state > $o,X_30: hoare_1167836817_state] :
% 0.29/0.68 ( ( insert2134838167_state @ Y_11 @ A_85 @ X_30 )
% 0.29/0.68 <=> ( ( Y_11 = X_30 )
% 0.29/0.68 | ( A_85 @ X_30 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_242_insert__code,axiom,
% 0.29/0.68 ! [Y_11: hoare_1775062406iple_a,A_85: hoare_1775062406iple_a > $o,X_30: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( insert1281456128iple_a @ Y_11 @ A_85 @ X_30 )
% 0.29/0.68 <=> ( ( Y_11 = X_30 )
% 0.29/0.68 | ( A_85 @ X_30 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_243_insert__code,axiom,
% 0.29/0.68 ! [Y_11: pname,A_85: pname > $o,X_30: pname] :
% 0.29/0.68 ( ( insert_pname @ Y_11 @ A_85 @ X_30 )
% 0.29/0.68 <=> ( ( Y_11 = X_30 )
% 0.29/0.68 | ( A_85 @ X_30 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_244_insert__ident,axiom,
% 0.29/0.68 ! [B_47: hoare_1167836817_state > $o,X_29: hoare_1167836817_state,A_84: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ~ ( member2058392318_state @ X_29 @ A_84 )
% 0.29/0.68 => ( ~ ( member2058392318_state @ X_29 @ B_47 )
% 0.29/0.68 => ( ( ( insert2134838167_state @ X_29 @ A_84 )
% 0.29/0.68 = ( insert2134838167_state @ X_29 @ B_47 ) )
% 0.29/0.68 <=> ( A_84 = B_47 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_245_insert__ident,axiom,
% 0.29/0.68 ! [B_47: hoare_1775062406iple_a > $o,X_29: hoare_1775062406iple_a,A_84: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ~ ( member2122167641iple_a @ X_29 @ A_84 )
% 0.29/0.68 => ( ~ ( member2122167641iple_a @ X_29 @ B_47 )
% 0.29/0.68 => ( ( ( insert1281456128iple_a @ X_29 @ A_84 )
% 0.29/0.68 = ( insert1281456128iple_a @ X_29 @ B_47 ) )
% 0.29/0.68 <=> ( A_84 = B_47 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_246_insert__ident,axiom,
% 0.29/0.68 ! [B_47: pname > $o,X_29: pname,A_84: pname > $o] :
% 0.29/0.68 ( ~ ( member_pname @ X_29 @ A_84 )
% 0.29/0.68 => ( ~ ( member_pname @ X_29 @ B_47 )
% 0.29/0.68 => ( ( ( insert_pname @ X_29 @ A_84 )
% 0.29/0.68 = ( insert_pname @ X_29 @ B_47 ) )
% 0.29/0.68 <=> ( A_84 = B_47 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_247_equals0D,axiom,
% 0.29/0.68 ! [A_83: hoare_1775062406iple_a,A_82: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( A_82 = bot_bo751897185le_a_o )
% 0.29/0.68 => ~ ( member2122167641iple_a @ A_83 @ A_82 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_248_equals0D,axiom,
% 0.29/0.68 ! [A_83: hoare_1167836817_state,A_82: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( A_82 = bot_bo70021908tate_o )
% 0.29/0.68 => ~ ( member2058392318_state @ A_83 @ A_82 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_249_equals0D,axiom,
% 0.29/0.68 ! [A_83: pname,A_82: pname > $o] :
% 0.29/0.68 ( ( A_82 = bot_bot_pname_o )
% 0.29/0.68 => ~ ( member_pname @ A_83 @ A_82 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_250_insertI2,axiom,
% 0.29/0.68 ! [B_46: hoare_1167836817_state,A_81: hoare_1167836817_state,B_45: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( member2058392318_state @ A_81 @ B_45 )
% 0.29/0.68 => ( member2058392318_state @ A_81 @ ( insert2134838167_state @ B_46 @ B_45 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_251_insertI2,axiom,
% 0.29/0.68 ! [B_46: hoare_1775062406iple_a,A_81: hoare_1775062406iple_a,B_45: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ A_81 @ B_45 )
% 0.29/0.68 => ( member2122167641iple_a @ A_81 @ ( insert1281456128iple_a @ B_46 @ B_45 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_252_insertI2,axiom,
% 0.29/0.68 ! [B_46: pname,A_81: pname,B_45: pname > $o] :
% 0.29/0.68 ( ( member_pname @ A_81 @ B_45 )
% 0.29/0.68 => ( member_pname @ A_81 @ ( insert_pname @ B_46 @ B_45 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_253_insert__absorb,axiom,
% 0.29/0.68 ! [A_80: hoare_1167836817_state,A_79: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( member2058392318_state @ A_80 @ A_79 )
% 0.29/0.68 => ( ( insert2134838167_state @ A_80 @ A_79 )
% 0.29/0.68 = A_79 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_254_insert__absorb,axiom,
% 0.29/0.68 ! [A_80: hoare_1775062406iple_a,A_79: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ A_80 @ A_79 )
% 0.29/0.68 => ( ( insert1281456128iple_a @ A_80 @ A_79 )
% 0.29/0.68 = A_79 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_255_insert__absorb,axiom,
% 0.29/0.68 ! [A_80: pname,A_79: pname > $o] :
% 0.29/0.68 ( ( member_pname @ A_80 @ A_79 )
% 0.29/0.68 => ( ( insert_pname @ A_80 @ A_79 )
% 0.29/0.68 = A_79 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_256_singletonE,axiom,
% 0.29/0.68 ! [B_44: hoare_1167836817_state,A_78: hoare_1167836817_state] :
% 0.29/0.68 ( ( member2058392318_state @ B_44 @ ( insert2134838167_state @ A_78 @ bot_bo70021908tate_o ) )
% 0.29/0.68 => ( B_44 = A_78 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_257_singletonE,axiom,
% 0.29/0.68 ! [B_44: hoare_1775062406iple_a,A_78: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( member2122167641iple_a @ B_44 @ ( insert1281456128iple_a @ A_78 @ bot_bo751897185le_a_o ) )
% 0.29/0.68 => ( B_44 = A_78 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_258_singletonE,axiom,
% 0.29/0.68 ! [B_44: pname,A_78: pname] :
% 0.29/0.68 ( ( member_pname @ B_44 @ ( insert_pname @ A_78 @ bot_bot_pname_o ) )
% 0.29/0.68 => ( B_44 = A_78 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_259_singleton__inject,axiom,
% 0.29/0.68 ! [A_77: hoare_1167836817_state,B_43: hoare_1167836817_state] :
% 0.29/0.68 ( ( ( insert2134838167_state @ A_77 @ bot_bo70021908tate_o )
% 0.29/0.68 = ( insert2134838167_state @ B_43 @ bot_bo70021908tate_o ) )
% 0.29/0.68 => ( A_77 = B_43 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_260_singleton__inject,axiom,
% 0.29/0.68 ! [A_77: hoare_1775062406iple_a,B_43: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( ( insert1281456128iple_a @ A_77 @ bot_bo751897185le_a_o )
% 0.29/0.68 = ( insert1281456128iple_a @ B_43 @ bot_bo751897185le_a_o ) )
% 0.29/0.68 => ( A_77 = B_43 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_261_singleton__inject,axiom,
% 0.29/0.68 ! [A_77: pname,B_43: pname] :
% 0.29/0.68 ( ( ( insert_pname @ A_77 @ bot_bot_pname_o )
% 0.29/0.68 = ( insert_pname @ B_43 @ bot_bot_pname_o ) )
% 0.29/0.68 => ( A_77 = B_43 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_262_com__det,axiom,
% 0.29/0.68 ! [U_1: state,C_19: com,S: state,T: state] :
% 0.29/0.68 ( ( evalc @ C_19 @ S @ T )
% 0.29/0.68 => ( ( evalc @ C_19 @ S @ U_1 )
% 0.29/0.68 => ( U_1 = T ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_263_insert__is__Un,axiom,
% 0.29/0.68 ! [A_76: hoare_1167836817_state,A_75: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( insert2134838167_state @ A_76 @ A_75 )
% 0.29/0.68 = ( semila1172322802tate_o @ ( insert2134838167_state @ A_76 @ bot_bo70021908tate_o ) @ A_75 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_264_insert__is__Un,axiom,
% 0.29/0.68 ! [A_76: pname,A_75: pname > $o] :
% 0.29/0.68 ( ( insert_pname @ A_76 @ A_75 )
% 0.29/0.68 = ( semila1780557381name_o @ ( insert_pname @ A_76 @ bot_bot_pname_o ) @ A_75 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_265_insert__is__Un,axiom,
% 0.29/0.68 ! [A_76: hoare_1775062406iple_a,A_75: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( insert1281456128iple_a @ A_76 @ A_75 )
% 0.29/0.68 = ( semila13410563le_a_o @ ( insert1281456128iple_a @ A_76 @ bot_bo751897185le_a_o ) @ A_75 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_266_insert__compr__raw,axiom,
% 0.29/0.68 ! [X: hoare_1167836817_state,Xa: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( insert2134838167_state @ X @ Xa )
% 0.29/0.68 = ( collec1027672124_state
% 0.29/0.68 @ ^ [Y_2: hoare_1167836817_state] : ( (|) @ ( Y_2 = X ) @ ( member2058392318_state @ Y_2 @ Xa ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_267_insert__compr__raw,axiom,
% 0.29/0.68 ! [X: hoare_1775062406iple_a,Xa: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( insert1281456128iple_a @ X @ Xa )
% 0.29/0.68 = ( collec676402587iple_a
% 0.29/0.68 @ ^ [Y_2: hoare_1775062406iple_a] : ( (|) @ ( Y_2 = X ) @ ( member2122167641iple_a @ Y_2 @ Xa ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_268_insert__compr__raw,axiom,
% 0.29/0.68 ! [X: pname,Xa: pname > $o] :
% 0.29/0.68 ( ( insert_pname @ X @ Xa )
% 0.29/0.68 = ( collect_pname
% 0.29/0.68 @ ^ [Y_2: pname] : ( (|) @ ( Y_2 = X ) @ ( member_pname @ Y_2 @ Xa ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_269_derivs__insertD,axiom,
% 0.29/0.68 ! [G_16: hoare_1167836817_state > $o,T_3: hoare_1167836817_state,Ts_2: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( hoare_123228589_state @ G_16 @ ( insert2134838167_state @ T_3 @ Ts_2 ) )
% 0.29/0.68 => ( ( hoare_123228589_state @ G_16 @ ( insert2134838167_state @ T_3 @ bot_bo70021908tate_o ) )
% 0.29/0.68 & ( hoare_123228589_state @ G_16 @ Ts_2 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_270_derivs__insertD,axiom,
% 0.29/0.68 ! [G_16: hoare_1775062406iple_a > $o,T_3: hoare_1775062406iple_a,Ts_2: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( hoare_1508237396rivs_a @ G_16 @ ( insert1281456128iple_a @ T_3 @ Ts_2 ) )
% 0.29/0.68 => ( ( hoare_1508237396rivs_a @ G_16 @ ( insert1281456128iple_a @ T_3 @ bot_bo751897185le_a_o ) )
% 0.29/0.68 & ( hoare_1508237396rivs_a @ G_16 @ Ts_2 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_271_hoare__derivs_Oinsert,axiom,
% 0.29/0.68 ! [Ts_1: hoare_1167836817_state > $o,G_15: hoare_1167836817_state > $o,T_2: hoare_1167836817_state] :
% 0.29/0.68 ( ( hoare_123228589_state @ G_15 @ ( insert2134838167_state @ T_2 @ bot_bo70021908tate_o ) )
% 0.29/0.68 => ( ( hoare_123228589_state @ G_15 @ Ts_1 )
% 0.29/0.68 => ( hoare_123228589_state @ G_15 @ ( insert2134838167_state @ T_2 @ Ts_1 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_272_hoare__derivs_Oinsert,axiom,
% 0.29/0.68 ! [Ts_1: hoare_1775062406iple_a > $o,G_15: hoare_1775062406iple_a > $o,T_2: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( hoare_1508237396rivs_a @ G_15 @ ( insert1281456128iple_a @ T_2 @ bot_bo751897185le_a_o ) )
% 0.29/0.68 => ( ( hoare_1508237396rivs_a @ G_15 @ Ts_1 )
% 0.29/0.68 => ( hoare_1508237396rivs_a @ G_15 @ ( insert1281456128iple_a @ T_2 @ Ts_1 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_273_image__constant__conv,axiom,
% 0.29/0.68 ! [C_31: hoare_1167836817_state,A_74: pname > $o] :
% 0.29/0.68 ( ( ( A_74 = bot_bot_pname_o )
% 0.29/0.68 => ( ( image_575578384_state
% 0.29/0.68 @ ^ [X: pname] : C_31
% 0.29/0.68 @ A_74 )
% 0.29/0.68 = bot_bo70021908tate_o ) )
% 0.29/0.68 & ( ( A_74 != bot_bot_pname_o )
% 0.29/0.68 => ( ( image_575578384_state
% 0.29/0.68 @ ^ [X: pname] : C_31
% 0.29/0.68 @ A_74 )
% 0.29/0.68 = ( insert2134838167_state @ C_31 @ bot_bo70021908tate_o ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_274_image__constant__conv,axiom,
% 0.29/0.68 ! [C_31: hoare_1775062406iple_a,A_74: pname > $o] :
% 0.29/0.68 ( ( ( A_74 = bot_bot_pname_o )
% 0.29/0.68 => ( ( image_2063119815iple_a
% 0.29/0.68 @ ^ [X: pname] : C_31
% 0.29/0.68 @ A_74 )
% 0.29/0.68 = bot_bo751897185le_a_o ) )
% 0.29/0.68 & ( ( A_74 != bot_bot_pname_o )
% 0.29/0.68 => ( ( image_2063119815iple_a
% 0.29/0.68 @ ^ [X: pname] : C_31
% 0.29/0.68 @ A_74 )
% 0.29/0.68 = ( insert1281456128iple_a @ C_31 @ bot_bo751897185le_a_o ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_275_image__constant,axiom,
% 0.29/0.68 ! [C_30: hoare_1167836817_state,X_28: pname,A_73: pname > $o] :
% 0.29/0.68 ( ( member_pname @ X_28 @ A_73 )
% 0.29/0.68 => ( ( image_575578384_state
% 0.29/0.68 @ ^ [X: pname] : C_30
% 0.29/0.68 @ A_73 )
% 0.29/0.68 = ( insert2134838167_state @ C_30 @ bot_bo70021908tate_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_276_image__constant,axiom,
% 0.29/0.68 ! [C_30: pname,X_28: pname,A_73: pname > $o] :
% 0.29/0.68 ( ( member_pname @ X_28 @ A_73 )
% 0.29/0.68 => ( ( image_pname_pname
% 0.29/0.68 @ ^ [X: pname] : C_30
% 0.29/0.68 @ A_73 )
% 0.29/0.68 = ( insert_pname @ C_30 @ bot_bot_pname_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_277_image__constant,axiom,
% 0.29/0.68 ! [C_30: hoare_1775062406iple_a,X_28: pname,A_73: pname > $o] :
% 0.29/0.68 ( ( member_pname @ X_28 @ A_73 )
% 0.29/0.68 => ( ( image_2063119815iple_a
% 0.29/0.68 @ ^ [X: pname] : C_30
% 0.29/0.68 @ A_73 )
% 0.29/0.68 = ( insert1281456128iple_a @ C_30 @ bot_bo751897185le_a_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_278_image__insert,axiom,
% 0.29/0.68 ! [F_31: pname > hoare_1167836817_state,A_72: pname,B_42: pname > $o] :
% 0.29/0.68 ( ( image_575578384_state @ F_31 @ ( insert_pname @ A_72 @ B_42 ) )
% 0.29/0.68 = ( insert2134838167_state @ ( F_31 @ A_72 ) @ ( image_575578384_state @ F_31 @ B_42 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_279_image__insert,axiom,
% 0.29/0.68 ! [F_31: pname > hoare_1775062406iple_a,A_72: pname,B_42: pname > $o] :
% 0.29/0.68 ( ( image_2063119815iple_a @ F_31 @ ( insert_pname @ A_72 @ B_42 ) )
% 0.29/0.68 = ( insert1281456128iple_a @ ( F_31 @ A_72 ) @ ( image_2063119815iple_a @ F_31 @ B_42 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_280_insert__image,axiom,
% 0.29/0.68 ! [F_30: pname > hoare_1167836817_state,X_27: pname,A_71: pname > $o] :
% 0.29/0.68 ( ( member_pname @ X_27 @ A_71 )
% 0.29/0.68 => ( ( insert2134838167_state @ ( F_30 @ X_27 ) @ ( image_575578384_state @ F_30 @ A_71 ) )
% 0.29/0.68 = ( image_575578384_state @ F_30 @ A_71 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_281_insert__image,axiom,
% 0.29/0.68 ! [F_30: pname > pname,X_27: pname,A_71: pname > $o] :
% 0.29/0.68 ( ( member_pname @ X_27 @ A_71 )
% 0.29/0.68 => ( ( insert_pname @ ( F_30 @ X_27 ) @ ( image_pname_pname @ F_30 @ A_71 ) )
% 0.29/0.68 = ( image_pname_pname @ F_30 @ A_71 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_282_insert__image,axiom,
% 0.29/0.68 ! [F_30: pname > hoare_1775062406iple_a,X_27: pname,A_71: pname > $o] :
% 0.29/0.68 ( ( member_pname @ X_27 @ A_71 )
% 0.29/0.68 => ( ( insert1281456128iple_a @ ( F_30 @ X_27 ) @ ( image_2063119815iple_a @ F_30 @ A_71 ) )
% 0.29/0.68 = ( image_2063119815iple_a @ F_30 @ A_71 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_283_Un__insert__right,axiom,
% 0.29/0.68 ! [A_70: hoare_1167836817_state > $o,A_69: hoare_1167836817_state,B_41: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ A_70 @ ( insert2134838167_state @ A_69 @ B_41 ) )
% 0.29/0.68 = ( insert2134838167_state @ A_69 @ ( semila1172322802tate_o @ A_70 @ B_41 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_284_Un__insert__right,axiom,
% 0.29/0.68 ! [A_70: pname > $o,A_69: pname,B_41: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ A_70 @ ( insert_pname @ A_69 @ B_41 ) )
% 0.29/0.68 = ( insert_pname @ A_69 @ ( semila1780557381name_o @ A_70 @ B_41 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_285_Un__insert__right,axiom,
% 0.29/0.68 ! [A_70: hoare_1775062406iple_a > $o,A_69: hoare_1775062406iple_a,B_41: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ A_70 @ ( insert1281456128iple_a @ A_69 @ B_41 ) )
% 0.29/0.68 = ( insert1281456128iple_a @ A_69 @ ( semila13410563le_a_o @ A_70 @ B_41 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_286_Un__insert__left,axiom,
% 0.29/0.68 ! [A_68: hoare_1167836817_state,B_40: hoare_1167836817_state > $o,C_29: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ ( insert2134838167_state @ A_68 @ B_40 ) @ C_29 )
% 0.29/0.68 = ( insert2134838167_state @ A_68 @ ( semila1172322802tate_o @ B_40 @ C_29 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_287_Un__insert__left,axiom,
% 0.29/0.68 ! [A_68: pname,B_40: pname > $o,C_29: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ ( insert_pname @ A_68 @ B_40 ) @ C_29 )
% 0.29/0.68 = ( insert_pname @ A_68 @ ( semila1780557381name_o @ B_40 @ C_29 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_288_Un__insert__left,axiom,
% 0.29/0.68 ! [A_68: hoare_1775062406iple_a,B_40: hoare_1775062406iple_a > $o,C_29: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ ( insert1281456128iple_a @ A_68 @ B_40 ) @ C_29 )
% 0.29/0.68 = ( insert1281456128iple_a @ A_68 @ ( semila13410563le_a_o @ B_40 @ C_29 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_289_empty__is__image,axiom,
% 0.29/0.68 ! [F_29: pname > hoare_1167836817_state,A_67: pname > $o] :
% 0.29/0.68 ( ( bot_bo70021908tate_o
% 0.29/0.68 = ( image_575578384_state @ F_29 @ A_67 ) )
% 0.29/0.68 <=> ( A_67 = bot_bot_pname_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_290_empty__is__image,axiom,
% 0.29/0.68 ! [F_29: pname > hoare_1775062406iple_a,A_67: pname > $o] :
% 0.29/0.68 ( ( bot_bo751897185le_a_o
% 0.29/0.68 = ( image_2063119815iple_a @ F_29 @ A_67 ) )
% 0.29/0.68 <=> ( A_67 = bot_bot_pname_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_291_image__empty,axiom,
% 0.29/0.68 ! [F_28: pname > hoare_1167836817_state] :
% 0.29/0.68 ( ( image_575578384_state @ F_28 @ bot_bot_pname_o )
% 0.29/0.68 = bot_bo70021908tate_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_292_image__empty,axiom,
% 0.29/0.68 ! [F_28: pname > hoare_1775062406iple_a] :
% 0.29/0.68 ( ( image_2063119815iple_a @ F_28 @ bot_bot_pname_o )
% 0.29/0.68 = bot_bo751897185le_a_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_293_image__is__empty,axiom,
% 0.29/0.68 ! [F_27: pname > hoare_1167836817_state,A_66: pname > $o] :
% 0.29/0.68 ( ( ( image_575578384_state @ F_27 @ A_66 )
% 0.29/0.68 = bot_bo70021908tate_o )
% 0.29/0.68 <=> ( A_66 = bot_bot_pname_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_294_image__is__empty,axiom,
% 0.29/0.68 ! [F_27: pname > hoare_1775062406iple_a,A_66: pname > $o] :
% 0.29/0.68 ( ( ( image_2063119815iple_a @ F_27 @ A_66 )
% 0.29/0.68 = bot_bo751897185le_a_o )
% 0.29/0.68 <=> ( A_66 = bot_bot_pname_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_295_ball__empty,axiom,
% 0.29/0.68 ! [P_24: hoare_1167836817_state > $o,X: hoare_1167836817_state] :
% 0.29/0.68 ( ( member2058392318_state @ X @ bot_bo70021908tate_o )
% 0.29/0.68 => ( P_24 @ X ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_296_ball__empty,axiom,
% 0.29/0.68 ! [P_24: hoare_1775062406iple_a > $o,X: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( member2122167641iple_a @ X @ bot_bo751897185le_a_o )
% 0.29/0.68 => ( P_24 @ X ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_297_ball__empty,axiom,
% 0.29/0.68 ! [P_24: pname > $o,X: pname] :
% 0.29/0.68 ( ( member_pname @ X @ bot_bot_pname_o )
% 0.29/0.68 => ( P_24 @ X ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_298_Un__empty__left,axiom,
% 0.29/0.68 ! [B_39: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ bot_bo70021908tate_o @ B_39 )
% 0.29/0.68 = B_39 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_299_Un__empty__left,axiom,
% 0.29/0.68 ! [B_39: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ bot_bot_pname_o @ B_39 )
% 0.29/0.68 = B_39 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_300_Un__empty__left,axiom,
% 0.29/0.68 ! [B_39: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ bot_bo751897185le_a_o @ B_39 )
% 0.29/0.68 = B_39 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_301_Un__empty__right,axiom,
% 0.29/0.68 ! [A_65: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ A_65 @ bot_bo70021908tate_o )
% 0.29/0.68 = A_65 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_302_Un__empty__right,axiom,
% 0.29/0.68 ! [A_65: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ A_65 @ bot_bot_pname_o )
% 0.29/0.68 = A_65 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_303_Un__empty__right,axiom,
% 0.29/0.68 ! [A_65: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ A_65 @ bot_bo751897185le_a_o )
% 0.29/0.68 = A_65 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_304_Un__empty,axiom,
% 0.29/0.68 ! [A_64: hoare_1167836817_state > $o,B_38: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( ( semila1172322802tate_o @ A_64 @ B_38 )
% 0.29/0.68 = bot_bo70021908tate_o )
% 0.29/0.68 <=> ( ( A_64 = bot_bo70021908tate_o )
% 0.29/0.68 & ( B_38 = bot_bo70021908tate_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_305_Un__empty,axiom,
% 0.29/0.68 ! [A_64: pname > $o,B_38: pname > $o] :
% 0.29/0.68 ( ( ( semila1780557381name_o @ A_64 @ B_38 )
% 0.29/0.68 = bot_bot_pname_o )
% 0.29/0.68 <=> ( ( A_64 = bot_bot_pname_o )
% 0.29/0.68 & ( B_38 = bot_bot_pname_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_306_Un__empty,axiom,
% 0.29/0.68 ! [A_64: hoare_1775062406iple_a > $o,B_38: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( ( semila13410563le_a_o @ A_64 @ B_38 )
% 0.29/0.68 = bot_bo751897185le_a_o )
% 0.29/0.68 <=> ( ( A_64 = bot_bo751897185le_a_o )
% 0.29/0.68 & ( B_38 = bot_bo751897185le_a_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_307_constant,axiom,
% 0.29/0.68 ! [G_14: hoare_1775062406iple_a > $o,P_23: x_a > state > $o,C_28: com,Q_15: x_a > state > $o,C_27: $o] :
% 0.29/0.68 ( ( C_27
% 0.29/0.68 => ( hoare_1508237396rivs_a @ G_14 @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ P_23 @ C_28 @ Q_15 ) @ bot_bo751897185le_a_o ) ) )
% 0.29/0.68 => ( hoare_1508237396rivs_a @ G_14
% 0.29/0.68 @ ( insert1281456128iple_a
% 0.29/0.68 @ ( hoare_1766022166iple_a
% 0.29/0.68 @ ^ [Z_8: x_a,S_3: state] : ( (&) @ ( P_23 @ Z_8 @ S_3 ) @ C_27 )
% 0.29/0.68 @ C_28
% 0.29/0.68 @ Q_15 )
% 0.29/0.68 @ bot_bo751897185le_a_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_308_constant,axiom,
% 0.29/0.68 ! [G_14: hoare_1167836817_state > $o,P_23: state > state > $o,C_28: com,Q_15: state > state > $o,C_27: $o] :
% 0.29/0.68 ( ( C_27
% 0.29/0.68 => ( hoare_123228589_state @ G_14 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_23 @ C_28 @ Q_15 ) @ bot_bo70021908tate_o ) ) )
% 0.29/0.68 => ( hoare_123228589_state @ G_14
% 0.29/0.68 @ ( insert2134838167_state
% 0.29/0.68 @ ( hoare_908217195_state
% 0.29/0.68 @ ^ [Z_8: state,S_3: state] : ( (&) @ ( P_23 @ Z_8 @ S_3 ) @ C_27 )
% 0.29/0.68 @ C_28
% 0.29/0.68 @ Q_15 )
% 0.29/0.68 @ bot_bo70021908tate_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_309_empty,axiom,
% 0.29/0.68 ! [G_13: hoare_1167836817_state > $o] : ( hoare_123228589_state @ G_13 @ bot_bo70021908tate_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_310_empty,axiom,
% 0.29/0.68 ! [G_13: hoare_1775062406iple_a > $o] : ( hoare_1508237396rivs_a @ G_13 @ bot_bo751897185le_a_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_311_sup__bot__left,axiom,
% 0.29/0.68 ! [X_26: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ bot_bo70021908tate_o @ X_26 )
% 0.29/0.68 = X_26 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_312_sup__bot__left,axiom,
% 0.29/0.68 ! [X_26: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ bot_bot_pname_o @ X_26 )
% 0.29/0.68 = X_26 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_313_sup__bot__left,axiom,
% 0.29/0.68 ! [X_26: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ bot_bot_o @ X_26 )
% 0.29/0.68 <=> X_26 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_314_sup__bot__left,axiom,
% 0.29/0.68 ! [X_26: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ bot_bo751897185le_a_o @ X_26 )
% 0.29/0.68 = X_26 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_315_sup__bot__right,axiom,
% 0.29/0.68 ! [X_25: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ X_25 @ bot_bo70021908tate_o )
% 0.29/0.68 = X_25 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_316_sup__bot__right,axiom,
% 0.29/0.68 ! [X_25: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ X_25 @ bot_bot_pname_o )
% 0.29/0.68 = X_25 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_317_sup__bot__right,axiom,
% 0.29/0.68 ! [X_25: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ X_25 @ bot_bot_o )
% 0.29/0.68 <=> X_25 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_318_sup__bot__right,axiom,
% 0.29/0.68 ! [X_25: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ X_25 @ bot_bo751897185le_a_o )
% 0.29/0.68 = X_25 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_319_sup__eq__bot__iff,axiom,
% 0.29/0.68 ! [X_24: hoare_1167836817_state > $o,Y_10: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( ( semila1172322802tate_o @ X_24 @ Y_10 )
% 0.29/0.68 = bot_bo70021908tate_o )
% 0.29/0.68 <=> ( ( X_24 = bot_bo70021908tate_o )
% 0.29/0.68 & ( Y_10 = bot_bo70021908tate_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_320_sup__eq__bot__iff,axiom,
% 0.29/0.68 ! [X_24: pname > $o,Y_10: pname > $o] :
% 0.29/0.68 ( ( ( semila1780557381name_o @ X_24 @ Y_10 )
% 0.29/0.68 = bot_bot_pname_o )
% 0.29/0.68 <=> ( ( X_24 = bot_bot_pname_o )
% 0.29/0.68 & ( Y_10 = bot_bot_pname_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_321_sup__eq__bot__iff,axiom,
% 0.29/0.68 ! [X_24: $o,Y_10: $o] :
% 0.29/0.68 ( ( ( semila10642723_sup_o @ X_24 @ Y_10 )
% 0.29/0.68 <=> bot_bot_o )
% 0.29/0.68 <=> ( ( X_24
% 0.29/0.68 <=> bot_bot_o )
% 0.29/0.68 & ( Y_10
% 0.29/0.68 <=> bot_bot_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_322_sup__eq__bot__iff,axiom,
% 0.29/0.68 ! [X_24: hoare_1775062406iple_a > $o,Y_10: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( ( semila13410563le_a_o @ X_24 @ Y_10 )
% 0.29/0.68 = bot_bo751897185le_a_o )
% 0.29/0.68 <=> ( ( X_24 = bot_bo751897185le_a_o )
% 0.29/0.68 & ( Y_10 = bot_bo751897185le_a_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_323_triple__valid__Suc,axiom,
% 0.29/0.68 ! [N_6: nat,T_1: hoare_1167836817_state] :
% 0.29/0.68 ( ( hoare_56934129_state @ ( suc @ N_6 ) @ T_1 )
% 0.29/0.68 => ( hoare_56934129_state @ N_6 @ T_1 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_324_triple__valid__Suc,axiom,
% 0.29/0.68 ! [N_6: nat,T_1: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( hoare_1462269968alid_a @ ( suc @ N_6 ) @ T_1 )
% 0.29/0.68 => ( hoare_1462269968alid_a @ N_6 @ T_1 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_325_insert__def,axiom,
% 0.29/0.68 ! [A_63: hoare_1167836817_state,B_37: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( insert2134838167_state @ A_63 @ B_37 )
% 0.29/0.68 = ( semila1172322802tate_o
% 0.29/0.68 @ ( collec1027672124_state
% 0.29/0.68 @ ^ [X: hoare_1167836817_state] : ( X = A_63 ) )
% 0.29/0.68 @ B_37 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_326_insert__def,axiom,
% 0.29/0.68 ! [A_63: pname,B_37: pname > $o] :
% 0.29/0.68 ( ( insert_pname @ A_63 @ B_37 )
% 0.29/0.68 = ( semila1780557381name_o
% 0.29/0.68 @ ( collect_pname
% 0.29/0.68 @ ^ [X: pname] : ( X = A_63 ) )
% 0.29/0.68 @ B_37 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_327_insert__def,axiom,
% 0.29/0.68 ! [A_63: hoare_1775062406iple_a,B_37: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( insert1281456128iple_a @ A_63 @ B_37 )
% 0.29/0.68 = ( semila13410563le_a_o
% 0.29/0.68 @ ( collec676402587iple_a
% 0.29/0.68 @ ^ [X: hoare_1775062406iple_a] : ( X = A_63 ) )
% 0.29/0.68 @ B_37 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_328_weak__Body,axiom,
% 0.29/0.68 ! [G_12: hoare_1775062406iple_a > $o,P_22: x_a > state > $o,Pn_3: pname,Q_14: x_a > state > $o] :
% 0.29/0.68 ( ( hoare_1508237396rivs_a @ G_12 @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ P_22 @ ( the_com @ ( body_1 @ Pn_3 ) ) @ Q_14 ) @ bot_bo751897185le_a_o ) )
% 0.29/0.68 => ( hoare_1508237396rivs_a @ G_12 @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ P_22 @ ( body @ Pn_3 ) @ Q_14 ) @ bot_bo751897185le_a_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_329_weak__Body,axiom,
% 0.29/0.68 ! [G_12: hoare_1167836817_state > $o,P_22: state > state > $o,Pn_3: pname,Q_14: state > state > $o] :
% 0.29/0.68 ( ( hoare_123228589_state @ G_12 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_22 @ ( the_com @ ( body_1 @ Pn_3 ) ) @ Q_14 ) @ bot_bo70021908tate_o ) )
% 0.29/0.68 => ( hoare_123228589_state @ G_12 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_22 @ ( body @ Pn_3 ) @ Q_14 ) @ bot_bo70021908tate_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_330_BodyN,axiom,
% 0.29/0.68 ! [P_21: x_a > state > $o,Pn_2: pname,Q_13: x_a > state > $o,G_11: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( hoare_1508237396rivs_a @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ P_21 @ ( body @ Pn_2 ) @ Q_13 ) @ G_11 ) @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ P_21 @ ( the_com @ ( body_1 @ Pn_2 ) ) @ Q_13 ) @ bot_bo751897185le_a_o ) )
% 0.29/0.68 => ( hoare_1508237396rivs_a @ G_11 @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ P_21 @ ( body @ Pn_2 ) @ Q_13 ) @ bot_bo751897185le_a_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_331_BodyN,axiom,
% 0.29/0.68 ! [P_21: state > state > $o,Pn_2: pname,Q_13: state > state > $o,G_11: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( hoare_123228589_state @ ( insert2134838167_state @ ( hoare_908217195_state @ P_21 @ ( body @ Pn_2 ) @ Q_13 ) @ G_11 ) @ ( insert2134838167_state @ ( hoare_908217195_state @ P_21 @ ( the_com @ ( body_1 @ Pn_2 ) ) @ Q_13 ) @ bot_bo70021908tate_o ) )
% 0.29/0.68 => ( hoare_123228589_state @ G_11 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_21 @ ( body @ Pn_2 ) @ Q_13 ) @ bot_bo70021908tate_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_332_triples__valid__Suc,axiom,
% 0.29/0.68 ! [N_5: nat,Ts: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ! [X: hoare_1167836817_state] :
% 0.29/0.68 ( ( member2058392318_state @ X @ Ts )
% 0.29/0.68 => ( hoare_56934129_state @ ( suc @ N_5 ) @ X ) )
% 0.29/0.68 => ! [X: hoare_1167836817_state] :
% 0.29/0.68 ( ( member2058392318_state @ X @ Ts )
% 0.29/0.68 => ( hoare_56934129_state @ N_5 @ X ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_333_triples__valid__Suc,axiom,
% 0.29/0.68 ! [N_5: nat,Ts: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ! [X: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( member2122167641iple_a @ X @ Ts )
% 0.29/0.68 => ( hoare_1462269968alid_a @ ( suc @ N_5 ) @ X ) )
% 0.29/0.68 => ! [X: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( member2122167641iple_a @ X @ Ts )
% 0.29/0.68 => ( hoare_1462269968alid_a @ N_5 @ X ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_334_escape,axiom,
% 0.29/0.68 ! [G_10: hoare_1775062406iple_a > $o,C_26: com,Q_12: x_a > state > $o,P_20: x_a > state > $o] :
% 0.29/0.68 ( ! [Z_8: x_a,S_3: state] :
% 0.29/0.68 ( ( P_20 @ Z_8 @ S_3 )
% 0.29/0.68 => ( hoare_1508237396rivs_a @ G_10
% 0.29/0.68 @ ( insert1281456128iple_a
% 0.29/0.68 @ ( hoare_1766022166iple_a
% 0.29/0.68 @ ^ [Za: x_a,S_4: state] : ( S_4 = S_3 )
% 0.29/0.68 @ C_26
% 0.29/0.68 @ ^ [Z_9: x_a] : ( Q_12 @ Z_8 ) )
% 0.29/0.68 @ bot_bo751897185le_a_o ) ) )
% 0.29/0.68 => ( hoare_1508237396rivs_a @ G_10 @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ P_20 @ C_26 @ Q_12 ) @ bot_bo751897185le_a_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_335_escape,axiom,
% 0.29/0.68 ! [G_10: hoare_1167836817_state > $o,C_26: com,Q_12: state > state > $o,P_20: state > state > $o] :
% 0.29/0.68 ( ! [Z_8: state,S_3: state] :
% 0.29/0.68 ( ( P_20 @ Z_8 @ S_3 )
% 0.29/0.68 => ( hoare_123228589_state @ G_10
% 0.29/0.68 @ ( insert2134838167_state
% 0.29/0.68 @ ( hoare_908217195_state
% 0.29/0.68 @ ^ [Za: state,S_4: state] : ( S_4 = S_3 )
% 0.29/0.68 @ C_26
% 0.29/0.68 @ ^ [Z_9: state] : ( Q_12 @ Z_8 ) )
% 0.29/0.68 @ bot_bo70021908tate_o ) ) )
% 0.29/0.68 => ( hoare_123228589_state @ G_10 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_20 @ C_26 @ Q_12 ) @ bot_bo70021908tate_o ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_336_conseq1,axiom,
% 0.29/0.68 ! [P_19: x_a > state > $o,G_9: hoare_1775062406iple_a > $o,P_18: x_a > state > $o,C_25: com,Q_11: x_a > state > $o] :
% 0.29/0.68 ( ( hoare_1508237396rivs_a @ G_9 @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ P_18 @ C_25 @ Q_11 ) @ bot_bo751897185le_a_o ) )
% 0.29/0.68 => ( ! [Z_8: x_a,S_3: state] :
% 0.29/0.68 ( ( P_19 @ Z_8 @ S_3 )
% 0.29/0.68 => ( P_18 @ Z_8 @ S_3 ) )
% 0.29/0.68 => ( hoare_1508237396rivs_a @ G_9 @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ P_19 @ C_25 @ Q_11 ) @ bot_bo751897185le_a_o ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_337_conseq1,axiom,
% 0.29/0.68 ! [P_19: state > state > $o,G_9: hoare_1167836817_state > $o,P_18: state > state > $o,C_25: com,Q_11: state > state > $o] :
% 0.29/0.68 ( ( hoare_123228589_state @ G_9 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_18 @ C_25 @ Q_11 ) @ bot_bo70021908tate_o ) )
% 0.29/0.68 => ( ! [Z_8: state,S_3: state] :
% 0.29/0.68 ( ( P_19 @ Z_8 @ S_3 )
% 0.29/0.68 => ( P_18 @ Z_8 @ S_3 ) )
% 0.29/0.68 => ( hoare_123228589_state @ G_9 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_19 @ C_25 @ Q_11 ) @ bot_bo70021908tate_o ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_338_conseq2,axiom,
% 0.29/0.68 ! [Q_10: x_a > state > $o,G_8: hoare_1775062406iple_a > $o,P_17: x_a > state > $o,C_24: com,Q_9: x_a > state > $o] :
% 0.29/0.68 ( ( hoare_1508237396rivs_a @ G_8 @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ P_17 @ C_24 @ Q_9 ) @ bot_bo751897185le_a_o ) )
% 0.29/0.68 => ( ! [Z_8: x_a,S_3: state] :
% 0.29/0.68 ( ( Q_9 @ Z_8 @ S_3 )
% 0.29/0.68 => ( Q_10 @ Z_8 @ S_3 ) )
% 0.29/0.68 => ( hoare_1508237396rivs_a @ G_8 @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ P_17 @ C_24 @ Q_10 ) @ bot_bo751897185le_a_o ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_339_conseq2,axiom,
% 0.29/0.68 ! [Q_10: state > state > $o,G_8: hoare_1167836817_state > $o,P_17: state > state > $o,C_24: com,Q_9: state > state > $o] :
% 0.29/0.68 ( ( hoare_123228589_state @ G_8 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_17 @ C_24 @ Q_9 ) @ bot_bo70021908tate_o ) )
% 0.29/0.68 => ( ! [Z_8: state,S_3: state] :
% 0.29/0.68 ( ( Q_9 @ Z_8 @ S_3 )
% 0.29/0.68 => ( Q_10 @ Z_8 @ S_3 ) )
% 0.29/0.68 => ( hoare_123228589_state @ G_8 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_17 @ C_24 @ Q_10 ) @ bot_bo70021908tate_o ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_340_triple_Osize_I1_J,axiom,
% 0.29/0.68 ! [Fa: state > nat,Fun1_1: state > state > $o,Com_3: com,Fun2_1: state > state > $o] :
% 0.29/0.68 ( ( hoare_545207370_state @ Fa @ ( hoare_908217195_state @ Fun1_1 @ Com_3 @ Fun2_1 ) )
% 0.29/0.68 = zero_zero_nat ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_341_triple_Osize_I1_J,axiom,
% 0.29/0.68 ! [Fa: x_a > nat,Fun1_1: x_a > state > $o,Com_3: com,Fun2_1: x_a > state > $o] :
% 0.29/0.68 ( ( hoare_1118907895size_a @ Fa @ ( hoare_1766022166iple_a @ Fun1_1 @ Com_3 @ Fun2_1 ) )
% 0.29/0.68 = zero_zero_nat ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_342_MGT__def,axiom,
% 0.29/0.68 ! [C_19: com] :
% 0.29/0.68 ( ( hoare_Mirabelle_MGT @ C_19 )
% 0.29/0.68 = ( hoare_908217195_state @ fequal_state @ C_19 @ ( evalc @ C_19 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_343_triple_Osize_I2_J,axiom,
% 0.29/0.68 ! [Fun1: state > state > $o,Com_2: com,Fun2: state > state > $o] :
% 0.29/0.68 ( ( size_s645941755_state @ ( hoare_908217195_state @ Fun1 @ Com_2 @ Fun2 ) )
% 0.29/0.68 = zero_zero_nat ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_344_triple_Osize_I2_J,axiom,
% 0.29/0.68 ! [Fun1: x_a > state > $o,Com_2: com,Fun2: x_a > state > $o] :
% 0.29/0.68 ( ( size_s724313756iple_a @ ( hoare_1766022166iple_a @ Fun1 @ Com_2 @ Fun2 ) )
% 0.29/0.68 = zero_zero_nat ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_345_conseq12,axiom,
% 0.29/0.68 ! [Q_8: state > state > $o,P_16: state > state > $o,G_7: hoare_1167836817_state > $o,P_15: state > state > $o,C_23: com,Q_7: state > state > $o] :
% 0.29/0.68 ( ( hoare_123228589_state @ G_7 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_15 @ C_23 @ Q_7 ) @ bot_bo70021908tate_o ) )
% 0.29/0.68 => ( ! [Z_8: state,S_3: state] :
% 0.29/0.68 ( ( P_16 @ Z_8 @ S_3 )
% 0.29/0.68 => ! [S_4: state] :
% 0.29/0.68 ( ! [Z_9: state] :
% 0.29/0.68 ( ( P_15 @ Z_9 @ S_3 )
% 0.29/0.68 => ( Q_7 @ Z_9 @ S_4 ) )
% 0.29/0.68 => ( Q_8 @ Z_8 @ S_4 ) ) )
% 0.29/0.68 => ( hoare_123228589_state @ G_7 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_16 @ C_23 @ Q_8 ) @ bot_bo70021908tate_o ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_346_conseq12,axiom,
% 0.29/0.68 ! [Q_8: x_a > state > $o,P_16: x_a > state > $o,G_7: hoare_1775062406iple_a > $o,P_15: x_a > state > $o,C_23: com,Q_7: x_a > state > $o] :
% 0.29/0.68 ( ( hoare_1508237396rivs_a @ G_7 @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ P_15 @ C_23 @ Q_7 ) @ bot_bo751897185le_a_o ) )
% 0.29/0.68 => ( ! [Z_8: x_a,S_3: state] :
% 0.29/0.68 ( ( P_16 @ Z_8 @ S_3 )
% 0.29/0.68 => ! [S_4: state] :
% 0.29/0.68 ( ! [Z_9: x_a] :
% 0.29/0.68 ( ( P_15 @ Z_9 @ S_3 )
% 0.29/0.68 => ( Q_7 @ Z_9 @ S_4 ) )
% 0.29/0.68 => ( Q_8 @ Z_8 @ S_4 ) ) )
% 0.29/0.68 => ( hoare_1508237396rivs_a @ G_7 @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ P_16 @ C_23 @ Q_8 ) @ bot_bo751897185le_a_o ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_347_the__elem__eq,axiom,
% 0.29/0.68 ! [X_23: hoare_1167836817_state] :
% 0.29/0.68 ( ( the_el323660082_state @ ( insert2134838167_state @ X_23 @ bot_bo70021908tate_o ) )
% 0.29/0.68 = X_23 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_348_the__elem__eq,axiom,
% 0.29/0.68 ! [X_23: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( the_el1844711461iple_a @ ( insert1281456128iple_a @ X_23 @ bot_bo751897185le_a_o ) )
% 0.29/0.68 = X_23 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_349_the__elem__eq,axiom,
% 0.29/0.68 ! [X_23: pname] :
% 0.29/0.68 ( ( the_elem_pname @ ( insert_pname @ X_23 @ bot_bot_pname_o ) )
% 0.29/0.68 = X_23 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_350_Zero__not__Suc,axiom,
% 0.29/0.68 ! [M: nat] :
% 0.29/0.68 ( zero_zero_nat
% 0.29/0.68 != ( suc @ M ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_351_nat_Osimps_I2_J,axiom,
% 0.29/0.68 ! [Nat_1: nat] :
% 0.29/0.68 ( zero_zero_nat
% 0.29/0.68 != ( suc @ Nat_1 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_352_Suc__not__Zero,axiom,
% 0.29/0.68 ! [M: nat] :
% 0.29/0.68 ( ( suc @ M )
% 0.29/0.68 != zero_zero_nat ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_353_nat_Osimps_I3_J,axiom,
% 0.29/0.68 ! [Nat_3: nat] :
% 0.29/0.68 ( ( suc @ Nat_3 )
% 0.29/0.68 != zero_zero_nat ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_354_Zero__neq__Suc,axiom,
% 0.29/0.68 ! [M: nat] :
% 0.29/0.68 ( zero_zero_nat
% 0.29/0.68 != ( suc @ M ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_355_Suc__neq__Zero,axiom,
% 0.29/0.68 ! [M: nat] :
% 0.29/0.68 ( ( suc @ M )
% 0.29/0.68 != zero_zero_nat ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_356_bot__fun__def,axiom,
% 0.29/0.68 ! [X: pname] :
% 0.29/0.68 ( ( bot_bot_pname_o @ X )
% 0.29/0.68 <=> bot_bot_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_357_bot__fun__def,axiom,
% 0.29/0.68 ! [X: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( bot_bo751897185le_a_o @ X )
% 0.29/0.68 <=> bot_bot_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_358_bot__fun__def,axiom,
% 0.29/0.68 ! [X: hoare_1167836817_state] :
% 0.29/0.68 ( ( bot_bo70021908tate_o @ X )
% 0.29/0.68 <=> bot_bot_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_359_bot__nat__def,axiom,
% 0.29/0.68 bot_bot_nat = zero_zero_nat ).
% 0.29/0.68
% 0.29/0.68 thf(fact_360_Suc__inject,axiom,
% 0.29/0.68 ! [X_1: nat,Y: nat] :
% 0.29/0.68 ( ( ( suc @ X_1 )
% 0.29/0.68 = ( suc @ Y ) )
% 0.29/0.68 => ( X_1 = Y ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_361_nat_Oinject,axiom,
% 0.29/0.68 ! [Nat_2: nat,Nat_1: nat] :
% 0.29/0.68 ( ( ( suc @ Nat_2 )
% 0.29/0.68 = ( suc @ Nat_1 ) )
% 0.29/0.68 <=> ( Nat_2 = Nat_1 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_362_Suc__n__not__n,axiom,
% 0.29/0.68 ! [N_1: nat] :
% 0.29/0.68 ( ( suc @ N_1 )
% 0.29/0.68 != N_1 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_363_n__not__Suc__n,axiom,
% 0.29/0.68 ! [N_1: nat] :
% 0.29/0.68 ( N_1
% 0.29/0.68 != ( suc @ N_1 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_364_bot__apply,axiom,
% 0.29/0.68 ! [X_22: pname] :
% 0.29/0.68 ( ( bot_bot_pname_o @ X_22 )
% 0.29/0.68 <=> bot_bot_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_365_bot__apply,axiom,
% 0.29/0.68 ! [X_22: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( bot_bo751897185le_a_o @ X_22 )
% 0.29/0.68 <=> bot_bot_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_366_bot__apply,axiom,
% 0.29/0.68 ! [X_22: hoare_1167836817_state] :
% 0.29/0.68 ( ( bot_bo70021908tate_o @ X_22 )
% 0.29/0.68 <=> bot_bot_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_367_nat_Oexhaust,axiom,
% 0.29/0.68 ! [Y: nat] :
% 0.29/0.68 ( ( Y != zero_zero_nat )
% 0.29/0.68 => ~ ! [Nat: nat] :
% 0.29/0.68 ( Y
% 0.29/0.68 != ( suc @ Nat ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_368_zero__induct,axiom,
% 0.29/0.68 ! [P: nat > $o,K: nat] :
% 0.29/0.68 ( ( P @ K )
% 0.29/0.68 => ( ! [N: nat] :
% 0.29/0.68 ( ( P @ ( suc @ N ) )
% 0.29/0.68 => ( P @ N ) )
% 0.29/0.68 => ( P @ zero_zero_nat ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_369_nat__induct,axiom,
% 0.29/0.68 ! [N_1: nat,P: nat > $o] :
% 0.29/0.68 ( ( P @ zero_zero_nat )
% 0.29/0.68 => ( ! [N: nat] :
% 0.29/0.68 ( ( P @ N )
% 0.29/0.68 => ( P @ ( suc @ N ) ) )
% 0.29/0.68 => ( P @ N_1 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_370_not0__implies__Suc,axiom,
% 0.29/0.68 ! [N_1: nat] :
% 0.29/0.68 ( ( N_1 != zero_zero_nat )
% 0.29/0.68 => ? [M_1: nat] :
% 0.29/0.68 ( N_1
% 0.29/0.68 = ( suc @ M_1 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_371_evaln_OBody,axiom,
% 0.29/0.68 ! [Pn_1: pname,S0: state,N_1: nat,S1: state] :
% 0.29/0.68 ( ( evaln @ ( the_com @ ( body_1 @ Pn_1 ) ) @ S0 @ N_1 @ S1 )
% 0.29/0.68 => ( evaln @ ( body @ Pn_1 ) @ S0 @ ( suc @ N_1 ) @ S1 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_372_hoare__derivs_OSkip,axiom,
% 0.29/0.68 ! [G_6: hoare_1167836817_state > $o,P_14: state > state > $o] : ( hoare_123228589_state @ G_6 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_14 @ skip @ P_14 ) @ bot_bo70021908tate_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_373_hoare__derivs_OSkip,axiom,
% 0.29/0.68 ! [G_6: hoare_1775062406iple_a > $o,P_14: x_a > state > $o] : ( hoare_1508237396rivs_a @ G_6 @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ P_14 @ skip @ P_14 ) @ bot_bo751897185le_a_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_374_evaln__elim__cases_I1_J,axiom,
% 0.29/0.68 ! [S: state,N_1: nat,T: state] :
% 0.29/0.68 ( ( evaln @ skip @ S @ N_1 @ T )
% 0.29/0.68 => ( T = S ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_375_evaln_OSkip,axiom,
% 0.29/0.68 ! [S: state,N_1: nat] : ( evaln @ skip @ S @ N_1 @ S ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_376_evalc_OSkip,axiom,
% 0.29/0.68 ! [S: state] : ( evalc @ skip @ S @ S ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_377_evalc__elim__cases_I1_J,axiom,
% 0.29/0.68 ! [S: state,T: state] :
% 0.29/0.68 ( ( evalc @ skip @ S @ T )
% 0.29/0.68 => ( T = S ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_378_evaln__Suc,axiom,
% 0.29/0.68 ! [C_19: com,S: state,N_1: nat,S_5: state] :
% 0.29/0.68 ( ( evaln @ C_19 @ S @ N_1 @ S_5 )
% 0.29/0.68 => ( evaln @ C_19 @ S @ ( suc @ N_1 ) @ S_5 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_379_eval__eq,axiom,
% 0.29/0.68 ! [C_19: com,S: state,T: state] :
% 0.29/0.68 ( ( evalc @ C_19 @ S @ T )
% 0.29/0.68 <=> ? [N: nat] : ( evaln @ C_19 @ S @ N @ T ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_380_evaln__evalc,axiom,
% 0.29/0.68 ! [C_19: com,S: state,N_1: nat,T: state] :
% 0.29/0.68 ( ( evaln @ C_19 @ S @ N_1 @ T )
% 0.29/0.68 => ( evalc @ C_19 @ S @ T ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_381_com_Osimps_I19_J,axiom,
% 0.29/0.68 ! [Pname_1: pname] :
% 0.29/0.68 ( ( body @ Pname_1 )
% 0.29/0.68 != skip ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_382_com_Osimps_I18_J,axiom,
% 0.29/0.68 ! [Pname_1: pname] :
% 0.29/0.68 ( skip
% 0.29/0.68 != ( body @ Pname_1 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_383_triple__valid__def2,axiom,
% 0.29/0.68 ! [N_4: nat,P_13: state > state > $o,C_22: com,Q_6: state > state > $o] :
% 0.29/0.68 ( ( hoare_56934129_state @ N_4 @ ( hoare_908217195_state @ P_13 @ C_22 @ Q_6 ) )
% 0.29/0.68 <=> ! [Z_8: state,S_3: state] :
% 0.29/0.68 ( ( P_13 @ Z_8 @ S_3 )
% 0.29/0.68 => ! [S_4: state] :
% 0.29/0.68 ( ( evaln @ C_22 @ S_3 @ N_4 @ S_4 )
% 0.29/0.68 => ( Q_6 @ Z_8 @ S_4 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_384_triple__valid__def2,axiom,
% 0.29/0.68 ! [N_4: nat,P_13: x_a > state > $o,C_22: com,Q_6: x_a > state > $o] :
% 0.29/0.68 ( ( hoare_1462269968alid_a @ N_4 @ ( hoare_1766022166iple_a @ P_13 @ C_22 @ Q_6 ) )
% 0.29/0.68 <=> ! [Z_8: x_a,S_3: state] :
% 0.29/0.68 ( ( P_13 @ Z_8 @ S_3 )
% 0.29/0.68 => ! [S_4: state] :
% 0.29/0.68 ( ( evaln @ C_22 @ S_3 @ N_4 @ S_4 )
% 0.29/0.68 => ( Q_6 @ Z_8 @ S_4 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_385_evaln__elim__cases_I6_J,axiom,
% 0.29/0.68 ! [P: pname,S: state,N_1: nat,S1: state] :
% 0.29/0.68 ( ( evaln @ ( body @ P ) @ S @ N_1 @ S1 )
% 0.29/0.68 => ~ ! [N: nat] :
% 0.29/0.68 ( ( N_1
% 0.29/0.68 = ( suc @ N ) )
% 0.29/0.68 => ~ ( evaln @ ( the_com @ ( body_1 @ P ) ) @ S @ N @ S1 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_386_evalc__evaln,axiom,
% 0.29/0.68 ! [C_19: com,S: state,T: state] :
% 0.29/0.68 ( ( evalc @ C_19 @ S @ T )
% 0.29/0.68 => ? [N: nat] : ( evaln @ C_19 @ S @ N @ T ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_387_LoopF,axiom,
% 0.29/0.68 ! [G_5: hoare_1167836817_state > $o,P_12: state > state > $o,B_36: state > $o,C_21: com] :
% 0.29/0.68 ( hoare_123228589_state @ G_5
% 0.29/0.68 @ ( insert2134838167_state
% 0.29/0.68 @ ( hoare_908217195_state
% 0.29/0.68 @ ^ [Z_8: state,S_3: state] : ( (&) @ ( P_12 @ Z_8 @ S_3 ) @ ( (~) @ ( B_36 @ S_3 ) ) )
% 0.29/0.68 @ ( while @ B_36 @ C_21 )
% 0.29/0.68 @ P_12 )
% 0.29/0.68 @ bot_bo70021908tate_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_388_LoopF,axiom,
% 0.29/0.68 ! [G_5: hoare_1775062406iple_a > $o,P_12: x_a > state > $o,B_36: state > $o,C_21: com] :
% 0.29/0.68 ( hoare_1508237396rivs_a @ G_5
% 0.29/0.68 @ ( insert1281456128iple_a
% 0.29/0.68 @ ( hoare_1766022166iple_a
% 0.29/0.68 @ ^ [Z_8: x_a,S_3: state] : ( (&) @ ( P_12 @ Z_8 @ S_3 ) @ ( (~) @ ( B_36 @ S_3 ) ) )
% 0.29/0.68 @ ( while @ B_36 @ C_21 )
% 0.29/0.68 @ P_12 )
% 0.29/0.68 @ bot_bo751897185le_a_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_389_Comp,axiom,
% 0.29/0.68 ! [D: com,R_1: state > state > $o,G_4: hoare_1167836817_state > $o,P_11: state > state > $o,C_20: com,Q_5: state > state > $o] :
% 0.29/0.68 ( ( hoare_123228589_state @ G_4 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_11 @ C_20 @ Q_5 ) @ bot_bo70021908tate_o ) )
% 0.29/0.68 => ( ( hoare_123228589_state @ G_4 @ ( insert2134838167_state @ ( hoare_908217195_state @ Q_5 @ D @ R_1 ) @ bot_bo70021908tate_o ) )
% 0.29/0.68 => ( hoare_123228589_state @ G_4 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_11 @ ( semi @ C_20 @ D ) @ R_1 ) @ bot_bo70021908tate_o ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_390_Comp,axiom,
% 0.29/0.68 ! [D: com,R_1: x_a > state > $o,G_4: hoare_1775062406iple_a > $o,P_11: x_a > state > $o,C_20: com,Q_5: x_a > state > $o] :
% 0.29/0.68 ( ( hoare_1508237396rivs_a @ G_4 @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ P_11 @ C_20 @ Q_5 ) @ bot_bo751897185le_a_o ) )
% 0.29/0.68 => ( ( hoare_1508237396rivs_a @ G_4 @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ Q_5 @ D @ R_1 ) @ bot_bo751897185le_a_o ) )
% 0.29/0.68 => ( hoare_1508237396rivs_a @ G_4 @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ P_11 @ ( semi @ C_20 @ D ) @ R_1 ) @ bot_bo751897185le_a_o ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_391_the__elem__def,axiom,
% 0.29/0.68 ! [X_21: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( the_el323660082_state @ X_21 )
% 0.29/0.68 = ( the_Ho310147232_state
% 0.29/0.68 @ ^ [X: hoare_1167836817_state] :
% 0.29/0.68 ( X_21
% 0.29/0.68 = ( insert2134838167_state @ X @ bot_bo70021908tate_o ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_392_the__elem__def,axiom,
% 0.29/0.68 ! [X_21: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( the_el1844711461iple_a @ X_21 )
% 0.29/0.68 = ( the_Ho1155011127iple_a
% 0.29/0.68 @ ^ [X: hoare_1775062406iple_a] :
% 0.29/0.68 ( X_21
% 0.29/0.68 = ( insert1281456128iple_a @ X @ bot_bo751897185le_a_o ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_393_the__elem__def,axiom,
% 0.29/0.68 ! [X_21: pname > $o] :
% 0.29/0.68 ( ( the_elem_pname @ X_21 )
% 0.29/0.68 = ( the_pname
% 0.29/0.68 @ ^ [X: pname] :
% 0.29/0.68 ( X_21
% 0.29/0.68 = ( insert_pname @ X @ bot_bot_pname_o ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_394_finite__pointwise,axiom,
% 0.29/0.68 ! [P_9: pname > state > state > $o,Q_4: pname > state > state > $o,G_3: hoare_1167836817_state > $o,P_8: pname > state > state > $o,C0_1: pname > com,Q_3: pname > state > state > $o,U: pname > $o] :
% 0.29/0.68 ( ( finite_finite_pname @ U )
% 0.29/0.68 => ( ! [P_10: pname] :
% 0.29/0.68 ( ( hoare_123228589_state @ G_3 @ ( insert2134838167_state @ ( hoare_908217195_state @ ( P_8 @ P_10 ) @ ( C0_1 @ P_10 ) @ ( Q_3 @ P_10 ) ) @ bot_bo70021908tate_o ) )
% 0.29/0.68 => ( hoare_123228589_state @ G_3 @ ( insert2134838167_state @ ( hoare_908217195_state @ ( P_9 @ P_10 ) @ ( C0_1 @ P_10 ) @ ( Q_4 @ P_10 ) ) @ bot_bo70021908tate_o ) ) )
% 0.29/0.68 => ( ( hoare_123228589_state @ G_3
% 0.29/0.68 @ ( image_575578384_state
% 0.29/0.68 @ ^ [P_10: pname] : ( hoare_908217195_state @ ( P_8 @ P_10 ) @ ( C0_1 @ P_10 ) @ ( Q_3 @ P_10 ) )
% 0.29/0.68 @ U ) )
% 0.29/0.68 => ( hoare_123228589_state @ G_3
% 0.29/0.68 @ ( image_575578384_state
% 0.29/0.68 @ ^ [P_10: pname] : ( hoare_908217195_state @ ( P_9 @ P_10 ) @ ( C0_1 @ P_10 ) @ ( Q_4 @ P_10 ) )
% 0.29/0.68 @ U ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_395_finite__pointwise,axiom,
% 0.29/0.68 ! [P_9: pname > x_a > state > $o,Q_4: pname > x_a > state > $o,G_3: hoare_1775062406iple_a > $o,P_8: pname > x_a > state > $o,C0_1: pname > com,Q_3: pname > x_a > state > $o,U: pname > $o] :
% 0.29/0.68 ( ( finite_finite_pname @ U )
% 0.29/0.68 => ( ! [P_10: pname] :
% 0.29/0.68 ( ( hoare_1508237396rivs_a @ G_3 @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ ( P_8 @ P_10 ) @ ( C0_1 @ P_10 ) @ ( Q_3 @ P_10 ) ) @ bot_bo751897185le_a_o ) )
% 0.29/0.68 => ( hoare_1508237396rivs_a @ G_3 @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ ( P_9 @ P_10 ) @ ( C0_1 @ P_10 ) @ ( Q_4 @ P_10 ) ) @ bot_bo751897185le_a_o ) ) )
% 0.29/0.68 => ( ( hoare_1508237396rivs_a @ G_3
% 0.29/0.68 @ ( image_2063119815iple_a
% 0.29/0.68 @ ^ [P_10: pname] : ( hoare_1766022166iple_a @ ( P_8 @ P_10 ) @ ( C0_1 @ P_10 ) @ ( Q_3 @ P_10 ) )
% 0.29/0.68 @ U ) )
% 0.29/0.68 => ( hoare_1508237396rivs_a @ G_3
% 0.29/0.68 @ ( image_2063119815iple_a
% 0.29/0.68 @ ^ [P_10: pname] : ( hoare_1766022166iple_a @ ( P_9 @ P_10 ) @ ( C0_1 @ P_10 ) @ ( Q_4 @ P_10 ) )
% 0.29/0.68 @ U ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_396_evaln_OWhileFalse,axiom,
% 0.29/0.68 ! [C_19: com,N_1: nat,B: state > $o,S: state] :
% 0.29/0.68 ( ~ ( B @ S )
% 0.29/0.68 => ( evaln @ ( while @ B @ C_19 ) @ S @ N_1 @ S ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_397_evaln_OWhileTrue,axiom,
% 0.29/0.68 ! [S2: state,C_19: com,N_1: nat,S1: state,B: state > $o,S0: state] :
% 0.29/0.68 ( ( B @ S0 )
% 0.29/0.68 => ( ( evaln @ C_19 @ S0 @ N_1 @ S1 )
% 0.29/0.68 => ( ( evaln @ ( while @ B @ C_19 ) @ S1 @ N_1 @ S2 )
% 0.29/0.68 => ( evaln @ ( while @ B @ C_19 ) @ S0 @ N_1 @ S2 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_398_evalc_OWhileTrue,axiom,
% 0.29/0.68 ! [S2: state,C_19: com,S1: state,B: state > $o,S0: state] :
% 0.29/0.68 ( ( B @ S0 )
% 0.29/0.68 => ( ( evalc @ C_19 @ S0 @ S1 )
% 0.29/0.68 => ( ( evalc @ ( while @ B @ C_19 ) @ S1 @ S2 )
% 0.29/0.68 => ( evalc @ ( while @ B @ C_19 ) @ S0 @ S2 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_399_evalc_OWhileFalse,axiom,
% 0.29/0.68 ! [C_19: com,B: state > $o,S: state] :
% 0.29/0.68 ( ~ ( B @ S )
% 0.29/0.68 => ( evalc @ ( while @ B @ C_19 ) @ S @ S ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_400_evaln_OSemi,axiom,
% 0.29/0.68 ! [C1: com,S2: state,C0: com,S0: state,N_1: nat,S1: state] :
% 0.29/0.68 ( ( evaln @ C0 @ S0 @ N_1 @ S1 )
% 0.29/0.68 => ( ( evaln @ C1 @ S1 @ N_1 @ S2 )
% 0.29/0.68 => ( evaln @ ( semi @ C0 @ C1 ) @ S0 @ N_1 @ S2 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_401_evalc_OSemi,axiom,
% 0.29/0.68 ! [C1: com,S2: state,C0: com,S0: state,S1: state] :
% 0.29/0.68 ( ( evalc @ C0 @ S0 @ S1 )
% 0.29/0.68 => ( ( evalc @ C1 @ S1 @ S2 )
% 0.29/0.68 => ( evalc @ ( semi @ C0 @ C1 ) @ S0 @ S2 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_402_com_Osimps_I46_J,axiom,
% 0.29/0.68 ! [Com1: com,Com2: com,Fun_1: state > $o,Com_1: com] :
% 0.29/0.68 ( ( semi @ Com1 @ Com2 )
% 0.29/0.68 != ( while @ Fun_1 @ Com_1 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_403_com_Osimps_I47_J,axiom,
% 0.29/0.68 ! [Fun_1: state > $o,Com_1: com,Com1: com,Com2: com] :
% 0.29/0.68 ( ( while @ Fun_1 @ Com_1 )
% 0.29/0.68 != ( semi @ Com1 @ Com2 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_404_com_Osimps_I3_J,axiom,
% 0.29/0.68 ! [Com1: com,Com2: com,Com1_1: com,Com2_1: com] :
% 0.29/0.68 ( ( ( semi @ Com1 @ Com2 )
% 0.29/0.68 = ( semi @ Com1_1 @ Com2_1 ) )
% 0.29/0.68 <=> ( ( Com1 = Com1_1 )
% 0.29/0.68 & ( Com2 = Com2_1 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_405_com_Osimps_I5_J,axiom,
% 0.29/0.68 ! [Fun: state > $o,Com: com,Fun_1: state > $o,Com_1: com] :
% 0.29/0.68 ( ( ( while @ Fun @ Com )
% 0.29/0.68 = ( while @ Fun_1 @ Com_1 ) )
% 0.29/0.68 <=> ( ( Fun = Fun_1 )
% 0.29/0.68 & ( Com = Com_1 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_406_com_Osimps_I59_J,axiom,
% 0.29/0.68 ! [Pname_1: pname,Fun: state > $o,Com: com] :
% 0.29/0.68 ( ( body @ Pname_1 )
% 0.29/0.68 != ( while @ Fun @ Com ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_407_com_Osimps_I58_J,axiom,
% 0.29/0.68 ! [Fun: state > $o,Com: com,Pname_1: pname] :
% 0.29/0.68 ( ( while @ Fun @ Com )
% 0.29/0.68 != ( body @ Pname_1 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_408_com_Osimps_I16_J,axiom,
% 0.29/0.68 ! [Fun_1: state > $o,Com_1: com] :
% 0.29/0.68 ( skip
% 0.29/0.68 != ( while @ Fun_1 @ Com_1 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_409_com_Osimps_I17_J,axiom,
% 0.29/0.68 ! [Fun_1: state > $o,Com_1: com] :
% 0.29/0.68 ( ( while @ Fun_1 @ Com_1 )
% 0.29/0.68 != skip ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_410_com_Osimps_I49_J,axiom,
% 0.29/0.68 ! [Pname_1: pname,Com1: com,Com2: com] :
% 0.29/0.68 ( ( body @ Pname_1 )
% 0.29/0.68 != ( semi @ Com1 @ Com2 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_411_com_Osimps_I48_J,axiom,
% 0.29/0.68 ! [Com1: com,Com2: com,Pname_1: pname] :
% 0.29/0.68 ( ( semi @ Com1 @ Com2 )
% 0.29/0.68 != ( body @ Pname_1 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_412_com_Osimps_I12_J,axiom,
% 0.29/0.68 ! [Com1_1: com,Com2_1: com] :
% 0.29/0.68 ( skip
% 0.29/0.68 != ( semi @ Com1_1 @ Com2_1 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_413_com_Osimps_I13_J,axiom,
% 0.29/0.68 ! [Com1_1: com,Com2_1: com] :
% 0.29/0.68 ( ( semi @ Com1_1 @ Com2_1 )
% 0.29/0.68 != skip ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_414_evalc__elim__cases_I4_J,axiom,
% 0.29/0.68 ! [C1: com,C2: com,S: state,T: state] :
% 0.29/0.68 ( ( evalc @ ( semi @ C1 @ C2 ) @ S @ T )
% 0.29/0.68 => ~ ! [S1_1: state] :
% 0.29/0.68 ( ( evalc @ C1 @ S @ S1_1 )
% 0.29/0.68 => ~ ( evalc @ C2 @ S1_1 @ T ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_415_evaln__elim__cases_I4_J,axiom,
% 0.29/0.68 ! [C1: com,C2: com,S: state,N_1: nat,T: state] :
% 0.29/0.68 ( ( evaln @ ( semi @ C1 @ C2 ) @ S @ N_1 @ T )
% 0.29/0.68 => ~ ! [S1_1: state] :
% 0.29/0.68 ( ( evaln @ C1 @ S @ N_1 @ S1_1 )
% 0.29/0.68 => ~ ( evaln @ C2 @ S1_1 @ N_1 @ T ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_416_finite__imageI,axiom,
% 0.29/0.68 ! [H_2: pname > hoare_1167836817_state,F_26: pname > $o] :
% 0.29/0.68 ( ( finite_finite_pname @ F_26 )
% 0.29/0.68 => ( finite1084549118_state @ ( image_575578384_state @ H_2 @ F_26 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_417_finite__imageI,axiom,
% 0.29/0.68 ! [H_2: pname > hoare_1775062406iple_a,F_26: pname > $o] :
% 0.29/0.68 ( ( finite_finite_pname @ F_26 )
% 0.29/0.68 => ( finite2063573081iple_a @ ( image_2063119815iple_a @ H_2 @ F_26 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_418_finite_OinsertI,axiom,
% 0.29/0.68 ! [A_62: hoare_1167836817_state,A_61: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( finite1084549118_state @ A_61 )
% 0.29/0.68 => ( finite1084549118_state @ ( insert2134838167_state @ A_62 @ A_61 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_419_finite_OinsertI,axiom,
% 0.29/0.68 ! [A_62: hoare_1775062406iple_a,A_61: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( finite2063573081iple_a @ A_61 )
% 0.29/0.68 => ( finite2063573081iple_a @ ( insert1281456128iple_a @ A_62 @ A_61 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_420_finite_OinsertI,axiom,
% 0.29/0.68 ! [A_62: pname,A_61: pname > $o] :
% 0.29/0.68 ( ( finite_finite_pname @ A_61 )
% 0.29/0.68 => ( finite_finite_pname @ ( insert_pname @ A_62 @ A_61 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_421_finite_OemptyI,axiom,
% 0.29/0.68 finite_finite_pname @ bot_bot_pname_o ).
% 0.29/0.68
% 0.29/0.68 thf(fact_422_finite_OemptyI,axiom,
% 0.29/0.68 finite2063573081iple_a @ bot_bo751897185le_a_o ).
% 0.29/0.68
% 0.29/0.68 thf(fact_423_finite_OemptyI,axiom,
% 0.29/0.68 finite1084549118_state @ bot_bo70021908tate_o ).
% 0.29/0.68
% 0.29/0.68 thf(fact_424_finite__Collect__conjI,axiom,
% 0.29/0.68 ! [Q_2: hoare_1775062406iple_a > $o,P_7: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( ( finite2063573081iple_a @ ( collec676402587iple_a @ P_7 ) )
% 0.29/0.68 | ( finite2063573081iple_a @ ( collec676402587iple_a @ Q_2 ) ) )
% 0.29/0.68 => ( finite2063573081iple_a
% 0.29/0.68 @ ( collec676402587iple_a
% 0.29/0.68 @ ^ [X: hoare_1775062406iple_a] : ( (&) @ ( P_7 @ X ) @ ( Q_2 @ X ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_425_finite__Collect__conjI,axiom,
% 0.29/0.68 ! [Q_2: pname > $o,P_7: pname > $o] :
% 0.29/0.68 ( ( ( finite_finite_pname @ ( collect_pname @ P_7 ) )
% 0.29/0.68 | ( finite_finite_pname @ ( collect_pname @ Q_2 ) ) )
% 0.29/0.68 => ( finite_finite_pname
% 0.29/0.68 @ ( collect_pname
% 0.29/0.68 @ ^ [X: pname] : ( (&) @ ( P_7 @ X ) @ ( Q_2 @ X ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_426_finite__Collect__disjI,axiom,
% 0.29/0.68 ! [P_6: hoare_1775062406iple_a > $o,Q_1: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( finite2063573081iple_a
% 0.29/0.68 @ ( collec676402587iple_a
% 0.29/0.68 @ ^ [X: hoare_1775062406iple_a] : ( (|) @ ( P_6 @ X ) @ ( Q_1 @ X ) ) ) )
% 0.29/0.68 <=> ( ( finite2063573081iple_a @ ( collec676402587iple_a @ P_6 ) )
% 0.29/0.68 & ( finite2063573081iple_a @ ( collec676402587iple_a @ Q_1 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_427_finite__Collect__disjI,axiom,
% 0.29/0.68 ! [P_6: pname > $o,Q_1: pname > $o] :
% 0.29/0.68 ( ( finite_finite_pname
% 0.29/0.68 @ ( collect_pname
% 0.29/0.68 @ ^ [X: pname] : ( (|) @ ( P_6 @ X ) @ ( Q_1 @ X ) ) ) )
% 0.29/0.68 <=> ( ( finite_finite_pname @ ( collect_pname @ P_6 ) )
% 0.29/0.68 & ( finite_finite_pname @ ( collect_pname @ Q_1 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_428_finite__insert,axiom,
% 0.29/0.68 ! [A_60: hoare_1167836817_state,A_59: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( finite1084549118_state @ ( insert2134838167_state @ A_60 @ A_59 ) )
% 0.29/0.68 <=> ( finite1084549118_state @ A_59 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_429_finite__insert,axiom,
% 0.29/0.68 ! [A_60: hoare_1775062406iple_a,A_59: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( finite2063573081iple_a @ ( insert1281456128iple_a @ A_60 @ A_59 ) )
% 0.29/0.68 <=> ( finite2063573081iple_a @ A_59 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_430_finite__insert,axiom,
% 0.29/0.68 ! [A_60: pname,A_59: pname > $o] :
% 0.29/0.68 ( ( finite_finite_pname @ ( insert_pname @ A_60 @ A_59 ) )
% 0.29/0.68 <=> ( finite_finite_pname @ A_59 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_431_finite__Un,axiom,
% 0.29/0.68 ! [F_25: pname > $o,G_2: pname > $o] :
% 0.29/0.68 ( ( finite_finite_pname @ ( semila1780557381name_o @ F_25 @ G_2 ) )
% 0.29/0.68 <=> ( ( finite_finite_pname @ F_25 )
% 0.29/0.68 & ( finite_finite_pname @ G_2 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_432_finite__Un,axiom,
% 0.29/0.68 ! [F_25: hoare_1167836817_state > $o,G_2: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( finite1084549118_state @ ( semila1172322802tate_o @ F_25 @ G_2 ) )
% 0.29/0.68 <=> ( ( finite1084549118_state @ F_25 )
% 0.29/0.68 & ( finite1084549118_state @ G_2 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_433_finite__Un,axiom,
% 0.29/0.68 ! [F_25: hoare_1775062406iple_a > $o,G_2: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( finite2063573081iple_a @ ( semila13410563le_a_o @ F_25 @ G_2 ) )
% 0.29/0.68 <=> ( ( finite2063573081iple_a @ F_25 )
% 0.29/0.68 & ( finite2063573081iple_a @ G_2 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_434_finite__UnI,axiom,
% 0.29/0.68 ! [G_1: pname > $o,F_24: pname > $o] :
% 0.29/0.68 ( ( finite_finite_pname @ F_24 )
% 0.29/0.68 => ( ( finite_finite_pname @ G_1 )
% 0.29/0.68 => ( finite_finite_pname @ ( semila1780557381name_o @ F_24 @ G_1 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_435_finite__UnI,axiom,
% 0.29/0.68 ! [G_1: hoare_1167836817_state > $o,F_24: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( finite1084549118_state @ F_24 )
% 0.29/0.68 => ( ( finite1084549118_state @ G_1 )
% 0.29/0.68 => ( finite1084549118_state @ ( semila1172322802tate_o @ F_24 @ G_1 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_436_finite__UnI,axiom,
% 0.29/0.68 ! [G_1: hoare_1775062406iple_a > $o,F_24: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( finite2063573081iple_a @ F_24 )
% 0.29/0.68 => ( ( finite2063573081iple_a @ G_1 )
% 0.29/0.68 => ( finite2063573081iple_a @ ( semila13410563le_a_o @ F_24 @ G_1 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_437_finite_Osimps,axiom,
% 0.29/0.68 ! [A_57: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( finite1084549118_state @ A_57 )
% 0.29/0.68 <=> ( ( A_57 = bot_bo70021908tate_o )
% 0.29/0.68 | ? [A_58: hoare_1167836817_state > $o,A_56: hoare_1167836817_state] :
% 0.29/0.68 ( ( A_57
% 0.29/0.68 = ( insert2134838167_state @ A_56 @ A_58 ) )
% 0.29/0.68 & ( finite1084549118_state @ A_58 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_438_finite_Osimps,axiom,
% 0.29/0.68 ! [A_57: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( finite2063573081iple_a @ A_57 )
% 0.29/0.68 <=> ( ( A_57 = bot_bo751897185le_a_o )
% 0.29/0.68 | ? [A_58: hoare_1775062406iple_a > $o,A_56: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( A_57
% 0.29/0.68 = ( insert1281456128iple_a @ A_56 @ A_58 ) )
% 0.29/0.68 & ( finite2063573081iple_a @ A_58 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_439_finite_Osimps,axiom,
% 0.29/0.68 ! [A_57: pname > $o] :
% 0.29/0.68 ( ( finite_finite_pname @ A_57 )
% 0.29/0.68 <=> ( ( A_57 = bot_bot_pname_o )
% 0.29/0.68 | ? [A_58: pname > $o,A_56: pname] :
% 0.29/0.68 ( ( A_57
% 0.29/0.68 = ( insert_pname @ A_56 @ A_58 ) )
% 0.29/0.68 & ( finite_finite_pname @ A_58 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_440_finite__induct,axiom,
% 0.29/0.68 ! [P_5: ( hoare_1167836817_state > $o ) > $o,F_23: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( finite1084549118_state @ F_23 )
% 0.29/0.68 => ( ( P_5 @ bot_bo70021908tate_o )
% 0.29/0.68 => ( ! [X: hoare_1167836817_state,F_16: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( finite1084549118_state @ F_16 )
% 0.29/0.68 => ( ~ ( member2058392318_state @ X @ F_16 )
% 0.29/0.68 => ( ( P_5 @ F_16 )
% 0.29/0.68 => ( P_5 @ ( insert2134838167_state @ X @ F_16 ) ) ) ) )
% 0.29/0.68 => ( P_5 @ F_23 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_441_finite__induct,axiom,
% 0.29/0.68 ! [P_5: ( hoare_1775062406iple_a > $o ) > $o,F_23: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( finite2063573081iple_a @ F_23 )
% 0.29/0.68 => ( ( P_5 @ bot_bo751897185le_a_o )
% 0.29/0.68 => ( ! [X: hoare_1775062406iple_a,F_16: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( finite2063573081iple_a @ F_16 )
% 0.29/0.68 => ( ~ ( member2122167641iple_a @ X @ F_16 )
% 0.29/0.68 => ( ( P_5 @ F_16 )
% 0.29/0.68 => ( P_5 @ ( insert1281456128iple_a @ X @ F_16 ) ) ) ) )
% 0.29/0.68 => ( P_5 @ F_23 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_442_finite__induct,axiom,
% 0.29/0.68 ! [P_5: ( pname > $o ) > $o,F_23: pname > $o] :
% 0.29/0.68 ( ( finite_finite_pname @ F_23 )
% 0.29/0.68 => ( ( P_5 @ bot_bot_pname_o )
% 0.29/0.68 => ( ! [X: pname,F_16: pname > $o] :
% 0.29/0.68 ( ( finite_finite_pname @ F_16 )
% 0.29/0.68 => ( ~ ( member_pname @ X @ F_16 )
% 0.29/0.68 => ( ( P_5 @ F_16 )
% 0.29/0.68 => ( P_5 @ ( insert_pname @ X @ F_16 ) ) ) ) )
% 0.29/0.68 => ( P_5 @ F_23 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_443_pigeonhole__infinite,axiom,
% 0.29/0.68 ! [F_22: pname > hoare_1167836817_state,A_55: pname > $o] :
% 0.29/0.68 ( ~ ( finite_finite_pname @ A_55 )
% 0.29/0.68 => ( ( finite1084549118_state @ ( image_575578384_state @ F_22 @ A_55 ) )
% 0.29/0.68 => ? [X: pname] :
% 0.29/0.68 ( ( member_pname @ X @ A_55 )
% 0.29/0.68 & ~ ( finite_finite_pname
% 0.29/0.68 @ ( collect_pname
% 0.29/0.68 @ ^ [A_56: pname] :
% 0.29/0.68 ( (&) @ ( member_pname @ A_56 @ A_55 )
% 0.29/0.68 @ ( ( F_22 @ A_56 )
% 0.29/0.68 = ( F_22 @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_444_pigeonhole__infinite,axiom,
% 0.29/0.68 ! [F_22: pname > hoare_1775062406iple_a,A_55: pname > $o] :
% 0.29/0.68 ( ~ ( finite_finite_pname @ A_55 )
% 0.29/0.68 => ( ( finite2063573081iple_a @ ( image_2063119815iple_a @ F_22 @ A_55 ) )
% 0.29/0.68 => ? [X: pname] :
% 0.29/0.68 ( ( member_pname @ X @ A_55 )
% 0.29/0.68 & ~ ( finite_finite_pname
% 0.29/0.68 @ ( collect_pname
% 0.29/0.68 @ ^ [A_56: pname] :
% 0.29/0.68 ( (&) @ ( member_pname @ A_56 @ A_55 )
% 0.29/0.68 @ ( ( F_22 @ A_56 )
% 0.29/0.68 = ( F_22 @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_445_evalc__WHILE__case,axiom,
% 0.29/0.68 ! [B: state > $o,C_19: com,S: state,T: state] :
% 0.29/0.68 ( ( evalc @ ( while @ B @ C_19 ) @ S @ T )
% 0.29/0.68 => ( ( ( T = S )
% 0.29/0.68 => ( B @ S ) )
% 0.29/0.68 => ~ ( ( B @ S )
% 0.29/0.68 => ! [S1_1: state] :
% 0.29/0.68 ( ( evalc @ C_19 @ S @ S1_1 )
% 0.29/0.68 => ~ ( evalc @ ( while @ B @ C_19 ) @ S1_1 @ T ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_446_evaln__WHILE__case,axiom,
% 0.29/0.68 ! [B: state > $o,C_19: com,S: state,N_1: nat,T: state] :
% 0.29/0.68 ( ( evaln @ ( while @ B @ C_19 ) @ S @ N_1 @ T )
% 0.29/0.68 => ( ( ( T = S )
% 0.29/0.68 => ( B @ S ) )
% 0.29/0.68 => ~ ( ( B @ S )
% 0.29/0.68 => ! [S1_1: state] :
% 0.29/0.68 ( ( evaln @ C_19 @ S @ N_1 @ S1_1 )
% 0.29/0.68 => ~ ( evaln @ ( while @ B @ C_19 ) @ S1_1 @ N_1 @ T ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_447_nonempty__iff,axiom,
% 0.29/0.68 ! [A_54: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( A_54 != bot_bo70021908tate_o )
% 0.29/0.68 <=> ? [X: hoare_1167836817_state,B_34: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( A_54
% 0.29/0.68 = ( insert2134838167_state @ X @ B_34 ) )
% 0.29/0.68 & ~ ( member2058392318_state @ X @ B_34 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_448_nonempty__iff,axiom,
% 0.29/0.68 ! [A_54: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( A_54 != bot_bo751897185le_a_o )
% 0.29/0.68 <=> ? [X: hoare_1775062406iple_a,B_34: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( A_54
% 0.29/0.68 = ( insert1281456128iple_a @ X @ B_34 ) )
% 0.29/0.68 & ~ ( member2122167641iple_a @ X @ B_34 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_449_nonempty__iff,axiom,
% 0.29/0.68 ! [A_54: pname > $o] :
% 0.29/0.68 ( ( A_54 != bot_bot_pname_o )
% 0.29/0.68 <=> ? [X: pname,B_34: pname > $o] :
% 0.29/0.68 ( ( A_54
% 0.29/0.68 = ( insert_pname @ X @ B_34 ) )
% 0.29/0.68 & ~ ( member_pname @ X @ B_34 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_450_folding__one__idem_Ounion__idem,axiom,
% 0.29/0.68 ! [B_35: pname > $o,A_53: pname > $o,F_21: pname > pname > pname,F_20: ( pname > $o ) > pname] :
% 0.29/0.68 ( ( finite89670078_pname @ F_21 @ F_20 )
% 0.29/0.68 => ( ( finite_finite_pname @ A_53 )
% 0.29/0.68 => ( ( A_53 != bot_bot_pname_o )
% 0.29/0.68 => ( ( finite_finite_pname @ B_35 )
% 0.29/0.68 => ( ( B_35 != bot_bot_pname_o )
% 0.29/0.68 => ( ( F_20 @ ( semila1780557381name_o @ A_53 @ B_35 ) )
% 0.29/0.68 = ( F_21 @ ( F_20 @ A_53 ) @ ( F_20 @ B_35 ) ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_451_folding__one__idem_Ounion__idem,axiom,
% 0.29/0.68 ! [B_35: hoare_1775062406iple_a > $o,A_53: hoare_1775062406iple_a > $o,F_21: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,F_20: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
% 0.29/0.68 ( ( finite1358382848iple_a @ F_21 @ F_20 )
% 0.29/0.68 => ( ( finite2063573081iple_a @ A_53 )
% 0.29/0.68 => ( ( A_53 != bot_bo751897185le_a_o )
% 0.29/0.68 => ( ( finite2063573081iple_a @ B_35 )
% 0.29/0.68 => ( ( B_35 != bot_bo751897185le_a_o )
% 0.29/0.68 => ( ( F_20 @ ( semila13410563le_a_o @ A_53 @ B_35 ) )
% 0.29/0.68 = ( F_21 @ ( F_20 @ A_53 ) @ ( F_20 @ B_35 ) ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_452_folding__one__idem_Ounion__idem,axiom,
% 0.29/0.68 ! [B_35: hoare_1167836817_state > $o,A_53: hoare_1167836817_state > $o,F_21: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_20: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.29/0.68 ( ( finite806517911_state @ F_21 @ F_20 )
% 0.29/0.68 => ( ( finite1084549118_state @ A_53 )
% 0.29/0.68 => ( ( A_53 != bot_bo70021908tate_o )
% 0.29/0.68 => ( ( finite1084549118_state @ B_35 )
% 0.29/0.68 => ( ( B_35 != bot_bo70021908tate_o )
% 0.29/0.68 => ( ( F_20 @ ( semila1172322802tate_o @ A_53 @ B_35 ) )
% 0.29/0.68 = ( F_21 @ ( F_20 @ A_53 ) @ ( F_20 @ B_35 ) ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_453_folding__one__idem_Oinsert__idem,axiom,
% 0.29/0.68 ! [X_20: hoare_1167836817_state,A_52: hoare_1167836817_state > $o,F_19: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_18: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.29/0.68 ( ( finite806517911_state @ F_19 @ F_18 )
% 0.29/0.68 => ( ( finite1084549118_state @ A_52 )
% 0.29/0.68 => ( ( A_52 != bot_bo70021908tate_o )
% 0.29/0.68 => ( ( F_18 @ ( insert2134838167_state @ X_20 @ A_52 ) )
% 0.29/0.68 = ( F_19 @ X_20 @ ( F_18 @ A_52 ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_454_folding__one__idem_Oinsert__idem,axiom,
% 0.29/0.68 ! [X_20: hoare_1775062406iple_a,A_52: hoare_1775062406iple_a > $o,F_19: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,F_18: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
% 0.29/0.68 ( ( finite1358382848iple_a @ F_19 @ F_18 )
% 0.29/0.68 => ( ( finite2063573081iple_a @ A_52 )
% 0.29/0.68 => ( ( A_52 != bot_bo751897185le_a_o )
% 0.29/0.68 => ( ( F_18 @ ( insert1281456128iple_a @ X_20 @ A_52 ) )
% 0.29/0.68 = ( F_19 @ X_20 @ ( F_18 @ A_52 ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_455_folding__one__idem_Oinsert__idem,axiom,
% 0.29/0.68 ! [X_20: pname,A_52: pname > $o,F_19: pname > pname > pname,F_18: ( pname > $o ) > pname] :
% 0.29/0.68 ( ( finite89670078_pname @ F_19 @ F_18 )
% 0.29/0.68 => ( ( finite_finite_pname @ A_52 )
% 0.29/0.68 => ( ( A_52 != bot_bot_pname_o )
% 0.29/0.68 => ( ( F_18 @ ( insert_pname @ X_20 @ A_52 ) )
% 0.29/0.68 = ( F_19 @ X_20 @ ( F_18 @ A_52 ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_456_image__eq__fold__image,axiom,
% 0.29/0.68 ! [F_17: pname > hoare_1167836817_state,A_51: pname > $o] :
% 0.29/0.68 ( ( finite_finite_pname @ A_51 )
% 0.29/0.68 => ( ( image_575578384_state @ F_17 @ A_51 )
% 0.29/0.68 = ( finite1068437657_pname @ semila1172322802tate_o
% 0.29/0.68 @ ^ [X: pname] : ( insert2134838167_state @ ( F_17 @ X ) @ bot_bo70021908tate_o )
% 0.29/0.68 @ bot_bo70021908tate_o
% 0.29/0.68 @ A_51 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_457_image__eq__fold__image,axiom,
% 0.29/0.68 ! [F_17: pname > hoare_1775062406iple_a,A_51: pname > $o] :
% 0.29/0.68 ( ( finite_finite_pname @ A_51 )
% 0.29/0.68 => ( ( image_2063119815iple_a @ F_17 @ A_51 )
% 0.29/0.68 = ( finite1805141964_pname @ semila13410563le_a_o
% 0.29/0.68 @ ^ [X: pname] : ( insert1281456128iple_a @ ( F_17 @ X ) @ bot_bo751897185le_a_o )
% 0.29/0.68 @ bot_bo751897185le_a_o
% 0.29/0.68 @ A_51 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_458_finite__ne__induct,axiom,
% 0.29/0.68 ! [P_4: ( hoare_1167836817_state > $o ) > $o,F_15: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( finite1084549118_state @ F_15 )
% 0.29/0.68 => ( ( F_15 != bot_bo70021908tate_o )
% 0.29/0.68 => ( ! [X: hoare_1167836817_state] : ( P_4 @ ( insert2134838167_state @ X @ bot_bo70021908tate_o ) )
% 0.29/0.68 => ( ! [X: hoare_1167836817_state,F_16: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( finite1084549118_state @ F_16 )
% 0.29/0.68 => ( ( F_16 != bot_bo70021908tate_o )
% 0.29/0.68 => ( ~ ( member2058392318_state @ X @ F_16 )
% 0.29/0.68 => ( ( P_4 @ F_16 )
% 0.29/0.68 => ( P_4 @ ( insert2134838167_state @ X @ F_16 ) ) ) ) ) )
% 0.29/0.68 => ( P_4 @ F_15 ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_459_finite__ne__induct,axiom,
% 0.29/0.68 ! [P_4: ( hoare_1775062406iple_a > $o ) > $o,F_15: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( finite2063573081iple_a @ F_15 )
% 0.29/0.68 => ( ( F_15 != bot_bo751897185le_a_o )
% 0.29/0.68 => ( ! [X: hoare_1775062406iple_a] : ( P_4 @ ( insert1281456128iple_a @ X @ bot_bo751897185le_a_o ) )
% 0.29/0.68 => ( ! [X: hoare_1775062406iple_a,F_16: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( finite2063573081iple_a @ F_16 )
% 0.29/0.68 => ( ( F_16 != bot_bo751897185le_a_o )
% 0.29/0.68 => ( ~ ( member2122167641iple_a @ X @ F_16 )
% 0.29/0.68 => ( ( P_4 @ F_16 )
% 0.29/0.68 => ( P_4 @ ( insert1281456128iple_a @ X @ F_16 ) ) ) ) ) )
% 0.29/0.68 => ( P_4 @ F_15 ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_460_finite__ne__induct,axiom,
% 0.29/0.68 ! [P_4: ( pname > $o ) > $o,F_15: pname > $o] :
% 0.29/0.68 ( ( finite_finite_pname @ F_15 )
% 0.29/0.68 => ( ( F_15 != bot_bot_pname_o )
% 0.29/0.68 => ( ! [X: pname] : ( P_4 @ ( insert_pname @ X @ bot_bot_pname_o ) )
% 0.29/0.68 => ( ! [X: pname,F_16: pname > $o] :
% 0.29/0.68 ( ( finite_finite_pname @ F_16 )
% 0.29/0.68 => ( ( F_16 != bot_bot_pname_o )
% 0.29/0.68 => ( ~ ( member_pname @ X @ F_16 )
% 0.29/0.68 => ( ( P_4 @ F_16 )
% 0.29/0.68 => ( P_4 @ ( insert_pname @ X @ F_16 ) ) ) ) ) )
% 0.29/0.68 => ( P_4 @ F_15 ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_461_folding__one__idem_Oin__idem,axiom,
% 0.29/0.68 ! [X_19: hoare_1775062406iple_a,A_50: hoare_1775062406iple_a > $o,F_14: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,F_13: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
% 0.29/0.68 ( ( finite1358382848iple_a @ F_14 @ F_13 )
% 0.29/0.68 => ( ( finite2063573081iple_a @ A_50 )
% 0.29/0.68 => ( ( member2122167641iple_a @ X_19 @ A_50 )
% 0.29/0.68 => ( ( F_14 @ X_19 @ ( F_13 @ A_50 ) )
% 0.29/0.68 = ( F_13 @ A_50 ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_462_folding__one__idem_Oin__idem,axiom,
% 0.29/0.68 ! [X_19: pname,A_50: pname > $o,F_14: pname > pname > pname,F_13: ( pname > $o ) > pname] :
% 0.29/0.68 ( ( finite89670078_pname @ F_14 @ F_13 )
% 0.29/0.68 => ( ( finite_finite_pname @ A_50 )
% 0.29/0.68 => ( ( member_pname @ X_19 @ A_50 )
% 0.29/0.68 => ( ( F_14 @ X_19 @ ( F_13 @ A_50 ) )
% 0.29/0.68 = ( F_13 @ A_50 ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_463_folding__one__idem_Ohom__commute,axiom,
% 0.29/0.68 ! [N_3: pname > $o,H_1: pname > pname,F_12: pname > pname > pname,F_11: ( pname > $o ) > pname] :
% 0.29/0.68 ( ( finite89670078_pname @ F_12 @ F_11 )
% 0.29/0.68 => ( ! [X: pname,Y_2: pname] :
% 0.29/0.68 ( ( H_1 @ ( F_12 @ X @ Y_2 ) )
% 0.29/0.68 = ( F_12 @ ( H_1 @ X ) @ ( H_1 @ Y_2 ) ) )
% 0.29/0.68 => ( ( finite_finite_pname @ N_3 )
% 0.29/0.68 => ( ( N_3 != bot_bot_pname_o )
% 0.29/0.68 => ( ( H_1 @ ( F_11 @ N_3 ) )
% 0.29/0.68 = ( F_11 @ ( image_pname_pname @ H_1 @ N_3 ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_464_folding__one__idem_Ohom__commute,axiom,
% 0.29/0.68 ! [N_3: hoare_1775062406iple_a > $o,H_1: hoare_1775062406iple_a > hoare_1775062406iple_a,F_12: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,F_11: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
% 0.29/0.68 ( ( finite1358382848iple_a @ F_12 @ F_11 )
% 0.29/0.68 => ( ! [X: hoare_1775062406iple_a,Y_2: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( H_1 @ ( F_12 @ X @ Y_2 ) )
% 0.29/0.68 = ( F_12 @ ( H_1 @ X ) @ ( H_1 @ Y_2 ) ) )
% 0.29/0.68 => ( ( finite2063573081iple_a @ N_3 )
% 0.29/0.68 => ( ( N_3 != bot_bo751897185le_a_o )
% 0.29/0.68 => ( ( H_1 @ ( F_11 @ N_3 ) )
% 0.29/0.68 = ( F_11 @ ( image_1170193413iple_a @ H_1 @ N_3 ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_465_folding__one__idem_Ohom__commute,axiom,
% 0.29/0.68 ! [N_3: hoare_1167836817_state > $o,H_1: hoare_1167836817_state > hoare_1167836817_state,F_12: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_11: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.29/0.68 ( ( finite806517911_state @ F_12 @ F_11 )
% 0.29/0.68 => ( ! [X: hoare_1167836817_state,Y_2: hoare_1167836817_state] :
% 0.29/0.68 ( ( H_1 @ ( F_12 @ X @ Y_2 ) )
% 0.29/0.68 = ( F_12 @ ( H_1 @ X ) @ ( H_1 @ Y_2 ) ) )
% 0.29/0.68 => ( ( finite1084549118_state @ N_3 )
% 0.29/0.68 => ( ( N_3 != bot_bo70021908tate_o )
% 0.29/0.68 => ( ( H_1 @ ( F_11 @ N_3 ) )
% 0.29/0.68 = ( F_11 @ ( image_31595733_state @ H_1 @ N_3 ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_466_folding__one_Oinsert,axiom,
% 0.29/0.68 ! [X_18: hoare_1167836817_state,A_49: hoare_1167836817_state > $o,F_10: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_9: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.29/0.68 ( ( finite1074406356_state @ F_10 @ F_9 )
% 0.29/0.68 => ( ( finite1084549118_state @ A_49 )
% 0.29/0.68 => ( ~ ( member2058392318_state @ X_18 @ A_49 )
% 0.29/0.68 => ( ( A_49 != bot_bo70021908tate_o )
% 0.29/0.68 => ( ( F_9 @ ( insert2134838167_state @ X_18 @ A_49 ) )
% 0.29/0.68 = ( F_10 @ X_18 @ ( F_9 @ A_49 ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_467_folding__one_Oinsert,axiom,
% 0.29/0.68 ! [X_18: hoare_1775062406iple_a,A_49: hoare_1775062406iple_a > $o,F_10: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,F_9: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
% 0.29/0.68 ( ( finite2078349315iple_a @ F_10 @ F_9 )
% 0.29/0.68 => ( ( finite2063573081iple_a @ A_49 )
% 0.29/0.68 => ( ~ ( member2122167641iple_a @ X_18 @ A_49 )
% 0.29/0.68 => ( ( A_49 != bot_bo751897185le_a_o )
% 0.29/0.68 => ( ( F_9 @ ( insert1281456128iple_a @ X_18 @ A_49 ) )
% 0.29/0.68 = ( F_10 @ X_18 @ ( F_9 @ A_49 ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_468_folding__one_Oinsert,axiom,
% 0.29/0.68 ! [X_18: pname,A_49: pname > $o,F_10: pname > pname > pname,F_9: ( pname > $o ) > pname] :
% 0.29/0.68 ( ( finite1282449217_pname @ F_10 @ F_9 )
% 0.29/0.68 => ( ( finite_finite_pname @ A_49 )
% 0.29/0.68 => ( ~ ( member_pname @ X_18 @ A_49 )
% 0.29/0.68 => ( ( A_49 != bot_bot_pname_o )
% 0.29/0.68 => ( ( F_9 @ ( insert_pname @ X_18 @ A_49 ) )
% 0.29/0.68 = ( F_10 @ X_18 @ ( F_9 @ A_49 ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_469_folding__one_Osingleton,axiom,
% 0.29/0.68 ! [X_17: hoare_1167836817_state,F_8: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_7: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.29/0.68 ( ( finite1074406356_state @ F_8 @ F_7 )
% 0.29/0.68 => ( ( F_7 @ ( insert2134838167_state @ X_17 @ bot_bo70021908tate_o ) )
% 0.29/0.68 = X_17 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_470_folding__one_Osingleton,axiom,
% 0.29/0.68 ! [X_17: hoare_1775062406iple_a,F_8: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,F_7: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
% 0.29/0.68 ( ( finite2078349315iple_a @ F_8 @ F_7 )
% 0.29/0.68 => ( ( F_7 @ ( insert1281456128iple_a @ X_17 @ bot_bo751897185le_a_o ) )
% 0.29/0.68 = X_17 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_471_folding__one_Osingleton,axiom,
% 0.29/0.68 ! [X_17: pname,F_8: pname > pname > pname,F_7: ( pname > $o ) > pname] :
% 0.29/0.68 ( ( finite1282449217_pname @ F_8 @ F_7 )
% 0.29/0.68 => ( ( F_7 @ ( insert_pname @ X_17 @ bot_bot_pname_o ) )
% 0.29/0.68 = X_17 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_472_folding__one_Oclosed,axiom,
% 0.29/0.68 ! [A_48: hoare_1167836817_state > $o,F_6: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_5: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.29/0.68 ( ( finite1074406356_state @ F_6 @ F_5 )
% 0.29/0.68 => ( ( finite1084549118_state @ A_48 )
% 0.29/0.68 => ( ( A_48 != bot_bo70021908tate_o )
% 0.29/0.68 => ( ! [X: hoare_1167836817_state,Y_2: hoare_1167836817_state] : ( member2058392318_state @ ( F_6 @ X @ Y_2 ) @ ( insert2134838167_state @ X @ ( insert2134838167_state @ Y_2 @ bot_bo70021908tate_o ) ) )
% 0.29/0.68 => ( member2058392318_state @ ( F_5 @ A_48 ) @ A_48 ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_473_folding__one_Oclosed,axiom,
% 0.29/0.68 ! [A_48: hoare_1775062406iple_a > $o,F_6: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,F_5: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
% 0.29/0.68 ( ( finite2078349315iple_a @ F_6 @ F_5 )
% 0.29/0.68 => ( ( finite2063573081iple_a @ A_48 )
% 0.29/0.68 => ( ( A_48 != bot_bo751897185le_a_o )
% 0.29/0.68 => ( ! [X: hoare_1775062406iple_a,Y_2: hoare_1775062406iple_a] : ( member2122167641iple_a @ ( F_6 @ X @ Y_2 ) @ ( insert1281456128iple_a @ X @ ( insert1281456128iple_a @ Y_2 @ bot_bo751897185le_a_o ) ) )
% 0.29/0.68 => ( member2122167641iple_a @ ( F_5 @ A_48 ) @ A_48 ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_474_folding__one_Oclosed,axiom,
% 0.29/0.68 ! [A_48: pname > $o,F_6: pname > pname > pname,F_5: ( pname > $o ) > pname] :
% 0.29/0.68 ( ( finite1282449217_pname @ F_6 @ F_5 )
% 0.29/0.68 => ( ( finite_finite_pname @ A_48 )
% 0.29/0.68 => ( ( A_48 != bot_bot_pname_o )
% 0.29/0.68 => ( ! [X: pname,Y_2: pname] : ( member_pname @ ( F_6 @ X @ Y_2 ) @ ( insert_pname @ X @ ( insert_pname @ Y_2 @ bot_bot_pname_o ) ) )
% 0.29/0.68 => ( member_pname @ ( F_5 @ A_48 ) @ A_48 ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_475_evaln__max2,axiom,
% 0.29/0.68 ! [C2: com,S2: state,N2: nat,T2: state,C1: com,S1: state,N1: nat,T1: state] :
% 0.29/0.68 ( ( evaln @ C1 @ S1 @ N1 @ T1 )
% 0.29/0.68 => ( ( evaln @ C2 @ S2 @ N2 @ T2 )
% 0.29/0.68 => ? [N: nat] :
% 0.29/0.68 ( ( evaln @ C1 @ S1 @ N @ T1 )
% 0.29/0.68 & ( evaln @ C2 @ S2 @ N @ T2 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_476_mk__disjoint__insert,axiom,
% 0.29/0.68 ! [A_47: hoare_1167836817_state,A_46: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( member2058392318_state @ A_47 @ A_46 )
% 0.29/0.68 => ? [B_34: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( A_46
% 0.29/0.68 = ( insert2134838167_state @ A_47 @ B_34 ) )
% 0.29/0.68 & ~ ( member2058392318_state @ A_47 @ B_34 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_477_mk__disjoint__insert,axiom,
% 0.29/0.68 ! [A_47: hoare_1775062406iple_a,A_46: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ A_47 @ A_46 )
% 0.29/0.68 => ? [B_34: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( A_46
% 0.29/0.68 = ( insert1281456128iple_a @ A_47 @ B_34 ) )
% 0.29/0.68 & ~ ( member2122167641iple_a @ A_47 @ B_34 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_478_mk__disjoint__insert,axiom,
% 0.29/0.68 ! [A_47: pname,A_46: pname > $o] :
% 0.29/0.68 ( ( member_pname @ A_47 @ A_46 )
% 0.29/0.68 => ? [B_34: pname > $o] :
% 0.29/0.68 ( ( A_46
% 0.29/0.68 = ( insert_pname @ A_47 @ B_34 ) )
% 0.29/0.68 & ~ ( member_pname @ A_47 @ B_34 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_479_Set_Oset__insert,axiom,
% 0.29/0.68 ! [X_16: hoare_1167836817_state,A_45: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( member2058392318_state @ X_16 @ A_45 )
% 0.29/0.68 => ~ ! [B_34: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( A_45
% 0.29/0.68 = ( insert2134838167_state @ X_16 @ B_34 ) )
% 0.29/0.68 => ( member2058392318_state @ X_16 @ B_34 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_480_Set_Oset__insert,axiom,
% 0.29/0.68 ! [X_16: hoare_1775062406iple_a,A_45: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ X_16 @ A_45 )
% 0.29/0.68 => ~ ! [B_34: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( A_45
% 0.29/0.68 = ( insert1281456128iple_a @ X_16 @ B_34 ) )
% 0.29/0.68 => ( member2122167641iple_a @ X_16 @ B_34 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_481_Set_Oset__insert,axiom,
% 0.29/0.68 ! [X_16: pname,A_45: pname > $o] :
% 0.29/0.68 ( ( member_pname @ X_16 @ A_45 )
% 0.29/0.68 => ~ ! [B_34: pname > $o] :
% 0.29/0.68 ( ( A_45
% 0.29/0.68 = ( insert_pname @ X_16 @ B_34 ) )
% 0.29/0.68 => ( member_pname @ X_16 @ B_34 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_482_equals0I,axiom,
% 0.29/0.68 ! [A_44: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ! [Y_2: hoare_1775062406iple_a] :
% 0.29/0.68 ~ ( member2122167641iple_a @ Y_2 @ A_44 )
% 0.29/0.68 => ( A_44 = bot_bo751897185le_a_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_483_equals0I,axiom,
% 0.29/0.68 ! [A_44: pname > $o] :
% 0.29/0.68 ( ! [Y_2: pname] :
% 0.29/0.68 ~ ( member_pname @ Y_2 @ A_44 )
% 0.29/0.68 => ( A_44 = bot_bot_pname_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_484_equals0I,axiom,
% 0.29/0.68 ! [A_44: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ! [Y_2: hoare_1167836817_state] :
% 0.29/0.68 ~ ( member2058392318_state @ Y_2 @ A_44 )
% 0.29/0.68 => ( A_44 = bot_bo70021908tate_o ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_485_Sup__fin_Ounion__idem,axiom,
% 0.29/0.68 ! [B_33: $o > $o,A_43: $o > $o] :
% 0.29/0.68 ( ( finite_finite_o @ A_43 )
% 0.29/0.68 => ( ( A_43 != bot_bot_o_o )
% 0.29/0.68 => ( ( finite_finite_o @ B_33 )
% 0.29/0.68 => ( ( B_33 != bot_bot_o_o )
% 0.29/0.68 => ( ( big_la727467310_fin_o @ ( semila2062604954up_o_o @ A_43 @ B_33 ) )
% 0.29/0.68 <=> ( semila10642723_sup_o @ ( big_la727467310_fin_o @ A_43 ) @ ( big_la727467310_fin_o @ B_33 ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_486_Sup__fin_Ounion__idem,axiom,
% 0.29/0.68 ! [B_33: ( pname > $o ) > $o,A_43: ( pname > $o ) > $o] :
% 0.29/0.68 ( ( finite297249702name_o @ A_43 )
% 0.29/0.68 => ( ( A_43 != bot_bot_pname_o_o )
% 0.29/0.68 => ( ( finite297249702name_o @ B_33 )
% 0.29/0.68 => ( ( B_33 != bot_bot_pname_o_o )
% 0.29/0.68 => ( ( big_la1286884090name_o @ ( semila181081674me_o_o @ A_43 @ B_33 ) )
% 0.29/0.68 = ( semila1780557381name_o @ ( big_la1286884090name_o @ A_43 ) @ ( big_la1286884090name_o @ B_33 ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_487_Sup__fin_Ounion__idem,axiom,
% 0.29/0.68 ! [B_33: ( hoare_1167836817_state > $o ) > $o,A_43: ( hoare_1167836817_state > $o ) > $o] :
% 0.29/0.68 ( ( finite1380128977tate_o @ A_43 )
% 0.29/0.68 => ( ( A_43 != bot_bo691907561te_o_o )
% 0.29/0.68 => ( ( finite1380128977tate_o @ B_33 )
% 0.29/0.68 => ( ( B_33 != bot_bo691907561te_o_o )
% 0.29/0.68 => ( ( big_la1138507389tate_o @ ( semila866907787te_o_o @ A_43 @ B_33 ) )
% 0.29/0.68 = ( semila1172322802tate_o @ ( big_la1138507389tate_o @ A_43 ) @ ( big_la1138507389tate_o @ B_33 ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_488_Sup__fin_Ounion__idem,axiom,
% 0.29/0.68 ! [B_33: ( hoare_1775062406iple_a > $o ) > $o,A_43: ( hoare_1775062406iple_a > $o ) > $o] :
% 0.29/0.68 ( ( finite789576932le_a_o @ A_43 )
% 0.29/0.68 => ( ( A_43 != bot_bo1976773294_a_o_o )
% 0.29/0.68 => ( ( finite789576932le_a_o @ B_33 )
% 0.29/0.68 => ( ( B_33 != bot_bo1976773294_a_o_o )
% 0.29/0.68 => ( ( big_la1843772984le_a_o @ ( semila2069193356_a_o_o @ A_43 @ B_33 ) )
% 0.29/0.68 = ( semila13410563le_a_o @ ( big_la1843772984le_a_o @ A_43 ) @ ( big_la1843772984le_a_o @ B_33 ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_489_Sup__fin_Oin__idem,axiom,
% 0.29/0.68 ! [X_15: $o,A_42: $o > $o] :
% 0.29/0.68 ( ( finite_finite_o @ A_42 )
% 0.29/0.68 => ( ( member_o @ X_15 @ A_42 )
% 0.29/0.68 => ( ( semila10642723_sup_o @ X_15 @ ( big_la727467310_fin_o @ A_42 ) )
% 0.29/0.68 <=> ( big_la727467310_fin_o @ A_42 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_490_Sup__fin_Oin__idem,axiom,
% 0.29/0.68 ! [X_15: pname > $o,A_42: ( pname > $o ) > $o] :
% 0.29/0.68 ( ( finite297249702name_o @ A_42 )
% 0.29/0.68 => ( ( member_pname_o @ X_15 @ A_42 )
% 0.29/0.68 => ( ( semila1780557381name_o @ X_15 @ ( big_la1286884090name_o @ A_42 ) )
% 0.29/0.68 = ( big_la1286884090name_o @ A_42 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_491_Sup__fin_Oin__idem,axiom,
% 0.29/0.68 ! [X_15: hoare_1167836817_state > $o,A_42: ( hoare_1167836817_state > $o ) > $o] :
% 0.29/0.68 ( ( finite1380128977tate_o @ A_42 )
% 0.29/0.68 => ( ( member864234961tate_o @ X_15 @ A_42 )
% 0.29/0.68 => ( ( semila1172322802tate_o @ X_15 @ ( big_la1138507389tate_o @ A_42 ) )
% 0.29/0.68 = ( big_la1138507389tate_o @ A_42 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_492_Sup__fin_Oin__idem,axiom,
% 0.29/0.68 ! [X_15: hoare_1775062406iple_a > $o,A_42: ( hoare_1775062406iple_a > $o ) > $o] :
% 0.29/0.68 ( ( finite789576932le_a_o @ A_42 )
% 0.29/0.68 => ( ( member1207314404le_a_o @ X_15 @ A_42 )
% 0.29/0.68 => ( ( semila13410563le_a_o @ X_15 @ ( big_la1843772984le_a_o @ A_42 ) )
% 0.29/0.68 = ( big_la1843772984le_a_o @ A_42 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_493_Sup__fin_Oinsert,axiom,
% 0.29/0.68 ! [X_14: $o,A_41: $o > $o] :
% 0.29/0.68 ( ( finite_finite_o @ A_41 )
% 0.29/0.68 => ( ~ ( member_o @ X_14 @ A_41 )
% 0.29/0.68 => ( ( A_41 != bot_bot_o_o )
% 0.29/0.68 => ( ( big_la727467310_fin_o @ ( insert_o @ X_14 @ A_41 ) )
% 0.29/0.68 <=> ( semila10642723_sup_o @ X_14 @ ( big_la727467310_fin_o @ A_41 ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_494_Sup__fin_Oinsert,axiom,
% 0.29/0.68 ! [X_14: pname > $o,A_41: ( pname > $o ) > $o] :
% 0.29/0.68 ( ( finite297249702name_o @ A_41 )
% 0.29/0.68 => ( ~ ( member_pname_o @ X_14 @ A_41 )
% 0.29/0.68 => ( ( A_41 != bot_bot_pname_o_o )
% 0.29/0.68 => ( ( big_la1286884090name_o @ ( insert_pname_o @ X_14 @ A_41 ) )
% 0.29/0.68 = ( semila1780557381name_o @ X_14 @ ( big_la1286884090name_o @ A_41 ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_495_Sup__fin_Oinsert,axiom,
% 0.29/0.68 ! [X_14: hoare_1167836817_state > $o,A_41: ( hoare_1167836817_state > $o ) > $o] :
% 0.29/0.68 ( ( finite1380128977tate_o @ A_41 )
% 0.29/0.68 => ( ~ ( member864234961tate_o @ X_14 @ A_41 )
% 0.29/0.68 => ( ( A_41 != bot_bo691907561te_o_o )
% 0.29/0.68 => ( ( big_la1138507389tate_o @ ( insert999278200tate_o @ X_14 @ A_41 ) )
% 0.29/0.68 = ( semila1172322802tate_o @ X_14 @ ( big_la1138507389tate_o @ A_41 ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_496_Sup__fin_Oinsert,axiom,
% 0.29/0.68 ! [X_14: hoare_1775062406iple_a > $o,A_41: ( hoare_1775062406iple_a > $o ) > $o] :
% 0.29/0.68 ( ( finite789576932le_a_o @ A_41 )
% 0.29/0.68 => ( ~ ( member1207314404le_a_o @ X_14 @ A_41 )
% 0.29/0.68 => ( ( A_41 != bot_bo1976773294_a_o_o )
% 0.29/0.68 => ( ( big_la1843772984le_a_o @ ( insert1210049533le_a_o @ X_14 @ A_41 ) )
% 0.29/0.68 = ( semila13410563le_a_o @ X_14 @ ( big_la1843772984le_a_o @ A_41 ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_497_Sup__fin_Oinsert__idem,axiom,
% 0.29/0.68 ! [X_13: $o,A_40: $o > $o] :
% 0.29/0.68 ( ( finite_finite_o @ A_40 )
% 0.29/0.68 => ( ( A_40 != bot_bot_o_o )
% 0.29/0.68 => ( ( big_la727467310_fin_o @ ( insert_o @ X_13 @ A_40 ) )
% 0.29/0.68 <=> ( semila10642723_sup_o @ X_13 @ ( big_la727467310_fin_o @ A_40 ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_498_Sup__fin_Oinsert__idem,axiom,
% 0.29/0.68 ! [X_13: pname > $o,A_40: ( pname > $o ) > $o] :
% 0.29/0.68 ( ( finite297249702name_o @ A_40 )
% 0.29/0.68 => ( ( A_40 != bot_bot_pname_o_o )
% 0.29/0.68 => ( ( big_la1286884090name_o @ ( insert_pname_o @ X_13 @ A_40 ) )
% 0.29/0.68 = ( semila1780557381name_o @ X_13 @ ( big_la1286884090name_o @ A_40 ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_499_Sup__fin_Oinsert__idem,axiom,
% 0.29/0.68 ! [X_13: hoare_1167836817_state > $o,A_40: ( hoare_1167836817_state > $o ) > $o] :
% 0.29/0.68 ( ( finite1380128977tate_o @ A_40 )
% 0.29/0.68 => ( ( A_40 != bot_bo691907561te_o_o )
% 0.29/0.68 => ( ( big_la1138507389tate_o @ ( insert999278200tate_o @ X_13 @ A_40 ) )
% 0.29/0.68 = ( semila1172322802tate_o @ X_13 @ ( big_la1138507389tate_o @ A_40 ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_500_Sup__fin_Oinsert__idem,axiom,
% 0.29/0.68 ! [X_13: hoare_1775062406iple_a > $o,A_40: ( hoare_1775062406iple_a > $o ) > $o] :
% 0.29/0.68 ( ( finite789576932le_a_o @ A_40 )
% 0.29/0.68 => ( ( A_40 != bot_bo1976773294_a_o_o )
% 0.29/0.68 => ( ( big_la1843772984le_a_o @ ( insert1210049533le_a_o @ X_13 @ A_40 ) )
% 0.29/0.68 = ( semila13410563le_a_o @ X_13 @ ( big_la1843772984le_a_o @ A_40 ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_501_Sup__fin_Ohom__commute,axiom,
% 0.29/0.68 ! [N_2: $o > $o,H: $o > $o] :
% 0.29/0.68 ( ! [X: $o,Y_2: $o] :
% 0.29/0.68 ( ( H @ ( semila10642723_sup_o @ X @ Y_2 ) )
% 0.29/0.68 <=> ( semila10642723_sup_o @ ( H @ X ) @ ( H @ Y_2 ) ) )
% 0.29/0.68 => ( ( finite_finite_o @ N_2 )
% 0.29/0.68 => ( ( N_2 != bot_bot_o_o )
% 0.29/0.68 => ( ( H @ ( big_la727467310_fin_o @ N_2 ) )
% 0.29/0.68 <=> ( big_la727467310_fin_o @ ( image_o_o @ H @ N_2 ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_502_Sup__fin_Ohom__commute,axiom,
% 0.29/0.68 ! [N_2: ( pname > $o ) > $o,H: ( pname > $o ) > pname > $o] :
% 0.29/0.68 ( ! [X: pname > $o,Y_2: pname > $o] :
% 0.29/0.68 ( ( H @ ( semila1780557381name_o @ X @ Y_2 ) )
% 0.29/0.68 = ( semila1780557381name_o @ ( H @ X ) @ ( H @ Y_2 ) ) )
% 0.29/0.68 => ( ( finite297249702name_o @ N_2 )
% 0.29/0.68 => ( ( N_2 != bot_bot_pname_o_o )
% 0.29/0.68 => ( ( H @ ( big_la1286884090name_o @ N_2 ) )
% 0.29/0.68 = ( big_la1286884090name_o @ ( image_1085733413name_o @ H @ N_2 ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_503_Sup__fin_Ohom__commute,axiom,
% 0.29/0.68 ! [N_2: ( hoare_1167836817_state > $o ) > $o,H: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o] :
% 0.29/0.68 ( ! [X: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( H @ ( semila1172322802tate_o @ X @ Y_2 ) )
% 0.29/0.68 = ( semila1172322802tate_o @ ( H @ X ) @ ( H @ Y_2 ) ) )
% 0.29/0.68 => ( ( finite1380128977tate_o @ N_2 )
% 0.29/0.68 => ( ( N_2 != bot_bo691907561te_o_o )
% 0.29/0.68 => ( ( H @ ( big_la1138507389tate_o @ N_2 ) )
% 0.29/0.68 = ( big_la1138507389tate_o @ ( image_1488525317tate_o @ H @ N_2 ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_504_Sup__fin_Ohom__commute,axiom,
% 0.29/0.68 ! [N_2: ( hoare_1775062406iple_a > $o ) > $o,H: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ! [X: hoare_1775062406iple_a > $o,Y_2: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( H @ ( semila13410563le_a_o @ X @ Y_2 ) )
% 0.29/0.68 = ( semila13410563le_a_o @ ( H @ X ) @ ( H @ Y_2 ) ) )
% 0.29/0.68 => ( ( finite789576932le_a_o @ N_2 )
% 0.29/0.68 => ( ( N_2 != bot_bo1976773294_a_o_o )
% 0.29/0.68 => ( ( H @ ( big_la1843772984le_a_o @ N_2 ) )
% 0.29/0.68 = ( big_la1843772984le_a_o @ ( image_2014247585le_a_o @ H @ N_2 ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_505_Sup__fin_Oclosed,axiom,
% 0.29/0.68 ! [A_39: $o > $o] :
% 0.29/0.68 ( ( finite_finite_o @ A_39 )
% 0.29/0.68 => ( ( A_39 != bot_bot_o_o )
% 0.29/0.68 => ( ! [X: $o,Y_2: $o] : ( member_o @ ( semila10642723_sup_o @ X @ Y_2 ) @ ( insert_o @ X @ ( insert_o @ Y_2 @ bot_bot_o_o ) ) )
% 0.29/0.68 => ( member_o @ ( big_la727467310_fin_o @ A_39 ) @ A_39 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_506_Sup__fin_Oclosed,axiom,
% 0.29/0.68 ! [A_39: ( pname > $o ) > $o] :
% 0.29/0.68 ( ( finite297249702name_o @ A_39 )
% 0.29/0.68 => ( ( A_39 != bot_bot_pname_o_o )
% 0.29/0.68 => ( ! [X: pname > $o,Y_2: pname > $o] : ( member_pname_o @ ( semila1780557381name_o @ X @ Y_2 ) @ ( insert_pname_o @ X @ ( insert_pname_o @ Y_2 @ bot_bot_pname_o_o ) ) )
% 0.29/0.68 => ( member_pname_o @ ( big_la1286884090name_o @ A_39 ) @ A_39 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_507_Sup__fin_Oclosed,axiom,
% 0.29/0.68 ! [A_39: ( hoare_1167836817_state > $o ) > $o] :
% 0.29/0.68 ( ( finite1380128977tate_o @ A_39 )
% 0.29/0.68 => ( ( A_39 != bot_bo691907561te_o_o )
% 0.29/0.68 => ( ! [X: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o] : ( member864234961tate_o @ ( semila1172322802tate_o @ X @ Y_2 ) @ ( insert999278200tate_o @ X @ ( insert999278200tate_o @ Y_2 @ bot_bo691907561te_o_o ) ) )
% 0.29/0.68 => ( member864234961tate_o @ ( big_la1138507389tate_o @ A_39 ) @ A_39 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_508_Sup__fin_Oclosed,axiom,
% 0.29/0.68 ! [A_39: ( hoare_1775062406iple_a > $o ) > $o] :
% 0.29/0.68 ( ( finite789576932le_a_o @ A_39 )
% 0.29/0.68 => ( ( A_39 != bot_bo1976773294_a_o_o )
% 0.29/0.68 => ( ! [X: hoare_1775062406iple_a > $o,Y_2: hoare_1775062406iple_a > $o] : ( member1207314404le_a_o @ ( semila13410563le_a_o @ X @ Y_2 ) @ ( insert1210049533le_a_o @ X @ ( insert1210049533le_a_o @ Y_2 @ bot_bo1976773294_a_o_o ) ) )
% 0.29/0.68 => ( member1207314404le_a_o @ ( big_la1843772984le_a_o @ A_39 ) @ A_39 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_509_Sup__fin_Ounion__inter,axiom,
% 0.29/0.68 ! [B_32: $o > $o,A_38: $o > $o] :
% 0.29/0.68 ( ( finite_finite_o @ A_38 )
% 0.29/0.68 => ( ( finite_finite_o @ B_32 )
% 0.29/0.68 => ( ( ( semila232696320nf_o_o @ A_38 @ B_32 )
% 0.29/0.68 != bot_bot_o_o )
% 0.29/0.68 => ( ( semila10642723_sup_o @ ( big_la727467310_fin_o @ ( semila2062604954up_o_o @ A_38 @ B_32 ) ) @ ( big_la727467310_fin_o @ ( semila232696320nf_o_o @ A_38 @ B_32 ) ) )
% 0.29/0.68 <=> ( semila10642723_sup_o @ ( big_la727467310_fin_o @ A_38 ) @ ( big_la727467310_fin_o @ B_32 ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_510_Sup__fin_Ounion__inter,axiom,
% 0.29/0.68 ! [B_32: ( pname > $o ) > $o,A_38: ( pname > $o ) > $o] :
% 0.29/0.68 ( ( finite297249702name_o @ A_38 )
% 0.29/0.68 => ( ( finite297249702name_o @ B_32 )
% 0.29/0.68 => ( ( ( semila2013987940me_o_o @ A_38 @ B_32 )
% 0.29/0.68 != bot_bot_pname_o_o )
% 0.29/0.68 => ( ( semila1780557381name_o @ ( big_la1286884090name_o @ ( semila181081674me_o_o @ A_38 @ B_32 ) ) @ ( big_la1286884090name_o @ ( semila2013987940me_o_o @ A_38 @ B_32 ) ) )
% 0.29/0.68 = ( semila1780557381name_o @ ( big_la1286884090name_o @ A_38 ) @ ( big_la1286884090name_o @ B_32 ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_511_Sup__fin_Ounion__inter,axiom,
% 0.29/0.68 ! [B_32: ( hoare_1167836817_state > $o ) > $o,A_38: ( hoare_1167836817_state > $o ) > $o] :
% 0.29/0.68 ( ( finite1380128977tate_o @ A_38 )
% 0.29/0.68 => ( ( finite1380128977tate_o @ B_32 )
% 0.29/0.68 => ( ( ( semila1758709489te_o_o @ A_38 @ B_32 )
% 0.29/0.68 != bot_bo691907561te_o_o )
% 0.29/0.68 => ( ( semila1172322802tate_o @ ( big_la1138507389tate_o @ ( semila866907787te_o_o @ A_38 @ B_32 ) ) @ ( big_la1138507389tate_o @ ( semila1758709489te_o_o @ A_38 @ B_32 ) ) )
% 0.29/0.68 = ( semila1172322802tate_o @ ( big_la1138507389tate_o @ A_38 ) @ ( big_la1138507389tate_o @ B_32 ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_512_Sup__fin_Ounion__inter,axiom,
% 0.29/0.68 ! [B_32: ( hoare_1775062406iple_a > $o ) > $o,A_38: ( hoare_1775062406iple_a > $o ) > $o] :
% 0.29/0.68 ( ( finite789576932le_a_o @ A_38 )
% 0.29/0.68 => ( ( finite789576932le_a_o @ B_32 )
% 0.29/0.68 => ( ( ( semila1691990438_a_o_o @ A_38 @ B_32 )
% 0.29/0.68 != bot_bo1976773294_a_o_o )
% 0.29/0.68 => ( ( semila13410563le_a_o @ ( big_la1843772984le_a_o @ ( semila2069193356_a_o_o @ A_38 @ B_32 ) ) @ ( big_la1843772984le_a_o @ ( semila1691990438_a_o_o @ A_38 @ B_32 ) ) )
% 0.29/0.68 = ( semila13410563le_a_o @ ( big_la1843772984le_a_o @ A_38 ) @ ( big_la1843772984le_a_o @ B_32 ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_513_Sup__fin_Ounion__disjoint,axiom,
% 0.29/0.68 ! [B_31: $o > $o,A_37: $o > $o] :
% 0.29/0.68 ( ( finite_finite_o @ A_37 )
% 0.29/0.68 => ( ( A_37 != bot_bot_o_o )
% 0.29/0.68 => ( ( finite_finite_o @ B_31 )
% 0.29/0.68 => ( ( B_31 != bot_bot_o_o )
% 0.29/0.68 => ( ( ( semila232696320nf_o_o @ A_37 @ B_31 )
% 0.29/0.68 = bot_bot_o_o )
% 0.29/0.68 => ( ( big_la727467310_fin_o @ ( semila2062604954up_o_o @ A_37 @ B_31 ) )
% 0.29/0.68 <=> ( semila10642723_sup_o @ ( big_la727467310_fin_o @ A_37 ) @ ( big_la727467310_fin_o @ B_31 ) ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_514_Sup__fin_Ounion__disjoint,axiom,
% 0.29/0.68 ! [B_31: ( pname > $o ) > $o,A_37: ( pname > $o ) > $o] :
% 0.29/0.68 ( ( finite297249702name_o @ A_37 )
% 0.29/0.68 => ( ( A_37 != bot_bot_pname_o_o )
% 0.29/0.68 => ( ( finite297249702name_o @ B_31 )
% 0.29/0.68 => ( ( B_31 != bot_bot_pname_o_o )
% 0.29/0.68 => ( ( ( semila2013987940me_o_o @ A_37 @ B_31 )
% 0.29/0.68 = bot_bot_pname_o_o )
% 0.29/0.68 => ( ( big_la1286884090name_o @ ( semila181081674me_o_o @ A_37 @ B_31 ) )
% 0.29/0.68 = ( semila1780557381name_o @ ( big_la1286884090name_o @ A_37 ) @ ( big_la1286884090name_o @ B_31 ) ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_515_Sup__fin_Ounion__disjoint,axiom,
% 0.29/0.68 ! [B_31: ( hoare_1167836817_state > $o ) > $o,A_37: ( hoare_1167836817_state > $o ) > $o] :
% 0.29/0.68 ( ( finite1380128977tate_o @ A_37 )
% 0.29/0.68 => ( ( A_37 != bot_bo691907561te_o_o )
% 0.29/0.68 => ( ( finite1380128977tate_o @ B_31 )
% 0.29/0.68 => ( ( B_31 != bot_bo691907561te_o_o )
% 0.29/0.68 => ( ( ( semila1758709489te_o_o @ A_37 @ B_31 )
% 0.29/0.68 = bot_bo691907561te_o_o )
% 0.29/0.68 => ( ( big_la1138507389tate_o @ ( semila866907787te_o_o @ A_37 @ B_31 ) )
% 0.29/0.68 = ( semila1172322802tate_o @ ( big_la1138507389tate_o @ A_37 ) @ ( big_la1138507389tate_o @ B_31 ) ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_516_Sup__fin_Ounion__disjoint,axiom,
% 0.29/0.68 ! [B_31: ( hoare_1775062406iple_a > $o ) > $o,A_37: ( hoare_1775062406iple_a > $o ) > $o] :
% 0.29/0.68 ( ( finite789576932le_a_o @ A_37 )
% 0.29/0.68 => ( ( A_37 != bot_bo1976773294_a_o_o )
% 0.29/0.68 => ( ( finite789576932le_a_o @ B_31 )
% 0.29/0.68 => ( ( B_31 != bot_bo1976773294_a_o_o )
% 0.29/0.68 => ( ( ( semila1691990438_a_o_o @ A_37 @ B_31 )
% 0.29/0.68 = bot_bo1976773294_a_o_o )
% 0.29/0.68 => ( ( big_la1843772984le_a_o @ ( semila2069193356_a_o_o @ A_37 @ B_31 ) )
% 0.29/0.68 = ( semila13410563le_a_o @ ( big_la1843772984le_a_o @ A_37 ) @ ( big_la1843772984le_a_o @ B_31 ) ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_517_IntI,axiom,
% 0.29/0.68 ! [B_30: hoare_1775062406iple_a > $o,C_18: hoare_1775062406iple_a,A_36: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ C_18 @ A_36 )
% 0.29/0.68 => ( ( member2122167641iple_a @ C_18 @ B_30 )
% 0.29/0.68 => ( member2122167641iple_a @ C_18 @ ( semila966743401le_a_o @ A_36 @ B_30 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_518_IntI,axiom,
% 0.29/0.68 ! [B_30: pname > $o,C_18: pname,A_36: pname > $o] :
% 0.29/0.68 ( ( member_pname @ C_18 @ A_36 )
% 0.29/0.68 => ( ( member_pname @ C_18 @ B_30 )
% 0.29/0.68 => ( member_pname @ C_18 @ ( semila1673364395name_o @ A_36 @ B_30 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_519_IntE,axiom,
% 0.29/0.68 ! [C_17: hoare_1775062406iple_a,A_35: hoare_1775062406iple_a > $o,B_29: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ C_17 @ ( semila966743401le_a_o @ A_35 @ B_29 ) )
% 0.29/0.68 => ~ ( ( member2122167641iple_a @ C_17 @ A_35 )
% 0.29/0.68 => ~ ( member2122167641iple_a @ C_17 @ B_29 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_520_IntE,axiom,
% 0.29/0.68 ! [C_17: pname,A_35: pname > $o,B_29: pname > $o] :
% 0.29/0.68 ( ( member_pname @ C_17 @ ( semila1673364395name_o @ A_35 @ B_29 ) )
% 0.29/0.68 => ~ ( ( member_pname @ C_17 @ A_35 )
% 0.29/0.68 => ~ ( member_pname @ C_17 @ B_29 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_521_inf__bot__right,axiom,
% 0.29/0.68 ! [X_12: pname > $o] :
% 0.29/0.68 ( ( semila1673364395name_o @ X_12 @ bot_bot_pname_o )
% 0.29/0.68 = bot_bot_pname_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_522_inf__bot__right,axiom,
% 0.29/0.68 ! [X_12: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila966743401le_a_o @ X_12 @ bot_bo751897185le_a_o )
% 0.29/0.68 = bot_bo751897185le_a_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_523_inf__bot__right,axiom,
% 0.29/0.68 ! [X_12: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila179895820tate_o @ X_12 @ bot_bo70021908tate_o )
% 0.29/0.68 = bot_bo70021908tate_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_524_inf__bot__left,axiom,
% 0.29/0.68 ! [X_11: pname > $o] :
% 0.29/0.68 ( ( semila1673364395name_o @ bot_bot_pname_o @ X_11 )
% 0.29/0.68 = bot_bot_pname_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_525_inf__bot__left,axiom,
% 0.29/0.68 ! [X_11: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila966743401le_a_o @ bot_bo751897185le_a_o @ X_11 )
% 0.29/0.68 = bot_bo751897185le_a_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_526_inf__bot__left,axiom,
% 0.29/0.68 ! [X_11: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila179895820tate_o @ bot_bo70021908tate_o @ X_11 )
% 0.29/0.68 = bot_bo70021908tate_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_527_sup__inf__distrib2,axiom,
% 0.29/0.68 ! [Y_9: $o,Z_7: $o,X_10: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ ( semila854092349_inf_o @ Y_9 @ Z_7 ) @ X_10 )
% 0.29/0.68 <=> ( semila854092349_inf_o @ ( semila10642723_sup_o @ Y_9 @ X_10 ) @ ( semila10642723_sup_o @ Z_7 @ X_10 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_528_sup__inf__distrib2,axiom,
% 0.29/0.68 ! [Y_9: pname > $o,Z_7: pname > $o,X_10: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ ( semila1673364395name_o @ Y_9 @ Z_7 ) @ X_10 )
% 0.29/0.68 = ( semila1673364395name_o @ ( semila1780557381name_o @ Y_9 @ X_10 ) @ ( semila1780557381name_o @ Z_7 @ X_10 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_529_sup__inf__distrib2,axiom,
% 0.29/0.68 ! [Y_9: hoare_1167836817_state > $o,Z_7: hoare_1167836817_state > $o,X_10: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ ( semila179895820tate_o @ Y_9 @ Z_7 ) @ X_10 )
% 0.29/0.68 = ( semila179895820tate_o @ ( semila1172322802tate_o @ Y_9 @ X_10 ) @ ( semila1172322802tate_o @ Z_7 @ X_10 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_530_sup__inf__distrib2,axiom,
% 0.29/0.68 ! [Y_9: hoare_1775062406iple_a > $o,Z_7: hoare_1775062406iple_a > $o,X_10: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ ( semila966743401le_a_o @ Y_9 @ Z_7 ) @ X_10 )
% 0.29/0.68 = ( semila966743401le_a_o @ ( semila13410563le_a_o @ Y_9 @ X_10 ) @ ( semila13410563le_a_o @ Z_7 @ X_10 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_531_inf__sup__distrib2,axiom,
% 0.29/0.68 ! [Y_8: $o,Z_6: $o,X_9: $o] :
% 0.29/0.68 ( ( semila854092349_inf_o @ ( semila10642723_sup_o @ Y_8 @ Z_6 ) @ X_9 )
% 0.29/0.68 <=> ( semila10642723_sup_o @ ( semila854092349_inf_o @ Y_8 @ X_9 ) @ ( semila854092349_inf_o @ Z_6 @ X_9 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_532_inf__sup__distrib2,axiom,
% 0.29/0.68 ! [Y_8: pname > $o,Z_6: pname > $o,X_9: pname > $o] :
% 0.29/0.68 ( ( semila1673364395name_o @ ( semila1780557381name_o @ Y_8 @ Z_6 ) @ X_9 )
% 0.29/0.68 = ( semila1780557381name_o @ ( semila1673364395name_o @ Y_8 @ X_9 ) @ ( semila1673364395name_o @ Z_6 @ X_9 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_533_inf__sup__distrib2,axiom,
% 0.29/0.68 ! [Y_8: hoare_1167836817_state > $o,Z_6: hoare_1167836817_state > $o,X_9: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila179895820tate_o @ ( semila1172322802tate_o @ Y_8 @ Z_6 ) @ X_9 )
% 0.29/0.68 = ( semila1172322802tate_o @ ( semila179895820tate_o @ Y_8 @ X_9 ) @ ( semila179895820tate_o @ Z_6 @ X_9 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_534_inf__sup__distrib2,axiom,
% 0.29/0.68 ! [Y_8: hoare_1775062406iple_a > $o,Z_6: hoare_1775062406iple_a > $o,X_9: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila966743401le_a_o @ ( semila13410563le_a_o @ Y_8 @ Z_6 ) @ X_9 )
% 0.29/0.68 = ( semila13410563le_a_o @ ( semila966743401le_a_o @ Y_8 @ X_9 ) @ ( semila966743401le_a_o @ Z_6 @ X_9 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_535_sup__inf__distrib1,axiom,
% 0.29/0.68 ! [X_8: $o,Y_7: $o,Z_5: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ X_8 @ ( semila854092349_inf_o @ Y_7 @ Z_5 ) )
% 0.29/0.68 <=> ( semila854092349_inf_o @ ( semila10642723_sup_o @ X_8 @ Y_7 ) @ ( semila10642723_sup_o @ X_8 @ Z_5 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_536_sup__inf__distrib1,axiom,
% 0.29/0.68 ! [X_8: pname > $o,Y_7: pname > $o,Z_5: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ X_8 @ ( semila1673364395name_o @ Y_7 @ Z_5 ) )
% 0.29/0.68 = ( semila1673364395name_o @ ( semila1780557381name_o @ X_8 @ Y_7 ) @ ( semila1780557381name_o @ X_8 @ Z_5 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_537_sup__inf__distrib1,axiom,
% 0.29/0.68 ! [X_8: hoare_1167836817_state > $o,Y_7: hoare_1167836817_state > $o,Z_5: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ X_8 @ ( semila179895820tate_o @ Y_7 @ Z_5 ) )
% 0.29/0.68 = ( semila179895820tate_o @ ( semila1172322802tate_o @ X_8 @ Y_7 ) @ ( semila1172322802tate_o @ X_8 @ Z_5 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_538_sup__inf__distrib1,axiom,
% 0.29/0.68 ! [X_8: hoare_1775062406iple_a > $o,Y_7: hoare_1775062406iple_a > $o,Z_5: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ X_8 @ ( semila966743401le_a_o @ Y_7 @ Z_5 ) )
% 0.29/0.68 = ( semila966743401le_a_o @ ( semila13410563le_a_o @ X_8 @ Y_7 ) @ ( semila13410563le_a_o @ X_8 @ Z_5 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_539_inf__sup__distrib1,axiom,
% 0.29/0.68 ! [X_7: $o,Y_6: $o,Z_4: $o] :
% 0.29/0.68 ( ( semila854092349_inf_o @ X_7 @ ( semila10642723_sup_o @ Y_6 @ Z_4 ) )
% 0.29/0.68 <=> ( semila10642723_sup_o @ ( semila854092349_inf_o @ X_7 @ Y_6 ) @ ( semila854092349_inf_o @ X_7 @ Z_4 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_540_inf__sup__distrib1,axiom,
% 0.29/0.68 ! [X_7: pname > $o,Y_6: pname > $o,Z_4: pname > $o] :
% 0.29/0.68 ( ( semila1673364395name_o @ X_7 @ ( semila1780557381name_o @ Y_6 @ Z_4 ) )
% 0.29/0.68 = ( semila1780557381name_o @ ( semila1673364395name_o @ X_7 @ Y_6 ) @ ( semila1673364395name_o @ X_7 @ Z_4 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_541_inf__sup__distrib1,axiom,
% 0.29/0.68 ! [X_7: hoare_1167836817_state > $o,Y_6: hoare_1167836817_state > $o,Z_4: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila179895820tate_o @ X_7 @ ( semila1172322802tate_o @ Y_6 @ Z_4 ) )
% 0.29/0.68 = ( semila1172322802tate_o @ ( semila179895820tate_o @ X_7 @ Y_6 ) @ ( semila179895820tate_o @ X_7 @ Z_4 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_542_inf__sup__distrib1,axiom,
% 0.29/0.68 ! [X_7: hoare_1775062406iple_a > $o,Y_6: hoare_1775062406iple_a > $o,Z_4: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila966743401le_a_o @ X_7 @ ( semila13410563le_a_o @ Y_6 @ Z_4 ) )
% 0.29/0.68 = ( semila13410563le_a_o @ ( semila966743401le_a_o @ X_7 @ Y_6 ) @ ( semila966743401le_a_o @ X_7 @ Z_4 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_543_sup__inf__absorb,axiom,
% 0.29/0.68 ! [X_6: $o,Y_5: $o] :
% 0.29/0.68 ( ( semila10642723_sup_o @ X_6 @ ( semila854092349_inf_o @ X_6 @ Y_5 ) )
% 0.29/0.68 <=> X_6 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_544_sup__inf__absorb,axiom,
% 0.29/0.68 ! [X_6: pname > $o,Y_5: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ X_6 @ ( semila1673364395name_o @ X_6 @ Y_5 ) )
% 0.29/0.68 = X_6 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_545_sup__inf__absorb,axiom,
% 0.29/0.68 ! [X_6: hoare_1167836817_state > $o,Y_5: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ X_6 @ ( semila179895820tate_o @ X_6 @ Y_5 ) )
% 0.29/0.68 = X_6 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_546_sup__inf__absorb,axiom,
% 0.29/0.68 ! [X_6: hoare_1775062406iple_a > $o,Y_5: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ X_6 @ ( semila966743401le_a_o @ X_6 @ Y_5 ) )
% 0.29/0.68 = X_6 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_547_inf__sup__absorb,axiom,
% 0.29/0.68 ! [X_5: $o,Y_4: $o] :
% 0.29/0.68 ( ( semila854092349_inf_o @ X_5 @ ( semila10642723_sup_o @ X_5 @ Y_4 ) )
% 0.29/0.68 <=> X_5 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_548_inf__sup__absorb,axiom,
% 0.29/0.68 ! [X_5: pname > $o,Y_4: pname > $o] :
% 0.29/0.68 ( ( semila1673364395name_o @ X_5 @ ( semila1780557381name_o @ X_5 @ Y_4 ) )
% 0.29/0.68 = X_5 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_549_inf__sup__absorb,axiom,
% 0.29/0.68 ! [X_5: hoare_1167836817_state > $o,Y_4: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila179895820tate_o @ X_5 @ ( semila1172322802tate_o @ X_5 @ Y_4 ) )
% 0.29/0.68 = X_5 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_550_inf__sup__absorb,axiom,
% 0.29/0.68 ! [X_5: hoare_1775062406iple_a > $o,Y_4: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila966743401le_a_o @ X_5 @ ( semila13410563le_a_o @ X_5 @ Y_4 ) )
% 0.29/0.68 = X_5 ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_551_disjoint__iff__not__equal,axiom,
% 0.29/0.68 ! [A_34: pname > $o,B_28: pname > $o] :
% 0.29/0.68 ( ( ( semila1673364395name_o @ A_34 @ B_28 )
% 0.29/0.68 = bot_bot_pname_o )
% 0.29/0.68 <=> ! [X: pname] :
% 0.29/0.68 ( ( member_pname @ X @ A_34 )
% 0.29/0.68 => ! [Xa: pname] :
% 0.29/0.68 ( ( member_pname @ Xa @ B_28 )
% 0.29/0.68 => ( X != Xa ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_552_disjoint__iff__not__equal,axiom,
% 0.29/0.68 ! [A_34: hoare_1775062406iple_a > $o,B_28: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( ( semila966743401le_a_o @ A_34 @ B_28 )
% 0.29/0.68 = bot_bo751897185le_a_o )
% 0.29/0.68 <=> ! [X: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( member2122167641iple_a @ X @ A_34 )
% 0.29/0.68 => ! [Xa: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( member2122167641iple_a @ Xa @ B_28 )
% 0.29/0.68 => ( X != Xa ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_553_disjoint__iff__not__equal,axiom,
% 0.29/0.68 ! [A_34: hoare_1167836817_state > $o,B_28: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( ( semila179895820tate_o @ A_34 @ B_28 )
% 0.29/0.68 = bot_bo70021908tate_o )
% 0.29/0.68 <=> ! [X: hoare_1167836817_state] :
% 0.29/0.68 ( ( member2058392318_state @ X @ A_34 )
% 0.29/0.68 => ! [Xa: hoare_1167836817_state] :
% 0.29/0.68 ( ( member2058392318_state @ Xa @ B_28 )
% 0.29/0.68 => ( X != Xa ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_554_Int__empty__right,axiom,
% 0.29/0.68 ! [A_33: pname > $o] :
% 0.29/0.68 ( ( semila1673364395name_o @ A_33 @ bot_bot_pname_o )
% 0.29/0.68 = bot_bot_pname_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_555_Int__empty__right,axiom,
% 0.29/0.68 ! [A_33: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila966743401le_a_o @ A_33 @ bot_bo751897185le_a_o )
% 0.29/0.68 = bot_bo751897185le_a_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_556_Int__empty__right,axiom,
% 0.29/0.68 ! [A_33: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila179895820tate_o @ A_33 @ bot_bo70021908tate_o )
% 0.29/0.68 = bot_bo70021908tate_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_557_Int__empty__left,axiom,
% 0.29/0.68 ! [B_27: pname > $o] :
% 0.29/0.68 ( ( semila1673364395name_o @ bot_bot_pname_o @ B_27 )
% 0.29/0.68 = bot_bot_pname_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_558_Int__empty__left,axiom,
% 0.29/0.68 ! [B_27: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila966743401le_a_o @ bot_bo751897185le_a_o @ B_27 )
% 0.29/0.68 = bot_bo751897185le_a_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_559_Int__empty__left,axiom,
% 0.29/0.68 ! [B_27: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila179895820tate_o @ bot_bo70021908tate_o @ B_27 )
% 0.29/0.68 = bot_bo70021908tate_o ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_560_Int__def,axiom,
% 0.29/0.68 ! [A_32: hoare_1775062406iple_a > $o,B_26: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila966743401le_a_o @ A_32 @ B_26 )
% 0.29/0.68 = ( collec676402587iple_a
% 0.29/0.68 @ ^ [X: hoare_1775062406iple_a] : ( (&) @ ( member2122167641iple_a @ X @ A_32 ) @ ( member2122167641iple_a @ X @ B_26 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_561_Int__def,axiom,
% 0.29/0.68 ! [A_32: pname > $o,B_26: pname > $o] :
% 0.29/0.68 ( ( semila1673364395name_o @ A_32 @ B_26 )
% 0.29/0.68 = ( collect_pname
% 0.29/0.68 @ ^ [X: pname] : ( (&) @ ( member_pname @ X @ A_32 ) @ ( member_pname @ X @ B_26 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_562_Int__iff,axiom,
% 0.29/0.68 ! [C_16: hoare_1775062406iple_a,A_31: hoare_1775062406iple_a > $o,B_25: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ C_16 @ ( semila966743401le_a_o @ A_31 @ B_25 ) )
% 0.29/0.68 <=> ( ( member2122167641iple_a @ C_16 @ A_31 )
% 0.29/0.68 & ( member2122167641iple_a @ C_16 @ B_25 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_563_Int__iff,axiom,
% 0.29/0.68 ! [C_16: pname,A_31: pname > $o,B_25: pname > $o] :
% 0.29/0.68 ( ( member_pname @ C_16 @ ( semila1673364395name_o @ A_31 @ B_25 ) )
% 0.29/0.68 <=> ( ( member_pname @ C_16 @ A_31 )
% 0.29/0.68 & ( member_pname @ C_16 @ B_25 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_564_IntD1,axiom,
% 0.29/0.68 ! [C_15: hoare_1775062406iple_a,A_30: hoare_1775062406iple_a > $o,B_24: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ C_15 @ ( semila966743401le_a_o @ A_30 @ B_24 ) )
% 0.29/0.68 => ( member2122167641iple_a @ C_15 @ A_30 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_565_IntD1,axiom,
% 0.29/0.68 ! [C_15: pname,A_30: pname > $o,B_24: pname > $o] :
% 0.29/0.68 ( ( member_pname @ C_15 @ ( semila1673364395name_o @ A_30 @ B_24 ) )
% 0.29/0.68 => ( member_pname @ C_15 @ A_30 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_566_IntD2,axiom,
% 0.29/0.68 ! [C_14: hoare_1775062406iple_a,A_29: hoare_1775062406iple_a > $o,B_23: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ C_14 @ ( semila966743401le_a_o @ A_29 @ B_23 ) )
% 0.29/0.68 => ( member2122167641iple_a @ C_14 @ B_23 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_567_IntD2,axiom,
% 0.29/0.68 ! [C_14: pname,A_29: pname > $o,B_23: pname > $o] :
% 0.29/0.68 ( ( member_pname @ C_14 @ ( semila1673364395name_o @ A_29 @ B_23 ) )
% 0.29/0.68 => ( member_pname @ C_14 @ B_23 ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_568_Collect__conj__eq,axiom,
% 0.29/0.68 ! [P_3: hoare_1775062406iple_a > $o,Q: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( collec676402587iple_a
% 0.29/0.68 @ ^ [X: hoare_1775062406iple_a] : ( (&) @ ( P_3 @ X ) @ ( Q @ X ) ) )
% 0.29/0.68 = ( semila966743401le_a_o @ ( collec676402587iple_a @ P_3 ) @ ( collec676402587iple_a @ Q ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_569_Collect__conj__eq,axiom,
% 0.29/0.68 ! [P_3: pname > $o,Q: pname > $o] :
% 0.29/0.68 ( ( collect_pname
% 0.29/0.68 @ ^ [X: pname] : ( (&) @ ( P_3 @ X ) @ ( Q @ X ) ) )
% 0.29/0.68 = ( semila1673364395name_o @ ( collect_pname @ P_3 ) @ ( collect_pname @ Q ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_570_Int__Collect,axiom,
% 0.29/0.68 ! [X_4: hoare_1775062406iple_a,A_28: hoare_1775062406iple_a > $o,P_2: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ X_4 @ ( semila966743401le_a_o @ A_28 @ ( collec676402587iple_a @ P_2 ) ) )
% 0.29/0.68 <=> ( ( member2122167641iple_a @ X_4 @ A_28 )
% 0.29/0.68 & ( P_2 @ X_4 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_571_Int__Collect,axiom,
% 0.29/0.68 ! [X_4: pname,A_28: pname > $o,P_2: pname > $o] :
% 0.29/0.68 ( ( member_pname @ X_4 @ ( semila1673364395name_o @ A_28 @ ( collect_pname @ P_2 ) ) )
% 0.29/0.68 <=> ( ( member_pname @ X_4 @ A_28 )
% 0.29/0.68 & ( P_2 @ X_4 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_572_inf__Int__eq,axiom,
% 0.29/0.68 ! [R: hoare_1775062406iple_a > $o,S_2: hoare_1775062406iple_a > $o,X: hoare_1775062406iple_a] :
% 0.29/0.68 ( ( semila966743401le_a_o
% 0.29/0.68 @ ^ [Y_2: hoare_1775062406iple_a] : ( member2122167641iple_a @ Y_2 @ R )
% 0.29/0.68 @ ^ [Y_2: hoare_1775062406iple_a] : ( member2122167641iple_a @ Y_2 @ S_2 )
% 0.29/0.68 @ X )
% 0.29/0.68 <=> ( member2122167641iple_a @ X @ ( semila966743401le_a_o @ R @ S_2 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_573_inf__Int__eq,axiom,
% 0.29/0.68 ! [R: pname > $o,S_2: pname > $o,X: pname] :
% 0.29/0.68 ( ( semila1673364395name_o
% 0.29/0.68 @ ^ [Y_2: pname] : ( member_pname @ Y_2 @ R )
% 0.29/0.68 @ ^ [Y_2: pname] : ( member_pname @ Y_2 @ S_2 )
% 0.29/0.68 @ X )
% 0.29/0.68 <=> ( member_pname @ X @ ( semila1673364395name_o @ R @ S_2 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_574_Un__Int__crazy,axiom,
% 0.29/0.68 ! [A_27: pname > $o,B_22: pname > $o,C_13: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ ( semila1780557381name_o @ ( semila1673364395name_o @ A_27 @ B_22 ) @ ( semila1673364395name_o @ B_22 @ C_13 ) ) @ ( semila1673364395name_o @ C_13 @ A_27 ) )
% 0.29/0.68 = ( semila1673364395name_o @ ( semila1673364395name_o @ ( semila1780557381name_o @ A_27 @ B_22 ) @ ( semila1780557381name_o @ B_22 @ C_13 ) ) @ ( semila1780557381name_o @ C_13 @ A_27 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_575_Un__Int__crazy,axiom,
% 0.29/0.68 ! [A_27: hoare_1167836817_state > $o,B_22: hoare_1167836817_state > $o,C_13: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ ( semila179895820tate_o @ A_27 @ B_22 ) @ ( semila179895820tate_o @ B_22 @ C_13 ) ) @ ( semila179895820tate_o @ C_13 @ A_27 ) )
% 0.29/0.68 = ( semila179895820tate_o @ ( semila179895820tate_o @ ( semila1172322802tate_o @ A_27 @ B_22 ) @ ( semila1172322802tate_o @ B_22 @ C_13 ) ) @ ( semila1172322802tate_o @ C_13 @ A_27 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_576_Un__Int__crazy,axiom,
% 0.29/0.68 ! [A_27: hoare_1775062406iple_a > $o,B_22: hoare_1775062406iple_a > $o,C_13: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ ( semila13410563le_a_o @ ( semila966743401le_a_o @ A_27 @ B_22 ) @ ( semila966743401le_a_o @ B_22 @ C_13 ) ) @ ( semila966743401le_a_o @ C_13 @ A_27 ) )
% 0.29/0.68 = ( semila966743401le_a_o @ ( semila966743401le_a_o @ ( semila13410563le_a_o @ A_27 @ B_22 ) @ ( semila13410563le_a_o @ B_22 @ C_13 ) ) @ ( semila13410563le_a_o @ C_13 @ A_27 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_577_Un__Int__distrib2,axiom,
% 0.29/0.68 ! [B_21: pname > $o,C_12: pname > $o,A_26: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ ( semila1673364395name_o @ B_21 @ C_12 ) @ A_26 )
% 0.29/0.68 = ( semila1673364395name_o @ ( semila1780557381name_o @ B_21 @ A_26 ) @ ( semila1780557381name_o @ C_12 @ A_26 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_578_Un__Int__distrib2,axiom,
% 0.29/0.68 ! [B_21: hoare_1167836817_state > $o,C_12: hoare_1167836817_state > $o,A_26: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ ( semila179895820tate_o @ B_21 @ C_12 ) @ A_26 )
% 0.29/0.68 = ( semila179895820tate_o @ ( semila1172322802tate_o @ B_21 @ A_26 ) @ ( semila1172322802tate_o @ C_12 @ A_26 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_579_Un__Int__distrib2,axiom,
% 0.29/0.68 ! [B_21: hoare_1775062406iple_a > $o,C_12: hoare_1775062406iple_a > $o,A_26: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ ( semila966743401le_a_o @ B_21 @ C_12 ) @ A_26 )
% 0.29/0.68 = ( semila966743401le_a_o @ ( semila13410563le_a_o @ B_21 @ A_26 ) @ ( semila13410563le_a_o @ C_12 @ A_26 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_580_Int__Un__distrib2,axiom,
% 0.29/0.68 ! [B_20: pname > $o,C_11: pname > $o,A_25: pname > $o] :
% 0.29/0.68 ( ( semila1673364395name_o @ ( semila1780557381name_o @ B_20 @ C_11 ) @ A_25 )
% 0.29/0.68 = ( semila1780557381name_o @ ( semila1673364395name_o @ B_20 @ A_25 ) @ ( semila1673364395name_o @ C_11 @ A_25 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_581_Int__Un__distrib2,axiom,
% 0.29/0.68 ! [B_20: hoare_1167836817_state > $o,C_11: hoare_1167836817_state > $o,A_25: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila179895820tate_o @ ( semila1172322802tate_o @ B_20 @ C_11 ) @ A_25 )
% 0.29/0.68 = ( semila1172322802tate_o @ ( semila179895820tate_o @ B_20 @ A_25 ) @ ( semila179895820tate_o @ C_11 @ A_25 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_582_Int__Un__distrib2,axiom,
% 0.29/0.68 ! [B_20: hoare_1775062406iple_a > $o,C_11: hoare_1775062406iple_a > $o,A_25: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila966743401le_a_o @ ( semila13410563le_a_o @ B_20 @ C_11 ) @ A_25 )
% 0.29/0.68 = ( semila13410563le_a_o @ ( semila966743401le_a_o @ B_20 @ A_25 ) @ ( semila966743401le_a_o @ C_11 @ A_25 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_583_Un__Int__distrib,axiom,
% 0.29/0.68 ! [A_24: pname > $o,B_19: pname > $o,C_10: pname > $o] :
% 0.29/0.68 ( ( semila1780557381name_o @ A_24 @ ( semila1673364395name_o @ B_19 @ C_10 ) )
% 0.29/0.68 = ( semila1673364395name_o @ ( semila1780557381name_o @ A_24 @ B_19 ) @ ( semila1780557381name_o @ A_24 @ C_10 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_584_Un__Int__distrib,axiom,
% 0.29/0.68 ! [A_24: hoare_1167836817_state > $o,B_19: hoare_1167836817_state > $o,C_10: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila1172322802tate_o @ A_24 @ ( semila179895820tate_o @ B_19 @ C_10 ) )
% 0.29/0.68 = ( semila179895820tate_o @ ( semila1172322802tate_o @ A_24 @ B_19 ) @ ( semila1172322802tate_o @ A_24 @ C_10 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_585_Un__Int__distrib,axiom,
% 0.29/0.68 ! [A_24: hoare_1775062406iple_a > $o,B_19: hoare_1775062406iple_a > $o,C_10: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila13410563le_a_o @ A_24 @ ( semila966743401le_a_o @ B_19 @ C_10 ) )
% 0.29/0.68 = ( semila966743401le_a_o @ ( semila13410563le_a_o @ A_24 @ B_19 ) @ ( semila13410563le_a_o @ A_24 @ C_10 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_586_Int__Un__distrib,axiom,
% 0.29/0.68 ! [A_23: pname > $o,B_18: pname > $o,C_9: pname > $o] :
% 0.29/0.68 ( ( semila1673364395name_o @ A_23 @ ( semila1780557381name_o @ B_18 @ C_9 ) )
% 0.29/0.68 = ( semila1780557381name_o @ ( semila1673364395name_o @ A_23 @ B_18 ) @ ( semila1673364395name_o @ A_23 @ C_9 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_587_Int__Un__distrib,axiom,
% 0.29/0.68 ! [A_23: hoare_1167836817_state > $o,B_18: hoare_1167836817_state > $o,C_9: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila179895820tate_o @ A_23 @ ( semila1172322802tate_o @ B_18 @ C_9 ) )
% 0.29/0.68 = ( semila1172322802tate_o @ ( semila179895820tate_o @ A_23 @ B_18 ) @ ( semila179895820tate_o @ A_23 @ C_9 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_588_Int__Un__distrib,axiom,
% 0.29/0.68 ! [A_23: hoare_1775062406iple_a > $o,B_18: hoare_1775062406iple_a > $o,C_9: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila966743401le_a_o @ A_23 @ ( semila13410563le_a_o @ B_18 @ C_9 ) )
% 0.29/0.68 = ( semila13410563le_a_o @ ( semila966743401le_a_o @ A_23 @ B_18 ) @ ( semila966743401le_a_o @ A_23 @ C_9 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_589_Int__insert__left__if1,axiom,
% 0.29/0.68 ! [B_17: hoare_1167836817_state > $o,A_22: hoare_1167836817_state,C_8: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( member2058392318_state @ A_22 @ C_8 )
% 0.29/0.68 => ( ( semila179895820tate_o @ ( insert2134838167_state @ A_22 @ B_17 ) @ C_8 )
% 0.29/0.68 = ( insert2134838167_state @ A_22 @ ( semila179895820tate_o @ B_17 @ C_8 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_590_Int__insert__left__if1,axiom,
% 0.29/0.68 ! [B_17: hoare_1775062406iple_a > $o,A_22: hoare_1775062406iple_a,C_8: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ A_22 @ C_8 )
% 0.29/0.68 => ( ( semila966743401le_a_o @ ( insert1281456128iple_a @ A_22 @ B_17 ) @ C_8 )
% 0.29/0.68 = ( insert1281456128iple_a @ A_22 @ ( semila966743401le_a_o @ B_17 @ C_8 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_591_Int__insert__left__if1,axiom,
% 0.29/0.68 ! [B_17: pname > $o,A_22: pname,C_8: pname > $o] :
% 0.29/0.68 ( ( member_pname @ A_22 @ C_8 )
% 0.29/0.68 => ( ( semila1673364395name_o @ ( insert_pname @ A_22 @ B_17 ) @ C_8 )
% 0.29/0.68 = ( insert_pname @ A_22 @ ( semila1673364395name_o @ B_17 @ C_8 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_592_Int__insert__right__if1,axiom,
% 0.29/0.68 ! [B_16: hoare_1167836817_state > $o,A_21: hoare_1167836817_state,A_20: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( member2058392318_state @ A_21 @ A_20 )
% 0.29/0.68 => ( ( semila179895820tate_o @ A_20 @ ( insert2134838167_state @ A_21 @ B_16 ) )
% 0.29/0.68 = ( insert2134838167_state @ A_21 @ ( semila179895820tate_o @ A_20 @ B_16 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_593_Int__insert__right__if1,axiom,
% 0.29/0.68 ! [B_16: hoare_1775062406iple_a > $o,A_21: hoare_1775062406iple_a,A_20: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( member2122167641iple_a @ A_21 @ A_20 )
% 0.29/0.68 => ( ( semila966743401le_a_o @ A_20 @ ( insert1281456128iple_a @ A_21 @ B_16 ) )
% 0.29/0.68 = ( insert1281456128iple_a @ A_21 @ ( semila966743401le_a_o @ A_20 @ B_16 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_594_Int__insert__right__if1,axiom,
% 0.29/0.68 ! [B_16: pname > $o,A_21: pname,A_20: pname > $o] :
% 0.29/0.68 ( ( member_pname @ A_21 @ A_20 )
% 0.29/0.68 => ( ( semila1673364395name_o @ A_20 @ ( insert_pname @ A_21 @ B_16 ) )
% 0.29/0.68 = ( insert_pname @ A_21 @ ( semila1673364395name_o @ A_20 @ B_16 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_595_Int__insert__left__if0,axiom,
% 0.29/0.68 ! [B_15: hoare_1167836817_state > $o,A_19: hoare_1167836817_state,C_7: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ~ ( member2058392318_state @ A_19 @ C_7 )
% 0.29/0.68 => ( ( semila179895820tate_o @ ( insert2134838167_state @ A_19 @ B_15 ) @ C_7 )
% 0.29/0.68 = ( semila179895820tate_o @ B_15 @ C_7 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_596_Int__insert__left__if0,axiom,
% 0.29/0.68 ! [B_15: hoare_1775062406iple_a > $o,A_19: hoare_1775062406iple_a,C_7: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ~ ( member2122167641iple_a @ A_19 @ C_7 )
% 0.29/0.68 => ( ( semila966743401le_a_o @ ( insert1281456128iple_a @ A_19 @ B_15 ) @ C_7 )
% 0.29/0.68 = ( semila966743401le_a_o @ B_15 @ C_7 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_597_Int__insert__left__if0,axiom,
% 0.29/0.68 ! [B_15: pname > $o,A_19: pname,C_7: pname > $o] :
% 0.29/0.68 ( ~ ( member_pname @ A_19 @ C_7 )
% 0.29/0.68 => ( ( semila1673364395name_o @ ( insert_pname @ A_19 @ B_15 ) @ C_7 )
% 0.29/0.68 = ( semila1673364395name_o @ B_15 @ C_7 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_598_Int__insert__right__if0,axiom,
% 0.29/0.68 ! [B_14: hoare_1167836817_state > $o,A_18: hoare_1167836817_state,A_17: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ~ ( member2058392318_state @ A_18 @ A_17 )
% 0.29/0.68 => ( ( semila179895820tate_o @ A_17 @ ( insert2134838167_state @ A_18 @ B_14 ) )
% 0.29/0.68 = ( semila179895820tate_o @ A_17 @ B_14 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_599_Int__insert__right__if0,axiom,
% 0.29/0.68 ! [B_14: hoare_1775062406iple_a > $o,A_18: hoare_1775062406iple_a,A_17: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ~ ( member2122167641iple_a @ A_18 @ A_17 )
% 0.29/0.68 => ( ( semila966743401le_a_o @ A_17 @ ( insert1281456128iple_a @ A_18 @ B_14 ) )
% 0.29/0.68 = ( semila966743401le_a_o @ A_17 @ B_14 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_600_Int__insert__right__if0,axiom,
% 0.29/0.68 ! [B_14: pname > $o,A_18: pname,A_17: pname > $o] :
% 0.29/0.68 ( ~ ( member_pname @ A_18 @ A_17 )
% 0.29/0.68 => ( ( semila1673364395name_o @ A_17 @ ( insert_pname @ A_18 @ B_14 ) )
% 0.29/0.68 = ( semila1673364395name_o @ A_17 @ B_14 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_601_insert__inter__insert,axiom,
% 0.29/0.68 ! [A_16: hoare_1167836817_state,A_15: hoare_1167836817_state > $o,B_13: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( semila179895820tate_o @ ( insert2134838167_state @ A_16 @ A_15 ) @ ( insert2134838167_state @ A_16 @ B_13 ) )
% 0.29/0.68 = ( insert2134838167_state @ A_16 @ ( semila179895820tate_o @ A_15 @ B_13 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_602_insert__inter__insert,axiom,
% 0.29/0.68 ! [A_16: hoare_1775062406iple_a,A_15: hoare_1775062406iple_a > $o,B_13: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( semila966743401le_a_o @ ( insert1281456128iple_a @ A_16 @ A_15 ) @ ( insert1281456128iple_a @ A_16 @ B_13 ) )
% 0.29/0.68 = ( insert1281456128iple_a @ A_16 @ ( semila966743401le_a_o @ A_15 @ B_13 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_603_insert__inter__insert,axiom,
% 0.29/0.68 ! [A_16: pname,A_15: pname > $o,B_13: pname > $o] :
% 0.29/0.68 ( ( semila1673364395name_o @ ( insert_pname @ A_16 @ A_15 ) @ ( insert_pname @ A_16 @ B_13 ) )
% 0.29/0.68 = ( insert_pname @ A_16 @ ( semila1673364395name_o @ A_15 @ B_13 ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_604_Int__insert__left,axiom,
% 0.29/0.68 ! [B_12: hoare_1167836817_state > $o,A_14: hoare_1167836817_state,C_6: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( ( member2058392318_state @ A_14 @ C_6 )
% 0.29/0.68 => ( ( semila179895820tate_o @ ( insert2134838167_state @ A_14 @ B_12 ) @ C_6 )
% 0.29/0.68 = ( insert2134838167_state @ A_14 @ ( semila179895820tate_o @ B_12 @ C_6 ) ) ) )
% 0.29/0.68 & ( ~ ( member2058392318_state @ A_14 @ C_6 )
% 0.29/0.68 => ( ( semila179895820tate_o @ ( insert2134838167_state @ A_14 @ B_12 ) @ C_6 )
% 0.29/0.68 = ( semila179895820tate_o @ B_12 @ C_6 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_605_Int__insert__left,axiom,
% 0.29/0.68 ! [B_12: hoare_1775062406iple_a > $o,A_14: hoare_1775062406iple_a,C_6: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( ( member2122167641iple_a @ A_14 @ C_6 )
% 0.29/0.68 => ( ( semila966743401le_a_o @ ( insert1281456128iple_a @ A_14 @ B_12 ) @ C_6 )
% 0.29/0.68 = ( insert1281456128iple_a @ A_14 @ ( semila966743401le_a_o @ B_12 @ C_6 ) ) ) )
% 0.29/0.68 & ( ~ ( member2122167641iple_a @ A_14 @ C_6 )
% 0.29/0.68 => ( ( semila966743401le_a_o @ ( insert1281456128iple_a @ A_14 @ B_12 ) @ C_6 )
% 0.29/0.68 = ( semila966743401le_a_o @ B_12 @ C_6 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_606_Int__insert__left,axiom,
% 0.29/0.68 ! [B_12: pname > $o,A_14: pname,C_6: pname > $o] :
% 0.29/0.68 ( ( ( member_pname @ A_14 @ C_6 )
% 0.29/0.68 => ( ( semila1673364395name_o @ ( insert_pname @ A_14 @ B_12 ) @ C_6 )
% 0.29/0.68 = ( insert_pname @ A_14 @ ( semila1673364395name_o @ B_12 @ C_6 ) ) ) )
% 0.29/0.68 & ( ~ ( member_pname @ A_14 @ C_6 )
% 0.29/0.68 => ( ( semila1673364395name_o @ ( insert_pname @ A_14 @ B_12 ) @ C_6 )
% 0.29/0.68 = ( semila1673364395name_o @ B_12 @ C_6 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_607_Int__insert__right,axiom,
% 0.29/0.68 ! [B_11: hoare_1167836817_state > $o,A_13: hoare_1167836817_state,A_12: hoare_1167836817_state > $o] :
% 0.29/0.68 ( ( ( member2058392318_state @ A_13 @ A_12 )
% 0.29/0.68 => ( ( semila179895820tate_o @ A_12 @ ( insert2134838167_state @ A_13 @ B_11 ) )
% 0.29/0.68 = ( insert2134838167_state @ A_13 @ ( semila179895820tate_o @ A_12 @ B_11 ) ) ) )
% 0.29/0.68 & ( ~ ( member2058392318_state @ A_13 @ A_12 )
% 0.29/0.68 => ( ( semila179895820tate_o @ A_12 @ ( insert2134838167_state @ A_13 @ B_11 ) )
% 0.29/0.68 = ( semila179895820tate_o @ A_12 @ B_11 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_608_Int__insert__right,axiom,
% 0.29/0.68 ! [B_11: hoare_1775062406iple_a > $o,A_13: hoare_1775062406iple_a,A_12: hoare_1775062406iple_a > $o] :
% 0.29/0.68 ( ( ( member2122167641iple_a @ A_13 @ A_12 )
% 0.29/0.68 => ( ( semila966743401le_a_o @ A_12 @ ( insert1281456128iple_a @ A_13 @ B_11 ) )
% 0.29/0.68 = ( insert1281456128iple_a @ A_13 @ ( semila966743401le_a_o @ A_12 @ B_11 ) ) ) )
% 0.29/0.68 & ( ~ ( member2122167641iple_a @ A_13 @ A_12 )
% 0.29/0.68 => ( ( semila966743401le_a_o @ A_12 @ ( insert1281456128iple_a @ A_13 @ B_11 ) )
% 0.29/0.68 = ( semila966743401le_a_o @ A_12 @ B_11 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_609_Int__insert__right,axiom,
% 0.29/0.68 ! [B_11: pname > $o,A_13: pname,A_12: pname > $o] :
% 0.29/0.68 ( ( ( member_pname @ A_13 @ A_12 )
% 0.29/0.68 => ( ( semila1673364395name_o @ A_12 @ ( insert_pname @ A_13 @ B_11 ) )
% 0.29/0.68 = ( insert_pname @ A_13 @ ( semila1673364395name_o @ A_12 @ B_11 ) ) ) )
% 0.29/0.68 & ( ~ ( member_pname @ A_13 @ A_12 )
% 0.29/0.68 => ( ( semila1673364395name_o @ A_12 @ ( insert_pname @ A_13 @ B_11 ) )
% 0.29/0.68 = ( semila1673364395name_o @ A_12 @ B_11 ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_610_if__image__distrib,axiom,
% 0.29/0.68 ! [P_1: pname > $o,F_4: pname > hoare_1167836817_state,G: pname > hoare_1167836817_state,S_1: pname > $o] :
% 0.29/0.68 ( ( image_575578384_state
% 0.29/0.68 @ ^ [X: pname] : ( if_Hoa833675553_state @ ( P_1 @ X ) @ ( F_4 @ X ) @ ( G @ X ) )
% 0.29/0.68 @ S_1 )
% 0.29/0.68 = ( semila1172322802tate_o @ ( image_575578384_state @ F_4 @ ( semila1673364395name_o @ S_1 @ ( collect_pname @ P_1 ) ) )
% 0.29/0.68 @ ( image_575578384_state @ G
% 0.29/0.68 @ ( semila1673364395name_o @ S_1
% 0.29/0.68 @ ( collect_pname
% 0.29/0.68 @ ^ [X: pname] : ( (~) @ ( P_1 @ X ) ) ) ) ) ) ) ).
% 0.29/0.68
% 0.29/0.68 thf(fact_611_if__image__distrib,axiom,
% 0.29/0.68 ! [P_1: pname > $o,F_4: pname > hoare_1775062406iple_a,G: pname > hoare_1775062406iple_a,S_1: pname > $o] :
% 0.29/0.68 ( ( image_2063119815iple_a
% 0.29/0.68 @ ^ [X: pname] : ( if_Hoa1047340790iple_a @ ( P_1 @ X ) @ ( F_4 @ X ) @ ( G @ X ) )
% 0.29/0.68 @ S_1 )
% 0.29/0.68 = ( semila13410563le_a_o @ ( image_2063119815iple_a @ F_4 @ ( semila1673364395name_o @ S_1 @ ( collect_pname @ P_1 ) ) )
% 0.29/0.68 @ ( image_2063119815iple_a @ G
% 0.29/0.68 @ ( semila1673364395name_o @ S_1
% 0.29/0.69 @ ( collect_pname
% 0.29/0.69 @ ^ [X: pname] : ( (~) @ ( P_1 @ X ) ) ) ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_612_folding__one_Ounion__inter,axiom,
% 0.29/0.69 ! [B_10: pname > $o,A_11: pname > $o,F_3: pname > pname > pname,F_2: ( pname > $o ) > pname] :
% 0.29/0.69 ( ( finite1282449217_pname @ F_3 @ F_2 )
% 0.29/0.69 => ( ( finite_finite_pname @ A_11 )
% 0.29/0.69 => ( ( finite_finite_pname @ B_10 )
% 0.29/0.69 => ( ( ( semila1673364395name_o @ A_11 @ B_10 )
% 0.29/0.69 != bot_bot_pname_o )
% 0.29/0.69 => ( ( F_3 @ ( F_2 @ ( semila1780557381name_o @ A_11 @ B_10 ) ) @ ( F_2 @ ( semila1673364395name_o @ A_11 @ B_10 ) ) )
% 0.29/0.69 = ( F_3 @ ( F_2 @ A_11 ) @ ( F_2 @ B_10 ) ) ) ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_613_folding__one_Ounion__inter,axiom,
% 0.29/0.69 ! [B_10: hoare_1775062406iple_a > $o,A_11: hoare_1775062406iple_a > $o,F_3: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,F_2: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
% 0.29/0.69 ( ( finite2078349315iple_a @ F_3 @ F_2 )
% 0.29/0.69 => ( ( finite2063573081iple_a @ A_11 )
% 0.29/0.69 => ( ( finite2063573081iple_a @ B_10 )
% 0.29/0.69 => ( ( ( semila966743401le_a_o @ A_11 @ B_10 )
% 0.29/0.69 != bot_bo751897185le_a_o )
% 0.29/0.69 => ( ( F_3 @ ( F_2 @ ( semila13410563le_a_o @ A_11 @ B_10 ) ) @ ( F_2 @ ( semila966743401le_a_o @ A_11 @ B_10 ) ) )
% 0.29/0.69 = ( F_3 @ ( F_2 @ A_11 ) @ ( F_2 @ B_10 ) ) ) ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_614_folding__one_Ounion__inter,axiom,
% 0.29/0.69 ! [B_10: hoare_1167836817_state > $o,A_11: hoare_1167836817_state > $o,F_3: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_2: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.29/0.69 ( ( finite1074406356_state @ F_3 @ F_2 )
% 0.29/0.69 => ( ( finite1084549118_state @ A_11 )
% 0.29/0.69 => ( ( finite1084549118_state @ B_10 )
% 0.29/0.69 => ( ( ( semila179895820tate_o @ A_11 @ B_10 )
% 0.29/0.69 != bot_bo70021908tate_o )
% 0.29/0.69 => ( ( F_3 @ ( F_2 @ ( semila1172322802tate_o @ A_11 @ B_10 ) ) @ ( F_2 @ ( semila179895820tate_o @ A_11 @ B_10 ) ) )
% 0.29/0.69 = ( F_3 @ ( F_2 @ A_11 ) @ ( F_2 @ B_10 ) ) ) ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_615_folding__one_Ounion__disjoint,axiom,
% 0.29/0.69 ! [B_9: pname > $o,A_10: pname > $o,F_1: pname > pname > pname,F: ( pname > $o ) > pname] :
% 0.29/0.69 ( ( finite1282449217_pname @ F_1 @ F )
% 0.29/0.69 => ( ( finite_finite_pname @ A_10 )
% 0.29/0.69 => ( ( A_10 != bot_bot_pname_o )
% 0.29/0.69 => ( ( finite_finite_pname @ B_9 )
% 0.29/0.69 => ( ( B_9 != bot_bot_pname_o )
% 0.29/0.69 => ( ( ( semila1673364395name_o @ A_10 @ B_9 )
% 0.29/0.69 = bot_bot_pname_o )
% 0.29/0.69 => ( ( F @ ( semila1780557381name_o @ A_10 @ B_9 ) )
% 0.29/0.69 = ( F_1 @ ( F @ A_10 ) @ ( F @ B_9 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_616_folding__one_Ounion__disjoint,axiom,
% 0.29/0.69 ! [B_9: hoare_1775062406iple_a > $o,A_10: hoare_1775062406iple_a > $o,F_1: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,F: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
% 0.29/0.69 ( ( finite2078349315iple_a @ F_1 @ F )
% 0.29/0.69 => ( ( finite2063573081iple_a @ A_10 )
% 0.29/0.69 => ( ( A_10 != bot_bo751897185le_a_o )
% 0.29/0.69 => ( ( finite2063573081iple_a @ B_9 )
% 0.29/0.69 => ( ( B_9 != bot_bo751897185le_a_o )
% 0.29/0.69 => ( ( ( semila966743401le_a_o @ A_10 @ B_9 )
% 0.29/0.69 = bot_bo751897185le_a_o )
% 0.29/0.69 => ( ( F @ ( semila13410563le_a_o @ A_10 @ B_9 ) )
% 0.29/0.69 = ( F_1 @ ( F @ A_10 ) @ ( F @ B_9 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_617_folding__one_Ounion__disjoint,axiom,
% 0.29/0.69 ! [B_9: hoare_1167836817_state > $o,A_10: hoare_1167836817_state > $o,F_1: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.29/0.69 ( ( finite1074406356_state @ F_1 @ F )
% 0.29/0.69 => ( ( finite1084549118_state @ A_10 )
% 0.29/0.69 => ( ( A_10 != bot_bo70021908tate_o )
% 0.29/0.69 => ( ( finite1084549118_state @ B_9 )
% 0.29/0.69 => ( ( B_9 != bot_bo70021908tate_o )
% 0.29/0.69 => ( ( ( semila179895820tate_o @ A_10 @ B_9 )
% 0.29/0.69 = bot_bo70021908tate_o )
% 0.29/0.69 => ( ( F @ ( semila1172322802tate_o @ A_10 @ B_9 ) )
% 0.29/0.69 = ( F_1 @ ( F @ A_10 ) @ ( F @ B_9 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_618_distrib__imp2,axiom,
% 0.29/0.69 ! [X_3: $o,Y_3: $o,Z_3: $o] :
% 0.29/0.69 ( ! [X: $o,Y_2: $o,Z_2: $o] :
% 0.29/0.69 ( ( semila10642723_sup_o @ X @ ( semila854092349_inf_o @ Y_2 @ Z_2 ) )
% 0.29/0.69 <=> ( semila854092349_inf_o @ ( semila10642723_sup_o @ X @ Y_2 ) @ ( semila10642723_sup_o @ X @ Z_2 ) ) )
% 0.29/0.69 => ( ( semila854092349_inf_o @ X_3 @ ( semila10642723_sup_o @ Y_3 @ Z_3 ) )
% 0.29/0.69 <=> ( semila10642723_sup_o @ ( semila854092349_inf_o @ X_3 @ Y_3 ) @ ( semila854092349_inf_o @ X_3 @ Z_3 ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_619_distrib__imp2,axiom,
% 0.29/0.69 ! [X_3: pname > $o,Y_3: pname > $o,Z_3: pname > $o] :
% 0.29/0.69 ( ! [X: pname > $o,Y_2: pname > $o,Z_2: pname > $o] :
% 0.29/0.69 ( ( semila1780557381name_o @ X @ ( semila1673364395name_o @ Y_2 @ Z_2 ) )
% 0.29/0.69 = ( semila1673364395name_o @ ( semila1780557381name_o @ X @ Y_2 ) @ ( semila1780557381name_o @ X @ Z_2 ) ) )
% 0.29/0.69 => ( ( semila1673364395name_o @ X_3 @ ( semila1780557381name_o @ Y_3 @ Z_3 ) )
% 0.29/0.69 = ( semila1780557381name_o @ ( semila1673364395name_o @ X_3 @ Y_3 ) @ ( semila1673364395name_o @ X_3 @ Z_3 ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_620_distrib__imp2,axiom,
% 0.29/0.69 ! [X_3: hoare_1167836817_state > $o,Y_3: hoare_1167836817_state > $o,Z_3: hoare_1167836817_state > $o] :
% 0.29/0.69 ( ! [X: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o,Z_2: hoare_1167836817_state > $o] :
% 0.29/0.69 ( ( semila1172322802tate_o @ X @ ( semila179895820tate_o @ Y_2 @ Z_2 ) )
% 0.29/0.69 = ( semila179895820tate_o @ ( semila1172322802tate_o @ X @ Y_2 ) @ ( semila1172322802tate_o @ X @ Z_2 ) ) )
% 0.29/0.69 => ( ( semila179895820tate_o @ X_3 @ ( semila1172322802tate_o @ Y_3 @ Z_3 ) )
% 0.29/0.69 = ( semila1172322802tate_o @ ( semila179895820tate_o @ X_3 @ Y_3 ) @ ( semila179895820tate_o @ X_3 @ Z_3 ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_621_distrib__imp2,axiom,
% 0.29/0.69 ! [X_3: hoare_1775062406iple_a > $o,Y_3: hoare_1775062406iple_a > $o,Z_3: hoare_1775062406iple_a > $o] :
% 0.29/0.69 ( ! [X: hoare_1775062406iple_a > $o,Y_2: hoare_1775062406iple_a > $o,Z_2: hoare_1775062406iple_a > $o] :
% 0.29/0.69 ( ( semila13410563le_a_o @ X @ ( semila966743401le_a_o @ Y_2 @ Z_2 ) )
% 0.29/0.69 = ( semila966743401le_a_o @ ( semila13410563le_a_o @ X @ Y_2 ) @ ( semila13410563le_a_o @ X @ Z_2 ) ) )
% 0.29/0.69 => ( ( semila966743401le_a_o @ X_3 @ ( semila13410563le_a_o @ Y_3 @ Z_3 ) )
% 0.29/0.69 = ( semila13410563le_a_o @ ( semila966743401le_a_o @ X_3 @ Y_3 ) @ ( semila966743401le_a_o @ X_3 @ Z_3 ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_622_distrib__imp1,axiom,
% 0.29/0.69 ! [X_2: $o,Y_1: $o,Z_1: $o] :
% 0.29/0.69 ( ! [X: $o,Y_2: $o,Z_2: $o] :
% 0.29/0.69 ( ( semila854092349_inf_o @ X @ ( semila10642723_sup_o @ Y_2 @ Z_2 ) )
% 0.29/0.69 <=> ( semila10642723_sup_o @ ( semila854092349_inf_o @ X @ Y_2 ) @ ( semila854092349_inf_o @ X @ Z_2 ) ) )
% 0.29/0.69 => ( ( semila10642723_sup_o @ X_2 @ ( semila854092349_inf_o @ Y_1 @ Z_1 ) )
% 0.29/0.69 <=> ( semila854092349_inf_o @ ( semila10642723_sup_o @ X_2 @ Y_1 ) @ ( semila10642723_sup_o @ X_2 @ Z_1 ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_623_distrib__imp1,axiom,
% 0.29/0.69 ! [X_2: pname > $o,Y_1: pname > $o,Z_1: pname > $o] :
% 0.29/0.69 ( ! [X: pname > $o,Y_2: pname > $o,Z_2: pname > $o] :
% 0.29/0.69 ( ( semila1673364395name_o @ X @ ( semila1780557381name_o @ Y_2 @ Z_2 ) )
% 0.29/0.69 = ( semila1780557381name_o @ ( semila1673364395name_o @ X @ Y_2 ) @ ( semila1673364395name_o @ X @ Z_2 ) ) )
% 0.29/0.69 => ( ( semila1780557381name_o @ X_2 @ ( semila1673364395name_o @ Y_1 @ Z_1 ) )
% 0.29/0.69 = ( semila1673364395name_o @ ( semila1780557381name_o @ X_2 @ Y_1 ) @ ( semila1780557381name_o @ X_2 @ Z_1 ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_624_distrib__imp1,axiom,
% 0.29/0.69 ! [X_2: hoare_1167836817_state > $o,Y_1: hoare_1167836817_state > $o,Z_1: hoare_1167836817_state > $o] :
% 0.29/0.69 ( ! [X: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o,Z_2: hoare_1167836817_state > $o] :
% 0.29/0.69 ( ( semila179895820tate_o @ X @ ( semila1172322802tate_o @ Y_2 @ Z_2 ) )
% 0.29/0.69 = ( semila1172322802tate_o @ ( semila179895820tate_o @ X @ Y_2 ) @ ( semila179895820tate_o @ X @ Z_2 ) ) )
% 0.29/0.69 => ( ( semila1172322802tate_o @ X_2 @ ( semila179895820tate_o @ Y_1 @ Z_1 ) )
% 0.29/0.69 = ( semila179895820tate_o @ ( semila1172322802tate_o @ X_2 @ Y_1 ) @ ( semila1172322802tate_o @ X_2 @ Z_1 ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_625_distrib__imp1,axiom,
% 0.29/0.69 ! [X_2: hoare_1775062406iple_a > $o,Y_1: hoare_1775062406iple_a > $o,Z_1: hoare_1775062406iple_a > $o] :
% 0.29/0.69 ( ! [X: hoare_1775062406iple_a > $o,Y_2: hoare_1775062406iple_a > $o,Z_2: hoare_1775062406iple_a > $o] :
% 0.29/0.69 ( ( semila966743401le_a_o @ X @ ( semila13410563le_a_o @ Y_2 @ Z_2 ) )
% 0.29/0.69 = ( semila13410563le_a_o @ ( semila966743401le_a_o @ X @ Y_2 ) @ ( semila966743401le_a_o @ X @ Z_2 ) ) )
% 0.29/0.69 => ( ( semila13410563le_a_o @ X_2 @ ( semila966743401le_a_o @ Y_1 @ Z_1 ) )
% 0.29/0.69 = ( semila966743401le_a_o @ ( semila13410563le_a_o @ X_2 @ Y_1 ) @ ( semila13410563le_a_o @ X_2 @ Z_1 ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_626_sup__Inf__absorb,axiom,
% 0.29/0.69 ! [A_9: $o,A_8: $o > $o] :
% 0.29/0.69 ( ( finite_finite_o @ A_8 )
% 0.29/0.69 => ( ( member_o @ A_9 @ A_8 )
% 0.29/0.69 => ( ( semila10642723_sup_o @ A_9 @ ( big_la1690136417_fin_o @ A_8 ) )
% 0.29/0.69 <=> A_9 ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_627_sup__Inf__absorb,axiom,
% 0.29/0.69 ! [A_9: pname > $o,A_8: ( pname > $o ) > $o] :
% 0.29/0.69 ( ( finite297249702name_o @ A_8 )
% 0.29/0.69 => ( ( member_pname_o @ A_9 @ A_8 )
% 0.29/0.69 => ( ( semila1780557381name_o @ A_9 @ ( big_la1126801287name_o @ A_8 ) )
% 0.29/0.69 = A_9 ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_628_sup__Inf__absorb,axiom,
% 0.29/0.69 ! [A_9: hoare_1167836817_state > $o,A_8: ( hoare_1167836817_state > $o ) > $o] :
% 0.29/0.69 ( ( finite1380128977tate_o @ A_8 )
% 0.29/0.69 => ( ( member864234961tate_o @ A_9 @ A_8 )
% 0.29/0.69 => ( ( semila1172322802tate_o @ A_9 @ ( big_la831793456tate_o @ A_8 ) )
% 0.29/0.69 = A_9 ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_629_sup__Inf__absorb,axiom,
% 0.29/0.69 ! [A_9: hoare_1775062406iple_a > $o,A_8: ( hoare_1775062406iple_a > $o ) > $o] :
% 0.29/0.69 ( ( finite789576932le_a_o @ A_8 )
% 0.29/0.69 => ( ( member1207314404le_a_o @ A_9 @ A_8 )
% 0.29/0.69 => ( ( semila13410563le_a_o @ A_9 @ ( big_la447547205le_a_o @ A_8 ) )
% 0.29/0.69 = A_9 ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_630_DiffE,axiom,
% 0.29/0.69 ! [C_5: hoare_1775062406iple_a,A_7: hoare_1775062406iple_a > $o,B_8: hoare_1775062406iple_a > $o] :
% 0.29/0.69 ( ( member2122167641iple_a @ C_5 @ ( minus_1944206118le_a_o @ A_7 @ B_8 ) )
% 0.29/0.69 => ~ ( ( member2122167641iple_a @ C_5 @ A_7 )
% 0.29/0.69 => ( member2122167641iple_a @ C_5 @ B_8 ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_631_DiffE,axiom,
% 0.29/0.69 ! [C_5: pname,A_7: pname > $o,B_8: pname > $o] :
% 0.29/0.69 ( ( member_pname @ C_5 @ ( minus_minus_pname_o @ A_7 @ B_8 ) )
% 0.29/0.69 => ~ ( ( member_pname @ C_5 @ A_7 )
% 0.29/0.69 => ( member_pname @ C_5 @ B_8 ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_632_DiffI,axiom,
% 0.29/0.69 ! [B_7: hoare_1775062406iple_a > $o,C_4: hoare_1775062406iple_a,A_6: hoare_1775062406iple_a > $o] :
% 0.29/0.69 ( ( member2122167641iple_a @ C_4 @ A_6 )
% 0.29/0.69 => ( ~ ( member2122167641iple_a @ C_4 @ B_7 )
% 0.29/0.69 => ( member2122167641iple_a @ C_4 @ ( minus_1944206118le_a_o @ A_6 @ B_7 ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_633_DiffI,axiom,
% 0.29/0.69 ! [B_7: pname > $o,C_4: pname,A_6: pname > $o] :
% 0.29/0.69 ( ( member_pname @ C_4 @ A_6 )
% 0.29/0.69 => ( ~ ( member_pname @ C_4 @ B_7 )
% 0.29/0.69 => ( member_pname @ C_4 @ ( minus_minus_pname_o @ A_6 @ B_7 ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_634_Un__Diff__cancel,axiom,
% 0.29/0.69 ! [A_5: pname > $o,B_6: pname > $o] :
% 0.29/0.69 ( ( semila1780557381name_o @ A_5 @ ( minus_minus_pname_o @ B_6 @ A_5 ) )
% 0.29/0.69 = ( semila1780557381name_o @ A_5 @ B_6 ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_635_Un__Diff__cancel,axiom,
% 0.29/0.69 ! [A_5: hoare_1167836817_state > $o,B_6: hoare_1167836817_state > $o] :
% 0.29/0.69 ( ( semila1172322802tate_o @ A_5 @ ( minus_2107060239tate_o @ B_6 @ A_5 ) )
% 0.29/0.69 = ( semila1172322802tate_o @ A_5 @ B_6 ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_636_Un__Diff__cancel,axiom,
% 0.29/0.69 ! [A_5: hoare_1775062406iple_a > $o,B_6: hoare_1775062406iple_a > $o] :
% 0.29/0.69 ( ( semila13410563le_a_o @ A_5 @ ( minus_1944206118le_a_o @ B_6 @ A_5 ) )
% 0.29/0.69 = ( semila13410563le_a_o @ A_5 @ B_6 ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_637_Un__Diff__cancel2,axiom,
% 0.29/0.69 ! [B_5: pname > $o,A_4: pname > $o] :
% 0.29/0.69 ( ( semila1780557381name_o @ ( minus_minus_pname_o @ B_5 @ A_4 ) @ A_4 )
% 0.29/0.69 = ( semila1780557381name_o @ B_5 @ A_4 ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_638_Un__Diff__cancel2,axiom,
% 0.29/0.69 ! [B_5: hoare_1167836817_state > $o,A_4: hoare_1167836817_state > $o] :
% 0.29/0.69 ( ( semila1172322802tate_o @ ( minus_2107060239tate_o @ B_5 @ A_4 ) @ A_4 )
% 0.29/0.69 = ( semila1172322802tate_o @ B_5 @ A_4 ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_639_Un__Diff__cancel2,axiom,
% 0.29/0.69 ! [B_5: hoare_1775062406iple_a > $o,A_4: hoare_1775062406iple_a > $o] :
% 0.29/0.69 ( ( semila13410563le_a_o @ ( minus_1944206118le_a_o @ B_5 @ A_4 ) @ A_4 )
% 0.29/0.69 = ( semila13410563le_a_o @ B_5 @ A_4 ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_640_Un__Diff,axiom,
% 0.29/0.69 ! [A_3: pname > $o,B_4: pname > $o,C_3: pname > $o] :
% 0.29/0.69 ( ( minus_minus_pname_o @ ( semila1780557381name_o @ A_3 @ B_4 ) @ C_3 )
% 0.29/0.69 = ( semila1780557381name_o @ ( minus_minus_pname_o @ A_3 @ C_3 ) @ ( minus_minus_pname_o @ B_4 @ C_3 ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_641_Un__Diff,axiom,
% 0.29/0.69 ! [A_3: hoare_1167836817_state > $o,B_4: hoare_1167836817_state > $o,C_3: hoare_1167836817_state > $o] :
% 0.29/0.69 ( ( minus_2107060239tate_o @ ( semila1172322802tate_o @ A_3 @ B_4 ) @ C_3 )
% 0.29/0.69 = ( semila1172322802tate_o @ ( minus_2107060239tate_o @ A_3 @ C_3 ) @ ( minus_2107060239tate_o @ B_4 @ C_3 ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_642_Un__Diff,axiom,
% 0.29/0.69 ! [A_3: hoare_1775062406iple_a > $o,B_4: hoare_1775062406iple_a > $o,C_3: hoare_1775062406iple_a > $o] :
% 0.29/0.69 ( ( minus_1944206118le_a_o @ ( semila13410563le_a_o @ A_3 @ B_4 ) @ C_3 )
% 0.29/0.69 = ( semila13410563le_a_o @ ( minus_1944206118le_a_o @ A_3 @ C_3 ) @ ( minus_1944206118le_a_o @ B_4 @ C_3 ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_643_DiffD2,axiom,
% 0.29/0.69 ! [C_2: hoare_1775062406iple_a,A_2: hoare_1775062406iple_a > $o,B_3: hoare_1775062406iple_a > $o] :
% 0.29/0.69 ( ( member2122167641iple_a @ C_2 @ ( minus_1944206118le_a_o @ A_2 @ B_3 ) )
% 0.29/0.69 => ~ ( member2122167641iple_a @ C_2 @ B_3 ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_644_DiffD2,axiom,
% 0.29/0.69 ! [C_2: pname,A_2: pname > $o,B_3: pname > $o] :
% 0.29/0.69 ( ( member_pname @ C_2 @ ( minus_minus_pname_o @ A_2 @ B_3 ) )
% 0.29/0.69 => ~ ( member_pname @ C_2 @ B_3 ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_645_DiffD1,axiom,
% 0.29/0.69 ! [C_1: hoare_1775062406iple_a,A_1: hoare_1775062406iple_a > $o,B_2: hoare_1775062406iple_a > $o] :
% 0.29/0.69 ( ( member2122167641iple_a @ C_1 @ ( minus_1944206118le_a_o @ A_1 @ B_2 ) )
% 0.29/0.69 => ( member2122167641iple_a @ C_1 @ A_1 ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_646_DiffD1,axiom,
% 0.29/0.69 ! [C_1: pname,A_1: pname > $o,B_2: pname > $o] :
% 0.29/0.69 ( ( member_pname @ C_1 @ ( minus_minus_pname_o @ A_1 @ B_2 ) )
% 0.29/0.69 => ( member_pname @ C_1 @ A_1 ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_647_Diff__iff,axiom,
% 0.29/0.69 ! [C: pname,A: pname > $o,B_1: pname > $o] :
% 0.29/0.69 ( ( member_pname @ C @ ( minus_minus_pname_o @ A @ B_1 ) )
% 0.29/0.69 <=> ( ( member_pname @ C @ A )
% 0.29/0.69 & ~ ( member_pname @ C @ B_1 ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_648_diff__Suc__Suc,axiom,
% 0.29/0.69 ! [M: nat,N_1: nat] :
% 0.29/0.69 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N_1 ) )
% 0.29/0.69 = ( minus_minus_nat @ M @ N_1 ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_649_Suc__diff__diff,axiom,
% 0.29/0.69 ! [M: nat,N_1: nat,K: nat] :
% 0.29/0.69 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N_1 ) @ ( suc @ K ) )
% 0.29/0.69 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N_1 ) @ K ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_650_diff__0__eq__0,axiom,
% 0.29/0.69 ! [N_1: nat] :
% 0.29/0.69 ( ( minus_minus_nat @ zero_zero_nat @ N_1 )
% 0.29/0.69 = zero_zero_nat ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_651_minus__nat_Odiff__0,axiom,
% 0.29/0.69 ! [M: nat] :
% 0.29/0.69 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.29/0.69 = M ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_652_diff__self__eq__0,axiom,
% 0.29/0.69 ! [M: nat] :
% 0.29/0.69 ( ( minus_minus_nat @ M @ M )
% 0.29/0.69 = zero_zero_nat ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_653_diffs0__imp__equal,axiom,
% 0.29/0.69 ! [M: nat,N_1: nat] :
% 0.29/0.69 ( ( ( minus_minus_nat @ M @ N_1 )
% 0.29/0.69 = zero_zero_nat )
% 0.29/0.69 => ( ( ( minus_minus_nat @ N_1 @ M )
% 0.29/0.69 = zero_zero_nat )
% 0.29/0.69 => ( M = N_1 ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_654_zero__induct__lemma,axiom,
% 0.29/0.69 ! [I: nat,P: nat > $o,K: nat] :
% 0.29/0.69 ( ( P @ K )
% 0.29/0.69 => ( ! [N: nat] :
% 0.29/0.69 ( ( P @ ( suc @ N ) )
% 0.29/0.69 => ( P @ N ) )
% 0.29/0.69 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_655_diff__commute,axiom,
% 0.29/0.69 ! [I: nat,J: nat,K: nat] :
% 0.29/0.69 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.29/0.69 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_656_diff__Suc,axiom,
% 0.29/0.69 ! [M: nat,N_1: nat] :
% 0.29/0.69 ( ( minus_minus_nat @ M @ ( suc @ N_1 ) )
% 0.29/0.69 = ( nat_case_nat @ zero_zero_nat
% 0.29/0.69 @ ^ [K_1: nat] : K_1
% 0.29/0.69 @ ( minus_minus_nat @ M @ N_1 ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_657_diff__Suc__1,axiom,
% 0.29/0.69 ! [N_1: nat] :
% 0.29/0.69 ( ( minus_minus_nat @ ( suc @ N_1 ) @ one_one_nat )
% 0.29/0.69 = N_1 ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_658_diff__Suc__eq__diff__pred,axiom,
% 0.29/0.69 ! [M: nat,N_1: nat] :
% 0.29/0.69 ( ( minus_minus_nat @ M @ ( suc @ N_1 ) )
% 0.29/0.69 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N_1 ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_659_One__nat__def,axiom,
% 0.29/0.69 ( one_one_nat
% 0.29/0.69 = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_660_Suc__eq__plus1,axiom,
% 0.29/0.69 ! [N_1: nat] :
% 0.29/0.69 ( ( suc @ N_1 )
% 0.29/0.69 = ( plus_plus_nat @ N_1 @ one_one_nat ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_661_Suc__eq__plus1__left,axiom,
% 0.29/0.69 ! [N_1: nat] :
% 0.29/0.69 ( ( suc @ N_1 )
% 0.29/0.69 = ( plus_plus_nat @ one_one_nat @ N_1 ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_662_diff__cancel2,axiom,
% 0.29/0.69 ! [M: nat,K: nat,N_1: nat] :
% 0.29/0.69 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N_1 @ K ) )
% 0.29/0.69 = ( minus_minus_nat @ M @ N_1 ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_663_diff__cancel,axiom,
% 0.29/0.69 ! [K: nat,M: nat,N_1: nat] :
% 0.29/0.69 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N_1 ) )
% 0.29/0.69 = ( minus_minus_nat @ M @ N_1 ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_664_diff__diff__left,axiom,
% 0.29/0.69 ! [I: nat,J: nat,K: nat] :
% 0.29/0.69 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.29/0.69 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_665_diff__add__inverse,axiom,
% 0.29/0.69 ! [N_1: nat,M: nat] :
% 0.29/0.69 ( ( minus_minus_nat @ ( plus_plus_nat @ N_1 @ M ) @ N_1 )
% 0.29/0.69 = M ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_666_diff__add__inverse2,axiom,
% 0.29/0.69 ! [M: nat,N_1: nat] :
% 0.29/0.69 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N_1 ) @ N_1 )
% 0.29/0.69 = M ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_667_diff__add__0,axiom,
% 0.29/0.69 ! [N_1: nat,M: nat] :
% 0.29/0.69 ( ( minus_minus_nat @ N_1 @ ( plus_plus_nat @ N_1 @ M ) )
% 0.29/0.69 = zero_zero_nat ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_668_nat__add__commute,axiom,
% 0.29/0.69 ! [M: nat,N_1: nat] :
% 0.29/0.69 ( ( plus_plus_nat @ M @ N_1 )
% 0.29/0.69 = ( plus_plus_nat @ N_1 @ M ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_669_nat__add__left__commute,axiom,
% 0.29/0.69 ! [X_1: nat,Y: nat,Z: nat] :
% 0.29/0.69 ( ( plus_plus_nat @ X_1 @ ( plus_plus_nat @ Y @ Z ) )
% 0.29/0.69 = ( plus_plus_nat @ Y @ ( plus_plus_nat @ X_1 @ Z ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_670_nat__add__assoc,axiom,
% 0.29/0.69 ! [M: nat,N_1: nat,K: nat] :
% 0.29/0.69 ( ( plus_plus_nat @ ( plus_plus_nat @ M @ N_1 ) @ K )
% 0.29/0.69 = ( plus_plus_nat @ M @ ( plus_plus_nat @ N_1 @ K ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_671_nat__add__left__cancel,axiom,
% 0.29/0.69 ! [K: nat,M: nat,N_1: nat] :
% 0.29/0.69 ( ( ( plus_plus_nat @ K @ M )
% 0.29/0.69 = ( plus_plus_nat @ K @ N_1 ) )
% 0.29/0.69 <=> ( M = N_1 ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_672_nat__add__right__cancel,axiom,
% 0.29/0.69 ! [M: nat,K: nat,N_1: nat] :
% 0.29/0.69 ( ( ( plus_plus_nat @ M @ K )
% 0.29/0.69 = ( plus_plus_nat @ N_1 @ K ) )
% 0.29/0.69 <=> ( M = N_1 ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_673_add__Suc__shift,axiom,
% 0.29/0.69 ! [M: nat,N_1: nat] :
% 0.29/0.69 ( ( plus_plus_nat @ ( suc @ M ) @ N_1 )
% 0.29/0.69 = ( plus_plus_nat @ M @ ( suc @ N_1 ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_674_add__Suc,axiom,
% 0.29/0.69 ! [M: nat,N_1: nat] :
% 0.29/0.69 ( ( plus_plus_nat @ ( suc @ M ) @ N_1 )
% 0.29/0.69 = ( suc @ ( plus_plus_nat @ M @ N_1 ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_675_add__Suc__right,axiom,
% 0.29/0.69 ! [M: nat,N_1: nat] :
% 0.29/0.69 ( ( plus_plus_nat @ M @ ( suc @ N_1 ) )
% 0.29/0.69 = ( suc @ ( plus_plus_nat @ M @ N_1 ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_676_one__is__add,axiom,
% 0.29/0.69 ! [M: nat,N_1: nat] :
% 0.29/0.69 ( ( ( suc @ zero_zero_nat )
% 0.29/0.69 = ( plus_plus_nat @ M @ N_1 ) )
% 0.29/0.69 <=> ( ( ( M
% 0.29/0.69 = ( suc @ zero_zero_nat ) )
% 0.29/0.69 & ( N_1 = zero_zero_nat ) )
% 0.29/0.69 | ( ( M = zero_zero_nat )
% 0.29/0.69 & ( N_1
% 0.29/0.69 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_677_add__is__1,axiom,
% 0.29/0.69 ! [M: nat,N_1: nat] :
% 0.29/0.69 ( ( ( plus_plus_nat @ M @ N_1 )
% 0.29/0.69 = ( suc @ zero_zero_nat ) )
% 0.29/0.69 <=> ( ( ( M
% 0.29/0.69 = ( suc @ zero_zero_nat ) )
% 0.29/0.69 & ( N_1 = zero_zero_nat ) )
% 0.29/0.69 | ( ( M = zero_zero_nat )
% 0.29/0.69 & ( N_1
% 0.29/0.69 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_678_plus__nat_Oadd__0,axiom,
% 0.29/0.69 ! [N_1: nat] :
% 0.29/0.69 ( ( plus_plus_nat @ zero_zero_nat @ N_1 )
% 0.29/0.69 = N_1 ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_679_Nat_Oadd__0__right,axiom,
% 0.29/0.69 ! [M: nat] :
% 0.29/0.69 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 0.29/0.69 = M ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_680_add__is__0,axiom,
% 0.29/0.69 ! [M: nat,N_1: nat] :
% 0.29/0.69 ( ( ( plus_plus_nat @ M @ N_1 )
% 0.29/0.69 = zero_zero_nat )
% 0.29/0.69 <=> ( ( M = zero_zero_nat )
% 0.29/0.69 & ( N_1 = zero_zero_nat ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_681_add__eq__self__zero,axiom,
% 0.29/0.69 ! [M: nat,N_1: nat] :
% 0.29/0.69 ( ( ( plus_plus_nat @ M @ N_1 )
% 0.29/0.69 = M )
% 0.29/0.69 => ( N_1 = zero_zero_nat ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_682_add__eq__if,axiom,
% 0.29/0.69 ! [N_1: nat,M: nat] :
% 0.29/0.69 ( ( ( M = zero_zero_nat )
% 0.29/0.69 => ( ( plus_plus_nat @ M @ N_1 )
% 0.29/0.69 = N_1 ) )
% 0.29/0.69 & ( ( M != zero_zero_nat )
% 0.29/0.69 => ( ( plus_plus_nat @ M @ N_1 )
% 0.29/0.69 = ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N_1 ) ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_683_com_Osize_I4_J,axiom,
% 0.29/0.69 ! [Com1: com,Com2: com] :
% 0.29/0.69 ( ( com_size @ ( semi @ Com1 @ Com2 ) )
% 0.29/0.69 = ( plus_plus_nat @ ( plus_plus_nat @ ( com_size @ Com1 ) @ ( com_size @ Com2 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_684_com_Osize_I7_J,axiom,
% 0.29/0.69 ! [Pname: pname] :
% 0.29/0.69 ( ( com_size @ ( body @ Pname ) )
% 0.29/0.69 = zero_zero_nat ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_685_com_Osize_I1_J,axiom,
% 0.29/0.69 ( ( com_size @ skip )
% 0.29/0.69 = zero_zero_nat ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_686_com_Osize_I6_J,axiom,
% 0.29/0.69 ! [Fun: state > $o,Com: com] :
% 0.29/0.69 ( ( com_size @ ( while @ Fun @ Com ) )
% 0.29/0.69 = ( plus_plus_nat @ ( com_size @ Com ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_687_com_Osize_I12_J,axiom,
% 0.29/0.69 ! [Com1: com,Com2: com] :
% 0.29/0.69 ( ( size_size_com @ ( semi @ Com1 @ Com2 ) )
% 0.29/0.69 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_size_com @ Com1 ) @ ( size_size_com @ Com2 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_688_com_Osize_I15_J,axiom,
% 0.29/0.69 ! [Pname: pname] :
% 0.29/0.69 ( ( size_size_com @ ( body @ Pname ) )
% 0.29/0.69 = zero_zero_nat ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_689_com_Osize_I9_J,axiom,
% 0.29/0.69 ( ( size_size_com @ skip )
% 0.29/0.69 = zero_zero_nat ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_690_com_Osize_I14_J,axiom,
% 0.29/0.69 ! [Fun: state > $o,Com: com] :
% 0.29/0.69 ( ( size_size_com @ ( while @ Fun @ Com ) )
% 0.29/0.69 = ( plus_plus_nat @ ( size_size_com @ Com ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_691_com_Osize_I13_J,axiom,
% 0.29/0.69 ! [Fun: state > $o,Com1: com,Com2: com] :
% 0.29/0.69 ( ( size_size_com @ ( cond @ Fun @ Com1 @ Com2 ) )
% 0.29/0.69 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_size_com @ Com1 ) @ ( size_size_com @ Com2 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_692_evaln_OIfFalse,axiom,
% 0.29/0.69 ! [C0: com,C1: com,N_1: nat,S1: state,B: state > $o,S: state] :
% 0.29/0.69 ( ~ ( B @ S )
% 0.29/0.69 => ( ( evaln @ C1 @ S @ N_1 @ S1 )
% 0.29/0.69 => ( evaln @ ( cond @ B @ C0 @ C1 ) @ S @ N_1 @ S1 ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_693_evaln_OIfTrue,axiom,
% 0.29/0.69 ! [C1: com,C0: com,N_1: nat,S1: state,B: state > $o,S: state] :
% 0.29/0.69 ( ( B @ S )
% 0.29/0.69 => ( ( evaln @ C0 @ S @ N_1 @ S1 )
% 0.29/0.69 => ( evaln @ ( cond @ B @ C0 @ C1 ) @ S @ N_1 @ S1 ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_694_evaln__elim__cases_I5_J,axiom,
% 0.29/0.69 ! [B: state > $o,C1: com,C2: com,S: state,N_1: nat,T: state] :
% 0.29/0.69 ( ( evaln @ ( cond @ B @ C1 @ C2 ) @ S @ N_1 @ T )
% 0.29/0.69 => ( ( ( B @ S )
% 0.29/0.69 => ~ ( evaln @ C1 @ S @ N_1 @ T ) )
% 0.29/0.69 => ~ ( ~ ( B @ S )
% 0.29/0.69 => ~ ( evaln @ C2 @ S @ N_1 @ T ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_695_evalc__elim__cases_I5_J,axiom,
% 0.29/0.69 ! [B: state > $o,C1: com,C2: com,S: state,T: state] :
% 0.29/0.69 ( ( evalc @ ( cond @ B @ C1 @ C2 ) @ S @ T )
% 0.29/0.69 => ( ( ( B @ S )
% 0.29/0.69 => ~ ( evalc @ C1 @ S @ T ) )
% 0.29/0.69 => ~ ( ~ ( B @ S )
% 0.29/0.69 => ~ ( evalc @ C2 @ S @ T ) ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_696_evalc_OIfTrue,axiom,
% 0.29/0.69 ! [C1: com,C0: com,S1: state,B: state > $o,S: state] :
% 0.29/0.69 ( ( B @ S )
% 0.29/0.69 => ( ( evalc @ C0 @ S @ S1 )
% 0.29/0.69 => ( evalc @ ( cond @ B @ C0 @ C1 ) @ S @ S1 ) ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(fact_697_evalc_OIfFalse,axiom,
% 0.29/0.69 ! [C0: com,C1: com,S1: state,B: state > $o,S: state] :
% 0.29/0.69 ( ~ ( B @ S )
% 0.29/0.69 => ( ( evalc @ C1 @ S @ S1 )
% 0.29/0.69 => ( evalc @ ( cond @ B @ C0 @ C1 ) @ S @ S1 ) ) ) ).
% 0.29/0.69
% 0.29/0.69 %----Helper facts (14)
% 0.29/0.69 thf(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,
% 0.29/0.69 ! [X_1: pname,Y: pname] :
% 0.29/0.69 ( ~ ( fequal_pname @ X_1 @ Y )
% 0.29/0.69 | ( X_1 = Y ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,
% 0.29/0.69 ! [X_1: pname,Y: pname] :
% 0.29/0.69 ( ( X_1 != Y )
% 0.29/0.69 | ( fequal_pname @ X_1 @ Y ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(help_fequal_1_1_fequal_000tc__Com__Ostate_T,axiom,
% 0.29/0.69 ! [X_1: state,Y: state] :
% 0.29/0.69 ( ~ ( fequal_state @ X_1 @ Y )
% 0.29/0.69 | ( X_1 = Y ) ) ).
% 0.29/0.69
% 0.29/0.69 thf(help_fequal_2_1_fequal_000tc__Com__Ostate_T,axiom,
% 0.29/0.69 ! [X_1: state,Y: state] :
% 0.51/0.83 ( ( X_1 != Y )
% 0.51/0.83 | ( fequal_state @ X_1 @ Y ) ) ).
% 0.51/0.83
% 0.51/0.83 thf(help_If_1_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_T,axiom,
% 0.51/0.83 ! [X_1: hoare_1775062406iple_a,Y: hoare_1775062406iple_a] :
% 0.51/0.83 ( ( if_Hoa1047340790iple_a @ $true @ X_1 @ Y )
% 0.51/0.83 = X_1 ) ).
% 0.51/0.83
% 0.51/0.83 thf(help_If_2_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_T,axiom,
% 0.51/0.83 ! [X_1: hoare_1775062406iple_a,Y: hoare_1775062406iple_a] :
% 0.51/0.83 ( ( if_Hoa1047340790iple_a @ $false @ X_1 @ Y )
% 0.51/0.83 = Y ) ).
% 0.51/0.83
% 0.51/0.83 thf(help_If_3_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_T,axiom,
% 0.51/0.83 ! [P: $o] :
% 0.51/0.83 ( ( P = $true )
% 0.51/0.83 | ( P = $false ) ) ).
% 0.51/0.83
% 0.51/0.83 thf(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_,axiom,
% 0.51/0.83 ! [X_1: hoare_1775062406iple_a,Y: hoare_1775062406iple_a] :
% 0.51/0.83 ( ~ ( fequal1288209029iple_a @ X_1 @ Y )
% 0.51/0.83 | ( X_1 = Y ) ) ).
% 0.51/0.83
% 0.51/0.83 thf(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_,axiom,
% 0.51/0.83 ! [X_1: hoare_1775062406iple_a,Y: hoare_1775062406iple_a] :
% 0.51/0.83 ( ( X_1 != Y )
% 0.51/0.83 | ( fequal1288209029iple_a @ X_1 @ Y ) ) ).
% 0.51/0.83
% 0.51/0.83 thf(help_If_1_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate,axiom,
% 0.51/0.83 ! [X_1: hoare_1167836817_state,Y: hoare_1167836817_state] :
% 0.51/0.83 ( ( if_Hoa833675553_state @ $true @ X_1 @ Y )
% 0.51/0.83 = X_1 ) ).
% 0.51/0.83
% 0.51/0.83 thf(help_If_2_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate,axiom,
% 0.51/0.83 ! [X_1: hoare_1167836817_state,Y: hoare_1167836817_state] :
% 0.51/0.83 ( ( if_Hoa833675553_state @ $false @ X_1 @ Y )
% 0.51/0.83 = Y ) ).
% 0.51/0.83
% 0.51/0.83 thf(help_If_3_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate,axiom,
% 0.51/0.83 ! [P: $o] :
% 0.51/0.83 ( ( P = $true )
% 0.51/0.83 | ( P = $false ) ) ).
% 0.51/0.83
% 0.51/0.83 thf(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com,axiom,
% 0.51/0.83 ! [X_1: hoare_1167836817_state,Y: hoare_1167836817_state] :
% 0.51/0.83 ( ~ ( fequal1831255762_state @ X_1 @ Y )
% 0.51/0.83 | ( X_1 = Y ) ) ).
% 0.51/0.83
% 0.51/0.83 thf(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com,axiom,
% 0.51/0.83 ! [X_1: hoare_1167836817_state,Y: hoare_1167836817_state] :
% 0.51/0.83 ( ( X_1 != Y )
% 0.51/0.83 | ( fequal1831255762_state @ X_1 @ Y ) ) ).
% 0.51/0.83
% 0.51/0.83 %----Conjectures (2)
% 0.51/0.83 thf(conj_0,hypothesis,
% 0.51/0.83 ! [N: nat] :
% 0.51/0.83 ( ! [X: hoare_1775062406iple_a] :
% 0.51/0.83 ( ( member2122167641iple_a @ X
% 0.51/0.83 @ ( semila13410563le_a_o @ g
% 0.51/0.83 @ ( image_2063119815iple_a
% 0.51/0.83 @ ^ [Pn: pname] : ( hoare_1766022166iple_a @ ( p @ Pn ) @ ( body @ Pn ) @ ( q @ Pn ) )
% 0.51/0.83 @ procs ) ) )
% 0.51/0.83 => ( hoare_1462269968alid_a @ N @ X ) )
% 0.51/0.83 => ! [X: hoare_1775062406iple_a] :
% 0.51/0.83 ( ( member2122167641iple_a @ X
% 0.51/0.83 @ ( image_2063119815iple_a
% 0.51/0.83 @ ^ [Pn: pname] : ( hoare_1766022166iple_a @ ( p @ Pn ) @ ( the_com @ ( body_1 @ Pn ) ) @ ( q @ Pn ) )
% 0.51/0.83 @ procs ) )
% 0.51/0.83 => ( hoare_1462269968alid_a @ N @ X ) ) ) ).
% 0.51/0.83
% 0.51/0.83 thf(conj_1,conjecture,
% 0.51/0.83 ( ! [X: hoare_1775062406iple_a] :
% 0.51/0.83 ( ( member2122167641iple_a @ X @ g )
% 0.51/0.83 => ( hoare_1462269968alid_a @ n @ X ) )
% 0.51/0.83 => ! [X: hoare_1775062406iple_a] :
% 0.51/0.83 ( ( member2122167641iple_a @ X
% 0.51/0.83 @ ( image_2063119815iple_a
% 0.51/0.83 @ ^ [Pn: pname] : ( hoare_1766022166iple_a @ ( p @ Pn ) @ ( body @ Pn ) @ ( q @ Pn ) )
% 0.51/0.83 @ procs ) )
% 0.51/0.83 => ( hoare_1462269968alid_a @ n @ X ) ) ) ).
% 0.51/0.83
% 0.51/0.83 %------------------------------------------------------------------------------
% 0.51/0.83 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.7KZioWgwIx/cvc5---1.0.5_6910.p...
% 0.51/0.83 (declare-sort $$unsorted 0)
% 0.51/0.83 (declare-sort tptp.x_a 0)
% 0.51/0.83 (declare-sort tptp.com 0)
% 0.51/0.83 (declare-sort tptp.pname 0)
% 0.51/0.83 (declare-sort tptp.state 0)
% 0.51/0.83 (declare-sort tptp.hoare_1775062406iple_a 0)
% 0.51/0.83 (declare-sort tptp.hoare_1167836817_state 0)
% 0.51/0.83 (declare-sort tptp.nat 0)
% 0.51/0.83 (declare-sort tptp.option_com 0)
% 0.51/0.83 (declare-fun tptp.big_la1126801287name_o ((-> (-> tptp.pname Bool) Bool) tptp.pname) Bool)
% 0.51/0.83 (declare-fun tptp.big_la447547205le_a_o ((-> (-> tptp.hoare_1775062406iple_a Bool) Bool) tptp.hoare_1775062406iple_a) Bool)
% 0.51/0.83 (declare-fun tptp.big_la831793456tate_o ((-> (-> tptp.hoare_1167836817_state Bool) Bool) tptp.hoare_1167836817_state) Bool)
% 0.51/0.83 (declare-fun tptp.big_la1690136417_fin_o ((-> Bool Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.big_la1286884090name_o ((-> (-> tptp.pname Bool) Bool) tptp.pname) Bool)
% 0.51/0.83 (declare-fun tptp.big_la1843772984le_a_o ((-> (-> tptp.hoare_1775062406iple_a Bool) Bool) tptp.hoare_1775062406iple_a) Bool)
% 0.51/0.83 (declare-fun tptp.big_la1138507389tate_o ((-> (-> tptp.hoare_1167836817_state Bool) Bool) tptp.hoare_1167836817_state) Bool)
% 0.51/0.83 (declare-fun tptp.big_la727467310_fin_o ((-> Bool Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.body_1 (tptp.pname) tptp.option_com)
% 0.51/0.83 (declare-fun tptp.body (tptp.pname) tptp.com)
% 0.51/0.83 (declare-fun tptp.cond ((-> tptp.state Bool) tptp.com tptp.com) tptp.com)
% 0.51/0.83 (declare-fun tptp.skip () tptp.com)
% 0.51/0.83 (declare-fun tptp.semi (tptp.com tptp.com) tptp.com)
% 0.51/0.83 (declare-fun tptp.while ((-> tptp.state Bool) tptp.com) tptp.com)
% 0.51/0.83 (declare-fun tptp.com_size (tptp.com) tptp.nat)
% 0.51/0.83 (declare-fun tptp.finite297249702name_o ((-> (-> tptp.pname Bool) Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.finite789576932le_a_o ((-> (-> tptp.hoare_1775062406iple_a Bool) Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.finite1380128977tate_o ((-> (-> tptp.hoare_1167836817_state Bool) Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.finite_finite_o ((-> Bool Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.finite_finite_pname ((-> tptp.pname Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.finite2063573081iple_a ((-> tptp.hoare_1775062406iple_a Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.finite1084549118_state ((-> tptp.hoare_1167836817_state Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.finite1805141964_pname ((-> (-> tptp.hoare_1775062406iple_a Bool) (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a Bool) (-> tptp.pname tptp.hoare_1775062406iple_a Bool) (-> tptp.hoare_1775062406iple_a Bool) (-> tptp.pname Bool) tptp.hoare_1775062406iple_a) Bool)
% 0.51/0.83 (declare-fun tptp.finite1068437657_pname ((-> (-> tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state Bool) (-> tptp.pname tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool) (-> tptp.pname Bool) tptp.hoare_1167836817_state) Bool)
% 0.51/0.83 (declare-fun tptp.finite1282449217_pname ((-> tptp.pname tptp.pname tptp.pname) (-> (-> tptp.pname Bool) tptp.pname)) Bool)
% 0.51/0.83 (declare-fun tptp.finite2078349315iple_a ((-> tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a) (-> (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a)) Bool)
% 0.51/0.83 (declare-fun tptp.finite1074406356_state ((-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state) (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state)) Bool)
% 0.51/0.83 (declare-fun tptp.finite89670078_pname ((-> tptp.pname tptp.pname tptp.pname) (-> (-> tptp.pname Bool) tptp.pname)) Bool)
% 0.51/0.83 (declare-fun tptp.finite1358382848iple_a ((-> tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a) (-> (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a)) Bool)
% 0.51/0.83 (declare-fun tptp.finite806517911_state ((-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state) (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state)) Bool)
% 0.51/0.83 (declare-fun tptp.minus_minus_pname_o ((-> tptp.pname Bool) (-> tptp.pname Bool) tptp.pname) Bool)
% 0.51/0.83 (declare-fun tptp.minus_1944206118le_a_o ((-> tptp.hoare_1775062406iple_a Bool) (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a) Bool)
% 0.51/0.83 (declare-fun tptp.minus_2107060239tate_o ((-> tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state) Bool)
% 0.51/0.83 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.51/0.83 (declare-fun tptp.one_one_nat () tptp.nat)
% 0.51/0.83 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.51/0.83 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 0.51/0.83 (declare-fun tptp.the_pname ((-> tptp.pname Bool)) tptp.pname)
% 0.51/0.83 (declare-fun tptp.the_Ho1155011127iple_a ((-> tptp.hoare_1775062406iple_a Bool)) tptp.hoare_1775062406iple_a)
% 0.51/0.83 (declare-fun tptp.the_Ho310147232_state ((-> tptp.hoare_1167836817_state Bool)) tptp.hoare_1167836817_state)
% 0.51/0.83 (declare-fun tptp.hoare_Mirabelle_MGT (tptp.com) tptp.hoare_1167836817_state)
% 0.51/0.83 (declare-fun tptp.hoare_1508237396rivs_a ((-> tptp.hoare_1775062406iple_a Bool) (-> tptp.hoare_1775062406iple_a Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.hoare_123228589_state ((-> tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.hoare_1846070742lids_a ((-> tptp.hoare_1775062406iple_a Bool) (-> tptp.hoare_1775062406iple_a Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.hoare_529639851_state ((-> tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.hoare_1766022166iple_a ((-> tptp.x_a tptp.state Bool) tptp.com (-> tptp.x_a tptp.state Bool)) tptp.hoare_1775062406iple_a)
% 0.51/0.83 (declare-fun tptp.hoare_908217195_state ((-> tptp.state tptp.state Bool) tptp.com (-> tptp.state tptp.state Bool)) tptp.hoare_1167836817_state)
% 0.51/0.83 (declare-fun tptp.hoare_1118907895size_a ((-> tptp.x_a tptp.nat) tptp.hoare_1775062406iple_a) tptp.nat)
% 0.51/0.83 (declare-fun tptp.hoare_545207370_state ((-> tptp.state tptp.nat) tptp.hoare_1167836817_state) tptp.nat)
% 0.51/0.83 (declare-fun tptp.hoare_1462269968alid_a (tptp.nat tptp.hoare_1775062406iple_a) Bool)
% 0.51/0.83 (declare-fun tptp.hoare_56934129_state (tptp.nat tptp.hoare_1167836817_state) Bool)
% 0.51/0.83 (declare-fun tptp.if_Hoa1047340790iple_a (Bool tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a) tptp.hoare_1775062406iple_a)
% 0.51/0.83 (declare-fun tptp.if_Hoa833675553_state (Bool tptp.hoare_1167836817_state tptp.hoare_1167836817_state) tptp.hoare_1167836817_state)
% 0.51/0.83 (declare-fun tptp.semila2013987940me_o_o ((-> (-> tptp.pname Bool) Bool) (-> (-> tptp.pname Bool) Bool) (-> tptp.pname Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.semila1691990438_a_o_o ((-> (-> tptp.hoare_1775062406iple_a Bool) Bool) (-> (-> tptp.hoare_1775062406iple_a Bool) Bool) (-> tptp.hoare_1775062406iple_a Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.semila1758709489te_o_o ((-> (-> tptp.hoare_1167836817_state Bool) Bool) (-> (-> tptp.hoare_1167836817_state Bool) Bool) (-> tptp.hoare_1167836817_state Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.semila232696320nf_o_o ((-> Bool Bool) (-> Bool Bool) Bool) Bool)
% 0.51/0.83 (declare-fun tptp.semila1673364395name_o ((-> tptp.pname Bool) (-> tptp.pname Bool) tptp.pname) Bool)
% 0.51/0.83 (declare-fun tptp.semila966743401le_a_o ((-> tptp.hoare_1775062406iple_a Bool) (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a) Bool)
% 0.51/0.83 (declare-fun tptp.semila179895820tate_o ((-> tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state) Bool)
% 0.51/0.83 (declare-fun tptp.semila854092349_inf_o (Bool Bool) Bool)
% 0.51/0.83 (declare-fun tptp.semila181081674me_o_o ((-> (-> tptp.pname Bool) Bool) (-> (-> tptp.pname Bool) Bool) (-> tptp.pname Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.semila2069193356_a_o_o ((-> (-> tptp.hoare_1775062406iple_a Bool) Bool) (-> (-> tptp.hoare_1775062406iple_a Bool) Bool) (-> tptp.hoare_1775062406iple_a Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.semila866907787te_o_o ((-> (-> tptp.hoare_1167836817_state Bool) Bool) (-> (-> tptp.hoare_1167836817_state Bool) Bool) (-> tptp.hoare_1167836817_state Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.semila2062604954up_o_o ((-> Bool Bool) (-> Bool Bool) Bool) Bool)
% 0.51/0.83 (declare-fun tptp.semila1780557381name_o ((-> tptp.pname Bool) (-> tptp.pname Bool) tptp.pname) Bool)
% 0.51/0.83 (declare-fun tptp.semila13410563le_a_o ((-> tptp.hoare_1775062406iple_a Bool) (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a) Bool)
% 0.51/0.83 (declare-fun tptp.semila1172322802tate_o ((-> tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state) Bool)
% 0.51/0.83 (declare-fun tptp.semila10642723_sup_o (Bool Bool) Bool)
% 0.51/0.83 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 0.51/0.83 (declare-fun tptp.nat_case_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 0.51/0.83 (declare-fun tptp.size_size_com (tptp.com) tptp.nat)
% 0.51/0.83 (declare-fun tptp.size_s724313756iple_a (tptp.hoare_1775062406iple_a) tptp.nat)
% 0.51/0.83 (declare-fun tptp.size_s645941755_state (tptp.hoare_1167836817_state) tptp.nat)
% 0.51/0.83 (declare-fun tptp.evalc (tptp.com tptp.state tptp.state) Bool)
% 0.51/0.83 (declare-fun tptp.evaln (tptp.com tptp.state tptp.nat tptp.state) Bool)
% 0.51/0.83 (declare-fun tptp.the_com (tptp.option_com) tptp.com)
% 0.51/0.83 (declare-fun tptp.bot_bot_pname_o_o ((-> tptp.pname Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.bot_bo1976773294_a_o_o ((-> tptp.hoare_1775062406iple_a Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.bot_bo691907561te_o_o ((-> tptp.hoare_1167836817_state Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.bot_bot_o_o (Bool) Bool)
% 0.51/0.83 (declare-fun tptp.bot_bot_pname_o (tptp.pname) Bool)
% 0.51/0.83 (declare-fun tptp.bot_bo751897185le_a_o (tptp.hoare_1775062406iple_a) Bool)
% 0.51/0.83 (declare-fun tptp.bot_bo70021908tate_o (tptp.hoare_1167836817_state) Bool)
% 0.51/0.83 (declare-fun tptp.bot_bot_o () Bool)
% 0.51/0.83 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 0.51/0.83 (declare-fun tptp.collect_pname ((-> tptp.pname Bool) tptp.pname) Bool)
% 0.51/0.83 (declare-fun tptp.collec676402587iple_a ((-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a) Bool)
% 0.51/0.83 (declare-fun tptp.collec1027672124_state ((-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state) Bool)
% 0.51/0.83 (declare-fun tptp.image_1085733413name_o ((-> (-> tptp.pname Bool) tptp.pname Bool) (-> (-> tptp.pname Bool) Bool) (-> tptp.pname Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.image_2014247585le_a_o ((-> (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a Bool) (-> (-> tptp.hoare_1775062406iple_a Bool) Bool) (-> tptp.hoare_1775062406iple_a Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.image_1488525317tate_o ((-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state Bool) (-> (-> tptp.hoare_1167836817_state Bool) Bool) (-> tptp.hoare_1167836817_state Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.image_o_o ((-> Bool Bool) (-> Bool Bool) Bool) Bool)
% 0.51/0.83 (declare-fun tptp.image_pname_pname ((-> tptp.pname tptp.pname) (-> tptp.pname Bool) tptp.pname) Bool)
% 0.51/0.83 (declare-fun tptp.image_2063119815iple_a ((-> tptp.pname tptp.hoare_1775062406iple_a) (-> tptp.pname Bool) tptp.hoare_1775062406iple_a) Bool)
% 0.51/0.83 (declare-fun tptp.image_575578384_state ((-> tptp.pname tptp.hoare_1167836817_state) (-> tptp.pname Bool) tptp.hoare_1167836817_state) Bool)
% 0.51/0.83 (declare-fun tptp.image_51246659_pname ((-> tptp.hoare_1775062406iple_a tptp.pname) (-> tptp.hoare_1775062406iple_a Bool) tptp.pname) Bool)
% 0.51/0.83 (declare-fun tptp.image_1170193413iple_a ((-> tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a) (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a) Bool)
% 0.51/0.83 (declare-fun tptp.image_1021683026_state ((-> tptp.hoare_1775062406iple_a tptp.hoare_1167836817_state) (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1167836817_state) Bool)
% 0.51/0.83 (declare-fun tptp.image_1802845250iple_a ((-> tptp.hoare_1167836817_state tptp.hoare_1775062406iple_a) (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1775062406iple_a) Bool)
% 0.51/0.83 (declare-fun tptp.image_31595733_state ((-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state) (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state) Bool)
% 0.51/0.83 (declare-fun tptp.insert_pname_o ((-> tptp.pname Bool) (-> (-> tptp.pname Bool) Bool) (-> tptp.pname Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.insert1210049533le_a_o ((-> tptp.hoare_1775062406iple_a Bool) (-> (-> tptp.hoare_1775062406iple_a Bool) Bool) (-> tptp.hoare_1775062406iple_a Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.insert999278200tate_o ((-> tptp.hoare_1167836817_state Bool) (-> (-> tptp.hoare_1167836817_state Bool) Bool) (-> tptp.hoare_1167836817_state Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.insert_o (Bool (-> Bool Bool) Bool) Bool)
% 0.51/0.83 (declare-fun tptp.insert_pname (tptp.pname (-> tptp.pname Bool) tptp.pname) Bool)
% 0.51/0.83 (declare-fun tptp.insert1281456128iple_a (tptp.hoare_1775062406iple_a (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a) Bool)
% 0.51/0.83 (declare-fun tptp.insert2134838167_state (tptp.hoare_1167836817_state (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state) Bool)
% 0.51/0.83 (declare-fun tptp.the_elem_pname ((-> tptp.pname Bool)) tptp.pname)
% 0.51/0.83 (declare-fun tptp.the_el1844711461iple_a ((-> tptp.hoare_1775062406iple_a Bool)) tptp.hoare_1775062406iple_a)
% 0.51/0.83 (declare-fun tptp.the_el323660082_state ((-> tptp.hoare_1167836817_state Bool)) tptp.hoare_1167836817_state)
% 0.51/0.83 (declare-fun tptp.fequal_pname (tptp.pname tptp.pname) Bool)
% 0.51/0.83 (declare-fun tptp.fequal_state (tptp.state tptp.state) Bool)
% 0.51/0.83 (declare-fun tptp.fequal1288209029iple_a (tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a) Bool)
% 0.51/0.83 (declare-fun tptp.fequal1831255762_state (tptp.hoare_1167836817_state tptp.hoare_1167836817_state) Bool)
% 0.51/0.83 (declare-fun tptp.member_pname_o ((-> tptp.pname Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.member1207314404le_a_o ((-> tptp.hoare_1775062406iple_a Bool) (-> (-> tptp.hoare_1775062406iple_a Bool) Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.member864234961tate_o ((-> tptp.hoare_1167836817_state Bool) (-> (-> tptp.hoare_1167836817_state Bool) Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.member_o (Bool (-> Bool Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.member_pname (tptp.pname (-> tptp.pname Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.member2122167641iple_a (tptp.hoare_1775062406iple_a (-> tptp.hoare_1775062406iple_a Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.member2058392318_state (tptp.hoare_1167836817_state (-> tptp.hoare_1167836817_state Bool)) Bool)
% 0.51/0.83 (declare-fun tptp.g (tptp.hoare_1775062406iple_a) Bool)
% 0.51/0.83 (declare-fun tptp.p (tptp.pname tptp.x_a tptp.state) Bool)
% 0.51/0.83 (declare-fun tptp.procs (tptp.pname) Bool)
% 0.51/0.83 (declare-fun tptp.q (tptp.pname tptp.x_a tptp.state) Bool)
% 0.51/0.83 (declare-fun tptp.n () tptp.nat)
% 0.51/0.83 (assert (forall ((Fun1_4 (-> tptp.x_a tptp.state Bool)) (Com tptp.com) (Fun2_4 (-> tptp.x_a tptp.state Bool)) (Fun1_3 (-> tptp.x_a tptp.state Bool)) (Com_1 tptp.com) (Fun2_3 (-> tptp.x_a tptp.state Bool))) (= (= (@ (@ (@ tptp.hoare_1766022166iple_a Fun1_4) Com) Fun2_4) (@ (@ (@ tptp.hoare_1766022166iple_a Fun1_3) Com_1) Fun2_3)) (and (= Fun1_4 Fun1_3) (= Com Com_1) (= Fun2_4 Fun2_3)))))
% 0.51/0.83 (assert (forall ((Fun1_4 (-> tptp.state tptp.state Bool)) (Com tptp.com) (Fun2_4 (-> tptp.state tptp.state Bool)) (Fun1_3 (-> tptp.state tptp.state Bool)) (Com_1 tptp.com) (Fun2_3 (-> tptp.state tptp.state Bool))) (= (= (@ (@ (@ tptp.hoare_908217195_state Fun1_4) Com) Fun2_4) (@ (@ (@ tptp.hoare_908217195_state Fun1_3) Com_1) Fun2_3)) (and (= Fun1_4 Fun1_3) (= Com Com_1) (= Fun2_4 Fun2_3)))))
% 0.51/0.83 (assert (forall ((G_25 (-> tptp.hoare_1167836817_state Bool)) (Ts_4 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.hoare_529639851_state G_25) Ts_4) (forall ((N tptp.nat)) (=> (forall ((X tptp.hoare_1167836817_state)) (=> (@ (@ tptp.member2058392318_state X) G_25) (@ (@ tptp.hoare_56934129_state N) X))) (forall ((X tptp.hoare_1167836817_state)) (=> (@ (@ tptp.member2058392318_state X) Ts_4) (@ (@ tptp.hoare_56934129_state N) X))))))))
% 0.51/0.83 (assert (forall ((G_25 (-> tptp.hoare_1775062406iple_a Bool)) (Ts_4 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.hoare_1846070742lids_a G_25) Ts_4) (forall ((N tptp.nat)) (=> (forall ((X tptp.hoare_1775062406iple_a)) (=> (@ (@ tptp.member2122167641iple_a X) G_25) (@ (@ tptp.hoare_1462269968alid_a N) X))) (forall ((X tptp.hoare_1775062406iple_a)) (=> (@ (@ tptp.member2122167641iple_a X) Ts_4) (@ (@ tptp.hoare_1462269968alid_a N) X))))))))
% 0.51/0.83 (assert (forall ((G_24 (-> tptp.hoare_1167836817_state Bool)) (P_37 (-> tptp.pname tptp.state tptp.state Bool)) (Q_20 (-> tptp.pname tptp.state tptp.state Bool)) (Procs_1 (-> tptp.pname Bool))) (=> (@ (@ tptp.hoare_123228589_state (@ (@ tptp.semila1172322802tate_o G_24) (@ (@ tptp.image_575578384_state (lambda ((P_10 tptp.pname)) (@ (@ (@ tptp.hoare_908217195_state (@ P_37 P_10)) (@ tptp.body P_10)) (@ Q_20 P_10)))) Procs_1))) (@ (@ tptp.image_575578384_state (lambda ((P_10 tptp.pname)) (@ (@ (@ tptp.hoare_908217195_state (@ P_37 P_10)) (@ tptp.the_com (@ tptp.body_1 P_10))) (@ Q_20 P_10)))) Procs_1)) (@ (@ tptp.hoare_123228589_state G_24) (@ (@ tptp.image_575578384_state (lambda ((P_10 tptp.pname)) (@ (@ (@ tptp.hoare_908217195_state (@ P_37 P_10)) (@ tptp.body P_10)) (@ Q_20 P_10)))) Procs_1)))))
% 0.51/0.83 (assert (forall ((G_24 (-> tptp.hoare_1775062406iple_a Bool)) (P_37 (-> tptp.pname tptp.x_a tptp.state Bool)) (Q_20 (-> tptp.pname tptp.x_a tptp.state Bool)) (Procs_1 (-> tptp.pname Bool))) (=> (@ (@ tptp.hoare_1508237396rivs_a (@ (@ tptp.semila13410563le_a_o G_24) (@ (@ tptp.image_2063119815iple_a (lambda ((P_10 tptp.pname)) (@ (@ (@ tptp.hoare_1766022166iple_a (@ P_37 P_10)) (@ tptp.body P_10)) (@ Q_20 P_10)))) Procs_1))) (@ (@ tptp.image_2063119815iple_a (lambda ((P_10 tptp.pname)) (@ (@ (@ tptp.hoare_1766022166iple_a (@ P_37 P_10)) (@ tptp.the_com (@ tptp.body_1 P_10))) (@ Q_20 P_10)))) Procs_1)) (@ (@ tptp.hoare_1508237396rivs_a G_24) (@ (@ tptp.image_2063119815iple_a (lambda ((P_10 tptp.pname)) (@ (@ (@ tptp.hoare_1766022166iple_a (@ P_37 P_10)) (@ tptp.body P_10)) (@ Q_20 P_10)))) Procs_1)))))
% 0.51/0.83 (assert (forall ((C_42 tptp.hoare_1167836817_state) (A_138 (-> tptp.hoare_1167836817_state Bool)) (B_79 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state C_42))) (=> (@ _let_1 (@ (@ tptp.semila1172322802tate_o A_138) B_79)) (=> (not (@ _let_1 A_138)) (@ _let_1 B_79))))))
% 0.51/0.83 (assert (forall ((C_42 tptp.hoare_1775062406iple_a) (A_138 (-> tptp.hoare_1775062406iple_a Bool)) (B_79 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.member2122167641iple_a C_42))) (=> (@ _let_1 (@ (@ tptp.semila13410563le_a_o A_138) B_79)) (=> (not (@ _let_1 A_138)) (@ _let_1 B_79))))))
% 0.51/0.83 (assert (forall ((C_42 tptp.pname) (A_138 (-> tptp.pname Bool)) (B_79 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_42))) (=> (@ _let_1 (@ (@ tptp.semila1780557381name_o A_138) B_79)) (=> (not (@ _let_1 A_138)) (@ _let_1 B_79))))))
% 0.51/0.83 (assert (forall ((A_137 (-> tptp.hoare_1167836817_state Bool)) (B_78 (-> tptp.hoare_1167836817_state Bool)) (X_51 tptp.hoare_1167836817_state)) (=> (@ (@ (@ tptp.semila1172322802tate_o A_137) B_78) X_51) (=> (not (@ A_137 X_51)) (@ B_78 X_51)))))
% 0.51/0.83 (assert (forall ((A_137 (-> tptp.pname Bool)) (B_78 (-> tptp.pname Bool)) (X_51 tptp.pname)) (=> (@ (@ (@ tptp.semila1780557381name_o A_137) B_78) X_51) (=> (not (@ A_137 X_51)) (@ B_78 X_51)))))
% 0.51/0.83 (assert (forall ((A_137 (-> tptp.hoare_1775062406iple_a Bool)) (B_78 (-> tptp.hoare_1775062406iple_a Bool)) (X_51 tptp.hoare_1775062406iple_a)) (=> (@ (@ (@ tptp.semila13410563le_a_o A_137) B_78) X_51) (=> (not (@ A_137 X_51)) (@ B_78 X_51)))))
% 0.51/0.83 (assert (forall ((A_136 (-> tptp.hoare_1167836817_state Bool)) (B_77 (-> tptp.hoare_1167836817_state Bool)) (X_50 tptp.hoare_1167836817_state)) (=> (=> (not (@ B_77 X_50)) (@ A_136 X_50)) (@ (@ (@ tptp.semila1172322802tate_o A_136) B_77) X_50))))
% 0.51/0.83 (assert (forall ((A_136 (-> tptp.pname Bool)) (B_77 (-> tptp.pname Bool)) (X_50 tptp.pname)) (=> (=> (not (@ B_77 X_50)) (@ A_136 X_50)) (@ (@ (@ tptp.semila1780557381name_o A_136) B_77) X_50))))
% 0.51/0.83 (assert (forall ((A_136 (-> tptp.hoare_1775062406iple_a Bool)) (B_77 (-> tptp.hoare_1775062406iple_a Bool)) (X_50 tptp.hoare_1775062406iple_a)) (=> (=> (not (@ B_77 X_50)) (@ A_136 X_50)) (@ (@ (@ tptp.semila13410563le_a_o A_136) B_77) X_50))))
% 0.51/0.83 (assert (forall ((A_135 (-> tptp.hoare_1167836817_state Bool)) (C_41 tptp.hoare_1167836817_state) (B_76 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state C_41))) (=> (=> (not (@ _let_1 B_76)) (@ _let_1 A_135)) (@ _let_1 (@ (@ tptp.semila1172322802tate_o A_135) B_76))))))
% 0.51/0.83 (assert (forall ((A_135 (-> tptp.hoare_1775062406iple_a Bool)) (C_41 tptp.hoare_1775062406iple_a) (B_76 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.member2122167641iple_a C_41))) (=> (=> (not (@ _let_1 B_76)) (@ _let_1 A_135)) (@ _let_1 (@ (@ tptp.semila13410563le_a_o A_135) B_76))))))
% 0.51/0.83 (assert (forall ((A_135 (-> tptp.pname Bool)) (C_41 tptp.pname) (B_76 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_41))) (=> (=> (not (@ _let_1 B_76)) (@ _let_1 A_135)) (@ _let_1 (@ (@ tptp.semila1780557381name_o A_135) B_76))))))
% 0.51/0.83 (assert (forall ((A_134 (-> tptp.pname Bool)) (B_75 tptp.hoare_1167836817_state) (F_41 (-> tptp.pname tptp.hoare_1167836817_state)) (X_49 tptp.pname)) (=> (= B_75 (@ F_41 X_49)) (=> (@ (@ tptp.member_pname X_49) A_134) (@ (@ tptp.member2058392318_state B_75) (@ (@ tptp.image_575578384_state F_41) A_134))))))
% 0.51/0.83 (assert (forall ((A_134 (-> tptp.hoare_1775062406iple_a Bool)) (B_75 tptp.pname) (F_41 (-> tptp.hoare_1775062406iple_a tptp.pname)) (X_49 tptp.hoare_1775062406iple_a)) (=> (= B_75 (@ F_41 X_49)) (=> (@ (@ tptp.member2122167641iple_a X_49) A_134) (@ (@ tptp.member_pname B_75) (@ (@ tptp.image_51246659_pname F_41) A_134))))))
% 0.51/0.83 (assert (forall ((A_134 (-> tptp.pname Bool)) (B_75 tptp.hoare_1775062406iple_a) (F_41 (-> tptp.pname tptp.hoare_1775062406iple_a)) (X_49 tptp.pname)) (=> (= B_75 (@ F_41 X_49)) (=> (@ (@ tptp.member_pname X_49) A_134) (@ (@ tptp.member2122167641iple_a B_75) (@ (@ tptp.image_2063119815iple_a F_41) A_134))))))
% 0.51/0.83 (assert (forall ((F_40 (-> tptp.pname tptp.hoare_1167836817_state)) (A_133 (-> tptp.pname Bool)) (B_74 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_575578384_state F_40))) (= (@ _let_1 (@ (@ tptp.semila1780557381name_o A_133) B_74)) (@ (@ tptp.semila1172322802tate_o (@ _let_1 A_133)) (@ _let_1 B_74))))))
% 0.51/0.83 (assert (forall ((F_40 (-> tptp.hoare_1775062406iple_a tptp.hoare_1167836817_state)) (A_133 (-> tptp.hoare_1775062406iple_a Bool)) (B_74 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.image_1021683026_state F_40))) (= (@ _let_1 (@ (@ tptp.semila13410563le_a_o A_133) B_74)) (@ (@ tptp.semila1172322802tate_o (@ _let_1 A_133)) (@ _let_1 B_74))))))
% 0.51/0.83 (assert (forall ((F_40 (-> tptp.hoare_1775062406iple_a tptp.pname)) (A_133 (-> tptp.hoare_1775062406iple_a Bool)) (B_74 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.image_51246659_pname F_40))) (= (@ _let_1 (@ (@ tptp.semila13410563le_a_o A_133) B_74)) (@ (@ tptp.semila1780557381name_o (@ _let_1 A_133)) (@ _let_1 B_74))))))
% 0.51/0.83 (assert (forall ((F_40 (-> tptp.hoare_1167836817_state tptp.hoare_1775062406iple_a)) (A_133 (-> tptp.hoare_1167836817_state Bool)) (B_74 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.image_1802845250iple_a F_40))) (= (@ _let_1 (@ (@ tptp.semila1172322802tate_o A_133) B_74)) (@ (@ tptp.semila13410563le_a_o (@ _let_1 A_133)) (@ _let_1 B_74))))))
% 0.51/0.83 (assert (forall ((F_40 (-> tptp.pname tptp.hoare_1775062406iple_a)) (A_133 (-> tptp.pname Bool)) (B_74 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_2063119815iple_a F_40))) (= (@ _let_1 (@ (@ tptp.semila1780557381name_o A_133) B_74)) (@ (@ tptp.semila13410563le_a_o (@ _let_1 A_133)) (@ _let_1 B_74))))))
% 0.51/0.83 (assert (forall ((F_39 (-> tptp.hoare_1167836817_state Bool)) (G_23 (-> tptp.hoare_1167836817_state Bool)) (X tptp.hoare_1167836817_state)) (= (@ (@ (@ tptp.semila1172322802tate_o F_39) G_23) X) (@ (@ tptp.semila10642723_sup_o (@ F_39 X)) (@ G_23 X)))))
% 0.51/0.83 (assert (forall ((F_39 (-> tptp.pname Bool)) (G_23 (-> tptp.pname Bool)) (X tptp.pname)) (= (@ (@ (@ tptp.semila1780557381name_o F_39) G_23) X) (@ (@ tptp.semila10642723_sup_o (@ F_39 X)) (@ G_23 X)))))
% 0.51/0.83 (assert (forall ((F_39 (-> tptp.hoare_1775062406iple_a Bool)) (G_23 (-> tptp.hoare_1775062406iple_a Bool)) (X tptp.hoare_1775062406iple_a)) (= (@ (@ (@ tptp.semila13410563le_a_o F_39) G_23) X) (@ (@ tptp.semila10642723_sup_o (@ F_39 X)) (@ G_23 X)))))
% 0.51/0.83 (assert (forall ((F_38 (-> tptp.hoare_1167836817_state Bool)) (G_22 (-> tptp.hoare_1167836817_state Bool)) (X_48 tptp.hoare_1167836817_state)) (= (@ (@ (@ tptp.semila1172322802tate_o F_38) G_22) X_48) (@ (@ tptp.semila10642723_sup_o (@ F_38 X_48)) (@ G_22 X_48)))))
% 0.51/0.83 (assert (forall ((F_38 (-> tptp.pname Bool)) (G_22 (-> tptp.pname Bool)) (X_48 tptp.pname)) (= (@ (@ (@ tptp.semila1780557381name_o F_38) G_22) X_48) (@ (@ tptp.semila10642723_sup_o (@ F_38 X_48)) (@ G_22 X_48)))))
% 0.51/0.83 (assert (forall ((F_38 (-> tptp.hoare_1775062406iple_a Bool)) (G_22 (-> tptp.hoare_1775062406iple_a Bool)) (X_48 tptp.hoare_1775062406iple_a)) (= (@ (@ (@ tptp.semila13410563le_a_o F_38) G_22) X_48) (@ (@ tptp.semila10642723_sup_o (@ F_38 X_48)) (@ G_22 X_48)))))
% 0.51/0.83 (assert (forall ((G_21 (-> tptp.hoare_1167836817_state Bool)) (G_20 (-> tptp.hoare_1167836817_state Bool)) (Ts_3 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.hoare_123228589_state G_21))) (=> (@ (@ tptp.hoare_123228589_state G_20) Ts_3) (=> (@ _let_1 G_20) (@ _let_1 Ts_3))))))
% 0.51/0.83 (assert (forall ((G_21 (-> tptp.hoare_1775062406iple_a Bool)) (G_20 (-> tptp.hoare_1775062406iple_a Bool)) (Ts_3 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.hoare_1508237396rivs_a G_21))) (=> (@ (@ tptp.hoare_1508237396rivs_a G_20) Ts_3) (=> (@ _let_1 G_20) (@ _let_1 Ts_3))))))
% 0.51/0.83 (assert (forall ((X_47 (-> tptp.hoare_1167836817_state Bool)) (Y_21 (-> tptp.hoare_1167836817_state Bool)) (Z_14 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila1172322802tate_o X_47))) (= (@ (@ tptp.semila1172322802tate_o (@ _let_1 Y_21)) Z_14) (@ _let_1 (@ (@ tptp.semila1172322802tate_o Y_21) Z_14))))))
% 0.51/0.83 (assert (forall ((X_47 (-> tptp.pname Bool)) (Y_21 (-> tptp.pname Bool)) (Z_14 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o X_47))) (= (@ (@ tptp.semila1780557381name_o (@ _let_1 Y_21)) Z_14) (@ _let_1 (@ (@ tptp.semila1780557381name_o Y_21) Z_14))))))
% 0.51/0.83 (assert (forall ((X_47 Bool) (Y_21 Bool) (Z_14 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o X_47))) (= (@ (@ tptp.semila10642723_sup_o (@ _let_1 Y_21)) Z_14) (@ _let_1 (@ (@ tptp.semila10642723_sup_o Y_21) Z_14))))))
% 0.51/0.83 (assert (forall ((X_47 (-> tptp.hoare_1775062406iple_a Bool)) (Y_21 (-> tptp.hoare_1775062406iple_a Bool)) (Z_14 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila13410563le_a_o X_47))) (= (@ (@ tptp.semila13410563le_a_o (@ _let_1 Y_21)) Z_14) (@ _let_1 (@ (@ tptp.semila13410563le_a_o Y_21) Z_14))))))
% 0.51/0.83 (assert (forall ((X_46 (-> tptp.hoare_1167836817_state Bool)) (Y_20 (-> tptp.hoare_1167836817_state Bool)) (Z_13 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila1172322802tate_o X_46))) (= (@ (@ tptp.semila1172322802tate_o (@ _let_1 Y_20)) Z_13) (@ _let_1 (@ (@ tptp.semila1172322802tate_o Y_20) Z_13))))))
% 0.51/0.83 (assert (forall ((X_46 (-> tptp.pname Bool)) (Y_20 (-> tptp.pname Bool)) (Z_13 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o X_46))) (= (@ (@ tptp.semila1780557381name_o (@ _let_1 Y_20)) Z_13) (@ _let_1 (@ (@ tptp.semila1780557381name_o Y_20) Z_13))))))
% 0.51/0.83 (assert (forall ((X_46 Bool) (Y_20 Bool) (Z_13 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o X_46))) (= (@ (@ tptp.semila10642723_sup_o (@ _let_1 Y_20)) Z_13) (@ _let_1 (@ (@ tptp.semila10642723_sup_o Y_20) Z_13))))))
% 0.51/0.83 (assert (forall ((X_46 (-> tptp.hoare_1775062406iple_a Bool)) (Y_20 (-> tptp.hoare_1775062406iple_a Bool)) (Z_13 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila13410563le_a_o X_46))) (= (@ (@ tptp.semila13410563le_a_o (@ _let_1 Y_20)) Z_13) (@ _let_1 (@ (@ tptp.semila13410563le_a_o Y_20) Z_13))))))
% 0.51/0.83 (assert (forall ((A_132 (-> tptp.hoare_1167836817_state Bool)) (B_73 (-> tptp.hoare_1167836817_state Bool)) (C_40 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila1172322802tate_o A_132))) (= (@ (@ tptp.semila1172322802tate_o (@ _let_1 B_73)) C_40) (@ _let_1 (@ (@ tptp.semila1172322802tate_o B_73) C_40))))))
% 0.51/0.83 (assert (forall ((A_132 (-> tptp.pname Bool)) (B_73 (-> tptp.pname Bool)) (C_40 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o A_132))) (= (@ (@ tptp.semila1780557381name_o (@ _let_1 B_73)) C_40) (@ _let_1 (@ (@ tptp.semila1780557381name_o B_73) C_40))))))
% 0.51/0.83 (assert (forall ((A_132 Bool) (B_73 Bool) (C_40 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o A_132))) (= (@ (@ tptp.semila10642723_sup_o (@ _let_1 B_73)) C_40) (@ _let_1 (@ (@ tptp.semila10642723_sup_o B_73) C_40))))))
% 0.51/0.83 (assert (forall ((A_132 (-> tptp.hoare_1775062406iple_a Bool)) (B_73 (-> tptp.hoare_1775062406iple_a Bool)) (C_40 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila13410563le_a_o A_132))) (= (@ (@ tptp.semila13410563le_a_o (@ _let_1 B_73)) C_40) (@ _let_1 (@ (@ tptp.semila13410563le_a_o B_73) C_40))))))
% 0.51/0.83 (assert (forall ((X_45 (-> tptp.hoare_1167836817_state Bool)) (Y_19 (-> tptp.hoare_1167836817_state Bool)) (Z_12 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila1172322802tate_o X_45))) (let ((_let_2 (@ tptp.semila1172322802tate_o Y_19))) (= (@ _let_1 (@ _let_2 Z_12)) (@ _let_2 (@ _let_1 Z_12)))))))
% 0.51/0.83 (assert (forall ((X_45 (-> tptp.pname Bool)) (Y_19 (-> tptp.pname Bool)) (Z_12 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o X_45))) (let ((_let_2 (@ tptp.semila1780557381name_o Y_19))) (= (@ _let_1 (@ _let_2 Z_12)) (@ _let_2 (@ _let_1 Z_12)))))))
% 0.51/0.83 (assert (forall ((X_45 Bool) (Y_19 Bool) (Z_12 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o X_45))) (let ((_let_2 (@ tptp.semila10642723_sup_o Y_19))) (= (@ _let_1 (@ _let_2 Z_12)) (@ _let_2 (@ _let_1 Z_12)))))))
% 0.51/0.83 (assert (forall ((X_45 (-> tptp.hoare_1775062406iple_a Bool)) (Y_19 (-> tptp.hoare_1775062406iple_a Bool)) (Z_12 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila13410563le_a_o X_45))) (let ((_let_2 (@ tptp.semila13410563le_a_o Y_19))) (= (@ _let_1 (@ _let_2 Z_12)) (@ _let_2 (@ _let_1 Z_12)))))))
% 0.51/0.83 (assert (forall ((X_44 (-> tptp.hoare_1167836817_state Bool)) (Y_18 (-> tptp.hoare_1167836817_state Bool)) (Z_11 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila1172322802tate_o X_44))) (let ((_let_2 (@ tptp.semila1172322802tate_o Y_18))) (= (@ _let_1 (@ _let_2 Z_11)) (@ _let_2 (@ _let_1 Z_11)))))))
% 0.51/0.83 (assert (forall ((X_44 (-> tptp.pname Bool)) (Y_18 (-> tptp.pname Bool)) (Z_11 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o X_44))) (let ((_let_2 (@ tptp.semila1780557381name_o Y_18))) (= (@ _let_1 (@ _let_2 Z_11)) (@ _let_2 (@ _let_1 Z_11)))))))
% 0.51/0.83 (assert (forall ((X_44 Bool) (Y_18 Bool) (Z_11 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o X_44))) (let ((_let_2 (@ tptp.semila10642723_sup_o Y_18))) (= (@ _let_1 (@ _let_2 Z_11)) (@ _let_2 (@ _let_1 Z_11)))))))
% 0.51/0.83 (assert (forall ((X_44 (-> tptp.hoare_1775062406iple_a Bool)) (Y_18 (-> tptp.hoare_1775062406iple_a Bool)) (Z_11 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila13410563le_a_o X_44))) (let ((_let_2 (@ tptp.semila13410563le_a_o Y_18))) (= (@ _let_1 (@ _let_2 Z_11)) (@ _let_2 (@ _let_1 Z_11)))))))
% 0.51/0.83 (assert (forall ((B_72 (-> tptp.hoare_1167836817_state Bool)) (A_131 (-> tptp.hoare_1167836817_state Bool)) (C_39 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila1172322802tate_o B_72))) (let ((_let_2 (@ tptp.semila1172322802tate_o A_131))) (= (@ _let_1 (@ _let_2 C_39)) (@ _let_2 (@ _let_1 C_39)))))))
% 0.51/0.83 (assert (forall ((B_72 (-> tptp.pname Bool)) (A_131 (-> tptp.pname Bool)) (C_39 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o B_72))) (let ((_let_2 (@ tptp.semila1780557381name_o A_131))) (= (@ _let_1 (@ _let_2 C_39)) (@ _let_2 (@ _let_1 C_39)))))))
% 0.51/0.83 (assert (forall ((B_72 Bool) (A_131 Bool) (C_39 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o B_72))) (let ((_let_2 (@ tptp.semila10642723_sup_o A_131))) (= (@ _let_1 (@ _let_2 C_39)) (@ _let_2 (@ _let_1 C_39)))))))
% 0.51/0.83 (assert (forall ((B_72 (-> tptp.hoare_1775062406iple_a Bool)) (A_131 (-> tptp.hoare_1775062406iple_a Bool)) (C_39 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila13410563le_a_o B_72))) (let ((_let_2 (@ tptp.semila13410563le_a_o A_131))) (= (@ _let_1 (@ _let_2 C_39)) (@ _let_2 (@ _let_1 C_39)))))))
% 0.51/0.83 (assert (forall ((X_43 (-> tptp.hoare_1167836817_state Bool)) (Y_17 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila1172322802tate_o X_43))) (let ((_let_2 (@ _let_1 Y_17))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.83 (assert (forall ((X_43 (-> tptp.pname Bool)) (Y_17 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o X_43))) (let ((_let_2 (@ _let_1 Y_17))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.83 (assert (forall ((X_43 Bool) (Y_17 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o X_43))) (let ((_let_2 (@ _let_1 Y_17))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.83 (assert (forall ((X_43 (-> tptp.hoare_1775062406iple_a Bool)) (Y_17 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila13410563le_a_o X_43))) (let ((_let_2 (@ _let_1 Y_17))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.83 (assert (forall ((X_42 (-> tptp.hoare_1167836817_state Bool)) (Y_16 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila1172322802tate_o X_42))) (let ((_let_2 (@ _let_1 Y_16))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.83 (assert (forall ((X_42 (-> tptp.pname Bool)) (Y_16 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o X_42))) (let ((_let_2 (@ _let_1 Y_16))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.83 (assert (forall ((X_42 Bool) (Y_16 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o X_42))) (let ((_let_2 (@ _let_1 Y_16))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.83 (assert (forall ((X_42 (-> tptp.hoare_1775062406iple_a Bool)) (Y_16 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila13410563le_a_o X_42))) (let ((_let_2 (@ _let_1 Y_16))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.83 (assert (forall ((A_130 (-> tptp.hoare_1167836817_state Bool)) (B_71 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila1172322802tate_o A_130))) (let ((_let_2 (@ _let_1 B_71))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.83 (assert (forall ((A_130 (-> tptp.pname Bool)) (B_71 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o A_130))) (let ((_let_2 (@ _let_1 B_71))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.83 (assert (forall ((A_130 Bool) (B_71 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o A_130))) (let ((_let_2 (@ _let_1 B_71))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.83 (assert (forall ((A_130 (-> tptp.hoare_1775062406iple_a Bool)) (B_71 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila13410563le_a_o A_130))) (let ((_let_2 (@ _let_1 B_71))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.83 (assert (forall ((X_41 (-> tptp.hoare_1167836817_state Bool)) (Y_15 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila1172322802tate_o X_41) Y_15) (@ (@ tptp.semila1172322802tate_o Y_15) X_41))))
% 0.51/0.83 (assert (forall ((X_41 (-> tptp.pname Bool)) (Y_15 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o X_41) Y_15) (@ (@ tptp.semila1780557381name_o Y_15) X_41))))
% 0.51/0.83 (assert (forall ((X_41 Bool) (Y_15 Bool)) (= (@ (@ tptp.semila10642723_sup_o X_41) Y_15) (@ (@ tptp.semila10642723_sup_o Y_15) X_41))))
% 0.51/0.83 (assert (forall ((X_41 (-> tptp.hoare_1775062406iple_a Bool)) (Y_15 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila13410563le_a_o X_41) Y_15) (@ (@ tptp.semila13410563le_a_o Y_15) X_41))))
% 0.51/0.83 (assert (forall ((X_40 (-> tptp.hoare_1167836817_state Bool)) (Y_14 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila1172322802tate_o X_40) Y_14) (@ (@ tptp.semila1172322802tate_o Y_14) X_40))))
% 0.51/0.83 (assert (forall ((X_40 (-> tptp.pname Bool)) (Y_14 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o X_40) Y_14) (@ (@ tptp.semila1780557381name_o Y_14) X_40))))
% 0.51/0.83 (assert (forall ((X_40 Bool) (Y_14 Bool)) (= (@ (@ tptp.semila10642723_sup_o X_40) Y_14) (@ (@ tptp.semila10642723_sup_o Y_14) X_40))))
% 0.51/0.83 (assert (forall ((X_40 (-> tptp.hoare_1775062406iple_a Bool)) (Y_14 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila13410563le_a_o X_40) Y_14) (@ (@ tptp.semila13410563le_a_o Y_14) X_40))))
% 0.51/0.83 (assert (forall ((A_129 (-> tptp.hoare_1167836817_state Bool)) (B_70 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila1172322802tate_o A_129) B_70) (@ (@ tptp.semila1172322802tate_o B_70) A_129))))
% 0.51/0.83 (assert (forall ((A_129 (-> tptp.pname Bool)) (B_70 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o A_129) B_70) (@ (@ tptp.semila1780557381name_o B_70) A_129))))
% 0.51/0.83 (assert (forall ((A_129 Bool) (B_70 Bool)) (= (@ (@ tptp.semila10642723_sup_o A_129) B_70) (@ (@ tptp.semila10642723_sup_o B_70) A_129))))
% 0.51/0.83 (assert (forall ((A_129 (-> tptp.hoare_1775062406iple_a Bool)) (B_70 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila13410563le_a_o A_129) B_70) (@ (@ tptp.semila13410563le_a_o B_70) A_129))))
% 0.51/0.83 (assert (forall ((X_39 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila1172322802tate_o X_39) X_39) X_39)))
% 0.51/0.83 (assert (forall ((X_39 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o X_39) X_39) X_39)))
% 0.51/0.83 (assert (forall ((X_39 Bool)) (= (@ (@ tptp.semila10642723_sup_o X_39) X_39) X_39)))
% 0.51/0.83 (assert (forall ((X_39 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila13410563le_a_o X_39) X_39) X_39)))
% 0.51/0.83 (assert (forall ((A_128 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila1172322802tate_o A_128) A_128) A_128)))
% 0.51/0.83 (assert (forall ((A_128 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o A_128) A_128) A_128)))
% 0.51/0.83 (assert (forall ((A_128 Bool)) (= (@ (@ tptp.semila10642723_sup_o A_128) A_128) A_128)))
% 0.51/0.83 (assert (forall ((A_128 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila13410563le_a_o A_128) A_128) A_128)))
% 0.51/0.83 (assert (forall ((B_69 tptp.hoare_1167836817_state) (F_37 (-> tptp.pname tptp.hoare_1167836817_state)) (X_38 tptp.pname) (A_127 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_38) A_127) (=> (= B_69 (@ F_37 X_38)) (@ (@ tptp.member2058392318_state B_69) (@ (@ tptp.image_575578384_state F_37) A_127))))))
% 0.51/0.83 (assert (forall ((B_69 tptp.pname) (F_37 (-> tptp.hoare_1775062406iple_a tptp.pname)) (X_38 tptp.hoare_1775062406iple_a) (A_127 (-> tptp.hoare_1775062406iple_a Bool))) (=> (@ (@ tptp.member2122167641iple_a X_38) A_127) (=> (= B_69 (@ F_37 X_38)) (@ (@ tptp.member_pname B_69) (@ (@ tptp.image_51246659_pname F_37) A_127))))))
% 0.51/0.83 (assert (forall ((B_69 tptp.hoare_1775062406iple_a) (F_37 (-> tptp.pname tptp.hoare_1775062406iple_a)) (X_38 tptp.pname) (A_127 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_38) A_127) (=> (= B_69 (@ F_37 X_38)) (@ (@ tptp.member2122167641iple_a B_69) (@ (@ tptp.image_2063119815iple_a F_37) A_127))))))
% 0.51/0.83 (assert (forall ((F_36 (-> tptp.pname tptp.hoare_1167836817_state)) (X_37 tptp.pname) (A_126 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_37) A_126) (@ (@ tptp.member2058392318_state (@ F_36 X_37)) (@ (@ tptp.image_575578384_state F_36) A_126)))))
% 0.51/0.83 (assert (forall ((F_36 (-> tptp.hoare_1775062406iple_a tptp.pname)) (X_37 tptp.hoare_1775062406iple_a) (A_126 (-> tptp.hoare_1775062406iple_a Bool))) (=> (@ (@ tptp.member2122167641iple_a X_37) A_126) (@ (@ tptp.member_pname (@ F_36 X_37)) (@ (@ tptp.image_51246659_pname F_36) A_126)))))
% 0.51/0.83 (assert (forall ((F_36 (-> tptp.pname tptp.hoare_1775062406iple_a)) (X_37 tptp.pname) (A_126 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_37) A_126) (@ (@ tptp.member2122167641iple_a (@ F_36 X_37)) (@ (@ tptp.image_2063119815iple_a F_36) A_126)))))
% 0.51/0.83 (assert (forall ((Z_10 tptp.hoare_1167836817_state) (F_35 (-> tptp.pname tptp.hoare_1167836817_state)) (A_125 (-> tptp.pname Bool))) (= (@ (@ tptp.member2058392318_state Z_10) (@ (@ tptp.image_575578384_state F_35) A_125)) (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) A_125) (= Z_10 (@ F_35 X)))))))
% 0.51/0.83 (assert (forall ((Z_10 tptp.hoare_1775062406iple_a) (F_35 (-> tptp.pname tptp.hoare_1775062406iple_a)) (A_125 (-> tptp.pname Bool))) (= (@ (@ tptp.member2122167641iple_a Z_10) (@ (@ tptp.image_2063119815iple_a F_35) A_125)) (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) A_125) (= Z_10 (@ F_35 X)))))))
% 0.51/0.83 (assert (forall ((A_124 (-> tptp.hoare_1167836817_state Bool)) (C_38 tptp.hoare_1167836817_state) (B_68 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state C_38))) (=> (@ _let_1 B_68) (@ _let_1 (@ (@ tptp.semila1172322802tate_o A_124) B_68))))))
% 0.51/0.83 (assert (forall ((A_124 (-> tptp.hoare_1775062406iple_a Bool)) (C_38 tptp.hoare_1775062406iple_a) (B_68 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.member2122167641iple_a C_38))) (=> (@ _let_1 B_68) (@ _let_1 (@ (@ tptp.semila13410563le_a_o A_124) B_68))))))
% 0.51/0.83 (assert (forall ((A_124 (-> tptp.pname Bool)) (C_38 tptp.pname) (B_68 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_38))) (=> (@ _let_1 B_68) (@ _let_1 (@ (@ tptp.semila1780557381name_o A_124) B_68))))))
% 0.51/0.83 (assert (forall ((B_67 (-> tptp.hoare_1167836817_state Bool)) (C_37 tptp.hoare_1167836817_state) (A_123 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state C_37))) (=> (@ _let_1 A_123) (@ _let_1 (@ (@ tptp.semila1172322802tate_o A_123) B_67))))))
% 0.51/0.83 (assert (forall ((B_67 (-> tptp.hoare_1775062406iple_a Bool)) (C_37 tptp.hoare_1775062406iple_a) (A_123 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.member2122167641iple_a C_37))) (=> (@ _let_1 A_123) (@ _let_1 (@ (@ tptp.semila13410563le_a_o A_123) B_67))))))
% 0.51/0.83 (assert (forall ((B_67 (-> tptp.pname Bool)) (C_37 tptp.pname) (A_123 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_37))) (=> (@ _let_1 A_123) (@ _let_1 (@ (@ tptp.semila1780557381name_o A_123) B_67))))))
% 0.51/0.83 (assert (forall ((A_122 (-> tptp.hoare_1167836817_state Bool)) (B_66 (-> tptp.hoare_1167836817_state Bool)) (X_36 tptp.hoare_1167836817_state)) (=> (@ B_66 X_36) (@ (@ (@ tptp.semila1172322802tate_o A_122) B_66) X_36))))
% 0.51/0.83 (assert (forall ((A_122 (-> tptp.pname Bool)) (B_66 (-> tptp.pname Bool)) (X_36 tptp.pname)) (=> (@ B_66 X_36) (@ (@ (@ tptp.semila1780557381name_o A_122) B_66) X_36))))
% 0.51/0.83 (assert (forall ((A_122 (-> tptp.hoare_1775062406iple_a Bool)) (B_66 (-> tptp.hoare_1775062406iple_a Bool)) (X_36 tptp.hoare_1775062406iple_a)) (=> (@ B_66 X_36) (@ (@ (@ tptp.semila13410563le_a_o A_122) B_66) X_36))))
% 0.51/0.83 (assert (forall ((B_65 (-> tptp.hoare_1167836817_state Bool)) (A_121 (-> tptp.hoare_1167836817_state Bool)) (X_35 tptp.hoare_1167836817_state)) (=> (@ A_121 X_35) (@ (@ (@ tptp.semila1172322802tate_o A_121) B_65) X_35))))
% 0.51/0.83 (assert (forall ((B_65 (-> tptp.pname Bool)) (A_121 (-> tptp.pname Bool)) (X_35 tptp.pname)) (=> (@ A_121 X_35) (@ (@ (@ tptp.semila1780557381name_o A_121) B_65) X_35))))
% 0.51/0.83 (assert (forall ((B_65 (-> tptp.hoare_1775062406iple_a Bool)) (A_121 (-> tptp.hoare_1775062406iple_a Bool)) (X_35 tptp.hoare_1775062406iple_a)) (=> (@ A_121 X_35) (@ (@ (@ tptp.semila13410563le_a_o A_121) B_65) X_35))))
% 0.51/0.83 (assert (forall ((P_36 (-> tptp.hoare_1167836817_state Bool)) (A_120 (-> tptp.hoare_1167836817_state Bool)) (B_64 (-> tptp.hoare_1167836817_state Bool))) (= (forall ((X tptp.hoare_1167836817_state)) (=> (@ (@ tptp.member2058392318_state X) (@ (@ tptp.semila1172322802tate_o A_120) B_64)) (@ P_36 X))) (and (forall ((X tptp.hoare_1167836817_state)) (=> (@ (@ tptp.member2058392318_state X) A_120) (@ P_36 X))) (forall ((X tptp.hoare_1167836817_state)) (=> (@ (@ tptp.member2058392318_state X) B_64) (@ P_36 X)))))))
% 0.51/0.83 (assert (forall ((P_36 (-> tptp.pname Bool)) (A_120 (-> tptp.pname Bool)) (B_64 (-> tptp.pname Bool))) (= (forall ((X tptp.pname)) (=> (@ (@ tptp.member_pname X) (@ (@ tptp.semila1780557381name_o A_120) B_64)) (@ P_36 X))) (and (forall ((X tptp.pname)) (=> (@ (@ tptp.member_pname X) A_120) (@ P_36 X))) (forall ((X tptp.pname)) (=> (@ (@ tptp.member_pname X) B_64) (@ P_36 X)))))))
% 0.51/0.83 (assert (forall ((P_36 (-> tptp.hoare_1775062406iple_a Bool)) (A_120 (-> tptp.hoare_1775062406iple_a Bool)) (B_64 (-> tptp.hoare_1775062406iple_a Bool))) (= (forall ((X tptp.hoare_1775062406iple_a)) (=> (@ (@ tptp.member2122167641iple_a X) (@ (@ tptp.semila13410563le_a_o A_120) B_64)) (@ P_36 X))) (and (forall ((X tptp.hoare_1775062406iple_a)) (=> (@ (@ tptp.member2122167641iple_a X) A_120) (@ P_36 X))) (forall ((X tptp.hoare_1775062406iple_a)) (=> (@ (@ tptp.member2122167641iple_a X) B_64) (@ P_36 X)))))))
% 0.51/0.83 (assert (forall ((P_35 (-> tptp.hoare_1167836817_state Bool)) (A_119 (-> tptp.hoare_1167836817_state Bool)) (B_63 (-> tptp.hoare_1167836817_state Bool))) (= (exists ((X tptp.hoare_1167836817_state)) (and (@ (@ tptp.member2058392318_state X) (@ (@ tptp.semila1172322802tate_o A_119) B_63)) (@ P_35 X))) (or (exists ((X tptp.hoare_1167836817_state)) (and (@ (@ tptp.member2058392318_state X) A_119) (@ P_35 X))) (exists ((X tptp.hoare_1167836817_state)) (and (@ (@ tptp.member2058392318_state X) B_63) (@ P_35 X)))))))
% 0.51/0.83 (assert (forall ((P_35 (-> tptp.pname Bool)) (A_119 (-> tptp.pname Bool)) (B_63 (-> tptp.pname Bool))) (= (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) (@ (@ tptp.semila1780557381name_o A_119) B_63)) (@ P_35 X))) (or (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) A_119) (@ P_35 X))) (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) B_63) (@ P_35 X)))))))
% 0.51/0.83 (assert (forall ((P_35 (-> tptp.hoare_1775062406iple_a Bool)) (A_119 (-> tptp.hoare_1775062406iple_a Bool)) (B_63 (-> tptp.hoare_1775062406iple_a Bool))) (= (exists ((X tptp.hoare_1775062406iple_a)) (and (@ (@ tptp.member2122167641iple_a X) (@ (@ tptp.semila13410563le_a_o A_119) B_63)) (@ P_35 X))) (or (exists ((X tptp.hoare_1775062406iple_a)) (and (@ (@ tptp.member2122167641iple_a X) A_119) (@ P_35 X))) (exists ((X tptp.hoare_1775062406iple_a)) (and (@ (@ tptp.member2122167641iple_a X) B_63) (@ P_35 X)))))))
% 0.51/0.83 (assert (forall ((A_118 (-> tptp.hoare_1167836817_state Bool)) (B_62 (-> tptp.hoare_1167836817_state Bool)) (C_36 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila1172322802tate_o A_118))) (= (@ (@ tptp.semila1172322802tate_o (@ _let_1 B_62)) C_36) (@ _let_1 (@ (@ tptp.semila1172322802tate_o B_62) C_36))))))
% 0.51/0.83 (assert (forall ((A_118 (-> tptp.pname Bool)) (B_62 (-> tptp.pname Bool)) (C_36 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o A_118))) (= (@ (@ tptp.semila1780557381name_o (@ _let_1 B_62)) C_36) (@ _let_1 (@ (@ tptp.semila1780557381name_o B_62) C_36))))))
% 0.51/0.83 (assert (forall ((A_118 (-> tptp.hoare_1775062406iple_a Bool)) (B_62 (-> tptp.hoare_1775062406iple_a Bool)) (C_36 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila13410563le_a_o A_118))) (= (@ (@ tptp.semila13410563le_a_o (@ _let_1 B_62)) C_36) (@ _let_1 (@ (@ tptp.semila13410563le_a_o B_62) C_36))))))
% 0.51/0.83 (assert (forall ((C_35 tptp.hoare_1167836817_state) (A_117 (-> tptp.hoare_1167836817_state Bool)) (B_61 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state C_35))) (= (@ _let_1 (@ (@ tptp.semila1172322802tate_o A_117) B_61)) (or (@ _let_1 A_117) (@ _let_1 B_61))))))
% 0.51/0.83 (assert (forall ((C_35 tptp.hoare_1775062406iple_a) (A_117 (-> tptp.hoare_1775062406iple_a Bool)) (B_61 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.member2122167641iple_a C_35))) (= (@ _let_1 (@ (@ tptp.semila13410563le_a_o A_117) B_61)) (or (@ _let_1 A_117) (@ _let_1 B_61))))))
% 0.51/0.83 (assert (forall ((C_35 tptp.pname) (A_117 (-> tptp.pname Bool)) (B_61 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_35))) (= (@ _let_1 (@ (@ tptp.semila1780557381name_o A_117) B_61)) (or (@ _let_1 A_117) (@ _let_1 B_61))))))
% 0.51/0.83 (assert (forall ((A_116 (-> tptp.hoare_1167836817_state Bool)) (B_60 (-> tptp.hoare_1167836817_state Bool)) (C_34 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila1172322802tate_o A_116))) (let ((_let_2 (@ tptp.semila1172322802tate_o B_60))) (= (@ _let_1 (@ _let_2 C_34)) (@ _let_2 (@ _let_1 C_34)))))))
% 0.51/0.83 (assert (forall ((A_116 (-> tptp.pname Bool)) (B_60 (-> tptp.pname Bool)) (C_34 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o A_116))) (let ((_let_2 (@ tptp.semila1780557381name_o B_60))) (= (@ _let_1 (@ _let_2 C_34)) (@ _let_2 (@ _let_1 C_34)))))))
% 0.51/0.83 (assert (forall ((A_116 (-> tptp.hoare_1775062406iple_a Bool)) (B_60 (-> tptp.hoare_1775062406iple_a Bool)) (C_34 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila13410563le_a_o A_116))) (let ((_let_2 (@ tptp.semila13410563le_a_o B_60))) (= (@ _let_1 (@ _let_2 C_34)) (@ _let_2 (@ _let_1 C_34)))))))
% 0.51/0.83 (assert (forall ((A_115 (-> tptp.hoare_1167836817_state Bool)) (B_59 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila1172322802tate_o A_115))) (let ((_let_2 (@ _let_1 B_59))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.83 (assert (forall ((A_115 (-> tptp.pname Bool)) (B_59 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o A_115))) (let ((_let_2 (@ _let_1 B_59))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.83 (assert (forall ((A_115 (-> tptp.hoare_1775062406iple_a Bool)) (B_59 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila13410563le_a_o A_115))) (let ((_let_2 (@ _let_1 B_59))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.83 (assert (forall ((A_114 (-> tptp.hoare_1167836817_state Bool)) (B_58 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila1172322802tate_o A_114) B_58) (@ (@ tptp.semila1172322802tate_o B_58) A_114))))
% 0.51/0.83 (assert (forall ((A_114 (-> tptp.pname Bool)) (B_58 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o A_114) B_58) (@ (@ tptp.semila1780557381name_o B_58) A_114))))
% 0.51/0.83 (assert (forall ((A_114 (-> tptp.hoare_1775062406iple_a Bool)) (B_58 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila13410563le_a_o A_114) B_58) (@ (@ tptp.semila13410563le_a_o B_58) A_114))))
% 0.51/0.83 (assert (forall ((A_113 (-> tptp.hoare_1167836817_state Bool)) (B_57 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila1172322802tate_o A_113) B_57) (@ tptp.collec1027672124_state (lambda ((X tptp.hoare_1167836817_state)) (let ((_let_1 (@ tptp.member2058392318_state X))) (or (@ _let_1 A_113) (@ _let_1 B_57))))))))
% 0.51/0.83 (assert (forall ((A_113 (-> tptp.hoare_1775062406iple_a Bool)) (B_57 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila13410563le_a_o A_113) B_57) (@ tptp.collec676402587iple_a (lambda ((X tptp.hoare_1775062406iple_a)) (let ((_let_1 (@ tptp.member2122167641iple_a X))) (or (@ _let_1 A_113) (@ _let_1 B_57))))))))
% 0.51/0.83 (assert (forall ((A_113 (-> tptp.pname Bool)) (B_57 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o A_113) B_57) (@ tptp.collect_pname (lambda ((X tptp.pname)) (let ((_let_1 (@ tptp.member_pname X))) (or (@ _let_1 A_113) (@ _let_1 B_57))))))))
% 0.51/0.83 (assert (forall ((A_112 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila1172322802tate_o A_112) A_112) A_112)))
% 0.51/0.83 (assert (forall ((A_112 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o A_112) A_112) A_112)))
% 0.51/0.83 (assert (forall ((A_112 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila13410563le_a_o A_112) A_112) A_112)))
% 0.51/0.83 (assert (forall ((F_34 (-> tptp.hoare_1775062406iple_a tptp.hoare_1167836817_state)) (G_19 (-> tptp.pname tptp.hoare_1775062406iple_a)) (A_111 (-> tptp.pname Bool))) (= (@ (@ tptp.image_1021683026_state F_34) (@ (@ tptp.image_2063119815iple_a G_19) A_111)) (@ (@ tptp.image_575578384_state (lambda ((X tptp.pname)) (@ F_34 (@ G_19 X)))) A_111))))
% 0.51/0.83 (assert (forall ((F_34 (-> tptp.hoare_1167836817_state tptp.hoare_1775062406iple_a)) (G_19 (-> tptp.pname tptp.hoare_1167836817_state)) (A_111 (-> tptp.pname Bool))) (= (@ (@ tptp.image_1802845250iple_a F_34) (@ (@ tptp.image_575578384_state G_19) A_111)) (@ (@ tptp.image_2063119815iple_a (lambda ((X tptp.pname)) (@ F_34 (@ G_19 X)))) A_111))))
% 0.51/0.83 (assert (forall ((R_2 (-> tptp.hoare_1167836817_state Bool)) (S_6 (-> tptp.hoare_1167836817_state Bool)) (X tptp.hoare_1167836817_state)) (= (@ (@ (@ tptp.semila1172322802tate_o (lambda ((Y_2 tptp.hoare_1167836817_state)) (@ (@ tptp.member2058392318_state Y_2) R_2))) (lambda ((Y_2 tptp.hoare_1167836817_state)) (@ (@ tptp.member2058392318_state Y_2) S_6))) X) (@ (@ tptp.member2058392318_state X) (@ (@ tptp.semila1172322802tate_o R_2) S_6)))))
% 0.51/0.83 (assert (forall ((R_2 (-> tptp.hoare_1775062406iple_a Bool)) (S_6 (-> tptp.hoare_1775062406iple_a Bool)) (X tptp.hoare_1775062406iple_a)) (= (@ (@ (@ tptp.semila13410563le_a_o (lambda ((Y_2 tptp.hoare_1775062406iple_a)) (@ (@ tptp.member2122167641iple_a Y_2) R_2))) (lambda ((Y_2 tptp.hoare_1775062406iple_a)) (@ (@ tptp.member2122167641iple_a Y_2) S_6))) X) (@ (@ tptp.member2122167641iple_a X) (@ (@ tptp.semila13410563le_a_o R_2) S_6)))))
% 0.51/0.83 (assert (forall ((R_2 (-> tptp.pname Bool)) (S_6 (-> tptp.pname Bool)) (X tptp.pname)) (= (@ (@ (@ tptp.semila1780557381name_o (lambda ((Y_2 tptp.pname)) (@ (@ tptp.member_pname Y_2) R_2))) (lambda ((Y_2 tptp.pname)) (@ (@ tptp.member_pname Y_2) S_6))) X) (@ (@ tptp.member_pname X) (@ (@ tptp.semila1780557381name_o R_2) S_6)))))
% 0.51/0.83 (assert (forall ((P_34 (-> tptp.pname Bool)) (Q_19 (-> tptp.pname Bool))) (= (@ tptp.collect_pname (lambda ((X tptp.pname)) (or (@ P_34 X) (@ Q_19 X)))) (@ (@ tptp.semila1780557381name_o (@ tptp.collect_pname P_34)) (@ tptp.collect_pname Q_19)))))
% 0.51/0.83 (assert (forall ((P_34 (-> tptp.hoare_1167836817_state Bool)) (Q_19 (-> tptp.hoare_1167836817_state Bool))) (= (@ tptp.collec1027672124_state (lambda ((X tptp.hoare_1167836817_state)) (or (@ P_34 X) (@ Q_19 X)))) (@ (@ tptp.semila1172322802tate_o (@ tptp.collec1027672124_state P_34)) (@ tptp.collec1027672124_state Q_19)))))
% 0.51/0.83 (assert (forall ((P_34 (-> tptp.hoare_1775062406iple_a Bool)) (Q_19 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ tptp.collec676402587iple_a (lambda ((X tptp.hoare_1775062406iple_a)) (or (@ P_34 X) (@ Q_19 X)))) (@ (@ tptp.semila13410563le_a_o (@ tptp.collec676402587iple_a P_34)) (@ tptp.collec676402587iple_a Q_19)))))
% 0.51/0.83 (assert (forall ((B_56 tptp.pname) (F_33 (-> tptp.hoare_1775062406iple_a tptp.pname)) (A_110 (-> tptp.hoare_1775062406iple_a Bool))) (=> (@ (@ tptp.member_pname B_56) (@ (@ tptp.image_51246659_pname F_33) A_110)) (not (forall ((X tptp.hoare_1775062406iple_a)) (=> (= B_56 (@ F_33 X)) (not (@ (@ tptp.member2122167641iple_a X) A_110))))))))
% 0.51/0.83 (assert (forall ((B_56 tptp.hoare_1167836817_state) (F_33 (-> tptp.pname tptp.hoare_1167836817_state)) (A_110 (-> tptp.pname Bool))) (=> (@ (@ tptp.member2058392318_state B_56) (@ (@ tptp.image_575578384_state F_33) A_110)) (not (forall ((X tptp.pname)) (=> (= B_56 (@ F_33 X)) (not (@ (@ tptp.member_pname X) A_110))))))))
% 0.51/0.83 (assert (forall ((B_56 tptp.hoare_1775062406iple_a) (F_33 (-> tptp.pname tptp.hoare_1775062406iple_a)) (A_110 (-> tptp.pname Bool))) (=> (@ (@ tptp.member2122167641iple_a B_56) (@ (@ tptp.image_2063119815iple_a F_33) A_110)) (not (forall ((X tptp.pname)) (=> (= B_56 (@ F_33 X)) (not (@ (@ tptp.member_pname X) A_110))))))))
% 0.51/0.83 (assert (forall ((N_8 tptp.nat) (P_33 (-> tptp.state tptp.state Bool)) (Pn_6 tptp.pname) (Q_18 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_908217195_state P_33))) (= (@ (@ tptp.hoare_56934129_state N_8) (@ (@ _let_1 (@ tptp.the_com (@ tptp.body_1 Pn_6))) Q_18)) (@ (@ tptp.hoare_56934129_state (@ tptp.suc N_8)) (@ (@ _let_1 (@ tptp.body Pn_6)) Q_18))))))
% 0.51/0.83 (assert (forall ((N_8 tptp.nat) (P_33 (-> tptp.x_a tptp.state Bool)) (Pn_6 tptp.pname) (Q_18 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_1766022166iple_a P_33))) (= (@ (@ tptp.hoare_1462269968alid_a N_8) (@ (@ _let_1 (@ tptp.the_com (@ tptp.body_1 Pn_6))) Q_18)) (@ (@ tptp.hoare_1462269968alid_a (@ tptp.suc N_8)) (@ (@ _let_1 (@ tptp.body Pn_6)) Q_18))))))
% 0.51/0.83 (assert (forall ((Y_13 tptp.hoare_1775062406iple_a)) (not (forall ((Fun1_2 (-> tptp.x_a tptp.state Bool)) (Com_4 tptp.com) (Fun2_2 (-> tptp.x_a tptp.state Bool))) (not (= Y_13 (@ (@ (@ tptp.hoare_1766022166iple_a Fun1_2) Com_4) Fun2_2)))))))
% 0.51/0.83 (assert (forall ((Y_13 tptp.hoare_1167836817_state)) (not (forall ((Fun1_2 (-> tptp.state tptp.state Bool)) (Com_4 tptp.com) (Fun2_2 (-> tptp.state tptp.state Bool))) (not (= Y_13 (@ (@ (@ tptp.hoare_908217195_state Fun1_2) Com_4) Fun2_2)))))))
% 0.51/0.83 (assert (forall ((Pn_5 tptp.pname) (G_18 (-> tptp.hoare_1167836817_state Bool)) (P_32 (-> tptp.pname tptp.state tptp.state Bool)) (Q_17 (-> tptp.pname tptp.state tptp.state Bool)) (Procs (-> tptp.pname Bool))) (=> (@ (@ tptp.hoare_123228589_state (@ (@ tptp.semila1172322802tate_o G_18) (@ (@ tptp.image_575578384_state (lambda ((P_10 tptp.pname)) (@ (@ (@ tptp.hoare_908217195_state (@ P_32 P_10)) (@ tptp.body P_10)) (@ Q_17 P_10)))) Procs))) (@ (@ tptp.image_575578384_state (lambda ((P_10 tptp.pname)) (@ (@ (@ tptp.hoare_908217195_state (@ P_32 P_10)) (@ tptp.the_com (@ tptp.body_1 P_10))) (@ Q_17 P_10)))) Procs)) (=> (@ (@ tptp.member_pname Pn_5) Procs) (@ (@ tptp.hoare_123228589_state G_18) (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state (@ P_32 Pn_5)) (@ tptp.body Pn_5)) (@ Q_17 Pn_5))) tptp.bot_bo70021908tate_o))))))
% 0.51/0.83 (assert (forall ((Pn_5 tptp.pname) (G_18 (-> tptp.hoare_1775062406iple_a Bool)) (P_32 (-> tptp.pname tptp.x_a tptp.state Bool)) (Q_17 (-> tptp.pname tptp.x_a tptp.state Bool)) (Procs (-> tptp.pname Bool))) (=> (@ (@ tptp.hoare_1508237396rivs_a (@ (@ tptp.semila13410563le_a_o G_18) (@ (@ tptp.image_2063119815iple_a (lambda ((P_10 tptp.pname)) (@ (@ (@ tptp.hoare_1766022166iple_a (@ P_32 P_10)) (@ tptp.body P_10)) (@ Q_17 P_10)))) Procs))) (@ (@ tptp.image_2063119815iple_a (lambda ((P_10 tptp.pname)) (@ (@ (@ tptp.hoare_1766022166iple_a (@ P_32 P_10)) (@ tptp.the_com (@ tptp.body_1 P_10))) (@ Q_17 P_10)))) Procs)) (=> (@ (@ tptp.member_pname Pn_5) Procs) (@ (@ tptp.hoare_1508237396rivs_a G_18) (@ (@ tptp.insert1281456128iple_a (@ (@ (@ tptp.hoare_1766022166iple_a (@ P_32 Pn_5)) (@ tptp.body Pn_5)) (@ Q_17 Pn_5))) tptp.bot_bo751897185le_a_o))))))
% 0.51/0.83 (assert (forall ((F_32 (-> tptp.pname tptp.hoare_1167836817_state)) (G_17 (-> tptp.pname tptp.hoare_1167836817_state)) (M_2 (-> tptp.pname Bool)) (N_7 (-> tptp.pname Bool))) (=> (= M_2 N_7) (=> (forall ((X tptp.pname)) (=> (@ (@ tptp.member_pname X) N_7) (= (@ F_32 X) (@ G_17 X)))) (= (@ (@ tptp.image_575578384_state F_32) M_2) (@ (@ tptp.image_575578384_state G_17) N_7))))))
% 0.51/0.83 (assert (forall ((F_32 (-> tptp.pname tptp.hoare_1775062406iple_a)) (G_17 (-> tptp.pname tptp.hoare_1775062406iple_a)) (M_2 (-> tptp.pname Bool)) (N_7 (-> tptp.pname Bool))) (=> (= M_2 N_7) (=> (forall ((X tptp.pname)) (=> (@ (@ tptp.member_pname X) N_7) (= (@ F_32 X) (@ G_17 X)))) (= (@ (@ tptp.image_2063119815iple_a F_32) M_2) (@ (@ tptp.image_2063119815iple_a G_17) N_7))))))
% 0.51/0.83 (assert (forall ((P_31 (-> tptp.state tptp.state Bool)) (Pn_4 tptp.pname) (Q_16 (-> tptp.state tptp.state Bool))) (@ (@ tptp.hoare_56934129_state tptp.zero_zero_nat) (@ (@ (@ tptp.hoare_908217195_state P_31) (@ tptp.body Pn_4)) Q_16))))
% 0.51/0.83 (assert (forall ((P_31 (-> tptp.x_a tptp.state Bool)) (Pn_4 tptp.pname) (Q_16 (-> tptp.x_a tptp.state Bool))) (@ (@ tptp.hoare_1462269968alid_a tptp.zero_zero_nat) (@ (@ (@ tptp.hoare_1766022166iple_a P_31) (@ tptp.body Pn_4)) Q_16))))
% 0.51/0.83 (assert (forall ((Pname tptp.pname) (Pname_1 tptp.pname)) (= (= (@ tptp.body Pname) (@ tptp.body Pname_1)) (= Pname Pname_1))))
% 0.51/0.83 (assert (forall ((Pn_1 tptp.pname) (S0 tptp.state) (S1 tptp.state)) (=> (@ (@ (@ tptp.evalc (@ tptp.the_com (@ tptp.body_1 Pn_1))) S0) S1) (@ (@ (@ tptp.evalc (@ tptp.body Pn_1)) S0) S1))))
% 0.51/0.83 (assert (forall ((P tptp.pname) (S tptp.state) (S1 tptp.state)) (=> (@ (@ (@ tptp.evalc (@ tptp.body P)) S) S1) (@ (@ (@ tptp.evalc (@ tptp.the_com (@ tptp.body_1 P))) S) S1))))
% 0.51/0.83 (assert (forall ((X_34 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila1172322802tate_o X_34) X_34) X_34)))
% 0.51/0.83 (assert (forall ((X_34 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o X_34) X_34) X_34)))
% 0.51/0.83 (assert (forall ((X_34 Bool)) (= (@ (@ tptp.semila10642723_sup_o X_34) X_34) X_34)))
% 0.51/0.83 (assert (forall ((X_34 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila13410563le_a_o X_34) X_34) X_34)))
% 0.51/0.83 (assert (forall ((A_109 tptp.hoare_1775062406iple_a)) (not (@ (@ tptp.member2122167641iple_a A_109) tptp.bot_bo751897185le_a_o))))
% 0.51/0.83 (assert (forall ((A_109 tptp.hoare_1167836817_state)) (not (@ (@ tptp.member2058392318_state A_109) tptp.bot_bo70021908tate_o))))
% 0.51/0.83 (assert (forall ((A_109 tptp.pname)) (not (@ (@ tptp.member_pname A_109) tptp.bot_bot_pname_o))))
% 0.51/0.83 (assert (forall ((A_108 tptp.hoare_1167836817_state) (B_55 tptp.hoare_1167836817_state) (A_107 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state A_108))) (=> (@ _let_1 (@ (@ tptp.insert2134838167_state B_55) A_107)) (=> (not (= A_108 B_55)) (@ _let_1 A_107))))))
% 0.51/0.83 (assert (forall ((A_108 tptp.hoare_1775062406iple_a) (B_55 tptp.hoare_1775062406iple_a) (A_107 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.member2122167641iple_a A_108))) (=> (@ _let_1 (@ (@ tptp.insert1281456128iple_a B_55) A_107)) (=> (not (= A_108 B_55)) (@ _let_1 A_107))))))
% 0.51/0.83 (assert (forall ((A_108 tptp.pname) (B_55 tptp.pname) (A_107 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_108))) (=> (@ _let_1 (@ (@ tptp.insert_pname B_55) A_107)) (=> (not (= A_108 B_55)) (@ _let_1 A_107))))))
% 0.51/0.83 (assert (forall ((B_54 tptp.hoare_1167836817_state) (A_106 tptp.hoare_1167836817_state) (B_53 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state A_106))) (=> (=> (not (@ _let_1 B_53)) (= A_106 B_54)) (@ _let_1 (@ (@ tptp.insert2134838167_state B_54) B_53))))))
% 0.51/0.83 (assert (forall ((B_54 tptp.hoare_1775062406iple_a) (A_106 tptp.hoare_1775062406iple_a) (B_53 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.member2122167641iple_a A_106))) (=> (=> (not (@ _let_1 B_53)) (= A_106 B_54)) (@ _let_1 (@ (@ tptp.insert1281456128iple_a B_54) B_53))))))
% 0.51/0.83 (assert (forall ((B_54 tptp.pname) (A_106 tptp.pname) (B_53 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_106))) (=> (=> (not (@ _let_1 B_53)) (= A_106 B_54)) (@ _let_1 (@ (@ tptp.insert_pname B_54) B_53))))))
% 0.51/0.83 (assert (forall ((A_105 tptp.hoare_1167836817_state) (A_104 (-> tptp.hoare_1167836817_state Bool))) (not (= tptp.bot_bo70021908tate_o (@ (@ tptp.insert2134838167_state A_105) A_104)))))
% 0.51/0.83 (assert (forall ((A_105 tptp.hoare_1775062406iple_a) (A_104 (-> tptp.hoare_1775062406iple_a Bool))) (not (= tptp.bot_bo751897185le_a_o (@ (@ tptp.insert1281456128iple_a A_105) A_104)))))
% 0.51/0.83 (assert (forall ((A_105 tptp.pname) (A_104 (-> tptp.pname Bool))) (not (= tptp.bot_bot_pname_o (@ (@ tptp.insert_pname A_105) A_104)))))
% 0.51/0.83 (assert (forall ((A_103 tptp.hoare_1167836817_state) (A_102 (-> tptp.hoare_1167836817_state Bool))) (not (= (@ (@ tptp.insert2134838167_state A_103) A_102) tptp.bot_bo70021908tate_o))))
% 0.51/0.83 (assert (forall ((A_103 tptp.hoare_1775062406iple_a) (A_102 (-> tptp.hoare_1775062406iple_a Bool))) (not (= (@ (@ tptp.insert1281456128iple_a A_103) A_102) tptp.bot_bo751897185le_a_o))))
% 0.51/0.83 (assert (forall ((A_103 tptp.pname) (A_102 (-> tptp.pname Bool))) (not (= (@ (@ tptp.insert_pname A_103) A_102) tptp.bot_bot_pname_o))))
% 0.51/0.83 (assert (forall ((X tptp.hoare_1775062406iple_a)) (= (@ tptp.bot_bo751897185le_a_o X) (@ (@ tptp.member2122167641iple_a X) tptp.bot_bo751897185le_a_o))))
% 0.51/0.83 (assert (forall ((X tptp.hoare_1167836817_state)) (= (@ tptp.bot_bo70021908tate_o X) (@ (@ tptp.member2058392318_state X) tptp.bot_bo70021908tate_o))))
% 0.51/0.83 (assert (forall ((X tptp.pname)) (= (@ tptp.bot_bot_pname_o X) (@ (@ tptp.member_pname X) tptp.bot_bot_pname_o))))
% 0.51/0.83 (assert (= tptp.bot_bo751897185le_a_o (@ tptp.collec676402587iple_a (lambda ((X tptp.hoare_1775062406iple_a)) false))))
% 0.51/0.83 (assert (= tptp.bot_bot_pname_o (@ tptp.collect_pname (lambda ((X tptp.pname)) false))))
% 0.51/0.83 (assert (= tptp.bot_bo70021908tate_o (@ tptp.collec1027672124_state (lambda ((X tptp.hoare_1167836817_state)) false))))
% 0.51/0.83 (assert (forall ((A_101 tptp.hoare_1167836817_state) (B_52 (-> tptp.hoare_1167836817_state Bool))) (@ (@ tptp.member2058392318_state A_101) (@ (@ tptp.insert2134838167_state A_101) B_52))))
% 0.51/0.83 (assert (forall ((A_101 tptp.hoare_1775062406iple_a) (B_52 (-> tptp.hoare_1775062406iple_a Bool))) (@ (@ tptp.member2122167641iple_a A_101) (@ (@ tptp.insert1281456128iple_a A_101) B_52))))
% 0.51/0.83 (assert (forall ((A_101 tptp.pname) (B_52 (-> tptp.pname Bool))) (@ (@ tptp.member_pname A_101) (@ (@ tptp.insert_pname A_101) B_52))))
% 0.51/0.83 (assert (forall ((A_100 (-> tptp.hoare_1775062406iple_a Bool))) (= (forall ((X tptp.hoare_1775062406iple_a)) (not (@ (@ tptp.member2122167641iple_a X) A_100))) (= A_100 tptp.bot_bo751897185le_a_o))))
% 0.51/0.83 (assert (forall ((A_100 (-> tptp.hoare_1167836817_state Bool))) (= (forall ((X tptp.hoare_1167836817_state)) (not (@ (@ tptp.member2058392318_state X) A_100))) (= A_100 tptp.bot_bo70021908tate_o))))
% 0.51/0.83 (assert (forall ((A_100 (-> tptp.pname Bool))) (= (forall ((X tptp.pname)) (not (@ (@ tptp.member_pname X) A_100))) (= A_100 tptp.bot_bot_pname_o))))
% 0.51/0.83 (assert (forall ((A_99 tptp.hoare_1167836817_state)) (= (@ tptp.collec1027672124_state (@ tptp.fequal1831255762_state A_99)) (@ (@ tptp.insert2134838167_state A_99) tptp.bot_bo70021908tate_o))))
% 0.51/0.83 (assert (forall ((A_99 tptp.hoare_1775062406iple_a)) (= (@ tptp.collec676402587iple_a (@ tptp.fequal1288209029iple_a A_99)) (@ (@ tptp.insert1281456128iple_a A_99) tptp.bot_bo751897185le_a_o))))
% 0.51/0.83 (assert (forall ((A_99 tptp.pname)) (= (@ tptp.collect_pname (@ tptp.fequal_pname A_99)) (@ (@ tptp.insert_pname A_99) tptp.bot_bot_pname_o))))
% 0.51/0.83 (assert (forall ((A_98 (-> tptp.hoare_1775062406iple_a Bool))) (= (exists ((X tptp.hoare_1775062406iple_a)) (@ (@ tptp.member2122167641iple_a X) A_98)) (not (= A_98 tptp.bot_bo751897185le_a_o)))))
% 0.51/0.83 (assert (forall ((A_98 (-> tptp.hoare_1167836817_state Bool))) (= (exists ((X tptp.hoare_1167836817_state)) (@ (@ tptp.member2058392318_state X) A_98)) (not (= A_98 tptp.bot_bo70021908tate_o)))))
% 0.51/0.83 (assert (forall ((A_98 (-> tptp.pname Bool))) (= (exists ((X tptp.pname)) (@ (@ tptp.member_pname X) A_98)) (not (= A_98 tptp.bot_bot_pname_o)))))
% 0.51/0.83 (assert (forall ((A_97 tptp.hoare_1167836817_state)) (= (@ tptp.collec1027672124_state (lambda ((X tptp.hoare_1167836817_state)) (= X A_97))) (@ (@ tptp.insert2134838167_state A_97) tptp.bot_bo70021908tate_o))))
% 0.51/0.83 (assert (forall ((A_97 tptp.hoare_1775062406iple_a)) (= (@ tptp.collec676402587iple_a (lambda ((X tptp.hoare_1775062406iple_a)) (= X A_97))) (@ (@ tptp.insert1281456128iple_a A_97) tptp.bot_bo751897185le_a_o))))
% 0.51/0.83 (assert (forall ((A_97 tptp.pname)) (= (@ tptp.collect_pname (lambda ((X tptp.pname)) (= X A_97))) (@ (@ tptp.insert_pname A_97) tptp.bot_bot_pname_o))))
% 0.51/0.83 (assert (forall ((P_30 (-> tptp.hoare_1167836817_state Bool)) (A_96 tptp.hoare_1167836817_state)) (let ((_let_1 (@ P_30 A_96))) (and (=> _let_1 (= (@ tptp.collec1027672124_state (lambda ((X tptp.hoare_1167836817_state)) (and (= A_96 X) (@ P_30 X)))) (@ (@ tptp.insert2134838167_state A_96) tptp.bot_bo70021908tate_o))) (=> (not _let_1) (= (@ tptp.collec1027672124_state (lambda ((X tptp.hoare_1167836817_state)) (and (= A_96 X) (@ P_30 X)))) tptp.bot_bo70021908tate_o))))))
% 0.51/0.83 (assert (forall ((P_30 (-> tptp.hoare_1775062406iple_a Bool)) (A_96 tptp.hoare_1775062406iple_a)) (let ((_let_1 (@ P_30 A_96))) (and (=> _let_1 (= (@ tptp.collec676402587iple_a (lambda ((X tptp.hoare_1775062406iple_a)) (and (= A_96 X) (@ P_30 X)))) (@ (@ tptp.insert1281456128iple_a A_96) tptp.bot_bo751897185le_a_o))) (=> (not _let_1) (= (@ tptp.collec676402587iple_a (lambda ((X tptp.hoare_1775062406iple_a)) (and (= A_96 X) (@ P_30 X)))) tptp.bot_bo751897185le_a_o))))))
% 0.51/0.83 (assert (forall ((P_30 (-> tptp.pname Bool)) (A_96 tptp.pname)) (let ((_let_1 (@ P_30 A_96))) (and (=> _let_1 (= (@ tptp.collect_pname (lambda ((X tptp.pname)) (and (= A_96 X) (@ P_30 X)))) (@ (@ tptp.insert_pname A_96) tptp.bot_bot_pname_o))) (=> (not _let_1) (= (@ tptp.collect_pname (lambda ((X tptp.pname)) (and (= A_96 X) (@ P_30 X)))) tptp.bot_bot_pname_o))))))
% 0.51/0.83 (assert (forall ((P_29 (-> tptp.hoare_1167836817_state Bool)) (A_95 tptp.hoare_1167836817_state)) (let ((_let_1 (@ P_29 A_95))) (and (=> _let_1 (= (@ tptp.collec1027672124_state (lambda ((X tptp.hoare_1167836817_state)) (and (= X A_95) (@ P_29 X)))) (@ (@ tptp.insert2134838167_state A_95) tptp.bot_bo70021908tate_o))) (=> (not _let_1) (= (@ tptp.collec1027672124_state (lambda ((X tptp.hoare_1167836817_state)) (and (= X A_95) (@ P_29 X)))) tptp.bot_bo70021908tate_o))))))
% 0.51/0.83 (assert (forall ((P_29 (-> tptp.hoare_1775062406iple_a Bool)) (A_95 tptp.hoare_1775062406iple_a)) (let ((_let_1 (@ P_29 A_95))) (and (=> _let_1 (= (@ tptp.collec676402587iple_a (lambda ((X tptp.hoare_1775062406iple_a)) (and (= X A_95) (@ P_29 X)))) (@ (@ tptp.insert1281456128iple_a A_95) tptp.bot_bo751897185le_a_o))) (=> (not _let_1) (= (@ tptp.collec676402587iple_a (lambda ((X tptp.hoare_1775062406iple_a)) (and (= X A_95) (@ P_29 X)))) tptp.bot_bo751897185le_a_o))))))
% 0.51/0.83 (assert (forall ((P_29 (-> tptp.pname Bool)) (A_95 tptp.pname)) (let ((_let_1 (@ P_29 A_95))) (and (=> _let_1 (= (@ tptp.collect_pname (lambda ((X tptp.pname)) (and (= X A_95) (@ P_29 X)))) (@ (@ tptp.insert_pname A_95) tptp.bot_bot_pname_o))) (=> (not _let_1) (= (@ tptp.collect_pname (lambda ((X tptp.pname)) (and (= X A_95) (@ P_29 X)))) tptp.bot_bot_pname_o))))))
% 0.51/0.83 (assert (forall ((P_28 (-> tptp.hoare_1775062406iple_a Bool))) (= (= tptp.bot_bo751897185le_a_o (@ tptp.collec676402587iple_a P_28)) (forall ((X tptp.hoare_1775062406iple_a)) (not (@ P_28 X))))))
% 0.51/0.83 (assert (forall ((P_28 (-> tptp.pname Bool))) (= (= tptp.bot_bot_pname_o (@ tptp.collect_pname P_28)) (forall ((X tptp.pname)) (not (@ P_28 X))))))
% 0.51/0.83 (assert (forall ((P_28 (-> tptp.hoare_1167836817_state Bool))) (= (= tptp.bot_bo70021908tate_o (@ tptp.collec1027672124_state P_28)) (forall ((X tptp.hoare_1167836817_state)) (not (@ P_28 X))))))
% 0.51/0.83 (assert (forall ((X_33 tptp.hoare_1775062406iple_a) (A_94 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.member2122167641iple_a X_33) A_94) (@ A_94 X_33))))
% 0.51/0.83 (assert (forall ((X_33 tptp.pname) (A_94 (-> tptp.pname Bool))) (= (@ (@ tptp.member_pname X_33) A_94) (@ A_94 X_33))))
% 0.51/0.83 (assert (forall ((P_27 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ tptp.collec676402587iple_a P_27) P_27)))
% 0.51/0.83 (assert (forall ((P_27 (-> tptp.pname Bool))) (= (@ tptp.collect_pname P_27) P_27)))
% 0.51/0.83 (assert (forall ((C_33 tptp.hoare_1775062406iple_a)) (not (@ (@ tptp.member2122167641iple_a C_33) tptp.bot_bo751897185le_a_o))))
% 0.51/0.83 (assert (forall ((C_33 tptp.hoare_1167836817_state)) (not (@ (@ tptp.member2058392318_state C_33) tptp.bot_bo70021908tate_o))))
% 0.51/0.83 (assert (forall ((C_33 tptp.pname)) (not (@ (@ tptp.member_pname C_33) tptp.bot_bot_pname_o))))
% 0.51/0.83 (assert (forall ((A_93 tptp.hoare_1167836817_state) (B_51 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.insert2134838167_state A_93) B_51) (@ tptp.collec1027672124_state (lambda ((X tptp.hoare_1167836817_state)) (or (= X A_93) (@ (@ tptp.member2058392318_state X) B_51)))))))
% 0.51/0.83 (assert (forall ((A_93 tptp.hoare_1775062406iple_a) (B_51 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.insert1281456128iple_a A_93) B_51) (@ tptp.collec676402587iple_a (lambda ((X tptp.hoare_1775062406iple_a)) (or (= X A_93) (@ (@ tptp.member2122167641iple_a X) B_51)))))))
% 0.51/0.83 (assert (forall ((A_93 tptp.pname) (B_51 (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname A_93) B_51) (@ tptp.collect_pname (lambda ((X tptp.pname)) (or (= X A_93) (@ (@ tptp.member_pname X) B_51)))))))
% 0.51/0.83 (assert (forall ((A_92 tptp.hoare_1167836817_state) (P_26 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.insert2134838167_state A_92) (@ tptp.collec1027672124_state P_26)) (@ tptp.collec1027672124_state (lambda ((U_2 tptp.hoare_1167836817_state)) (=> (not (= U_2 A_92)) (@ P_26 U_2)))))))
% 0.51/0.83 (assert (forall ((A_92 tptp.hoare_1775062406iple_a) (P_26 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.insert1281456128iple_a A_92) (@ tptp.collec676402587iple_a P_26)) (@ tptp.collec676402587iple_a (lambda ((U_2 tptp.hoare_1775062406iple_a)) (=> (not (= U_2 A_92)) (@ P_26 U_2)))))))
% 0.51/0.83 (assert (forall ((A_92 tptp.pname) (P_26 (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname A_92) (@ tptp.collect_pname P_26)) (@ tptp.collect_pname (lambda ((U_2 tptp.pname)) (=> (not (= U_2 A_92)) (@ P_26 U_2)))))))
% 0.51/0.83 (assert (forall ((B_50 tptp.hoare_1167836817_state) (A_91 tptp.hoare_1167836817_state)) (= (@ (@ tptp.member2058392318_state B_50) (@ (@ tptp.insert2134838167_state A_91) tptp.bot_bo70021908tate_o)) (= B_50 A_91))))
% 0.51/0.83 (assert (forall ((B_50 tptp.hoare_1775062406iple_a) (A_91 tptp.hoare_1775062406iple_a)) (= (@ (@ tptp.member2122167641iple_a B_50) (@ (@ tptp.insert1281456128iple_a A_91) tptp.bot_bo751897185le_a_o)) (= B_50 A_91))))
% 0.51/0.83 (assert (forall ((B_50 tptp.pname) (A_91 tptp.pname)) (= (@ (@ tptp.member_pname B_50) (@ (@ tptp.insert_pname A_91) tptp.bot_bot_pname_o)) (= B_50 A_91))))
% 0.51/0.83 (assert (forall ((X_32 tptp.hoare_1167836817_state) (A_90 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.insert2134838167_state X_32))) (let ((_let_2 (@ _let_1 A_90))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.83 (assert (forall ((X_32 tptp.hoare_1775062406iple_a) (A_90 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.insert1281456128iple_a X_32))) (let ((_let_2 (@ _let_1 A_90))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.83 (assert (forall ((X_32 tptp.pname) (A_90 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_32))) (let ((_let_2 (@ _let_1 A_90))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.83 (assert (forall ((X_31 tptp.hoare_1167836817_state) (Y_12 tptp.hoare_1167836817_state) (A_89 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.insert2134838167_state X_31))) (let ((_let_2 (@ tptp.insert2134838167_state Y_12))) (= (@ _let_1 (@ _let_2 A_89)) (@ _let_2 (@ _let_1 A_89)))))))
% 0.51/0.83 (assert (forall ((X_31 tptp.hoare_1775062406iple_a) (Y_12 tptp.hoare_1775062406iple_a) (A_89 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.insert1281456128iple_a X_31))) (let ((_let_2 (@ tptp.insert1281456128iple_a Y_12))) (= (@ _let_1 (@ _let_2 A_89)) (@ _let_2 (@ _let_1 A_89)))))))
% 0.51/0.83 (assert (forall ((X_31 tptp.pname) (Y_12 tptp.pname) (A_89 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_31))) (let ((_let_2 (@ tptp.insert_pname Y_12))) (= (@ _let_1 (@ _let_2 A_89)) (@ _let_2 (@ _let_1 A_89)))))))
% 0.51/0.83 (assert (forall ((A_88 tptp.hoare_1167836817_state) (B_49 tptp.hoare_1167836817_state) (A_87 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state A_88))) (= (@ _let_1 (@ (@ tptp.insert2134838167_state B_49) A_87)) (or (= A_88 B_49) (@ _let_1 A_87))))))
% 0.51/0.83 (assert (forall ((A_88 tptp.hoare_1775062406iple_a) (B_49 tptp.hoare_1775062406iple_a) (A_87 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.member2122167641iple_a A_88))) (= (@ _let_1 (@ (@ tptp.insert1281456128iple_a B_49) A_87)) (or (= A_88 B_49) (@ _let_1 A_87))))))
% 0.51/0.83 (assert (forall ((A_88 tptp.pname) (B_49 tptp.pname) (A_87 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_88))) (= (@ _let_1 (@ (@ tptp.insert_pname B_49) A_87)) (or (= A_88 B_49) (@ _let_1 A_87))))))
% 0.51/0.83 (assert (forall ((P_25 (-> tptp.hoare_1775062406iple_a Bool))) (= (= (@ tptp.collec676402587iple_a P_25) tptp.bot_bo751897185le_a_o) (forall ((X tptp.hoare_1775062406iple_a)) (not (@ P_25 X))))))
% 0.51/0.83 (assert (forall ((P_25 (-> tptp.pname Bool))) (= (= (@ tptp.collect_pname P_25) tptp.bot_bot_pname_o) (forall ((X tptp.pname)) (not (@ P_25 X))))))
% 0.51/0.83 (assert (forall ((P_25 (-> tptp.hoare_1167836817_state Bool))) (= (= (@ tptp.collec1027672124_state P_25) tptp.bot_bo70021908tate_o) (forall ((X tptp.hoare_1167836817_state)) (not (@ P_25 X))))))
% 0.51/0.83 (assert (forall ((A_86 tptp.hoare_1167836817_state) (B_48 tptp.hoare_1167836817_state) (C_32 tptp.hoare_1167836817_state) (D_1 tptp.hoare_1167836817_state)) (= (= (@ (@ tptp.insert2134838167_state A_86) (@ (@ tptp.insert2134838167_state B_48) tptp.bot_bo70021908tate_o)) (@ (@ tptp.insert2134838167_state C_32) (@ (@ tptp.insert2134838167_state D_1) tptp.bot_bo70021908tate_o))) (or (and (= A_86 C_32) (= B_48 D_1)) (and (= A_86 D_1) (= B_48 C_32))))))
% 0.51/0.83 (assert (forall ((A_86 tptp.hoare_1775062406iple_a) (B_48 tptp.hoare_1775062406iple_a) (C_32 tptp.hoare_1775062406iple_a) (D_1 tptp.hoare_1775062406iple_a)) (= (= (@ (@ tptp.insert1281456128iple_a A_86) (@ (@ tptp.insert1281456128iple_a B_48) tptp.bot_bo751897185le_a_o)) (@ (@ tptp.insert1281456128iple_a C_32) (@ (@ tptp.insert1281456128iple_a D_1) tptp.bot_bo751897185le_a_o))) (or (and (= A_86 C_32) (= B_48 D_1)) (and (= A_86 D_1) (= B_48 C_32))))))
% 0.51/0.83 (assert (forall ((A_86 tptp.pname) (B_48 tptp.pname) (C_32 tptp.pname) (D_1 tptp.pname)) (= (= (@ (@ tptp.insert_pname A_86) (@ (@ tptp.insert_pname B_48) tptp.bot_bot_pname_o)) (@ (@ tptp.insert_pname C_32) (@ (@ tptp.insert_pname D_1) tptp.bot_bot_pname_o))) (or (and (= A_86 C_32) (= B_48 D_1)) (and (= A_86 D_1) (= B_48 C_32))))))
% 0.51/0.83 (assert (forall ((Y_11 tptp.hoare_1167836817_state) (A_85 (-> tptp.hoare_1167836817_state Bool)) (X_30 tptp.hoare_1167836817_state)) (= (@ (@ (@ tptp.insert2134838167_state Y_11) A_85) X_30) (or (= Y_11 X_30) (@ A_85 X_30)))))
% 0.51/0.83 (assert (forall ((Y_11 tptp.hoare_1775062406iple_a) (A_85 (-> tptp.hoare_1775062406iple_a Bool)) (X_30 tptp.hoare_1775062406iple_a)) (= (@ (@ (@ tptp.insert1281456128iple_a Y_11) A_85) X_30) (or (= Y_11 X_30) (@ A_85 X_30)))))
% 0.51/0.83 (assert (forall ((Y_11 tptp.pname) (A_85 (-> tptp.pname Bool)) (X_30 tptp.pname)) (= (@ (@ (@ tptp.insert_pname Y_11) A_85) X_30) (or (= Y_11 X_30) (@ A_85 X_30)))))
% 0.51/0.83 (assert (forall ((B_47 (-> tptp.hoare_1167836817_state Bool)) (X_29 tptp.hoare_1167836817_state) (A_84 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.insert2134838167_state X_29))) (let ((_let_2 (@ tptp.member2058392318_state X_29))) (=> (not (@ _let_2 A_84)) (=> (not (@ _let_2 B_47)) (= (= (@ _let_1 A_84) (@ _let_1 B_47)) (= A_84 B_47))))))))
% 0.51/0.83 (assert (forall ((B_47 (-> tptp.hoare_1775062406iple_a Bool)) (X_29 tptp.hoare_1775062406iple_a) (A_84 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.insert1281456128iple_a X_29))) (let ((_let_2 (@ tptp.member2122167641iple_a X_29))) (=> (not (@ _let_2 A_84)) (=> (not (@ _let_2 B_47)) (= (= (@ _let_1 A_84) (@ _let_1 B_47)) (= A_84 B_47))))))))
% 0.51/0.83 (assert (forall ((B_47 (-> tptp.pname Bool)) (X_29 tptp.pname) (A_84 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_29))) (let ((_let_2 (@ tptp.member_pname X_29))) (=> (not (@ _let_2 A_84)) (=> (not (@ _let_2 B_47)) (= (= (@ _let_1 A_84) (@ _let_1 B_47)) (= A_84 B_47))))))))
% 0.51/0.83 (assert (forall ((A_83 tptp.hoare_1775062406iple_a) (A_82 (-> tptp.hoare_1775062406iple_a Bool))) (=> (= A_82 tptp.bot_bo751897185le_a_o) (not (@ (@ tptp.member2122167641iple_a A_83) A_82)))))
% 0.51/0.83 (assert (forall ((A_83 tptp.hoare_1167836817_state) (A_82 (-> tptp.hoare_1167836817_state Bool))) (=> (= A_82 tptp.bot_bo70021908tate_o) (not (@ (@ tptp.member2058392318_state A_83) A_82)))))
% 0.51/0.83 (assert (forall ((A_83 tptp.pname) (A_82 (-> tptp.pname Bool))) (=> (= A_82 tptp.bot_bot_pname_o) (not (@ (@ tptp.member_pname A_83) A_82)))))
% 0.51/0.83 (assert (forall ((B_46 tptp.hoare_1167836817_state) (A_81 tptp.hoare_1167836817_state) (B_45 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state A_81))) (=> (@ _let_1 B_45) (@ _let_1 (@ (@ tptp.insert2134838167_state B_46) B_45))))))
% 0.51/0.83 (assert (forall ((B_46 tptp.hoare_1775062406iple_a) (A_81 tptp.hoare_1775062406iple_a) (B_45 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.member2122167641iple_a A_81))) (=> (@ _let_1 B_45) (@ _let_1 (@ (@ tptp.insert1281456128iple_a B_46) B_45))))))
% 0.51/0.83 (assert (forall ((B_46 tptp.pname) (A_81 tptp.pname) (B_45 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_81))) (=> (@ _let_1 B_45) (@ _let_1 (@ (@ tptp.insert_pname B_46) B_45))))))
% 0.51/0.83 (assert (forall ((A_80 tptp.hoare_1167836817_state) (A_79 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.member2058392318_state A_80) A_79) (= (@ (@ tptp.insert2134838167_state A_80) A_79) A_79))))
% 0.51/0.83 (assert (forall ((A_80 tptp.hoare_1775062406iple_a) (A_79 (-> tptp.hoare_1775062406iple_a Bool))) (=> (@ (@ tptp.member2122167641iple_a A_80) A_79) (= (@ (@ tptp.insert1281456128iple_a A_80) A_79) A_79))))
% 0.51/0.83 (assert (forall ((A_80 tptp.pname) (A_79 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname A_80) A_79) (= (@ (@ tptp.insert_pname A_80) A_79) A_79))))
% 0.51/0.83 (assert (forall ((B_44 tptp.hoare_1167836817_state) (A_78 tptp.hoare_1167836817_state)) (=> (@ (@ tptp.member2058392318_state B_44) (@ (@ tptp.insert2134838167_state A_78) tptp.bot_bo70021908tate_o)) (= B_44 A_78))))
% 0.51/0.83 (assert (forall ((B_44 tptp.hoare_1775062406iple_a) (A_78 tptp.hoare_1775062406iple_a)) (=> (@ (@ tptp.member2122167641iple_a B_44) (@ (@ tptp.insert1281456128iple_a A_78) tptp.bot_bo751897185le_a_o)) (= B_44 A_78))))
% 0.51/0.83 (assert (forall ((B_44 tptp.pname) (A_78 tptp.pname)) (=> (@ (@ tptp.member_pname B_44) (@ (@ tptp.insert_pname A_78) tptp.bot_bot_pname_o)) (= B_44 A_78))))
% 0.51/0.83 (assert (forall ((A_77 tptp.hoare_1167836817_state) (B_43 tptp.hoare_1167836817_state)) (=> (= (@ (@ tptp.insert2134838167_state A_77) tptp.bot_bo70021908tate_o) (@ (@ tptp.insert2134838167_state B_43) tptp.bot_bo70021908tate_o)) (= A_77 B_43))))
% 0.51/0.83 (assert (forall ((A_77 tptp.hoare_1775062406iple_a) (B_43 tptp.hoare_1775062406iple_a)) (=> (= (@ (@ tptp.insert1281456128iple_a A_77) tptp.bot_bo751897185le_a_o) (@ (@ tptp.insert1281456128iple_a B_43) tptp.bot_bo751897185le_a_o)) (= A_77 B_43))))
% 0.51/0.83 (assert (forall ((A_77 tptp.pname) (B_43 tptp.pname)) (=> (= (@ (@ tptp.insert_pname A_77) tptp.bot_bot_pname_o) (@ (@ tptp.insert_pname B_43) tptp.bot_bot_pname_o)) (= A_77 B_43))))
% 0.51/0.83 (assert (forall ((U_1 tptp.state) (C_19 tptp.com) (S tptp.state) (T tptp.state)) (let ((_let_1 (@ (@ tptp.evalc C_19) S))) (=> (@ _let_1 T) (=> (@ _let_1 U_1) (= U_1 T))))))
% 0.51/0.83 (assert (forall ((A_76 tptp.hoare_1167836817_state) (A_75 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.insert2134838167_state A_76))) (= (@ _let_1 A_75) (@ (@ tptp.semila1172322802tate_o (@ _let_1 tptp.bot_bo70021908tate_o)) A_75)))))
% 0.51/0.83 (assert (forall ((A_76 tptp.pname) (A_75 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname A_76))) (= (@ _let_1 A_75) (@ (@ tptp.semila1780557381name_o (@ _let_1 tptp.bot_bot_pname_o)) A_75)))))
% 0.51/0.83 (assert (forall ((A_76 tptp.hoare_1775062406iple_a) (A_75 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.insert1281456128iple_a A_76))) (= (@ _let_1 A_75) (@ (@ tptp.semila13410563le_a_o (@ _let_1 tptp.bot_bo751897185le_a_o)) A_75)))))
% 0.51/0.83 (assert (forall ((X tptp.hoare_1167836817_state) (Xa (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.insert2134838167_state X) Xa) (@ tptp.collec1027672124_state (lambda ((Y_2 tptp.hoare_1167836817_state)) (or (= Y_2 X) (@ (@ tptp.member2058392318_state Y_2) Xa)))))))
% 0.51/0.83 (assert (forall ((X tptp.hoare_1775062406iple_a) (Xa (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.insert1281456128iple_a X) Xa) (@ tptp.collec676402587iple_a (lambda ((Y_2 tptp.hoare_1775062406iple_a)) (or (= Y_2 X) (@ (@ tptp.member2122167641iple_a Y_2) Xa)))))))
% 0.51/0.83 (assert (forall ((X tptp.pname) (Xa (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname X) Xa) (@ tptp.collect_pname (lambda ((Y_2 tptp.pname)) (or (= Y_2 X) (@ (@ tptp.member_pname Y_2) Xa)))))))
% 0.51/0.83 (assert (forall ((G_16 (-> tptp.hoare_1167836817_state Bool)) (T_3 tptp.hoare_1167836817_state) (Ts_2 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.hoare_123228589_state G_16))) (let ((_let_2 (@ tptp.insert2134838167_state T_3))) (=> (@ _let_1 (@ _let_2 Ts_2)) (and (@ _let_1 (@ _let_2 tptp.bot_bo70021908tate_o)) (@ _let_1 Ts_2)))))))
% 0.51/0.83 (assert (forall ((G_16 (-> tptp.hoare_1775062406iple_a Bool)) (T_3 tptp.hoare_1775062406iple_a) (Ts_2 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.hoare_1508237396rivs_a G_16))) (let ((_let_2 (@ tptp.insert1281456128iple_a T_3))) (=> (@ _let_1 (@ _let_2 Ts_2)) (and (@ _let_1 (@ _let_2 tptp.bot_bo751897185le_a_o)) (@ _let_1 Ts_2)))))))
% 0.51/0.83 (assert (forall ((Ts_1 (-> tptp.hoare_1167836817_state Bool)) (G_15 (-> tptp.hoare_1167836817_state Bool)) (T_2 tptp.hoare_1167836817_state)) (let ((_let_1 (@ tptp.insert2134838167_state T_2))) (let ((_let_2 (@ tptp.hoare_123228589_state G_15))) (=> (@ _let_2 (@ _let_1 tptp.bot_bo70021908tate_o)) (=> (@ _let_2 Ts_1) (@ _let_2 (@ _let_1 Ts_1))))))))
% 0.51/0.83 (assert (forall ((Ts_1 (-> tptp.hoare_1775062406iple_a Bool)) (G_15 (-> tptp.hoare_1775062406iple_a Bool)) (T_2 tptp.hoare_1775062406iple_a)) (let ((_let_1 (@ tptp.insert1281456128iple_a T_2))) (let ((_let_2 (@ tptp.hoare_1508237396rivs_a G_15))) (=> (@ _let_2 (@ _let_1 tptp.bot_bo751897185le_a_o)) (=> (@ _let_2 Ts_1) (@ _let_2 (@ _let_1 Ts_1))))))))
% 0.51/0.83 (assert (forall ((C_31 tptp.hoare_1167836817_state) (A_74 (-> tptp.pname Bool))) (let ((_let_1 (= A_74 tptp.bot_bot_pname_o))) (and (=> _let_1 (= (@ (@ tptp.image_575578384_state (lambda ((X tptp.pname)) C_31)) A_74) tptp.bot_bo70021908tate_o)) (=> (not _let_1) (= (@ (@ tptp.image_575578384_state (lambda ((X tptp.pname)) C_31)) A_74) (@ (@ tptp.insert2134838167_state C_31) tptp.bot_bo70021908tate_o)))))))
% 0.51/0.83 (assert (forall ((C_31 tptp.hoare_1775062406iple_a) (A_74 (-> tptp.pname Bool))) (let ((_let_1 (= A_74 tptp.bot_bot_pname_o))) (and (=> _let_1 (= (@ (@ tptp.image_2063119815iple_a (lambda ((X tptp.pname)) C_31)) A_74) tptp.bot_bo751897185le_a_o)) (=> (not _let_1) (= (@ (@ tptp.image_2063119815iple_a (lambda ((X tptp.pname)) C_31)) A_74) (@ (@ tptp.insert1281456128iple_a C_31) tptp.bot_bo751897185le_a_o)))))))
% 0.51/0.83 (assert (forall ((C_30 tptp.hoare_1167836817_state) (X_28 tptp.pname) (A_73 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_28) A_73) (= (@ (@ tptp.image_575578384_state (lambda ((X tptp.pname)) C_30)) A_73) (@ (@ tptp.insert2134838167_state C_30) tptp.bot_bo70021908tate_o)))))
% 0.51/0.83 (assert (forall ((C_30 tptp.pname) (X_28 tptp.pname) (A_73 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_28) A_73) (= (@ (@ tptp.image_pname_pname (lambda ((X tptp.pname)) C_30)) A_73) (@ (@ tptp.insert_pname C_30) tptp.bot_bot_pname_o)))))
% 0.51/0.83 (assert (forall ((C_30 tptp.hoare_1775062406iple_a) (X_28 tptp.pname) (A_73 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_28) A_73) (= (@ (@ tptp.image_2063119815iple_a (lambda ((X tptp.pname)) C_30)) A_73) (@ (@ tptp.insert1281456128iple_a C_30) tptp.bot_bo751897185le_a_o)))))
% 0.51/0.83 (assert (forall ((F_31 (-> tptp.pname tptp.hoare_1167836817_state)) (A_72 tptp.pname) (B_42 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_575578384_state F_31))) (= (@ _let_1 (@ (@ tptp.insert_pname A_72) B_42)) (@ (@ tptp.insert2134838167_state (@ F_31 A_72)) (@ _let_1 B_42))))))
% 0.51/0.83 (assert (forall ((F_31 (-> tptp.pname tptp.hoare_1775062406iple_a)) (A_72 tptp.pname) (B_42 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_2063119815iple_a F_31))) (= (@ _let_1 (@ (@ tptp.insert_pname A_72) B_42)) (@ (@ tptp.insert1281456128iple_a (@ F_31 A_72)) (@ _let_1 B_42))))))
% 0.51/0.83 (assert (forall ((F_30 (-> tptp.pname tptp.hoare_1167836817_state)) (X_27 tptp.pname) (A_71 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_575578384_state F_30) A_71))) (=> (@ (@ tptp.member_pname X_27) A_71) (= (@ (@ tptp.insert2134838167_state (@ F_30 X_27)) _let_1) _let_1)))))
% 0.51/0.83 (assert (forall ((F_30 (-> tptp.pname tptp.pname)) (X_27 tptp.pname) (A_71 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_pname_pname F_30) A_71))) (=> (@ (@ tptp.member_pname X_27) A_71) (= (@ (@ tptp.insert_pname (@ F_30 X_27)) _let_1) _let_1)))))
% 0.51/0.83 (assert (forall ((F_30 (-> tptp.pname tptp.hoare_1775062406iple_a)) (X_27 tptp.pname) (A_71 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_2063119815iple_a F_30) A_71))) (=> (@ (@ tptp.member_pname X_27) A_71) (= (@ (@ tptp.insert1281456128iple_a (@ F_30 X_27)) _let_1) _let_1)))))
% 0.51/0.83 (assert (forall ((A_70 (-> tptp.hoare_1167836817_state Bool)) (A_69 tptp.hoare_1167836817_state) (B_41 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila1172322802tate_o A_70))) (let ((_let_2 (@ tptp.insert2134838167_state A_69))) (= (@ _let_1 (@ _let_2 B_41)) (@ _let_2 (@ _let_1 B_41)))))))
% 0.51/0.83 (assert (forall ((A_70 (-> tptp.pname Bool)) (A_69 tptp.pname) (B_41 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o A_70))) (let ((_let_2 (@ tptp.insert_pname A_69))) (= (@ _let_1 (@ _let_2 B_41)) (@ _let_2 (@ _let_1 B_41)))))))
% 0.51/0.83 (assert (forall ((A_70 (-> tptp.hoare_1775062406iple_a Bool)) (A_69 tptp.hoare_1775062406iple_a) (B_41 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila13410563le_a_o A_70))) (let ((_let_2 (@ tptp.insert1281456128iple_a A_69))) (= (@ _let_1 (@ _let_2 B_41)) (@ _let_2 (@ _let_1 B_41)))))))
% 0.51/0.83 (assert (forall ((A_68 tptp.hoare_1167836817_state) (B_40 (-> tptp.hoare_1167836817_state Bool)) (C_29 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.insert2134838167_state A_68))) (= (@ (@ tptp.semila1172322802tate_o (@ _let_1 B_40)) C_29) (@ _let_1 (@ (@ tptp.semila1172322802tate_o B_40) C_29))))))
% 0.51/0.83 (assert (forall ((A_68 tptp.pname) (B_40 (-> tptp.pname Bool)) (C_29 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname A_68))) (= (@ (@ tptp.semila1780557381name_o (@ _let_1 B_40)) C_29) (@ _let_1 (@ (@ tptp.semila1780557381name_o B_40) C_29))))))
% 0.51/0.83 (assert (forall ((A_68 tptp.hoare_1775062406iple_a) (B_40 (-> tptp.hoare_1775062406iple_a Bool)) (C_29 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.insert1281456128iple_a A_68))) (= (@ (@ tptp.semila13410563le_a_o (@ _let_1 B_40)) C_29) (@ _let_1 (@ (@ tptp.semila13410563le_a_o B_40) C_29))))))
% 0.51/0.83 (assert (forall ((F_29 (-> tptp.pname tptp.hoare_1167836817_state)) (A_67 (-> tptp.pname Bool))) (= (= tptp.bot_bo70021908tate_o (@ (@ tptp.image_575578384_state F_29) A_67)) (= A_67 tptp.bot_bot_pname_o))))
% 0.51/0.83 (assert (forall ((F_29 (-> tptp.pname tptp.hoare_1775062406iple_a)) (A_67 (-> tptp.pname Bool))) (= (= tptp.bot_bo751897185le_a_o (@ (@ tptp.image_2063119815iple_a F_29) A_67)) (= A_67 tptp.bot_bot_pname_o))))
% 0.51/0.83 (assert (forall ((F_28 (-> tptp.pname tptp.hoare_1167836817_state))) (= (@ (@ tptp.image_575578384_state F_28) tptp.bot_bot_pname_o) tptp.bot_bo70021908tate_o)))
% 0.51/0.83 (assert (forall ((F_28 (-> tptp.pname tptp.hoare_1775062406iple_a))) (= (@ (@ tptp.image_2063119815iple_a F_28) tptp.bot_bot_pname_o) tptp.bot_bo751897185le_a_o)))
% 0.51/0.83 (assert (forall ((F_27 (-> tptp.pname tptp.hoare_1167836817_state)) (A_66 (-> tptp.pname Bool))) (= (= (@ (@ tptp.image_575578384_state F_27) A_66) tptp.bot_bo70021908tate_o) (= A_66 tptp.bot_bot_pname_o))))
% 0.51/0.83 (assert (forall ((F_27 (-> tptp.pname tptp.hoare_1775062406iple_a)) (A_66 (-> tptp.pname Bool))) (= (= (@ (@ tptp.image_2063119815iple_a F_27) A_66) tptp.bot_bo751897185le_a_o) (= A_66 tptp.bot_bot_pname_o))))
% 0.51/0.83 (assert (forall ((P_24 (-> tptp.hoare_1167836817_state Bool)) (X tptp.hoare_1167836817_state)) (=> (@ (@ tptp.member2058392318_state X) tptp.bot_bo70021908tate_o) (@ P_24 X))))
% 0.51/0.83 (assert (forall ((P_24 (-> tptp.hoare_1775062406iple_a Bool)) (X tptp.hoare_1775062406iple_a)) (=> (@ (@ tptp.member2122167641iple_a X) tptp.bot_bo751897185le_a_o) (@ P_24 X))))
% 0.51/0.83 (assert (forall ((P_24 (-> tptp.pname Bool)) (X tptp.pname)) (=> (@ (@ tptp.member_pname X) tptp.bot_bot_pname_o) (@ P_24 X))))
% 0.51/0.83 (assert (forall ((B_39 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila1172322802tate_o tptp.bot_bo70021908tate_o) B_39) B_39)))
% 0.51/0.83 (assert (forall ((B_39 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o tptp.bot_bot_pname_o) B_39) B_39)))
% 0.51/0.83 (assert (forall ((B_39 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila13410563le_a_o tptp.bot_bo751897185le_a_o) B_39) B_39)))
% 0.51/0.83 (assert (forall ((A_65 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila1172322802tate_o A_65) tptp.bot_bo70021908tate_o) A_65)))
% 0.51/0.83 (assert (forall ((A_65 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o A_65) tptp.bot_bot_pname_o) A_65)))
% 0.51/0.83 (assert (forall ((A_65 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila13410563le_a_o A_65) tptp.bot_bo751897185le_a_o) A_65)))
% 0.51/0.83 (assert (forall ((A_64 (-> tptp.hoare_1167836817_state Bool)) (B_38 (-> tptp.hoare_1167836817_state Bool))) (= (= (@ (@ tptp.semila1172322802tate_o A_64) B_38) tptp.bot_bo70021908tate_o) (and (= A_64 tptp.bot_bo70021908tate_o) (= B_38 tptp.bot_bo70021908tate_o)))))
% 0.51/0.83 (assert (forall ((A_64 (-> tptp.pname Bool)) (B_38 (-> tptp.pname Bool))) (= (= (@ (@ tptp.semila1780557381name_o A_64) B_38) tptp.bot_bot_pname_o) (and (= A_64 tptp.bot_bot_pname_o) (= B_38 tptp.bot_bot_pname_o)))))
% 0.51/0.83 (assert (forall ((A_64 (-> tptp.hoare_1775062406iple_a Bool)) (B_38 (-> tptp.hoare_1775062406iple_a Bool))) (= (= (@ (@ tptp.semila13410563le_a_o A_64) B_38) tptp.bot_bo751897185le_a_o) (and (= A_64 tptp.bot_bo751897185le_a_o) (= B_38 tptp.bot_bo751897185le_a_o)))))
% 0.51/0.83 (assert (forall ((G_14 (-> tptp.hoare_1775062406iple_a Bool)) (P_23 (-> tptp.x_a tptp.state Bool)) (C_28 tptp.com) (Q_15 (-> tptp.x_a tptp.state Bool)) (C_27 Bool)) (let ((_let_1 (@ tptp.hoare_1508237396rivs_a G_14))) (=> (=> C_27 (@ _let_1 (@ (@ tptp.insert1281456128iple_a (@ (@ (@ tptp.hoare_1766022166iple_a P_23) C_28) Q_15)) tptp.bot_bo751897185le_a_o))) (@ _let_1 (@ (@ tptp.insert1281456128iple_a (@ (@ (@ tptp.hoare_1766022166iple_a (lambda ((Z_8 tptp.x_a) (S_3 tptp.state)) (and (@ (@ P_23 Z_8) S_3) C_27))) C_28) Q_15)) tptp.bot_bo751897185le_a_o))))))
% 0.51/0.83 (assert (forall ((G_14 (-> tptp.hoare_1167836817_state Bool)) (P_23 (-> tptp.state tptp.state Bool)) (C_28 tptp.com) (Q_15 (-> tptp.state tptp.state Bool)) (C_27 Bool)) (let ((_let_1 (@ tptp.hoare_123228589_state G_14))) (=> (=> C_27 (@ _let_1 (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state P_23) C_28) Q_15)) tptp.bot_bo70021908tate_o))) (@ _let_1 (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state (lambda ((Z_8 tptp.state) (S_3 tptp.state)) (and (@ (@ P_23 Z_8) S_3) C_27))) C_28) Q_15)) tptp.bot_bo70021908tate_o))))))
% 0.51/0.83 (assert (forall ((G_13 (-> tptp.hoare_1167836817_state Bool))) (@ (@ tptp.hoare_123228589_state G_13) tptp.bot_bo70021908tate_o)))
% 0.51/0.83 (assert (forall ((G_13 (-> tptp.hoare_1775062406iple_a Bool))) (@ (@ tptp.hoare_1508237396rivs_a G_13) tptp.bot_bo751897185le_a_o)))
% 0.51/0.83 (assert (forall ((X_26 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila1172322802tate_o tptp.bot_bo70021908tate_o) X_26) X_26)))
% 0.51/0.83 (assert (forall ((X_26 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o tptp.bot_bot_pname_o) X_26) X_26)))
% 0.51/0.83 (assert (forall ((X_26 Bool)) (= (@ (@ tptp.semila10642723_sup_o tptp.bot_bot_o) X_26) X_26)))
% 0.51/0.83 (assert (forall ((X_26 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila13410563le_a_o tptp.bot_bo751897185le_a_o) X_26) X_26)))
% 0.51/0.83 (assert (forall ((X_25 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila1172322802tate_o X_25) tptp.bot_bo70021908tate_o) X_25)))
% 0.51/0.83 (assert (forall ((X_25 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o X_25) tptp.bot_bot_pname_o) X_25)))
% 0.51/0.83 (assert (forall ((X_25 Bool)) (= (@ (@ tptp.semila10642723_sup_o X_25) tptp.bot_bot_o) X_25)))
% 0.51/0.83 (assert (forall ((X_25 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila13410563le_a_o X_25) tptp.bot_bo751897185le_a_o) X_25)))
% 0.51/0.83 (assert (forall ((X_24 (-> tptp.hoare_1167836817_state Bool)) (Y_10 (-> tptp.hoare_1167836817_state Bool))) (= (= (@ (@ tptp.semila1172322802tate_o X_24) Y_10) tptp.bot_bo70021908tate_o) (and (= X_24 tptp.bot_bo70021908tate_o) (= Y_10 tptp.bot_bo70021908tate_o)))))
% 0.51/0.83 (assert (forall ((X_24 (-> tptp.pname Bool)) (Y_10 (-> tptp.pname Bool))) (= (= (@ (@ tptp.semila1780557381name_o X_24) Y_10) tptp.bot_bot_pname_o) (and (= X_24 tptp.bot_bot_pname_o) (= Y_10 tptp.bot_bot_pname_o)))))
% 0.51/0.83 (assert (forall ((X_24 Bool) (Y_10 Bool)) (= (= (@ (@ tptp.semila10642723_sup_o X_24) Y_10) tptp.bot_bot_o) (and (= X_24 tptp.bot_bot_o) (= Y_10 tptp.bot_bot_o)))))
% 0.51/0.83 (assert (forall ((X_24 (-> tptp.hoare_1775062406iple_a Bool)) (Y_10 (-> tptp.hoare_1775062406iple_a Bool))) (= (= (@ (@ tptp.semila13410563le_a_o X_24) Y_10) tptp.bot_bo751897185le_a_o) (and (= X_24 tptp.bot_bo751897185le_a_o) (= Y_10 tptp.bot_bo751897185le_a_o)))))
% 0.51/0.83 (assert (forall ((N_6 tptp.nat) (T_1 tptp.hoare_1167836817_state)) (=> (@ (@ tptp.hoare_56934129_state (@ tptp.suc N_6)) T_1) (@ (@ tptp.hoare_56934129_state N_6) T_1))))
% 0.51/0.83 (assert (forall ((N_6 tptp.nat) (T_1 tptp.hoare_1775062406iple_a)) (=> (@ (@ tptp.hoare_1462269968alid_a (@ tptp.suc N_6)) T_1) (@ (@ tptp.hoare_1462269968alid_a N_6) T_1))))
% 0.51/0.83 (assert (forall ((A_63 tptp.hoare_1167836817_state) (B_37 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.insert2134838167_state A_63) B_37) (@ (@ tptp.semila1172322802tate_o (@ tptp.collec1027672124_state (lambda ((X tptp.hoare_1167836817_state)) (= X A_63)))) B_37))))
% 0.51/0.83 (assert (forall ((A_63 tptp.pname) (B_37 (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname A_63) B_37) (@ (@ tptp.semila1780557381name_o (@ tptp.collect_pname (lambda ((X tptp.pname)) (= X A_63)))) B_37))))
% 0.51/0.83 (assert (forall ((A_63 tptp.hoare_1775062406iple_a) (B_37 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.insert1281456128iple_a A_63) B_37) (@ (@ tptp.semila13410563le_a_o (@ tptp.collec676402587iple_a (lambda ((X tptp.hoare_1775062406iple_a)) (= X A_63)))) B_37))))
% 0.51/0.83 (assert (forall ((G_12 (-> tptp.hoare_1775062406iple_a Bool)) (P_22 (-> tptp.x_a tptp.state Bool)) (Pn_3 tptp.pname) (Q_14 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_1766022166iple_a P_22))) (let ((_let_2 (@ tptp.hoare_1508237396rivs_a G_12))) (=> (@ _let_2 (@ (@ tptp.insert1281456128iple_a (@ (@ _let_1 (@ tptp.the_com (@ tptp.body_1 Pn_3))) Q_14)) tptp.bot_bo751897185le_a_o)) (@ _let_2 (@ (@ tptp.insert1281456128iple_a (@ (@ _let_1 (@ tptp.body Pn_3)) Q_14)) tptp.bot_bo751897185le_a_o)))))))
% 0.51/0.83 (assert (forall ((G_12 (-> tptp.hoare_1167836817_state Bool)) (P_22 (-> tptp.state tptp.state Bool)) (Pn_3 tptp.pname) (Q_14 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_908217195_state P_22))) (let ((_let_2 (@ tptp.hoare_123228589_state G_12))) (=> (@ _let_2 (@ (@ tptp.insert2134838167_state (@ (@ _let_1 (@ tptp.the_com (@ tptp.body_1 Pn_3))) Q_14)) tptp.bot_bo70021908tate_o)) (@ _let_2 (@ (@ tptp.insert2134838167_state (@ (@ _let_1 (@ tptp.body Pn_3)) Q_14)) tptp.bot_bo70021908tate_o)))))))
% 0.51/0.83 (assert (forall ((P_21 (-> tptp.x_a tptp.state Bool)) (Pn_2 tptp.pname) (Q_13 (-> tptp.x_a tptp.state Bool)) (G_11 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.hoare_1766022166iple_a P_21))) (let ((_let_2 (@ tptp.insert1281456128iple_a (@ (@ _let_1 (@ tptp.body Pn_2)) Q_13)))) (=> (@ (@ tptp.hoare_1508237396rivs_a (@ _let_2 G_11)) (@ (@ tptp.insert1281456128iple_a (@ (@ _let_1 (@ tptp.the_com (@ tptp.body_1 Pn_2))) Q_13)) tptp.bot_bo751897185le_a_o)) (@ (@ tptp.hoare_1508237396rivs_a G_11) (@ _let_2 tptp.bot_bo751897185le_a_o)))))))
% 0.51/0.83 (assert (forall ((P_21 (-> tptp.state tptp.state Bool)) (Pn_2 tptp.pname) (Q_13 (-> tptp.state tptp.state Bool)) (G_11 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.hoare_908217195_state P_21))) (let ((_let_2 (@ tptp.insert2134838167_state (@ (@ _let_1 (@ tptp.body Pn_2)) Q_13)))) (=> (@ (@ tptp.hoare_123228589_state (@ _let_2 G_11)) (@ (@ tptp.insert2134838167_state (@ (@ _let_1 (@ tptp.the_com (@ tptp.body_1 Pn_2))) Q_13)) tptp.bot_bo70021908tate_o)) (@ (@ tptp.hoare_123228589_state G_11) (@ _let_2 tptp.bot_bo70021908tate_o)))))))
% 0.51/0.83 (assert (forall ((N_5 tptp.nat) (Ts (-> tptp.hoare_1167836817_state Bool))) (=> (forall ((X tptp.hoare_1167836817_state)) (=> (@ (@ tptp.member2058392318_state X) Ts) (@ (@ tptp.hoare_56934129_state (@ tptp.suc N_5)) X))) (forall ((X tptp.hoare_1167836817_state)) (=> (@ (@ tptp.member2058392318_state X) Ts) (@ (@ tptp.hoare_56934129_state N_5) X))))))
% 0.51/0.83 (assert (forall ((N_5 tptp.nat) (Ts (-> tptp.hoare_1775062406iple_a Bool))) (=> (forall ((X tptp.hoare_1775062406iple_a)) (=> (@ (@ tptp.member2122167641iple_a X) Ts) (@ (@ tptp.hoare_1462269968alid_a (@ tptp.suc N_5)) X))) (forall ((X tptp.hoare_1775062406iple_a)) (=> (@ (@ tptp.member2122167641iple_a X) Ts) (@ (@ tptp.hoare_1462269968alid_a N_5) X))))))
% 0.51/0.83 (assert (forall ((G_10 (-> tptp.hoare_1775062406iple_a Bool)) (C_26 tptp.com) (Q_12 (-> tptp.x_a tptp.state Bool)) (P_20 (-> tptp.x_a tptp.state Bool))) (=> (forall ((Z_8 tptp.x_a) (S_3 tptp.state)) (=> (@ (@ P_20 Z_8) S_3) (@ (@ tptp.hoare_1508237396rivs_a G_10) (@ (@ tptp.insert1281456128iple_a (@ (@ (@ tptp.hoare_1766022166iple_a (lambda ((Za tptp.x_a) (S_4 tptp.state)) (= S_4 S_3))) C_26) (lambda ((Z_9 tptp.x_a) (__flatten_var_0 tptp.state)) (@ (@ Q_12 Z_8) __flatten_var_0)))) tptp.bot_bo751897185le_a_o)))) (@ (@ tptp.hoare_1508237396rivs_a G_10) (@ (@ tptp.insert1281456128iple_a (@ (@ (@ tptp.hoare_1766022166iple_a P_20) C_26) Q_12)) tptp.bot_bo751897185le_a_o)))))
% 0.51/0.83 (assert (forall ((G_10 (-> tptp.hoare_1167836817_state Bool)) (C_26 tptp.com) (Q_12 (-> tptp.state tptp.state Bool)) (P_20 (-> tptp.state tptp.state Bool))) (=> (forall ((Z_8 tptp.state) (S_3 tptp.state)) (=> (@ (@ P_20 Z_8) S_3) (@ (@ tptp.hoare_123228589_state G_10) (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state (lambda ((Za tptp.state) (S_4 tptp.state)) (= S_4 S_3))) C_26) (lambda ((Z_9 tptp.state) (__flatten_var_0 tptp.state)) (@ (@ Q_12 Z_8) __flatten_var_0)))) tptp.bot_bo70021908tate_o)))) (@ (@ tptp.hoare_123228589_state G_10) (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state P_20) C_26) Q_12)) tptp.bot_bo70021908tate_o)))))
% 0.51/0.83 (assert (forall ((P_19 (-> tptp.x_a tptp.state Bool)) (G_9 (-> tptp.hoare_1775062406iple_a Bool)) (P_18 (-> tptp.x_a tptp.state Bool)) (C_25 tptp.com) (Q_11 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_1508237396rivs_a G_9))) (=> (@ _let_1 (@ (@ tptp.insert1281456128iple_a (@ (@ (@ tptp.hoare_1766022166iple_a P_18) C_25) Q_11)) tptp.bot_bo751897185le_a_o)) (=> (forall ((Z_8 tptp.x_a) (S_3 tptp.state)) (=> (@ (@ P_19 Z_8) S_3) (@ (@ P_18 Z_8) S_3))) (@ _let_1 (@ (@ tptp.insert1281456128iple_a (@ (@ (@ tptp.hoare_1766022166iple_a P_19) C_25) Q_11)) tptp.bot_bo751897185le_a_o)))))))
% 0.51/0.83 (assert (forall ((P_19 (-> tptp.state tptp.state Bool)) (G_9 (-> tptp.hoare_1167836817_state Bool)) (P_18 (-> tptp.state tptp.state Bool)) (C_25 tptp.com) (Q_11 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_123228589_state G_9))) (=> (@ _let_1 (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state P_18) C_25) Q_11)) tptp.bot_bo70021908tate_o)) (=> (forall ((Z_8 tptp.state) (S_3 tptp.state)) (=> (@ (@ P_19 Z_8) S_3) (@ (@ P_18 Z_8) S_3))) (@ _let_1 (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state P_19) C_25) Q_11)) tptp.bot_bo70021908tate_o)))))))
% 0.51/0.83 (assert (forall ((Q_10 (-> tptp.x_a tptp.state Bool)) (G_8 (-> tptp.hoare_1775062406iple_a Bool)) (P_17 (-> tptp.x_a tptp.state Bool)) (C_24 tptp.com) (Q_9 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ (@ tptp.hoare_1766022166iple_a P_17) C_24))) (let ((_let_2 (@ tptp.hoare_1508237396rivs_a G_8))) (=> (@ _let_2 (@ (@ tptp.insert1281456128iple_a (@ _let_1 Q_9)) tptp.bot_bo751897185le_a_o)) (=> (forall ((Z_8 tptp.x_a) (S_3 tptp.state)) (=> (@ (@ Q_9 Z_8) S_3) (@ (@ Q_10 Z_8) S_3))) (@ _let_2 (@ (@ tptp.insert1281456128iple_a (@ _let_1 Q_10)) tptp.bot_bo751897185le_a_o))))))))
% 0.51/0.83 (assert (forall ((Q_10 (-> tptp.state tptp.state Bool)) (G_8 (-> tptp.hoare_1167836817_state Bool)) (P_17 (-> tptp.state tptp.state Bool)) (C_24 tptp.com) (Q_9 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ (@ tptp.hoare_908217195_state P_17) C_24))) (let ((_let_2 (@ tptp.hoare_123228589_state G_8))) (=> (@ _let_2 (@ (@ tptp.insert2134838167_state (@ _let_1 Q_9)) tptp.bot_bo70021908tate_o)) (=> (forall ((Z_8 tptp.state) (S_3 tptp.state)) (=> (@ (@ Q_9 Z_8) S_3) (@ (@ Q_10 Z_8) S_3))) (@ _let_2 (@ (@ tptp.insert2134838167_state (@ _let_1 Q_10)) tptp.bot_bo70021908tate_o))))))))
% 0.51/0.83 (assert (forall ((Fa (-> tptp.state tptp.nat)) (Fun1_1 (-> tptp.state tptp.state Bool)) (Com_3 tptp.com) (Fun2_1 (-> tptp.state tptp.state Bool))) (= (@ (@ tptp.hoare_545207370_state Fa) (@ (@ (@ tptp.hoare_908217195_state Fun1_1) Com_3) Fun2_1)) tptp.zero_zero_nat)))
% 0.51/0.83 (assert (forall ((Fa (-> tptp.x_a tptp.nat)) (Fun1_1 (-> tptp.x_a tptp.state Bool)) (Com_3 tptp.com) (Fun2_1 (-> tptp.x_a tptp.state Bool))) (= (@ (@ tptp.hoare_1118907895size_a Fa) (@ (@ (@ tptp.hoare_1766022166iple_a Fun1_1) Com_3) Fun2_1)) tptp.zero_zero_nat)))
% 0.51/0.83 (assert (forall ((C_19 tptp.com)) (= (@ tptp.hoare_Mirabelle_MGT C_19) (@ (@ (@ tptp.hoare_908217195_state tptp.fequal_state) C_19) (@ tptp.evalc C_19)))))
% 0.51/0.83 (assert (forall ((Fun1 (-> tptp.state tptp.state Bool)) (Com_2 tptp.com) (Fun2 (-> tptp.state tptp.state Bool))) (= (@ tptp.size_s645941755_state (@ (@ (@ tptp.hoare_908217195_state Fun1) Com_2) Fun2)) tptp.zero_zero_nat)))
% 0.51/0.83 (assert (forall ((Fun1 (-> tptp.x_a tptp.state Bool)) (Com_2 tptp.com) (Fun2 (-> tptp.x_a tptp.state Bool))) (= (@ tptp.size_s724313756iple_a (@ (@ (@ tptp.hoare_1766022166iple_a Fun1) Com_2) Fun2)) tptp.zero_zero_nat)))
% 0.51/0.83 (assert (forall ((Q_8 (-> tptp.state tptp.state Bool)) (P_16 (-> tptp.state tptp.state Bool)) (G_7 (-> tptp.hoare_1167836817_state Bool)) (P_15 (-> tptp.state tptp.state Bool)) (C_23 tptp.com) (Q_7 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_123228589_state G_7))) (=> (@ _let_1 (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state P_15) C_23) Q_7)) tptp.bot_bo70021908tate_o)) (=> (forall ((Z_8 tptp.state) (S_3 tptp.state)) (=> (@ (@ P_16 Z_8) S_3) (forall ((S_4 tptp.state)) (=> (forall ((Z_9 tptp.state)) (=> (@ (@ P_15 Z_9) S_3) (@ (@ Q_7 Z_9) S_4))) (@ (@ Q_8 Z_8) S_4))))) (@ _let_1 (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state P_16) C_23) Q_8)) tptp.bot_bo70021908tate_o)))))))
% 0.51/0.83 (assert (forall ((Q_8 (-> tptp.x_a tptp.state Bool)) (P_16 (-> tptp.x_a tptp.state Bool)) (G_7 (-> tptp.hoare_1775062406iple_a Bool)) (P_15 (-> tptp.x_a tptp.state Bool)) (C_23 tptp.com) (Q_7 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_1508237396rivs_a G_7))) (=> (@ _let_1 (@ (@ tptp.insert1281456128iple_a (@ (@ (@ tptp.hoare_1766022166iple_a P_15) C_23) Q_7)) tptp.bot_bo751897185le_a_o)) (=> (forall ((Z_8 tptp.x_a) (S_3 tptp.state)) (=> (@ (@ P_16 Z_8) S_3) (forall ((S_4 tptp.state)) (=> (forall ((Z_9 tptp.x_a)) (=> (@ (@ P_15 Z_9) S_3) (@ (@ Q_7 Z_9) S_4))) (@ (@ Q_8 Z_8) S_4))))) (@ _let_1 (@ (@ tptp.insert1281456128iple_a (@ (@ (@ tptp.hoare_1766022166iple_a P_16) C_23) Q_8)) tptp.bot_bo751897185le_a_o)))))))
% 0.51/0.83 (assert (forall ((X_23 tptp.hoare_1167836817_state)) (= (@ tptp.the_el323660082_state (@ (@ tptp.insert2134838167_state X_23) tptp.bot_bo70021908tate_o)) X_23)))
% 0.51/0.83 (assert (forall ((X_23 tptp.hoare_1775062406iple_a)) (= (@ tptp.the_el1844711461iple_a (@ (@ tptp.insert1281456128iple_a X_23) tptp.bot_bo751897185le_a_o)) X_23)))
% 0.51/0.83 (assert (forall ((X_23 tptp.pname)) (= (@ tptp.the_elem_pname (@ (@ tptp.insert_pname X_23) tptp.bot_bot_pname_o)) X_23)))
% 0.51/0.83 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.51/0.83 (assert (forall ((Nat_1 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat_1)))))
% 0.51/0.83 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 0.51/0.83 (assert (forall ((Nat_3 tptp.nat)) (not (= (@ tptp.suc Nat_3) tptp.zero_zero_nat))))
% 0.51/0.83 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.51/0.83 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 0.51/0.83 (assert (forall ((X tptp.pname)) (= (@ tptp.bot_bot_pname_o X) tptp.bot_bot_o)))
% 0.51/0.83 (assert (forall ((X tptp.hoare_1775062406iple_a)) (= (@ tptp.bot_bo751897185le_a_o X) tptp.bot_bot_o)))
% 0.51/0.83 (assert (forall ((X tptp.hoare_1167836817_state)) (= (@ tptp.bot_bo70021908tate_o X) tptp.bot_bot_o)))
% 0.51/0.83 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 0.51/0.83 (assert (forall ((X_1 tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X_1) (@ tptp.suc Y)) (= X_1 Y))))
% 0.51/0.83 (assert (forall ((Nat_2 tptp.nat) (Nat_1 tptp.nat)) (= (= (@ tptp.suc Nat_2) (@ tptp.suc Nat_1)) (= Nat_2 Nat_1))))
% 0.51/0.83 (assert (forall ((N_1 tptp.nat)) (not (= (@ tptp.suc N_1) N_1))))
% 0.51/0.83 (assert (forall ((N_1 tptp.nat)) (not (= N_1 (@ tptp.suc N_1)))))
% 0.51/0.83 (assert (forall ((X_22 tptp.pname)) (= (@ tptp.bot_bot_pname_o X_22) tptp.bot_bot_o)))
% 0.51/0.83 (assert (forall ((X_22 tptp.hoare_1775062406iple_a)) (= (@ tptp.bot_bo751897185le_a_o X_22) tptp.bot_bot_o)))
% 0.51/0.83 (assert (forall ((X_22 tptp.hoare_1167836817_state)) (= (@ tptp.bot_bo70021908tate_o X_22) tptp.bot_bot_o)))
% 0.51/0.83 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat tptp.nat)) (not (= Y (@ tptp.suc Nat))))))))
% 0.51/0.83 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N tptp.nat)) (=> (@ P (@ tptp.suc N)) (@ P N))) (@ P tptp.zero_zero_nat)))))
% 0.51/0.83 (assert (forall ((N_1 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N tptp.nat)) (=> (@ P N) (@ P (@ tptp.suc N)))) (@ P N_1)))))
% 0.51/0.83 (assert (forall ((N_1 tptp.nat)) (=> (not (= N_1 tptp.zero_zero_nat)) (exists ((M_1 tptp.nat)) (= N_1 (@ tptp.suc M_1))))))
% 0.51/0.83 (assert (forall ((Pn_1 tptp.pname) (S0 tptp.state) (N_1 tptp.nat) (S1 tptp.state)) (=> (@ (@ (@ (@ tptp.evaln (@ tptp.the_com (@ tptp.body_1 Pn_1))) S0) N_1) S1) (@ (@ (@ (@ tptp.evaln (@ tptp.body Pn_1)) S0) (@ tptp.suc N_1)) S1))))
% 0.51/0.83 (assert (forall ((G_6 (-> tptp.hoare_1167836817_state Bool)) (P_14 (-> tptp.state tptp.state Bool))) (@ (@ tptp.hoare_123228589_state G_6) (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state P_14) tptp.skip) P_14)) tptp.bot_bo70021908tate_o))))
% 0.51/0.83 (assert (forall ((G_6 (-> tptp.hoare_1775062406iple_a Bool)) (P_14 (-> tptp.x_a tptp.state Bool))) (@ (@ tptp.hoare_1508237396rivs_a G_6) (@ (@ tptp.insert1281456128iple_a (@ (@ (@ tptp.hoare_1766022166iple_a P_14) tptp.skip) P_14)) tptp.bot_bo751897185le_a_o))))
% 0.51/0.83 (assert (forall ((S tptp.state) (N_1 tptp.nat) (T tptp.state)) (=> (@ (@ (@ (@ tptp.evaln tptp.skip) S) N_1) T) (= T S))))
% 0.51/0.83 (assert (forall ((S tptp.state) (N_1 tptp.nat)) (@ (@ (@ (@ tptp.evaln tptp.skip) S) N_1) S)))
% 0.51/0.83 (assert (forall ((S tptp.state)) (@ (@ (@ tptp.evalc tptp.skip) S) S)))
% 0.51/0.83 (assert (forall ((S tptp.state) (T tptp.state)) (=> (@ (@ (@ tptp.evalc tptp.skip) S) T) (= T S))))
% 0.51/0.83 (assert (forall ((C_19 tptp.com) (S tptp.state) (N_1 tptp.nat) (S_5 tptp.state)) (let ((_let_1 (@ (@ tptp.evaln C_19) S))) (=> (@ (@ _let_1 N_1) S_5) (@ (@ _let_1 (@ tptp.suc N_1)) S_5)))))
% 0.51/0.83 (assert (forall ((C_19 tptp.com) (S tptp.state) (T tptp.state)) (= (@ (@ (@ tptp.evalc C_19) S) T) (exists ((N tptp.nat)) (@ (@ (@ (@ tptp.evaln C_19) S) N) T)))))
% 0.51/0.83 (assert (forall ((C_19 tptp.com) (S tptp.state) (N_1 tptp.nat) (T tptp.state)) (=> (@ (@ (@ (@ tptp.evaln C_19) S) N_1) T) (@ (@ (@ tptp.evalc C_19) S) T))))
% 0.51/0.83 (assert (forall ((Pname_1 tptp.pname)) (not (= (@ tptp.body Pname_1) tptp.skip))))
% 0.51/0.83 (assert (forall ((Pname_1 tptp.pname)) (not (= tptp.skip (@ tptp.body Pname_1)))))
% 0.51/0.83 (assert (forall ((N_4 tptp.nat) (P_13 (-> tptp.state tptp.state Bool)) (C_22 tptp.com) (Q_6 (-> tptp.state tptp.state Bool))) (= (@ (@ tptp.hoare_56934129_state N_4) (@ (@ (@ tptp.hoare_908217195_state P_13) C_22) Q_6)) (forall ((Z_8 tptp.state) (S_3 tptp.state)) (=> (@ (@ P_13 Z_8) S_3) (forall ((S_4 tptp.state)) (=> (@ (@ (@ (@ tptp.evaln C_22) S_3) N_4) S_4) (@ (@ Q_6 Z_8) S_4))))))))
% 0.51/0.83 (assert (forall ((N_4 tptp.nat) (P_13 (-> tptp.x_a tptp.state Bool)) (C_22 tptp.com) (Q_6 (-> tptp.x_a tptp.state Bool))) (= (@ (@ tptp.hoare_1462269968alid_a N_4) (@ (@ (@ tptp.hoare_1766022166iple_a P_13) C_22) Q_6)) (forall ((Z_8 tptp.x_a) (S_3 tptp.state)) (=> (@ (@ P_13 Z_8) S_3) (forall ((S_4 tptp.state)) (=> (@ (@ (@ (@ tptp.evaln C_22) S_3) N_4) S_4) (@ (@ Q_6 Z_8) S_4))))))))
% 0.51/0.83 (assert (forall ((P tptp.pname) (S tptp.state) (N_1 tptp.nat) (S1 tptp.state)) (=> (@ (@ (@ (@ tptp.evaln (@ tptp.body P)) S) N_1) S1) (not (forall ((N tptp.nat)) (=> (= N_1 (@ tptp.suc N)) (not (@ (@ (@ (@ tptp.evaln (@ tptp.the_com (@ tptp.body_1 P))) S) N) S1))))))))
% 0.51/0.83 (assert (forall ((C_19 tptp.com) (S tptp.state) (T tptp.state)) (=> (@ (@ (@ tptp.evalc C_19) S) T) (exists ((N tptp.nat)) (@ (@ (@ (@ tptp.evaln C_19) S) N) T)))))
% 0.51/0.83 (assert (forall ((G_5 (-> tptp.hoare_1167836817_state Bool)) (P_12 (-> tptp.state tptp.state Bool)) (B_36 (-> tptp.state Bool)) (C_21 tptp.com)) (@ (@ tptp.hoare_123228589_state G_5) (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state (lambda ((Z_8 tptp.state) (S_3 tptp.state)) (and (@ (@ P_12 Z_8) S_3) (not (@ B_36 S_3))))) (@ (@ tptp.while B_36) C_21)) P_12)) tptp.bot_bo70021908tate_o))))
% 0.51/0.83 (assert (forall ((G_5 (-> tptp.hoare_1775062406iple_a Bool)) (P_12 (-> tptp.x_a tptp.state Bool)) (B_36 (-> tptp.state Bool)) (C_21 tptp.com)) (@ (@ tptp.hoare_1508237396rivs_a G_5) (@ (@ tptp.insert1281456128iple_a (@ (@ (@ tptp.hoare_1766022166iple_a (lambda ((Z_8 tptp.x_a) (S_3 tptp.state)) (and (@ (@ P_12 Z_8) S_3) (not (@ B_36 S_3))))) (@ (@ tptp.while B_36) C_21)) P_12)) tptp.bot_bo751897185le_a_o))))
% 0.51/0.83 (assert (forall ((D tptp.com) (R_1 (-> tptp.state tptp.state Bool)) (G_4 (-> tptp.hoare_1167836817_state Bool)) (P_11 (-> tptp.state tptp.state Bool)) (C_20 tptp.com) (Q_5 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_908217195_state P_11))) (let ((_let_2 (@ tptp.hoare_123228589_state G_4))) (=> (@ _let_2 (@ (@ tptp.insert2134838167_state (@ (@ _let_1 C_20) Q_5)) tptp.bot_bo70021908tate_o)) (=> (@ _let_2 (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state Q_5) D) R_1)) tptp.bot_bo70021908tate_o)) (@ _let_2 (@ (@ tptp.insert2134838167_state (@ (@ _let_1 (@ (@ tptp.semi C_20) D)) R_1)) tptp.bot_bo70021908tate_o))))))))
% 0.51/0.83 (assert (forall ((D tptp.com) (R_1 (-> tptp.x_a tptp.state Bool)) (G_4 (-> tptp.hoare_1775062406iple_a Bool)) (P_11 (-> tptp.x_a tptp.state Bool)) (C_20 tptp.com) (Q_5 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_1766022166iple_a P_11))) (let ((_let_2 (@ tptp.hoare_1508237396rivs_a G_4))) (=> (@ _let_2 (@ (@ tptp.insert1281456128iple_a (@ (@ _let_1 C_20) Q_5)) tptp.bot_bo751897185le_a_o)) (=> (@ _let_2 (@ (@ tptp.insert1281456128iple_a (@ (@ (@ tptp.hoare_1766022166iple_a Q_5) D) R_1)) tptp.bot_bo751897185le_a_o)) (@ _let_2 (@ (@ tptp.insert1281456128iple_a (@ (@ _let_1 (@ (@ tptp.semi C_20) D)) R_1)) tptp.bot_bo751897185le_a_o))))))))
% 0.51/0.83 (assert (forall ((X_21 (-> tptp.hoare_1167836817_state Bool))) (= (@ tptp.the_el323660082_state X_21) (@ tptp.the_Ho310147232_state (lambda ((X tptp.hoare_1167836817_state)) (= X_21 (@ (@ tptp.insert2134838167_state X) tptp.bot_bo70021908tate_o)))))))
% 0.51/0.83 (assert (forall ((X_21 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ tptp.the_el1844711461iple_a X_21) (@ tptp.the_Ho1155011127iple_a (lambda ((X tptp.hoare_1775062406iple_a)) (= X_21 (@ (@ tptp.insert1281456128iple_a X) tptp.bot_bo751897185le_a_o)))))))
% 0.51/0.83 (assert (forall ((X_21 (-> tptp.pname Bool))) (= (@ tptp.the_elem_pname X_21) (@ tptp.the_pname (lambda ((X tptp.pname)) (= X_21 (@ (@ tptp.insert_pname X) tptp.bot_bot_pname_o)))))))
% 0.51/0.83 (assert (forall ((P_9 (-> tptp.pname tptp.state tptp.state Bool)) (Q_4 (-> tptp.pname tptp.state tptp.state Bool)) (G_3 (-> tptp.hoare_1167836817_state Bool)) (P_8 (-> tptp.pname tptp.state tptp.state Bool)) (C0_1 (-> tptp.pname tptp.com)) (Q_3 (-> tptp.pname tptp.state tptp.state Bool)) (U (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.hoare_123228589_state G_3))) (=> (@ tptp.finite_finite_pname U) (=> (forall ((P_10 tptp.pname)) (let ((_let_1 (@ C0_1 P_10))) (let ((_let_2 (@ tptp.hoare_123228589_state G_3))) (=> (@ _let_2 (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state (@ P_8 P_10)) _let_1) (@ Q_3 P_10))) tptp.bot_bo70021908tate_o)) (@ _let_2 (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state (@ P_9 P_10)) _let_1) (@ Q_4 P_10))) tptp.bot_bo70021908tate_o)))))) (=> (@ _let_1 (@ (@ tptp.image_575578384_state (lambda ((P_10 tptp.pname)) (@ (@ (@ tptp.hoare_908217195_state (@ P_8 P_10)) (@ C0_1 P_10)) (@ Q_3 P_10)))) U)) (@ _let_1 (@ (@ tptp.image_575578384_state (lambda ((P_10 tptp.pname)) (@ (@ (@ tptp.hoare_908217195_state (@ P_9 P_10)) (@ C0_1 P_10)) (@ Q_4 P_10)))) U))))))))
% 0.51/0.83 (assert (forall ((P_9 (-> tptp.pname tptp.x_a tptp.state Bool)) (Q_4 (-> tptp.pname tptp.x_a tptp.state Bool)) (G_3 (-> tptp.hoare_1775062406iple_a Bool)) (P_8 (-> tptp.pname tptp.x_a tptp.state Bool)) (C0_1 (-> tptp.pname tptp.com)) (Q_3 (-> tptp.pname tptp.x_a tptp.state Bool)) (U (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.hoare_1508237396rivs_a G_3))) (=> (@ tptp.finite_finite_pname U) (=> (forall ((P_10 tptp.pname)) (let ((_let_1 (@ C0_1 P_10))) (let ((_let_2 (@ tptp.hoare_1508237396rivs_a G_3))) (=> (@ _let_2 (@ (@ tptp.insert1281456128iple_a (@ (@ (@ tptp.hoare_1766022166iple_a (@ P_8 P_10)) _let_1) (@ Q_3 P_10))) tptp.bot_bo751897185le_a_o)) (@ _let_2 (@ (@ tptp.insert1281456128iple_a (@ (@ (@ tptp.hoare_1766022166iple_a (@ P_9 P_10)) _let_1) (@ Q_4 P_10))) tptp.bot_bo751897185le_a_o)))))) (=> (@ _let_1 (@ (@ tptp.image_2063119815iple_a (lambda ((P_10 tptp.pname)) (@ (@ (@ tptp.hoare_1766022166iple_a (@ P_8 P_10)) (@ C0_1 P_10)) (@ Q_3 P_10)))) U)) (@ _let_1 (@ (@ tptp.image_2063119815iple_a (lambda ((P_10 tptp.pname)) (@ (@ (@ tptp.hoare_1766022166iple_a (@ P_9 P_10)) (@ C0_1 P_10)) (@ Q_4 P_10)))) U))))))))
% 0.51/0.83 (assert (forall ((C_19 tptp.com) (N_1 tptp.nat) (B (-> tptp.state Bool)) (S tptp.state)) (=> (not (@ B S)) (@ (@ (@ (@ tptp.evaln (@ (@ tptp.while B) C_19)) S) N_1) S))))
% 0.51/0.83 (assert (forall ((S2 tptp.state) (C_19 tptp.com) (N_1 tptp.nat) (S1 tptp.state) (B (-> tptp.state Bool)) (S0 tptp.state)) (let ((_let_1 (@ tptp.evaln (@ (@ tptp.while B) C_19)))) (=> (@ B S0) (=> (@ (@ (@ (@ tptp.evaln C_19) S0) N_1) S1) (=> (@ (@ (@ _let_1 S1) N_1) S2) (@ (@ (@ _let_1 S0) N_1) S2)))))))
% 0.51/0.83 (assert (forall ((S2 tptp.state) (C_19 tptp.com) (S1 tptp.state) (B (-> tptp.state Bool)) (S0 tptp.state)) (let ((_let_1 (@ tptp.evalc (@ (@ tptp.while B) C_19)))) (=> (@ B S0) (=> (@ (@ (@ tptp.evalc C_19) S0) S1) (=> (@ (@ _let_1 S1) S2) (@ (@ _let_1 S0) S2)))))))
% 0.51/0.83 (assert (forall ((C_19 tptp.com) (B (-> tptp.state Bool)) (S tptp.state)) (=> (not (@ B S)) (@ (@ (@ tptp.evalc (@ (@ tptp.while B) C_19)) S) S))))
% 0.51/0.83 (assert (forall ((C1 tptp.com) (S2 tptp.state) (C0 tptp.com) (S0 tptp.state) (N_1 tptp.nat) (S1 tptp.state)) (=> (@ (@ (@ (@ tptp.evaln C0) S0) N_1) S1) (=> (@ (@ (@ (@ tptp.evaln C1) S1) N_1) S2) (@ (@ (@ (@ tptp.evaln (@ (@ tptp.semi C0) C1)) S0) N_1) S2)))))
% 0.51/0.83 (assert (forall ((C1 tptp.com) (S2 tptp.state) (C0 tptp.com) (S0 tptp.state) (S1 tptp.state)) (=> (@ (@ (@ tptp.evalc C0) S0) S1) (=> (@ (@ (@ tptp.evalc C1) S1) S2) (@ (@ (@ tptp.evalc (@ (@ tptp.semi C0) C1)) S0) S2)))))
% 0.51/0.83 (assert (forall ((Com1 tptp.com) (Com2 tptp.com) (Fun_1 (-> tptp.state Bool)) (Com_1 tptp.com)) (not (= (@ (@ tptp.semi Com1) Com2) (@ (@ tptp.while Fun_1) Com_1)))))
% 0.51/0.83 (assert (forall ((Fun_1 (-> tptp.state Bool)) (Com_1 tptp.com) (Com1 tptp.com) (Com2 tptp.com)) (not (= (@ (@ tptp.while Fun_1) Com_1) (@ (@ tptp.semi Com1) Com2)))))
% 0.51/0.83 (assert (forall ((Com1 tptp.com) (Com2 tptp.com) (Com1_1 tptp.com) (Com2_1 tptp.com)) (= (= (@ (@ tptp.semi Com1) Com2) (@ (@ tptp.semi Com1_1) Com2_1)) (and (= Com1 Com1_1) (= Com2 Com2_1)))))
% 0.51/0.83 (assert (forall ((Fun (-> tptp.state Bool)) (Com tptp.com) (Fun_1 (-> tptp.state Bool)) (Com_1 tptp.com)) (= (= (@ (@ tptp.while Fun) Com) (@ (@ tptp.while Fun_1) Com_1)) (and (= Fun Fun_1) (= Com Com_1)))))
% 0.51/0.83 (assert (forall ((Pname_1 tptp.pname) (Fun (-> tptp.state Bool)) (Com tptp.com)) (not (= (@ tptp.body Pname_1) (@ (@ tptp.while Fun) Com)))))
% 0.51/0.83 (assert (forall ((Fun (-> tptp.state Bool)) (Com tptp.com) (Pname_1 tptp.pname)) (not (= (@ (@ tptp.while Fun) Com) (@ tptp.body Pname_1)))))
% 0.51/0.83 (assert (forall ((Fun_1 (-> tptp.state Bool)) (Com_1 tptp.com)) (not (= tptp.skip (@ (@ tptp.while Fun_1) Com_1)))))
% 0.51/0.83 (assert (forall ((Fun_1 (-> tptp.state Bool)) (Com_1 tptp.com)) (not (= (@ (@ tptp.while Fun_1) Com_1) tptp.skip))))
% 0.51/0.83 (assert (forall ((Pname_1 tptp.pname) (Com1 tptp.com) (Com2 tptp.com)) (not (= (@ tptp.body Pname_1) (@ (@ tptp.semi Com1) Com2)))))
% 0.51/0.83 (assert (forall ((Com1 tptp.com) (Com2 tptp.com) (Pname_1 tptp.pname)) (not (= (@ (@ tptp.semi Com1) Com2) (@ tptp.body Pname_1)))))
% 0.51/0.83 (assert (forall ((Com1_1 tptp.com) (Com2_1 tptp.com)) (not (= tptp.skip (@ (@ tptp.semi Com1_1) Com2_1)))))
% 0.51/0.83 (assert (forall ((Com1_1 tptp.com) (Com2_1 tptp.com)) (not (= (@ (@ tptp.semi Com1_1) Com2_1) tptp.skip))))
% 0.51/0.83 (assert (forall ((C1 tptp.com) (C2 tptp.com) (S tptp.state) (T tptp.state)) (=> (@ (@ (@ tptp.evalc (@ (@ tptp.semi C1) C2)) S) T) (not (forall ((S1_1 tptp.state)) (=> (@ (@ (@ tptp.evalc C1) S) S1_1) (not (@ (@ (@ tptp.evalc C2) S1_1) T))))))))
% 0.51/0.83 (assert (forall ((C1 tptp.com) (C2 tptp.com) (S tptp.state) (N_1 tptp.nat) (T tptp.state)) (=> (@ (@ (@ (@ tptp.evaln (@ (@ tptp.semi C1) C2)) S) N_1) T) (not (forall ((S1_1 tptp.state)) (=> (@ (@ (@ (@ tptp.evaln C1) S) N_1) S1_1) (not (@ (@ (@ (@ tptp.evaln C2) S1_1) N_1) T))))))))
% 0.51/0.83 (assert (forall ((H_2 (-> tptp.pname tptp.hoare_1167836817_state)) (F_26 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_26) (@ tptp.finite1084549118_state (@ (@ tptp.image_575578384_state H_2) F_26)))))
% 0.51/0.83 (assert (forall ((H_2 (-> tptp.pname tptp.hoare_1775062406iple_a)) (F_26 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_26) (@ tptp.finite2063573081iple_a (@ (@ tptp.image_2063119815iple_a H_2) F_26)))))
% 0.51/0.83 (assert (forall ((A_62 tptp.hoare_1167836817_state) (A_61 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state A_61) (@ tptp.finite1084549118_state (@ (@ tptp.insert2134838167_state A_62) A_61)))))
% 0.51/0.83 (assert (forall ((A_62 tptp.hoare_1775062406iple_a) (A_61 (-> tptp.hoare_1775062406iple_a Bool))) (=> (@ tptp.finite2063573081iple_a A_61) (@ tptp.finite2063573081iple_a (@ (@ tptp.insert1281456128iple_a A_62) A_61)))))
% 0.51/0.83 (assert (forall ((A_62 tptp.pname) (A_61 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_61) (@ tptp.finite_finite_pname (@ (@ tptp.insert_pname A_62) A_61)))))
% 0.51/0.83 (assert (@ tptp.finite_finite_pname tptp.bot_bot_pname_o))
% 0.51/0.83 (assert (@ tptp.finite2063573081iple_a tptp.bot_bo751897185le_a_o))
% 0.51/0.83 (assert (@ tptp.finite1084549118_state tptp.bot_bo70021908tate_o))
% 0.51/0.83 (assert (forall ((Q_2 (-> tptp.hoare_1775062406iple_a Bool)) (P_7 (-> tptp.hoare_1775062406iple_a Bool))) (=> (or (@ tptp.finite2063573081iple_a (@ tptp.collec676402587iple_a P_7)) (@ tptp.finite2063573081iple_a (@ tptp.collec676402587iple_a Q_2))) (@ tptp.finite2063573081iple_a (@ tptp.collec676402587iple_a (lambda ((X tptp.hoare_1775062406iple_a)) (and (@ P_7 X) (@ Q_2 X))))))))
% 0.51/0.83 (assert (forall ((Q_2 (-> tptp.pname Bool)) (P_7 (-> tptp.pname Bool))) (=> (or (@ tptp.finite_finite_pname (@ tptp.collect_pname P_7)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q_2))) (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X tptp.pname)) (and (@ P_7 X) (@ Q_2 X))))))))
% 0.51/0.83 (assert (forall ((P_6 (-> tptp.hoare_1775062406iple_a Bool)) (Q_1 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ tptp.finite2063573081iple_a (@ tptp.collec676402587iple_a (lambda ((X tptp.hoare_1775062406iple_a)) (or (@ P_6 X) (@ Q_1 X))))) (and (@ tptp.finite2063573081iple_a (@ tptp.collec676402587iple_a P_6)) (@ tptp.finite2063573081iple_a (@ tptp.collec676402587iple_a Q_1))))))
% 0.51/0.83 (assert (forall ((P_6 (-> tptp.pname Bool)) (Q_1 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X tptp.pname)) (or (@ P_6 X) (@ Q_1 X))))) (and (@ tptp.finite_finite_pname (@ tptp.collect_pname P_6)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q_1))))))
% 0.51/0.83 (assert (forall ((A_60 tptp.hoare_1167836817_state) (A_59 (-> tptp.hoare_1167836817_state Bool))) (= (@ tptp.finite1084549118_state (@ (@ tptp.insert2134838167_state A_60) A_59)) (@ tptp.finite1084549118_state A_59))))
% 0.51/0.83 (assert (forall ((A_60 tptp.hoare_1775062406iple_a) (A_59 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ tptp.finite2063573081iple_a (@ (@ tptp.insert1281456128iple_a A_60) A_59)) (@ tptp.finite2063573081iple_a A_59))))
% 0.51/0.83 (assert (forall ((A_60 tptp.pname) (A_59 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ (@ tptp.insert_pname A_60) A_59)) (@ tptp.finite_finite_pname A_59))))
% 0.51/0.83 (assert (forall ((F_25 (-> tptp.pname Bool)) (G_2 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ (@ tptp.semila1780557381name_o F_25) G_2)) (and (@ tptp.finite_finite_pname F_25) (@ tptp.finite_finite_pname G_2)))))
% 0.51/0.83 (assert (forall ((F_25 (-> tptp.hoare_1167836817_state Bool)) (G_2 (-> tptp.hoare_1167836817_state Bool))) (= (@ tptp.finite1084549118_state (@ (@ tptp.semila1172322802tate_o F_25) G_2)) (and (@ tptp.finite1084549118_state F_25) (@ tptp.finite1084549118_state G_2)))))
% 0.51/0.83 (assert (forall ((F_25 (-> tptp.hoare_1775062406iple_a Bool)) (G_2 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ tptp.finite2063573081iple_a (@ (@ tptp.semila13410563le_a_o F_25) G_2)) (and (@ tptp.finite2063573081iple_a F_25) (@ tptp.finite2063573081iple_a G_2)))))
% 0.51/0.83 (assert (forall ((G_1 (-> tptp.pname Bool)) (F_24 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_24) (=> (@ tptp.finite_finite_pname G_1) (@ tptp.finite_finite_pname (@ (@ tptp.semila1780557381name_o F_24) G_1))))))
% 0.51/0.83 (assert (forall ((G_1 (-> tptp.hoare_1167836817_state Bool)) (F_24 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state F_24) (=> (@ tptp.finite1084549118_state G_1) (@ tptp.finite1084549118_state (@ (@ tptp.semila1172322802tate_o F_24) G_1))))))
% 0.51/0.83 (assert (forall ((G_1 (-> tptp.hoare_1775062406iple_a Bool)) (F_24 (-> tptp.hoare_1775062406iple_a Bool))) (=> (@ tptp.finite2063573081iple_a F_24) (=> (@ tptp.finite2063573081iple_a G_1) (@ tptp.finite2063573081iple_a (@ (@ tptp.semila13410563le_a_o F_24) G_1))))))
% 0.51/0.83 (assert (forall ((A_57 (-> tptp.hoare_1167836817_state Bool))) (= (@ tptp.finite1084549118_state A_57) (or (= A_57 tptp.bot_bo70021908tate_o) (exists ((A_58 (-> tptp.hoare_1167836817_state Bool)) (A_56 tptp.hoare_1167836817_state)) (and (= A_57 (@ (@ tptp.insert2134838167_state A_56) A_58)) (@ tptp.finite1084549118_state A_58)))))))
% 0.51/0.83 (assert (forall ((A_57 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ tptp.finite2063573081iple_a A_57) (or (= A_57 tptp.bot_bo751897185le_a_o) (exists ((A_58 (-> tptp.hoare_1775062406iple_a Bool)) (A_56 tptp.hoare_1775062406iple_a)) (and (= A_57 (@ (@ tptp.insert1281456128iple_a A_56) A_58)) (@ tptp.finite2063573081iple_a A_58)))))))
% 0.51/0.83 (assert (forall ((A_57 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname A_57) (or (= A_57 tptp.bot_bot_pname_o) (exists ((A_58 (-> tptp.pname Bool)) (A_56 tptp.pname)) (and (= A_57 (@ (@ tptp.insert_pname A_56) A_58)) (@ tptp.finite_finite_pname A_58)))))))
% 0.51/0.83 (assert (forall ((P_5 (-> (-> tptp.hoare_1167836817_state Bool) Bool)) (F_23 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state F_23) (=> (@ P_5 tptp.bot_bo70021908tate_o) (=> (forall ((X tptp.hoare_1167836817_state) (F_16 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state F_16) (=> (not (@ (@ tptp.member2058392318_state X) F_16)) (=> (@ P_5 F_16) (@ P_5 (@ (@ tptp.insert2134838167_state X) F_16)))))) (@ P_5 F_23))))))
% 0.51/0.83 (assert (forall ((P_5 (-> (-> tptp.hoare_1775062406iple_a Bool) Bool)) (F_23 (-> tptp.hoare_1775062406iple_a Bool))) (=> (@ tptp.finite2063573081iple_a F_23) (=> (@ P_5 tptp.bot_bo751897185le_a_o) (=> (forall ((X tptp.hoare_1775062406iple_a) (F_16 (-> tptp.hoare_1775062406iple_a Bool))) (=> (@ tptp.finite2063573081iple_a F_16) (=> (not (@ (@ tptp.member2122167641iple_a X) F_16)) (=> (@ P_5 F_16) (@ P_5 (@ (@ tptp.insert1281456128iple_a X) F_16)))))) (@ P_5 F_23))))))
% 0.51/0.83 (assert (forall ((P_5 (-> (-> tptp.pname Bool) Bool)) (F_23 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_23) (=> (@ P_5 tptp.bot_bot_pname_o) (=> (forall ((X tptp.pname) (F_16 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_16) (=> (not (@ (@ tptp.member_pname X) F_16)) (=> (@ P_5 F_16) (@ P_5 (@ (@ tptp.insert_pname X) F_16)))))) (@ P_5 F_23))))))
% 0.51/0.83 (assert (forall ((F_22 (-> tptp.pname tptp.hoare_1167836817_state)) (A_55 (-> tptp.pname Bool))) (=> (not (@ tptp.finite_finite_pname A_55)) (=> (@ tptp.finite1084549118_state (@ (@ tptp.image_575578384_state F_22) A_55)) (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) A_55) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_56 tptp.pname)) (and (@ (@ tptp.member_pname A_56) A_55) (= (@ F_22 A_56) (@ F_22 X)))))))))))))
% 0.51/0.83 (assert (forall ((F_22 (-> tptp.pname tptp.hoare_1775062406iple_a)) (A_55 (-> tptp.pname Bool))) (=> (not (@ tptp.finite_finite_pname A_55)) (=> (@ tptp.finite2063573081iple_a (@ (@ tptp.image_2063119815iple_a F_22) A_55)) (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) A_55) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_56 tptp.pname)) (and (@ (@ tptp.member_pname A_56) A_55) (= (@ F_22 A_56) (@ F_22 X)))))))))))))
% 0.51/0.83 (assert (forall ((B (-> tptp.state Bool)) (C_19 tptp.com) (S tptp.state) (T tptp.state)) (let ((_let_1 (@ B S))) (=> (@ (@ (@ tptp.evalc (@ (@ tptp.while B) C_19)) S) T) (=> (=> (= T S) _let_1) (not (=> _let_1 (forall ((S1_1 tptp.state)) (=> (@ (@ (@ tptp.evalc C_19) S) S1_1) (not (@ (@ (@ tptp.evalc (@ (@ tptp.while B) C_19)) S1_1) T)))))))))))
% 0.51/0.83 (assert (forall ((B (-> tptp.state Bool)) (C_19 tptp.com) (S tptp.state) (N_1 tptp.nat) (T tptp.state)) (let ((_let_1 (@ B S))) (=> (@ (@ (@ (@ tptp.evaln (@ (@ tptp.while B) C_19)) S) N_1) T) (=> (=> (= T S) _let_1) (not (=> _let_1 (forall ((S1_1 tptp.state)) (=> (@ (@ (@ (@ tptp.evaln C_19) S) N_1) S1_1) (not (@ (@ (@ (@ tptp.evaln (@ (@ tptp.while B) C_19)) S1_1) N_1) T)))))))))))
% 0.51/0.83 (assert (forall ((A_54 (-> tptp.hoare_1167836817_state Bool))) (= (not (= A_54 tptp.bot_bo70021908tate_o)) (exists ((X tptp.hoare_1167836817_state) (B_34 (-> tptp.hoare_1167836817_state Bool))) (and (= A_54 (@ (@ tptp.insert2134838167_state X) B_34)) (not (@ (@ tptp.member2058392318_state X) B_34)))))))
% 0.51/0.83 (assert (forall ((A_54 (-> tptp.hoare_1775062406iple_a Bool))) (= (not (= A_54 tptp.bot_bo751897185le_a_o)) (exists ((X tptp.hoare_1775062406iple_a) (B_34 (-> tptp.hoare_1775062406iple_a Bool))) (and (= A_54 (@ (@ tptp.insert1281456128iple_a X) B_34)) (not (@ (@ tptp.member2122167641iple_a X) B_34)))))))
% 0.51/0.83 (assert (forall ((A_54 (-> tptp.pname Bool))) (= (not (= A_54 tptp.bot_bot_pname_o)) (exists ((X tptp.pname) (B_34 (-> tptp.pname Bool))) (and (= A_54 (@ (@ tptp.insert_pname X) B_34)) (not (@ (@ tptp.member_pname X) B_34)))))))
% 0.51/0.83 (assert (forall ((B_35 (-> tptp.pname Bool)) (A_53 (-> tptp.pname Bool)) (F_21 (-> tptp.pname tptp.pname tptp.pname)) (F_20 (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite89670078_pname F_21) F_20) (=> (@ tptp.finite_finite_pname A_53) (=> (not (= A_53 tptp.bot_bot_pname_o)) (=> (@ tptp.finite_finite_pname B_35) (=> (not (= B_35 tptp.bot_bot_pname_o)) (= (@ F_20 (@ (@ tptp.semila1780557381name_o A_53) B_35)) (@ (@ F_21 (@ F_20 A_53)) (@ F_20 B_35))))))))))
% 0.51/0.83 (assert (forall ((B_35 (-> tptp.hoare_1775062406iple_a Bool)) (A_53 (-> tptp.hoare_1775062406iple_a Bool)) (F_21 (-> tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a)) (F_20 (-> (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a))) (=> (@ (@ tptp.finite1358382848iple_a F_21) F_20) (=> (@ tptp.finite2063573081iple_a A_53) (=> (not (= A_53 tptp.bot_bo751897185le_a_o)) (=> (@ tptp.finite2063573081iple_a B_35) (=> (not (= B_35 tptp.bot_bo751897185le_a_o)) (= (@ F_20 (@ (@ tptp.semila13410563le_a_o A_53) B_35)) (@ (@ F_21 (@ F_20 A_53)) (@ F_20 B_35))))))))))
% 0.51/0.83 (assert (forall ((B_35 (-> tptp.hoare_1167836817_state Bool)) (A_53 (-> tptp.hoare_1167836817_state Bool)) (F_21 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_20 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (=> (@ (@ tptp.finite806517911_state F_21) F_20) (=> (@ tptp.finite1084549118_state A_53) (=> (not (= A_53 tptp.bot_bo70021908tate_o)) (=> (@ tptp.finite1084549118_state B_35) (=> (not (= B_35 tptp.bot_bo70021908tate_o)) (= (@ F_20 (@ (@ tptp.semila1172322802tate_o A_53) B_35)) (@ (@ F_21 (@ F_20 A_53)) (@ F_20 B_35))))))))))
% 0.51/0.83 (assert (forall ((X_20 tptp.hoare_1167836817_state) (A_52 (-> tptp.hoare_1167836817_state Bool)) (F_19 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_18 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (=> (@ (@ tptp.finite806517911_state F_19) F_18) (=> (@ tptp.finite1084549118_state A_52) (=> (not (= A_52 tptp.bot_bo70021908tate_o)) (= (@ F_18 (@ (@ tptp.insert2134838167_state X_20) A_52)) (@ (@ F_19 X_20) (@ F_18 A_52))))))))
% 0.51/0.83 (assert (forall ((X_20 tptp.hoare_1775062406iple_a) (A_52 (-> tptp.hoare_1775062406iple_a Bool)) (F_19 (-> tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a)) (F_18 (-> (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a))) (=> (@ (@ tptp.finite1358382848iple_a F_19) F_18) (=> (@ tptp.finite2063573081iple_a A_52) (=> (not (= A_52 tptp.bot_bo751897185le_a_o)) (= (@ F_18 (@ (@ tptp.insert1281456128iple_a X_20) A_52)) (@ (@ F_19 X_20) (@ F_18 A_52))))))))
% 0.51/0.83 (assert (forall ((X_20 tptp.pname) (A_52 (-> tptp.pname Bool)) (F_19 (-> tptp.pname tptp.pname tptp.pname)) (F_18 (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite89670078_pname F_19) F_18) (=> (@ tptp.finite_finite_pname A_52) (=> (not (= A_52 tptp.bot_bot_pname_o)) (= (@ F_18 (@ (@ tptp.insert_pname X_20) A_52)) (@ (@ F_19 X_20) (@ F_18 A_52))))))))
% 0.51/0.83 (assert (forall ((F_17 (-> tptp.pname tptp.hoare_1167836817_state)) (A_51 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_51) (= (@ (@ tptp.image_575578384_state F_17) A_51) (@ (@ (@ (@ tptp.finite1068437657_pname tptp.semila1172322802tate_o) (lambda ((X tptp.pname) (__flatten_var_0 tptp.hoare_1167836817_state)) (@ (@ (@ tptp.insert2134838167_state (@ F_17 X)) tptp.bot_bo70021908tate_o) __flatten_var_0))) tptp.bot_bo70021908tate_o) A_51)))))
% 0.51/0.83 (assert (forall ((F_17 (-> tptp.pname tptp.hoare_1775062406iple_a)) (A_51 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_51) (= (@ (@ tptp.image_2063119815iple_a F_17) A_51) (@ (@ (@ (@ tptp.finite1805141964_pname tptp.semila13410563le_a_o) (lambda ((X tptp.pname) (__flatten_var_0 tptp.hoare_1775062406iple_a)) (@ (@ (@ tptp.insert1281456128iple_a (@ F_17 X)) tptp.bot_bo751897185le_a_o) __flatten_var_0))) tptp.bot_bo751897185le_a_o) A_51)))))
% 0.51/0.83 (assert (forall ((P_4 (-> (-> tptp.hoare_1167836817_state Bool) Bool)) (F_15 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state F_15) (=> (not (= F_15 tptp.bot_bo70021908tate_o)) (=> (forall ((X tptp.hoare_1167836817_state)) (@ P_4 (@ (@ tptp.insert2134838167_state X) tptp.bot_bo70021908tate_o))) (=> (forall ((X tptp.hoare_1167836817_state) (F_16 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state F_16) (=> (not (= F_16 tptp.bot_bo70021908tate_o)) (=> (not (@ (@ tptp.member2058392318_state X) F_16)) (=> (@ P_4 F_16) (@ P_4 (@ (@ tptp.insert2134838167_state X) F_16))))))) (@ P_4 F_15)))))))
% 0.51/0.83 (assert (forall ((P_4 (-> (-> tptp.hoare_1775062406iple_a Bool) Bool)) (F_15 (-> tptp.hoare_1775062406iple_a Bool))) (=> (@ tptp.finite2063573081iple_a F_15) (=> (not (= F_15 tptp.bot_bo751897185le_a_o)) (=> (forall ((X tptp.hoare_1775062406iple_a)) (@ P_4 (@ (@ tptp.insert1281456128iple_a X) tptp.bot_bo751897185le_a_o))) (=> (forall ((X tptp.hoare_1775062406iple_a) (F_16 (-> tptp.hoare_1775062406iple_a Bool))) (=> (@ tptp.finite2063573081iple_a F_16) (=> (not (= F_16 tptp.bot_bo751897185le_a_o)) (=> (not (@ (@ tptp.member2122167641iple_a X) F_16)) (=> (@ P_4 F_16) (@ P_4 (@ (@ tptp.insert1281456128iple_a X) F_16))))))) (@ P_4 F_15)))))))
% 0.51/0.83 (assert (forall ((P_4 (-> (-> tptp.pname Bool) Bool)) (F_15 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_15) (=> (not (= F_15 tptp.bot_bot_pname_o)) (=> (forall ((X tptp.pname)) (@ P_4 (@ (@ tptp.insert_pname X) tptp.bot_bot_pname_o))) (=> (forall ((X tptp.pname) (F_16 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_16) (=> (not (= F_16 tptp.bot_bot_pname_o)) (=> (not (@ (@ tptp.member_pname X) F_16)) (=> (@ P_4 F_16) (@ P_4 (@ (@ tptp.insert_pname X) F_16))))))) (@ P_4 F_15)))))))
% 0.51/0.83 (assert (forall ((X_19 tptp.hoare_1775062406iple_a) (A_50 (-> tptp.hoare_1775062406iple_a Bool)) (F_14 (-> tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a)) (F_13 (-> (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a))) (let ((_let_1 (@ F_13 A_50))) (=> (@ (@ tptp.finite1358382848iple_a F_14) F_13) (=> (@ tptp.finite2063573081iple_a A_50) (=> (@ (@ tptp.member2122167641iple_a X_19) A_50) (= (@ (@ F_14 X_19) _let_1) _let_1)))))))
% 0.51/0.83 (assert (forall ((X_19 tptp.pname) (A_50 (-> tptp.pname Bool)) (F_14 (-> tptp.pname tptp.pname tptp.pname)) (F_13 (-> (-> tptp.pname Bool) tptp.pname))) (let ((_let_1 (@ F_13 A_50))) (=> (@ (@ tptp.finite89670078_pname F_14) F_13) (=> (@ tptp.finite_finite_pname A_50) (=> (@ (@ tptp.member_pname X_19) A_50) (= (@ (@ F_14 X_19) _let_1) _let_1)))))))
% 0.51/0.83 (assert (forall ((N_3 (-> tptp.pname Bool)) (H_1 (-> tptp.pname tptp.pname)) (F_12 (-> tptp.pname tptp.pname tptp.pname)) (F_11 (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite89670078_pname F_12) F_11) (=> (forall ((X tptp.pname) (Y_2 tptp.pname)) (= (@ H_1 (@ (@ F_12 X) Y_2)) (@ (@ F_12 (@ H_1 X)) (@ H_1 Y_2)))) (=> (@ tptp.finite_finite_pname N_3) (=> (not (= N_3 tptp.bot_bot_pname_o)) (= (@ H_1 (@ F_11 N_3)) (@ F_11 (@ (@ tptp.image_pname_pname H_1) N_3)))))))))
% 0.51/0.83 (assert (forall ((N_3 (-> tptp.hoare_1775062406iple_a Bool)) (H_1 (-> tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a)) (F_12 (-> tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a)) (F_11 (-> (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a))) (=> (@ (@ tptp.finite1358382848iple_a F_12) F_11) (=> (forall ((X tptp.hoare_1775062406iple_a) (Y_2 tptp.hoare_1775062406iple_a)) (= (@ H_1 (@ (@ F_12 X) Y_2)) (@ (@ F_12 (@ H_1 X)) (@ H_1 Y_2)))) (=> (@ tptp.finite2063573081iple_a N_3) (=> (not (= N_3 tptp.bot_bo751897185le_a_o)) (= (@ H_1 (@ F_11 N_3)) (@ F_11 (@ (@ tptp.image_1170193413iple_a H_1) N_3)))))))))
% 0.51/0.83 (assert (forall ((N_3 (-> tptp.hoare_1167836817_state Bool)) (H_1 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_12 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_11 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (=> (@ (@ tptp.finite806517911_state F_12) F_11) (=> (forall ((X tptp.hoare_1167836817_state) (Y_2 tptp.hoare_1167836817_state)) (= (@ H_1 (@ (@ F_12 X) Y_2)) (@ (@ F_12 (@ H_1 X)) (@ H_1 Y_2)))) (=> (@ tptp.finite1084549118_state N_3) (=> (not (= N_3 tptp.bot_bo70021908tate_o)) (= (@ H_1 (@ F_11 N_3)) (@ F_11 (@ (@ tptp.image_31595733_state H_1) N_3)))))))))
% 0.51/0.83 (assert (forall ((X_18 tptp.hoare_1167836817_state) (A_49 (-> tptp.hoare_1167836817_state Bool)) (F_10 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_9 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (=> (@ (@ tptp.finite1074406356_state F_10) F_9) (=> (@ tptp.finite1084549118_state A_49) (=> (not (@ (@ tptp.member2058392318_state X_18) A_49)) (=> (not (= A_49 tptp.bot_bo70021908tate_o)) (= (@ F_9 (@ (@ tptp.insert2134838167_state X_18) A_49)) (@ (@ F_10 X_18) (@ F_9 A_49)))))))))
% 0.51/0.83 (assert (forall ((X_18 tptp.hoare_1775062406iple_a) (A_49 (-> tptp.hoare_1775062406iple_a Bool)) (F_10 (-> tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a)) (F_9 (-> (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a))) (=> (@ (@ tptp.finite2078349315iple_a F_10) F_9) (=> (@ tptp.finite2063573081iple_a A_49) (=> (not (@ (@ tptp.member2122167641iple_a X_18) A_49)) (=> (not (= A_49 tptp.bot_bo751897185le_a_o)) (= (@ F_9 (@ (@ tptp.insert1281456128iple_a X_18) A_49)) (@ (@ F_10 X_18) (@ F_9 A_49)))))))))
% 0.51/0.83 (assert (forall ((X_18 tptp.pname) (A_49 (-> tptp.pname Bool)) (F_10 (-> tptp.pname tptp.pname tptp.pname)) (F_9 (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite1282449217_pname F_10) F_9) (=> (@ tptp.finite_finite_pname A_49) (=> (not (@ (@ tptp.member_pname X_18) A_49)) (=> (not (= A_49 tptp.bot_bot_pname_o)) (= (@ F_9 (@ (@ tptp.insert_pname X_18) A_49)) (@ (@ F_10 X_18) (@ F_9 A_49)))))))))
% 0.51/0.83 (assert (forall ((X_17 tptp.hoare_1167836817_state) (F_8 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_7 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (=> (@ (@ tptp.finite1074406356_state F_8) F_7) (= (@ F_7 (@ (@ tptp.insert2134838167_state X_17) tptp.bot_bo70021908tate_o)) X_17))))
% 0.51/0.83 (assert (forall ((X_17 tptp.hoare_1775062406iple_a) (F_8 (-> tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a)) (F_7 (-> (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a))) (=> (@ (@ tptp.finite2078349315iple_a F_8) F_7) (= (@ F_7 (@ (@ tptp.insert1281456128iple_a X_17) tptp.bot_bo751897185le_a_o)) X_17))))
% 0.51/0.83 (assert (forall ((X_17 tptp.pname) (F_8 (-> tptp.pname tptp.pname tptp.pname)) (F_7 (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite1282449217_pname F_8) F_7) (= (@ F_7 (@ (@ tptp.insert_pname X_17) tptp.bot_bot_pname_o)) X_17))))
% 0.51/0.83 (assert (forall ((A_48 (-> tptp.hoare_1167836817_state Bool)) (F_6 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_5 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (=> (@ (@ tptp.finite1074406356_state F_6) F_5) (=> (@ tptp.finite1084549118_state A_48) (=> (not (= A_48 tptp.bot_bo70021908tate_o)) (=> (forall ((X tptp.hoare_1167836817_state) (Y_2 tptp.hoare_1167836817_state)) (@ (@ tptp.member2058392318_state (@ (@ F_6 X) Y_2)) (@ (@ tptp.insert2134838167_state X) (@ (@ tptp.insert2134838167_state Y_2) tptp.bot_bo70021908tate_o)))) (@ (@ tptp.member2058392318_state (@ F_5 A_48)) A_48)))))))
% 0.51/0.83 (assert (forall ((A_48 (-> tptp.hoare_1775062406iple_a Bool)) (F_6 (-> tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a)) (F_5 (-> (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a))) (=> (@ (@ tptp.finite2078349315iple_a F_6) F_5) (=> (@ tptp.finite2063573081iple_a A_48) (=> (not (= A_48 tptp.bot_bo751897185le_a_o)) (=> (forall ((X tptp.hoare_1775062406iple_a) (Y_2 tptp.hoare_1775062406iple_a)) (@ (@ tptp.member2122167641iple_a (@ (@ F_6 X) Y_2)) (@ (@ tptp.insert1281456128iple_a X) (@ (@ tptp.insert1281456128iple_a Y_2) tptp.bot_bo751897185le_a_o)))) (@ (@ tptp.member2122167641iple_a (@ F_5 A_48)) A_48)))))))
% 0.51/0.83 (assert (forall ((A_48 (-> tptp.pname Bool)) (F_6 (-> tptp.pname tptp.pname tptp.pname)) (F_5 (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite1282449217_pname F_6) F_5) (=> (@ tptp.finite_finite_pname A_48) (=> (not (= A_48 tptp.bot_bot_pname_o)) (=> (forall ((X tptp.pname) (Y_2 tptp.pname)) (@ (@ tptp.member_pname (@ (@ F_6 X) Y_2)) (@ (@ tptp.insert_pname X) (@ (@ tptp.insert_pname Y_2) tptp.bot_bot_pname_o)))) (@ (@ tptp.member_pname (@ F_5 A_48)) A_48)))))))
% 0.51/0.83 (assert (forall ((C2 tptp.com) (S2 tptp.state) (N2 tptp.nat) (T2 tptp.state) (C1 tptp.com) (S1 tptp.state) (N1 tptp.nat) (T1 tptp.state)) (=> (@ (@ (@ (@ tptp.evaln C1) S1) N1) T1) (=> (@ (@ (@ (@ tptp.evaln C2) S2) N2) T2) (exists ((N tptp.nat)) (and (@ (@ (@ (@ tptp.evaln C1) S1) N) T1) (@ (@ (@ (@ tptp.evaln C2) S2) N) T2)))))))
% 0.51/0.83 (assert (forall ((A_47 tptp.hoare_1167836817_state) (A_46 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.member2058392318_state A_47) A_46) (exists ((B_34 (-> tptp.hoare_1167836817_state Bool))) (and (= A_46 (@ (@ tptp.insert2134838167_state A_47) B_34)) (not (@ (@ tptp.member2058392318_state A_47) B_34)))))))
% 0.51/0.83 (assert (forall ((A_47 tptp.hoare_1775062406iple_a) (A_46 (-> tptp.hoare_1775062406iple_a Bool))) (=> (@ (@ tptp.member2122167641iple_a A_47) A_46) (exists ((B_34 (-> tptp.hoare_1775062406iple_a Bool))) (and (= A_46 (@ (@ tptp.insert1281456128iple_a A_47) B_34)) (not (@ (@ tptp.member2122167641iple_a A_47) B_34)))))))
% 0.51/0.83 (assert (forall ((A_47 tptp.pname) (A_46 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname A_47) A_46) (exists ((B_34 (-> tptp.pname Bool))) (and (= A_46 (@ (@ tptp.insert_pname A_47) B_34)) (not (@ (@ tptp.member_pname A_47) B_34)))))))
% 0.51/0.83 (assert (forall ((X_16 tptp.hoare_1167836817_state) (A_45 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.member2058392318_state X_16) A_45) (not (forall ((B_34 (-> tptp.hoare_1167836817_state Bool))) (=> (= A_45 (@ (@ tptp.insert2134838167_state X_16) B_34)) (@ (@ tptp.member2058392318_state X_16) B_34)))))))
% 0.51/0.83 (assert (forall ((X_16 tptp.hoare_1775062406iple_a) (A_45 (-> tptp.hoare_1775062406iple_a Bool))) (=> (@ (@ tptp.member2122167641iple_a X_16) A_45) (not (forall ((B_34 (-> tptp.hoare_1775062406iple_a Bool))) (=> (= A_45 (@ (@ tptp.insert1281456128iple_a X_16) B_34)) (@ (@ tptp.member2122167641iple_a X_16) B_34)))))))
% 0.51/0.83 (assert (forall ((X_16 tptp.pname) (A_45 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_16) A_45) (not (forall ((B_34 (-> tptp.pname Bool))) (=> (= A_45 (@ (@ tptp.insert_pname X_16) B_34)) (@ (@ tptp.member_pname X_16) B_34)))))))
% 0.51/0.83 (assert (forall ((A_44 (-> tptp.hoare_1775062406iple_a Bool))) (=> (forall ((Y_2 tptp.hoare_1775062406iple_a)) (not (@ (@ tptp.member2122167641iple_a Y_2) A_44))) (= A_44 tptp.bot_bo751897185le_a_o))))
% 0.51/0.83 (assert (forall ((A_44 (-> tptp.pname Bool))) (=> (forall ((Y_2 tptp.pname)) (not (@ (@ tptp.member_pname Y_2) A_44))) (= A_44 tptp.bot_bot_pname_o))))
% 0.51/0.83 (assert (forall ((A_44 (-> tptp.hoare_1167836817_state Bool))) (=> (forall ((Y_2 tptp.hoare_1167836817_state)) (not (@ (@ tptp.member2058392318_state Y_2) A_44))) (= A_44 tptp.bot_bo70021908tate_o))))
% 0.51/0.83 (assert (forall ((B_33 (-> Bool Bool)) (A_43 (-> Bool Bool))) (=> (@ tptp.finite_finite_o A_43) (=> (not (= A_43 tptp.bot_bot_o_o)) (=> (@ tptp.finite_finite_o B_33) (=> (not (= B_33 tptp.bot_bot_o_o)) (= (@ tptp.big_la727467310_fin_o (@ (@ tptp.semila2062604954up_o_o A_43) B_33)) (@ (@ tptp.semila10642723_sup_o (@ tptp.big_la727467310_fin_o A_43)) (@ tptp.big_la727467310_fin_o B_33)))))))))
% 0.51/0.83 (assert (forall ((B_33 (-> (-> tptp.pname Bool) Bool)) (A_43 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_43) (=> (not (= A_43 tptp.bot_bot_pname_o_o)) (=> (@ tptp.finite297249702name_o B_33) (=> (not (= B_33 tptp.bot_bot_pname_o_o)) (= (@ tptp.big_la1286884090name_o (@ (@ tptp.semila181081674me_o_o A_43) B_33)) (@ (@ tptp.semila1780557381name_o (@ tptp.big_la1286884090name_o A_43)) (@ tptp.big_la1286884090name_o B_33)))))))))
% 0.51/0.83 (assert (forall ((B_33 (-> (-> tptp.hoare_1167836817_state Bool) Bool)) (A_43 (-> (-> tptp.hoare_1167836817_state Bool) Bool))) (=> (@ tptp.finite1380128977tate_o A_43) (=> (not (= A_43 tptp.bot_bo691907561te_o_o)) (=> (@ tptp.finite1380128977tate_o B_33) (=> (not (= B_33 tptp.bot_bo691907561te_o_o)) (= (@ tptp.big_la1138507389tate_o (@ (@ tptp.semila866907787te_o_o A_43) B_33)) (@ (@ tptp.semila1172322802tate_o (@ tptp.big_la1138507389tate_o A_43)) (@ tptp.big_la1138507389tate_o B_33)))))))))
% 0.51/0.83 (assert (forall ((B_33 (-> (-> tptp.hoare_1775062406iple_a Bool) Bool)) (A_43 (-> (-> tptp.hoare_1775062406iple_a Bool) Bool))) (=> (@ tptp.finite789576932le_a_o A_43) (=> (not (= A_43 tptp.bot_bo1976773294_a_o_o)) (=> (@ tptp.finite789576932le_a_o B_33) (=> (not (= B_33 tptp.bot_bo1976773294_a_o_o)) (= (@ tptp.big_la1843772984le_a_o (@ (@ tptp.semila2069193356_a_o_o A_43) B_33)) (@ (@ tptp.semila13410563le_a_o (@ tptp.big_la1843772984le_a_o A_43)) (@ tptp.big_la1843772984le_a_o B_33)))))))))
% 0.51/0.83 (assert (forall ((X_15 Bool) (A_42 (-> Bool Bool))) (let ((_let_1 (@ tptp.big_la727467310_fin_o A_42))) (=> (@ tptp.finite_finite_o A_42) (=> (@ (@ tptp.member_o X_15) A_42) (= (@ (@ tptp.semila10642723_sup_o X_15) _let_1) _let_1))))))
% 0.51/0.83 (assert (forall ((X_15 (-> tptp.pname Bool)) (A_42 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (@ tptp.big_la1286884090name_o A_42))) (=> (@ tptp.finite297249702name_o A_42) (=> (@ (@ tptp.member_pname_o X_15) A_42) (= (@ (@ tptp.semila1780557381name_o X_15) _let_1) _let_1))))))
% 0.51/0.83 (assert (forall ((X_15 (-> tptp.hoare_1167836817_state Bool)) (A_42 (-> (-> tptp.hoare_1167836817_state Bool) Bool))) (let ((_let_1 (@ tptp.big_la1138507389tate_o A_42))) (=> (@ tptp.finite1380128977tate_o A_42) (=> (@ (@ tptp.member864234961tate_o X_15) A_42) (= (@ (@ tptp.semila1172322802tate_o X_15) _let_1) _let_1))))))
% 0.51/0.83 (assert (forall ((X_15 (-> tptp.hoare_1775062406iple_a Bool)) (A_42 (-> (-> tptp.hoare_1775062406iple_a Bool) Bool))) (let ((_let_1 (@ tptp.big_la1843772984le_a_o A_42))) (=> (@ tptp.finite789576932le_a_o A_42) (=> (@ (@ tptp.member1207314404le_a_o X_15) A_42) (= (@ (@ tptp.semila13410563le_a_o X_15) _let_1) _let_1))))))
% 0.51/0.83 (assert (forall ((X_14 Bool) (A_41 (-> Bool Bool))) (=> (@ tptp.finite_finite_o A_41) (=> (not (@ (@ tptp.member_o X_14) A_41)) (=> (not (= A_41 tptp.bot_bot_o_o)) (= (@ tptp.big_la727467310_fin_o (@ (@ tptp.insert_o X_14) A_41)) (@ (@ tptp.semila10642723_sup_o X_14) (@ tptp.big_la727467310_fin_o A_41))))))))
% 0.51/0.83 (assert (forall ((X_14 (-> tptp.pname Bool)) (A_41 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_41) (=> (not (@ (@ tptp.member_pname_o X_14) A_41)) (=> (not (= A_41 tptp.bot_bot_pname_o_o)) (= (@ tptp.big_la1286884090name_o (@ (@ tptp.insert_pname_o X_14) A_41)) (@ (@ tptp.semila1780557381name_o X_14) (@ tptp.big_la1286884090name_o A_41))))))))
% 0.51/0.83 (assert (forall ((X_14 (-> tptp.hoare_1167836817_state Bool)) (A_41 (-> (-> tptp.hoare_1167836817_state Bool) Bool))) (=> (@ tptp.finite1380128977tate_o A_41) (=> (not (@ (@ tptp.member864234961tate_o X_14) A_41)) (=> (not (= A_41 tptp.bot_bo691907561te_o_o)) (= (@ tptp.big_la1138507389tate_o (@ (@ tptp.insert999278200tate_o X_14) A_41)) (@ (@ tptp.semila1172322802tate_o X_14) (@ tptp.big_la1138507389tate_o A_41))))))))
% 0.51/0.83 (assert (forall ((X_14 (-> tptp.hoare_1775062406iple_a Bool)) (A_41 (-> (-> tptp.hoare_1775062406iple_a Bool) Bool))) (=> (@ tptp.finite789576932le_a_o A_41) (=> (not (@ (@ tptp.member1207314404le_a_o X_14) A_41)) (=> (not (= A_41 tptp.bot_bo1976773294_a_o_o)) (= (@ tptp.big_la1843772984le_a_o (@ (@ tptp.insert1210049533le_a_o X_14) A_41)) (@ (@ tptp.semila13410563le_a_o X_14) (@ tptp.big_la1843772984le_a_o A_41))))))))
% 0.51/0.83 (assert (forall ((X_13 Bool) (A_40 (-> Bool Bool))) (=> (@ tptp.finite_finite_o A_40) (=> (not (= A_40 tptp.bot_bot_o_o)) (= (@ tptp.big_la727467310_fin_o (@ (@ tptp.insert_o X_13) A_40)) (@ (@ tptp.semila10642723_sup_o X_13) (@ tptp.big_la727467310_fin_o A_40)))))))
% 0.51/0.83 (assert (forall ((X_13 (-> tptp.pname Bool)) (A_40 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_40) (=> (not (= A_40 tptp.bot_bot_pname_o_o)) (= (@ tptp.big_la1286884090name_o (@ (@ tptp.insert_pname_o X_13) A_40)) (@ (@ tptp.semila1780557381name_o X_13) (@ tptp.big_la1286884090name_o A_40)))))))
% 0.51/0.83 (assert (forall ((X_13 (-> tptp.hoare_1167836817_state Bool)) (A_40 (-> (-> tptp.hoare_1167836817_state Bool) Bool))) (=> (@ tptp.finite1380128977tate_o A_40) (=> (not (= A_40 tptp.bot_bo691907561te_o_o)) (= (@ tptp.big_la1138507389tate_o (@ (@ tptp.insert999278200tate_o X_13) A_40)) (@ (@ tptp.semila1172322802tate_o X_13) (@ tptp.big_la1138507389tate_o A_40)))))))
% 0.51/0.83 (assert (forall ((X_13 (-> tptp.hoare_1775062406iple_a Bool)) (A_40 (-> (-> tptp.hoare_1775062406iple_a Bool) Bool))) (=> (@ tptp.finite789576932le_a_o A_40) (=> (not (= A_40 tptp.bot_bo1976773294_a_o_o)) (= (@ tptp.big_la1843772984le_a_o (@ (@ tptp.insert1210049533le_a_o X_13) A_40)) (@ (@ tptp.semila13410563le_a_o X_13) (@ tptp.big_la1843772984le_a_o A_40)))))))
% 0.51/0.83 (assert (forall ((N_2 (-> Bool Bool)) (H (-> Bool Bool))) (=> (forall ((X Bool) (Y_2 Bool)) (= (@ H (@ (@ tptp.semila10642723_sup_o X) Y_2)) (@ (@ tptp.semila10642723_sup_o (@ H X)) (@ H Y_2)))) (=> (@ tptp.finite_finite_o N_2) (=> (not (= N_2 tptp.bot_bot_o_o)) (= (@ H (@ tptp.big_la727467310_fin_o N_2)) (@ tptp.big_la727467310_fin_o (@ (@ tptp.image_o_o H) N_2))))))))
% 0.51/0.83 (assert (forall ((N_2 (-> (-> tptp.pname Bool) Bool)) (H (-> (-> tptp.pname Bool) tptp.pname Bool))) (=> (forall ((X (-> tptp.pname Bool)) (Y_2 (-> tptp.pname Bool))) (= (@ H (@ (@ tptp.semila1780557381name_o X) Y_2)) (@ (@ tptp.semila1780557381name_o (@ H X)) (@ H Y_2)))) (=> (@ tptp.finite297249702name_o N_2) (=> (not (= N_2 tptp.bot_bot_pname_o_o)) (= (@ H (@ tptp.big_la1286884090name_o N_2)) (@ tptp.big_la1286884090name_o (@ (@ tptp.image_1085733413name_o H) N_2))))))))
% 0.51/0.83 (assert (forall ((N_2 (-> (-> tptp.hoare_1167836817_state Bool) Bool)) (H (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state Bool))) (=> (forall ((X (-> tptp.hoare_1167836817_state Bool)) (Y_2 (-> tptp.hoare_1167836817_state Bool))) (= (@ H (@ (@ tptp.semila1172322802tate_o X) Y_2)) (@ (@ tptp.semila1172322802tate_o (@ H X)) (@ H Y_2)))) (=> (@ tptp.finite1380128977tate_o N_2) (=> (not (= N_2 tptp.bot_bo691907561te_o_o)) (= (@ H (@ tptp.big_la1138507389tate_o N_2)) (@ tptp.big_la1138507389tate_o (@ (@ tptp.image_1488525317tate_o H) N_2))))))))
% 0.51/0.83 (assert (forall ((N_2 (-> (-> tptp.hoare_1775062406iple_a Bool) Bool)) (H (-> (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a Bool))) (=> (forall ((X (-> tptp.hoare_1775062406iple_a Bool)) (Y_2 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ H (@ (@ tptp.semila13410563le_a_o X) Y_2)) (@ (@ tptp.semila13410563le_a_o (@ H X)) (@ H Y_2)))) (=> (@ tptp.finite789576932le_a_o N_2) (=> (not (= N_2 tptp.bot_bo1976773294_a_o_o)) (= (@ H (@ tptp.big_la1843772984le_a_o N_2)) (@ tptp.big_la1843772984le_a_o (@ (@ tptp.image_2014247585le_a_o H) N_2))))))))
% 0.51/0.83 (assert (forall ((A_39 (-> Bool Bool))) (=> (@ tptp.finite_finite_o A_39) (=> (not (= A_39 tptp.bot_bot_o_o)) (=> (forall ((X Bool) (Y_2 Bool)) (@ (@ tptp.member_o (@ (@ tptp.semila10642723_sup_o X) Y_2)) (@ (@ tptp.insert_o X) (@ (@ tptp.insert_o Y_2) tptp.bot_bot_o_o)))) (@ (@ tptp.member_o (@ tptp.big_la727467310_fin_o A_39)) A_39))))))
% 0.51/0.83 (assert (forall ((A_39 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_39) (=> (not (= A_39 tptp.bot_bot_pname_o_o)) (=> (forall ((X (-> tptp.pname Bool)) (Y_2 (-> tptp.pname Bool))) (@ (@ tptp.member_pname_o (@ (@ tptp.semila1780557381name_o X) Y_2)) (@ (@ tptp.insert_pname_o X) (@ (@ tptp.insert_pname_o Y_2) tptp.bot_bot_pname_o_o)))) (@ (@ tptp.member_pname_o (@ tptp.big_la1286884090name_o A_39)) A_39))))))
% 0.51/0.83 (assert (forall ((A_39 (-> (-> tptp.hoare_1167836817_state Bool) Bool))) (=> (@ tptp.finite1380128977tate_o A_39) (=> (not (= A_39 tptp.bot_bo691907561te_o_o)) (=> (forall ((X (-> tptp.hoare_1167836817_state Bool)) (Y_2 (-> tptp.hoare_1167836817_state Bool))) (@ (@ tptp.member864234961tate_o (@ (@ tptp.semila1172322802tate_o X) Y_2)) (@ (@ tptp.insert999278200tate_o X) (@ (@ tptp.insert999278200tate_o Y_2) tptp.bot_bo691907561te_o_o)))) (@ (@ tptp.member864234961tate_o (@ tptp.big_la1138507389tate_o A_39)) A_39))))))
% 0.51/0.83 (assert (forall ((A_39 (-> (-> tptp.hoare_1775062406iple_a Bool) Bool))) (=> (@ tptp.finite789576932le_a_o A_39) (=> (not (= A_39 tptp.bot_bo1976773294_a_o_o)) (=> (forall ((X (-> tptp.hoare_1775062406iple_a Bool)) (Y_2 (-> tptp.hoare_1775062406iple_a Bool))) (@ (@ tptp.member1207314404le_a_o (@ (@ tptp.semila13410563le_a_o X) Y_2)) (@ (@ tptp.insert1210049533le_a_o X) (@ (@ tptp.insert1210049533le_a_o Y_2) tptp.bot_bo1976773294_a_o_o)))) (@ (@ tptp.member1207314404le_a_o (@ tptp.big_la1843772984le_a_o A_39)) A_39))))))
% 0.51/0.83 (assert (forall ((B_32 (-> Bool Bool)) (A_38 (-> Bool Bool))) (let ((_let_1 (@ (@ tptp.semila232696320nf_o_o A_38) B_32))) (=> (@ tptp.finite_finite_o A_38) (=> (@ tptp.finite_finite_o B_32) (=> (not (= _let_1 tptp.bot_bot_o_o)) (= (@ (@ tptp.semila10642723_sup_o (@ tptp.big_la727467310_fin_o (@ (@ tptp.semila2062604954up_o_o A_38) B_32))) (@ tptp.big_la727467310_fin_o _let_1)) (@ (@ tptp.semila10642723_sup_o (@ tptp.big_la727467310_fin_o A_38)) (@ tptp.big_la727467310_fin_o B_32)))))))))
% 0.51/0.83 (assert (forall ((B_32 (-> (-> tptp.pname Bool) Bool)) (A_38 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (@ (@ tptp.semila2013987940me_o_o A_38) B_32))) (=> (@ tptp.finite297249702name_o A_38) (=> (@ tptp.finite297249702name_o B_32) (=> (not (= _let_1 tptp.bot_bot_pname_o_o)) (= (@ (@ tptp.semila1780557381name_o (@ tptp.big_la1286884090name_o (@ (@ tptp.semila181081674me_o_o A_38) B_32))) (@ tptp.big_la1286884090name_o _let_1)) (@ (@ tptp.semila1780557381name_o (@ tptp.big_la1286884090name_o A_38)) (@ tptp.big_la1286884090name_o B_32)))))))))
% 0.51/0.83 (assert (forall ((B_32 (-> (-> tptp.hoare_1167836817_state Bool) Bool)) (A_38 (-> (-> tptp.hoare_1167836817_state Bool) Bool))) (let ((_let_1 (@ (@ tptp.semila1758709489te_o_o A_38) B_32))) (=> (@ tptp.finite1380128977tate_o A_38) (=> (@ tptp.finite1380128977tate_o B_32) (=> (not (= _let_1 tptp.bot_bo691907561te_o_o)) (= (@ (@ tptp.semila1172322802tate_o (@ tptp.big_la1138507389tate_o (@ (@ tptp.semila866907787te_o_o A_38) B_32))) (@ tptp.big_la1138507389tate_o _let_1)) (@ (@ tptp.semila1172322802tate_o (@ tptp.big_la1138507389tate_o A_38)) (@ tptp.big_la1138507389tate_o B_32)))))))))
% 0.51/0.83 (assert (forall ((B_32 (-> (-> tptp.hoare_1775062406iple_a Bool) Bool)) (A_38 (-> (-> tptp.hoare_1775062406iple_a Bool) Bool))) (let ((_let_1 (@ (@ tptp.semila1691990438_a_o_o A_38) B_32))) (=> (@ tptp.finite789576932le_a_o A_38) (=> (@ tptp.finite789576932le_a_o B_32) (=> (not (= _let_1 tptp.bot_bo1976773294_a_o_o)) (= (@ (@ tptp.semila13410563le_a_o (@ tptp.big_la1843772984le_a_o (@ (@ tptp.semila2069193356_a_o_o A_38) B_32))) (@ tptp.big_la1843772984le_a_o _let_1)) (@ (@ tptp.semila13410563le_a_o (@ tptp.big_la1843772984le_a_o A_38)) (@ tptp.big_la1843772984le_a_o B_32)))))))))
% 0.51/0.83 (assert (forall ((B_31 (-> Bool Bool)) (A_37 (-> Bool Bool))) (=> (@ tptp.finite_finite_o A_37) (=> (not (= A_37 tptp.bot_bot_o_o)) (=> (@ tptp.finite_finite_o B_31) (=> (not (= B_31 tptp.bot_bot_o_o)) (=> (= (@ (@ tptp.semila232696320nf_o_o A_37) B_31) tptp.bot_bot_o_o) (= (@ tptp.big_la727467310_fin_o (@ (@ tptp.semila2062604954up_o_o A_37) B_31)) (@ (@ tptp.semila10642723_sup_o (@ tptp.big_la727467310_fin_o A_37)) (@ tptp.big_la727467310_fin_o B_31))))))))))
% 0.51/0.83 (assert (forall ((B_31 (-> (-> tptp.pname Bool) Bool)) (A_37 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_37) (=> (not (= A_37 tptp.bot_bot_pname_o_o)) (=> (@ tptp.finite297249702name_o B_31) (=> (not (= B_31 tptp.bot_bot_pname_o_o)) (=> (= (@ (@ tptp.semila2013987940me_o_o A_37) B_31) tptp.bot_bot_pname_o_o) (= (@ tptp.big_la1286884090name_o (@ (@ tptp.semila181081674me_o_o A_37) B_31)) (@ (@ tptp.semila1780557381name_o (@ tptp.big_la1286884090name_o A_37)) (@ tptp.big_la1286884090name_o B_31))))))))))
% 0.51/0.83 (assert (forall ((B_31 (-> (-> tptp.hoare_1167836817_state Bool) Bool)) (A_37 (-> (-> tptp.hoare_1167836817_state Bool) Bool))) (=> (@ tptp.finite1380128977tate_o A_37) (=> (not (= A_37 tptp.bot_bo691907561te_o_o)) (=> (@ tptp.finite1380128977tate_o B_31) (=> (not (= B_31 tptp.bot_bo691907561te_o_o)) (=> (= (@ (@ tptp.semila1758709489te_o_o A_37) B_31) tptp.bot_bo691907561te_o_o) (= (@ tptp.big_la1138507389tate_o (@ (@ tptp.semila866907787te_o_o A_37) B_31)) (@ (@ tptp.semila1172322802tate_o (@ tptp.big_la1138507389tate_o A_37)) (@ tptp.big_la1138507389tate_o B_31))))))))))
% 0.51/0.83 (assert (forall ((B_31 (-> (-> tptp.hoare_1775062406iple_a Bool) Bool)) (A_37 (-> (-> tptp.hoare_1775062406iple_a Bool) Bool))) (=> (@ tptp.finite789576932le_a_o A_37) (=> (not (= A_37 tptp.bot_bo1976773294_a_o_o)) (=> (@ tptp.finite789576932le_a_o B_31) (=> (not (= B_31 tptp.bot_bo1976773294_a_o_o)) (=> (= (@ (@ tptp.semila1691990438_a_o_o A_37) B_31) tptp.bot_bo1976773294_a_o_o) (= (@ tptp.big_la1843772984le_a_o (@ (@ tptp.semila2069193356_a_o_o A_37) B_31)) (@ (@ tptp.semila13410563le_a_o (@ tptp.big_la1843772984le_a_o A_37)) (@ tptp.big_la1843772984le_a_o B_31))))))))))
% 0.51/0.83 (assert (forall ((B_30 (-> tptp.hoare_1775062406iple_a Bool)) (C_18 tptp.hoare_1775062406iple_a) (A_36 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.member2122167641iple_a C_18))) (=> (@ _let_1 A_36) (=> (@ _let_1 B_30) (@ _let_1 (@ (@ tptp.semila966743401le_a_o A_36) B_30)))))))
% 0.51/0.83 (assert (forall ((B_30 (-> tptp.pname Bool)) (C_18 tptp.pname) (A_36 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_18))) (=> (@ _let_1 A_36) (=> (@ _let_1 B_30) (@ _let_1 (@ (@ tptp.semila1673364395name_o A_36) B_30)))))))
% 0.51/0.83 (assert (forall ((C_17 tptp.hoare_1775062406iple_a) (A_35 (-> tptp.hoare_1775062406iple_a Bool)) (B_29 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.member2122167641iple_a C_17))) (=> (@ _let_1 (@ (@ tptp.semila966743401le_a_o A_35) B_29)) (not (=> (@ _let_1 A_35) (not (@ _let_1 B_29))))))))
% 0.51/0.83 (assert (forall ((C_17 tptp.pname) (A_35 (-> tptp.pname Bool)) (B_29 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_17))) (=> (@ _let_1 (@ (@ tptp.semila1673364395name_o A_35) B_29)) (not (=> (@ _let_1 A_35) (not (@ _let_1 B_29))))))))
% 0.51/0.83 (assert (forall ((X_12 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1673364395name_o X_12) tptp.bot_bot_pname_o) tptp.bot_bot_pname_o)))
% 0.51/0.83 (assert (forall ((X_12 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila966743401le_a_o X_12) tptp.bot_bo751897185le_a_o) tptp.bot_bo751897185le_a_o)))
% 0.51/0.83 (assert (forall ((X_12 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila179895820tate_o X_12) tptp.bot_bo70021908tate_o) tptp.bot_bo70021908tate_o)))
% 0.51/0.83 (assert (forall ((X_11 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1673364395name_o tptp.bot_bot_pname_o) X_11) tptp.bot_bot_pname_o)))
% 0.51/0.83 (assert (forall ((X_11 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila966743401le_a_o tptp.bot_bo751897185le_a_o) X_11) tptp.bot_bo751897185le_a_o)))
% 0.51/0.83 (assert (forall ((X_11 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila179895820tate_o tptp.bot_bo70021908tate_o) X_11) tptp.bot_bo70021908tate_o)))
% 0.51/0.83 (assert (forall ((Y_9 Bool) (Z_7 Bool) (X_10 Bool)) (= (@ (@ tptp.semila10642723_sup_o (@ (@ tptp.semila854092349_inf_o Y_9) Z_7)) X_10) (@ (@ tptp.semila854092349_inf_o (@ (@ tptp.semila10642723_sup_o Y_9) X_10)) (@ (@ tptp.semila10642723_sup_o Z_7) X_10)))))
% 0.51/0.83 (assert (forall ((Y_9 (-> tptp.pname Bool)) (Z_7 (-> tptp.pname Bool)) (X_10 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o (@ (@ tptp.semila1673364395name_o Y_9) Z_7)) X_10) (@ (@ tptp.semila1673364395name_o (@ (@ tptp.semila1780557381name_o Y_9) X_10)) (@ (@ tptp.semila1780557381name_o Z_7) X_10)))))
% 0.51/0.83 (assert (forall ((Y_9 (-> tptp.hoare_1167836817_state Bool)) (Z_7 (-> tptp.hoare_1167836817_state Bool)) (X_10 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila1172322802tate_o (@ (@ tptp.semila179895820tate_o Y_9) Z_7)) X_10) (@ (@ tptp.semila179895820tate_o (@ (@ tptp.semila1172322802tate_o Y_9) X_10)) (@ (@ tptp.semila1172322802tate_o Z_7) X_10)))))
% 0.51/0.83 (assert (forall ((Y_9 (-> tptp.hoare_1775062406iple_a Bool)) (Z_7 (-> tptp.hoare_1775062406iple_a Bool)) (X_10 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila13410563le_a_o (@ (@ tptp.semila966743401le_a_o Y_9) Z_7)) X_10) (@ (@ tptp.semila966743401le_a_o (@ (@ tptp.semila13410563le_a_o Y_9) X_10)) (@ (@ tptp.semila13410563le_a_o Z_7) X_10)))))
% 0.51/0.83 (assert (forall ((Y_8 Bool) (Z_6 Bool) (X_9 Bool)) (= (@ (@ tptp.semila854092349_inf_o (@ (@ tptp.semila10642723_sup_o Y_8) Z_6)) X_9) (@ (@ tptp.semila10642723_sup_o (@ (@ tptp.semila854092349_inf_o Y_8) X_9)) (@ (@ tptp.semila854092349_inf_o Z_6) X_9)))))
% 0.51/0.83 (assert (forall ((Y_8 (-> tptp.pname Bool)) (Z_6 (-> tptp.pname Bool)) (X_9 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1673364395name_o (@ (@ tptp.semila1780557381name_o Y_8) Z_6)) X_9) (@ (@ tptp.semila1780557381name_o (@ (@ tptp.semila1673364395name_o Y_8) X_9)) (@ (@ tptp.semila1673364395name_o Z_6) X_9)))))
% 0.51/0.83 (assert (forall ((Y_8 (-> tptp.hoare_1167836817_state Bool)) (Z_6 (-> tptp.hoare_1167836817_state Bool)) (X_9 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila179895820tate_o (@ (@ tptp.semila1172322802tate_o Y_8) Z_6)) X_9) (@ (@ tptp.semila1172322802tate_o (@ (@ tptp.semila179895820tate_o Y_8) X_9)) (@ (@ tptp.semila179895820tate_o Z_6) X_9)))))
% 0.51/0.83 (assert (forall ((Y_8 (-> tptp.hoare_1775062406iple_a Bool)) (Z_6 (-> tptp.hoare_1775062406iple_a Bool)) (X_9 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila966743401le_a_o (@ (@ tptp.semila13410563le_a_o Y_8) Z_6)) X_9) (@ (@ tptp.semila13410563le_a_o (@ (@ tptp.semila966743401le_a_o Y_8) X_9)) (@ (@ tptp.semila966743401le_a_o Z_6) X_9)))))
% 0.51/0.83 (assert (forall ((X_8 Bool) (Y_7 Bool) (Z_5 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o X_8))) (= (@ _let_1 (@ (@ tptp.semila854092349_inf_o Y_7) Z_5)) (@ (@ tptp.semila854092349_inf_o (@ _let_1 Y_7)) (@ _let_1 Z_5))))))
% 0.51/0.83 (assert (forall ((X_8 (-> tptp.pname Bool)) (Y_7 (-> tptp.pname Bool)) (Z_5 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o X_8))) (= (@ _let_1 (@ (@ tptp.semila1673364395name_o Y_7) Z_5)) (@ (@ tptp.semila1673364395name_o (@ _let_1 Y_7)) (@ _let_1 Z_5))))))
% 0.51/0.83 (assert (forall ((X_8 (-> tptp.hoare_1167836817_state Bool)) (Y_7 (-> tptp.hoare_1167836817_state Bool)) (Z_5 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila1172322802tate_o X_8))) (= (@ _let_1 (@ (@ tptp.semila179895820tate_o Y_7) Z_5)) (@ (@ tptp.semila179895820tate_o (@ _let_1 Y_7)) (@ _let_1 Z_5))))))
% 0.51/0.83 (assert (forall ((X_8 (-> tptp.hoare_1775062406iple_a Bool)) (Y_7 (-> tptp.hoare_1775062406iple_a Bool)) (Z_5 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila13410563le_a_o X_8))) (= (@ _let_1 (@ (@ tptp.semila966743401le_a_o Y_7) Z_5)) (@ (@ tptp.semila966743401le_a_o (@ _let_1 Y_7)) (@ _let_1 Z_5))))))
% 0.51/0.83 (assert (forall ((X_7 Bool) (Y_6 Bool) (Z_4 Bool)) (let ((_let_1 (@ tptp.semila854092349_inf_o X_7))) (= (@ _let_1 (@ (@ tptp.semila10642723_sup_o Y_6) Z_4)) (@ (@ tptp.semila10642723_sup_o (@ _let_1 Y_6)) (@ _let_1 Z_4))))))
% 0.51/0.83 (assert (forall ((X_7 (-> tptp.pname Bool)) (Y_6 (-> tptp.pname Bool)) (Z_4 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1673364395name_o X_7))) (= (@ _let_1 (@ (@ tptp.semila1780557381name_o Y_6) Z_4)) (@ (@ tptp.semila1780557381name_o (@ _let_1 Y_6)) (@ _let_1 Z_4))))))
% 0.51/0.83 (assert (forall ((X_7 (-> tptp.hoare_1167836817_state Bool)) (Y_6 (-> tptp.hoare_1167836817_state Bool)) (Z_4 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila179895820tate_o X_7))) (= (@ _let_1 (@ (@ tptp.semila1172322802tate_o Y_6) Z_4)) (@ (@ tptp.semila1172322802tate_o (@ _let_1 Y_6)) (@ _let_1 Z_4))))))
% 0.51/0.83 (assert (forall ((X_7 (-> tptp.hoare_1775062406iple_a Bool)) (Y_6 (-> tptp.hoare_1775062406iple_a Bool)) (Z_4 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila966743401le_a_o X_7))) (= (@ _let_1 (@ (@ tptp.semila13410563le_a_o Y_6) Z_4)) (@ (@ tptp.semila13410563le_a_o (@ _let_1 Y_6)) (@ _let_1 Z_4))))))
% 0.51/0.83 (assert (forall ((X_6 Bool) (Y_5 Bool)) (= (@ (@ tptp.semila10642723_sup_o X_6) (@ (@ tptp.semila854092349_inf_o X_6) Y_5)) X_6)))
% 0.51/0.83 (assert (forall ((X_6 (-> tptp.pname Bool)) (Y_5 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o X_6) (@ (@ tptp.semila1673364395name_o X_6) Y_5)) X_6)))
% 0.51/0.83 (assert (forall ((X_6 (-> tptp.hoare_1167836817_state Bool)) (Y_5 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila1172322802tate_o X_6) (@ (@ tptp.semila179895820tate_o X_6) Y_5)) X_6)))
% 0.51/0.83 (assert (forall ((X_6 (-> tptp.hoare_1775062406iple_a Bool)) (Y_5 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila13410563le_a_o X_6) (@ (@ tptp.semila966743401le_a_o X_6) Y_5)) X_6)))
% 0.51/0.83 (assert (forall ((X_5 Bool) (Y_4 Bool)) (= (@ (@ tptp.semila854092349_inf_o X_5) (@ (@ tptp.semila10642723_sup_o X_5) Y_4)) X_5)))
% 0.51/0.83 (assert (forall ((X_5 (-> tptp.pname Bool)) (Y_4 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1673364395name_o X_5) (@ (@ tptp.semila1780557381name_o X_5) Y_4)) X_5)))
% 0.51/0.83 (assert (forall ((X_5 (-> tptp.hoare_1167836817_state Bool)) (Y_4 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila179895820tate_o X_5) (@ (@ tptp.semila1172322802tate_o X_5) Y_4)) X_5)))
% 0.51/0.83 (assert (forall ((X_5 (-> tptp.hoare_1775062406iple_a Bool)) (Y_4 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila966743401le_a_o X_5) (@ (@ tptp.semila13410563le_a_o X_5) Y_4)) X_5)))
% 0.51/0.83 (assert (forall ((A_34 (-> tptp.pname Bool)) (B_28 (-> tptp.pname Bool))) (= (= (@ (@ tptp.semila1673364395name_o A_34) B_28) tptp.bot_bot_pname_o) (forall ((X tptp.pname)) (=> (@ (@ tptp.member_pname X) A_34) (forall ((Xa tptp.pname)) (=> (@ (@ tptp.member_pname Xa) B_28) (not (= X Xa)))))))))
% 0.51/0.83 (assert (forall ((A_34 (-> tptp.hoare_1775062406iple_a Bool)) (B_28 (-> tptp.hoare_1775062406iple_a Bool))) (= (= (@ (@ tptp.semila966743401le_a_o A_34) B_28) tptp.bot_bo751897185le_a_o) (forall ((X tptp.hoare_1775062406iple_a)) (=> (@ (@ tptp.member2122167641iple_a X) A_34) (forall ((Xa tptp.hoare_1775062406iple_a)) (=> (@ (@ tptp.member2122167641iple_a Xa) B_28) (not (= X Xa)))))))))
% 0.51/0.83 (assert (forall ((A_34 (-> tptp.hoare_1167836817_state Bool)) (B_28 (-> tptp.hoare_1167836817_state Bool))) (= (= (@ (@ tptp.semila179895820tate_o A_34) B_28) tptp.bot_bo70021908tate_o) (forall ((X tptp.hoare_1167836817_state)) (=> (@ (@ tptp.member2058392318_state X) A_34) (forall ((Xa tptp.hoare_1167836817_state)) (=> (@ (@ tptp.member2058392318_state Xa) B_28) (not (= X Xa)))))))))
% 0.51/0.83 (assert (forall ((A_33 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1673364395name_o A_33) tptp.bot_bot_pname_o) tptp.bot_bot_pname_o)))
% 0.51/0.83 (assert (forall ((A_33 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila966743401le_a_o A_33) tptp.bot_bo751897185le_a_o) tptp.bot_bo751897185le_a_o)))
% 0.51/0.83 (assert (forall ((A_33 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila179895820tate_o A_33) tptp.bot_bo70021908tate_o) tptp.bot_bo70021908tate_o)))
% 0.51/0.83 (assert (forall ((B_27 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1673364395name_o tptp.bot_bot_pname_o) B_27) tptp.bot_bot_pname_o)))
% 0.51/0.83 (assert (forall ((B_27 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila966743401le_a_o tptp.bot_bo751897185le_a_o) B_27) tptp.bot_bo751897185le_a_o)))
% 0.51/0.83 (assert (forall ((B_27 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila179895820tate_o tptp.bot_bo70021908tate_o) B_27) tptp.bot_bo70021908tate_o)))
% 0.51/0.83 (assert (forall ((A_32 (-> tptp.hoare_1775062406iple_a Bool)) (B_26 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila966743401le_a_o A_32) B_26) (@ tptp.collec676402587iple_a (lambda ((X tptp.hoare_1775062406iple_a)) (let ((_let_1 (@ tptp.member2122167641iple_a X))) (and (@ _let_1 A_32) (@ _let_1 B_26))))))))
% 0.51/0.83 (assert (forall ((A_32 (-> tptp.pname Bool)) (B_26 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1673364395name_o A_32) B_26) (@ tptp.collect_pname (lambda ((X tptp.pname)) (let ((_let_1 (@ tptp.member_pname X))) (and (@ _let_1 A_32) (@ _let_1 B_26))))))))
% 0.51/0.83 (assert (forall ((C_16 tptp.hoare_1775062406iple_a) (A_31 (-> tptp.hoare_1775062406iple_a Bool)) (B_25 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.member2122167641iple_a C_16))) (= (@ _let_1 (@ (@ tptp.semila966743401le_a_o A_31) B_25)) (and (@ _let_1 A_31) (@ _let_1 B_25))))))
% 0.51/0.83 (assert (forall ((C_16 tptp.pname) (A_31 (-> tptp.pname Bool)) (B_25 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_16))) (= (@ _let_1 (@ (@ tptp.semila1673364395name_o A_31) B_25)) (and (@ _let_1 A_31) (@ _let_1 B_25))))))
% 0.51/0.83 (assert (forall ((C_15 tptp.hoare_1775062406iple_a) (A_30 (-> tptp.hoare_1775062406iple_a Bool)) (B_24 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.member2122167641iple_a C_15))) (=> (@ _let_1 (@ (@ tptp.semila966743401le_a_o A_30) B_24)) (@ _let_1 A_30)))))
% 0.51/0.83 (assert (forall ((C_15 tptp.pname) (A_30 (-> tptp.pname Bool)) (B_24 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_15))) (=> (@ _let_1 (@ (@ tptp.semila1673364395name_o A_30) B_24)) (@ _let_1 A_30)))))
% 0.51/0.83 (assert (forall ((C_14 tptp.hoare_1775062406iple_a) (A_29 (-> tptp.hoare_1775062406iple_a Bool)) (B_23 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.member2122167641iple_a C_14))) (=> (@ _let_1 (@ (@ tptp.semila966743401le_a_o A_29) B_23)) (@ _let_1 B_23)))))
% 0.51/0.83 (assert (forall ((C_14 tptp.pname) (A_29 (-> tptp.pname Bool)) (B_23 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_14))) (=> (@ _let_1 (@ (@ tptp.semila1673364395name_o A_29) B_23)) (@ _let_1 B_23)))))
% 0.51/0.83 (assert (forall ((P_3 (-> tptp.hoare_1775062406iple_a Bool)) (Q (-> tptp.hoare_1775062406iple_a Bool))) (= (@ tptp.collec676402587iple_a (lambda ((X tptp.hoare_1775062406iple_a)) (and (@ P_3 X) (@ Q X)))) (@ (@ tptp.semila966743401le_a_o (@ tptp.collec676402587iple_a P_3)) (@ tptp.collec676402587iple_a Q)))))
% 0.51/0.83 (assert (forall ((P_3 (-> tptp.pname Bool)) (Q (-> tptp.pname Bool))) (= (@ tptp.collect_pname (lambda ((X tptp.pname)) (and (@ P_3 X) (@ Q X)))) (@ (@ tptp.semila1673364395name_o (@ tptp.collect_pname P_3)) (@ tptp.collect_pname Q)))))
% 0.51/0.83 (assert (forall ((X_4 tptp.hoare_1775062406iple_a) (A_28 (-> tptp.hoare_1775062406iple_a Bool)) (P_2 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.member2122167641iple_a X_4))) (= (@ _let_1 (@ (@ tptp.semila966743401le_a_o A_28) (@ tptp.collec676402587iple_a P_2))) (and (@ _let_1 A_28) (@ P_2 X_4))))))
% 0.51/0.83 (assert (forall ((X_4 tptp.pname) (A_28 (-> tptp.pname Bool)) (P_2 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_4))) (= (@ _let_1 (@ (@ tptp.semila1673364395name_o A_28) (@ tptp.collect_pname P_2))) (and (@ _let_1 A_28) (@ P_2 X_4))))))
% 0.51/0.83 (assert (forall ((R (-> tptp.hoare_1775062406iple_a Bool)) (S_2 (-> tptp.hoare_1775062406iple_a Bool)) (X tptp.hoare_1775062406iple_a)) (= (@ (@ (@ tptp.semila966743401le_a_o (lambda ((Y_2 tptp.hoare_1775062406iple_a)) (@ (@ tptp.member2122167641iple_a Y_2) R))) (lambda ((Y_2 tptp.hoare_1775062406iple_a)) (@ (@ tptp.member2122167641iple_a Y_2) S_2))) X) (@ (@ tptp.member2122167641iple_a X) (@ (@ tptp.semila966743401le_a_o R) S_2)))))
% 0.51/0.83 (assert (forall ((R (-> tptp.pname Bool)) (S_2 (-> tptp.pname Bool)) (X tptp.pname)) (= (@ (@ (@ tptp.semila1673364395name_o (lambda ((Y_2 tptp.pname)) (@ (@ tptp.member_pname Y_2) R))) (lambda ((Y_2 tptp.pname)) (@ (@ tptp.member_pname Y_2) S_2))) X) (@ (@ tptp.member_pname X) (@ (@ tptp.semila1673364395name_o R) S_2)))))
% 0.51/0.83 (assert (forall ((A_27 (-> tptp.pname Bool)) (B_22 (-> tptp.pname Bool)) (C_13 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o (@ (@ tptp.semila1780557381name_o (@ (@ tptp.semila1673364395name_o A_27) B_22)) (@ (@ tptp.semila1673364395name_o B_22) C_13))) (@ (@ tptp.semila1673364395name_o C_13) A_27)) (@ (@ tptp.semila1673364395name_o (@ (@ tptp.semila1673364395name_o (@ (@ tptp.semila1780557381name_o A_27) B_22)) (@ (@ tptp.semila1780557381name_o B_22) C_13))) (@ (@ tptp.semila1780557381name_o C_13) A_27)))))
% 0.51/0.83 (assert (forall ((A_27 (-> tptp.hoare_1167836817_state Bool)) (B_22 (-> tptp.hoare_1167836817_state Bool)) (C_13 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila1172322802tate_o (@ (@ tptp.semila1172322802tate_o (@ (@ tptp.semila179895820tate_o A_27) B_22)) (@ (@ tptp.semila179895820tate_o B_22) C_13))) (@ (@ tptp.semila179895820tate_o C_13) A_27)) (@ (@ tptp.semila179895820tate_o (@ (@ tptp.semila179895820tate_o (@ (@ tptp.semila1172322802tate_o A_27) B_22)) (@ (@ tptp.semila1172322802tate_o B_22) C_13))) (@ (@ tptp.semila1172322802tate_o C_13) A_27)))))
% 0.51/0.83 (assert (forall ((A_27 (-> tptp.hoare_1775062406iple_a Bool)) (B_22 (-> tptp.hoare_1775062406iple_a Bool)) (C_13 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila13410563le_a_o (@ (@ tptp.semila13410563le_a_o (@ (@ tptp.semila966743401le_a_o A_27) B_22)) (@ (@ tptp.semila966743401le_a_o B_22) C_13))) (@ (@ tptp.semila966743401le_a_o C_13) A_27)) (@ (@ tptp.semila966743401le_a_o (@ (@ tptp.semila966743401le_a_o (@ (@ tptp.semila13410563le_a_o A_27) B_22)) (@ (@ tptp.semila13410563le_a_o B_22) C_13))) (@ (@ tptp.semila13410563le_a_o C_13) A_27)))))
% 0.51/0.83 (assert (forall ((B_21 (-> tptp.pname Bool)) (C_12 (-> tptp.pname Bool)) (A_26 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o (@ (@ tptp.semila1673364395name_o B_21) C_12)) A_26) (@ (@ tptp.semila1673364395name_o (@ (@ tptp.semila1780557381name_o B_21) A_26)) (@ (@ tptp.semila1780557381name_o C_12) A_26)))))
% 0.51/0.83 (assert (forall ((B_21 (-> tptp.hoare_1167836817_state Bool)) (C_12 (-> tptp.hoare_1167836817_state Bool)) (A_26 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila1172322802tate_o (@ (@ tptp.semila179895820tate_o B_21) C_12)) A_26) (@ (@ tptp.semila179895820tate_o (@ (@ tptp.semila1172322802tate_o B_21) A_26)) (@ (@ tptp.semila1172322802tate_o C_12) A_26)))))
% 0.51/0.83 (assert (forall ((B_21 (-> tptp.hoare_1775062406iple_a Bool)) (C_12 (-> tptp.hoare_1775062406iple_a Bool)) (A_26 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila13410563le_a_o (@ (@ tptp.semila966743401le_a_o B_21) C_12)) A_26) (@ (@ tptp.semila966743401le_a_o (@ (@ tptp.semila13410563le_a_o B_21) A_26)) (@ (@ tptp.semila13410563le_a_o C_12) A_26)))))
% 0.51/0.83 (assert (forall ((B_20 (-> tptp.pname Bool)) (C_11 (-> tptp.pname Bool)) (A_25 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1673364395name_o (@ (@ tptp.semila1780557381name_o B_20) C_11)) A_25) (@ (@ tptp.semila1780557381name_o (@ (@ tptp.semila1673364395name_o B_20) A_25)) (@ (@ tptp.semila1673364395name_o C_11) A_25)))))
% 0.51/0.83 (assert (forall ((B_20 (-> tptp.hoare_1167836817_state Bool)) (C_11 (-> tptp.hoare_1167836817_state Bool)) (A_25 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila179895820tate_o (@ (@ tptp.semila1172322802tate_o B_20) C_11)) A_25) (@ (@ tptp.semila1172322802tate_o (@ (@ tptp.semila179895820tate_o B_20) A_25)) (@ (@ tptp.semila179895820tate_o C_11) A_25)))))
% 0.51/0.83 (assert (forall ((B_20 (-> tptp.hoare_1775062406iple_a Bool)) (C_11 (-> tptp.hoare_1775062406iple_a Bool)) (A_25 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila966743401le_a_o (@ (@ tptp.semila13410563le_a_o B_20) C_11)) A_25) (@ (@ tptp.semila13410563le_a_o (@ (@ tptp.semila966743401le_a_o B_20) A_25)) (@ (@ tptp.semila966743401le_a_o C_11) A_25)))))
% 0.51/0.83 (assert (forall ((A_24 (-> tptp.pname Bool)) (B_19 (-> tptp.pname Bool)) (C_10 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o A_24))) (= (@ _let_1 (@ (@ tptp.semila1673364395name_o B_19) C_10)) (@ (@ tptp.semila1673364395name_o (@ _let_1 B_19)) (@ _let_1 C_10))))))
% 0.51/0.83 (assert (forall ((A_24 (-> tptp.hoare_1167836817_state Bool)) (B_19 (-> tptp.hoare_1167836817_state Bool)) (C_10 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila1172322802tate_o A_24))) (= (@ _let_1 (@ (@ tptp.semila179895820tate_o B_19) C_10)) (@ (@ tptp.semila179895820tate_o (@ _let_1 B_19)) (@ _let_1 C_10))))))
% 0.51/0.83 (assert (forall ((A_24 (-> tptp.hoare_1775062406iple_a Bool)) (B_19 (-> tptp.hoare_1775062406iple_a Bool)) (C_10 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila13410563le_a_o A_24))) (= (@ _let_1 (@ (@ tptp.semila966743401le_a_o B_19) C_10)) (@ (@ tptp.semila966743401le_a_o (@ _let_1 B_19)) (@ _let_1 C_10))))))
% 0.51/0.83 (assert (forall ((A_23 (-> tptp.pname Bool)) (B_18 (-> tptp.pname Bool)) (C_9 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1673364395name_o A_23))) (= (@ _let_1 (@ (@ tptp.semila1780557381name_o B_18) C_9)) (@ (@ tptp.semila1780557381name_o (@ _let_1 B_18)) (@ _let_1 C_9))))))
% 0.51/0.83 (assert (forall ((A_23 (-> tptp.hoare_1167836817_state Bool)) (B_18 (-> tptp.hoare_1167836817_state Bool)) (C_9 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila179895820tate_o A_23))) (= (@ _let_1 (@ (@ tptp.semila1172322802tate_o B_18) C_9)) (@ (@ tptp.semila1172322802tate_o (@ _let_1 B_18)) (@ _let_1 C_9))))))
% 0.51/0.83 (assert (forall ((A_23 (-> tptp.hoare_1775062406iple_a Bool)) (B_18 (-> tptp.hoare_1775062406iple_a Bool)) (C_9 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila966743401le_a_o A_23))) (= (@ _let_1 (@ (@ tptp.semila13410563le_a_o B_18) C_9)) (@ (@ tptp.semila13410563le_a_o (@ _let_1 B_18)) (@ _let_1 C_9))))))
% 0.51/0.83 (assert (forall ((B_17 (-> tptp.hoare_1167836817_state Bool)) (A_22 tptp.hoare_1167836817_state) (C_8 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.insert2134838167_state A_22))) (=> (@ (@ tptp.member2058392318_state A_22) C_8) (= (@ (@ tptp.semila179895820tate_o (@ _let_1 B_17)) C_8) (@ _let_1 (@ (@ tptp.semila179895820tate_o B_17) C_8)))))))
% 0.51/0.83 (assert (forall ((B_17 (-> tptp.hoare_1775062406iple_a Bool)) (A_22 tptp.hoare_1775062406iple_a) (C_8 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.insert1281456128iple_a A_22))) (=> (@ (@ tptp.member2122167641iple_a A_22) C_8) (= (@ (@ tptp.semila966743401le_a_o (@ _let_1 B_17)) C_8) (@ _let_1 (@ (@ tptp.semila966743401le_a_o B_17) C_8)))))))
% 0.51/0.83 (assert (forall ((B_17 (-> tptp.pname Bool)) (A_22 tptp.pname) (C_8 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname A_22))) (=> (@ (@ tptp.member_pname A_22) C_8) (= (@ (@ tptp.semila1673364395name_o (@ _let_1 B_17)) C_8) (@ _let_1 (@ (@ tptp.semila1673364395name_o B_17) C_8)))))))
% 0.51/0.83 (assert (forall ((B_16 (-> tptp.hoare_1167836817_state Bool)) (A_21 tptp.hoare_1167836817_state) (A_20 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila179895820tate_o A_20))) (let ((_let_2 (@ tptp.insert2134838167_state A_21))) (=> (@ (@ tptp.member2058392318_state A_21) A_20) (= (@ _let_1 (@ _let_2 B_16)) (@ _let_2 (@ _let_1 B_16))))))))
% 0.51/0.83 (assert (forall ((B_16 (-> tptp.hoare_1775062406iple_a Bool)) (A_21 tptp.hoare_1775062406iple_a) (A_20 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila966743401le_a_o A_20))) (let ((_let_2 (@ tptp.insert1281456128iple_a A_21))) (=> (@ (@ tptp.member2122167641iple_a A_21) A_20) (= (@ _let_1 (@ _let_2 B_16)) (@ _let_2 (@ _let_1 B_16))))))))
% 0.51/0.83 (assert (forall ((B_16 (-> tptp.pname Bool)) (A_21 tptp.pname) (A_20 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1673364395name_o A_20))) (let ((_let_2 (@ tptp.insert_pname A_21))) (=> (@ (@ tptp.member_pname A_21) A_20) (= (@ _let_1 (@ _let_2 B_16)) (@ _let_2 (@ _let_1 B_16))))))))
% 0.51/0.83 (assert (forall ((B_15 (-> tptp.hoare_1167836817_state Bool)) (A_19 tptp.hoare_1167836817_state) (C_7 (-> tptp.hoare_1167836817_state Bool))) (=> (not (@ (@ tptp.member2058392318_state A_19) C_7)) (= (@ (@ tptp.semila179895820tate_o (@ (@ tptp.insert2134838167_state A_19) B_15)) C_7) (@ (@ tptp.semila179895820tate_o B_15) C_7)))))
% 0.51/0.83 (assert (forall ((B_15 (-> tptp.hoare_1775062406iple_a Bool)) (A_19 tptp.hoare_1775062406iple_a) (C_7 (-> tptp.hoare_1775062406iple_a Bool))) (=> (not (@ (@ tptp.member2122167641iple_a A_19) C_7)) (= (@ (@ tptp.semila966743401le_a_o (@ (@ tptp.insert1281456128iple_a A_19) B_15)) C_7) (@ (@ tptp.semila966743401le_a_o B_15) C_7)))))
% 0.51/0.83 (assert (forall ((B_15 (-> tptp.pname Bool)) (A_19 tptp.pname) (C_7 (-> tptp.pname Bool))) (=> (not (@ (@ tptp.member_pname A_19) C_7)) (= (@ (@ tptp.semila1673364395name_o (@ (@ tptp.insert_pname A_19) B_15)) C_7) (@ (@ tptp.semila1673364395name_o B_15) C_7)))))
% 0.51/0.83 (assert (forall ((B_14 (-> tptp.hoare_1167836817_state Bool)) (A_18 tptp.hoare_1167836817_state) (A_17 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila179895820tate_o A_17))) (=> (not (@ (@ tptp.member2058392318_state A_18) A_17)) (= (@ _let_1 (@ (@ tptp.insert2134838167_state A_18) B_14)) (@ _let_1 B_14))))))
% 0.51/0.83 (assert (forall ((B_14 (-> tptp.hoare_1775062406iple_a Bool)) (A_18 tptp.hoare_1775062406iple_a) (A_17 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila966743401le_a_o A_17))) (=> (not (@ (@ tptp.member2122167641iple_a A_18) A_17)) (= (@ _let_1 (@ (@ tptp.insert1281456128iple_a A_18) B_14)) (@ _let_1 B_14))))))
% 0.51/0.83 (assert (forall ((B_14 (-> tptp.pname Bool)) (A_18 tptp.pname) (A_17 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1673364395name_o A_17))) (=> (not (@ (@ tptp.member_pname A_18) A_17)) (= (@ _let_1 (@ (@ tptp.insert_pname A_18) B_14)) (@ _let_1 B_14))))))
% 0.51/0.83 (assert (forall ((A_16 tptp.hoare_1167836817_state) (A_15 (-> tptp.hoare_1167836817_state Bool)) (B_13 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.insert2134838167_state A_16))) (= (@ (@ tptp.semila179895820tate_o (@ _let_1 A_15)) (@ _let_1 B_13)) (@ _let_1 (@ (@ tptp.semila179895820tate_o A_15) B_13))))))
% 0.51/0.83 (assert (forall ((A_16 tptp.hoare_1775062406iple_a) (A_15 (-> tptp.hoare_1775062406iple_a Bool)) (B_13 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.insert1281456128iple_a A_16))) (= (@ (@ tptp.semila966743401le_a_o (@ _let_1 A_15)) (@ _let_1 B_13)) (@ _let_1 (@ (@ tptp.semila966743401le_a_o A_15) B_13))))))
% 0.51/0.83 (assert (forall ((A_16 tptp.pname) (A_15 (-> tptp.pname Bool)) (B_13 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname A_16))) (= (@ (@ tptp.semila1673364395name_o (@ _let_1 A_15)) (@ _let_1 B_13)) (@ _let_1 (@ (@ tptp.semila1673364395name_o A_15) B_13))))))
% 0.51/0.83 (assert (forall ((B_12 (-> tptp.hoare_1167836817_state Bool)) (A_14 tptp.hoare_1167836817_state) (C_6 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ (@ tptp.semila179895820tate_o B_12) C_6))) (let ((_let_2 (@ tptp.insert2134838167_state A_14))) (let ((_let_3 (@ (@ tptp.semila179895820tate_o (@ _let_2 B_12)) C_6))) (let ((_let_4 (@ (@ tptp.member2058392318_state A_14) C_6))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 0.51/0.83 (assert (forall ((B_12 (-> tptp.hoare_1775062406iple_a Bool)) (A_14 tptp.hoare_1775062406iple_a) (C_6 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ (@ tptp.semila966743401le_a_o B_12) C_6))) (let ((_let_2 (@ tptp.insert1281456128iple_a A_14))) (let ((_let_3 (@ (@ tptp.semila966743401le_a_o (@ _let_2 B_12)) C_6))) (let ((_let_4 (@ (@ tptp.member2122167641iple_a A_14) C_6))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 0.51/0.83 (assert (forall ((B_12 (-> tptp.pname Bool)) (A_14 tptp.pname) (C_6 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.semila1673364395name_o B_12) C_6))) (let ((_let_2 (@ tptp.insert_pname A_14))) (let ((_let_3 (@ (@ tptp.semila1673364395name_o (@ _let_2 B_12)) C_6))) (let ((_let_4 (@ (@ tptp.member_pname A_14) C_6))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 0.51/0.83 (assert (forall ((B_11 (-> tptp.hoare_1167836817_state Bool)) (A_13 tptp.hoare_1167836817_state) (A_12 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila179895820tate_o A_12))) (let ((_let_2 (@ _let_1 B_11))) (let ((_let_3 (@ tptp.insert2134838167_state A_13))) (let ((_let_4 (@ _let_1 (@ _let_3 B_11)))) (let ((_let_5 (@ (@ tptp.member2058392318_state A_13) A_12))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 0.51/0.83 (assert (forall ((B_11 (-> tptp.hoare_1775062406iple_a Bool)) (A_13 tptp.hoare_1775062406iple_a) (A_12 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila966743401le_a_o A_12))) (let ((_let_2 (@ _let_1 B_11))) (let ((_let_3 (@ tptp.insert1281456128iple_a A_13))) (let ((_let_4 (@ _let_1 (@ _let_3 B_11)))) (let ((_let_5 (@ (@ tptp.member2122167641iple_a A_13) A_12))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 0.51/0.83 (assert (forall ((B_11 (-> tptp.pname Bool)) (A_13 tptp.pname) (A_12 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1673364395name_o A_12))) (let ((_let_2 (@ _let_1 B_11))) (let ((_let_3 (@ tptp.insert_pname A_13))) (let ((_let_4 (@ _let_1 (@ _let_3 B_11)))) (let ((_let_5 (@ (@ tptp.member_pname A_13) A_12))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 0.51/0.83 (assert (forall ((P_1 (-> tptp.pname Bool)) (F_4 (-> tptp.pname tptp.hoare_1167836817_state)) (G (-> tptp.pname tptp.hoare_1167836817_state)) (S_1 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1673364395name_o S_1))) (= (@ (@ tptp.image_575578384_state (lambda ((X tptp.pname)) (@ (@ (@ tptp.if_Hoa833675553_state (@ P_1 X)) (@ F_4 X)) (@ G X)))) S_1) (@ (@ tptp.semila1172322802tate_o (@ (@ tptp.image_575578384_state F_4) (@ _let_1 (@ tptp.collect_pname P_1)))) (@ (@ tptp.image_575578384_state G) (@ _let_1 (@ tptp.collect_pname (lambda ((X tptp.pname)) (not (@ P_1 X)))))))))))
% 0.51/0.83 (assert (forall ((P_1 (-> tptp.pname Bool)) (F_4 (-> tptp.pname tptp.hoare_1775062406iple_a)) (G (-> tptp.pname tptp.hoare_1775062406iple_a)) (S_1 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1673364395name_o S_1))) (= (@ (@ tptp.image_2063119815iple_a (lambda ((X tptp.pname)) (@ (@ (@ tptp.if_Hoa1047340790iple_a (@ P_1 X)) (@ F_4 X)) (@ G X)))) S_1) (@ (@ tptp.semila13410563le_a_o (@ (@ tptp.image_2063119815iple_a F_4) (@ _let_1 (@ tptp.collect_pname P_1)))) (@ (@ tptp.image_2063119815iple_a G) (@ _let_1 (@ tptp.collect_pname (lambda ((X tptp.pname)) (not (@ P_1 X)))))))))))
% 0.51/0.83 (assert (forall ((B_10 (-> tptp.pname Bool)) (A_11 (-> tptp.pname Bool)) (F_3 (-> tptp.pname tptp.pname tptp.pname)) (F_2 (-> (-> tptp.pname Bool) tptp.pname))) (let ((_let_1 (@ (@ tptp.semila1673364395name_o A_11) B_10))) (=> (@ (@ tptp.finite1282449217_pname F_3) F_2) (=> (@ tptp.finite_finite_pname A_11) (=> (@ tptp.finite_finite_pname B_10) (=> (not (= _let_1 tptp.bot_bot_pname_o)) (= (@ (@ F_3 (@ F_2 (@ (@ tptp.semila1780557381name_o A_11) B_10))) (@ F_2 _let_1)) (@ (@ F_3 (@ F_2 A_11)) (@ F_2 B_10))))))))))
% 0.51/0.83 (assert (forall ((B_10 (-> tptp.hoare_1775062406iple_a Bool)) (A_11 (-> tptp.hoare_1775062406iple_a Bool)) (F_3 (-> tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a)) (F_2 (-> (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a))) (let ((_let_1 (@ (@ tptp.semila966743401le_a_o A_11) B_10))) (=> (@ (@ tptp.finite2078349315iple_a F_3) F_2) (=> (@ tptp.finite2063573081iple_a A_11) (=> (@ tptp.finite2063573081iple_a B_10) (=> (not (= _let_1 tptp.bot_bo751897185le_a_o)) (= (@ (@ F_3 (@ F_2 (@ (@ tptp.semila13410563le_a_o A_11) B_10))) (@ F_2 _let_1)) (@ (@ F_3 (@ F_2 A_11)) (@ F_2 B_10))))))))))
% 0.51/0.83 (assert (forall ((B_10 (-> tptp.hoare_1167836817_state Bool)) (A_11 (-> tptp.hoare_1167836817_state Bool)) (F_3 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_2 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (let ((_let_1 (@ (@ tptp.semila179895820tate_o A_11) B_10))) (=> (@ (@ tptp.finite1074406356_state F_3) F_2) (=> (@ tptp.finite1084549118_state A_11) (=> (@ tptp.finite1084549118_state B_10) (=> (not (= _let_1 tptp.bot_bo70021908tate_o)) (= (@ (@ F_3 (@ F_2 (@ (@ tptp.semila1172322802tate_o A_11) B_10))) (@ F_2 _let_1)) (@ (@ F_3 (@ F_2 A_11)) (@ F_2 B_10))))))))))
% 0.51/0.83 (assert (forall ((B_9 (-> tptp.pname Bool)) (A_10 (-> tptp.pname Bool)) (F_1 (-> tptp.pname tptp.pname tptp.pname)) (F (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite1282449217_pname F_1) F) (=> (@ tptp.finite_finite_pname A_10) (=> (not (= A_10 tptp.bot_bot_pname_o)) (=> (@ tptp.finite_finite_pname B_9) (=> (not (= B_9 tptp.bot_bot_pname_o)) (=> (= (@ (@ tptp.semila1673364395name_o A_10) B_9) tptp.bot_bot_pname_o) (= (@ F (@ (@ tptp.semila1780557381name_o A_10) B_9)) (@ (@ F_1 (@ F A_10)) (@ F B_9)))))))))))
% 0.51/0.83 (assert (forall ((B_9 (-> tptp.hoare_1775062406iple_a Bool)) (A_10 (-> tptp.hoare_1775062406iple_a Bool)) (F_1 (-> tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a tptp.hoare_1775062406iple_a)) (F (-> (-> tptp.hoare_1775062406iple_a Bool) tptp.hoare_1775062406iple_a))) (=> (@ (@ tptp.finite2078349315iple_a F_1) F) (=> (@ tptp.finite2063573081iple_a A_10) (=> (not (= A_10 tptp.bot_bo751897185le_a_o)) (=> (@ tptp.finite2063573081iple_a B_9) (=> (not (= B_9 tptp.bot_bo751897185le_a_o)) (=> (= (@ (@ tptp.semila966743401le_a_o A_10) B_9) tptp.bot_bo751897185le_a_o) (= (@ F (@ (@ tptp.semila13410563le_a_o A_10) B_9)) (@ (@ F_1 (@ F A_10)) (@ F B_9)))))))))))
% 0.51/0.83 (assert (forall ((B_9 (-> tptp.hoare_1167836817_state Bool)) (A_10 (-> tptp.hoare_1167836817_state Bool)) (F_1 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (=> (@ (@ tptp.finite1074406356_state F_1) F) (=> (@ tptp.finite1084549118_state A_10) (=> (not (= A_10 tptp.bot_bo70021908tate_o)) (=> (@ tptp.finite1084549118_state B_9) (=> (not (= B_9 tptp.bot_bo70021908tate_o)) (=> (= (@ (@ tptp.semila179895820tate_o A_10) B_9) tptp.bot_bo70021908tate_o) (= (@ F (@ (@ tptp.semila1172322802tate_o A_10) B_9)) (@ (@ F_1 (@ F A_10)) (@ F B_9)))))))))))
% 0.51/0.83 (assert (forall ((X_3 Bool) (Y_3 Bool) (Z_3 Bool)) (let ((_let_1 (@ tptp.semila854092349_inf_o X_3))) (=> (forall ((X Bool) (Y_2 Bool) (Z_2 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o X))) (= (@ _let_1 (@ (@ tptp.semila854092349_inf_o Y_2) Z_2)) (@ (@ tptp.semila854092349_inf_o (@ _let_1 Y_2)) (@ _let_1 Z_2))))) (= (@ _let_1 (@ (@ tptp.semila10642723_sup_o Y_3) Z_3)) (@ (@ tptp.semila10642723_sup_o (@ _let_1 Y_3)) (@ _let_1 Z_3)))))))
% 0.51/0.83 (assert (forall ((X_3 (-> tptp.pname Bool)) (Y_3 (-> tptp.pname Bool)) (Z_3 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1673364395name_o X_3))) (=> (forall ((X (-> tptp.pname Bool)) (Y_2 (-> tptp.pname Bool)) (Z_2 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o X))) (= (@ _let_1 (@ (@ tptp.semila1673364395name_o Y_2) Z_2)) (@ (@ tptp.semila1673364395name_o (@ _let_1 Y_2)) (@ _let_1 Z_2))))) (= (@ _let_1 (@ (@ tptp.semila1780557381name_o Y_3) Z_3)) (@ (@ tptp.semila1780557381name_o (@ _let_1 Y_3)) (@ _let_1 Z_3)))))))
% 0.51/0.83 (assert (forall ((X_3 (-> tptp.hoare_1167836817_state Bool)) (Y_3 (-> tptp.hoare_1167836817_state Bool)) (Z_3 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila179895820tate_o X_3))) (=> (forall ((X (-> tptp.hoare_1167836817_state Bool)) (Y_2 (-> tptp.hoare_1167836817_state Bool)) (Z_2 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila1172322802tate_o X))) (= (@ _let_1 (@ (@ tptp.semila179895820tate_o Y_2) Z_2)) (@ (@ tptp.semila179895820tate_o (@ _let_1 Y_2)) (@ _let_1 Z_2))))) (= (@ _let_1 (@ (@ tptp.semila1172322802tate_o Y_3) Z_3)) (@ (@ tptp.semila1172322802tate_o (@ _let_1 Y_3)) (@ _let_1 Z_3)))))))
% 0.51/0.83 (assert (forall ((X_3 (-> tptp.hoare_1775062406iple_a Bool)) (Y_3 (-> tptp.hoare_1775062406iple_a Bool)) (Z_3 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila966743401le_a_o X_3))) (=> (forall ((X (-> tptp.hoare_1775062406iple_a Bool)) (Y_2 (-> tptp.hoare_1775062406iple_a Bool)) (Z_2 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila13410563le_a_o X))) (= (@ _let_1 (@ (@ tptp.semila966743401le_a_o Y_2) Z_2)) (@ (@ tptp.semila966743401le_a_o (@ _let_1 Y_2)) (@ _let_1 Z_2))))) (= (@ _let_1 (@ (@ tptp.semila13410563le_a_o Y_3) Z_3)) (@ (@ tptp.semila13410563le_a_o (@ _let_1 Y_3)) (@ _let_1 Z_3)))))))
% 0.51/0.83 (assert (forall ((X_2 Bool) (Y_1 Bool) (Z_1 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o X_2))) (=> (forall ((X Bool) (Y_2 Bool) (Z_2 Bool)) (let ((_let_1 (@ tptp.semila854092349_inf_o X))) (= (@ _let_1 (@ (@ tptp.semila10642723_sup_o Y_2) Z_2)) (@ (@ tptp.semila10642723_sup_o (@ _let_1 Y_2)) (@ _let_1 Z_2))))) (= (@ _let_1 (@ (@ tptp.semila854092349_inf_o Y_1) Z_1)) (@ (@ tptp.semila854092349_inf_o (@ _let_1 Y_1)) (@ _let_1 Z_1)))))))
% 0.51/0.83 (assert (forall ((X_2 (-> tptp.pname Bool)) (Y_1 (-> tptp.pname Bool)) (Z_1 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o X_2))) (=> (forall ((X (-> tptp.pname Bool)) (Y_2 (-> tptp.pname Bool)) (Z_2 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1673364395name_o X))) (= (@ _let_1 (@ (@ tptp.semila1780557381name_o Y_2) Z_2)) (@ (@ tptp.semila1780557381name_o (@ _let_1 Y_2)) (@ _let_1 Z_2))))) (= (@ _let_1 (@ (@ tptp.semila1673364395name_o Y_1) Z_1)) (@ (@ tptp.semila1673364395name_o (@ _let_1 Y_1)) (@ _let_1 Z_1)))))))
% 0.51/0.83 (assert (forall ((X_2 (-> tptp.hoare_1167836817_state Bool)) (Y_1 (-> tptp.hoare_1167836817_state Bool)) (Z_1 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila1172322802tate_o X_2))) (=> (forall ((X (-> tptp.hoare_1167836817_state Bool)) (Y_2 (-> tptp.hoare_1167836817_state Bool)) (Z_2 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila179895820tate_o X))) (= (@ _let_1 (@ (@ tptp.semila1172322802tate_o Y_2) Z_2)) (@ (@ tptp.semila1172322802tate_o (@ _let_1 Y_2)) (@ _let_1 Z_2))))) (= (@ _let_1 (@ (@ tptp.semila179895820tate_o Y_1) Z_1)) (@ (@ tptp.semila179895820tate_o (@ _let_1 Y_1)) (@ _let_1 Z_1)))))))
% 0.51/0.83 (assert (forall ((X_2 (-> tptp.hoare_1775062406iple_a Bool)) (Y_1 (-> tptp.hoare_1775062406iple_a Bool)) (Z_1 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila13410563le_a_o X_2))) (=> (forall ((X (-> tptp.hoare_1775062406iple_a Bool)) (Y_2 (-> tptp.hoare_1775062406iple_a Bool)) (Z_2 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila966743401le_a_o X))) (= (@ _let_1 (@ (@ tptp.semila13410563le_a_o Y_2) Z_2)) (@ (@ tptp.semila13410563le_a_o (@ _let_1 Y_2)) (@ _let_1 Z_2))))) (= (@ _let_1 (@ (@ tptp.semila966743401le_a_o Y_1) Z_1)) (@ (@ tptp.semila966743401le_a_o (@ _let_1 Y_1)) (@ _let_1 Z_1)))))))
% 0.51/0.83 (assert (forall ((A_9 Bool) (A_8 (-> Bool Bool))) (=> (@ tptp.finite_finite_o A_8) (=> (@ (@ tptp.member_o A_9) A_8) (= (@ (@ tptp.semila10642723_sup_o A_9) (@ tptp.big_la1690136417_fin_o A_8)) A_9)))))
% 0.51/0.83 (assert (forall ((A_9 (-> tptp.pname Bool)) (A_8 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_8) (=> (@ (@ tptp.member_pname_o A_9) A_8) (= (@ (@ tptp.semila1780557381name_o A_9) (@ tptp.big_la1126801287name_o A_8)) A_9)))))
% 0.51/0.83 (assert (forall ((A_9 (-> tptp.hoare_1167836817_state Bool)) (A_8 (-> (-> tptp.hoare_1167836817_state Bool) Bool))) (=> (@ tptp.finite1380128977tate_o A_8) (=> (@ (@ tptp.member864234961tate_o A_9) A_8) (= (@ (@ tptp.semila1172322802tate_o A_9) (@ tptp.big_la831793456tate_o A_8)) A_9)))))
% 0.51/0.83 (assert (forall ((A_9 (-> tptp.hoare_1775062406iple_a Bool)) (A_8 (-> (-> tptp.hoare_1775062406iple_a Bool) Bool))) (=> (@ tptp.finite789576932le_a_o A_8) (=> (@ (@ tptp.member1207314404le_a_o A_9) A_8) (= (@ (@ tptp.semila13410563le_a_o A_9) (@ tptp.big_la447547205le_a_o A_8)) A_9)))))
% 0.51/0.83 (assert (forall ((C_5 tptp.hoare_1775062406iple_a) (A_7 (-> tptp.hoare_1775062406iple_a Bool)) (B_8 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.member2122167641iple_a C_5))) (=> (@ _let_1 (@ (@ tptp.minus_1944206118le_a_o A_7) B_8)) (not (=> (@ _let_1 A_7) (@ _let_1 B_8)))))))
% 0.51/0.83 (assert (forall ((C_5 tptp.pname) (A_7 (-> tptp.pname Bool)) (B_8 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_5))) (=> (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_7) B_8)) (not (=> (@ _let_1 A_7) (@ _let_1 B_8)))))))
% 0.51/0.83 (assert (forall ((B_7 (-> tptp.hoare_1775062406iple_a Bool)) (C_4 tptp.hoare_1775062406iple_a) (A_6 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.member2122167641iple_a C_4))) (=> (@ _let_1 A_6) (=> (not (@ _let_1 B_7)) (@ _let_1 (@ (@ tptp.minus_1944206118le_a_o A_6) B_7)))))))
% 0.51/0.83 (assert (forall ((B_7 (-> tptp.pname Bool)) (C_4 tptp.pname) (A_6 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_4))) (=> (@ _let_1 A_6) (=> (not (@ _let_1 B_7)) (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_6) B_7)))))))
% 0.51/0.83 (assert (forall ((A_5 (-> tptp.pname Bool)) (B_6 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o A_5))) (= (@ _let_1 (@ (@ tptp.minus_minus_pname_o B_6) A_5)) (@ _let_1 B_6)))))
% 0.51/0.83 (assert (forall ((A_5 (-> tptp.hoare_1167836817_state Bool)) (B_6 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.semila1172322802tate_o A_5))) (= (@ _let_1 (@ (@ tptp.minus_2107060239tate_o B_6) A_5)) (@ _let_1 B_6)))))
% 0.51/0.83 (assert (forall ((A_5 (-> tptp.hoare_1775062406iple_a Bool)) (B_6 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.semila13410563le_a_o A_5))) (= (@ _let_1 (@ (@ tptp.minus_1944206118le_a_o B_6) A_5)) (@ _let_1 B_6)))))
% 0.51/0.83 (assert (forall ((B_5 (-> tptp.pname Bool)) (A_4 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o (@ (@ tptp.minus_minus_pname_o B_5) A_4)) A_4) (@ (@ tptp.semila1780557381name_o B_5) A_4))))
% 0.51/0.83 (assert (forall ((B_5 (-> tptp.hoare_1167836817_state Bool)) (A_4 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.semila1172322802tate_o (@ (@ tptp.minus_2107060239tate_o B_5) A_4)) A_4) (@ (@ tptp.semila1172322802tate_o B_5) A_4))))
% 0.51/0.83 (assert (forall ((B_5 (-> tptp.hoare_1775062406iple_a Bool)) (A_4 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.semila13410563le_a_o (@ (@ tptp.minus_1944206118le_a_o B_5) A_4)) A_4) (@ (@ tptp.semila13410563le_a_o B_5) A_4))))
% 0.51/0.83 (assert (forall ((A_3 (-> tptp.pname Bool)) (B_4 (-> tptp.pname Bool)) (C_3 (-> tptp.pname Bool))) (= (@ (@ tptp.minus_minus_pname_o (@ (@ tptp.semila1780557381name_o A_3) B_4)) C_3) (@ (@ tptp.semila1780557381name_o (@ (@ tptp.minus_minus_pname_o A_3) C_3)) (@ (@ tptp.minus_minus_pname_o B_4) C_3)))))
% 0.51/0.83 (assert (forall ((A_3 (-> tptp.hoare_1167836817_state Bool)) (B_4 (-> tptp.hoare_1167836817_state Bool)) (C_3 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.minus_2107060239tate_o (@ (@ tptp.semila1172322802tate_o A_3) B_4)) C_3) (@ (@ tptp.semila1172322802tate_o (@ (@ tptp.minus_2107060239tate_o A_3) C_3)) (@ (@ tptp.minus_2107060239tate_o B_4) C_3)))))
% 0.51/0.83 (assert (forall ((A_3 (-> tptp.hoare_1775062406iple_a Bool)) (B_4 (-> tptp.hoare_1775062406iple_a Bool)) (C_3 (-> tptp.hoare_1775062406iple_a Bool))) (= (@ (@ tptp.minus_1944206118le_a_o (@ (@ tptp.semila13410563le_a_o A_3) B_4)) C_3) (@ (@ tptp.semila13410563le_a_o (@ (@ tptp.minus_1944206118le_a_o A_3) C_3)) (@ (@ tptp.minus_1944206118le_a_o B_4) C_3)))))
% 0.51/0.83 (assert (forall ((C_2 tptp.hoare_1775062406iple_a) (A_2 (-> tptp.hoare_1775062406iple_a Bool)) (B_3 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.member2122167641iple_a C_2))) (=> (@ _let_1 (@ (@ tptp.minus_1944206118le_a_o A_2) B_3)) (not (@ _let_1 B_3))))))
% 0.51/0.83 (assert (forall ((C_2 tptp.pname) (A_2 (-> tptp.pname Bool)) (B_3 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_2) B_3)) (not (@ _let_1 B_3))))))
% 0.51/0.83 (assert (forall ((C_1 tptp.hoare_1775062406iple_a) (A_1 (-> tptp.hoare_1775062406iple_a Bool)) (B_2 (-> tptp.hoare_1775062406iple_a Bool))) (let ((_let_1 (@ tptp.member2122167641iple_a C_1))) (=> (@ _let_1 (@ (@ tptp.minus_1944206118le_a_o A_1) B_2)) (@ _let_1 A_1)))))
% 0.51/0.83 (assert (forall ((C_1 tptp.pname) (A_1 (-> tptp.pname Bool)) (B_2 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_1))) (=> (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_1) B_2)) (@ _let_1 A_1)))))
% 0.51/0.83 (assert (forall ((C tptp.pname) (A (-> tptp.pname Bool)) (B_1 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C))) (= (@ _let_1 (@ (@ tptp.minus_minus_pname_o A) B_1)) (and (@ _let_1 A) (not (@ _let_1 B_1)))))))
% 0.51/0.83 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N_1)) (@ (@ tptp.minus_minus_nat M) N_1))))
% 0.51/0.83 (assert (forall ((M tptp.nat) (N_1 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N_1)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N_1)) K))))
% 0.51/0.83 (assert (forall ((N_1 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N_1) tptp.zero_zero_nat)))
% 0.51/0.83 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 0.51/0.83 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 0.51/0.83 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N_1) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N_1) M) tptp.zero_zero_nat) (= M N_1)))))
% 0.51/0.83 (assert (forall ((I tptp.nat) (P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N tptp.nat)) (=> (@ P (@ tptp.suc N)) (@ P N))) (@ P (@ (@ tptp.minus_minus_nat K) I))))))
% 0.51/0.83 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))))
% 0.51/0.83 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N_1)) (@ (@ (@ tptp.nat_case_nat tptp.zero_zero_nat) (lambda ((K_1 tptp.nat)) K_1)) (@ _let_1 N_1))))))
% 0.51/0.83 (assert (forall ((N_1 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N_1)) tptp.one_one_nat) N_1)))
% 0.51/0.83 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N_1)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N_1)))))
% 0.51/0.83 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 0.51/0.83 (assert (forall ((N_1 tptp.nat)) (= (@ tptp.suc N_1) (@ (@ tptp.plus_plus_nat N_1) tptp.one_one_nat))))
% 0.51/0.83 (assert (forall ((N_1 tptp.nat)) (= (@ tptp.suc N_1) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) N_1))))
% 0.51/0.83 (assert (forall ((M tptp.nat) (K tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N_1) K)) (@ (@ tptp.minus_minus_nat M) N_1))))
% 0.51/0.83 (assert (forall ((K tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N_1)) (@ (@ tptp.minus_minus_nat M) N_1)))))
% 0.51/0.83 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))))
% 0.51/0.83 (assert (forall ((N_1 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N_1) M)) N_1) M)))
% 0.51/0.83 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N_1)) N_1) M)))
% 0.51/0.83 (assert (forall ((N_1 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N_1) (@ (@ tptp.plus_plus_nat N_1) M)) tptp.zero_zero_nat)))
% 0.51/0.83 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) N_1) (@ (@ tptp.plus_plus_nat N_1) M))))
% 0.51/0.83 (assert (forall ((X_1 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X_1))) (let ((_let_2 (@ tptp.plus_plus_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.51/0.83 (assert (forall ((M tptp.nat) (N_1 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 N_1)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat N_1) K))))))
% 0.51/0.83 (assert (forall ((K tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (= (@ _let_1 M) (@ _let_1 N_1)) (= M N_1)))))
% 0.51/0.83 (assert (forall ((M tptp.nat) (K tptp.nat) (N_1 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) K) (@ (@ tptp.plus_plus_nat N_1) K)) (= M N_1))))
% 0.51/0.83 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N_1) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N_1)))))
% 0.51/0.83 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N_1) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N_1)))))
% 0.51/0.83 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N_1)) (@ tptp.suc (@ _let_1 N_1))))))
% 0.51/0.83 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N_1)) (or (and (= M _let_1) (= N_1 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N_1 _let_1)))))))
% 0.51/0.83 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N_1) _let_1) (or (and (= M _let_1) (= N_1 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N_1 _let_1)))))))
% 0.51/0.83 (assert (forall ((N_1 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N_1) N_1)))
% 0.51/0.83 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 0.51/0.83 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N_1) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N_1 tptp.zero_zero_nat)))))
% 0.51/0.83 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N_1) M) (= N_1 tptp.zero_zero_nat))))
% 0.51/0.83 (assert (forall ((N_1 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N_1))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 N_1)) (=> (not _let_2) (= _let_1 (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) N_1)))))))))
% 0.51/0.83 (assert (forall ((Com1 tptp.com) (Com2 tptp.com)) (= (@ tptp.com_size (@ (@ tptp.semi Com1) Com2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.com_size Com1)) (@ tptp.com_size Com2))) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.51/0.83 (assert (forall ((Pname tptp.pname)) (= (@ tptp.com_size (@ tptp.body Pname)) tptp.zero_zero_nat)))
% 0.51/0.83 (assert (= (@ tptp.com_size tptp.skip) tptp.zero_zero_nat))
% 0.51/0.83 (assert (forall ((Fun (-> tptp.state Bool)) (Com tptp.com)) (= (@ tptp.com_size (@ (@ tptp.while Fun) Com)) (@ (@ tptp.plus_plus_nat (@ tptp.com_size Com)) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.51/0.83 (assert (forall ((Com1 tptp.com) (Com2 tptp.com)) (= (@ tptp.size_size_com (@ (@ tptp.semi Com1) Com2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.size_size_com Com1)) (@ tptp.size_size_com Com2))) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.51/0.83 (assert (forall ((Pname tptp.pname)) (= (@ tptp.size_size_com (@ tptp.body Pname)) tptp.zero_zero_nat)))
% 0.51/0.83 (assert (= (@ tptp.size_size_com tptp.skip) tptp.zero_zero_nat))
% 0.51/0.83 (assert (forall ((Fun (-> tptp.state Bool)) (Com tptp.com)) (= (@ tptp.size_size_com (@ (@ tptp.while Fun) Com)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_com Com)) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.51/0.83 (assert (forall ((Fun (-> tptp.state Bool)) (Com1 tptp.com) (Com2 tptp.com)) (= (@ tptp.size_size_com (@ (@ (@ tptp.cond Fun) Com1) Com2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.size_size_com Com1)) (@ tptp.size_size_com Com2))) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.51/0.83 (assert (forall ((C0 tptp.com) (C1 tptp.com) (N_1 tptp.nat) (S1 tptp.state) (B (-> tptp.state Bool)) (S tptp.state)) (=> (not (@ B S)) (=> (@ (@ (@ (@ tptp.evaln C1) S) N_1) S1) (@ (@ (@ (@ tptp.evaln (@ (@ (@ tptp.cond B) C0) C1)) S) N_1) S1)))))
% 0.51/0.83 (assert (forall ((C1 tptp.com) (C0 tptp.com) (N_1 tptp.nat) (S1 tptp.state) (B (-> tptp.state Bool)) (S tptp.state)) (=> (@ B S) (=> (@ (@ (@ (@ tptp.evaln C0) S) N_1) S1) (@ (@ (@ (@ tptp.evaln (@ (@ (@ tptp.cond B) C0) C1)) S) N_1) S1)))))
% 0.51/0.83 (assert (forall ((B (-> tptp.state Bool)) (C1 tptp.com) (C2 tptp.com) (S tptp.state) (N_1 tptp.nat) (T tptp.state)) (let ((_let_1 (@ B S))) (=> (@ (@ (@ (@ tptp.evaln (@ (@ (@ tptp.cond B) C1) C2)) S) N_1) T) (=> (=> _let_1 (not (@ (@ (@ (@ tptp.evaln C1) S) N_1) T))) (not (=> (not _let_1) (not (@ (@ (@ (@ tptp.evaln C2) S) N_1) T)))))))))
% 0.51/0.83 (assert (forall ((B (-> tptp.state Bool)) (C1 tptp.com) (C2 tptp.com) (S tptp.state) (T tptp.state)) (let ((_let_1 (@ B S))) (=> (@ (@ (@ tptp.evalc (@ (@ (@ tptp.cond B) C1) C2)) S) T) (=> (=> _let_1 (not (@ (@ (@ tptp.evalc C1) S) T))) (not (=> (not _let_1) (not (@ (@ (@ tptp.evalc C2) S) T)))))))))
% 0.51/0.83 (assert (forall ((C1 tptp.com) (C0 tptp.com) (S1 tptp.state) (B (-> tptp.state Bool)) (S tptp.state)) (=> (@ B S) (=> (@ (@ (@ tptp.evalc C0) S) S1) (@ (@ (@ tptp.evalc (@ (@ (@ tptp.cond B) C0) C1)) S) S1)))))
% 0.51/0.83 (assert (forall ((C0 tptp.com) (C1 tptp.com)/export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 7114 Alarm clock ( read result; case "$result" in
% 299.76/300.17 unsat)
% 299.76/300.17 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.76/300.17 ;;
% 299.76/300.17 sat)
% 299.76/300.17 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.76/300.17 ;;
% 299.76/300.17 esac; exit 1 )
% 299.76/300.17 Alarm clock
% 299.76/300.18 % cvc5---1.0.5 exiting
% 299.76/300.18 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------