TSTP Solution File: SWW471^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW471^3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n021.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 00:20:59 EDT 2023
% Result : Timeout 299.87s 300.30s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.27 % Problem : SWW471^3 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.28 % Command : do_cvc5 %s %d
% 0.27/0.49 % Computer : n021.cluster.edu
% 0.27/0.49 % Model : x86_64 x86_64
% 0.27/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.27/0.49 % Memory : 8042.1875MB
% 0.27/0.49 % OS : Linux 3.10.0-693.el7.x86_64
% 0.27/0.49 % CPULimit : 300
% 0.27/0.49 % WCLimit : 300
% 0.27/0.49 % DateTime : Sun Aug 27 20:21:13 EDT 2023
% 0.27/0.49 % CPUTime :
% 0.34/0.77 %----Proving TH0
% 0.34/0.78 %------------------------------------------------------------------------------
% 0.34/0.78 % File : SWW471^3 : TPTP v8.1.2. Released v5.3.0.
% 0.34/0.78 % Domain : Software Verification
% 0.34/0.78 % Problem : Hoare's Logic with Procedures line 269, 1000 axioms selected
% 0.34/0.78 % Version : Especial.
% 0.34/0.78 % English :
% 0.34/0.78
% 0.34/0.78 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.34/0.78 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.34/0.78 % Source : [Bla11]
% 0.34/0.78 % Names : hoare_1000_thf_l269 [Bla11]
% 0.34/0.78
% 0.34/0.78 % Status : Theorem
% 0.34/0.78 % Rating : 1.00 v5.3.0
% 0.34/0.78 % Syntax : Number of formulae : 1395 ( 491 unt; 185 typ; 0 def)
% 0.34/0.78 % Number of atoms : 4733 (1094 equ; 91 cnn)
% 0.34/0.78 % Maximal formula atoms : 14 ( 3 avg)
% 0.34/0.78 % Number of connectives : 10204 ( 409 ~; 89 |; 188 &;8244 @)
% 0.34/0.78 % ( 258 <=>;1016 =>; 0 <=; 0 <~>)
% 0.34/0.78 % Maximal formula depth : 19 ( 7 avg)
% 0.34/0.78 % Number of types : 9 ( 8 usr)
% 0.34/0.78 % Number of type conns : 3193 (3193 >; 0 *; 0 +; 0 <<)
% 0.34/0.78 % Number of symbols : 183 ( 177 usr; 11 con; 0-5 aty)
% 0.34/0.78 % Number of variables : 3370 ( 187 ^;3113 !; 70 ?;3370 :)
% 0.34/0.78 % SPC : TH0_THM_EQU_NAR
% 0.34/0.78
% 0.34/0.78 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.34/0.78 % 2011-08-09 19:44:03
% 0.34/0.78 %------------------------------------------------------------------------------
% 0.34/0.78 %----Should-be-implicit typings (8)
% 0.34/0.78 thf(ty_ty_t__a,type,
% 0.34/0.78 x_a: $tType ).
% 0.34/0.78
% 0.34/0.78 thf(ty_ty_tc__Com__Ocom,type,
% 0.34/0.78 com: $tType ).
% 0.34/0.78
% 0.34/0.78 thf(ty_ty_tc__Com__Opname,type,
% 0.34/0.78 pname: $tType ).
% 0.34/0.78
% 0.34/0.78 thf(ty_ty_tc__Com__Ostate,type,
% 0.34/0.78 state: $tType ).
% 0.34/0.78
% 0.34/0.78 thf(ty_ty_tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J,type,
% 0.34/0.78 hoare_2091234717iple_a: $tType ).
% 0.34/0.78
% 0.34/0.78 thf(ty_ty_tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J,type,
% 0.34/0.78 hoare_1708887482_state: $tType ).
% 0.34/0.78
% 0.34/0.78 thf(ty_ty_tc__Nat__Onat,type,
% 0.34/0.78 nat: $tType ).
% 0.34/0.78
% 0.34/0.78 thf(ty_ty_tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 0.34/0.78 option_com: $tType ).
% 0.34/0.78
% 0.34/0.78 %----Explicit typings (177)
% 0.34/0.78 thf(sy_c_Big__Operators_Ocomm__monoid__big_000_062_Itc__Hoare____Mirabelle____nqhfsd,type,
% 0.34/0.78 big_co1924420859_pname: ( ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > ( ( pname > hoare_2091234717iple_a > $o ) > ( pname > $o ) > hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Big__Operators_Olattice__class_OSup__fin_000_062_I_062_Itc__Hoare____Mirabe,type,
% 0.34/0.78 big_la1994307886_a_o_o: ( ( ( hoare_2091234717iple_a > $o ) > $o ) > $o ) > ( hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Big__Operators_Olattice__class_OSup__fin_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.34/0.78 big_la1286884090name_o: ( ( pname > $o ) > $o ) > pname > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Big__Operators_Olattice__class_OSup__fin_000_062_Itc__Hoare____Mirabelle___,type,
% 0.34/0.78 big_la735727201le_a_o: ( ( hoare_2091234717iple_a > $o ) > $o ) > hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Big__Operators_Olattice__class_OSup__fin_000_062_Itc__Hoare____Mirabelle____001,type,
% 0.34/0.78 big_la1088302868tate_o: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Big__Operators_Olattice__class_OSup__fin_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.34/0.78 big_la1658356148_nat_o: ( ( nat > $o ) > $o ) > nat > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Big__Operators_Olattice__class_OSup__fin_000_Eo,type,
% 0.34/0.78 big_la727467310_fin_o: ( $o > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Big__Operators_Olattice__class_OSup__fin_000tc__Nat__Onat,type,
% 0.34/0.78 big_la43341705in_nat: ( nat > $o ) > nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Com_Obody,type,
% 0.34/0.78 body_1: pname > option_com ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Com_Ocom_OBODY,type,
% 0.34/0.78 body: pname > com ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Com_Ocom_OCond,type,
% 0.34/0.78 cond: ( state > $o ) > com > com > com ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Com_Ocom_OSKIP,type,
% 0.34/0.78 skip: com ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Com_Ocom_OSemi,type,
% 0.34/0.78 semi: com > com > com ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Com_Ocom_OWhile,type,
% 0.34/0.78 while: ( state > $o ) > com > com ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Com_Ocom_Ocom__size,type,
% 0.34/0.78 com_size: com > nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ocard_000tc__Nat__Onat,type,
% 0.34/0.78 finite_card_nat: ( nat > $o ) > nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Ot,type,
% 0.34/0.78 finite886417794_a_o_o: ( ( ( hoare_2091234717iple_a > $o ) > $o ) > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.34/0.78 finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_,type,
% 0.34/0.78 finite1829014797le_a_o: ( ( hoare_2091234717iple_a > $o ) > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple__002,type,
% 0.34/0.78 finite1329924456tate_o: ( ( hoare_1708887482_state > $o ) > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.34/0.78 finite_finite_nat_o: ( ( nat > $o ) > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofinite_000_Eo,type,
% 0.34/0.78 finite_finite_o: ( $o > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofinite_000tc__Com__Opname,type,
% 0.34/0.78 finite_finite_pname: ( pname > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_,type,
% 0.34/0.78 finite232261744iple_a: ( hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__C,type,
% 0.34/0.78 finite1625599783_state: ( hoare_1708887482_state > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofinite_000tc__Nat__Onat,type,
% 0.34/0.78 finite_finite_nat: ( nat > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofold__image_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdfvy,type,
% 0.34/0.78 finite2009943022_o_nat: ( ( ( hoare_2091234717iple_a > $o ) > $o ) > ( ( hoare_2091234717iple_a > $o ) > $o ) > ( hoare_2091234717iple_a > $o ) > $o ) > ( nat > ( hoare_2091234717iple_a > $o ) > $o ) > ( ( hoare_2091234717iple_a > $o ) > $o ) > ( nat > $o ) > ( hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofold__image_000_062_Itc__Com__Opname_M_Eo_J_000tc__Nat__Onat,type,
% 0.34/0.78 finite1427591632_o_nat: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( nat > pname > $o ) > ( pname > $o ) > ( nat > $o ) > pname > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otr,type,
% 0.34/0.78 finite903029825le_a_o: ( ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ) > ( ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > ( ( hoare_2091234717iple_a > $o ) > $o ) > hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otr_003,type,
% 0.34/0.78 finite1290357347_pname: ( ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ) > ( pname > hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > ( pname > $o ) > hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otr_004,type,
% 0.34/0.78 finite1481787452iple_a: ( ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otr_005,type,
% 0.34/0.78 finite2100865449_o_nat: ( ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ) > ( nat > hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > ( nat > $o ) > hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otr_006,type,
% 0.34/0.78 finite2139561282_pname: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( pname > hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( pname > $o ) > hoare_1708887482_state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otr_007,type,
% 0.34/0.78 finite1400355848_o_nat: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( nat > hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( nat > $o ) > hoare_1708887482_state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofold__image_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Nat__Onat,type,
% 0.34/0.78 finite141655318_o_nat: ( ( nat > $o ) > ( nat > $o ) > nat > $o ) > ( nat > nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofolding__one_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Ot,type,
% 0.34/0.78 finite14499299le_a_o: ( ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ) > ( ( ( hoare_2091234717iple_a > $o ) > $o ) > hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofolding__one_000tc__Com__Opname,type,
% 0.34/0.78 finite1282449217_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_,type,
% 0.34/0.78 finite247037978iple_a: ( hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a ) > ( ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple__008,type,
% 0.34/0.78 finite1615457021_state: ( hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ) > ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofolding__one_000tc__Nat__Onat,type,
% 0.34/0.78 finite988810631ne_nat: ( nat > nat > nat ) > ( ( nat > $o ) > nat ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofolding__one__idem_000_062_Itc__Hoare____Mirabelle____nqhfsdfv,type,
% 0.34/0.78 finite574580006le_a_o: ( ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ) > ( ( ( hoare_2091234717iple_a > $o ) > $o ) > hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname,type,
% 0.34/0.78 finite89670078_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____nqhfsdfvyv__Ot,type,
% 0.34/0.78 finite1674555159iple_a: ( hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a ) > ( ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____nqhfsdfvyv__Ot_009,type,
% 0.34/0.78 finite1347568576_state: ( hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ) > ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Nat__Onat,type,
% 0.34/0.78 finite795500164em_nat: ( nat > nat > nat ) > ( ( nat > $o ) > nat ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Groups_Ominus__class_Ominus_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsd,type,
% 0.34/0.78 minus_1746272704_a_o_o: ( ( hoare_2091234717iple_a > $o ) > $o ) > ( ( hoare_2091234717iple_a > $o ) > $o ) > ( hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.34/0.78 minus_minus_pname_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__,type,
% 0.34/0.78 minus_836160335le_a_o: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv___010,type,
% 0.34/0.78 minus_2056855718tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.34/0.78 minus_minus_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Groups_Ominus__class_Ominus_000_Eo,type,
% 0.34/0.78 minus_minus_o: $o > $o > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat,type,
% 0.34/0.78 minus_minus_nat: nat > nat > nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat,type,
% 0.34/0.78 one_one_nat: nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat,type,
% 0.34/0.78 plus_plus_nat: nat > nat > nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Groups_Otimes__class_Otimes_000tc__Nat__Onat,type,
% 0.34/0.78 times_times_nat: nat > nat > nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat,type,
% 0.34/0.78 zero_zero_nat: nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_HOL_OThe_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_M_E,type,
% 0.34/0.78 the_Ho2077879471le_a_o: ( ( hoare_2091234717iple_a > $o ) > $o ) > hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_HOL_OThe_000tc__Com__Opname,type,
% 0.34/0.78 the_pname: ( pname > $o ) > pname ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_HOL_OThe_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J,type,
% 0.34/0.78 the_Ho1471183438iple_a: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_HOL_OThe_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_,type,
% 0.34/0.78 the_Ho851197897_state: ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_HOL_OThe_000tc__Nat__Onat,type,
% 0.34/0.78 the_nat: ( nat > $o ) > nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_OMGT,type,
% 0.34/0.78 hoare_Mirabelle_MGT: com > hoare_1708887482_state ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ohoare__derivs_000t__a,type,
% 0.34/0.78 hoare_1467856363rivs_a: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ohoare__derivs_000tc__Com__Ostate,type,
% 0.34/0.78 hoare_90032982_state: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ohoare__valids_000t__a,type,
% 0.34/0.78 hoare_1805689709lids_a: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ohoare__valids_000tc__Com__Ostate,type,
% 0.34/0.78 hoare_496444244_state: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Otriple_Otriple_000t__a,type,
% 0.34/0.78 hoare_657976383iple_a: ( x_a > state > $o ) > com > ( x_a > state > $o ) > hoare_2091234717iple_a ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Otriple_Otriple_000tc__Com__Ostate,type,
% 0.34/0.78 hoare_858012674_state: ( state > state > $o ) > com > ( state > state > $o ) > hoare_1708887482_state ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Otriple_Otriple__size_000t__a,type,
% 0.34/0.78 hoare_1169027232size_a: ( x_a > nat ) > hoare_2091234717iple_a > nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Otriple_Otriple__size_000tc__Com__Ostate,type,
% 0.34/0.78 hoare_518771297_state: ( state > nat ) > hoare_1708887482_state > nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Otriple__valid_000t__a,type,
% 0.34/0.78 hoare_1421888935alid_a: nat > hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Otriple__valid_000tc__Com__Ostate,type,
% 0.34/0.78 hoare_23738522_state: nat > hoare_1708887482_state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Hoare____Mirabell,type,
% 0.34/0.78 semila1672913213_a_o_o: ( ( hoare_2091234717iple_a > $o ) > $o ) > ( ( hoare_2091234717iple_a > $o ) > $o ) > ( hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.34/0.78 semila1673364395name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Hoare____Mirabelle____n,type,
% 0.34/0.78 semila2006181266le_a_o: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Hoare____Mirabelle____n_011,type,
% 0.34/0.78 semila129691299tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.34/0.78 semila1947288293_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_Eo,type,
% 0.34/0.78 semila854092349_inf_o: $o > $o > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000tc__Nat__Onat,type,
% 0.34/0.78 semila80283416nf_nat: nat > nat > nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_I_062_Itc__Hoare____Mi,type,
% 0.34/0.78 semila484278426_o_o_o: ( ( ( hoare_2091234717iple_a > $o ) > $o ) > $o ) > ( ( ( hoare_2091234717iple_a > $o ) > $o ) > $o ) > ( ( hoare_2091234717iple_a > $o ) > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Com__Opname_M_Eo_,type,
% 0.34/0.78 semila181081674me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Hoare____Mirabell,type,
% 0.34/0.78 semila2050116131_a_o_o: ( ( hoare_2091234717iple_a > $o ) > $o ) > ( ( hoare_2091234717iple_a > $o ) > $o ) > ( hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Hoare____Mirabell_012,type,
% 0.34/0.78 semila1853742644te_o_o: ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Nat__Onat_M_Eo_J_,type,
% 0.34/0.78 semila72246288at_o_o: ( ( nat > $o ) > $o ) > ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_Eo_M_Eo_J,type,
% 0.34/0.78 semila2062604954up_o_o: ( $o > $o ) > ( $o > $o ) > $o > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.34/0.78 semila1780557381name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Hoare____Mirabelle____n,type,
% 0.34/0.78 semila1052848428le_a_o: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Hoare____Mirabelle____n_013,type,
% 0.34/0.78 semila1122118281tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.34/0.78 semila848761471_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_Eo,type,
% 0.34/0.78 semila10642723_sup_o: $o > $o > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000tc__Nat__Onat,type,
% 0.34/0.78 semila972727038up_nat: nat > nat > nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Nat_OSuc,type,
% 0.34/0.78 suc: nat > nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Nat_Onat_Onat__case_000_Eo,type,
% 0.34/0.78 nat_case_o: $o > ( nat > $o ) > nat > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Nat_Onat_Onat__case_000tc__Nat__Onat,type,
% 0.34/0.78 nat_case_nat: nat > ( nat > nat ) > nat > nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Nat_Osize__class_Osize_000tc__Com__Ocom,type,
% 0.34/0.78 size_size_com: com > nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Nat_Osize__class_Osize_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It_,type,
% 0.34/0.78 size_s1040486067iple_a: hoare_2091234717iple_a > nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Nat_Osize__class_Osize_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc,type,
% 0.34/0.78 size_s1186992420_state: hoare_1708887482_state > nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Natural_Oevalc,type,
% 0.34/0.78 evalc: com > state > state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Natural_Oevaln,type,
% 0.34/0.78 evaln: com > state > nat > state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Option_Othe_000tc__Com__Ocom,type,
% 0.34/0.78 the_com: option_com > com ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_I_062_Itc__Hoare____Mirabelle____n,type,
% 0.34/0.78 bot_bo690906872_o_o_o: ( ( hoare_2091234717iple_a > $o ) > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.34/0.78 bot_bot_pname_o_o: ( pname > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdf,type,
% 0.34/0.78 bot_bo1957696069_a_o_o: ( hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdf_014,type,
% 0.34/0.78 bot_bo1678742418te_o_o: ( hoare_1708887482_state > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.34/0.78 bot_bot_nat_o_o: ( nat > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_Eo_M_Eo_J,type,
% 0.34/0.78 bot_bot_o_o: $o > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.34/0.78 bot_bot_pname_o: pname > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__O,type,
% 0.34/0.78 bot_bo1791335050le_a_o: hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__O_015,type,
% 0.34/0.78 bot_bo19817387tate_o: hoare_1708887482_state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.34/0.78 bot_bot_nat_o: nat > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Orderings_Obot__class_Obot_000_Eo,type,
% 0.34/0.78 bot_bot_o: $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Orderings_Obot__class_Obot_000tc__Nat__Onat,type,
% 0.34/0.78 bot_bot_nat: nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat,type,
% 0.34/0.78 ord_less_nat: nat > nat > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat,type,
% 0.34/0.78 ord_less_eq_nat: nat > nat > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_OCollect_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J,type,
% 0.34/0.78 collec1008234059le_a_o: ( ( hoare_2091234717iple_a > $o ) > $o ) > ( hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_OCollect_000tc__Com__Opname,type,
% 0.34/0.78 collect_pname: ( pname > $o ) > pname > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_OCollect_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J,type,
% 0.34/0.78 collec992574898iple_a: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_OCollect_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost,type,
% 0.34/0.78 collec1568722789_state: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_OCollect_000tc__Nat__Onat,type,
% 0.34/0.78 collect_nat: ( nat > $o ) > nat > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_M,type,
% 0.34/0.78 image_784579955le_a_o: ( ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ) > ( ( hoare_2091234717iple_a > $o ) > $o ) > ( hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_M_016,type,
% 0.34/0.78 image_1908519857_pname: ( ( hoare_2091234717iple_a > $o ) > pname ) > ( ( hoare_2091234717iple_a > $o ) > $o ) > pname > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_M_017,type,
% 0.34/0.78 image_136408202iple_a: ( ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a ) > ( ( hoare_2091234717iple_a > $o ) > $o ) > hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_M_018,type,
% 0.34/0.78 image_1501246093_state: ( ( hoare_2091234717iple_a > $o ) > hoare_1708887482_state ) > ( ( hoare_2091234717iple_a > $o ) > $o ) > hoare_1708887482_state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_M_019,type,
% 0.34/0.78 image_75520503_o_nat: ( ( hoare_2091234717iple_a > $o ) > nat ) > ( ( hoare_2091234717iple_a > $o ) > $o ) > nat > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv,type,
% 0.34/0.78 image_742317343le_a_o: ( pname > hoare_2091234717iple_a > $o ) > ( pname > $o ) > ( hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,type,
% 0.34/0.78 image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otri,type,
% 0.34/0.78 image_231808478iple_a: ( pname > hoare_2091234717iple_a ) > ( pname > $o ) > hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otri_020,type,
% 0.34/0.78 image_1116629049_state: ( pname > hoare_1708887482_state ) > ( pname > $o ) > hoare_1708887482_state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Nat__Onat,type,
% 0.34/0.78 image_pname_nat: ( pname > nat ) > ( pname > $o ) > nat > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_000_062,type,
% 0.34/0.78 image_1642350072le_a_o: ( hoare_2091234717iple_a > hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_000tc__,type,
% 0.34/0.78 image_924789612_pname: ( hoare_2091234717iple_a > pname ) > ( hoare_2091234717iple_a > $o ) > pname > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_000tc___021,type,
% 0.34/0.78 image_1661191109iple_a: ( hoare_2091234717iple_a > hoare_2091234717iple_a ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_000tc___022,type,
% 0.34/0.78 image_1884482962_state: ( hoare_2091234717iple_a > hoare_1708887482_state ) > ( hoare_2091234717iple_a > $o ) > hoare_1708887482_state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_000tc___023,type,
% 0.34/0.78 image_1773322034_a_nat: ( hoare_2091234717iple_a > nat ) > ( hoare_2091234717iple_a > $o ) > nat > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostat,type,
% 0.34/0.78 image_293283184iple_a: ( hoare_1708887482_state > hoare_2091234717iple_a ) > ( hoare_1708887482_state > $o ) > hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostat_024,type,
% 0.34/0.78 image_757158439_state: ( hoare_1708887482_state > hoare_1708887482_state ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__,type,
% 0.34/0.78 image_1995609573le_a_o: ( nat > hoare_2091234717iple_a > $o ) > ( nat > $o ) > ( hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname,type,
% 0.34/0.78 image_nat_pname: ( nat > pname ) > ( nat > $o ) > pname > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otripl,type,
% 0.34/0.78 image_359186840iple_a: ( nat > hoare_2091234717iple_a ) > ( nat > $o ) > hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otripl_025,type,
% 0.34/0.78 image_514827263_state: ( nat > hoare_1708887482_state ) > ( nat > $o ) > hoare_1708887482_state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Nat__Onat,type,
% 0.34/0.78 image_nat_nat: ( nat > nat ) > ( nat > $o ) > nat > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oinsert_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It,type,
% 0.34/0.78 insert987231145_a_o_o: ( ( hoare_2091234717iple_a > $o ) > $o ) > ( ( ( hoare_2091234717iple_a > $o ) > $o ) > $o ) > ( ( hoare_2091234717iple_a > $o ) > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oinsert_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.34/0.78 insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oinsert_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_,type,
% 0.34/0.78 insert102003750le_a_o: ( hoare_2091234717iple_a > $o ) > ( ( hoare_2091234717iple_a > $o ) > $o ) > ( hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oinsert_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com,type,
% 0.34/0.78 insert949073679tate_o: ( hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oinsert_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.34/0.78 insert_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oinsert_000_Eo,type,
% 0.34/0.78 insert_o: $o > ( $o > $o ) > $o > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oinsert_000tc__Com__Opname,type,
% 0.34/0.78 insert_pname: pname > ( pname > $o ) > pname > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J,type,
% 0.34/0.78 insert1597628439iple_a: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Osta,type,
% 0.34/0.78 insert528405184_state: hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Oinsert_000tc__Nat__Onat,type,
% 0.34/0.78 insert_nat: nat > ( nat > $o ) > nat > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Othe__elem_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a,type,
% 0.34/0.78 the_el1618277441le_a_o: ( ( hoare_2091234717iple_a > $o ) > $o ) > hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Othe__elem_000tc__Com__Opname,type,
% 0.34/0.78 the_elem_pname: ( pname > $o ) > pname ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Othe__elem_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J,type,
% 0.34/0.78 the_el13400124iple_a: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Othe__elem_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__O,type,
% 0.34/0.78 the_el864710747_state: ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_Set_Othe__elem_000tc__Nat__Onat,type,
% 0.34/0.78 the_elem_nat: ( nat > $o ) > nat ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_fequal_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_M_Eo_,type,
% 0.34/0.78 fequal845167073le_a_o: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_fequal_000tc__Com__Opname,type,
% 0.34/0.78 fequal_pname: pname > pname > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_fequal_000tc__Com__Ostate,type,
% 0.34/0.78 fequal_state: state > state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J,type,
% 0.34/0.78 fequal1604381340iple_a: hoare_2091234717iple_a > hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J,type,
% 0.34/0.78 fequal224822779_state: hoare_1708887482_state > hoare_1708887482_state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_fequal_000tc__Nat__Onat,type,
% 0.34/0.78 fequal_nat: nat > nat > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_member_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J,type,
% 0.34/0.78 member1297825410_a_o_o: ( ( hoare_2091234717iple_a > $o ) > $o ) > ( ( ( hoare_2091234717iple_a > $o ) > $o ) > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_member_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.34/0.78 member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_member_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_M_Eo_,type,
% 0.34/0.78 member99268621le_a_o: ( hoare_2091234717iple_a > $o ) > ( ( hoare_2091234717iple_a > $o ) > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_member_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost,type,
% 0.34/0.78 member814030440tate_o: ( hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_member_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.34/0.78 member_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_member_000_Eo,type,
% 0.34/0.78 member_o: $o > ( $o > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_member_000tc__Com__Opname,type,
% 0.34/0.78 member_pname: pname > ( pname > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_member_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J,type,
% 0.34/0.78 member290856304iple_a: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_member_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J,type,
% 0.34/0.78 member451959335_state: hoare_1708887482_state > ( hoare_1708887482_state > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_c_member_000tc__Nat__Onat,type,
% 0.34/0.78 member_nat: nat > ( nat > $o ) > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_v_G,type,
% 0.34/0.78 g: hoare_2091234717iple_a > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_v_P,type,
% 0.34/0.78 p: pname > x_a > state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_v_Procs,type,
% 0.34/0.78 procs: pname > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_v_Q,type,
% 0.34/0.78 q: pname > x_a > state > $o ).
% 0.34/0.78
% 0.34/0.78 thf(sy_v_n,type,
% 0.34/0.78 n: nat ).
% 0.34/0.78
% 0.34/0.78 %----Relevant facts (1196)
% 0.34/0.78 thf(fact_0_triple_Oinject,axiom,
% 0.34/0.78 ! [Fun1_4: x_a > state > $o,Com_1: com,Fun2_4: x_a > state > $o,Fun1_3: x_a > state > $o,Com: com,Fun2_3: x_a > state > $o] :
% 0.34/0.78 ( ( ( hoare_657976383iple_a @ Fun1_4 @ Com_1 @ Fun2_4 )
% 0.34/0.78 = ( hoare_657976383iple_a @ Fun1_3 @ Com @ Fun2_3 ) )
% 0.34/0.78 <=> ( ( Fun1_4 = Fun1_3 )
% 0.34/0.78 & ( Com_1 = Com )
% 0.34/0.78 & ( Fun2_4 = Fun2_3 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_1_triple_Oinject,axiom,
% 0.34/0.78 ! [Fun1_4: state > state > $o,Com_1: com,Fun2_4: state > state > $o,Fun1_3: state > state > $o,Com: com,Fun2_3: state > state > $o] :
% 0.34/0.78 ( ( ( hoare_858012674_state @ Fun1_4 @ Com_1 @ Fun2_4 )
% 0.34/0.78 = ( hoare_858012674_state @ Fun1_3 @ Com @ Fun2_3 ) )
% 0.34/0.78 <=> ( ( Fun1_4 = Fun1_3 )
% 0.34/0.78 & ( Com_1 = Com )
% 0.34/0.78 & ( Fun2_4 = Fun2_3 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_2_hoare__valids__def,axiom,
% 0.34/0.78 ! [G_28: hoare_1708887482_state > $o,Ts_4: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( hoare_496444244_state @ G_28 @ Ts_4 )
% 0.34/0.78 <=> ! [N: nat] :
% 0.34/0.78 ( ! [X: hoare_1708887482_state] :
% 0.34/0.78 ( ( member451959335_state @ X @ G_28 )
% 0.34/0.78 => ( hoare_23738522_state @ N @ X ) )
% 0.34/0.78 => ! [X: hoare_1708887482_state] :
% 0.34/0.78 ( ( member451959335_state @ X @ Ts_4 )
% 0.34/0.78 => ( hoare_23738522_state @ N @ X ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_3_hoare__valids__def,axiom,
% 0.34/0.78 ! [G_28: hoare_2091234717iple_a > $o,Ts_4: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( hoare_1805689709lids_a @ G_28 @ Ts_4 )
% 0.34/0.78 <=> ! [N: nat] :
% 0.34/0.78 ( ! [X: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( member290856304iple_a @ X @ G_28 )
% 0.34/0.78 => ( hoare_1421888935alid_a @ N @ X ) )
% 0.34/0.78 => ! [X: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( member290856304iple_a @ X @ Ts_4 )
% 0.34/0.78 => ( hoare_1421888935alid_a @ N @ X ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_4_hoare__derivs_OBody,axiom,
% 0.34/0.78 ! [G_27: hoare_1708887482_state > $o,P_36: pname > state > state > $o,Q_20: pname > state > state > $o,Procs_1: pname > $o] :
% 0.34/0.78 ( ( hoare_90032982_state
% 0.34/0.78 @ ( semila1122118281tate_o @ G_27
% 0.34/0.78 @ ( image_1116629049_state
% 0.34/0.78 @ ^ [P_9: pname] : ( hoare_858012674_state @ ( P_36 @ P_9 ) @ ( body @ P_9 ) @ ( Q_20 @ P_9 ) )
% 0.34/0.78 @ Procs_1 ) )
% 0.34/0.78 @ ( image_1116629049_state
% 0.34/0.78 @ ^ [P_9: pname] : ( hoare_858012674_state @ ( P_36 @ P_9 ) @ ( the_com @ ( body_1 @ P_9 ) ) @ ( Q_20 @ P_9 ) )
% 0.34/0.78 @ Procs_1 ) )
% 0.34/0.78 => ( hoare_90032982_state @ G_27
% 0.34/0.78 @ ( image_1116629049_state
% 0.34/0.78 @ ^ [P_9: pname] : ( hoare_858012674_state @ ( P_36 @ P_9 ) @ ( body @ P_9 ) @ ( Q_20 @ P_9 ) )
% 0.34/0.78 @ Procs_1 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_5_hoare__derivs_OBody,axiom,
% 0.34/0.78 ! [G_27: hoare_2091234717iple_a > $o,P_36: pname > x_a > state > $o,Q_20: pname > x_a > state > $o,Procs_1: pname > $o] :
% 0.34/0.78 ( ( hoare_1467856363rivs_a
% 0.34/0.78 @ ( semila1052848428le_a_o @ G_27
% 0.34/0.78 @ ( image_231808478iple_a
% 0.34/0.78 @ ^ [P_9: pname] : ( hoare_657976383iple_a @ ( P_36 @ P_9 ) @ ( body @ P_9 ) @ ( Q_20 @ P_9 ) )
% 0.34/0.78 @ Procs_1 ) )
% 0.34/0.78 @ ( image_231808478iple_a
% 0.34/0.78 @ ^ [P_9: pname] : ( hoare_657976383iple_a @ ( P_36 @ P_9 ) @ ( the_com @ ( body_1 @ P_9 ) ) @ ( Q_20 @ P_9 ) )
% 0.34/0.78 @ Procs_1 ) )
% 0.34/0.78 => ( hoare_1467856363rivs_a @ G_27
% 0.34/0.78 @ ( image_231808478iple_a
% 0.34/0.78 @ ^ [P_9: pname] : ( hoare_657976383iple_a @ ( P_36 @ P_9 ) @ ( body @ P_9 ) @ ( Q_20 @ P_9 ) )
% 0.34/0.78 @ Procs_1 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_6_UnE,axiom,
% 0.34/0.78 ! [C_34: nat,A_129: nat > $o,B_71: nat > $o] :
% 0.34/0.78 ( ( member_nat @ C_34 @ ( semila848761471_nat_o @ A_129 @ B_71 ) )
% 0.34/0.78 => ( ~ ( member_nat @ C_34 @ A_129 )
% 0.34/0.78 => ( member_nat @ C_34 @ B_71 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_7_UnE,axiom,
% 0.34/0.78 ! [C_34: hoare_2091234717iple_a > $o,A_129: ( hoare_2091234717iple_a > $o ) > $o,B_71: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( member99268621le_a_o @ C_34 @ ( semila2050116131_a_o_o @ A_129 @ B_71 ) )
% 0.34/0.78 => ( ~ ( member99268621le_a_o @ C_34 @ A_129 )
% 0.34/0.78 => ( member99268621le_a_o @ C_34 @ B_71 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_8_UnE,axiom,
% 0.34/0.78 ! [C_34: hoare_1708887482_state,A_129: hoare_1708887482_state > $o,B_71: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( member451959335_state @ C_34 @ ( semila1122118281tate_o @ A_129 @ B_71 ) )
% 0.34/0.78 => ( ~ ( member451959335_state @ C_34 @ A_129 )
% 0.34/0.78 => ( member451959335_state @ C_34 @ B_71 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_9_UnE,axiom,
% 0.34/0.78 ! [C_34: hoare_2091234717iple_a,A_129: hoare_2091234717iple_a > $o,B_71: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( member290856304iple_a @ C_34 @ ( semila1052848428le_a_o @ A_129 @ B_71 ) )
% 0.34/0.78 => ( ~ ( member290856304iple_a @ C_34 @ A_129 )
% 0.34/0.78 => ( member290856304iple_a @ C_34 @ B_71 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_10_UnE,axiom,
% 0.34/0.78 ! [C_34: pname,A_129: pname > $o,B_71: pname > $o] :
% 0.34/0.78 ( ( member_pname @ C_34 @ ( semila1780557381name_o @ A_129 @ B_71 ) )
% 0.34/0.78 => ( ~ ( member_pname @ C_34 @ A_129 )
% 0.34/0.78 => ( member_pname @ C_34 @ B_71 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_11_sup1E,axiom,
% 0.34/0.78 ! [A_128: nat > $o,B_70: nat > $o,X_51: nat] :
% 0.34/0.78 ( ( semila848761471_nat_o @ A_128 @ B_70 @ X_51 )
% 0.34/0.78 => ( ~ ( A_128 @ X_51 )
% 0.34/0.78 => ( B_70 @ X_51 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_12_sup1E,axiom,
% 0.34/0.78 ! [A_128: ( hoare_2091234717iple_a > $o ) > $o,B_70: ( hoare_2091234717iple_a > $o ) > $o,X_51: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ A_128 @ B_70 @ X_51 )
% 0.34/0.78 => ( ~ ( A_128 @ X_51 )
% 0.34/0.78 => ( B_70 @ X_51 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_13_sup1E,axiom,
% 0.34/0.78 ! [A_128: hoare_1708887482_state > $o,B_70: hoare_1708887482_state > $o,X_51: hoare_1708887482_state] :
% 0.34/0.78 ( ( semila1122118281tate_o @ A_128 @ B_70 @ X_51 )
% 0.34/0.78 => ( ~ ( A_128 @ X_51 )
% 0.34/0.78 => ( B_70 @ X_51 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_14_sup1E,axiom,
% 0.34/0.78 ! [A_128: pname > $o,B_70: pname > $o,X_51: pname] :
% 0.34/0.78 ( ( semila1780557381name_o @ A_128 @ B_70 @ X_51 )
% 0.34/0.78 => ( ~ ( A_128 @ X_51 )
% 0.34/0.78 => ( B_70 @ X_51 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_15_sup1E,axiom,
% 0.34/0.78 ! [A_128: hoare_2091234717iple_a > $o,B_70: hoare_2091234717iple_a > $o,X_51: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ A_128 @ B_70 @ X_51 )
% 0.34/0.78 => ( ~ ( A_128 @ X_51 )
% 0.34/0.78 => ( B_70 @ X_51 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_16_sup1CI,axiom,
% 0.34/0.78 ! [A_127: nat > $o,B_69: nat > $o,X_50: nat] :
% 0.34/0.78 ( ( ~ ( B_69 @ X_50 )
% 0.34/0.78 => ( A_127 @ X_50 ) )
% 0.34/0.78 => ( semila848761471_nat_o @ A_127 @ B_69 @ X_50 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_17_sup1CI,axiom,
% 0.34/0.78 ! [A_127: ( hoare_2091234717iple_a > $o ) > $o,B_69: ( hoare_2091234717iple_a > $o ) > $o,X_50: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( ~ ( B_69 @ X_50 )
% 0.34/0.78 => ( A_127 @ X_50 ) )
% 0.34/0.78 => ( semila2050116131_a_o_o @ A_127 @ B_69 @ X_50 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_18_sup1CI,axiom,
% 0.34/0.78 ! [A_127: hoare_1708887482_state > $o,B_69: hoare_1708887482_state > $o,X_50: hoare_1708887482_state] :
% 0.34/0.78 ( ( ~ ( B_69 @ X_50 )
% 0.34/0.78 => ( A_127 @ X_50 ) )
% 0.34/0.78 => ( semila1122118281tate_o @ A_127 @ B_69 @ X_50 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_19_sup1CI,axiom,
% 0.34/0.78 ! [A_127: pname > $o,B_69: pname > $o,X_50: pname] :
% 0.34/0.78 ( ( ~ ( B_69 @ X_50 )
% 0.34/0.78 => ( A_127 @ X_50 ) )
% 0.34/0.78 => ( semila1780557381name_o @ A_127 @ B_69 @ X_50 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_20_sup1CI,axiom,
% 0.34/0.78 ! [A_127: hoare_2091234717iple_a > $o,B_69: hoare_2091234717iple_a > $o,X_50: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( ~ ( B_69 @ X_50 )
% 0.34/0.78 => ( A_127 @ X_50 ) )
% 0.34/0.78 => ( semila1052848428le_a_o @ A_127 @ B_69 @ X_50 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_21_UnCI,axiom,
% 0.34/0.78 ! [A_126: nat > $o,C_33: nat,B_68: nat > $o] :
% 0.34/0.78 ( ( ~ ( member_nat @ C_33 @ B_68 )
% 0.34/0.78 => ( member_nat @ C_33 @ A_126 ) )
% 0.34/0.78 => ( member_nat @ C_33 @ ( semila848761471_nat_o @ A_126 @ B_68 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_22_UnCI,axiom,
% 0.34/0.78 ! [A_126: ( hoare_2091234717iple_a > $o ) > $o,C_33: hoare_2091234717iple_a > $o,B_68: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( ~ ( member99268621le_a_o @ C_33 @ B_68 )
% 0.34/0.78 => ( member99268621le_a_o @ C_33 @ A_126 ) )
% 0.34/0.78 => ( member99268621le_a_o @ C_33 @ ( semila2050116131_a_o_o @ A_126 @ B_68 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_23_UnCI,axiom,
% 0.34/0.78 ! [A_126: hoare_1708887482_state > $o,C_33: hoare_1708887482_state,B_68: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( ~ ( member451959335_state @ C_33 @ B_68 )
% 0.34/0.78 => ( member451959335_state @ C_33 @ A_126 ) )
% 0.34/0.78 => ( member451959335_state @ C_33 @ ( semila1122118281tate_o @ A_126 @ B_68 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_24_UnCI,axiom,
% 0.34/0.78 ! [A_126: hoare_2091234717iple_a > $o,C_33: hoare_2091234717iple_a,B_68: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( ~ ( member290856304iple_a @ C_33 @ B_68 )
% 0.34/0.78 => ( member290856304iple_a @ C_33 @ A_126 ) )
% 0.34/0.78 => ( member290856304iple_a @ C_33 @ ( semila1052848428le_a_o @ A_126 @ B_68 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_25_UnCI,axiom,
% 0.34/0.78 ! [A_126: pname > $o,C_33: pname,B_68: pname > $o] :
% 0.34/0.78 ( ( ~ ( member_pname @ C_33 @ B_68 )
% 0.34/0.78 => ( member_pname @ C_33 @ A_126 ) )
% 0.34/0.78 => ( member_pname @ C_33 @ ( semila1780557381name_o @ A_126 @ B_68 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_26_image__eqI,axiom,
% 0.34/0.78 ! [A_125: nat > $o,B_67: nat,F_50: nat > nat,X_49: nat] :
% 0.34/0.78 ( ( B_67
% 0.34/0.78 = ( F_50 @ X_49 ) )
% 0.34/0.78 => ( ( member_nat @ X_49 @ A_125 )
% 0.34/0.78 => ( member_nat @ B_67 @ ( image_nat_nat @ F_50 @ A_125 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_27_image__eqI,axiom,
% 0.34/0.78 ! [A_125: pname > $o,B_67: hoare_1708887482_state,F_50: pname > hoare_1708887482_state,X_49: pname] :
% 0.34/0.78 ( ( B_67
% 0.34/0.78 = ( F_50 @ X_49 ) )
% 0.34/0.78 => ( ( member_pname @ X_49 @ A_125 )
% 0.34/0.78 => ( member451959335_state @ B_67 @ ( image_1116629049_state @ F_50 @ A_125 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_28_image__eqI,axiom,
% 0.34/0.78 ! [A_125: pname > $o,B_67: nat,F_50: pname > nat,X_49: pname] :
% 0.34/0.78 ( ( B_67
% 0.34/0.78 = ( F_50 @ X_49 ) )
% 0.34/0.78 => ( ( member_pname @ X_49 @ A_125 )
% 0.34/0.78 => ( member_nat @ B_67 @ ( image_pname_nat @ F_50 @ A_125 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_29_image__eqI,axiom,
% 0.34/0.78 ! [A_125: pname > $o,B_67: hoare_2091234717iple_a > $o,F_50: pname > hoare_2091234717iple_a > $o,X_49: pname] :
% 0.34/0.78 ( ( B_67
% 0.34/0.78 = ( F_50 @ X_49 ) )
% 0.34/0.78 => ( ( member_pname @ X_49 @ A_125 )
% 0.34/0.78 => ( member99268621le_a_o @ B_67 @ ( image_742317343le_a_o @ F_50 @ A_125 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_30_image__eqI,axiom,
% 0.34/0.78 ! [A_125: nat > $o,B_67: pname,F_50: nat > pname,X_49: nat] :
% 0.34/0.78 ( ( B_67
% 0.34/0.78 = ( F_50 @ X_49 ) )
% 0.34/0.78 => ( ( member_nat @ X_49 @ A_125 )
% 0.34/0.78 => ( member_pname @ B_67 @ ( image_nat_pname @ F_50 @ A_125 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_31_image__eqI,axiom,
% 0.34/0.78 ! [A_125: ( hoare_2091234717iple_a > $o ) > $o,B_67: pname,F_50: ( hoare_2091234717iple_a > $o ) > pname,X_49: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( B_67
% 0.34/0.78 = ( F_50 @ X_49 ) )
% 0.34/0.78 => ( ( member99268621le_a_o @ X_49 @ A_125 )
% 0.34/0.78 => ( member_pname @ B_67 @ ( image_1908519857_pname @ F_50 @ A_125 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_32_image__eqI,axiom,
% 0.34/0.78 ! [A_125: hoare_2091234717iple_a > $o,B_67: pname,F_50: hoare_2091234717iple_a > pname,X_49: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( B_67
% 0.34/0.78 = ( F_50 @ X_49 ) )
% 0.34/0.78 => ( ( member290856304iple_a @ X_49 @ A_125 )
% 0.34/0.78 => ( member_pname @ B_67 @ ( image_924789612_pname @ F_50 @ A_125 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_33_image__eqI,axiom,
% 0.34/0.78 ! [A_125: pname > $o,B_67: hoare_2091234717iple_a,F_50: pname > hoare_2091234717iple_a,X_49: pname] :
% 0.34/0.78 ( ( B_67
% 0.34/0.78 = ( F_50 @ X_49 ) )
% 0.34/0.78 => ( ( member_pname @ X_49 @ A_125 )
% 0.34/0.78 => ( member290856304iple_a @ B_67 @ ( image_231808478iple_a @ F_50 @ A_125 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_34_image__Un,axiom,
% 0.34/0.78 ! [F_49: nat > nat,A_124: nat > $o,B_66: nat > $o] :
% 0.34/0.78 ( ( image_nat_nat @ F_49 @ ( semila848761471_nat_o @ A_124 @ B_66 ) )
% 0.34/0.78 = ( semila848761471_nat_o @ ( image_nat_nat @ F_49 @ A_124 ) @ ( image_nat_nat @ F_49 @ B_66 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_35_image__Un,axiom,
% 0.34/0.78 ! [F_49: pname > hoare_1708887482_state,A_124: pname > $o,B_66: pname > $o] :
% 0.34/0.78 ( ( image_1116629049_state @ F_49 @ ( semila1780557381name_o @ A_124 @ B_66 ) )
% 0.34/0.78 = ( semila1122118281tate_o @ ( image_1116629049_state @ F_49 @ A_124 ) @ ( image_1116629049_state @ F_49 @ B_66 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_36_image__Un,axiom,
% 0.34/0.78 ! [F_49: hoare_2091234717iple_a > nat,A_124: hoare_2091234717iple_a > $o,B_66: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( image_1773322034_a_nat @ F_49 @ ( semila1052848428le_a_o @ A_124 @ B_66 ) )
% 0.34/0.78 = ( semila848761471_nat_o @ ( image_1773322034_a_nat @ F_49 @ A_124 ) @ ( image_1773322034_a_nat @ F_49 @ B_66 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_37_image__Un,axiom,
% 0.34/0.78 ! [F_49: hoare_2091234717iple_a > hoare_2091234717iple_a > $o,A_124: hoare_2091234717iple_a > $o,B_66: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( image_1642350072le_a_o @ F_49 @ ( semila1052848428le_a_o @ A_124 @ B_66 ) )
% 0.34/0.78 = ( semila2050116131_a_o_o @ ( image_1642350072le_a_o @ F_49 @ A_124 ) @ ( image_1642350072le_a_o @ F_49 @ B_66 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_38_image__Un,axiom,
% 0.34/0.78 ! [F_49: hoare_2091234717iple_a > hoare_1708887482_state,A_124: hoare_2091234717iple_a > $o,B_66: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( image_1884482962_state @ F_49 @ ( semila1052848428le_a_o @ A_124 @ B_66 ) )
% 0.34/0.78 = ( semila1122118281tate_o @ ( image_1884482962_state @ F_49 @ A_124 ) @ ( image_1884482962_state @ F_49 @ B_66 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_39_image__Un,axiom,
% 0.34/0.78 ! [F_49: hoare_2091234717iple_a > pname,A_124: hoare_2091234717iple_a > $o,B_66: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( image_924789612_pname @ F_49 @ ( semila1052848428le_a_o @ A_124 @ B_66 ) )
% 0.34/0.78 = ( semila1780557381name_o @ ( image_924789612_pname @ F_49 @ A_124 ) @ ( image_924789612_pname @ F_49 @ B_66 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_40_image__Un,axiom,
% 0.34/0.78 ! [F_49: nat > hoare_2091234717iple_a,A_124: nat > $o,B_66: nat > $o] :
% 0.34/0.78 ( ( image_359186840iple_a @ F_49 @ ( semila848761471_nat_o @ A_124 @ B_66 ) )
% 0.34/0.78 = ( semila1052848428le_a_o @ ( image_359186840iple_a @ F_49 @ A_124 ) @ ( image_359186840iple_a @ F_49 @ B_66 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_41_image__Un,axiom,
% 0.34/0.78 ! [F_49: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a,A_124: ( hoare_2091234717iple_a > $o ) > $o,B_66: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( image_136408202iple_a @ F_49 @ ( semila2050116131_a_o_o @ A_124 @ B_66 ) )
% 0.34/0.78 = ( semila1052848428le_a_o @ ( image_136408202iple_a @ F_49 @ A_124 ) @ ( image_136408202iple_a @ F_49 @ B_66 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_42_image__Un,axiom,
% 0.34/0.78 ! [F_49: hoare_1708887482_state > hoare_2091234717iple_a,A_124: hoare_1708887482_state > $o,B_66: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( image_293283184iple_a @ F_49 @ ( semila1122118281tate_o @ A_124 @ B_66 ) )
% 0.34/0.78 = ( semila1052848428le_a_o @ ( image_293283184iple_a @ F_49 @ A_124 ) @ ( image_293283184iple_a @ F_49 @ B_66 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_43_image__Un,axiom,
% 0.34/0.78 ! [F_49: pname > hoare_2091234717iple_a,A_124: pname > $o,B_66: pname > $o] :
% 0.34/0.78 ( ( image_231808478iple_a @ F_49 @ ( semila1780557381name_o @ A_124 @ B_66 ) )
% 0.34/0.78 = ( semila1052848428le_a_o @ ( image_231808478iple_a @ F_49 @ A_124 ) @ ( image_231808478iple_a @ F_49 @ B_66 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_44_sup__fun__def,axiom,
% 0.34/0.78 ! [F_48: nat > $o,G_26: nat > $o,X: nat] :
% 0.34/0.78 ( ( semila848761471_nat_o @ F_48 @ G_26 @ X )
% 0.34/0.78 <=> ( semila10642723_sup_o @ ( F_48 @ X ) @ ( G_26 @ X ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_45_sup__fun__def,axiom,
% 0.34/0.78 ! [F_48: ( hoare_2091234717iple_a > $o ) > $o,G_26: ( hoare_2091234717iple_a > $o ) > $o,X: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ F_48 @ G_26 @ X )
% 0.34/0.78 <=> ( semila10642723_sup_o @ ( F_48 @ X ) @ ( G_26 @ X ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_46_sup__fun__def,axiom,
% 0.34/0.78 ! [F_48: hoare_1708887482_state > $o,G_26: hoare_1708887482_state > $o,X: hoare_1708887482_state] :
% 0.34/0.78 ( ( semila1122118281tate_o @ F_48 @ G_26 @ X )
% 0.34/0.78 <=> ( semila10642723_sup_o @ ( F_48 @ X ) @ ( G_26 @ X ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_47_sup__fun__def,axiom,
% 0.34/0.78 ! [F_48: pname > $o,G_26: pname > $o,X: pname] :
% 0.34/0.78 ( ( semila1780557381name_o @ F_48 @ G_26 @ X )
% 0.34/0.78 <=> ( semila10642723_sup_o @ ( F_48 @ X ) @ ( G_26 @ X ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_48_sup__fun__def,axiom,
% 0.34/0.78 ! [F_48: hoare_2091234717iple_a > $o,G_26: hoare_2091234717iple_a > $o,X: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ F_48 @ G_26 @ X )
% 0.34/0.78 <=> ( semila10642723_sup_o @ ( F_48 @ X ) @ ( G_26 @ X ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_49_sup__apply,axiom,
% 0.34/0.78 ! [F_47: nat > $o,G_25: nat > $o,X_48: nat] :
% 0.34/0.78 ( ( semila848761471_nat_o @ F_47 @ G_25 @ X_48 )
% 0.34/0.78 <=> ( semila10642723_sup_o @ ( F_47 @ X_48 ) @ ( G_25 @ X_48 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_50_sup__apply,axiom,
% 0.34/0.78 ! [F_47: ( hoare_2091234717iple_a > $o ) > $o,G_25: ( hoare_2091234717iple_a > $o ) > $o,X_48: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ F_47 @ G_25 @ X_48 )
% 0.34/0.78 <=> ( semila10642723_sup_o @ ( F_47 @ X_48 ) @ ( G_25 @ X_48 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_51_sup__apply,axiom,
% 0.34/0.78 ! [F_47: hoare_1708887482_state > $o,G_25: hoare_1708887482_state > $o,X_48: hoare_1708887482_state] :
% 0.34/0.78 ( ( semila1122118281tate_o @ F_47 @ G_25 @ X_48 )
% 0.34/0.78 <=> ( semila10642723_sup_o @ ( F_47 @ X_48 ) @ ( G_25 @ X_48 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_52_sup__apply,axiom,
% 0.34/0.78 ! [F_47: pname > $o,G_25: pname > $o,X_48: pname] :
% 0.34/0.78 ( ( semila1780557381name_o @ F_47 @ G_25 @ X_48 )
% 0.34/0.78 <=> ( semila10642723_sup_o @ ( F_47 @ X_48 ) @ ( G_25 @ X_48 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_53_sup__apply,axiom,
% 0.34/0.78 ! [F_47: hoare_2091234717iple_a > $o,G_25: hoare_2091234717iple_a > $o,X_48: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ F_47 @ G_25 @ X_48 )
% 0.34/0.78 <=> ( semila10642723_sup_o @ ( F_47 @ X_48 ) @ ( G_25 @ X_48 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_54_cut,axiom,
% 0.34/0.78 ! [G_24: hoare_2091234717iple_a > $o,G_23: hoare_2091234717iple_a > $o,Ts_3: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( hoare_1467856363rivs_a @ G_23 @ Ts_3 )
% 0.34/0.78 => ( ( hoare_1467856363rivs_a @ G_24 @ G_23 )
% 0.34/0.78 => ( hoare_1467856363rivs_a @ G_24 @ Ts_3 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_55_cut,axiom,
% 0.34/0.78 ! [G_24: hoare_1708887482_state > $o,G_23: hoare_1708887482_state > $o,Ts_3: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( hoare_90032982_state @ G_23 @ Ts_3 )
% 0.34/0.78 => ( ( hoare_90032982_state @ G_24 @ G_23 )
% 0.34/0.78 => ( hoare_90032982_state @ G_24 @ Ts_3 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_56_sup__assoc,axiom,
% 0.34/0.78 ! [X_47: nat > $o,Y_20: nat > $o,Z_11: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ ( semila848761471_nat_o @ X_47 @ Y_20 ) @ Z_11 )
% 0.34/0.78 = ( semila848761471_nat_o @ X_47 @ ( semila848761471_nat_o @ Y_20 @ Z_11 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_57_sup__assoc,axiom,
% 0.34/0.78 ! [X_47: nat,Y_20: nat,Z_11: nat] :
% 0.34/0.78 ( ( semila972727038up_nat @ ( semila972727038up_nat @ X_47 @ Y_20 ) @ Z_11 )
% 0.34/0.78 = ( semila972727038up_nat @ X_47 @ ( semila972727038up_nat @ Y_20 @ Z_11 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_58_sup__assoc,axiom,
% 0.34/0.78 ! [X_47: ( hoare_2091234717iple_a > $o ) > $o,Y_20: ( hoare_2091234717iple_a > $o ) > $o,Z_11: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ ( semila2050116131_a_o_o @ X_47 @ Y_20 ) @ Z_11 )
% 0.34/0.78 = ( semila2050116131_a_o_o @ X_47 @ ( semila2050116131_a_o_o @ Y_20 @ Z_11 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_59_sup__assoc,axiom,
% 0.34/0.78 ! [X_47: hoare_1708887482_state > $o,Y_20: hoare_1708887482_state > $o,Z_11: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ ( semila1122118281tate_o @ X_47 @ Y_20 ) @ Z_11 )
% 0.34/0.78 = ( semila1122118281tate_o @ X_47 @ ( semila1122118281tate_o @ Y_20 @ Z_11 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_60_sup__assoc,axiom,
% 0.34/0.78 ! [X_47: pname > $o,Y_20: pname > $o,Z_11: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ ( semila1780557381name_o @ X_47 @ Y_20 ) @ Z_11 )
% 0.34/0.78 = ( semila1780557381name_o @ X_47 @ ( semila1780557381name_o @ Y_20 @ Z_11 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_61_sup__assoc,axiom,
% 0.34/0.78 ! [X_47: $o,Y_20: $o,Z_11: $o] :
% 0.34/0.78 ( ( semila10642723_sup_o @ ( semila10642723_sup_o @ X_47 @ Y_20 ) @ Z_11 )
% 0.34/0.78 <=> ( semila10642723_sup_o @ X_47 @ ( semila10642723_sup_o @ Y_20 @ Z_11 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_62_sup__assoc,axiom,
% 0.34/0.78 ! [X_47: hoare_2091234717iple_a > $o,Y_20: hoare_2091234717iple_a > $o,Z_11: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ ( semila1052848428le_a_o @ X_47 @ Y_20 ) @ Z_11 )
% 0.34/0.78 = ( semila1052848428le_a_o @ X_47 @ ( semila1052848428le_a_o @ Y_20 @ Z_11 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_63_inf__sup__aci_I6_J,axiom,
% 0.34/0.78 ! [X_46: nat > $o,Y_19: nat > $o,Z_10: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ ( semila848761471_nat_o @ X_46 @ Y_19 ) @ Z_10 )
% 0.34/0.78 = ( semila848761471_nat_o @ X_46 @ ( semila848761471_nat_o @ Y_19 @ Z_10 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_64_inf__sup__aci_I6_J,axiom,
% 0.34/0.78 ! [X_46: nat,Y_19: nat,Z_10: nat] :
% 0.34/0.78 ( ( semila972727038up_nat @ ( semila972727038up_nat @ X_46 @ Y_19 ) @ Z_10 )
% 0.34/0.78 = ( semila972727038up_nat @ X_46 @ ( semila972727038up_nat @ Y_19 @ Z_10 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_65_inf__sup__aci_I6_J,axiom,
% 0.34/0.78 ! [X_46: ( hoare_2091234717iple_a > $o ) > $o,Y_19: ( hoare_2091234717iple_a > $o ) > $o,Z_10: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ ( semila2050116131_a_o_o @ X_46 @ Y_19 ) @ Z_10 )
% 0.34/0.78 = ( semila2050116131_a_o_o @ X_46 @ ( semila2050116131_a_o_o @ Y_19 @ Z_10 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_66_inf__sup__aci_I6_J,axiom,
% 0.34/0.78 ! [X_46: hoare_1708887482_state > $o,Y_19: hoare_1708887482_state > $o,Z_10: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ ( semila1122118281tate_o @ X_46 @ Y_19 ) @ Z_10 )
% 0.34/0.78 = ( semila1122118281tate_o @ X_46 @ ( semila1122118281tate_o @ Y_19 @ Z_10 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_67_inf__sup__aci_I6_J,axiom,
% 0.34/0.78 ! [X_46: pname > $o,Y_19: pname > $o,Z_10: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ ( semila1780557381name_o @ X_46 @ Y_19 ) @ Z_10 )
% 0.34/0.78 = ( semila1780557381name_o @ X_46 @ ( semila1780557381name_o @ Y_19 @ Z_10 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_68_inf__sup__aci_I6_J,axiom,
% 0.34/0.78 ! [X_46: $o,Y_19: $o,Z_10: $o] :
% 0.34/0.78 ( ( semila10642723_sup_o @ ( semila10642723_sup_o @ X_46 @ Y_19 ) @ Z_10 )
% 0.34/0.78 <=> ( semila10642723_sup_o @ X_46 @ ( semila10642723_sup_o @ Y_19 @ Z_10 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_69_inf__sup__aci_I6_J,axiom,
% 0.34/0.78 ! [X_46: hoare_2091234717iple_a > $o,Y_19: hoare_2091234717iple_a > $o,Z_10: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ ( semila1052848428le_a_o @ X_46 @ Y_19 ) @ Z_10 )
% 0.34/0.78 = ( semila1052848428le_a_o @ X_46 @ ( semila1052848428le_a_o @ Y_19 @ Z_10 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_70_sup_Oassoc,axiom,
% 0.34/0.78 ! [A_123: nat > $o,B_65: nat > $o,C_32: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ ( semila848761471_nat_o @ A_123 @ B_65 ) @ C_32 )
% 0.34/0.78 = ( semila848761471_nat_o @ A_123 @ ( semila848761471_nat_o @ B_65 @ C_32 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_71_sup_Oassoc,axiom,
% 0.34/0.78 ! [A_123: nat,B_65: nat,C_32: nat] :
% 0.34/0.78 ( ( semila972727038up_nat @ ( semila972727038up_nat @ A_123 @ B_65 ) @ C_32 )
% 0.34/0.78 = ( semila972727038up_nat @ A_123 @ ( semila972727038up_nat @ B_65 @ C_32 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_72_sup_Oassoc,axiom,
% 0.34/0.78 ! [A_123: ( hoare_2091234717iple_a > $o ) > $o,B_65: ( hoare_2091234717iple_a > $o ) > $o,C_32: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ ( semila2050116131_a_o_o @ A_123 @ B_65 ) @ C_32 )
% 0.34/0.78 = ( semila2050116131_a_o_o @ A_123 @ ( semila2050116131_a_o_o @ B_65 @ C_32 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_73_sup_Oassoc,axiom,
% 0.34/0.78 ! [A_123: hoare_1708887482_state > $o,B_65: hoare_1708887482_state > $o,C_32: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ ( semila1122118281tate_o @ A_123 @ B_65 ) @ C_32 )
% 0.34/0.78 = ( semila1122118281tate_o @ A_123 @ ( semila1122118281tate_o @ B_65 @ C_32 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_74_sup_Oassoc,axiom,
% 0.34/0.78 ! [A_123: pname > $o,B_65: pname > $o,C_32: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ ( semila1780557381name_o @ A_123 @ B_65 ) @ C_32 )
% 0.34/0.78 = ( semila1780557381name_o @ A_123 @ ( semila1780557381name_o @ B_65 @ C_32 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_75_sup_Oassoc,axiom,
% 0.34/0.78 ! [A_123: $o,B_65: $o,C_32: $o] :
% 0.34/0.78 ( ( semila10642723_sup_o @ ( semila10642723_sup_o @ A_123 @ B_65 ) @ C_32 )
% 0.34/0.78 <=> ( semila10642723_sup_o @ A_123 @ ( semila10642723_sup_o @ B_65 @ C_32 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_76_sup_Oassoc,axiom,
% 0.34/0.78 ! [A_123: hoare_2091234717iple_a > $o,B_65: hoare_2091234717iple_a > $o,C_32: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ ( semila1052848428le_a_o @ A_123 @ B_65 ) @ C_32 )
% 0.34/0.78 = ( semila1052848428le_a_o @ A_123 @ ( semila1052848428le_a_o @ B_65 @ C_32 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_77_sup__left__commute,axiom,
% 0.34/0.78 ! [X_45: nat > $o,Y_18: nat > $o,Z_9: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ X_45 @ ( semila848761471_nat_o @ Y_18 @ Z_9 ) )
% 0.34/0.78 = ( semila848761471_nat_o @ Y_18 @ ( semila848761471_nat_o @ X_45 @ Z_9 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_78_sup__left__commute,axiom,
% 0.34/0.78 ! [X_45: nat,Y_18: nat,Z_9: nat] :
% 0.34/0.78 ( ( semila972727038up_nat @ X_45 @ ( semila972727038up_nat @ Y_18 @ Z_9 ) )
% 0.34/0.78 = ( semila972727038up_nat @ Y_18 @ ( semila972727038up_nat @ X_45 @ Z_9 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_79_sup__left__commute,axiom,
% 0.34/0.78 ! [X_45: ( hoare_2091234717iple_a > $o ) > $o,Y_18: ( hoare_2091234717iple_a > $o ) > $o,Z_9: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ X_45 @ ( semila2050116131_a_o_o @ Y_18 @ Z_9 ) )
% 0.34/0.78 = ( semila2050116131_a_o_o @ Y_18 @ ( semila2050116131_a_o_o @ X_45 @ Z_9 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_80_sup__left__commute,axiom,
% 0.34/0.78 ! [X_45: hoare_1708887482_state > $o,Y_18: hoare_1708887482_state > $o,Z_9: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ X_45 @ ( semila1122118281tate_o @ Y_18 @ Z_9 ) )
% 0.34/0.78 = ( semila1122118281tate_o @ Y_18 @ ( semila1122118281tate_o @ X_45 @ Z_9 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_81_sup__left__commute,axiom,
% 0.34/0.78 ! [X_45: pname > $o,Y_18: pname > $o,Z_9: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ X_45 @ ( semila1780557381name_o @ Y_18 @ Z_9 ) )
% 0.34/0.78 = ( semila1780557381name_o @ Y_18 @ ( semila1780557381name_o @ X_45 @ Z_9 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_82_sup__left__commute,axiom,
% 0.34/0.78 ! [X_45: $o,Y_18: $o,Z_9: $o] :
% 0.34/0.78 ( ( semila10642723_sup_o @ X_45 @ ( semila10642723_sup_o @ Y_18 @ Z_9 ) )
% 0.34/0.78 <=> ( semila10642723_sup_o @ Y_18 @ ( semila10642723_sup_o @ X_45 @ Z_9 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_83_sup__left__commute,axiom,
% 0.34/0.78 ! [X_45: hoare_2091234717iple_a > $o,Y_18: hoare_2091234717iple_a > $o,Z_9: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ X_45 @ ( semila1052848428le_a_o @ Y_18 @ Z_9 ) )
% 0.34/0.78 = ( semila1052848428le_a_o @ Y_18 @ ( semila1052848428le_a_o @ X_45 @ Z_9 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_84_inf__sup__aci_I7_J,axiom,
% 0.34/0.78 ! [X_44: nat > $o,Y_17: nat > $o,Z_8: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ X_44 @ ( semila848761471_nat_o @ Y_17 @ Z_8 ) )
% 0.34/0.78 = ( semila848761471_nat_o @ Y_17 @ ( semila848761471_nat_o @ X_44 @ Z_8 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_85_inf__sup__aci_I7_J,axiom,
% 0.34/0.78 ! [X_44: nat,Y_17: nat,Z_8: nat] :
% 0.34/0.78 ( ( semila972727038up_nat @ X_44 @ ( semila972727038up_nat @ Y_17 @ Z_8 ) )
% 0.34/0.78 = ( semila972727038up_nat @ Y_17 @ ( semila972727038up_nat @ X_44 @ Z_8 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_86_inf__sup__aci_I7_J,axiom,
% 0.34/0.78 ! [X_44: ( hoare_2091234717iple_a > $o ) > $o,Y_17: ( hoare_2091234717iple_a > $o ) > $o,Z_8: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ X_44 @ ( semila2050116131_a_o_o @ Y_17 @ Z_8 ) )
% 0.34/0.78 = ( semila2050116131_a_o_o @ Y_17 @ ( semila2050116131_a_o_o @ X_44 @ Z_8 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_87_inf__sup__aci_I7_J,axiom,
% 0.34/0.78 ! [X_44: hoare_1708887482_state > $o,Y_17: hoare_1708887482_state > $o,Z_8: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ X_44 @ ( semila1122118281tate_o @ Y_17 @ Z_8 ) )
% 0.34/0.78 = ( semila1122118281tate_o @ Y_17 @ ( semila1122118281tate_o @ X_44 @ Z_8 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_88_inf__sup__aci_I7_J,axiom,
% 0.34/0.78 ! [X_44: pname > $o,Y_17: pname > $o,Z_8: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ X_44 @ ( semila1780557381name_o @ Y_17 @ Z_8 ) )
% 0.34/0.78 = ( semila1780557381name_o @ Y_17 @ ( semila1780557381name_o @ X_44 @ Z_8 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_89_inf__sup__aci_I7_J,axiom,
% 0.34/0.78 ! [X_44: $o,Y_17: $o,Z_8: $o] :
% 0.34/0.78 ( ( semila10642723_sup_o @ X_44 @ ( semila10642723_sup_o @ Y_17 @ Z_8 ) )
% 0.34/0.78 <=> ( semila10642723_sup_o @ Y_17 @ ( semila10642723_sup_o @ X_44 @ Z_8 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_90_inf__sup__aci_I7_J,axiom,
% 0.34/0.78 ! [X_44: hoare_2091234717iple_a > $o,Y_17: hoare_2091234717iple_a > $o,Z_8: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ X_44 @ ( semila1052848428le_a_o @ Y_17 @ Z_8 ) )
% 0.34/0.78 = ( semila1052848428le_a_o @ Y_17 @ ( semila1052848428le_a_o @ X_44 @ Z_8 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_91_sup_Oleft__commute,axiom,
% 0.34/0.78 ! [B_64: nat > $o,A_122: nat > $o,C_31: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ B_64 @ ( semila848761471_nat_o @ A_122 @ C_31 ) )
% 0.34/0.78 = ( semila848761471_nat_o @ A_122 @ ( semila848761471_nat_o @ B_64 @ C_31 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_92_sup_Oleft__commute,axiom,
% 0.34/0.78 ! [B_64: nat,A_122: nat,C_31: nat] :
% 0.34/0.78 ( ( semila972727038up_nat @ B_64 @ ( semila972727038up_nat @ A_122 @ C_31 ) )
% 0.34/0.78 = ( semila972727038up_nat @ A_122 @ ( semila972727038up_nat @ B_64 @ C_31 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_93_sup_Oleft__commute,axiom,
% 0.34/0.78 ! [B_64: ( hoare_2091234717iple_a > $o ) > $o,A_122: ( hoare_2091234717iple_a > $o ) > $o,C_31: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ B_64 @ ( semila2050116131_a_o_o @ A_122 @ C_31 ) )
% 0.34/0.78 = ( semila2050116131_a_o_o @ A_122 @ ( semila2050116131_a_o_o @ B_64 @ C_31 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_94_sup_Oleft__commute,axiom,
% 0.34/0.78 ! [B_64: hoare_1708887482_state > $o,A_122: hoare_1708887482_state > $o,C_31: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ B_64 @ ( semila1122118281tate_o @ A_122 @ C_31 ) )
% 0.34/0.78 = ( semila1122118281tate_o @ A_122 @ ( semila1122118281tate_o @ B_64 @ C_31 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_95_sup_Oleft__commute,axiom,
% 0.34/0.78 ! [B_64: pname > $o,A_122: pname > $o,C_31: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ B_64 @ ( semila1780557381name_o @ A_122 @ C_31 ) )
% 0.34/0.78 = ( semila1780557381name_o @ A_122 @ ( semila1780557381name_o @ B_64 @ C_31 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_96_sup_Oleft__commute,axiom,
% 0.34/0.78 ! [B_64: $o,A_122: $o,C_31: $o] :
% 0.34/0.78 ( ( semila10642723_sup_o @ B_64 @ ( semila10642723_sup_o @ A_122 @ C_31 ) )
% 0.34/0.78 <=> ( semila10642723_sup_o @ A_122 @ ( semila10642723_sup_o @ B_64 @ C_31 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_97_sup_Oleft__commute,axiom,
% 0.34/0.78 ! [B_64: hoare_2091234717iple_a > $o,A_122: hoare_2091234717iple_a > $o,C_31: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ B_64 @ ( semila1052848428le_a_o @ A_122 @ C_31 ) )
% 0.34/0.78 = ( semila1052848428le_a_o @ A_122 @ ( semila1052848428le_a_o @ B_64 @ C_31 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_98_sup__left__idem,axiom,
% 0.34/0.78 ! [X_43: nat > $o,Y_16: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ X_43 @ ( semila848761471_nat_o @ X_43 @ Y_16 ) )
% 0.34/0.78 = ( semila848761471_nat_o @ X_43 @ Y_16 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_99_sup__left__idem,axiom,
% 0.34/0.78 ! [X_43: nat,Y_16: nat] :
% 0.34/0.78 ( ( semila972727038up_nat @ X_43 @ ( semila972727038up_nat @ X_43 @ Y_16 ) )
% 0.34/0.78 = ( semila972727038up_nat @ X_43 @ Y_16 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_100_sup__left__idem,axiom,
% 0.34/0.78 ! [X_43: ( hoare_2091234717iple_a > $o ) > $o,Y_16: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ X_43 @ ( semila2050116131_a_o_o @ X_43 @ Y_16 ) )
% 0.34/0.78 = ( semila2050116131_a_o_o @ X_43 @ Y_16 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_101_sup__left__idem,axiom,
% 0.34/0.78 ! [X_43: hoare_1708887482_state > $o,Y_16: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ X_43 @ ( semila1122118281tate_o @ X_43 @ Y_16 ) )
% 0.34/0.78 = ( semila1122118281tate_o @ X_43 @ Y_16 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_102_sup__left__idem,axiom,
% 0.34/0.78 ! [X_43: pname > $o,Y_16: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ X_43 @ ( semila1780557381name_o @ X_43 @ Y_16 ) )
% 0.34/0.78 = ( semila1780557381name_o @ X_43 @ Y_16 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_103_sup__left__idem,axiom,
% 0.34/0.78 ! [X_43: $o,Y_16: $o] :
% 0.34/0.78 ( ( semila10642723_sup_o @ X_43 @ ( semila10642723_sup_o @ X_43 @ Y_16 ) )
% 0.34/0.78 <=> ( semila10642723_sup_o @ X_43 @ Y_16 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_104_sup__left__idem,axiom,
% 0.34/0.78 ! [X_43: hoare_2091234717iple_a > $o,Y_16: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ X_43 @ ( semila1052848428le_a_o @ X_43 @ Y_16 ) )
% 0.34/0.78 = ( semila1052848428le_a_o @ X_43 @ Y_16 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_105_inf__sup__aci_I8_J,axiom,
% 0.34/0.78 ! [X_42: nat > $o,Y_15: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ X_42 @ ( semila848761471_nat_o @ X_42 @ Y_15 ) )
% 0.34/0.78 = ( semila848761471_nat_o @ X_42 @ Y_15 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_106_inf__sup__aci_I8_J,axiom,
% 0.34/0.78 ! [X_42: nat,Y_15: nat] :
% 0.34/0.78 ( ( semila972727038up_nat @ X_42 @ ( semila972727038up_nat @ X_42 @ Y_15 ) )
% 0.34/0.78 = ( semila972727038up_nat @ X_42 @ Y_15 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_107_inf__sup__aci_I8_J,axiom,
% 0.34/0.78 ! [X_42: ( hoare_2091234717iple_a > $o ) > $o,Y_15: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ X_42 @ ( semila2050116131_a_o_o @ X_42 @ Y_15 ) )
% 0.34/0.78 = ( semila2050116131_a_o_o @ X_42 @ Y_15 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_108_inf__sup__aci_I8_J,axiom,
% 0.34/0.78 ! [X_42: hoare_1708887482_state > $o,Y_15: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ X_42 @ ( semila1122118281tate_o @ X_42 @ Y_15 ) )
% 0.34/0.78 = ( semila1122118281tate_o @ X_42 @ Y_15 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_109_inf__sup__aci_I8_J,axiom,
% 0.34/0.78 ! [X_42: pname > $o,Y_15: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ X_42 @ ( semila1780557381name_o @ X_42 @ Y_15 ) )
% 0.34/0.78 = ( semila1780557381name_o @ X_42 @ Y_15 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_110_inf__sup__aci_I8_J,axiom,
% 0.34/0.78 ! [X_42: $o,Y_15: $o] :
% 0.34/0.78 ( ( semila10642723_sup_o @ X_42 @ ( semila10642723_sup_o @ X_42 @ Y_15 ) )
% 0.34/0.78 <=> ( semila10642723_sup_o @ X_42 @ Y_15 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_111_inf__sup__aci_I8_J,axiom,
% 0.34/0.78 ! [X_42: hoare_2091234717iple_a > $o,Y_15: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ X_42 @ ( semila1052848428le_a_o @ X_42 @ Y_15 ) )
% 0.34/0.78 = ( semila1052848428le_a_o @ X_42 @ Y_15 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_112_sup_Oleft__idem,axiom,
% 0.34/0.78 ! [A_121: nat > $o,B_63: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ A_121 @ ( semila848761471_nat_o @ A_121 @ B_63 ) )
% 0.34/0.78 = ( semila848761471_nat_o @ A_121 @ B_63 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_113_sup_Oleft__idem,axiom,
% 0.34/0.78 ! [A_121: nat,B_63: nat] :
% 0.34/0.78 ( ( semila972727038up_nat @ A_121 @ ( semila972727038up_nat @ A_121 @ B_63 ) )
% 0.34/0.78 = ( semila972727038up_nat @ A_121 @ B_63 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_114_sup_Oleft__idem,axiom,
% 0.34/0.78 ! [A_121: ( hoare_2091234717iple_a > $o ) > $o,B_63: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ A_121 @ ( semila2050116131_a_o_o @ A_121 @ B_63 ) )
% 0.34/0.78 = ( semila2050116131_a_o_o @ A_121 @ B_63 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_115_sup_Oleft__idem,axiom,
% 0.34/0.78 ! [A_121: hoare_1708887482_state > $o,B_63: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ A_121 @ ( semila1122118281tate_o @ A_121 @ B_63 ) )
% 0.34/0.78 = ( semila1122118281tate_o @ A_121 @ B_63 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_116_sup_Oleft__idem,axiom,
% 0.34/0.78 ! [A_121: pname > $o,B_63: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ A_121 @ ( semila1780557381name_o @ A_121 @ B_63 ) )
% 0.34/0.78 = ( semila1780557381name_o @ A_121 @ B_63 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_117_sup_Oleft__idem,axiom,
% 0.34/0.78 ! [A_121: $o,B_63: $o] :
% 0.34/0.78 ( ( semila10642723_sup_o @ A_121 @ ( semila10642723_sup_o @ A_121 @ B_63 ) )
% 0.34/0.78 <=> ( semila10642723_sup_o @ A_121 @ B_63 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_118_sup_Oleft__idem,axiom,
% 0.34/0.78 ! [A_121: hoare_2091234717iple_a > $o,B_63: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ A_121 @ ( semila1052848428le_a_o @ A_121 @ B_63 ) )
% 0.34/0.78 = ( semila1052848428le_a_o @ A_121 @ B_63 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_119_sup__commute,axiom,
% 0.34/0.78 ! [X_41: nat > $o,Y_14: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ X_41 @ Y_14 )
% 0.34/0.78 = ( semila848761471_nat_o @ Y_14 @ X_41 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_120_sup__commute,axiom,
% 0.34/0.78 ! [X_41: nat,Y_14: nat] :
% 0.34/0.78 ( ( semila972727038up_nat @ X_41 @ Y_14 )
% 0.34/0.78 = ( semila972727038up_nat @ Y_14 @ X_41 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_121_sup__commute,axiom,
% 0.34/0.78 ! [X_41: ( hoare_2091234717iple_a > $o ) > $o,Y_14: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ X_41 @ Y_14 )
% 0.34/0.78 = ( semila2050116131_a_o_o @ Y_14 @ X_41 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_122_sup__commute,axiom,
% 0.34/0.78 ! [X_41: hoare_1708887482_state > $o,Y_14: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ X_41 @ Y_14 )
% 0.34/0.78 = ( semila1122118281tate_o @ Y_14 @ X_41 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_123_sup__commute,axiom,
% 0.34/0.78 ! [X_41: pname > $o,Y_14: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ X_41 @ Y_14 )
% 0.34/0.78 = ( semila1780557381name_o @ Y_14 @ X_41 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_124_sup__commute,axiom,
% 0.34/0.78 ! [X_41: $o,Y_14: $o] :
% 0.34/0.78 ( ( semila10642723_sup_o @ X_41 @ Y_14 )
% 0.34/0.78 <=> ( semila10642723_sup_o @ Y_14 @ X_41 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_125_sup__commute,axiom,
% 0.34/0.78 ! [X_41: hoare_2091234717iple_a > $o,Y_14: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ X_41 @ Y_14 )
% 0.34/0.78 = ( semila1052848428le_a_o @ Y_14 @ X_41 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_126_inf__sup__aci_I5_J,axiom,
% 0.34/0.78 ! [X_40: nat > $o,Y_13: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ X_40 @ Y_13 )
% 0.34/0.78 = ( semila848761471_nat_o @ Y_13 @ X_40 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_127_inf__sup__aci_I5_J,axiom,
% 0.34/0.78 ! [X_40: nat,Y_13: nat] :
% 0.34/0.78 ( ( semila972727038up_nat @ X_40 @ Y_13 )
% 0.34/0.78 = ( semila972727038up_nat @ Y_13 @ X_40 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_128_inf__sup__aci_I5_J,axiom,
% 0.34/0.78 ! [X_40: ( hoare_2091234717iple_a > $o ) > $o,Y_13: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ X_40 @ Y_13 )
% 0.34/0.78 = ( semila2050116131_a_o_o @ Y_13 @ X_40 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_129_inf__sup__aci_I5_J,axiom,
% 0.34/0.78 ! [X_40: hoare_1708887482_state > $o,Y_13: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ X_40 @ Y_13 )
% 0.34/0.78 = ( semila1122118281tate_o @ Y_13 @ X_40 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_130_inf__sup__aci_I5_J,axiom,
% 0.34/0.78 ! [X_40: pname > $o,Y_13: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ X_40 @ Y_13 )
% 0.34/0.78 = ( semila1780557381name_o @ Y_13 @ X_40 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_131_inf__sup__aci_I5_J,axiom,
% 0.34/0.78 ! [X_40: $o,Y_13: $o] :
% 0.34/0.78 ( ( semila10642723_sup_o @ X_40 @ Y_13 )
% 0.34/0.78 <=> ( semila10642723_sup_o @ Y_13 @ X_40 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_132_inf__sup__aci_I5_J,axiom,
% 0.34/0.78 ! [X_40: hoare_2091234717iple_a > $o,Y_13: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ X_40 @ Y_13 )
% 0.34/0.78 = ( semila1052848428le_a_o @ Y_13 @ X_40 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_133_sup_Ocommute,axiom,
% 0.34/0.78 ! [A_120: nat > $o,B_62: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ A_120 @ B_62 )
% 0.34/0.78 = ( semila848761471_nat_o @ B_62 @ A_120 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_134_sup_Ocommute,axiom,
% 0.34/0.78 ! [A_120: nat,B_62: nat] :
% 0.34/0.78 ( ( semila972727038up_nat @ A_120 @ B_62 )
% 0.34/0.78 = ( semila972727038up_nat @ B_62 @ A_120 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_135_sup_Ocommute,axiom,
% 0.34/0.78 ! [A_120: ( hoare_2091234717iple_a > $o ) > $o,B_62: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ A_120 @ B_62 )
% 0.34/0.78 = ( semila2050116131_a_o_o @ B_62 @ A_120 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_136_sup_Ocommute,axiom,
% 0.34/0.78 ! [A_120: hoare_1708887482_state > $o,B_62: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ A_120 @ B_62 )
% 0.34/0.78 = ( semila1122118281tate_o @ B_62 @ A_120 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_137_sup_Ocommute,axiom,
% 0.34/0.78 ! [A_120: pname > $o,B_62: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ A_120 @ B_62 )
% 0.34/0.78 = ( semila1780557381name_o @ B_62 @ A_120 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_138_sup_Ocommute,axiom,
% 0.34/0.78 ! [A_120: $o,B_62: $o] :
% 0.34/0.78 ( ( semila10642723_sup_o @ A_120 @ B_62 )
% 0.34/0.78 <=> ( semila10642723_sup_o @ B_62 @ A_120 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_139_sup_Ocommute,axiom,
% 0.34/0.78 ! [A_120: hoare_2091234717iple_a > $o,B_62: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ A_120 @ B_62 )
% 0.34/0.78 = ( semila1052848428le_a_o @ B_62 @ A_120 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_140_sup__idem,axiom,
% 0.34/0.78 ! [X_39: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ X_39 @ X_39 )
% 0.34/0.78 = X_39 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_141_sup__idem,axiom,
% 0.34/0.78 ! [X_39: nat] :
% 0.34/0.78 ( ( semila972727038up_nat @ X_39 @ X_39 )
% 0.34/0.78 = X_39 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_142_sup__idem,axiom,
% 0.34/0.78 ! [X_39: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ X_39 @ X_39 )
% 0.34/0.78 = X_39 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_143_sup__idem,axiom,
% 0.34/0.78 ! [X_39: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ X_39 @ X_39 )
% 0.34/0.78 = X_39 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_144_sup__idem,axiom,
% 0.34/0.78 ! [X_39: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ X_39 @ X_39 )
% 0.34/0.78 = X_39 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_145_sup__idem,axiom,
% 0.34/0.78 ! [X_39: $o] :
% 0.34/0.78 ( ( semila10642723_sup_o @ X_39 @ X_39 )
% 0.34/0.78 <=> X_39 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_146_sup__idem,axiom,
% 0.34/0.78 ! [X_39: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ X_39 @ X_39 )
% 0.34/0.78 = X_39 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_147_sup_Oidem,axiom,
% 0.34/0.78 ! [A_119: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ A_119 @ A_119 )
% 0.34/0.78 = A_119 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_148_sup_Oidem,axiom,
% 0.34/0.78 ! [A_119: nat] :
% 0.34/0.78 ( ( semila972727038up_nat @ A_119 @ A_119 )
% 0.34/0.78 = A_119 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_149_sup_Oidem,axiom,
% 0.34/0.78 ! [A_119: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ A_119 @ A_119 )
% 0.34/0.78 = A_119 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_150_sup_Oidem,axiom,
% 0.34/0.78 ! [A_119: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ A_119 @ A_119 )
% 0.34/0.78 = A_119 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_151_sup_Oidem,axiom,
% 0.34/0.78 ! [A_119: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ A_119 @ A_119 )
% 0.34/0.78 = A_119 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_152_sup_Oidem,axiom,
% 0.34/0.78 ! [A_119: $o] :
% 0.34/0.78 ( ( semila10642723_sup_o @ A_119 @ A_119 )
% 0.34/0.78 <=> A_119 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_153_sup_Oidem,axiom,
% 0.34/0.78 ! [A_119: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ A_119 @ A_119 )
% 0.34/0.78 = A_119 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_154_rev__image__eqI,axiom,
% 0.34/0.78 ! [B_61: nat,F_46: nat > nat,X_38: nat,A_118: nat > $o] :
% 0.34/0.78 ( ( member_nat @ X_38 @ A_118 )
% 0.34/0.78 => ( ( B_61
% 0.34/0.78 = ( F_46 @ X_38 ) )
% 0.34/0.78 => ( member_nat @ B_61 @ ( image_nat_nat @ F_46 @ A_118 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_155_rev__image__eqI,axiom,
% 0.34/0.78 ! [B_61: hoare_1708887482_state,F_46: pname > hoare_1708887482_state,X_38: pname,A_118: pname > $o] :
% 0.34/0.78 ( ( member_pname @ X_38 @ A_118 )
% 0.34/0.78 => ( ( B_61
% 0.34/0.78 = ( F_46 @ X_38 ) )
% 0.34/0.78 => ( member451959335_state @ B_61 @ ( image_1116629049_state @ F_46 @ A_118 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_156_rev__image__eqI,axiom,
% 0.34/0.78 ! [B_61: nat,F_46: pname > nat,X_38: pname,A_118: pname > $o] :
% 0.34/0.78 ( ( member_pname @ X_38 @ A_118 )
% 0.34/0.78 => ( ( B_61
% 0.34/0.78 = ( F_46 @ X_38 ) )
% 0.34/0.78 => ( member_nat @ B_61 @ ( image_pname_nat @ F_46 @ A_118 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_157_rev__image__eqI,axiom,
% 0.34/0.78 ! [B_61: hoare_2091234717iple_a > $o,F_46: pname > hoare_2091234717iple_a > $o,X_38: pname,A_118: pname > $o] :
% 0.34/0.78 ( ( member_pname @ X_38 @ A_118 )
% 0.34/0.78 => ( ( B_61
% 0.34/0.78 = ( F_46 @ X_38 ) )
% 0.34/0.78 => ( member99268621le_a_o @ B_61 @ ( image_742317343le_a_o @ F_46 @ A_118 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_158_rev__image__eqI,axiom,
% 0.34/0.78 ! [B_61: pname,F_46: nat > pname,X_38: nat,A_118: nat > $o] :
% 0.34/0.78 ( ( member_nat @ X_38 @ A_118 )
% 0.34/0.78 => ( ( B_61
% 0.34/0.78 = ( F_46 @ X_38 ) )
% 0.34/0.78 => ( member_pname @ B_61 @ ( image_nat_pname @ F_46 @ A_118 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_159_rev__image__eqI,axiom,
% 0.34/0.78 ! [B_61: pname,F_46: ( hoare_2091234717iple_a > $o ) > pname,X_38: hoare_2091234717iple_a > $o,A_118: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( member99268621le_a_o @ X_38 @ A_118 )
% 0.34/0.78 => ( ( B_61
% 0.34/0.78 = ( F_46 @ X_38 ) )
% 0.34/0.78 => ( member_pname @ B_61 @ ( image_1908519857_pname @ F_46 @ A_118 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_160_rev__image__eqI,axiom,
% 0.34/0.78 ! [B_61: pname,F_46: hoare_2091234717iple_a > pname,X_38: hoare_2091234717iple_a,A_118: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( member290856304iple_a @ X_38 @ A_118 )
% 0.34/0.78 => ( ( B_61
% 0.34/0.78 = ( F_46 @ X_38 ) )
% 0.34/0.78 => ( member_pname @ B_61 @ ( image_924789612_pname @ F_46 @ A_118 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_161_rev__image__eqI,axiom,
% 0.34/0.78 ! [B_61: hoare_2091234717iple_a,F_46: pname > hoare_2091234717iple_a,X_38: pname,A_118: pname > $o] :
% 0.34/0.78 ( ( member_pname @ X_38 @ A_118 )
% 0.34/0.78 => ( ( B_61
% 0.34/0.78 = ( F_46 @ X_38 ) )
% 0.34/0.78 => ( member290856304iple_a @ B_61 @ ( image_231808478iple_a @ F_46 @ A_118 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_162_imageI,axiom,
% 0.34/0.78 ! [F_45: nat > nat,X_37: nat,A_117: nat > $o] :
% 0.34/0.78 ( ( member_nat @ X_37 @ A_117 )
% 0.34/0.78 => ( member_nat @ ( F_45 @ X_37 ) @ ( image_nat_nat @ F_45 @ A_117 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_163_imageI,axiom,
% 0.34/0.78 ! [F_45: pname > hoare_1708887482_state,X_37: pname,A_117: pname > $o] :
% 0.34/0.78 ( ( member_pname @ X_37 @ A_117 )
% 0.34/0.78 => ( member451959335_state @ ( F_45 @ X_37 ) @ ( image_1116629049_state @ F_45 @ A_117 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_164_imageI,axiom,
% 0.34/0.78 ! [F_45: pname > nat,X_37: pname,A_117: pname > $o] :
% 0.34/0.78 ( ( member_pname @ X_37 @ A_117 )
% 0.34/0.78 => ( member_nat @ ( F_45 @ X_37 ) @ ( image_pname_nat @ F_45 @ A_117 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_165_imageI,axiom,
% 0.34/0.78 ! [F_45: pname > hoare_2091234717iple_a > $o,X_37: pname,A_117: pname > $o] :
% 0.34/0.78 ( ( member_pname @ X_37 @ A_117 )
% 0.34/0.78 => ( member99268621le_a_o @ ( F_45 @ X_37 ) @ ( image_742317343le_a_o @ F_45 @ A_117 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_166_imageI,axiom,
% 0.34/0.78 ! [F_45: nat > pname,X_37: nat,A_117: nat > $o] :
% 0.34/0.78 ( ( member_nat @ X_37 @ A_117 )
% 0.34/0.78 => ( member_pname @ ( F_45 @ X_37 ) @ ( image_nat_pname @ F_45 @ A_117 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_167_imageI,axiom,
% 0.34/0.78 ! [F_45: ( hoare_2091234717iple_a > $o ) > pname,X_37: hoare_2091234717iple_a > $o,A_117: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( member99268621le_a_o @ X_37 @ A_117 )
% 0.34/0.78 => ( member_pname @ ( F_45 @ X_37 ) @ ( image_1908519857_pname @ F_45 @ A_117 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_168_imageI,axiom,
% 0.34/0.78 ! [F_45: hoare_2091234717iple_a > pname,X_37: hoare_2091234717iple_a,A_117: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( member290856304iple_a @ X_37 @ A_117 )
% 0.34/0.78 => ( member_pname @ ( F_45 @ X_37 ) @ ( image_924789612_pname @ F_45 @ A_117 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_169_imageI,axiom,
% 0.34/0.78 ! [F_45: pname > hoare_2091234717iple_a,X_37: pname,A_117: pname > $o] :
% 0.34/0.78 ( ( member_pname @ X_37 @ A_117 )
% 0.34/0.78 => ( member290856304iple_a @ ( F_45 @ X_37 ) @ ( image_231808478iple_a @ F_45 @ A_117 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_170_image__iff,axiom,
% 0.34/0.78 ! [Z_7: nat,F_44: nat > nat,A_116: nat > $o] :
% 0.34/0.78 ( ( member_nat @ Z_7 @ ( image_nat_nat @ F_44 @ A_116 ) )
% 0.34/0.78 <=> ? [X: nat] :
% 0.34/0.78 ( ( member_nat @ X @ A_116 )
% 0.34/0.78 & ( Z_7
% 0.34/0.78 = ( F_44 @ X ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_171_image__iff,axiom,
% 0.34/0.78 ! [Z_7: hoare_1708887482_state,F_44: pname > hoare_1708887482_state,A_116: pname > $o] :
% 0.34/0.78 ( ( member451959335_state @ Z_7 @ ( image_1116629049_state @ F_44 @ A_116 ) )
% 0.34/0.78 <=> ? [X: pname] :
% 0.34/0.78 ( ( member_pname @ X @ A_116 )
% 0.34/0.78 & ( Z_7
% 0.34/0.78 = ( F_44 @ X ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_172_image__iff,axiom,
% 0.34/0.78 ! [Z_7: hoare_2091234717iple_a,F_44: pname > hoare_2091234717iple_a,A_116: pname > $o] :
% 0.34/0.78 ( ( member290856304iple_a @ Z_7 @ ( image_231808478iple_a @ F_44 @ A_116 ) )
% 0.34/0.78 <=> ? [X: pname] :
% 0.34/0.78 ( ( member_pname @ X @ A_116 )
% 0.34/0.78 & ( Z_7
% 0.34/0.78 = ( F_44 @ X ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_173_UnI2,axiom,
% 0.34/0.78 ! [A_115: nat > $o,C_30: nat,B_60: nat > $o] :
% 0.34/0.78 ( ( member_nat @ C_30 @ B_60 )
% 0.34/0.78 => ( member_nat @ C_30 @ ( semila848761471_nat_o @ A_115 @ B_60 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_174_UnI2,axiom,
% 0.34/0.78 ! [A_115: ( hoare_2091234717iple_a > $o ) > $o,C_30: hoare_2091234717iple_a > $o,B_60: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( member99268621le_a_o @ C_30 @ B_60 )
% 0.34/0.78 => ( member99268621le_a_o @ C_30 @ ( semila2050116131_a_o_o @ A_115 @ B_60 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_175_UnI2,axiom,
% 0.34/0.78 ! [A_115: hoare_1708887482_state > $o,C_30: hoare_1708887482_state,B_60: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( member451959335_state @ C_30 @ B_60 )
% 0.34/0.78 => ( member451959335_state @ C_30 @ ( semila1122118281tate_o @ A_115 @ B_60 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_176_UnI2,axiom,
% 0.34/0.78 ! [A_115: hoare_2091234717iple_a > $o,C_30: hoare_2091234717iple_a,B_60: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( member290856304iple_a @ C_30 @ B_60 )
% 0.34/0.78 => ( member290856304iple_a @ C_30 @ ( semila1052848428le_a_o @ A_115 @ B_60 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_177_UnI2,axiom,
% 0.34/0.78 ! [A_115: pname > $o,C_30: pname,B_60: pname > $o] :
% 0.34/0.78 ( ( member_pname @ C_30 @ B_60 )
% 0.34/0.78 => ( member_pname @ C_30 @ ( semila1780557381name_o @ A_115 @ B_60 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_178_UnI1,axiom,
% 0.34/0.78 ! [B_59: nat > $o,C_29: nat,A_114: nat > $o] :
% 0.34/0.78 ( ( member_nat @ C_29 @ A_114 )
% 0.34/0.78 => ( member_nat @ C_29 @ ( semila848761471_nat_o @ A_114 @ B_59 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_179_UnI1,axiom,
% 0.34/0.78 ! [B_59: ( hoare_2091234717iple_a > $o ) > $o,C_29: hoare_2091234717iple_a > $o,A_114: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( member99268621le_a_o @ C_29 @ A_114 )
% 0.34/0.78 => ( member99268621le_a_o @ C_29 @ ( semila2050116131_a_o_o @ A_114 @ B_59 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_180_UnI1,axiom,
% 0.34/0.78 ! [B_59: hoare_1708887482_state > $o,C_29: hoare_1708887482_state,A_114: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( member451959335_state @ C_29 @ A_114 )
% 0.34/0.78 => ( member451959335_state @ C_29 @ ( semila1122118281tate_o @ A_114 @ B_59 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_181_UnI1,axiom,
% 0.34/0.78 ! [B_59: hoare_2091234717iple_a > $o,C_29: hoare_2091234717iple_a,A_114: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( member290856304iple_a @ C_29 @ A_114 )
% 0.34/0.78 => ( member290856304iple_a @ C_29 @ ( semila1052848428le_a_o @ A_114 @ B_59 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_182_UnI1,axiom,
% 0.34/0.78 ! [B_59: pname > $o,C_29: pname,A_114: pname > $o] :
% 0.34/0.78 ( ( member_pname @ C_29 @ A_114 )
% 0.34/0.78 => ( member_pname @ C_29 @ ( semila1780557381name_o @ A_114 @ B_59 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_183_sup1I2,axiom,
% 0.34/0.78 ! [A_113: nat > $o,B_58: nat > $o,X_36: nat] :
% 0.34/0.78 ( ( B_58 @ X_36 )
% 0.34/0.78 => ( semila848761471_nat_o @ A_113 @ B_58 @ X_36 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_184_sup1I2,axiom,
% 0.34/0.78 ! [A_113: ( hoare_2091234717iple_a > $o ) > $o,B_58: ( hoare_2091234717iple_a > $o ) > $o,X_36: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( B_58 @ X_36 )
% 0.34/0.78 => ( semila2050116131_a_o_o @ A_113 @ B_58 @ X_36 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_185_sup1I2,axiom,
% 0.34/0.78 ! [A_113: hoare_1708887482_state > $o,B_58: hoare_1708887482_state > $o,X_36: hoare_1708887482_state] :
% 0.34/0.78 ( ( B_58 @ X_36 )
% 0.34/0.78 => ( semila1122118281tate_o @ A_113 @ B_58 @ X_36 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_186_sup1I2,axiom,
% 0.34/0.78 ! [A_113: pname > $o,B_58: pname > $o,X_36: pname] :
% 0.34/0.78 ( ( B_58 @ X_36 )
% 0.34/0.78 => ( semila1780557381name_o @ A_113 @ B_58 @ X_36 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_187_sup1I2,axiom,
% 0.34/0.78 ! [A_113: hoare_2091234717iple_a > $o,B_58: hoare_2091234717iple_a > $o,X_36: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( B_58 @ X_36 )
% 0.34/0.78 => ( semila1052848428le_a_o @ A_113 @ B_58 @ X_36 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_188_sup1I1,axiom,
% 0.34/0.78 ! [B_57: nat > $o,A_112: nat > $o,X_35: nat] :
% 0.34/0.78 ( ( A_112 @ X_35 )
% 0.34/0.78 => ( semila848761471_nat_o @ A_112 @ B_57 @ X_35 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_189_sup1I1,axiom,
% 0.34/0.78 ! [B_57: ( hoare_2091234717iple_a > $o ) > $o,A_112: ( hoare_2091234717iple_a > $o ) > $o,X_35: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( A_112 @ X_35 )
% 0.34/0.78 => ( semila2050116131_a_o_o @ A_112 @ B_57 @ X_35 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_190_sup1I1,axiom,
% 0.34/0.78 ! [B_57: hoare_1708887482_state > $o,A_112: hoare_1708887482_state > $o,X_35: hoare_1708887482_state] :
% 0.34/0.78 ( ( A_112 @ X_35 )
% 0.34/0.78 => ( semila1122118281tate_o @ A_112 @ B_57 @ X_35 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_191_sup1I1,axiom,
% 0.34/0.78 ! [B_57: pname > $o,A_112: pname > $o,X_35: pname] :
% 0.34/0.78 ( ( A_112 @ X_35 )
% 0.34/0.78 => ( semila1780557381name_o @ A_112 @ B_57 @ X_35 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_192_sup1I1,axiom,
% 0.34/0.78 ! [B_57: hoare_2091234717iple_a > $o,A_112: hoare_2091234717iple_a > $o,X_35: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( A_112 @ X_35 )
% 0.34/0.78 => ( semila1052848428le_a_o @ A_112 @ B_57 @ X_35 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_193_ball__Un,axiom,
% 0.34/0.78 ! [P_35: nat > $o,A_111: nat > $o,B_56: nat > $o] :
% 0.34/0.78 ( ! [X: nat] :
% 0.34/0.78 ( ( member_nat @ X @ ( semila848761471_nat_o @ A_111 @ B_56 ) )
% 0.34/0.78 => ( P_35 @ X ) )
% 0.34/0.78 <=> ( ! [X: nat] :
% 0.34/0.78 ( ( member_nat @ X @ A_111 )
% 0.34/0.78 => ( P_35 @ X ) )
% 0.34/0.78 & ! [X: nat] :
% 0.34/0.78 ( ( member_nat @ X @ B_56 )
% 0.34/0.78 => ( P_35 @ X ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_194_ball__Un,axiom,
% 0.34/0.78 ! [P_35: ( hoare_2091234717iple_a > $o ) > $o,A_111: ( hoare_2091234717iple_a > $o ) > $o,B_56: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ! [X: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( member99268621le_a_o @ X @ ( semila2050116131_a_o_o @ A_111 @ B_56 ) )
% 0.34/0.78 => ( P_35 @ X ) )
% 0.34/0.78 <=> ( ! [X: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( member99268621le_a_o @ X @ A_111 )
% 0.34/0.78 => ( P_35 @ X ) )
% 0.34/0.78 & ! [X: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( member99268621le_a_o @ X @ B_56 )
% 0.34/0.78 => ( P_35 @ X ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_195_ball__Un,axiom,
% 0.34/0.78 ! [P_35: hoare_1708887482_state > $o,A_111: hoare_1708887482_state > $o,B_56: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ! [X: hoare_1708887482_state] :
% 0.34/0.78 ( ( member451959335_state @ X @ ( semila1122118281tate_o @ A_111 @ B_56 ) )
% 0.34/0.78 => ( P_35 @ X ) )
% 0.34/0.78 <=> ( ! [X: hoare_1708887482_state] :
% 0.34/0.78 ( ( member451959335_state @ X @ A_111 )
% 0.34/0.78 => ( P_35 @ X ) )
% 0.34/0.78 & ! [X: hoare_1708887482_state] :
% 0.34/0.78 ( ( member451959335_state @ X @ B_56 )
% 0.34/0.78 => ( P_35 @ X ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_196_ball__Un,axiom,
% 0.34/0.78 ! [P_35: pname > $o,A_111: pname > $o,B_56: pname > $o] :
% 0.34/0.78 ( ! [X: pname] :
% 0.34/0.78 ( ( member_pname @ X @ ( semila1780557381name_o @ A_111 @ B_56 ) )
% 0.34/0.78 => ( P_35 @ X ) )
% 0.34/0.78 <=> ( ! [X: pname] :
% 0.34/0.78 ( ( member_pname @ X @ A_111 )
% 0.34/0.78 => ( P_35 @ X ) )
% 0.34/0.78 & ! [X: pname] :
% 0.34/0.78 ( ( member_pname @ X @ B_56 )
% 0.34/0.78 => ( P_35 @ X ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_197_ball__Un,axiom,
% 0.34/0.78 ! [P_35: hoare_2091234717iple_a > $o,A_111: hoare_2091234717iple_a > $o,B_56: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ! [X: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( member290856304iple_a @ X @ ( semila1052848428le_a_o @ A_111 @ B_56 ) )
% 0.34/0.78 => ( P_35 @ X ) )
% 0.34/0.78 <=> ( ! [X: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( member290856304iple_a @ X @ A_111 )
% 0.34/0.78 => ( P_35 @ X ) )
% 0.34/0.78 & ! [X: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( member290856304iple_a @ X @ B_56 )
% 0.34/0.78 => ( P_35 @ X ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_198_bex__Un,axiom,
% 0.34/0.78 ! [P_34: nat > $o,A_110: nat > $o,B_55: nat > $o] :
% 0.34/0.78 ( ? [X: nat] :
% 0.34/0.78 ( ( member_nat @ X @ ( semila848761471_nat_o @ A_110 @ B_55 ) )
% 0.34/0.78 & ( P_34 @ X ) )
% 0.34/0.78 <=> ( ? [X: nat] :
% 0.34/0.78 ( ( member_nat @ X @ A_110 )
% 0.34/0.78 & ( P_34 @ X ) )
% 0.34/0.78 | ? [X: nat] :
% 0.34/0.78 ( ( member_nat @ X @ B_55 )
% 0.34/0.78 & ( P_34 @ X ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_199_bex__Un,axiom,
% 0.34/0.78 ! [P_34: ( hoare_2091234717iple_a > $o ) > $o,A_110: ( hoare_2091234717iple_a > $o ) > $o,B_55: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ? [X: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( member99268621le_a_o @ X @ ( semila2050116131_a_o_o @ A_110 @ B_55 ) )
% 0.34/0.78 & ( P_34 @ X ) )
% 0.34/0.78 <=> ( ? [X: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( member99268621le_a_o @ X @ A_110 )
% 0.34/0.78 & ( P_34 @ X ) )
% 0.34/0.78 | ? [X: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( member99268621le_a_o @ X @ B_55 )
% 0.34/0.78 & ( P_34 @ X ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_200_bex__Un,axiom,
% 0.34/0.78 ! [P_34: hoare_1708887482_state > $o,A_110: hoare_1708887482_state > $o,B_55: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ? [X: hoare_1708887482_state] :
% 0.34/0.78 ( ( member451959335_state @ X @ ( semila1122118281tate_o @ A_110 @ B_55 ) )
% 0.34/0.78 & ( P_34 @ X ) )
% 0.34/0.78 <=> ( ? [X: hoare_1708887482_state] :
% 0.34/0.78 ( ( member451959335_state @ X @ A_110 )
% 0.34/0.78 & ( P_34 @ X ) )
% 0.34/0.78 | ? [X: hoare_1708887482_state] :
% 0.34/0.78 ( ( member451959335_state @ X @ B_55 )
% 0.34/0.78 & ( P_34 @ X ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_201_bex__Un,axiom,
% 0.34/0.78 ! [P_34: pname > $o,A_110: pname > $o,B_55: pname > $o] :
% 0.34/0.78 ( ? [X: pname] :
% 0.34/0.78 ( ( member_pname @ X @ ( semila1780557381name_o @ A_110 @ B_55 ) )
% 0.34/0.78 & ( P_34 @ X ) )
% 0.34/0.78 <=> ( ? [X: pname] :
% 0.34/0.78 ( ( member_pname @ X @ A_110 )
% 0.34/0.78 & ( P_34 @ X ) )
% 0.34/0.78 | ? [X: pname] :
% 0.34/0.78 ( ( member_pname @ X @ B_55 )
% 0.34/0.78 & ( P_34 @ X ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_202_bex__Un,axiom,
% 0.34/0.78 ! [P_34: hoare_2091234717iple_a > $o,A_110: hoare_2091234717iple_a > $o,B_55: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ? [X: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( member290856304iple_a @ X @ ( semila1052848428le_a_o @ A_110 @ B_55 ) )
% 0.34/0.78 & ( P_34 @ X ) )
% 0.34/0.78 <=> ( ? [X: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( member290856304iple_a @ X @ A_110 )
% 0.34/0.78 & ( P_34 @ X ) )
% 0.34/0.78 | ? [X: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( member290856304iple_a @ X @ B_55 )
% 0.34/0.78 & ( P_34 @ X ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_203_Un__assoc,axiom,
% 0.34/0.78 ! [A_109: nat > $o,B_54: nat > $o,C_28: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ ( semila848761471_nat_o @ A_109 @ B_54 ) @ C_28 )
% 0.34/0.78 = ( semila848761471_nat_o @ A_109 @ ( semila848761471_nat_o @ B_54 @ C_28 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_204_Un__assoc,axiom,
% 0.34/0.78 ! [A_109: ( hoare_2091234717iple_a > $o ) > $o,B_54: ( hoare_2091234717iple_a > $o ) > $o,C_28: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ ( semila2050116131_a_o_o @ A_109 @ B_54 ) @ C_28 )
% 0.34/0.78 = ( semila2050116131_a_o_o @ A_109 @ ( semila2050116131_a_o_o @ B_54 @ C_28 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_205_Un__assoc,axiom,
% 0.34/0.78 ! [A_109: hoare_1708887482_state > $o,B_54: hoare_1708887482_state > $o,C_28: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ ( semila1122118281tate_o @ A_109 @ B_54 ) @ C_28 )
% 0.34/0.78 = ( semila1122118281tate_o @ A_109 @ ( semila1122118281tate_o @ B_54 @ C_28 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_206_Un__assoc,axiom,
% 0.34/0.78 ! [A_109: pname > $o,B_54: pname > $o,C_28: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ ( semila1780557381name_o @ A_109 @ B_54 ) @ C_28 )
% 0.34/0.78 = ( semila1780557381name_o @ A_109 @ ( semila1780557381name_o @ B_54 @ C_28 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_207_Un__assoc,axiom,
% 0.34/0.78 ! [A_109: hoare_2091234717iple_a > $o,B_54: hoare_2091234717iple_a > $o,C_28: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ ( semila1052848428le_a_o @ A_109 @ B_54 ) @ C_28 )
% 0.34/0.78 = ( semila1052848428le_a_o @ A_109 @ ( semila1052848428le_a_o @ B_54 @ C_28 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_208_Un__iff,axiom,
% 0.34/0.78 ! [C_27: nat,A_108: nat > $o,B_53: nat > $o] :
% 0.34/0.78 ( ( member_nat @ C_27 @ ( semila848761471_nat_o @ A_108 @ B_53 ) )
% 0.34/0.78 <=> ( ( member_nat @ C_27 @ A_108 )
% 0.34/0.78 | ( member_nat @ C_27 @ B_53 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_209_Un__iff,axiom,
% 0.34/0.78 ! [C_27: hoare_2091234717iple_a > $o,A_108: ( hoare_2091234717iple_a > $o ) > $o,B_53: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( member99268621le_a_o @ C_27 @ ( semila2050116131_a_o_o @ A_108 @ B_53 ) )
% 0.34/0.78 <=> ( ( member99268621le_a_o @ C_27 @ A_108 )
% 0.34/0.78 | ( member99268621le_a_o @ C_27 @ B_53 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_210_Un__iff,axiom,
% 0.34/0.78 ! [C_27: hoare_1708887482_state,A_108: hoare_1708887482_state > $o,B_53: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( member451959335_state @ C_27 @ ( semila1122118281tate_o @ A_108 @ B_53 ) )
% 0.34/0.78 <=> ( ( member451959335_state @ C_27 @ A_108 )
% 0.34/0.78 | ( member451959335_state @ C_27 @ B_53 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_211_Un__iff,axiom,
% 0.34/0.78 ! [C_27: hoare_2091234717iple_a,A_108: hoare_2091234717iple_a > $o,B_53: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( member290856304iple_a @ C_27 @ ( semila1052848428le_a_o @ A_108 @ B_53 ) )
% 0.34/0.78 <=> ( ( member290856304iple_a @ C_27 @ A_108 )
% 0.34/0.78 | ( member290856304iple_a @ C_27 @ B_53 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_212_Un__iff,axiom,
% 0.34/0.78 ! [C_27: pname,A_108: pname > $o,B_53: pname > $o] :
% 0.34/0.78 ( ( member_pname @ C_27 @ ( semila1780557381name_o @ A_108 @ B_53 ) )
% 0.34/0.78 <=> ( ( member_pname @ C_27 @ A_108 )
% 0.34/0.78 | ( member_pname @ C_27 @ B_53 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_213_Un__left__commute,axiom,
% 0.34/0.78 ! [A_107: nat > $o,B_52: nat > $o,C_26: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ A_107 @ ( semila848761471_nat_o @ B_52 @ C_26 ) )
% 0.34/0.78 = ( semila848761471_nat_o @ B_52 @ ( semila848761471_nat_o @ A_107 @ C_26 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_214_Un__left__commute,axiom,
% 0.34/0.78 ! [A_107: ( hoare_2091234717iple_a > $o ) > $o,B_52: ( hoare_2091234717iple_a > $o ) > $o,C_26: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ A_107 @ ( semila2050116131_a_o_o @ B_52 @ C_26 ) )
% 0.34/0.78 = ( semila2050116131_a_o_o @ B_52 @ ( semila2050116131_a_o_o @ A_107 @ C_26 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_215_Un__left__commute,axiom,
% 0.34/0.78 ! [A_107: hoare_1708887482_state > $o,B_52: hoare_1708887482_state > $o,C_26: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ A_107 @ ( semila1122118281tate_o @ B_52 @ C_26 ) )
% 0.34/0.78 = ( semila1122118281tate_o @ B_52 @ ( semila1122118281tate_o @ A_107 @ C_26 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_216_Un__left__commute,axiom,
% 0.34/0.78 ! [A_107: pname > $o,B_52: pname > $o,C_26: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ A_107 @ ( semila1780557381name_o @ B_52 @ C_26 ) )
% 0.34/0.78 = ( semila1780557381name_o @ B_52 @ ( semila1780557381name_o @ A_107 @ C_26 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_217_Un__left__commute,axiom,
% 0.34/0.78 ! [A_107: hoare_2091234717iple_a > $o,B_52: hoare_2091234717iple_a > $o,C_26: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ A_107 @ ( semila1052848428le_a_o @ B_52 @ C_26 ) )
% 0.34/0.78 = ( semila1052848428le_a_o @ B_52 @ ( semila1052848428le_a_o @ A_107 @ C_26 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_218_Un__left__absorb,axiom,
% 0.34/0.78 ! [A_106: nat > $o,B_51: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ A_106 @ ( semila848761471_nat_o @ A_106 @ B_51 ) )
% 0.34/0.78 = ( semila848761471_nat_o @ A_106 @ B_51 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_219_Un__left__absorb,axiom,
% 0.34/0.78 ! [A_106: ( hoare_2091234717iple_a > $o ) > $o,B_51: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ A_106 @ ( semila2050116131_a_o_o @ A_106 @ B_51 ) )
% 0.34/0.78 = ( semila2050116131_a_o_o @ A_106 @ B_51 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_220_Un__left__absorb,axiom,
% 0.34/0.78 ! [A_106: hoare_1708887482_state > $o,B_51: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ A_106 @ ( semila1122118281tate_o @ A_106 @ B_51 ) )
% 0.34/0.78 = ( semila1122118281tate_o @ A_106 @ B_51 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_221_Un__left__absorb,axiom,
% 0.34/0.78 ! [A_106: pname > $o,B_51: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ A_106 @ ( semila1780557381name_o @ A_106 @ B_51 ) )
% 0.34/0.78 = ( semila1780557381name_o @ A_106 @ B_51 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_222_Un__left__absorb,axiom,
% 0.34/0.78 ! [A_106: hoare_2091234717iple_a > $o,B_51: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ A_106 @ ( semila1052848428le_a_o @ A_106 @ B_51 ) )
% 0.34/0.78 = ( semila1052848428le_a_o @ A_106 @ B_51 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_223_Un__commute,axiom,
% 0.34/0.78 ! [A_105: nat > $o,B_50: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ A_105 @ B_50 )
% 0.34/0.78 = ( semila848761471_nat_o @ B_50 @ A_105 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_224_Un__commute,axiom,
% 0.34/0.78 ! [A_105: ( hoare_2091234717iple_a > $o ) > $o,B_50: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ A_105 @ B_50 )
% 0.34/0.78 = ( semila2050116131_a_o_o @ B_50 @ A_105 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_225_Un__commute,axiom,
% 0.34/0.78 ! [A_105: hoare_1708887482_state > $o,B_50: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ A_105 @ B_50 )
% 0.34/0.78 = ( semila1122118281tate_o @ B_50 @ A_105 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_226_Un__commute,axiom,
% 0.34/0.78 ! [A_105: pname > $o,B_50: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ A_105 @ B_50 )
% 0.34/0.78 = ( semila1780557381name_o @ B_50 @ A_105 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_227_Un__commute,axiom,
% 0.34/0.78 ! [A_105: hoare_2091234717iple_a > $o,B_50: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ A_105 @ B_50 )
% 0.34/0.78 = ( semila1052848428le_a_o @ B_50 @ A_105 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_228_Un__def,axiom,
% 0.34/0.78 ! [A_104: ( hoare_2091234717iple_a > $o ) > $o,B_49: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ A_104 @ B_49 )
% 0.34/0.78 = ( collec1008234059le_a_o
% 0.34/0.78 @ ^ [X: hoare_2091234717iple_a > $o] : ( (|) @ ( member99268621le_a_o @ X @ A_104 ) @ ( member99268621le_a_o @ X @ B_49 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_229_Un__def,axiom,
% 0.34/0.78 ! [A_104: hoare_1708887482_state > $o,B_49: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ A_104 @ B_49 )
% 0.34/0.78 = ( collec1568722789_state
% 0.34/0.78 @ ^ [X: hoare_1708887482_state] : ( (|) @ ( member451959335_state @ X @ A_104 ) @ ( member451959335_state @ X @ B_49 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_230_Un__def,axiom,
% 0.34/0.78 ! [A_104: hoare_2091234717iple_a > $o,B_49: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ A_104 @ B_49 )
% 0.34/0.78 = ( collec992574898iple_a
% 0.34/0.78 @ ^ [X: hoare_2091234717iple_a] : ( (|) @ ( member290856304iple_a @ X @ A_104 ) @ ( member290856304iple_a @ X @ B_49 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_231_Un__def,axiom,
% 0.34/0.78 ! [A_104: nat > $o,B_49: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ A_104 @ B_49 )
% 0.34/0.78 = ( collect_nat
% 0.34/0.78 @ ^ [X: nat] : ( (|) @ ( member_nat @ X @ A_104 ) @ ( member_nat @ X @ B_49 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_232_Un__def,axiom,
% 0.34/0.78 ! [A_104: pname > $o,B_49: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ A_104 @ B_49 )
% 0.34/0.78 = ( collect_pname
% 0.34/0.78 @ ^ [X: pname] : ( (|) @ ( member_pname @ X @ A_104 ) @ ( member_pname @ X @ B_49 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_233_Un__absorb,axiom,
% 0.34/0.78 ! [A_103: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ A_103 @ A_103 )
% 0.34/0.78 = A_103 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_234_Un__absorb,axiom,
% 0.34/0.78 ! [A_103: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ A_103 @ A_103 )
% 0.34/0.78 = A_103 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_235_Un__absorb,axiom,
% 0.34/0.78 ! [A_103: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ A_103 @ A_103 )
% 0.34/0.78 = A_103 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_236_Un__absorb,axiom,
% 0.34/0.78 ! [A_103: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ A_103 @ A_103 )
% 0.34/0.78 = A_103 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_237_Un__absorb,axiom,
% 0.34/0.78 ! [A_103: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ A_103 @ A_103 )
% 0.34/0.78 = A_103 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_238_image__ident,axiom,
% 0.34/0.78 ! [Y_12: nat > $o] :
% 0.34/0.78 ( ( image_nat_nat
% 0.34/0.78 @ ^ [X: nat] : X
% 0.34/0.78 @ Y_12 )
% 0.34/0.78 = Y_12 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_239_image__image,axiom,
% 0.34/0.78 ! [F_43: hoare_2091234717iple_a > hoare_1708887482_state,G_22: pname > hoare_2091234717iple_a,A_102: pname > $o] :
% 0.34/0.78 ( ( image_1884482962_state @ F_43 @ ( image_231808478iple_a @ G_22 @ A_102 ) )
% 0.34/0.78 = ( image_1116629049_state
% 0.34/0.78 @ ^ [X: pname] : ( F_43 @ ( G_22 @ X ) )
% 0.34/0.78 @ A_102 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_240_image__image,axiom,
% 0.34/0.78 ! [F_43: hoare_1708887482_state > hoare_2091234717iple_a,G_22: pname > hoare_1708887482_state,A_102: pname > $o] :
% 0.34/0.78 ( ( image_293283184iple_a @ F_43 @ ( image_1116629049_state @ G_22 @ A_102 ) )
% 0.34/0.78 = ( image_231808478iple_a
% 0.34/0.78 @ ^ [X: pname] : ( F_43 @ ( G_22 @ X ) )
% 0.34/0.78 @ A_102 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_241_sup__Un__eq,axiom,
% 0.34/0.78 ! [R_2: nat > $o,S_5: nat > $o,X: nat] :
% 0.34/0.78 ( ( semila848761471_nat_o
% 0.34/0.78 @ ^ [Y_7: nat] : ( member_nat @ Y_7 @ R_2 )
% 0.34/0.78 @ ^ [Y_7: nat] : ( member_nat @ Y_7 @ S_5 )
% 0.34/0.78 @ X )
% 0.34/0.78 <=> ( member_nat @ X @ ( semila848761471_nat_o @ R_2 @ S_5 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_242_sup__Un__eq,axiom,
% 0.34/0.78 ! [R_2: ( hoare_2091234717iple_a > $o ) > $o,S_5: ( hoare_2091234717iple_a > $o ) > $o,X: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o
% 0.34/0.78 @ ^ [Y_7: hoare_2091234717iple_a > $o] : ( member99268621le_a_o @ Y_7 @ R_2 )
% 0.34/0.78 @ ^ [Y_7: hoare_2091234717iple_a > $o] : ( member99268621le_a_o @ Y_7 @ S_5 )
% 0.34/0.78 @ X )
% 0.34/0.78 <=> ( member99268621le_a_o @ X @ ( semila2050116131_a_o_o @ R_2 @ S_5 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_243_sup__Un__eq,axiom,
% 0.34/0.78 ! [R_2: hoare_1708887482_state > $o,S_5: hoare_1708887482_state > $o,X: hoare_1708887482_state] :
% 0.34/0.78 ( ( semila1122118281tate_o
% 0.34/0.78 @ ^ [Y_7: hoare_1708887482_state] : ( member451959335_state @ Y_7 @ R_2 )
% 0.34/0.78 @ ^ [Y_7: hoare_1708887482_state] : ( member451959335_state @ Y_7 @ S_5 )
% 0.34/0.78 @ X )
% 0.34/0.78 <=> ( member451959335_state @ X @ ( semila1122118281tate_o @ R_2 @ S_5 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_244_sup__Un__eq,axiom,
% 0.34/0.78 ! [R_2: hoare_2091234717iple_a > $o,S_5: hoare_2091234717iple_a > $o,X: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( semila1052848428le_a_o
% 0.34/0.78 @ ^ [Y_7: hoare_2091234717iple_a] : ( member290856304iple_a @ Y_7 @ R_2 )
% 0.34/0.78 @ ^ [Y_7: hoare_2091234717iple_a] : ( member290856304iple_a @ Y_7 @ S_5 )
% 0.34/0.78 @ X )
% 0.34/0.78 <=> ( member290856304iple_a @ X @ ( semila1052848428le_a_o @ R_2 @ S_5 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_245_sup__Un__eq,axiom,
% 0.34/0.78 ! [R_2: pname > $o,S_5: pname > $o,X: pname] :
% 0.34/0.78 ( ( semila1780557381name_o
% 0.34/0.78 @ ^ [Y_7: pname] : ( member_pname @ Y_7 @ R_2 )
% 0.34/0.78 @ ^ [Y_7: pname] : ( member_pname @ Y_7 @ S_5 )
% 0.34/0.78 @ X )
% 0.34/0.78 <=> ( member_pname @ X @ ( semila1780557381name_o @ R_2 @ S_5 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_246_Collect__disj__eq,axiom,
% 0.34/0.78 ! [P_33: pname > $o,Q_19: pname > $o] :
% 0.34/0.78 ( ( collect_pname
% 0.34/0.78 @ ^ [X: pname] : ( (|) @ ( P_33 @ X ) @ ( Q_19 @ X ) ) )
% 0.34/0.78 = ( semila1780557381name_o @ ( collect_pname @ P_33 ) @ ( collect_pname @ Q_19 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_247_Collect__disj__eq,axiom,
% 0.34/0.78 ! [P_33: ( hoare_2091234717iple_a > $o ) > $o,Q_19: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( collec1008234059le_a_o
% 0.34/0.78 @ ^ [X: hoare_2091234717iple_a > $o] : ( (|) @ ( P_33 @ X ) @ ( Q_19 @ X ) ) )
% 0.34/0.78 = ( semila2050116131_a_o_o @ ( collec1008234059le_a_o @ P_33 ) @ ( collec1008234059le_a_o @ Q_19 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_248_Collect__disj__eq,axiom,
% 0.34/0.78 ! [P_33: hoare_1708887482_state > $o,Q_19: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( collec1568722789_state
% 0.34/0.78 @ ^ [X: hoare_1708887482_state] : ( (|) @ ( P_33 @ X ) @ ( Q_19 @ X ) ) )
% 0.34/0.78 = ( semila1122118281tate_o @ ( collec1568722789_state @ P_33 ) @ ( collec1568722789_state @ Q_19 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_249_Collect__disj__eq,axiom,
% 0.34/0.78 ! [P_33: hoare_2091234717iple_a > $o,Q_19: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( collec992574898iple_a
% 0.34/0.78 @ ^ [X: hoare_2091234717iple_a] : ( (|) @ ( P_33 @ X ) @ ( Q_19 @ X ) ) )
% 0.34/0.78 = ( semila1052848428le_a_o @ ( collec992574898iple_a @ P_33 ) @ ( collec992574898iple_a @ Q_19 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_250_Collect__disj__eq,axiom,
% 0.34/0.78 ! [P_33: nat > $o,Q_19: nat > $o] :
% 0.34/0.78 ( ( collect_nat
% 0.34/0.78 @ ^ [X: nat] : ( (|) @ ( P_33 @ X ) @ ( Q_19 @ X ) ) )
% 0.34/0.78 = ( semila848761471_nat_o @ ( collect_nat @ P_33 ) @ ( collect_nat @ Q_19 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_251_imageE,axiom,
% 0.34/0.78 ! [B_48: nat,F_42: nat > nat,A_101: nat > $o] :
% 0.34/0.78 ( ( member_nat @ B_48 @ ( image_nat_nat @ F_42 @ A_101 ) )
% 0.34/0.78 => ~ ! [X: nat] :
% 0.34/0.78 ( ( B_48
% 0.34/0.78 = ( F_42 @ X ) )
% 0.34/0.78 => ~ ( member_nat @ X @ A_101 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_252_imageE,axiom,
% 0.34/0.78 ! [B_48: pname,F_42: nat > pname,A_101: nat > $o] :
% 0.34/0.78 ( ( member_pname @ B_48 @ ( image_nat_pname @ F_42 @ A_101 ) )
% 0.34/0.78 => ~ ! [X: nat] :
% 0.34/0.78 ( ( B_48
% 0.34/0.78 = ( F_42 @ X ) )
% 0.34/0.78 => ~ ( member_nat @ X @ A_101 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_253_imageE,axiom,
% 0.34/0.78 ! [B_48: pname,F_42: ( hoare_2091234717iple_a > $o ) > pname,A_101: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( member_pname @ B_48 @ ( image_1908519857_pname @ F_42 @ A_101 ) )
% 0.34/0.78 => ~ ! [X: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( B_48
% 0.34/0.78 = ( F_42 @ X ) )
% 0.34/0.78 => ~ ( member99268621le_a_o @ X @ A_101 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_254_imageE,axiom,
% 0.34/0.78 ! [B_48: pname,F_42: hoare_2091234717iple_a > pname,A_101: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( member_pname @ B_48 @ ( image_924789612_pname @ F_42 @ A_101 ) )
% 0.34/0.78 => ~ ! [X: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( B_48
% 0.34/0.78 = ( F_42 @ X ) )
% 0.34/0.78 => ~ ( member290856304iple_a @ X @ A_101 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_255_imageE,axiom,
% 0.34/0.78 ! [B_48: hoare_1708887482_state,F_42: pname > hoare_1708887482_state,A_101: pname > $o] :
% 0.34/0.78 ( ( member451959335_state @ B_48 @ ( image_1116629049_state @ F_42 @ A_101 ) )
% 0.34/0.78 => ~ ! [X: pname] :
% 0.34/0.78 ( ( B_48
% 0.34/0.78 = ( F_42 @ X ) )
% 0.34/0.78 => ~ ( member_pname @ X @ A_101 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_256_imageE,axiom,
% 0.34/0.78 ! [B_48: nat,F_42: pname > nat,A_101: pname > $o] :
% 0.34/0.78 ( ( member_nat @ B_48 @ ( image_pname_nat @ F_42 @ A_101 ) )
% 0.34/0.78 => ~ ! [X: pname] :
% 0.34/0.78 ( ( B_48
% 0.34/0.78 = ( F_42 @ X ) )
% 0.34/0.78 => ~ ( member_pname @ X @ A_101 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_257_imageE,axiom,
% 0.34/0.78 ! [B_48: hoare_2091234717iple_a > $o,F_42: pname > hoare_2091234717iple_a > $o,A_101: pname > $o] :
% 0.34/0.78 ( ( member99268621le_a_o @ B_48 @ ( image_742317343le_a_o @ F_42 @ A_101 ) )
% 0.34/0.78 => ~ ! [X: pname] :
% 0.34/0.78 ( ( B_48
% 0.34/0.78 = ( F_42 @ X ) )
% 0.34/0.78 => ~ ( member_pname @ X @ A_101 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_258_imageE,axiom,
% 0.34/0.78 ! [B_48: hoare_2091234717iple_a,F_42: pname > hoare_2091234717iple_a,A_101: pname > $o] :
% 0.34/0.78 ( ( member290856304iple_a @ B_48 @ ( image_231808478iple_a @ F_42 @ A_101 ) )
% 0.34/0.78 => ~ ! [X: pname] :
% 0.34/0.78 ( ( B_48
% 0.34/0.78 = ( F_42 @ X ) )
% 0.34/0.78 => ~ ( member_pname @ X @ A_101 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_259_Body__triple__valid__Suc,axiom,
% 0.34/0.78 ! [N_8: nat,P_32: state > state > $o,Pn_6: pname,Q_18: state > state > $o] :
% 0.34/0.78 ( ( hoare_23738522_state @ N_8 @ ( hoare_858012674_state @ P_32 @ ( the_com @ ( body_1 @ Pn_6 ) ) @ Q_18 ) )
% 0.34/0.78 <=> ( hoare_23738522_state @ ( suc @ N_8 ) @ ( hoare_858012674_state @ P_32 @ ( body @ Pn_6 ) @ Q_18 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_260_Body__triple__valid__Suc,axiom,
% 0.34/0.78 ! [N_8: nat,P_32: x_a > state > $o,Pn_6: pname,Q_18: x_a > state > $o] :
% 0.34/0.78 ( ( hoare_1421888935alid_a @ N_8 @ ( hoare_657976383iple_a @ P_32 @ ( the_com @ ( body_1 @ Pn_6 ) ) @ Q_18 ) )
% 0.34/0.78 <=> ( hoare_1421888935alid_a @ ( suc @ N_8 ) @ ( hoare_657976383iple_a @ P_32 @ ( body @ Pn_6 ) @ Q_18 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_261_triple_Oexhaust,axiom,
% 0.34/0.78 ! [Y_11: hoare_2091234717iple_a] :
% 0.34/0.78 ~ ! [Fun1_2: x_a > state > $o,Com_4: com,Fun2_2: x_a > state > $o] :
% 0.34/0.78 ( Y_11
% 0.34/0.78 != ( hoare_657976383iple_a @ Fun1_2 @ Com_4 @ Fun2_2 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_262_triple_Oexhaust,axiom,
% 0.34/0.78 ! [Y_11: hoare_1708887482_state] :
% 0.34/0.78 ~ ! [Fun1_2: state > state > $o,Com_4: com,Fun2_2: state > state > $o] :
% 0.34/0.78 ( Y_11
% 0.34/0.78 != ( hoare_858012674_state @ Fun1_2 @ Com_4 @ Fun2_2 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_263_Body1,axiom,
% 0.34/0.78 ! [Pn_5: pname,G_21: hoare_1708887482_state > $o,P_31: pname > state > state > $o,Q_17: pname > state > state > $o,Procs: pname > $o] :
% 0.34/0.78 ( ( hoare_90032982_state
% 0.34/0.78 @ ( semila1122118281tate_o @ G_21
% 0.34/0.78 @ ( image_1116629049_state
% 0.34/0.78 @ ^ [P_9: pname] : ( hoare_858012674_state @ ( P_31 @ P_9 ) @ ( body @ P_9 ) @ ( Q_17 @ P_9 ) )
% 0.34/0.78 @ Procs ) )
% 0.34/0.78 @ ( image_1116629049_state
% 0.34/0.78 @ ^ [P_9: pname] : ( hoare_858012674_state @ ( P_31 @ P_9 ) @ ( the_com @ ( body_1 @ P_9 ) ) @ ( Q_17 @ P_9 ) )
% 0.34/0.78 @ Procs ) )
% 0.34/0.78 => ( ( member_pname @ Pn_5 @ Procs )
% 0.34/0.78 => ( hoare_90032982_state @ G_21 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_31 @ Pn_5 ) @ ( body @ Pn_5 ) @ ( Q_17 @ Pn_5 ) ) @ bot_bo19817387tate_o ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_264_Body1,axiom,
% 0.34/0.78 ! [Pn_5: pname,G_21: hoare_2091234717iple_a > $o,P_31: pname > x_a > state > $o,Q_17: pname > x_a > state > $o,Procs: pname > $o] :
% 0.34/0.78 ( ( hoare_1467856363rivs_a
% 0.34/0.78 @ ( semila1052848428le_a_o @ G_21
% 0.34/0.78 @ ( image_231808478iple_a
% 0.34/0.78 @ ^ [P_9: pname] : ( hoare_657976383iple_a @ ( P_31 @ P_9 ) @ ( body @ P_9 ) @ ( Q_17 @ P_9 ) )
% 0.34/0.78 @ Procs ) )
% 0.34/0.78 @ ( image_231808478iple_a
% 0.34/0.78 @ ^ [P_9: pname] : ( hoare_657976383iple_a @ ( P_31 @ P_9 ) @ ( the_com @ ( body_1 @ P_9 ) ) @ ( Q_17 @ P_9 ) )
% 0.34/0.78 @ Procs ) )
% 0.34/0.78 => ( ( member_pname @ Pn_5 @ Procs )
% 0.34/0.78 => ( hoare_1467856363rivs_a @ G_21 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ ( P_31 @ Pn_5 ) @ ( body @ Pn_5 ) @ ( Q_17 @ Pn_5 ) ) @ bot_bo1791335050le_a_o ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_265_image__cong,axiom,
% 0.34/0.78 ! [F_41: nat > nat,G_20: nat > nat,M_3: nat > $o,N_7: nat > $o] :
% 0.34/0.78 ( ( M_3 = N_7 )
% 0.34/0.78 => ( ! [X: nat] :
% 0.34/0.78 ( ( member_nat @ X @ N_7 )
% 0.34/0.78 => ( ( F_41 @ X )
% 0.34/0.78 = ( G_20 @ X ) ) )
% 0.34/0.78 => ( ( image_nat_nat @ F_41 @ M_3 )
% 0.34/0.78 = ( image_nat_nat @ G_20 @ N_7 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_266_image__cong,axiom,
% 0.34/0.78 ! [F_41: pname > hoare_1708887482_state,G_20: pname > hoare_1708887482_state,M_3: pname > $o,N_7: pname > $o] :
% 0.34/0.78 ( ( M_3 = N_7 )
% 0.34/0.78 => ( ! [X: pname] :
% 0.34/0.78 ( ( member_pname @ X @ N_7 )
% 0.34/0.78 => ( ( F_41 @ X )
% 0.34/0.78 = ( G_20 @ X ) ) )
% 0.34/0.78 => ( ( image_1116629049_state @ F_41 @ M_3 )
% 0.34/0.78 = ( image_1116629049_state @ G_20 @ N_7 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_267_image__cong,axiom,
% 0.34/0.78 ! [F_41: pname > hoare_2091234717iple_a,G_20: pname > hoare_2091234717iple_a,M_3: pname > $o,N_7: pname > $o] :
% 0.34/0.78 ( ( M_3 = N_7 )
% 0.34/0.78 => ( ! [X: pname] :
% 0.34/0.78 ( ( member_pname @ X @ N_7 )
% 0.34/0.78 => ( ( F_41 @ X )
% 0.34/0.78 = ( G_20 @ X ) ) )
% 0.34/0.78 => ( ( image_231808478iple_a @ F_41 @ M_3 )
% 0.34/0.78 = ( image_231808478iple_a @ G_20 @ N_7 ) ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_268_Body__triple__valid__0,axiom,
% 0.34/0.78 ! [P_30: state > state > $o,Pn_4: pname,Q_16: state > state > $o] : ( hoare_23738522_state @ zero_zero_nat @ ( hoare_858012674_state @ P_30 @ ( body @ Pn_4 ) @ Q_16 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_269_Body__triple__valid__0,axiom,
% 0.34/0.78 ! [P_30: x_a > state > $o,Pn_4: pname,Q_16: x_a > state > $o] : ( hoare_1421888935alid_a @ zero_zero_nat @ ( hoare_657976383iple_a @ P_30 @ ( body @ Pn_4 ) @ Q_16 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_270_com_Osimps_I6_J,axiom,
% 0.34/0.78 ! [Pname_1: pname,Pname: pname] :
% 0.34/0.78 ( ( ( body @ Pname_1 )
% 0.34/0.78 = ( body @ Pname ) )
% 0.34/0.78 <=> ( Pname_1 = Pname ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_271_evalc_OBody,axiom,
% 0.34/0.78 ! [Pn_1: pname,S0: state,S1: state] :
% 0.34/0.78 ( ( evalc @ ( the_com @ ( body_1 @ Pn_1 ) ) @ S0 @ S1 )
% 0.34/0.78 => ( evalc @ ( body @ Pn_1 ) @ S0 @ S1 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_272_evalc__elim__cases_I6_J,axiom,
% 0.34/0.78 ! [P: pname,S: state,S1: state] :
% 0.34/0.78 ( ( evalc @ ( body @ P ) @ S @ S1 )
% 0.34/0.78 => ( evalc @ ( the_com @ ( body_1 @ P ) ) @ S @ S1 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_273_Sup__fin_Oidem,axiom,
% 0.34/0.78 ! [X_34: nat > $o] :
% 0.34/0.78 ( ( semila848761471_nat_o @ X_34 @ X_34 )
% 0.34/0.78 = X_34 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_274_Sup__fin_Oidem,axiom,
% 0.34/0.78 ! [X_34: nat] :
% 0.34/0.78 ( ( semila972727038up_nat @ X_34 @ X_34 )
% 0.34/0.78 = X_34 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_275_Sup__fin_Oidem,axiom,
% 0.34/0.78 ! [X_34: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( semila2050116131_a_o_o @ X_34 @ X_34 )
% 0.34/0.78 = X_34 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_276_Sup__fin_Oidem,axiom,
% 0.34/0.78 ! [X_34: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( semila1122118281tate_o @ X_34 @ X_34 )
% 0.34/0.78 = X_34 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_277_Sup__fin_Oidem,axiom,
% 0.34/0.78 ! [X_34: pname > $o] :
% 0.34/0.78 ( ( semila1780557381name_o @ X_34 @ X_34 )
% 0.34/0.78 = X_34 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_278_Sup__fin_Oidem,axiom,
% 0.34/0.78 ! [X_34: $o] :
% 0.34/0.78 ( ( semila10642723_sup_o @ X_34 @ X_34 )
% 0.34/0.78 <=> X_34 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_279_Sup__fin_Oidem,axiom,
% 0.34/0.78 ! [X_34: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( semila1052848428le_a_o @ X_34 @ X_34 )
% 0.34/0.78 = X_34 ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_280_triples__valid__Suc,axiom,
% 0.34/0.78 ! [N_6: nat,Ts_2: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ! [X: hoare_1708887482_state] :
% 0.34/0.78 ( ( member451959335_state @ X @ Ts_2 )
% 0.34/0.78 => ( hoare_23738522_state @ ( suc @ N_6 ) @ X ) )
% 0.34/0.78 => ! [X: hoare_1708887482_state] :
% 0.34/0.78 ( ( member451959335_state @ X @ Ts_2 )
% 0.34/0.78 => ( hoare_23738522_state @ N_6 @ X ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_281_triples__valid__Suc,axiom,
% 0.34/0.78 ! [N_6: nat,Ts_2: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ! [X: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( member290856304iple_a @ X @ Ts_2 )
% 0.34/0.78 => ( hoare_1421888935alid_a @ ( suc @ N_6 ) @ X ) )
% 0.34/0.78 => ! [X: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( member290856304iple_a @ X @ Ts_2 )
% 0.34/0.78 => ( hoare_1421888935alid_a @ N_6 @ X ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_282_emptyE,axiom,
% 0.34/0.78 ! [A_100: nat] :
% 0.34/0.78 ~ ( member_nat @ A_100 @ bot_bot_nat_o ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_283_emptyE,axiom,
% 0.34/0.78 ! [A_100: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ~ ( member99268621le_a_o @ A_100 @ bot_bo1957696069_a_o_o ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_284_emptyE,axiom,
% 0.34/0.78 ! [A_100: hoare_2091234717iple_a] :
% 0.34/0.78 ~ ( member290856304iple_a @ A_100 @ bot_bo1791335050le_a_o ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_285_emptyE,axiom,
% 0.34/0.78 ! [A_100: hoare_1708887482_state] :
% 0.34/0.78 ~ ( member451959335_state @ A_100 @ bot_bo19817387tate_o ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_286_emptyE,axiom,
% 0.34/0.78 ! [A_100: pname] :
% 0.34/0.78 ~ ( member_pname @ A_100 @ bot_bot_pname_o ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_287_insertE,axiom,
% 0.34/0.78 ! [A_99: nat,B_47: nat,A_98: nat > $o] :
% 0.34/0.78 ( ( member_nat @ A_99 @ ( insert_nat @ B_47 @ A_98 ) )
% 0.34/0.78 => ( ( A_99 != B_47 )
% 0.34/0.78 => ( member_nat @ A_99 @ A_98 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_288_insertE,axiom,
% 0.34/0.78 ! [A_99: hoare_2091234717iple_a > $o,B_47: hoare_2091234717iple_a > $o,A_98: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( member99268621le_a_o @ A_99 @ ( insert102003750le_a_o @ B_47 @ A_98 ) )
% 0.34/0.78 => ( ( A_99 != B_47 )
% 0.34/0.78 => ( member99268621le_a_o @ A_99 @ A_98 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_289_insertE,axiom,
% 0.34/0.78 ! [A_99: hoare_2091234717iple_a,B_47: hoare_2091234717iple_a,A_98: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( member290856304iple_a @ A_99 @ ( insert1597628439iple_a @ B_47 @ A_98 ) )
% 0.34/0.78 => ( ( A_99 != B_47 )
% 0.34/0.78 => ( member290856304iple_a @ A_99 @ A_98 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_290_insertE,axiom,
% 0.34/0.78 ! [A_99: hoare_1708887482_state,B_47: hoare_1708887482_state,A_98: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( member451959335_state @ A_99 @ ( insert528405184_state @ B_47 @ A_98 ) )
% 0.34/0.78 => ( ( A_99 != B_47 )
% 0.34/0.78 => ( member451959335_state @ A_99 @ A_98 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_291_insertE,axiom,
% 0.34/0.78 ! [A_99: pname,B_47: pname,A_98: pname > $o] :
% 0.34/0.78 ( ( member_pname @ A_99 @ ( insert_pname @ B_47 @ A_98 ) )
% 0.34/0.78 => ( ( A_99 != B_47 )
% 0.34/0.78 => ( member_pname @ A_99 @ A_98 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_292_insertCI,axiom,
% 0.34/0.78 ! [B_46: nat,A_97: nat,B_45: nat > $o] :
% 0.34/0.78 ( ( ~ ( member_nat @ A_97 @ B_45 )
% 0.34/0.78 => ( A_97 = B_46 ) )
% 0.34/0.78 => ( member_nat @ A_97 @ ( insert_nat @ B_46 @ B_45 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_293_insertCI,axiom,
% 0.34/0.78 ! [B_46: hoare_2091234717iple_a > $o,A_97: hoare_2091234717iple_a > $o,B_45: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( ~ ( member99268621le_a_o @ A_97 @ B_45 )
% 0.34/0.78 => ( A_97 = B_46 ) )
% 0.34/0.78 => ( member99268621le_a_o @ A_97 @ ( insert102003750le_a_o @ B_46 @ B_45 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_294_insertCI,axiom,
% 0.34/0.78 ! [B_46: hoare_2091234717iple_a,A_97: hoare_2091234717iple_a,B_45: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( ~ ( member290856304iple_a @ A_97 @ B_45 )
% 0.34/0.78 => ( A_97 = B_46 ) )
% 0.34/0.78 => ( member290856304iple_a @ A_97 @ ( insert1597628439iple_a @ B_46 @ B_45 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_295_insertCI,axiom,
% 0.34/0.78 ! [B_46: hoare_1708887482_state,A_97: hoare_1708887482_state,B_45: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( ~ ( member451959335_state @ A_97 @ B_45 )
% 0.34/0.78 => ( A_97 = B_46 ) )
% 0.34/0.78 => ( member451959335_state @ A_97 @ ( insert528405184_state @ B_46 @ B_45 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_296_insertCI,axiom,
% 0.34/0.78 ! [B_46: pname,A_97: pname,B_45: pname > $o] :
% 0.34/0.78 ( ( ~ ( member_pname @ A_97 @ B_45 )
% 0.34/0.78 => ( A_97 = B_46 ) )
% 0.34/0.78 => ( member_pname @ A_97 @ ( insert_pname @ B_46 @ B_45 ) ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_297_empty__not__insert,axiom,
% 0.34/0.78 ! [A_96: nat,A_95: nat > $o] :
% 0.34/0.78 ( bot_bot_nat_o
% 0.34/0.78 != ( insert_nat @ A_96 @ A_95 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_298_empty__not__insert,axiom,
% 0.34/0.78 ! [A_96: hoare_2091234717iple_a > $o,A_95: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( bot_bo1957696069_a_o_o
% 0.34/0.78 != ( insert102003750le_a_o @ A_96 @ A_95 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_299_empty__not__insert,axiom,
% 0.34/0.78 ! [A_96: pname,A_95: pname > $o] :
% 0.34/0.78 ( bot_bot_pname_o
% 0.34/0.78 != ( insert_pname @ A_96 @ A_95 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_300_empty__not__insert,axiom,
% 0.34/0.78 ! [A_96: hoare_2091234717iple_a,A_95: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( bot_bo1791335050le_a_o
% 0.34/0.78 != ( insert1597628439iple_a @ A_96 @ A_95 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_301_empty__not__insert,axiom,
% 0.34/0.78 ! [A_96: hoare_1708887482_state,A_95: hoare_1708887482_state > $o] :
% 0.34/0.78 ( bot_bo19817387tate_o
% 0.34/0.78 != ( insert528405184_state @ A_96 @ A_95 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_302_insert__not__empty,axiom,
% 0.34/0.78 ! [A_94: nat,A_93: nat > $o] :
% 0.34/0.78 ( ( insert_nat @ A_94 @ A_93 )
% 0.34/0.78 != bot_bot_nat_o ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_303_insert__not__empty,axiom,
% 0.34/0.78 ! [A_94: hoare_2091234717iple_a > $o,A_93: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ( insert102003750le_a_o @ A_94 @ A_93 )
% 0.34/0.78 != bot_bo1957696069_a_o_o ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_304_insert__not__empty,axiom,
% 0.34/0.78 ! [A_94: pname,A_93: pname > $o] :
% 0.34/0.78 ( ( insert_pname @ A_94 @ A_93 )
% 0.34/0.78 != bot_bot_pname_o ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_305_insert__not__empty,axiom,
% 0.34/0.78 ! [A_94: hoare_2091234717iple_a,A_93: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( insert1597628439iple_a @ A_94 @ A_93 )
% 0.34/0.78 != bot_bo1791335050le_a_o ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_306_insert__not__empty,axiom,
% 0.34/0.78 ! [A_94: hoare_1708887482_state,A_93: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ( insert528405184_state @ A_94 @ A_93 )
% 0.34/0.78 != bot_bo19817387tate_o ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_307_bot__empty__eq,axiom,
% 0.34/0.78 ! [X: nat] :
% 0.34/0.78 ( ( bot_bot_nat_o @ X )
% 0.34/0.78 <=> ( member_nat @ X @ bot_bot_nat_o ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_308_bot__empty__eq,axiom,
% 0.34/0.78 ! [X: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( bot_bo1957696069_a_o_o @ X )
% 0.34/0.78 <=> ( member99268621le_a_o @ X @ bot_bo1957696069_a_o_o ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_309_bot__empty__eq,axiom,
% 0.34/0.78 ! [X: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( bot_bo1791335050le_a_o @ X )
% 0.34/0.78 <=> ( member290856304iple_a @ X @ bot_bo1791335050le_a_o ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_310_bot__empty__eq,axiom,
% 0.34/0.78 ! [X: hoare_1708887482_state] :
% 0.34/0.78 ( ( bot_bo19817387tate_o @ X )
% 0.34/0.78 <=> ( member451959335_state @ X @ bot_bo19817387tate_o ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_311_bot__empty__eq,axiom,
% 0.34/0.78 ! [X: pname] :
% 0.34/0.78 ( ( bot_bot_pname_o @ X )
% 0.34/0.78 <=> ( member_pname @ X @ bot_bot_pname_o ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_312_empty__def,axiom,
% 0.34/0.78 ( bot_bot_pname_o
% 0.34/0.78 = ( collect_pname
% 0.34/0.78 @ ^ [X: pname] : $false ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_313_empty__def,axiom,
% 0.34/0.78 ( bot_bo1791335050le_a_o
% 0.34/0.78 = ( collec992574898iple_a
% 0.34/0.78 @ ^ [X: hoare_2091234717iple_a] : $false ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_314_empty__def,axiom,
% 0.34/0.78 ( bot_bo1957696069_a_o_o
% 0.34/0.78 = ( collec1008234059le_a_o
% 0.34/0.78 @ ^ [X: hoare_2091234717iple_a > $o] : $false ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_315_empty__def,axiom,
% 0.34/0.78 ( bot_bo19817387tate_o
% 0.34/0.78 = ( collec1568722789_state
% 0.34/0.78 @ ^ [X: hoare_1708887482_state] : $false ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_316_empty__def,axiom,
% 0.34/0.78 ( bot_bot_nat_o
% 0.34/0.78 = ( collect_nat
% 0.34/0.78 @ ^ [X: nat] : $false ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_317_insertI1,axiom,
% 0.34/0.78 ! [A_92: nat,B_44: nat > $o] : ( member_nat @ A_92 @ ( insert_nat @ A_92 @ B_44 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_318_insertI1,axiom,
% 0.34/0.78 ! [A_92: hoare_2091234717iple_a > $o,B_44: ( hoare_2091234717iple_a > $o ) > $o] : ( member99268621le_a_o @ A_92 @ ( insert102003750le_a_o @ A_92 @ B_44 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_319_insertI1,axiom,
% 0.34/0.78 ! [A_92: hoare_2091234717iple_a,B_44: hoare_2091234717iple_a > $o] : ( member290856304iple_a @ A_92 @ ( insert1597628439iple_a @ A_92 @ B_44 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_320_insertI1,axiom,
% 0.34/0.78 ! [A_92: hoare_1708887482_state,B_44: hoare_1708887482_state > $o] : ( member451959335_state @ A_92 @ ( insert528405184_state @ A_92 @ B_44 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_321_insertI1,axiom,
% 0.34/0.78 ! [A_92: pname,B_44: pname > $o] : ( member_pname @ A_92 @ ( insert_pname @ A_92 @ B_44 ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_322_all__not__in__conv,axiom,
% 0.34/0.78 ! [A_91: nat > $o] :
% 0.34/0.78 ( ! [X: nat] :
% 0.34/0.78 ~ ( member_nat @ X @ A_91 )
% 0.34/0.78 <=> ( A_91 = bot_bot_nat_o ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_323_all__not__in__conv,axiom,
% 0.34/0.78 ! [A_91: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.78 ( ! [X: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ~ ( member99268621le_a_o @ X @ A_91 )
% 0.34/0.78 <=> ( A_91 = bot_bo1957696069_a_o_o ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_324_all__not__in__conv,axiom,
% 0.34/0.78 ! [A_91: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ! [X: hoare_2091234717iple_a] :
% 0.34/0.78 ~ ( member290856304iple_a @ X @ A_91 )
% 0.34/0.78 <=> ( A_91 = bot_bo1791335050le_a_o ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_325_all__not__in__conv,axiom,
% 0.34/0.78 ! [A_91: hoare_1708887482_state > $o] :
% 0.34/0.78 ( ! [X: hoare_1708887482_state] :
% 0.34/0.78 ~ ( member451959335_state @ X @ A_91 )
% 0.34/0.78 <=> ( A_91 = bot_bo19817387tate_o ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_326_all__not__in__conv,axiom,
% 0.34/0.78 ! [A_91: pname > $o] :
% 0.34/0.78 ( ! [X: pname] :
% 0.34/0.78 ~ ( member_pname @ X @ A_91 )
% 0.34/0.78 <=> ( A_91 = bot_bot_pname_o ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_327_singleton__conv2,axiom,
% 0.34/0.78 ! [A_90: hoare_2091234717iple_a > $o] :
% 0.34/0.78 ( ( collec1008234059le_a_o @ ( fequal845167073le_a_o @ A_90 ) )
% 0.34/0.78 = ( insert102003750le_a_o @ A_90 @ bot_bo1957696069_a_o_o ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_328_singleton__conv2,axiom,
% 0.34/0.78 ! [A_90: pname] :
% 0.34/0.78 ( ( collect_pname @ ( fequal_pname @ A_90 ) )
% 0.34/0.78 = ( insert_pname @ A_90 @ bot_bot_pname_o ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_329_singleton__conv2,axiom,
% 0.34/0.78 ! [A_90: hoare_2091234717iple_a] :
% 0.34/0.78 ( ( collec992574898iple_a @ ( fequal1604381340iple_a @ A_90 ) )
% 0.34/0.78 = ( insert1597628439iple_a @ A_90 @ bot_bo1791335050le_a_o ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_330_singleton__conv2,axiom,
% 0.34/0.78 ! [A_90: hoare_1708887482_state] :
% 0.34/0.78 ( ( collec1568722789_state @ ( fequal224822779_state @ A_90 ) )
% 0.34/0.78 = ( insert528405184_state @ A_90 @ bot_bo19817387tate_o ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_331_singleton__conv2,axiom,
% 0.34/0.78 ! [A_90: nat] :
% 0.34/0.78 ( ( collect_nat @ ( fequal_nat @ A_90 ) )
% 0.34/0.78 = ( insert_nat @ A_90 @ bot_bot_nat_o ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_332_ex__in__conv,axiom,
% 0.34/0.78 ! [A_89: nat > $o] :
% 0.34/0.78 ( ? [X: nat] : ( member_nat @ X @ A_89 )
% 0.34/0.78 <=> ( A_89 != bot_bot_nat_o ) ) ).
% 0.34/0.78
% 0.34/0.78 thf(fact_333_ex__in__conv,axiom,
% 0.34/0.78 ! [A_89: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ? [X: hoare_2091234717iple_a > $o] : ( member99268621le_a_o @ X @ A_89 )
% 0.34/0.79 <=> ( A_89 != bot_bo1957696069_a_o_o ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_334_ex__in__conv,axiom,
% 0.34/0.79 ! [A_89: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ? [X: hoare_2091234717iple_a] : ( member290856304iple_a @ X @ A_89 )
% 0.34/0.79 <=> ( A_89 != bot_bo1791335050le_a_o ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_335_ex__in__conv,axiom,
% 0.34/0.79 ! [A_89: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ? [X: hoare_1708887482_state] : ( member451959335_state @ X @ A_89 )
% 0.34/0.79 <=> ( A_89 != bot_bo19817387tate_o ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_336_ex__in__conv,axiom,
% 0.34/0.79 ! [A_89: pname > $o] :
% 0.34/0.79 ( ? [X: pname] : ( member_pname @ X @ A_89 )
% 0.34/0.79 <=> ( A_89 != bot_bot_pname_o ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_337_singleton__conv,axiom,
% 0.34/0.79 ! [A_88: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( collec1008234059le_a_o
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a > $o] : ( X = A_88 ) )
% 0.34/0.79 = ( insert102003750le_a_o @ A_88 @ bot_bo1957696069_a_o_o ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_338_singleton__conv,axiom,
% 0.34/0.79 ! [A_88: pname] :
% 0.34/0.79 ( ( collect_pname
% 0.34/0.79 @ ^ [X: pname] : ( X = A_88 ) )
% 0.34/0.79 = ( insert_pname @ A_88 @ bot_bot_pname_o ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_339_singleton__conv,axiom,
% 0.34/0.79 ! [A_88: hoare_2091234717iple_a] :
% 0.34/0.79 ( ( collec992574898iple_a
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a] : ( X = A_88 ) )
% 0.34/0.79 = ( insert1597628439iple_a @ A_88 @ bot_bo1791335050le_a_o ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_340_singleton__conv,axiom,
% 0.34/0.79 ! [A_88: hoare_1708887482_state] :
% 0.34/0.79 ( ( collec1568722789_state
% 0.34/0.79 @ ^ [X: hoare_1708887482_state] : ( X = A_88 ) )
% 0.34/0.79 = ( insert528405184_state @ A_88 @ bot_bo19817387tate_o ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_341_singleton__conv,axiom,
% 0.34/0.79 ! [A_88: nat] :
% 0.34/0.79 ( ( collect_nat
% 0.34/0.79 @ ^ [X: nat] : ( X = A_88 ) )
% 0.34/0.79 = ( insert_nat @ A_88 @ bot_bot_nat_o ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_342_Collect__conv__if2,axiom,
% 0.34/0.79 ! [P_29: ( hoare_2091234717iple_a > $o ) > $o,A_87: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( ( P_29 @ A_87 )
% 0.34/0.79 => ( ( collec1008234059le_a_o
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a > $o] : ( (&) @ ( A_87 = X ) @ ( P_29 @ X ) ) )
% 0.34/0.79 = ( insert102003750le_a_o @ A_87 @ bot_bo1957696069_a_o_o ) ) )
% 0.34/0.79 & ( ~ ( P_29 @ A_87 )
% 0.34/0.79 => ( ( collec1008234059le_a_o
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a > $o] : ( (&) @ ( A_87 = X ) @ ( P_29 @ X ) ) )
% 0.34/0.79 = bot_bo1957696069_a_o_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_343_Collect__conv__if2,axiom,
% 0.34/0.79 ! [P_29: pname > $o,A_87: pname] :
% 0.34/0.79 ( ( ( P_29 @ A_87 )
% 0.34/0.79 => ( ( collect_pname
% 0.34/0.79 @ ^ [X: pname] : ( (&) @ ( A_87 = X ) @ ( P_29 @ X ) ) )
% 0.34/0.79 = ( insert_pname @ A_87 @ bot_bot_pname_o ) ) )
% 0.34/0.79 & ( ~ ( P_29 @ A_87 )
% 0.34/0.79 => ( ( collect_pname
% 0.34/0.79 @ ^ [X: pname] : ( (&) @ ( A_87 = X ) @ ( P_29 @ X ) ) )
% 0.34/0.79 = bot_bot_pname_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_344_Collect__conv__if2,axiom,
% 0.34/0.79 ! [P_29: hoare_2091234717iple_a > $o,A_87: hoare_2091234717iple_a] :
% 0.34/0.79 ( ( ( P_29 @ A_87 )
% 0.34/0.79 => ( ( collec992574898iple_a
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a] : ( (&) @ ( A_87 = X ) @ ( P_29 @ X ) ) )
% 0.34/0.79 = ( insert1597628439iple_a @ A_87 @ bot_bo1791335050le_a_o ) ) )
% 0.34/0.79 & ( ~ ( P_29 @ A_87 )
% 0.34/0.79 => ( ( collec992574898iple_a
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a] : ( (&) @ ( A_87 = X ) @ ( P_29 @ X ) ) )
% 0.34/0.79 = bot_bo1791335050le_a_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_345_Collect__conv__if2,axiom,
% 0.34/0.79 ! [P_29: hoare_1708887482_state > $o,A_87: hoare_1708887482_state] :
% 0.34/0.79 ( ( ( P_29 @ A_87 )
% 0.34/0.79 => ( ( collec1568722789_state
% 0.34/0.79 @ ^ [X: hoare_1708887482_state] : ( (&) @ ( A_87 = X ) @ ( P_29 @ X ) ) )
% 0.34/0.79 = ( insert528405184_state @ A_87 @ bot_bo19817387tate_o ) ) )
% 0.34/0.79 & ( ~ ( P_29 @ A_87 )
% 0.34/0.79 => ( ( collec1568722789_state
% 0.34/0.79 @ ^ [X: hoare_1708887482_state] : ( (&) @ ( A_87 = X ) @ ( P_29 @ X ) ) )
% 0.34/0.79 = bot_bo19817387tate_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_346_Collect__conv__if2,axiom,
% 0.34/0.79 ! [P_29: nat > $o,A_87: nat] :
% 0.34/0.79 ( ( ( P_29 @ A_87 )
% 0.34/0.79 => ( ( collect_nat
% 0.34/0.79 @ ^ [X: nat] : ( (&) @ ( A_87 = X ) @ ( P_29 @ X ) ) )
% 0.34/0.79 = ( insert_nat @ A_87 @ bot_bot_nat_o ) ) )
% 0.34/0.79 & ( ~ ( P_29 @ A_87 )
% 0.34/0.79 => ( ( collect_nat
% 0.34/0.79 @ ^ [X: nat] : ( (&) @ ( A_87 = X ) @ ( P_29 @ X ) ) )
% 0.34/0.79 = bot_bot_nat_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_347_Collect__conv__if,axiom,
% 0.34/0.79 ! [P_28: ( hoare_2091234717iple_a > $o ) > $o,A_86: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( ( P_28 @ A_86 )
% 0.34/0.79 => ( ( collec1008234059le_a_o
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a > $o] : ( (&) @ ( X = A_86 ) @ ( P_28 @ X ) ) )
% 0.34/0.79 = ( insert102003750le_a_o @ A_86 @ bot_bo1957696069_a_o_o ) ) )
% 0.34/0.79 & ( ~ ( P_28 @ A_86 )
% 0.34/0.79 => ( ( collec1008234059le_a_o
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a > $o] : ( (&) @ ( X = A_86 ) @ ( P_28 @ X ) ) )
% 0.34/0.79 = bot_bo1957696069_a_o_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_348_Collect__conv__if,axiom,
% 0.34/0.79 ! [P_28: pname > $o,A_86: pname] :
% 0.34/0.79 ( ( ( P_28 @ A_86 )
% 0.34/0.79 => ( ( collect_pname
% 0.34/0.79 @ ^ [X: pname] : ( (&) @ ( X = A_86 ) @ ( P_28 @ X ) ) )
% 0.34/0.79 = ( insert_pname @ A_86 @ bot_bot_pname_o ) ) )
% 0.34/0.79 & ( ~ ( P_28 @ A_86 )
% 0.34/0.79 => ( ( collect_pname
% 0.34/0.79 @ ^ [X: pname] : ( (&) @ ( X = A_86 ) @ ( P_28 @ X ) ) )
% 0.34/0.79 = bot_bot_pname_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_349_Collect__conv__if,axiom,
% 0.34/0.79 ! [P_28: hoare_2091234717iple_a > $o,A_86: hoare_2091234717iple_a] :
% 0.34/0.79 ( ( ( P_28 @ A_86 )
% 0.34/0.79 => ( ( collec992574898iple_a
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a] : ( (&) @ ( X = A_86 ) @ ( P_28 @ X ) ) )
% 0.34/0.79 = ( insert1597628439iple_a @ A_86 @ bot_bo1791335050le_a_o ) ) )
% 0.34/0.79 & ( ~ ( P_28 @ A_86 )
% 0.34/0.79 => ( ( collec992574898iple_a
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a] : ( (&) @ ( X = A_86 ) @ ( P_28 @ X ) ) )
% 0.34/0.79 = bot_bo1791335050le_a_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_350_Collect__conv__if,axiom,
% 0.34/0.79 ! [P_28: hoare_1708887482_state > $o,A_86: hoare_1708887482_state] :
% 0.34/0.79 ( ( ( P_28 @ A_86 )
% 0.34/0.79 => ( ( collec1568722789_state
% 0.34/0.79 @ ^ [X: hoare_1708887482_state] : ( (&) @ ( X = A_86 ) @ ( P_28 @ X ) ) )
% 0.34/0.79 = ( insert528405184_state @ A_86 @ bot_bo19817387tate_o ) ) )
% 0.34/0.79 & ( ~ ( P_28 @ A_86 )
% 0.34/0.79 => ( ( collec1568722789_state
% 0.34/0.79 @ ^ [X: hoare_1708887482_state] : ( (&) @ ( X = A_86 ) @ ( P_28 @ X ) ) )
% 0.34/0.79 = bot_bo19817387tate_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_351_Collect__conv__if,axiom,
% 0.34/0.79 ! [P_28: nat > $o,A_86: nat] :
% 0.34/0.79 ( ( ( P_28 @ A_86 )
% 0.34/0.79 => ( ( collect_nat
% 0.34/0.79 @ ^ [X: nat] : ( (&) @ ( X = A_86 ) @ ( P_28 @ X ) ) )
% 0.34/0.79 = ( insert_nat @ A_86 @ bot_bot_nat_o ) ) )
% 0.34/0.79 & ( ~ ( P_28 @ A_86 )
% 0.34/0.79 => ( ( collect_nat
% 0.34/0.79 @ ^ [X: nat] : ( (&) @ ( X = A_86 ) @ ( P_28 @ X ) ) )
% 0.34/0.79 = bot_bot_nat_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_352_mem__def,axiom,
% 0.34/0.79 ! [X_33: nat,A_85: nat > $o] :
% 0.34/0.79 ( ( member_nat @ X_33 @ A_85 )
% 0.34/0.79 <=> ( A_85 @ X_33 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_353_mem__def,axiom,
% 0.34/0.79 ! [X_33: hoare_2091234717iple_a > $o,A_85: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( member99268621le_a_o @ X_33 @ A_85 )
% 0.34/0.79 <=> ( A_85 @ X_33 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_354_mem__def,axiom,
% 0.34/0.79 ! [X_33: hoare_2091234717iple_a,A_85: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( member290856304iple_a @ X_33 @ A_85 )
% 0.34/0.79 <=> ( A_85 @ X_33 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_355_mem__def,axiom,
% 0.34/0.79 ! [X_33: pname,A_85: pname > $o] :
% 0.34/0.79 ( ( member_pname @ X_33 @ A_85 )
% 0.34/0.79 <=> ( A_85 @ X_33 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_356_Collect__def,axiom,
% 0.34/0.79 ! [P_27: pname > $o] :
% 0.34/0.79 ( ( collect_pname @ P_27 )
% 0.34/0.79 = P_27 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_357_Collect__def,axiom,
% 0.34/0.79 ! [P_27: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( collec992574898iple_a @ P_27 )
% 0.34/0.79 = P_27 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_358_Collect__def,axiom,
% 0.34/0.79 ! [P_27: nat > $o] :
% 0.34/0.79 ( ( collect_nat @ P_27 )
% 0.34/0.79 = P_27 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_359_empty__Collect__eq,axiom,
% 0.34/0.79 ! [P_26: pname > $o] :
% 0.34/0.79 ( ( bot_bot_pname_o
% 0.34/0.79 = ( collect_pname @ P_26 ) )
% 0.34/0.79 <=> ! [X: pname] :
% 0.34/0.79 ~ ( P_26 @ X ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_360_empty__Collect__eq,axiom,
% 0.34/0.79 ! [P_26: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( bot_bo1791335050le_a_o
% 0.34/0.79 = ( collec992574898iple_a @ P_26 ) )
% 0.34/0.79 <=> ! [X: hoare_2091234717iple_a] :
% 0.34/0.79 ~ ( P_26 @ X ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_361_empty__Collect__eq,axiom,
% 0.34/0.79 ! [P_26: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( bot_bo1957696069_a_o_o
% 0.34/0.79 = ( collec1008234059le_a_o @ P_26 ) )
% 0.34/0.79 <=> ! [X: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ~ ( P_26 @ X ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_362_empty__Collect__eq,axiom,
% 0.34/0.79 ! [P_26: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( bot_bo19817387tate_o
% 0.34/0.79 = ( collec1568722789_state @ P_26 ) )
% 0.34/0.79 <=> ! [X: hoare_1708887482_state] :
% 0.34/0.79 ~ ( P_26 @ X ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_363_empty__Collect__eq,axiom,
% 0.34/0.79 ! [P_26: nat > $o] :
% 0.34/0.79 ( ( bot_bot_nat_o
% 0.34/0.79 = ( collect_nat @ P_26 ) )
% 0.34/0.79 <=> ! [X: nat] :
% 0.34/0.79 ~ ( P_26 @ X ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_364_empty__iff,axiom,
% 0.34/0.79 ! [C_25: nat] :
% 0.34/0.79 ~ ( member_nat @ C_25 @ bot_bot_nat_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_365_empty__iff,axiom,
% 0.34/0.79 ! [C_25: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ~ ( member99268621le_a_o @ C_25 @ bot_bo1957696069_a_o_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_366_empty__iff,axiom,
% 0.34/0.79 ! [C_25: hoare_2091234717iple_a] :
% 0.34/0.79 ~ ( member290856304iple_a @ C_25 @ bot_bo1791335050le_a_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_367_empty__iff,axiom,
% 0.34/0.79 ! [C_25: hoare_1708887482_state] :
% 0.34/0.79 ~ ( member451959335_state @ C_25 @ bot_bo19817387tate_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_368_empty__iff,axiom,
% 0.34/0.79 ! [C_25: pname] :
% 0.34/0.79 ~ ( member_pname @ C_25 @ bot_bot_pname_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_369_insert__compr,axiom,
% 0.34/0.79 ! [A_84: hoare_2091234717iple_a > $o,B_43: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( insert102003750le_a_o @ A_84 @ B_43 )
% 0.34/0.79 = ( collec1008234059le_a_o
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a > $o] : ( (|) @ ( X = A_84 ) @ ( member99268621le_a_o @ X @ B_43 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_370_insert__compr,axiom,
% 0.34/0.79 ! [A_84: hoare_2091234717iple_a,B_43: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( insert1597628439iple_a @ A_84 @ B_43 )
% 0.34/0.79 = ( collec992574898iple_a
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a] : ( (|) @ ( X = A_84 ) @ ( member290856304iple_a @ X @ B_43 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_371_insert__compr,axiom,
% 0.34/0.79 ! [A_84: hoare_1708887482_state,B_43: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( insert528405184_state @ A_84 @ B_43 )
% 0.34/0.79 = ( collec1568722789_state
% 0.34/0.79 @ ^ [X: hoare_1708887482_state] : ( (|) @ ( X = A_84 ) @ ( member451959335_state @ X @ B_43 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_372_insert__compr,axiom,
% 0.34/0.79 ! [A_84: nat,B_43: nat > $o] :
% 0.34/0.79 ( ( insert_nat @ A_84 @ B_43 )
% 0.34/0.79 = ( collect_nat
% 0.34/0.79 @ ^ [X: nat] : ( (|) @ ( X = A_84 ) @ ( member_nat @ X @ B_43 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_373_insert__compr,axiom,
% 0.34/0.79 ! [A_84: pname,B_43: pname > $o] :
% 0.34/0.79 ( ( insert_pname @ A_84 @ B_43 )
% 0.34/0.79 = ( collect_pname
% 0.34/0.79 @ ^ [X: pname] : ( (|) @ ( X = A_84 ) @ ( member_pname @ X @ B_43 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_374_insert__Collect,axiom,
% 0.34/0.79 ! [A_83: hoare_2091234717iple_a > $o,P_25: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( insert102003750le_a_o @ A_83 @ ( collec1008234059le_a_o @ P_25 ) )
% 0.34/0.79 = ( collec1008234059le_a_o
% 0.34/0.79 @ ^ [U_2: hoare_2091234717iple_a > $o] : ( (=>) @ ( (~) @ ( U_2 = A_83 ) ) @ ( P_25 @ U_2 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_375_insert__Collect,axiom,
% 0.34/0.79 ! [A_83: pname,P_25: pname > $o] :
% 0.34/0.79 ( ( insert_pname @ A_83 @ ( collect_pname @ P_25 ) )
% 0.34/0.79 = ( collect_pname
% 0.34/0.79 @ ^ [U_2: pname] : ( (=>) @ ( (~) @ ( U_2 = A_83 ) ) @ ( P_25 @ U_2 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_376_insert__Collect,axiom,
% 0.34/0.79 ! [A_83: hoare_2091234717iple_a,P_25: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( insert1597628439iple_a @ A_83 @ ( collec992574898iple_a @ P_25 ) )
% 0.34/0.79 = ( collec992574898iple_a
% 0.34/0.79 @ ^ [U_2: hoare_2091234717iple_a] : ( (=>) @ ( (~) @ ( U_2 = A_83 ) ) @ ( P_25 @ U_2 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_377_insert__Collect,axiom,
% 0.34/0.79 ! [A_83: hoare_1708887482_state,P_25: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( insert528405184_state @ A_83 @ ( collec1568722789_state @ P_25 ) )
% 0.34/0.79 = ( collec1568722789_state
% 0.34/0.79 @ ^ [U_2: hoare_1708887482_state] : ( (=>) @ ( (~) @ ( U_2 = A_83 ) ) @ ( P_25 @ U_2 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_378_insert__Collect,axiom,
% 0.34/0.79 ! [A_83: nat,P_25: nat > $o] :
% 0.34/0.79 ( ( insert_nat @ A_83 @ ( collect_nat @ P_25 ) )
% 0.34/0.79 = ( collect_nat
% 0.34/0.79 @ ^ [U_2: nat] : ( (=>) @ ( (~) @ ( U_2 = A_83 ) ) @ ( P_25 @ U_2 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_379_singleton__iff,axiom,
% 0.34/0.79 ! [B_42: nat,A_82: nat] :
% 0.34/0.79 ( ( member_nat @ B_42 @ ( insert_nat @ A_82 @ bot_bot_nat_o ) )
% 0.34/0.79 <=> ( B_42 = A_82 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_380_singleton__iff,axiom,
% 0.34/0.79 ! [B_42: hoare_2091234717iple_a > $o,A_82: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( member99268621le_a_o @ B_42 @ ( insert102003750le_a_o @ A_82 @ bot_bo1957696069_a_o_o ) )
% 0.34/0.79 <=> ( B_42 = A_82 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_381_singleton__iff,axiom,
% 0.34/0.79 ! [B_42: hoare_2091234717iple_a,A_82: hoare_2091234717iple_a] :
% 0.34/0.79 ( ( member290856304iple_a @ B_42 @ ( insert1597628439iple_a @ A_82 @ bot_bo1791335050le_a_o ) )
% 0.34/0.79 <=> ( B_42 = A_82 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_382_singleton__iff,axiom,
% 0.34/0.79 ! [B_42: hoare_1708887482_state,A_82: hoare_1708887482_state] :
% 0.34/0.79 ( ( member451959335_state @ B_42 @ ( insert528405184_state @ A_82 @ bot_bo19817387tate_o ) )
% 0.34/0.79 <=> ( B_42 = A_82 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_383_singleton__iff,axiom,
% 0.34/0.79 ! [B_42: pname,A_82: pname] :
% 0.34/0.79 ( ( member_pname @ B_42 @ ( insert_pname @ A_82 @ bot_bot_pname_o ) )
% 0.34/0.79 <=> ( B_42 = A_82 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_384_insert__absorb2,axiom,
% 0.34/0.79 ! [X_32: nat,A_81: nat > $o] :
% 0.34/0.79 ( ( insert_nat @ X_32 @ ( insert_nat @ X_32 @ A_81 ) )
% 0.34/0.79 = ( insert_nat @ X_32 @ A_81 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_385_insert__absorb2,axiom,
% 0.34/0.79 ! [X_32: hoare_2091234717iple_a > $o,A_81: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( insert102003750le_a_o @ X_32 @ ( insert102003750le_a_o @ X_32 @ A_81 ) )
% 0.34/0.79 = ( insert102003750le_a_o @ X_32 @ A_81 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_386_insert__absorb2,axiom,
% 0.34/0.79 ! [X_32: pname,A_81: pname > $o] :
% 0.34/0.79 ( ( insert_pname @ X_32 @ ( insert_pname @ X_32 @ A_81 ) )
% 0.34/0.79 = ( insert_pname @ X_32 @ A_81 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_387_insert__absorb2,axiom,
% 0.34/0.79 ! [X_32: hoare_2091234717iple_a,A_81: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( insert1597628439iple_a @ X_32 @ ( insert1597628439iple_a @ X_32 @ A_81 ) )
% 0.34/0.79 = ( insert1597628439iple_a @ X_32 @ A_81 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_388_insert__absorb2,axiom,
% 0.34/0.79 ! [X_32: hoare_1708887482_state,A_81: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( insert528405184_state @ X_32 @ ( insert528405184_state @ X_32 @ A_81 ) )
% 0.34/0.79 = ( insert528405184_state @ X_32 @ A_81 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_389_insert__commute,axiom,
% 0.34/0.79 ! [X_31: nat,Y_10: nat,A_80: nat > $o] :
% 0.34/0.79 ( ( insert_nat @ X_31 @ ( insert_nat @ Y_10 @ A_80 ) )
% 0.34/0.79 = ( insert_nat @ Y_10 @ ( insert_nat @ X_31 @ A_80 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_390_insert__commute,axiom,
% 0.34/0.79 ! [X_31: hoare_2091234717iple_a > $o,Y_10: hoare_2091234717iple_a > $o,A_80: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( insert102003750le_a_o @ X_31 @ ( insert102003750le_a_o @ Y_10 @ A_80 ) )
% 0.34/0.79 = ( insert102003750le_a_o @ Y_10 @ ( insert102003750le_a_o @ X_31 @ A_80 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_391_insert__commute,axiom,
% 0.34/0.79 ! [X_31: pname,Y_10: pname,A_80: pname > $o] :
% 0.34/0.79 ( ( insert_pname @ X_31 @ ( insert_pname @ Y_10 @ A_80 ) )
% 0.34/0.79 = ( insert_pname @ Y_10 @ ( insert_pname @ X_31 @ A_80 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_392_insert__commute,axiom,
% 0.34/0.79 ! [X_31: hoare_2091234717iple_a,Y_10: hoare_2091234717iple_a,A_80: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( insert1597628439iple_a @ X_31 @ ( insert1597628439iple_a @ Y_10 @ A_80 ) )
% 0.34/0.79 = ( insert1597628439iple_a @ Y_10 @ ( insert1597628439iple_a @ X_31 @ A_80 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_393_insert__commute,axiom,
% 0.34/0.79 ! [X_31: hoare_1708887482_state,Y_10: hoare_1708887482_state,A_80: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( insert528405184_state @ X_31 @ ( insert528405184_state @ Y_10 @ A_80 ) )
% 0.34/0.79 = ( insert528405184_state @ Y_10 @ ( insert528405184_state @ X_31 @ A_80 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_394_insert__iff,axiom,
% 0.34/0.79 ! [A_79: nat,B_41: nat,A_78: nat > $o] :
% 0.34/0.79 ( ( member_nat @ A_79 @ ( insert_nat @ B_41 @ A_78 ) )
% 0.34/0.79 <=> ( ( A_79 = B_41 )
% 0.34/0.79 | ( member_nat @ A_79 @ A_78 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_395_insert__iff,axiom,
% 0.34/0.79 ! [A_79: hoare_2091234717iple_a > $o,B_41: hoare_2091234717iple_a > $o,A_78: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( member99268621le_a_o @ A_79 @ ( insert102003750le_a_o @ B_41 @ A_78 ) )
% 0.34/0.79 <=> ( ( A_79 = B_41 )
% 0.34/0.79 | ( member99268621le_a_o @ A_79 @ A_78 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_396_insert__iff,axiom,
% 0.34/0.79 ! [A_79: hoare_2091234717iple_a,B_41: hoare_2091234717iple_a,A_78: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( member290856304iple_a @ A_79 @ ( insert1597628439iple_a @ B_41 @ A_78 ) )
% 0.34/0.79 <=> ( ( A_79 = B_41 )
% 0.34/0.79 | ( member290856304iple_a @ A_79 @ A_78 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_397_insert__iff,axiom,
% 0.34/0.79 ! [A_79: hoare_1708887482_state,B_41: hoare_1708887482_state,A_78: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( member451959335_state @ A_79 @ ( insert528405184_state @ B_41 @ A_78 ) )
% 0.34/0.79 <=> ( ( A_79 = B_41 )
% 0.34/0.79 | ( member451959335_state @ A_79 @ A_78 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_398_insert__iff,axiom,
% 0.34/0.79 ! [A_79: pname,B_41: pname,A_78: pname > $o] :
% 0.34/0.79 ( ( member_pname @ A_79 @ ( insert_pname @ B_41 @ A_78 ) )
% 0.34/0.79 <=> ( ( A_79 = B_41 )
% 0.34/0.79 | ( member_pname @ A_79 @ A_78 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_399_Collect__empty__eq,axiom,
% 0.34/0.79 ! [P_24: pname > $o] :
% 0.34/0.79 ( ( ( collect_pname @ P_24 )
% 0.34/0.79 = bot_bot_pname_o )
% 0.34/0.79 <=> ! [X: pname] :
% 0.34/0.79 ~ ( P_24 @ X ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_400_Collect__empty__eq,axiom,
% 0.34/0.79 ! [P_24: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( ( collec992574898iple_a @ P_24 )
% 0.34/0.79 = bot_bo1791335050le_a_o )
% 0.34/0.79 <=> ! [X: hoare_2091234717iple_a] :
% 0.34/0.79 ~ ( P_24 @ X ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_401_Collect__empty__eq,axiom,
% 0.34/0.79 ! [P_24: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( ( collec1008234059le_a_o @ P_24 )
% 0.34/0.79 = bot_bo1957696069_a_o_o )
% 0.34/0.79 <=> ! [X: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ~ ( P_24 @ X ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_402_Collect__empty__eq,axiom,
% 0.34/0.79 ! [P_24: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( ( collec1568722789_state @ P_24 )
% 0.34/0.79 = bot_bo19817387tate_o )
% 0.34/0.79 <=> ! [X: hoare_1708887482_state] :
% 0.34/0.79 ~ ( P_24 @ X ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_403_Collect__empty__eq,axiom,
% 0.34/0.79 ! [P_24: nat > $o] :
% 0.34/0.79 ( ( ( collect_nat @ P_24 )
% 0.34/0.79 = bot_bot_nat_o )
% 0.34/0.79 <=> ! [X: nat] :
% 0.34/0.79 ~ ( P_24 @ X ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_404_doubleton__eq__iff,axiom,
% 0.34/0.79 ! [A_77: nat,B_40: nat,C_24: nat,D_1: nat] :
% 0.34/0.79 ( ( ( insert_nat @ A_77 @ ( insert_nat @ B_40 @ bot_bot_nat_o ) )
% 0.34/0.79 = ( insert_nat @ C_24 @ ( insert_nat @ D_1 @ bot_bot_nat_o ) ) )
% 0.34/0.79 <=> ( ( ( A_77 = C_24 )
% 0.34/0.79 & ( B_40 = D_1 ) )
% 0.34/0.79 | ( ( A_77 = D_1 )
% 0.34/0.79 & ( B_40 = C_24 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_405_doubleton__eq__iff,axiom,
% 0.34/0.79 ! [A_77: hoare_2091234717iple_a > $o,B_40: hoare_2091234717iple_a > $o,C_24: hoare_2091234717iple_a > $o,D_1: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( ( insert102003750le_a_o @ A_77 @ ( insert102003750le_a_o @ B_40 @ bot_bo1957696069_a_o_o ) )
% 0.34/0.79 = ( insert102003750le_a_o @ C_24 @ ( insert102003750le_a_o @ D_1 @ bot_bo1957696069_a_o_o ) ) )
% 0.34/0.79 <=> ( ( ( A_77 = C_24 )
% 0.34/0.79 & ( B_40 = D_1 ) )
% 0.34/0.79 | ( ( A_77 = D_1 )
% 0.34/0.79 & ( B_40 = C_24 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_406_doubleton__eq__iff,axiom,
% 0.34/0.79 ! [A_77: pname,B_40: pname,C_24: pname,D_1: pname] :
% 0.34/0.79 ( ( ( insert_pname @ A_77 @ ( insert_pname @ B_40 @ bot_bot_pname_o ) )
% 0.34/0.79 = ( insert_pname @ C_24 @ ( insert_pname @ D_1 @ bot_bot_pname_o ) ) )
% 0.34/0.79 <=> ( ( ( A_77 = C_24 )
% 0.34/0.79 & ( B_40 = D_1 ) )
% 0.34/0.79 | ( ( A_77 = D_1 )
% 0.34/0.79 & ( B_40 = C_24 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_407_doubleton__eq__iff,axiom,
% 0.34/0.79 ! [A_77: hoare_2091234717iple_a,B_40: hoare_2091234717iple_a,C_24: hoare_2091234717iple_a,D_1: hoare_2091234717iple_a] :
% 0.34/0.79 ( ( ( insert1597628439iple_a @ A_77 @ ( insert1597628439iple_a @ B_40 @ bot_bo1791335050le_a_o ) )
% 0.34/0.79 = ( insert1597628439iple_a @ C_24 @ ( insert1597628439iple_a @ D_1 @ bot_bo1791335050le_a_o ) ) )
% 0.34/0.79 <=> ( ( ( A_77 = C_24 )
% 0.34/0.79 & ( B_40 = D_1 ) )
% 0.34/0.79 | ( ( A_77 = D_1 )
% 0.34/0.79 & ( B_40 = C_24 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_408_doubleton__eq__iff,axiom,
% 0.34/0.79 ! [A_77: hoare_1708887482_state,B_40: hoare_1708887482_state,C_24: hoare_1708887482_state,D_1: hoare_1708887482_state] :
% 0.34/0.79 ( ( ( insert528405184_state @ A_77 @ ( insert528405184_state @ B_40 @ bot_bo19817387tate_o ) )
% 0.34/0.79 = ( insert528405184_state @ C_24 @ ( insert528405184_state @ D_1 @ bot_bo19817387tate_o ) ) )
% 0.34/0.79 <=> ( ( ( A_77 = C_24 )
% 0.34/0.79 & ( B_40 = D_1 ) )
% 0.34/0.79 | ( ( A_77 = D_1 )
% 0.34/0.79 & ( B_40 = C_24 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_409_insert__code,axiom,
% 0.34/0.79 ! [Y_9: nat,A_76: nat > $o,X_30: nat] :
% 0.34/0.79 ( ( insert_nat @ Y_9 @ A_76 @ X_30 )
% 0.34/0.79 <=> ( ( Y_9 = X_30 )
% 0.34/0.79 | ( A_76 @ X_30 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_410_insert__code,axiom,
% 0.34/0.79 ! [Y_9: hoare_2091234717iple_a > $o,A_76: ( hoare_2091234717iple_a > $o ) > $o,X_30: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( insert102003750le_a_o @ Y_9 @ A_76 @ X_30 )
% 0.34/0.79 <=> ( ( Y_9 = X_30 )
% 0.34/0.79 | ( A_76 @ X_30 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_411_insert__code,axiom,
% 0.34/0.79 ! [Y_9: pname,A_76: pname > $o,X_30: pname] :
% 0.34/0.79 ( ( insert_pname @ Y_9 @ A_76 @ X_30 )
% 0.34/0.79 <=> ( ( Y_9 = X_30 )
% 0.34/0.79 | ( A_76 @ X_30 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_412_insert__code,axiom,
% 0.34/0.79 ! [Y_9: hoare_2091234717iple_a,A_76: hoare_2091234717iple_a > $o,X_30: hoare_2091234717iple_a] :
% 0.34/0.79 ( ( insert1597628439iple_a @ Y_9 @ A_76 @ X_30 )
% 0.34/0.79 <=> ( ( Y_9 = X_30 )
% 0.34/0.79 | ( A_76 @ X_30 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_413_insert__code,axiom,
% 0.34/0.79 ! [Y_9: hoare_1708887482_state,A_76: hoare_1708887482_state > $o,X_30: hoare_1708887482_state] :
% 0.34/0.79 ( ( insert528405184_state @ Y_9 @ A_76 @ X_30 )
% 0.34/0.79 <=> ( ( Y_9 = X_30 )
% 0.34/0.79 | ( A_76 @ X_30 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_414_insert__ident,axiom,
% 0.34/0.79 ! [B_39: nat > $o,X_29: nat,A_75: nat > $o] :
% 0.34/0.79 ( ~ ( member_nat @ X_29 @ A_75 )
% 0.34/0.79 => ( ~ ( member_nat @ X_29 @ B_39 )
% 0.34/0.79 => ( ( ( insert_nat @ X_29 @ A_75 )
% 0.34/0.79 = ( insert_nat @ X_29 @ B_39 ) )
% 0.34/0.79 <=> ( A_75 = B_39 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_415_insert__ident,axiom,
% 0.34/0.79 ! [B_39: ( hoare_2091234717iple_a > $o ) > $o,X_29: hoare_2091234717iple_a > $o,A_75: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ~ ( member99268621le_a_o @ X_29 @ A_75 )
% 0.34/0.79 => ( ~ ( member99268621le_a_o @ X_29 @ B_39 )
% 0.34/0.79 => ( ( ( insert102003750le_a_o @ X_29 @ A_75 )
% 0.34/0.79 = ( insert102003750le_a_o @ X_29 @ B_39 ) )
% 0.34/0.79 <=> ( A_75 = B_39 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_416_insert__ident,axiom,
% 0.34/0.79 ! [B_39: hoare_2091234717iple_a > $o,X_29: hoare_2091234717iple_a,A_75: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ~ ( member290856304iple_a @ X_29 @ A_75 )
% 0.34/0.79 => ( ~ ( member290856304iple_a @ X_29 @ B_39 )
% 0.34/0.79 => ( ( ( insert1597628439iple_a @ X_29 @ A_75 )
% 0.34/0.79 = ( insert1597628439iple_a @ X_29 @ B_39 ) )
% 0.34/0.79 <=> ( A_75 = B_39 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_417_insert__ident,axiom,
% 0.34/0.79 ! [B_39: hoare_1708887482_state > $o,X_29: hoare_1708887482_state,A_75: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ~ ( member451959335_state @ X_29 @ A_75 )
% 0.34/0.79 => ( ~ ( member451959335_state @ X_29 @ B_39 )
% 0.34/0.79 => ( ( ( insert528405184_state @ X_29 @ A_75 )
% 0.34/0.79 = ( insert528405184_state @ X_29 @ B_39 ) )
% 0.34/0.79 <=> ( A_75 = B_39 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_418_insert__ident,axiom,
% 0.34/0.79 ! [B_39: pname > $o,X_29: pname,A_75: pname > $o] :
% 0.34/0.79 ( ~ ( member_pname @ X_29 @ A_75 )
% 0.34/0.79 => ( ~ ( member_pname @ X_29 @ B_39 )
% 0.34/0.79 => ( ( ( insert_pname @ X_29 @ A_75 )
% 0.34/0.79 = ( insert_pname @ X_29 @ B_39 ) )
% 0.34/0.79 <=> ( A_75 = B_39 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_419_equals0D,axiom,
% 0.34/0.79 ! [A_74: nat,A_73: nat > $o] :
% 0.34/0.79 ( ( A_73 = bot_bot_nat_o )
% 0.34/0.79 => ~ ( member_nat @ A_74 @ A_73 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_420_equals0D,axiom,
% 0.34/0.79 ! [A_74: hoare_2091234717iple_a > $o,A_73: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( A_73 = bot_bo1957696069_a_o_o )
% 0.34/0.79 => ~ ( member99268621le_a_o @ A_74 @ A_73 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_421_equals0D,axiom,
% 0.34/0.79 ! [A_74: hoare_2091234717iple_a,A_73: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( A_73 = bot_bo1791335050le_a_o )
% 0.34/0.79 => ~ ( member290856304iple_a @ A_74 @ A_73 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_422_equals0D,axiom,
% 0.34/0.79 ! [A_74: hoare_1708887482_state,A_73: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( A_73 = bot_bo19817387tate_o )
% 0.34/0.79 => ~ ( member451959335_state @ A_74 @ A_73 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_423_equals0D,axiom,
% 0.34/0.79 ! [A_74: pname,A_73: pname > $o] :
% 0.34/0.79 ( ( A_73 = bot_bot_pname_o )
% 0.34/0.79 => ~ ( member_pname @ A_74 @ A_73 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_424_insertI2,axiom,
% 0.34/0.79 ! [B_38: nat,A_72: nat,B_37: nat > $o] :
% 0.34/0.79 ( ( member_nat @ A_72 @ B_37 )
% 0.34/0.79 => ( member_nat @ A_72 @ ( insert_nat @ B_38 @ B_37 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_425_insertI2,axiom,
% 0.34/0.79 ! [B_38: hoare_2091234717iple_a > $o,A_72: hoare_2091234717iple_a > $o,B_37: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( member99268621le_a_o @ A_72 @ B_37 )
% 0.34/0.79 => ( member99268621le_a_o @ A_72 @ ( insert102003750le_a_o @ B_38 @ B_37 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_426_insertI2,axiom,
% 0.34/0.79 ! [B_38: hoare_2091234717iple_a,A_72: hoare_2091234717iple_a,B_37: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( member290856304iple_a @ A_72 @ B_37 )
% 0.34/0.79 => ( member290856304iple_a @ A_72 @ ( insert1597628439iple_a @ B_38 @ B_37 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_427_insertI2,axiom,
% 0.34/0.79 ! [B_38: hoare_1708887482_state,A_72: hoare_1708887482_state,B_37: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( member451959335_state @ A_72 @ B_37 )
% 0.34/0.79 => ( member451959335_state @ A_72 @ ( insert528405184_state @ B_38 @ B_37 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_428_insertI2,axiom,
% 0.34/0.79 ! [B_38: pname,A_72: pname,B_37: pname > $o] :
% 0.34/0.79 ( ( member_pname @ A_72 @ B_37 )
% 0.34/0.79 => ( member_pname @ A_72 @ ( insert_pname @ B_38 @ B_37 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_429_insert__absorb,axiom,
% 0.34/0.79 ! [A_71: nat,A_70: nat > $o] :
% 0.34/0.79 ( ( member_nat @ A_71 @ A_70 )
% 0.34/0.79 => ( ( insert_nat @ A_71 @ A_70 )
% 0.34/0.79 = A_70 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_430_insert__absorb,axiom,
% 0.34/0.79 ! [A_71: hoare_2091234717iple_a > $o,A_70: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( member99268621le_a_o @ A_71 @ A_70 )
% 0.34/0.79 => ( ( insert102003750le_a_o @ A_71 @ A_70 )
% 0.34/0.79 = A_70 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_431_insert__absorb,axiom,
% 0.34/0.79 ! [A_71: hoare_2091234717iple_a,A_70: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( member290856304iple_a @ A_71 @ A_70 )
% 0.34/0.79 => ( ( insert1597628439iple_a @ A_71 @ A_70 )
% 0.34/0.79 = A_70 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_432_insert__absorb,axiom,
% 0.34/0.79 ! [A_71: hoare_1708887482_state,A_70: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( member451959335_state @ A_71 @ A_70 )
% 0.34/0.79 => ( ( insert528405184_state @ A_71 @ A_70 )
% 0.34/0.79 = A_70 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_433_insert__absorb,axiom,
% 0.34/0.79 ! [A_71: pname,A_70: pname > $o] :
% 0.34/0.79 ( ( member_pname @ A_71 @ A_70 )
% 0.34/0.79 => ( ( insert_pname @ A_71 @ A_70 )
% 0.34/0.79 = A_70 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_434_singletonE,axiom,
% 0.34/0.79 ! [B_36: nat,A_69: nat] :
% 0.34/0.79 ( ( member_nat @ B_36 @ ( insert_nat @ A_69 @ bot_bot_nat_o ) )
% 0.34/0.79 => ( B_36 = A_69 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_435_singletonE,axiom,
% 0.34/0.79 ! [B_36: hoare_2091234717iple_a > $o,A_69: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( member99268621le_a_o @ B_36 @ ( insert102003750le_a_o @ A_69 @ bot_bo1957696069_a_o_o ) )
% 0.34/0.79 => ( B_36 = A_69 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_436_singletonE,axiom,
% 0.34/0.79 ! [B_36: hoare_2091234717iple_a,A_69: hoare_2091234717iple_a] :
% 0.34/0.79 ( ( member290856304iple_a @ B_36 @ ( insert1597628439iple_a @ A_69 @ bot_bo1791335050le_a_o ) )
% 0.34/0.79 => ( B_36 = A_69 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_437_singletonE,axiom,
% 0.34/0.79 ! [B_36: hoare_1708887482_state,A_69: hoare_1708887482_state] :
% 0.34/0.79 ( ( member451959335_state @ B_36 @ ( insert528405184_state @ A_69 @ bot_bo19817387tate_o ) )
% 0.34/0.79 => ( B_36 = A_69 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_438_singletonE,axiom,
% 0.34/0.79 ! [B_36: pname,A_69: pname] :
% 0.34/0.79 ( ( member_pname @ B_36 @ ( insert_pname @ A_69 @ bot_bot_pname_o ) )
% 0.34/0.79 => ( B_36 = A_69 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_439_singleton__inject,axiom,
% 0.34/0.79 ! [A_68: nat,B_35: nat] :
% 0.34/0.79 ( ( ( insert_nat @ A_68 @ bot_bot_nat_o )
% 0.34/0.79 = ( insert_nat @ B_35 @ bot_bot_nat_o ) )
% 0.34/0.79 => ( A_68 = B_35 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_440_singleton__inject,axiom,
% 0.34/0.79 ! [A_68: hoare_2091234717iple_a > $o,B_35: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( ( insert102003750le_a_o @ A_68 @ bot_bo1957696069_a_o_o )
% 0.34/0.79 = ( insert102003750le_a_o @ B_35 @ bot_bo1957696069_a_o_o ) )
% 0.34/0.79 => ( A_68 = B_35 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_441_singleton__inject,axiom,
% 0.34/0.79 ! [A_68: pname,B_35: pname] :
% 0.34/0.79 ( ( ( insert_pname @ A_68 @ bot_bot_pname_o )
% 0.34/0.79 = ( insert_pname @ B_35 @ bot_bot_pname_o ) )
% 0.34/0.79 => ( A_68 = B_35 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_442_singleton__inject,axiom,
% 0.34/0.79 ! [A_68: hoare_2091234717iple_a,B_35: hoare_2091234717iple_a] :
% 0.34/0.79 ( ( ( insert1597628439iple_a @ A_68 @ bot_bo1791335050le_a_o )
% 0.34/0.79 = ( insert1597628439iple_a @ B_35 @ bot_bo1791335050le_a_o ) )
% 0.34/0.79 => ( A_68 = B_35 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_443_singleton__inject,axiom,
% 0.34/0.79 ! [A_68: hoare_1708887482_state,B_35: hoare_1708887482_state] :
% 0.34/0.79 ( ( ( insert528405184_state @ A_68 @ bot_bo19817387tate_o )
% 0.34/0.79 = ( insert528405184_state @ B_35 @ bot_bo19817387tate_o ) )
% 0.34/0.79 => ( A_68 = B_35 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_444_com__det,axiom,
% 0.34/0.79 ! [U: state,C: com,S: state,T: state] :
% 0.34/0.79 ( ( evalc @ C @ S @ T )
% 0.34/0.79 => ( ( evalc @ C @ S @ U )
% 0.34/0.79 => ( U = T ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_445_insert__is__Un,axiom,
% 0.34/0.79 ! [A_67: nat,A_66: nat > $o] :
% 0.34/0.79 ( ( insert_nat @ A_67 @ A_66 )
% 0.34/0.79 = ( semila848761471_nat_o @ ( insert_nat @ A_67 @ bot_bot_nat_o ) @ A_66 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_446_insert__is__Un,axiom,
% 0.34/0.79 ! [A_67: hoare_2091234717iple_a > $o,A_66: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( insert102003750le_a_o @ A_67 @ A_66 )
% 0.34/0.79 = ( semila2050116131_a_o_o @ ( insert102003750le_a_o @ A_67 @ bot_bo1957696069_a_o_o ) @ A_66 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_447_insert__is__Un,axiom,
% 0.34/0.79 ! [A_67: pname,A_66: pname > $o] :
% 0.34/0.79 ( ( insert_pname @ A_67 @ A_66 )
% 0.34/0.79 = ( semila1780557381name_o @ ( insert_pname @ A_67 @ bot_bot_pname_o ) @ A_66 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_448_insert__is__Un,axiom,
% 0.34/0.79 ! [A_67: hoare_1708887482_state,A_66: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( insert528405184_state @ A_67 @ A_66 )
% 0.34/0.79 = ( semila1122118281tate_o @ ( insert528405184_state @ A_67 @ bot_bo19817387tate_o ) @ A_66 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_449_insert__is__Un,axiom,
% 0.34/0.79 ! [A_67: hoare_2091234717iple_a,A_66: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( insert1597628439iple_a @ A_67 @ A_66 )
% 0.34/0.79 = ( semila1052848428le_a_o @ ( insert1597628439iple_a @ A_67 @ bot_bo1791335050le_a_o ) @ A_66 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_450_insert__compr__raw,axiom,
% 0.34/0.79 ! [X: hoare_2091234717iple_a > $o,Xa: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( insert102003750le_a_o @ X @ Xa )
% 0.34/0.79 = ( collec1008234059le_a_o
% 0.34/0.79 @ ^ [Y_7: hoare_2091234717iple_a > $o] : ( (|) @ ( Y_7 = X ) @ ( member99268621le_a_o @ Y_7 @ Xa ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_451_insert__compr__raw,axiom,
% 0.34/0.79 ! [X: hoare_2091234717iple_a,Xa: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( insert1597628439iple_a @ X @ Xa )
% 0.34/0.79 = ( collec992574898iple_a
% 0.34/0.79 @ ^ [Y_7: hoare_2091234717iple_a] : ( (|) @ ( Y_7 = X ) @ ( member290856304iple_a @ Y_7 @ Xa ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_452_insert__compr__raw,axiom,
% 0.34/0.79 ! [X: hoare_1708887482_state,Xa: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( insert528405184_state @ X @ Xa )
% 0.34/0.79 = ( collec1568722789_state
% 0.34/0.79 @ ^ [Y_7: hoare_1708887482_state] : ( (|) @ ( Y_7 = X ) @ ( member451959335_state @ Y_7 @ Xa ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_453_insert__compr__raw,axiom,
% 0.34/0.79 ! [X: nat,Xa: nat > $o] :
% 0.34/0.79 ( ( insert_nat @ X @ Xa )
% 0.34/0.79 = ( collect_nat
% 0.34/0.79 @ ^ [Y_7: nat] : ( (|) @ ( Y_7 = X ) @ ( member_nat @ Y_7 @ Xa ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_454_insert__compr__raw,axiom,
% 0.34/0.79 ! [X: pname,Xa: pname > $o] :
% 0.34/0.79 ( ( insert_pname @ X @ Xa )
% 0.34/0.79 = ( collect_pname
% 0.34/0.79 @ ^ [Y_7: pname] : ( (|) @ ( Y_7 = X ) @ ( member_pname @ Y_7 @ Xa ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_455_derivs__insertD,axiom,
% 0.34/0.79 ! [G_19: hoare_2091234717iple_a > $o,T_3: hoare_2091234717iple_a,Ts_1: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( hoare_1467856363rivs_a @ G_19 @ ( insert1597628439iple_a @ T_3 @ Ts_1 ) )
% 0.34/0.79 => ( ( hoare_1467856363rivs_a @ G_19 @ ( insert1597628439iple_a @ T_3 @ bot_bo1791335050le_a_o ) )
% 0.34/0.79 & ( hoare_1467856363rivs_a @ G_19 @ Ts_1 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_456_derivs__insertD,axiom,
% 0.34/0.79 ! [G_19: hoare_1708887482_state > $o,T_3: hoare_1708887482_state,Ts_1: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( hoare_90032982_state @ G_19 @ ( insert528405184_state @ T_3 @ Ts_1 ) )
% 0.34/0.79 => ( ( hoare_90032982_state @ G_19 @ ( insert528405184_state @ T_3 @ bot_bo19817387tate_o ) )
% 0.34/0.79 & ( hoare_90032982_state @ G_19 @ Ts_1 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_457_hoare__derivs_Oinsert,axiom,
% 0.34/0.79 ! [Ts: hoare_2091234717iple_a > $o,G_18: hoare_2091234717iple_a > $o,T_2: hoare_2091234717iple_a] :
% 0.34/0.79 ( ( hoare_1467856363rivs_a @ G_18 @ ( insert1597628439iple_a @ T_2 @ bot_bo1791335050le_a_o ) )
% 0.34/0.79 => ( ( hoare_1467856363rivs_a @ G_18 @ Ts )
% 0.34/0.79 => ( hoare_1467856363rivs_a @ G_18 @ ( insert1597628439iple_a @ T_2 @ Ts ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_458_hoare__derivs_Oinsert,axiom,
% 0.34/0.79 ! [Ts: hoare_1708887482_state > $o,G_18: hoare_1708887482_state > $o,T_2: hoare_1708887482_state] :
% 0.34/0.79 ( ( hoare_90032982_state @ G_18 @ ( insert528405184_state @ T_2 @ bot_bo19817387tate_o ) )
% 0.34/0.79 => ( ( hoare_90032982_state @ G_18 @ Ts )
% 0.34/0.79 => ( hoare_90032982_state @ G_18 @ ( insert528405184_state @ T_2 @ Ts ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_459_image__constant__conv,axiom,
% 0.34/0.79 ! [C_23: nat,A_65: nat > $o] :
% 0.34/0.79 ( ( ( A_65 = bot_bot_nat_o )
% 0.34/0.79 => ( ( image_nat_nat
% 0.34/0.79 @ ^ [X: nat] : C_23
% 0.34/0.79 @ A_65 )
% 0.34/0.79 = bot_bot_nat_o ) )
% 0.34/0.79 & ( ( A_65 != bot_bot_nat_o )
% 0.34/0.79 => ( ( image_nat_nat
% 0.34/0.79 @ ^ [X: nat] : C_23
% 0.34/0.79 @ A_65 )
% 0.34/0.79 = ( insert_nat @ C_23 @ bot_bot_nat_o ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_460_image__constant__conv,axiom,
% 0.34/0.79 ! [C_23: hoare_1708887482_state,A_65: pname > $o] :
% 0.34/0.79 ( ( ( A_65 = bot_bot_pname_o )
% 0.34/0.79 => ( ( image_1116629049_state
% 0.34/0.79 @ ^ [X: pname] : C_23
% 0.34/0.79 @ A_65 )
% 0.34/0.79 = bot_bo19817387tate_o ) )
% 0.34/0.79 & ( ( A_65 != bot_bot_pname_o )
% 0.34/0.79 => ( ( image_1116629049_state
% 0.34/0.79 @ ^ [X: pname] : C_23
% 0.34/0.79 @ A_65 )
% 0.34/0.79 = ( insert528405184_state @ C_23 @ bot_bo19817387tate_o ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_461_image__constant__conv,axiom,
% 0.34/0.79 ! [C_23: hoare_2091234717iple_a,A_65: pname > $o] :
% 0.34/0.79 ( ( ( A_65 = bot_bot_pname_o )
% 0.34/0.79 => ( ( image_231808478iple_a
% 0.34/0.79 @ ^ [X: pname] : C_23
% 0.34/0.79 @ A_65 )
% 0.34/0.79 = bot_bo1791335050le_a_o ) )
% 0.34/0.79 & ( ( A_65 != bot_bot_pname_o )
% 0.34/0.79 => ( ( image_231808478iple_a
% 0.34/0.79 @ ^ [X: pname] : C_23
% 0.34/0.79 @ A_65 )
% 0.34/0.79 = ( insert1597628439iple_a @ C_23 @ bot_bo1791335050le_a_o ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_462_image__constant,axiom,
% 0.34/0.79 ! [C_22: nat,X_28: nat,A_64: nat > $o] :
% 0.34/0.79 ( ( member_nat @ X_28 @ A_64 )
% 0.34/0.79 => ( ( image_nat_nat
% 0.34/0.79 @ ^ [X: nat] : C_22
% 0.34/0.79 @ A_64 )
% 0.34/0.79 = ( insert_nat @ C_22 @ bot_bot_nat_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_463_image__constant,axiom,
% 0.34/0.79 ! [C_22: hoare_1708887482_state,X_28: pname,A_64: pname > $o] :
% 0.34/0.79 ( ( member_pname @ X_28 @ A_64 )
% 0.34/0.79 => ( ( image_1116629049_state
% 0.34/0.79 @ ^ [X: pname] : C_22
% 0.34/0.79 @ A_64 )
% 0.34/0.79 = ( insert528405184_state @ C_22 @ bot_bo19817387tate_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_464_image__constant,axiom,
% 0.34/0.79 ! [C_22: nat,X_28: pname,A_64: pname > $o] :
% 0.34/0.79 ( ( member_pname @ X_28 @ A_64 )
% 0.34/0.79 => ( ( image_pname_nat
% 0.34/0.79 @ ^ [X: pname] : C_22
% 0.34/0.79 @ A_64 )
% 0.34/0.79 = ( insert_nat @ C_22 @ bot_bot_nat_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_465_image__constant,axiom,
% 0.34/0.79 ! [C_22: hoare_2091234717iple_a > $o,X_28: pname,A_64: pname > $o] :
% 0.34/0.79 ( ( member_pname @ X_28 @ A_64 )
% 0.34/0.79 => ( ( image_742317343le_a_o
% 0.34/0.79 @ ^ [X: pname] : C_22
% 0.34/0.79 @ A_64 )
% 0.34/0.79 = ( insert102003750le_a_o @ C_22 @ bot_bo1957696069_a_o_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_466_image__constant,axiom,
% 0.34/0.79 ! [C_22: pname,X_28: pname,A_64: pname > $o] :
% 0.34/0.79 ( ( member_pname @ X_28 @ A_64 )
% 0.34/0.79 => ( ( image_pname_pname
% 0.34/0.79 @ ^ [X: pname] : C_22
% 0.34/0.79 @ A_64 )
% 0.34/0.79 = ( insert_pname @ C_22 @ bot_bot_pname_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_467_image__constant,axiom,
% 0.34/0.79 ! [C_22: hoare_2091234717iple_a,X_28: pname,A_64: pname > $o] :
% 0.34/0.79 ( ( member_pname @ X_28 @ A_64 )
% 0.34/0.79 => ( ( image_231808478iple_a
% 0.34/0.79 @ ^ [X: pname] : C_22
% 0.34/0.79 @ A_64 )
% 0.34/0.79 = ( insert1597628439iple_a @ C_22 @ bot_bo1791335050le_a_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_468_image__insert,axiom,
% 0.34/0.79 ! [F_40: nat > nat,A_63: nat,B_34: nat > $o] :
% 0.34/0.79 ( ( image_nat_nat @ F_40 @ ( insert_nat @ A_63 @ B_34 ) )
% 0.34/0.79 = ( insert_nat @ ( F_40 @ A_63 ) @ ( image_nat_nat @ F_40 @ B_34 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_469_image__insert,axiom,
% 0.34/0.79 ! [F_40: pname > hoare_1708887482_state,A_63: pname,B_34: pname > $o] :
% 0.34/0.79 ( ( image_1116629049_state @ F_40 @ ( insert_pname @ A_63 @ B_34 ) )
% 0.34/0.79 = ( insert528405184_state @ ( F_40 @ A_63 ) @ ( image_1116629049_state @ F_40 @ B_34 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_470_image__insert,axiom,
% 0.34/0.79 ! [F_40: pname > hoare_2091234717iple_a,A_63: pname,B_34: pname > $o] :
% 0.34/0.79 ( ( image_231808478iple_a @ F_40 @ ( insert_pname @ A_63 @ B_34 ) )
% 0.34/0.79 = ( insert1597628439iple_a @ ( F_40 @ A_63 ) @ ( image_231808478iple_a @ F_40 @ B_34 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_471_insert__image,axiom,
% 0.34/0.79 ! [F_39: nat > nat,X_27: nat,A_62: nat > $o] :
% 0.34/0.79 ( ( member_nat @ X_27 @ A_62 )
% 0.34/0.79 => ( ( insert_nat @ ( F_39 @ X_27 ) @ ( image_nat_nat @ F_39 @ A_62 ) )
% 0.34/0.79 = ( image_nat_nat @ F_39 @ A_62 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_472_insert__image,axiom,
% 0.34/0.79 ! [F_39: pname > hoare_1708887482_state,X_27: pname,A_62: pname > $o] :
% 0.34/0.79 ( ( member_pname @ X_27 @ A_62 )
% 0.34/0.79 => ( ( insert528405184_state @ ( F_39 @ X_27 ) @ ( image_1116629049_state @ F_39 @ A_62 ) )
% 0.34/0.79 = ( image_1116629049_state @ F_39 @ A_62 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_473_insert__image,axiom,
% 0.34/0.79 ! [F_39: pname > nat,X_27: pname,A_62: pname > $o] :
% 0.34/0.79 ( ( member_pname @ X_27 @ A_62 )
% 0.34/0.79 => ( ( insert_nat @ ( F_39 @ X_27 ) @ ( image_pname_nat @ F_39 @ A_62 ) )
% 0.34/0.79 = ( image_pname_nat @ F_39 @ A_62 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_474_insert__image,axiom,
% 0.34/0.79 ! [F_39: pname > hoare_2091234717iple_a > $o,X_27: pname,A_62: pname > $o] :
% 0.34/0.79 ( ( member_pname @ X_27 @ A_62 )
% 0.34/0.79 => ( ( insert102003750le_a_o @ ( F_39 @ X_27 ) @ ( image_742317343le_a_o @ F_39 @ A_62 ) )
% 0.34/0.79 = ( image_742317343le_a_o @ F_39 @ A_62 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_475_insert__image,axiom,
% 0.34/0.79 ! [F_39: pname > pname,X_27: pname,A_62: pname > $o] :
% 0.34/0.79 ( ( member_pname @ X_27 @ A_62 )
% 0.34/0.79 => ( ( insert_pname @ ( F_39 @ X_27 ) @ ( image_pname_pname @ F_39 @ A_62 ) )
% 0.34/0.79 = ( image_pname_pname @ F_39 @ A_62 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_476_insert__image,axiom,
% 0.34/0.79 ! [F_39: pname > hoare_2091234717iple_a,X_27: pname,A_62: pname > $o] :
% 0.34/0.79 ( ( member_pname @ X_27 @ A_62 )
% 0.34/0.79 => ( ( insert1597628439iple_a @ ( F_39 @ X_27 ) @ ( image_231808478iple_a @ F_39 @ A_62 ) )
% 0.34/0.79 = ( image_231808478iple_a @ F_39 @ A_62 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_477_Un__insert__right,axiom,
% 0.34/0.79 ! [A_61: nat > $o,A_60: nat,B_33: nat > $o] :
% 0.34/0.79 ( ( semila848761471_nat_o @ A_61 @ ( insert_nat @ A_60 @ B_33 ) )
% 0.34/0.79 = ( insert_nat @ A_60 @ ( semila848761471_nat_o @ A_61 @ B_33 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_478_Un__insert__right,axiom,
% 0.34/0.79 ! [A_61: ( hoare_2091234717iple_a > $o ) > $o,A_60: hoare_2091234717iple_a > $o,B_33: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( semila2050116131_a_o_o @ A_61 @ ( insert102003750le_a_o @ A_60 @ B_33 ) )
% 0.34/0.79 = ( insert102003750le_a_o @ A_60 @ ( semila2050116131_a_o_o @ A_61 @ B_33 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_479_Un__insert__right,axiom,
% 0.34/0.79 ! [A_61: pname > $o,A_60: pname,B_33: pname > $o] :
% 0.34/0.79 ( ( semila1780557381name_o @ A_61 @ ( insert_pname @ A_60 @ B_33 ) )
% 0.34/0.79 = ( insert_pname @ A_60 @ ( semila1780557381name_o @ A_61 @ B_33 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_480_Un__insert__right,axiom,
% 0.34/0.79 ! [A_61: hoare_1708887482_state > $o,A_60: hoare_1708887482_state,B_33: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( semila1122118281tate_o @ A_61 @ ( insert528405184_state @ A_60 @ B_33 ) )
% 0.34/0.79 = ( insert528405184_state @ A_60 @ ( semila1122118281tate_o @ A_61 @ B_33 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_481_Un__insert__right,axiom,
% 0.34/0.79 ! [A_61: hoare_2091234717iple_a > $o,A_60: hoare_2091234717iple_a,B_33: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( semila1052848428le_a_o @ A_61 @ ( insert1597628439iple_a @ A_60 @ B_33 ) )
% 0.34/0.79 = ( insert1597628439iple_a @ A_60 @ ( semila1052848428le_a_o @ A_61 @ B_33 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_482_Un__insert__left,axiom,
% 0.34/0.79 ! [A_59: nat,B_32: nat > $o,C_21: nat > $o] :
% 0.34/0.79 ( ( semila848761471_nat_o @ ( insert_nat @ A_59 @ B_32 ) @ C_21 )
% 0.34/0.79 = ( insert_nat @ A_59 @ ( semila848761471_nat_o @ B_32 @ C_21 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_483_Un__insert__left,axiom,
% 0.34/0.79 ! [A_59: hoare_2091234717iple_a > $o,B_32: ( hoare_2091234717iple_a > $o ) > $o,C_21: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( semila2050116131_a_o_o @ ( insert102003750le_a_o @ A_59 @ B_32 ) @ C_21 )
% 0.34/0.79 = ( insert102003750le_a_o @ A_59 @ ( semila2050116131_a_o_o @ B_32 @ C_21 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_484_Un__insert__left,axiom,
% 0.34/0.79 ! [A_59: pname,B_32: pname > $o,C_21: pname > $o] :
% 0.34/0.79 ( ( semila1780557381name_o @ ( insert_pname @ A_59 @ B_32 ) @ C_21 )
% 0.34/0.79 = ( insert_pname @ A_59 @ ( semila1780557381name_o @ B_32 @ C_21 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_485_Un__insert__left,axiom,
% 0.34/0.79 ! [A_59: hoare_1708887482_state,B_32: hoare_1708887482_state > $o,C_21: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( semila1122118281tate_o @ ( insert528405184_state @ A_59 @ B_32 ) @ C_21 )
% 0.34/0.79 = ( insert528405184_state @ A_59 @ ( semila1122118281tate_o @ B_32 @ C_21 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_486_Un__insert__left,axiom,
% 0.34/0.79 ! [A_59: hoare_2091234717iple_a,B_32: hoare_2091234717iple_a > $o,C_21: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( semila1052848428le_a_o @ ( insert1597628439iple_a @ A_59 @ B_32 ) @ C_21 )
% 0.34/0.79 = ( insert1597628439iple_a @ A_59 @ ( semila1052848428le_a_o @ B_32 @ C_21 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_487_empty__is__image,axiom,
% 0.34/0.79 ! [F_38: nat > nat,A_58: nat > $o] :
% 0.34/0.79 ( ( bot_bot_nat_o
% 0.34/0.79 = ( image_nat_nat @ F_38 @ A_58 ) )
% 0.34/0.79 <=> ( A_58 = bot_bot_nat_o ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_488_empty__is__image,axiom,
% 0.34/0.79 ! [F_38: pname > hoare_1708887482_state,A_58: pname > $o] :
% 0.34/0.79 ( ( bot_bo19817387tate_o
% 0.34/0.79 = ( image_1116629049_state @ F_38 @ A_58 ) )
% 0.34/0.79 <=> ( A_58 = bot_bot_pname_o ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_489_empty__is__image,axiom,
% 0.34/0.79 ! [F_38: pname > hoare_2091234717iple_a,A_58: pname > $o] :
% 0.34/0.79 ( ( bot_bo1791335050le_a_o
% 0.34/0.79 = ( image_231808478iple_a @ F_38 @ A_58 ) )
% 0.34/0.79 <=> ( A_58 = bot_bot_pname_o ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_490_image__empty,axiom,
% 0.34/0.79 ! [F_37: nat > nat] :
% 0.34/0.79 ( ( image_nat_nat @ F_37 @ bot_bot_nat_o )
% 0.34/0.79 = bot_bot_nat_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_491_image__empty,axiom,
% 0.34/0.79 ! [F_37: pname > hoare_1708887482_state] :
% 0.34/0.79 ( ( image_1116629049_state @ F_37 @ bot_bot_pname_o )
% 0.34/0.79 = bot_bo19817387tate_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_492_image__empty,axiom,
% 0.34/0.79 ! [F_37: pname > hoare_2091234717iple_a] :
% 0.34/0.79 ( ( image_231808478iple_a @ F_37 @ bot_bot_pname_o )
% 0.34/0.79 = bot_bo1791335050le_a_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_493_image__is__empty,axiom,
% 0.34/0.79 ! [F_36: nat > nat,A_57: nat > $o] :
% 0.34/0.79 ( ( ( image_nat_nat @ F_36 @ A_57 )
% 0.34/0.79 = bot_bot_nat_o )
% 0.34/0.79 <=> ( A_57 = bot_bot_nat_o ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_494_image__is__empty,axiom,
% 0.34/0.79 ! [F_36: pname > hoare_1708887482_state,A_57: pname > $o] :
% 0.34/0.79 ( ( ( image_1116629049_state @ F_36 @ A_57 )
% 0.34/0.79 = bot_bo19817387tate_o )
% 0.34/0.79 <=> ( A_57 = bot_bot_pname_o ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_495_image__is__empty,axiom,
% 0.34/0.79 ! [F_36: pname > hoare_2091234717iple_a,A_57: pname > $o] :
% 0.34/0.79 ( ( ( image_231808478iple_a @ F_36 @ A_57 )
% 0.34/0.79 = bot_bo1791335050le_a_o )
% 0.34/0.79 <=> ( A_57 = bot_bot_pname_o ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_496_ball__empty,axiom,
% 0.34/0.79 ! [P_23: nat > $o,X: nat] :
% 0.34/0.79 ( ( member_nat @ X @ bot_bot_nat_o )
% 0.34/0.79 => ( P_23 @ X ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_497_ball__empty,axiom,
% 0.34/0.79 ! [P_23: hoare_2091234717iple_a > $o,X: hoare_2091234717iple_a] :
% 0.34/0.79 ( ( member290856304iple_a @ X @ bot_bo1791335050le_a_o )
% 0.34/0.79 => ( P_23 @ X ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_498_ball__empty,axiom,
% 0.34/0.79 ! [P_23: ( hoare_2091234717iple_a > $o ) > $o,X: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( member99268621le_a_o @ X @ bot_bo1957696069_a_o_o )
% 0.34/0.79 => ( P_23 @ X ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_499_ball__empty,axiom,
% 0.34/0.79 ! [P_23: pname > $o,X: pname] :
% 0.34/0.79 ( ( member_pname @ X @ bot_bot_pname_o )
% 0.34/0.79 => ( P_23 @ X ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_500_ball__empty,axiom,
% 0.34/0.79 ! [P_23: hoare_1708887482_state > $o,X: hoare_1708887482_state] :
% 0.34/0.79 ( ( member451959335_state @ X @ bot_bo19817387tate_o )
% 0.34/0.79 => ( P_23 @ X ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_501_Un__empty__left,axiom,
% 0.34/0.79 ! [B_31: nat > $o] :
% 0.34/0.79 ( ( semila848761471_nat_o @ bot_bot_nat_o @ B_31 )
% 0.34/0.79 = B_31 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_502_Un__empty__left,axiom,
% 0.34/0.79 ! [B_31: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( semila2050116131_a_o_o @ bot_bo1957696069_a_o_o @ B_31 )
% 0.34/0.79 = B_31 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_503_Un__empty__left,axiom,
% 0.34/0.79 ! [B_31: pname > $o] :
% 0.34/0.79 ( ( semila1780557381name_o @ bot_bot_pname_o @ B_31 )
% 0.34/0.79 = B_31 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_504_Un__empty__left,axiom,
% 0.34/0.79 ! [B_31: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( semila1122118281tate_o @ bot_bo19817387tate_o @ B_31 )
% 0.34/0.79 = B_31 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_505_Un__empty__left,axiom,
% 0.34/0.79 ! [B_31: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( semila1052848428le_a_o @ bot_bo1791335050le_a_o @ B_31 )
% 0.34/0.79 = B_31 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_506_Un__empty__right,axiom,
% 0.34/0.79 ! [A_56: nat > $o] :
% 0.34/0.79 ( ( semila848761471_nat_o @ A_56 @ bot_bot_nat_o )
% 0.34/0.79 = A_56 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_507_Un__empty__right,axiom,
% 0.34/0.79 ! [A_56: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( semila2050116131_a_o_o @ A_56 @ bot_bo1957696069_a_o_o )
% 0.34/0.79 = A_56 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_508_Un__empty__right,axiom,
% 0.34/0.79 ! [A_56: pname > $o] :
% 0.34/0.79 ( ( semila1780557381name_o @ A_56 @ bot_bot_pname_o )
% 0.34/0.79 = A_56 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_509_Un__empty__right,axiom,
% 0.34/0.79 ! [A_56: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( semila1122118281tate_o @ A_56 @ bot_bo19817387tate_o )
% 0.34/0.79 = A_56 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_510_Un__empty__right,axiom,
% 0.34/0.79 ! [A_56: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( semila1052848428le_a_o @ A_56 @ bot_bo1791335050le_a_o )
% 0.34/0.79 = A_56 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_511_Un__empty,axiom,
% 0.34/0.79 ! [A_55: nat > $o,B_30: nat > $o] :
% 0.34/0.79 ( ( ( semila848761471_nat_o @ A_55 @ B_30 )
% 0.34/0.79 = bot_bot_nat_o )
% 0.34/0.79 <=> ( ( A_55 = bot_bot_nat_o )
% 0.34/0.79 & ( B_30 = bot_bot_nat_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_512_Un__empty,axiom,
% 0.34/0.79 ! [A_55: ( hoare_2091234717iple_a > $o ) > $o,B_30: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( ( semila2050116131_a_o_o @ A_55 @ B_30 )
% 0.34/0.79 = bot_bo1957696069_a_o_o )
% 0.34/0.79 <=> ( ( A_55 = bot_bo1957696069_a_o_o )
% 0.34/0.79 & ( B_30 = bot_bo1957696069_a_o_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_513_Un__empty,axiom,
% 0.34/0.79 ! [A_55: pname > $o,B_30: pname > $o] :
% 0.34/0.79 ( ( ( semila1780557381name_o @ A_55 @ B_30 )
% 0.34/0.79 = bot_bot_pname_o )
% 0.34/0.79 <=> ( ( A_55 = bot_bot_pname_o )
% 0.34/0.79 & ( B_30 = bot_bot_pname_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_514_Un__empty,axiom,
% 0.34/0.79 ! [A_55: hoare_1708887482_state > $o,B_30: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( ( semila1122118281tate_o @ A_55 @ B_30 )
% 0.34/0.79 = bot_bo19817387tate_o )
% 0.34/0.79 <=> ( ( A_55 = bot_bo19817387tate_o )
% 0.34/0.79 & ( B_30 = bot_bo19817387tate_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_515_Un__empty,axiom,
% 0.34/0.79 ! [A_55: hoare_2091234717iple_a > $o,B_30: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( ( semila1052848428le_a_o @ A_55 @ B_30 )
% 0.34/0.79 = bot_bo1791335050le_a_o )
% 0.34/0.79 <=> ( ( A_55 = bot_bo1791335050le_a_o )
% 0.34/0.79 & ( B_30 = bot_bo1791335050le_a_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_516_constant,axiom,
% 0.34/0.79 ! [G_17: hoare_2091234717iple_a > $o,P_22: x_a > state > $o,C_20: com,Q_15: x_a > state > $o,C_19: $o] :
% 0.34/0.79 ( ( C_19
% 0.34/0.79 => ( hoare_1467856363rivs_a @ G_17 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ P_22 @ C_20 @ Q_15 ) @ bot_bo1791335050le_a_o ) ) )
% 0.34/0.79 => ( hoare_1467856363rivs_a @ G_17
% 0.34/0.79 @ ( insert1597628439iple_a
% 0.34/0.79 @ ( hoare_657976383iple_a
% 0.34/0.79 @ ^ [Z_5: x_a,S_2: state] : ( (&) @ ( P_22 @ Z_5 @ S_2 ) @ C_19 )
% 0.34/0.79 @ C_20
% 0.34/0.79 @ Q_15 )
% 0.34/0.79 @ bot_bo1791335050le_a_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_517_constant,axiom,
% 0.34/0.79 ! [G_17: hoare_1708887482_state > $o,P_22: state > state > $o,C_20: com,Q_15: state > state > $o,C_19: $o] :
% 0.34/0.79 ( ( C_19
% 0.34/0.79 => ( hoare_90032982_state @ G_17 @ ( insert528405184_state @ ( hoare_858012674_state @ P_22 @ C_20 @ Q_15 ) @ bot_bo19817387tate_o ) ) )
% 0.34/0.79 => ( hoare_90032982_state @ G_17
% 0.34/0.79 @ ( insert528405184_state
% 0.34/0.79 @ ( hoare_858012674_state
% 0.34/0.79 @ ^ [Z_5: state,S_2: state] : ( (&) @ ( P_22 @ Z_5 @ S_2 ) @ C_19 )
% 0.34/0.79 @ C_20
% 0.34/0.79 @ Q_15 )
% 0.34/0.79 @ bot_bo19817387tate_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_518_empty,axiom,
% 0.34/0.79 ! [G_16: hoare_2091234717iple_a > $o] : ( hoare_1467856363rivs_a @ G_16 @ bot_bo1791335050le_a_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_519_empty,axiom,
% 0.34/0.79 ! [G_16: hoare_1708887482_state > $o] : ( hoare_90032982_state @ G_16 @ bot_bo19817387tate_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_520_sup__bot__left,axiom,
% 0.34/0.79 ! [X_26: nat > $o] :
% 0.34/0.79 ( ( semila848761471_nat_o @ bot_bot_nat_o @ X_26 )
% 0.34/0.79 = X_26 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_521_sup__bot__left,axiom,
% 0.34/0.79 ! [X_26: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( semila2050116131_a_o_o @ bot_bo1957696069_a_o_o @ X_26 )
% 0.34/0.79 = X_26 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_522_sup__bot__left,axiom,
% 0.34/0.79 ! [X_26: pname > $o] :
% 0.34/0.79 ( ( semila1780557381name_o @ bot_bot_pname_o @ X_26 )
% 0.34/0.79 = X_26 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_523_sup__bot__left,axiom,
% 0.34/0.79 ! [X_26: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( semila1122118281tate_o @ bot_bo19817387tate_o @ X_26 )
% 0.34/0.79 = X_26 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_524_sup__bot__left,axiom,
% 0.34/0.79 ! [X_26: $o] :
% 0.34/0.79 ( ( semila10642723_sup_o @ bot_bot_o @ X_26 )
% 0.34/0.79 <=> X_26 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_525_sup__bot__left,axiom,
% 0.34/0.79 ! [X_26: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( semila1052848428le_a_o @ bot_bo1791335050le_a_o @ X_26 )
% 0.34/0.79 = X_26 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_526_sup__bot__right,axiom,
% 0.34/0.79 ! [X_25: nat > $o] :
% 0.34/0.79 ( ( semila848761471_nat_o @ X_25 @ bot_bot_nat_o )
% 0.34/0.79 = X_25 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_527_sup__bot__right,axiom,
% 0.34/0.79 ! [X_25: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( semila2050116131_a_o_o @ X_25 @ bot_bo1957696069_a_o_o )
% 0.34/0.79 = X_25 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_528_sup__bot__right,axiom,
% 0.34/0.79 ! [X_25: pname > $o] :
% 0.34/0.79 ( ( semila1780557381name_o @ X_25 @ bot_bot_pname_o )
% 0.34/0.79 = X_25 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_529_sup__bot__right,axiom,
% 0.34/0.79 ! [X_25: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( semila1122118281tate_o @ X_25 @ bot_bo19817387tate_o )
% 0.34/0.79 = X_25 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_530_sup__bot__right,axiom,
% 0.34/0.79 ! [X_25: $o] :
% 0.34/0.79 ( ( semila10642723_sup_o @ X_25 @ bot_bot_o )
% 0.34/0.79 <=> X_25 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_531_sup__bot__right,axiom,
% 0.34/0.79 ! [X_25: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( semila1052848428le_a_o @ X_25 @ bot_bo1791335050le_a_o )
% 0.34/0.79 = X_25 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_532_sup__eq__bot__iff,axiom,
% 0.34/0.79 ! [X_24: nat > $o,Y_8: nat > $o] :
% 0.34/0.79 ( ( ( semila848761471_nat_o @ X_24 @ Y_8 )
% 0.34/0.79 = bot_bot_nat_o )
% 0.34/0.79 <=> ( ( X_24 = bot_bot_nat_o )
% 0.34/0.79 & ( Y_8 = bot_bot_nat_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_533_sup__eq__bot__iff,axiom,
% 0.34/0.79 ! [X_24: ( hoare_2091234717iple_a > $o ) > $o,Y_8: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( ( semila2050116131_a_o_o @ X_24 @ Y_8 )
% 0.34/0.79 = bot_bo1957696069_a_o_o )
% 0.34/0.79 <=> ( ( X_24 = bot_bo1957696069_a_o_o )
% 0.34/0.79 & ( Y_8 = bot_bo1957696069_a_o_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_534_sup__eq__bot__iff,axiom,
% 0.34/0.79 ! [X_24: pname > $o,Y_8: pname > $o] :
% 0.34/0.79 ( ( ( semila1780557381name_o @ X_24 @ Y_8 )
% 0.34/0.79 = bot_bot_pname_o )
% 0.34/0.79 <=> ( ( X_24 = bot_bot_pname_o )
% 0.34/0.79 & ( Y_8 = bot_bot_pname_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_535_sup__eq__bot__iff,axiom,
% 0.34/0.79 ! [X_24: hoare_1708887482_state > $o,Y_8: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( ( semila1122118281tate_o @ X_24 @ Y_8 )
% 0.34/0.79 = bot_bo19817387tate_o )
% 0.34/0.79 <=> ( ( X_24 = bot_bo19817387tate_o )
% 0.34/0.79 & ( Y_8 = bot_bo19817387tate_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_536_sup__eq__bot__iff,axiom,
% 0.34/0.79 ! [X_24: $o,Y_8: $o] :
% 0.34/0.79 ( ( ( semila10642723_sup_o @ X_24 @ Y_8 )
% 0.34/0.79 <=> bot_bot_o )
% 0.34/0.79 <=> ( ( X_24
% 0.34/0.79 <=> bot_bot_o )
% 0.34/0.79 & ( Y_8
% 0.34/0.79 <=> bot_bot_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_537_sup__eq__bot__iff,axiom,
% 0.34/0.79 ! [X_24: hoare_2091234717iple_a > $o,Y_8: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( ( semila1052848428le_a_o @ X_24 @ Y_8 )
% 0.34/0.79 = bot_bo1791335050le_a_o )
% 0.34/0.79 <=> ( ( X_24 = bot_bo1791335050le_a_o )
% 0.34/0.79 & ( Y_8 = bot_bo1791335050le_a_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_538_triple__valid__Suc,axiom,
% 0.34/0.79 ! [N_5: nat,T_1: hoare_1708887482_state] :
% 0.34/0.79 ( ( hoare_23738522_state @ ( suc @ N_5 ) @ T_1 )
% 0.34/0.79 => ( hoare_23738522_state @ N_5 @ T_1 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_539_triple__valid__Suc,axiom,
% 0.34/0.79 ! [N_5: nat,T_1: hoare_2091234717iple_a] :
% 0.34/0.79 ( ( hoare_1421888935alid_a @ ( suc @ N_5 ) @ T_1 )
% 0.34/0.79 => ( hoare_1421888935alid_a @ N_5 @ T_1 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_540_insert__def,axiom,
% 0.34/0.79 ! [A_54: hoare_2091234717iple_a > $o,B_29: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( insert102003750le_a_o @ A_54 @ B_29 )
% 0.34/0.79 = ( semila2050116131_a_o_o
% 0.34/0.79 @ ( collec1008234059le_a_o
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a > $o] : ( X = A_54 ) )
% 0.34/0.79 @ B_29 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_541_insert__def,axiom,
% 0.34/0.79 ! [A_54: pname,B_29: pname > $o] :
% 0.34/0.79 ( ( insert_pname @ A_54 @ B_29 )
% 0.34/0.79 = ( semila1780557381name_o
% 0.34/0.79 @ ( collect_pname
% 0.34/0.79 @ ^ [X: pname] : ( X = A_54 ) )
% 0.34/0.79 @ B_29 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_542_insert__def,axiom,
% 0.34/0.79 ! [A_54: hoare_1708887482_state,B_29: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( insert528405184_state @ A_54 @ B_29 )
% 0.34/0.79 = ( semila1122118281tate_o
% 0.34/0.79 @ ( collec1568722789_state
% 0.34/0.79 @ ^ [X: hoare_1708887482_state] : ( X = A_54 ) )
% 0.34/0.79 @ B_29 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_543_insert__def,axiom,
% 0.34/0.79 ! [A_54: hoare_2091234717iple_a,B_29: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( insert1597628439iple_a @ A_54 @ B_29 )
% 0.34/0.79 = ( semila1052848428le_a_o
% 0.34/0.79 @ ( collec992574898iple_a
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a] : ( X = A_54 ) )
% 0.34/0.79 @ B_29 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_544_insert__def,axiom,
% 0.34/0.79 ! [A_54: nat,B_29: nat > $o] :
% 0.34/0.79 ( ( insert_nat @ A_54 @ B_29 )
% 0.34/0.79 = ( semila848761471_nat_o
% 0.34/0.79 @ ( collect_nat
% 0.34/0.79 @ ^ [X: nat] : ( X = A_54 ) )
% 0.34/0.79 @ B_29 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_545_weak__Body,axiom,
% 0.34/0.79 ! [G_15: hoare_2091234717iple_a > $o,P_21: x_a > state > $o,Pn_3: pname,Q_14: x_a > state > $o] :
% 0.34/0.79 ( ( hoare_1467856363rivs_a @ G_15 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ P_21 @ ( the_com @ ( body_1 @ Pn_3 ) ) @ Q_14 ) @ bot_bo1791335050le_a_o ) )
% 0.34/0.79 => ( hoare_1467856363rivs_a @ G_15 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ P_21 @ ( body @ Pn_3 ) @ Q_14 ) @ bot_bo1791335050le_a_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_546_weak__Body,axiom,
% 0.34/0.79 ! [G_15: hoare_1708887482_state > $o,P_21: state > state > $o,Pn_3: pname,Q_14: state > state > $o] :
% 0.34/0.79 ( ( hoare_90032982_state @ G_15 @ ( insert528405184_state @ ( hoare_858012674_state @ P_21 @ ( the_com @ ( body_1 @ Pn_3 ) ) @ Q_14 ) @ bot_bo19817387tate_o ) )
% 0.34/0.79 => ( hoare_90032982_state @ G_15 @ ( insert528405184_state @ ( hoare_858012674_state @ P_21 @ ( body @ Pn_3 ) @ Q_14 ) @ bot_bo19817387tate_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_547_BodyN,axiom,
% 0.34/0.79 ! [P_20: x_a > state > $o,Pn_2: pname,Q_13: x_a > state > $o,G_14: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( hoare_1467856363rivs_a @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ P_20 @ ( body @ Pn_2 ) @ Q_13 ) @ G_14 ) @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ P_20 @ ( the_com @ ( body_1 @ Pn_2 ) ) @ Q_13 ) @ bot_bo1791335050le_a_o ) )
% 0.34/0.79 => ( hoare_1467856363rivs_a @ G_14 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ P_20 @ ( body @ Pn_2 ) @ Q_13 ) @ bot_bo1791335050le_a_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_548_BodyN,axiom,
% 0.34/0.79 ! [P_20: state > state > $o,Pn_2: pname,Q_13: state > state > $o,G_14: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( hoare_90032982_state @ ( insert528405184_state @ ( hoare_858012674_state @ P_20 @ ( body @ Pn_2 ) @ Q_13 ) @ G_14 ) @ ( insert528405184_state @ ( hoare_858012674_state @ P_20 @ ( the_com @ ( body_1 @ Pn_2 ) ) @ Q_13 ) @ bot_bo19817387tate_o ) )
% 0.34/0.79 => ( hoare_90032982_state @ G_14 @ ( insert528405184_state @ ( hoare_858012674_state @ P_20 @ ( body @ Pn_2 ) @ Q_13 ) @ bot_bo19817387tate_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_549_escape,axiom,
% 0.34/0.79 ! [G_13: hoare_2091234717iple_a > $o,C_18: com,Q_12: x_a > state > $o,P_19: x_a > state > $o] :
% 0.34/0.79 ( ! [Z_5: x_a,S_2: state] :
% 0.34/0.79 ( ( P_19 @ Z_5 @ S_2 )
% 0.34/0.79 => ( hoare_1467856363rivs_a @ G_13
% 0.34/0.79 @ ( insert1597628439iple_a
% 0.34/0.79 @ ( hoare_657976383iple_a
% 0.34/0.79 @ ^ [Za: x_a,S_3: state] : ( S_3 = S_2 )
% 0.34/0.79 @ C_18
% 0.34/0.79 @ ^ [Z_6: x_a] : ( Q_12 @ Z_5 ) )
% 0.34/0.79 @ bot_bo1791335050le_a_o ) ) )
% 0.34/0.79 => ( hoare_1467856363rivs_a @ G_13 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ P_19 @ C_18 @ Q_12 ) @ bot_bo1791335050le_a_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_550_escape,axiom,
% 0.34/0.79 ! [G_13: hoare_1708887482_state > $o,C_18: com,Q_12: state > state > $o,P_19: state > state > $o] :
% 0.34/0.79 ( ! [Z_5: state,S_2: state] :
% 0.34/0.79 ( ( P_19 @ Z_5 @ S_2 )
% 0.34/0.79 => ( hoare_90032982_state @ G_13
% 0.34/0.79 @ ( insert528405184_state
% 0.34/0.79 @ ( hoare_858012674_state
% 0.34/0.79 @ ^ [Za: state,S_3: state] : ( S_3 = S_2 )
% 0.34/0.79 @ C_18
% 0.34/0.79 @ ^ [Z_6: state] : ( Q_12 @ Z_5 ) )
% 0.34/0.79 @ bot_bo19817387tate_o ) ) )
% 0.34/0.79 => ( hoare_90032982_state @ G_13 @ ( insert528405184_state @ ( hoare_858012674_state @ P_19 @ C_18 @ Q_12 ) @ bot_bo19817387tate_o ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_551_conseq1,axiom,
% 0.34/0.79 ! [P_18: x_a > state > $o,G_12: hoare_2091234717iple_a > $o,P_17: x_a > state > $o,C_17: com,Q_11: x_a > state > $o] :
% 0.34/0.79 ( ( hoare_1467856363rivs_a @ G_12 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ P_17 @ C_17 @ Q_11 ) @ bot_bo1791335050le_a_o ) )
% 0.34/0.79 => ( ! [Z_5: x_a,S_2: state] :
% 0.34/0.79 ( ( P_18 @ Z_5 @ S_2 )
% 0.34/0.79 => ( P_17 @ Z_5 @ S_2 ) )
% 0.34/0.79 => ( hoare_1467856363rivs_a @ G_12 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ P_18 @ C_17 @ Q_11 ) @ bot_bo1791335050le_a_o ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_552_conseq1,axiom,
% 0.34/0.79 ! [P_18: state > state > $o,G_12: hoare_1708887482_state > $o,P_17: state > state > $o,C_17: com,Q_11: state > state > $o] :
% 0.34/0.79 ( ( hoare_90032982_state @ G_12 @ ( insert528405184_state @ ( hoare_858012674_state @ P_17 @ C_17 @ Q_11 ) @ bot_bo19817387tate_o ) )
% 0.34/0.79 => ( ! [Z_5: state,S_2: state] :
% 0.34/0.79 ( ( P_18 @ Z_5 @ S_2 )
% 0.34/0.79 => ( P_17 @ Z_5 @ S_2 ) )
% 0.34/0.79 => ( hoare_90032982_state @ G_12 @ ( insert528405184_state @ ( hoare_858012674_state @ P_18 @ C_17 @ Q_11 ) @ bot_bo19817387tate_o ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_553_conseq2,axiom,
% 0.34/0.79 ! [Q_10: x_a > state > $o,G_11: hoare_2091234717iple_a > $o,P_16: x_a > state > $o,C_16: com,Q_9: x_a > state > $o] :
% 0.34/0.79 ( ( hoare_1467856363rivs_a @ G_11 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ P_16 @ C_16 @ Q_9 ) @ bot_bo1791335050le_a_o ) )
% 0.34/0.79 => ( ! [Z_5: x_a,S_2: state] :
% 0.34/0.79 ( ( Q_9 @ Z_5 @ S_2 )
% 0.34/0.79 => ( Q_10 @ Z_5 @ S_2 ) )
% 0.34/0.79 => ( hoare_1467856363rivs_a @ G_11 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ P_16 @ C_16 @ Q_10 ) @ bot_bo1791335050le_a_o ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_554_conseq2,axiom,
% 0.34/0.79 ! [Q_10: state > state > $o,G_11: hoare_1708887482_state > $o,P_16: state > state > $o,C_16: com,Q_9: state > state > $o] :
% 0.34/0.79 ( ( hoare_90032982_state @ G_11 @ ( insert528405184_state @ ( hoare_858012674_state @ P_16 @ C_16 @ Q_9 ) @ bot_bo19817387tate_o ) )
% 0.34/0.79 => ( ! [Z_5: state,S_2: state] :
% 0.34/0.79 ( ( Q_9 @ Z_5 @ S_2 )
% 0.34/0.79 => ( Q_10 @ Z_5 @ S_2 ) )
% 0.34/0.79 => ( hoare_90032982_state @ G_11 @ ( insert528405184_state @ ( hoare_858012674_state @ P_16 @ C_16 @ Q_10 ) @ bot_bo19817387tate_o ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_555_triple_Osize_I1_J,axiom,
% 0.34/0.79 ! [Fa: x_a > nat,Fun1_1: x_a > state > $o,Com_3: com,Fun2_1: x_a > state > $o] :
% 0.34/0.79 ( ( hoare_1169027232size_a @ Fa @ ( hoare_657976383iple_a @ Fun1_1 @ Com_3 @ Fun2_1 ) )
% 0.34/0.79 = zero_zero_nat ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_556_triple_Osize_I1_J,axiom,
% 0.34/0.79 ! [Fa: state > nat,Fun1_1: state > state > $o,Com_3: com,Fun2_1: state > state > $o] :
% 0.34/0.79 ( ( hoare_518771297_state @ Fa @ ( hoare_858012674_state @ Fun1_1 @ Com_3 @ Fun2_1 ) )
% 0.34/0.79 = zero_zero_nat ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_557_MGT__def,axiom,
% 0.34/0.79 ! [C: com] :
% 0.34/0.79 ( ( hoare_Mirabelle_MGT @ C )
% 0.34/0.79 = ( hoare_858012674_state @ fequal_state @ C @ ( evalc @ C ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_558_triple_Osize_I2_J,axiom,
% 0.34/0.79 ! [Fun1: x_a > state > $o,Com_2: com,Fun2: x_a > state > $o] :
% 0.34/0.79 ( ( size_s1040486067iple_a @ ( hoare_657976383iple_a @ Fun1 @ Com_2 @ Fun2 ) )
% 0.34/0.79 = zero_zero_nat ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_559_triple_Osize_I2_J,axiom,
% 0.34/0.79 ! [Fun1: state > state > $o,Com_2: com,Fun2: state > state > $o] :
% 0.34/0.79 ( ( size_s1186992420_state @ ( hoare_858012674_state @ Fun1 @ Com_2 @ Fun2 ) )
% 0.34/0.79 = zero_zero_nat ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_560_conseq12,axiom,
% 0.34/0.79 ! [Q_8: x_a > state > $o,P_15: x_a > state > $o,G_10: hoare_2091234717iple_a > $o,P_14: x_a > state > $o,C_15: com,Q_7: x_a > state > $o] :
% 0.34/0.79 ( ( hoare_1467856363rivs_a @ G_10 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ P_14 @ C_15 @ Q_7 ) @ bot_bo1791335050le_a_o ) )
% 0.34/0.79 => ( ! [Z_5: x_a,S_2: state] :
% 0.34/0.79 ( ( P_15 @ Z_5 @ S_2 )
% 0.34/0.79 => ! [S_3: state] :
% 0.34/0.79 ( ! [Z_6: x_a] :
% 0.34/0.79 ( ( P_14 @ Z_6 @ S_2 )
% 0.34/0.79 => ( Q_7 @ Z_6 @ S_3 ) )
% 0.34/0.79 => ( Q_8 @ Z_5 @ S_3 ) ) )
% 0.34/0.79 => ( hoare_1467856363rivs_a @ G_10 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ P_15 @ C_15 @ Q_8 ) @ bot_bo1791335050le_a_o ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_561_conseq12,axiom,
% 0.34/0.79 ! [Q_8: state > state > $o,P_15: state > state > $o,G_10: hoare_1708887482_state > $o,P_14: state > state > $o,C_15: com,Q_7: state > state > $o] :
% 0.34/0.79 ( ( hoare_90032982_state @ G_10 @ ( insert528405184_state @ ( hoare_858012674_state @ P_14 @ C_15 @ Q_7 ) @ bot_bo19817387tate_o ) )
% 0.34/0.79 => ( ! [Z_5: state,S_2: state] :
% 0.34/0.79 ( ( P_15 @ Z_5 @ S_2 )
% 0.34/0.79 => ! [S_3: state] :
% 0.34/0.79 ( ! [Z_6: state] :
% 0.34/0.79 ( ( P_14 @ Z_6 @ S_2 )
% 0.34/0.79 => ( Q_7 @ Z_6 @ S_3 ) )
% 0.34/0.79 => ( Q_8 @ Z_5 @ S_3 ) ) )
% 0.34/0.79 => ( hoare_90032982_state @ G_10 @ ( insert528405184_state @ ( hoare_858012674_state @ P_15 @ C_15 @ Q_8 ) @ bot_bo19817387tate_o ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_562_the__elem__eq,axiom,
% 0.34/0.79 ! [X_23: nat] :
% 0.34/0.79 ( ( the_elem_nat @ ( insert_nat @ X_23 @ bot_bot_nat_o ) )
% 0.34/0.79 = X_23 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_563_the__elem__eq,axiom,
% 0.34/0.79 ! [X_23: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( the_el1618277441le_a_o @ ( insert102003750le_a_o @ X_23 @ bot_bo1957696069_a_o_o ) )
% 0.34/0.79 = X_23 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_564_the__elem__eq,axiom,
% 0.34/0.79 ! [X_23: pname] :
% 0.34/0.79 ( ( the_elem_pname @ ( insert_pname @ X_23 @ bot_bot_pname_o ) )
% 0.34/0.79 = X_23 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_565_the__elem__eq,axiom,
% 0.34/0.79 ! [X_23: hoare_2091234717iple_a] :
% 0.34/0.79 ( ( the_el13400124iple_a @ ( insert1597628439iple_a @ X_23 @ bot_bo1791335050le_a_o ) )
% 0.34/0.79 = X_23 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_566_the__elem__eq,axiom,
% 0.34/0.79 ! [X_23: hoare_1708887482_state] :
% 0.34/0.79 ( ( the_el864710747_state @ ( insert528405184_state @ X_23 @ bot_bo19817387tate_o ) )
% 0.34/0.79 = X_23 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_567_Suc__neq__Zero,axiom,
% 0.34/0.79 ! [M: nat] :
% 0.34/0.79 ( ( suc @ M )
% 0.34/0.79 != zero_zero_nat ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_568_bot__nat__def,axiom,
% 0.34/0.79 bot_bot_nat = zero_zero_nat ).
% 0.34/0.79
% 0.34/0.79 thf(fact_569_n__not__Suc__n,axiom,
% 0.34/0.79 ! [N_1: nat] :
% 0.34/0.79 ( N_1
% 0.34/0.79 != ( suc @ N_1 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_570_Suc__n__not__n,axiom,
% 0.34/0.79 ! [N_1: nat] :
% 0.34/0.79 ( ( suc @ N_1 )
% 0.34/0.79 != N_1 ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_571_nat_Oinject,axiom,
% 0.34/0.79 ! [Nat_3: nat,Nat_2: nat] :
% 0.34/0.79 ( ( ( suc @ Nat_3 )
% 0.34/0.79 = ( suc @ Nat_2 ) )
% 0.34/0.79 <=> ( Nat_3 = Nat_2 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_572_Suc__inject,axiom,
% 0.34/0.79 ! [X_1: nat,Y: nat] :
% 0.34/0.79 ( ( ( suc @ X_1 )
% 0.34/0.79 = ( suc @ Y ) )
% 0.34/0.79 => ( X_1 = Y ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_573_Zero__not__Suc,axiom,
% 0.34/0.79 ! [M: nat] :
% 0.34/0.79 ( zero_zero_nat
% 0.34/0.79 != ( suc @ M ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_574_nat_Osimps_I2_J,axiom,
% 0.34/0.79 ! [Nat_2: nat] :
% 0.34/0.79 ( zero_zero_nat
% 0.34/0.79 != ( suc @ Nat_2 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_575_Suc__not__Zero,axiom,
% 0.34/0.79 ! [M: nat] :
% 0.34/0.79 ( ( suc @ M )
% 0.34/0.79 != zero_zero_nat ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_576_nat_Osimps_I3_J,axiom,
% 0.34/0.79 ! [Nat_1: nat] :
% 0.34/0.79 ( ( suc @ Nat_1 )
% 0.34/0.79 != zero_zero_nat ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_577_Zero__neq__Suc,axiom,
% 0.34/0.79 ! [M: nat] :
% 0.34/0.79 ( zero_zero_nat
% 0.34/0.79 != ( suc @ M ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_578_not0__implies__Suc,axiom,
% 0.34/0.79 ! [N_1: nat] :
% 0.34/0.79 ( ( N_1 != zero_zero_nat )
% 0.34/0.79 => ? [M_1: nat] :
% 0.34/0.79 ( N_1
% 0.34/0.79 = ( suc @ M_1 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_579_nat__induct,axiom,
% 0.34/0.79 ! [N_1: nat,P: nat > $o] :
% 0.34/0.79 ( ( P @ zero_zero_nat )
% 0.34/0.79 => ( ! [N: nat] :
% 0.34/0.79 ( ( P @ N )
% 0.34/0.79 => ( P @ ( suc @ N ) ) )
% 0.34/0.79 => ( P @ N_1 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_580_zero__induct,axiom,
% 0.34/0.79 ! [P: nat > $o,K_1: nat] :
% 0.34/0.79 ( ( P @ K_1 )
% 0.34/0.79 => ( ! [N: nat] :
% 0.34/0.79 ( ( P @ ( suc @ N ) )
% 0.34/0.79 => ( P @ N ) )
% 0.34/0.79 => ( P @ zero_zero_nat ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_581_nat_Oexhaust,axiom,
% 0.34/0.79 ! [Y: nat] :
% 0.34/0.79 ( ( Y != zero_zero_nat )
% 0.34/0.79 => ~ ! [Nat: nat] :
% 0.34/0.79 ( Y
% 0.34/0.79 != ( suc @ Nat ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_582_bot__fun__def,axiom,
% 0.34/0.79 ! [X: nat] :
% 0.34/0.79 ( ( bot_bot_nat_o @ X )
% 0.34/0.79 <=> bot_bot_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_583_bot__fun__def,axiom,
% 0.34/0.79 ! [X: hoare_2091234717iple_a] :
% 0.34/0.79 ( ( bot_bo1791335050le_a_o @ X )
% 0.34/0.79 <=> bot_bot_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_584_bot__fun__def,axiom,
% 0.34/0.79 ! [X: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( bot_bo1957696069_a_o_o @ X )
% 0.34/0.79 <=> bot_bot_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_585_bot__fun__def,axiom,
% 0.34/0.79 ! [X: pname] :
% 0.34/0.79 ( ( bot_bot_pname_o @ X )
% 0.34/0.79 <=> bot_bot_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_586_bot__fun__def,axiom,
% 0.34/0.79 ! [X: hoare_1708887482_state] :
% 0.34/0.79 ( ( bot_bo19817387tate_o @ X )
% 0.34/0.79 <=> bot_bot_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_587_bot__apply,axiom,
% 0.34/0.79 ! [X_22: nat] :
% 0.34/0.79 ( ( bot_bot_nat_o @ X_22 )
% 0.34/0.79 <=> bot_bot_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_588_bot__apply,axiom,
% 0.34/0.79 ! [X_22: hoare_2091234717iple_a] :
% 0.34/0.79 ( ( bot_bo1791335050le_a_o @ X_22 )
% 0.34/0.79 <=> bot_bot_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_589_bot__apply,axiom,
% 0.34/0.79 ! [X_22: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( bot_bo1957696069_a_o_o @ X_22 )
% 0.34/0.79 <=> bot_bot_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_590_bot__apply,axiom,
% 0.34/0.79 ! [X_22: pname] :
% 0.34/0.79 ( ( bot_bot_pname_o @ X_22 )
% 0.34/0.79 <=> bot_bot_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_591_bot__apply,axiom,
% 0.34/0.79 ! [X_22: hoare_1708887482_state] :
% 0.34/0.79 ( ( bot_bo19817387tate_o @ X_22 )
% 0.34/0.79 <=> bot_bot_o ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_592_evaln_OBody,axiom,
% 0.34/0.79 ! [Pn_1: pname,S0: state,N_1: nat,S1: state] :
% 0.34/0.79 ( ( evaln @ ( the_com @ ( body_1 @ Pn_1 ) ) @ S0 @ N_1 @ S1 )
% 0.34/0.79 => ( evaln @ ( body @ Pn_1 ) @ S0 @ ( suc @ N_1 ) @ S1 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_593_hoare__derivs_OSkip,axiom,
% 0.34/0.79 ! [G_9: hoare_2091234717iple_a > $o,P_13: x_a > state > $o] : ( hoare_1467856363rivs_a @ G_9 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ P_13 @ skip @ P_13 ) @ bot_bo1791335050le_a_o ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_594_hoare__derivs_OSkip,axiom,
% 0.34/0.79 ! [G_9: hoare_1708887482_state > $o,P_13: state > state > $o] : ( hoare_90032982_state @ G_9 @ ( insert528405184_state @ ( hoare_858012674_state @ P_13 @ skip @ P_13 ) @ bot_bo19817387tate_o ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_595_LoopF,axiom,
% 0.34/0.79 ! [G_8: hoare_2091234717iple_a > $o,P_12: x_a > state > $o,B_28: state > $o,C_14: com] :
% 0.34/0.79 ( hoare_1467856363rivs_a @ G_8
% 0.34/0.79 @ ( insert1597628439iple_a
% 0.34/0.79 @ ( hoare_657976383iple_a
% 0.34/0.79 @ ^ [Z_5: x_a,S_2: state] : ( (&) @ ( P_12 @ Z_5 @ S_2 ) @ ( (~) @ ( B_28 @ S_2 ) ) )
% 0.34/0.79 @ ( while @ B_28 @ C_14 )
% 0.34/0.79 @ P_12 )
% 0.34/0.79 @ bot_bo1791335050le_a_o ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_596_LoopF,axiom,
% 0.34/0.79 ! [G_8: hoare_1708887482_state > $o,P_12: state > state > $o,B_28: state > $o,C_14: com] :
% 0.34/0.79 ( hoare_90032982_state @ G_8
% 0.34/0.79 @ ( insert528405184_state
% 0.34/0.79 @ ( hoare_858012674_state
% 0.34/0.79 @ ^ [Z_5: state,S_2: state] : ( (&) @ ( P_12 @ Z_5 @ S_2 ) @ ( (~) @ ( B_28 @ S_2 ) ) )
% 0.34/0.79 @ ( while @ B_28 @ C_14 )
% 0.34/0.79 @ P_12 )
% 0.34/0.79 @ bot_bo19817387tate_o ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_597_evaln_OWhileFalse,axiom,
% 0.34/0.79 ! [C: com,N_1: nat,B: state > $o,S: state] :
% 0.34/0.79 ( ~ ( B @ S )
% 0.34/0.79 => ( evaln @ ( while @ B @ C ) @ S @ N_1 @ S ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_598_evaln_OWhileTrue,axiom,
% 0.34/0.79 ! [S2: state,C: com,N_1: nat,S1: state,B: state > $o,S0: state] :
% 0.34/0.79 ( ( B @ S0 )
% 0.34/0.79 => ( ( evaln @ C @ S0 @ N_1 @ S1 )
% 0.34/0.79 => ( ( evaln @ ( while @ B @ C ) @ S1 @ N_1 @ S2 )
% 0.34/0.79 => ( evaln @ ( while @ B @ C ) @ S0 @ N_1 @ S2 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_599_evalc_OWhileTrue,axiom,
% 0.34/0.79 ! [S2: state,C: com,S1: state,B: state > $o,S0: state] :
% 0.34/0.79 ( ( B @ S0 )
% 0.34/0.79 => ( ( evalc @ C @ S0 @ S1 )
% 0.34/0.79 => ( ( evalc @ ( while @ B @ C ) @ S1 @ S2 )
% 0.34/0.79 => ( evalc @ ( while @ B @ C ) @ S0 @ S2 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_600_evalc_OWhileFalse,axiom,
% 0.34/0.79 ! [C: com,B: state > $o,S: state] :
% 0.34/0.79 ( ~ ( B @ S )
% 0.34/0.79 => ( evalc @ ( while @ B @ C ) @ S @ S ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_601_evaln_OSkip,axiom,
% 0.34/0.79 ! [S: state,N_1: nat] : ( evaln @ skip @ S @ N_1 @ S ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_602_evaln__elim__cases_I1_J,axiom,
% 0.34/0.79 ! [S: state,N_1: nat,T: state] :
% 0.34/0.79 ( ( evaln @ skip @ S @ N_1 @ T )
% 0.34/0.79 => ( T = S ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_603_evalc__elim__cases_I1_J,axiom,
% 0.34/0.79 ! [S: state,T: state] :
% 0.34/0.79 ( ( evalc @ skip @ S @ T )
% 0.34/0.79 => ( T = S ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_604_evalc_OSkip,axiom,
% 0.34/0.79 ! [S: state] : ( evalc @ skip @ S @ S ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_605_com_Osimps_I16_J,axiom,
% 0.34/0.79 ! [Fun: state > $o,Com: com] :
% 0.34/0.79 ( skip
% 0.34/0.79 != ( while @ Fun @ Com ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_606_com_Osimps_I17_J,axiom,
% 0.34/0.79 ! [Fun: state > $o,Com: com] :
% 0.34/0.79 ( ( while @ Fun @ Com )
% 0.34/0.79 != skip ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_607_com_Osimps_I5_J,axiom,
% 0.34/0.79 ! [Fun_1: state > $o,Com_1: com,Fun: state > $o,Com: com] :
% 0.34/0.79 ( ( ( while @ Fun_1 @ Com_1 )
% 0.34/0.79 = ( while @ Fun @ Com ) )
% 0.34/0.79 <=> ( ( Fun_1 = Fun )
% 0.34/0.79 & ( Com_1 = Com ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_608_evaln__Suc,axiom,
% 0.34/0.79 ! [C: com,S: state,N_1: nat,S_4: state] :
% 0.34/0.79 ( ( evaln @ C @ S @ N_1 @ S_4 )
% 0.34/0.79 => ( evaln @ C @ S @ ( suc @ N_1 ) @ S_4 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_609_evaln__evalc,axiom,
% 0.34/0.79 ! [C: com,S: state,N_1: nat,T: state] :
% 0.34/0.79 ( ( evaln @ C @ S @ N_1 @ T )
% 0.34/0.79 => ( evalc @ C @ S @ T ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_610_eval__eq,axiom,
% 0.34/0.79 ! [C: com,S: state,T: state] :
% 0.34/0.79 ( ( evalc @ C @ S @ T )
% 0.34/0.79 <=> ? [N: nat] : ( evaln @ C @ S @ N @ T ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_611_com_Osimps_I59_J,axiom,
% 0.34/0.79 ! [Pname: pname,Fun_1: state > $o,Com_1: com] :
% 0.34/0.79 ( ( body @ Pname )
% 0.34/0.79 != ( while @ Fun_1 @ Com_1 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_612_com_Osimps_I58_J,axiom,
% 0.34/0.79 ! [Fun_1: state > $o,Com_1: com,Pname: pname] :
% 0.34/0.79 ( ( while @ Fun_1 @ Com_1 )
% 0.34/0.79 != ( body @ Pname ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_613_com_Osimps_I18_J,axiom,
% 0.34/0.79 ! [Pname: pname] :
% 0.34/0.79 ( skip
% 0.34/0.79 != ( body @ Pname ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_614_com_Osimps_I19_J,axiom,
% 0.34/0.79 ! [Pname: pname] :
% 0.34/0.79 ( ( body @ Pname )
% 0.34/0.79 != skip ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_615_triple__valid__def2,axiom,
% 0.34/0.79 ! [N_4: nat,P_11: state > state > $o,C_13: com,Q_6: state > state > $o] :
% 0.34/0.79 ( ( hoare_23738522_state @ N_4 @ ( hoare_858012674_state @ P_11 @ C_13 @ Q_6 ) )
% 0.34/0.79 <=> ! [Z_5: state,S_2: state] :
% 0.34/0.79 ( ( P_11 @ Z_5 @ S_2 )
% 0.34/0.79 => ! [S_3: state] :
% 0.34/0.79 ( ( evaln @ C_13 @ S_2 @ N_4 @ S_3 )
% 0.34/0.79 => ( Q_6 @ Z_5 @ S_3 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_616_triple__valid__def2,axiom,
% 0.34/0.79 ! [N_4: nat,P_11: x_a > state > $o,C_13: com,Q_6: x_a > state > $o] :
% 0.34/0.79 ( ( hoare_1421888935alid_a @ N_4 @ ( hoare_657976383iple_a @ P_11 @ C_13 @ Q_6 ) )
% 0.34/0.79 <=> ! [Z_5: x_a,S_2: state] :
% 0.34/0.79 ( ( P_11 @ Z_5 @ S_2 )
% 0.34/0.79 => ! [S_3: state] :
% 0.34/0.79 ( ( evaln @ C_13 @ S_2 @ N_4 @ S_3 )
% 0.34/0.79 => ( Q_6 @ Z_5 @ S_3 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_617_evaln__elim__cases_I6_J,axiom,
% 0.34/0.79 ! [P: pname,S: state,N_1: nat,S1: state] :
% 0.34/0.79 ( ( evaln @ ( body @ P ) @ S @ N_1 @ S1 )
% 0.34/0.79 => ~ ! [N: nat] :
% 0.34/0.79 ( ( N_1
% 0.34/0.79 = ( suc @ N ) )
% 0.34/0.79 => ~ ( evaln @ ( the_com @ ( body_1 @ P ) ) @ S @ N @ S1 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_618_evalc__WHILE__case,axiom,
% 0.34/0.79 ! [B: state > $o,C: com,S: state,T: state] :
% 0.34/0.79 ( ( evalc @ ( while @ B @ C ) @ S @ T )
% 0.34/0.79 => ( ( ( T = S )
% 0.34/0.79 => ( B @ S ) )
% 0.34/0.79 => ~ ( ( B @ S )
% 0.34/0.79 => ! [S1_1: state] :
% 0.34/0.79 ( ( evalc @ C @ S @ S1_1 )
% 0.34/0.79 => ~ ( evalc @ ( while @ B @ C ) @ S1_1 @ T ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_619_evaln__WHILE__case,axiom,
% 0.34/0.79 ! [B: state > $o,C: com,S: state,N_1: nat,T: state] :
% 0.34/0.79 ( ( evaln @ ( while @ B @ C ) @ S @ N_1 @ T )
% 0.34/0.79 => ( ( ( T = S )
% 0.34/0.79 => ( B @ S ) )
% 0.34/0.79 => ~ ( ( B @ S )
% 0.34/0.79 => ! [S1_1: state] :
% 0.34/0.79 ( ( evaln @ C @ S @ N_1 @ S1_1 )
% 0.34/0.79 => ~ ( evaln @ ( while @ B @ C ) @ S1_1 @ N_1 @ T ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_620_evalc__evaln,axiom,
% 0.34/0.79 ! [C: com,S: state,T: state] :
% 0.34/0.79 ( ( evalc @ C @ S @ T )
% 0.34/0.79 => ? [N: nat] : ( evaln @ C @ S @ N @ T ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_621_Comp,axiom,
% 0.34/0.79 ! [D: com,R_1: x_a > state > $o,G_7: hoare_2091234717iple_a > $o,P_10: x_a > state > $o,C_12: com,Q_5: x_a > state > $o] :
% 0.34/0.79 ( ( hoare_1467856363rivs_a @ G_7 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ P_10 @ C_12 @ Q_5 ) @ bot_bo1791335050le_a_o ) )
% 0.34/0.79 => ( ( hoare_1467856363rivs_a @ G_7 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ Q_5 @ D @ R_1 ) @ bot_bo1791335050le_a_o ) )
% 0.34/0.79 => ( hoare_1467856363rivs_a @ G_7 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ P_10 @ ( semi @ C_12 @ D ) @ R_1 ) @ bot_bo1791335050le_a_o ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_622_Comp,axiom,
% 0.34/0.79 ! [D: com,R_1: state > state > $o,G_7: hoare_1708887482_state > $o,P_10: state > state > $o,C_12: com,Q_5: state > state > $o] :
% 0.34/0.79 ( ( hoare_90032982_state @ G_7 @ ( insert528405184_state @ ( hoare_858012674_state @ P_10 @ C_12 @ Q_5 ) @ bot_bo19817387tate_o ) )
% 0.34/0.79 => ( ( hoare_90032982_state @ G_7 @ ( insert528405184_state @ ( hoare_858012674_state @ Q_5 @ D @ R_1 ) @ bot_bo19817387tate_o ) )
% 0.34/0.79 => ( hoare_90032982_state @ G_7 @ ( insert528405184_state @ ( hoare_858012674_state @ P_10 @ ( semi @ C_12 @ D ) @ R_1 ) @ bot_bo19817387tate_o ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_623_the__elem__def,axiom,
% 0.34/0.79 ! [X_21: nat > $o] :
% 0.34/0.79 ( ( the_elem_nat @ X_21 )
% 0.34/0.79 = ( the_nat
% 0.34/0.79 @ ^ [X: nat] :
% 0.34/0.79 ( X_21
% 0.34/0.79 = ( insert_nat @ X @ bot_bot_nat_o ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_624_the__elem__def,axiom,
% 0.34/0.79 ! [X_21: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( the_el1618277441le_a_o @ X_21 )
% 0.34/0.79 = ( the_Ho2077879471le_a_o
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( X_21
% 0.34/0.79 = ( insert102003750le_a_o @ X @ bot_bo1957696069_a_o_o ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_625_the__elem__def,axiom,
% 0.34/0.79 ! [X_21: pname > $o] :
% 0.34/0.79 ( ( the_elem_pname @ X_21 )
% 0.34/0.79 = ( the_pname
% 0.34/0.79 @ ^ [X: pname] :
% 0.34/0.79 ( X_21
% 0.34/0.79 = ( insert_pname @ X @ bot_bot_pname_o ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_626_the__elem__def,axiom,
% 0.34/0.79 ! [X_21: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( the_el13400124iple_a @ X_21 )
% 0.34/0.79 = ( the_Ho1471183438iple_a
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a] :
% 0.34/0.79 ( X_21
% 0.34/0.79 = ( insert1597628439iple_a @ X @ bot_bo1791335050le_a_o ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_627_the__elem__def,axiom,
% 0.34/0.79 ! [X_21: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( the_el864710747_state @ X_21 )
% 0.34/0.79 = ( the_Ho851197897_state
% 0.34/0.79 @ ^ [X: hoare_1708887482_state] :
% 0.34/0.79 ( X_21
% 0.34/0.79 = ( insert528405184_state @ X @ bot_bo19817387tate_o ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_628_finite__pointwise,axiom,
% 0.34/0.79 ! [P_8: hoare_2091234717iple_a > x_a > state > $o,Q_4: hoare_2091234717iple_a > x_a > state > $o,G_6: hoare_2091234717iple_a > $o,P_7: hoare_2091234717iple_a > x_a > state > $o,C0_1: hoare_2091234717iple_a > com,Q_3: hoare_2091234717iple_a > x_a > state > $o,U_1: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( finite232261744iple_a @ U_1 )
% 0.34/0.79 => ( ! [P_9: hoare_2091234717iple_a] :
% 0.34/0.79 ( ( hoare_1467856363rivs_a @ G_6 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ ( P_7 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_3 @ P_9 ) ) @ bot_bo1791335050le_a_o ) )
% 0.34/0.79 => ( hoare_1467856363rivs_a @ G_6 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ ( P_8 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_4 @ P_9 ) ) @ bot_bo1791335050le_a_o ) ) )
% 0.34/0.79 => ( ( hoare_1467856363rivs_a @ G_6
% 0.34/0.79 @ ( image_1661191109iple_a
% 0.34/0.79 @ ^ [P_9: hoare_2091234717iple_a] : ( hoare_657976383iple_a @ ( P_7 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_3 @ P_9 ) )
% 0.34/0.79 @ U_1 ) )
% 0.34/0.79 => ( hoare_1467856363rivs_a @ G_6
% 0.34/0.79 @ ( image_1661191109iple_a
% 0.34/0.79 @ ^ [P_9: hoare_2091234717iple_a] : ( hoare_657976383iple_a @ ( P_8 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_4 @ P_9 ) )
% 0.34/0.79 @ U_1 ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_629_finite__pointwise,axiom,
% 0.34/0.79 ! [P_8: ( hoare_2091234717iple_a > $o ) > x_a > state > $o,Q_4: ( hoare_2091234717iple_a > $o ) > x_a > state > $o,G_6: hoare_2091234717iple_a > $o,P_7: ( hoare_2091234717iple_a > $o ) > x_a > state > $o,C0_1: ( hoare_2091234717iple_a > $o ) > com,Q_3: ( hoare_2091234717iple_a > $o ) > x_a > state > $o,U_1: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( finite1829014797le_a_o @ U_1 )
% 0.34/0.79 => ( ! [P_9: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( hoare_1467856363rivs_a @ G_6 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ ( P_7 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_3 @ P_9 ) ) @ bot_bo1791335050le_a_o ) )
% 0.34/0.79 => ( hoare_1467856363rivs_a @ G_6 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ ( P_8 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_4 @ P_9 ) ) @ bot_bo1791335050le_a_o ) ) )
% 0.34/0.79 => ( ( hoare_1467856363rivs_a @ G_6
% 0.34/0.79 @ ( image_136408202iple_a
% 0.34/0.79 @ ^ [P_9: hoare_2091234717iple_a > $o] : ( hoare_657976383iple_a @ ( P_7 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_3 @ P_9 ) )
% 0.34/0.79 @ U_1 ) )
% 0.34/0.79 => ( hoare_1467856363rivs_a @ G_6
% 0.34/0.79 @ ( image_136408202iple_a
% 0.34/0.79 @ ^ [P_9: hoare_2091234717iple_a > $o] : ( hoare_657976383iple_a @ ( P_8 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_4 @ P_9 ) )
% 0.34/0.79 @ U_1 ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_630_finite__pointwise,axiom,
% 0.34/0.79 ! [P_8: pname > state > state > $o,Q_4: pname > state > state > $o,G_6: hoare_1708887482_state > $o,P_7: pname > state > state > $o,C0_1: pname > com,Q_3: pname > state > state > $o,U_1: pname > $o] :
% 0.34/0.79 ( ( finite_finite_pname @ U_1 )
% 0.34/0.79 => ( ! [P_9: pname] :
% 0.34/0.79 ( ( hoare_90032982_state @ G_6 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_7 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_3 @ P_9 ) ) @ bot_bo19817387tate_o ) )
% 0.34/0.79 => ( hoare_90032982_state @ G_6 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_8 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_4 @ P_9 ) ) @ bot_bo19817387tate_o ) ) )
% 0.34/0.79 => ( ( hoare_90032982_state @ G_6
% 0.34/0.79 @ ( image_1116629049_state
% 0.34/0.79 @ ^ [P_9: pname] : ( hoare_858012674_state @ ( P_7 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_3 @ P_9 ) )
% 0.34/0.79 @ U_1 ) )
% 0.34/0.79 => ( hoare_90032982_state @ G_6
% 0.34/0.79 @ ( image_1116629049_state
% 0.34/0.79 @ ^ [P_9: pname] : ( hoare_858012674_state @ ( P_8 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_4 @ P_9 ) )
% 0.34/0.79 @ U_1 ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_631_finite__pointwise,axiom,
% 0.34/0.79 ! [P_8: hoare_2091234717iple_a > state > state > $o,Q_4: hoare_2091234717iple_a > state > state > $o,G_6: hoare_1708887482_state > $o,P_7: hoare_2091234717iple_a > state > state > $o,C0_1: hoare_2091234717iple_a > com,Q_3: hoare_2091234717iple_a > state > state > $o,U_1: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( finite232261744iple_a @ U_1 )
% 0.34/0.79 => ( ! [P_9: hoare_2091234717iple_a] :
% 0.34/0.79 ( ( hoare_90032982_state @ G_6 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_7 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_3 @ P_9 ) ) @ bot_bo19817387tate_o ) )
% 0.34/0.79 => ( hoare_90032982_state @ G_6 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_8 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_4 @ P_9 ) ) @ bot_bo19817387tate_o ) ) )
% 0.34/0.79 => ( ( hoare_90032982_state @ G_6
% 0.34/0.79 @ ( image_1884482962_state
% 0.34/0.79 @ ^ [P_9: hoare_2091234717iple_a] : ( hoare_858012674_state @ ( P_7 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_3 @ P_9 ) )
% 0.34/0.79 @ U_1 ) )
% 0.34/0.79 => ( hoare_90032982_state @ G_6
% 0.34/0.79 @ ( image_1884482962_state
% 0.34/0.79 @ ^ [P_9: hoare_2091234717iple_a] : ( hoare_858012674_state @ ( P_8 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_4 @ P_9 ) )
% 0.34/0.79 @ U_1 ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_632_finite__pointwise,axiom,
% 0.34/0.79 ! [P_8: ( hoare_2091234717iple_a > $o ) > state > state > $o,Q_4: ( hoare_2091234717iple_a > $o ) > state > state > $o,G_6: hoare_1708887482_state > $o,P_7: ( hoare_2091234717iple_a > $o ) > state > state > $o,C0_1: ( hoare_2091234717iple_a > $o ) > com,Q_3: ( hoare_2091234717iple_a > $o ) > state > state > $o,U_1: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( finite1829014797le_a_o @ U_1 )
% 0.34/0.79 => ( ! [P_9: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( hoare_90032982_state @ G_6 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_7 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_3 @ P_9 ) ) @ bot_bo19817387tate_o ) )
% 0.34/0.79 => ( hoare_90032982_state @ G_6 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_8 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_4 @ P_9 ) ) @ bot_bo19817387tate_o ) ) )
% 0.34/0.79 => ( ( hoare_90032982_state @ G_6
% 0.34/0.79 @ ( image_1501246093_state
% 0.34/0.79 @ ^ [P_9: hoare_2091234717iple_a > $o] : ( hoare_858012674_state @ ( P_7 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_3 @ P_9 ) )
% 0.34/0.79 @ U_1 ) )
% 0.34/0.79 => ( hoare_90032982_state @ G_6
% 0.34/0.79 @ ( image_1501246093_state
% 0.34/0.79 @ ^ [P_9: hoare_2091234717iple_a > $o] : ( hoare_858012674_state @ ( P_8 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_4 @ P_9 ) )
% 0.34/0.79 @ U_1 ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_633_finite__pointwise,axiom,
% 0.34/0.79 ! [P_8: nat > x_a > state > $o,Q_4: nat > x_a > state > $o,G_6: hoare_2091234717iple_a > $o,P_7: nat > x_a > state > $o,C0_1: nat > com,Q_3: nat > x_a > state > $o,U_1: nat > $o] :
% 0.34/0.79 ( ( finite_finite_nat @ U_1 )
% 0.34/0.79 => ( ! [P_9: nat] :
% 0.34/0.79 ( ( hoare_1467856363rivs_a @ G_6 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ ( P_7 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_3 @ P_9 ) ) @ bot_bo1791335050le_a_o ) )
% 0.34/0.79 => ( hoare_1467856363rivs_a @ G_6 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ ( P_8 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_4 @ P_9 ) ) @ bot_bo1791335050le_a_o ) ) )
% 0.34/0.79 => ( ( hoare_1467856363rivs_a @ G_6
% 0.34/0.79 @ ( image_359186840iple_a
% 0.34/0.79 @ ^ [P_9: nat] : ( hoare_657976383iple_a @ ( P_7 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_3 @ P_9 ) )
% 0.34/0.79 @ U_1 ) )
% 0.34/0.79 => ( hoare_1467856363rivs_a @ G_6
% 0.34/0.79 @ ( image_359186840iple_a
% 0.34/0.79 @ ^ [P_9: nat] : ( hoare_657976383iple_a @ ( P_8 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_4 @ P_9 ) )
% 0.34/0.79 @ U_1 ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_634_finite__pointwise,axiom,
% 0.34/0.79 ! [P_8: nat > state > state > $o,Q_4: nat > state > state > $o,G_6: hoare_1708887482_state > $o,P_7: nat > state > state > $o,C0_1: nat > com,Q_3: nat > state > state > $o,U_1: nat > $o] :
% 0.34/0.79 ( ( finite_finite_nat @ U_1 )
% 0.34/0.79 => ( ! [P_9: nat] :
% 0.34/0.79 ( ( hoare_90032982_state @ G_6 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_7 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_3 @ P_9 ) ) @ bot_bo19817387tate_o ) )
% 0.34/0.79 => ( hoare_90032982_state @ G_6 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_8 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_4 @ P_9 ) ) @ bot_bo19817387tate_o ) ) )
% 0.34/0.79 => ( ( hoare_90032982_state @ G_6
% 0.34/0.79 @ ( image_514827263_state
% 0.34/0.79 @ ^ [P_9: nat] : ( hoare_858012674_state @ ( P_7 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_3 @ P_9 ) )
% 0.34/0.79 @ U_1 ) )
% 0.34/0.79 => ( hoare_90032982_state @ G_6
% 0.34/0.79 @ ( image_514827263_state
% 0.34/0.79 @ ^ [P_9: nat] : ( hoare_858012674_state @ ( P_8 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_4 @ P_9 ) )
% 0.34/0.79 @ U_1 ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_635_finite__pointwise,axiom,
% 0.34/0.79 ! [P_8: pname > x_a > state > $o,Q_4: pname > x_a > state > $o,G_6: hoare_2091234717iple_a > $o,P_7: pname > x_a > state > $o,C0_1: pname > com,Q_3: pname > x_a > state > $o,U_1: pname > $o] :
% 0.34/0.79 ( ( finite_finite_pname @ U_1 )
% 0.34/0.79 => ( ! [P_9: pname] :
% 0.34/0.79 ( ( hoare_1467856363rivs_a @ G_6 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ ( P_7 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_3 @ P_9 ) ) @ bot_bo1791335050le_a_o ) )
% 0.34/0.79 => ( hoare_1467856363rivs_a @ G_6 @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ ( P_8 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_4 @ P_9 ) ) @ bot_bo1791335050le_a_o ) ) )
% 0.34/0.79 => ( ( hoare_1467856363rivs_a @ G_6
% 0.34/0.79 @ ( image_231808478iple_a
% 0.34/0.79 @ ^ [P_9: pname] : ( hoare_657976383iple_a @ ( P_7 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_3 @ P_9 ) )
% 0.34/0.79 @ U_1 ) )
% 0.34/0.79 => ( hoare_1467856363rivs_a @ G_6
% 0.34/0.79 @ ( image_231808478iple_a
% 0.34/0.79 @ ^ [P_9: pname] : ( hoare_657976383iple_a @ ( P_8 @ P_9 ) @ ( C0_1 @ P_9 ) @ ( Q_4 @ P_9 ) )
% 0.34/0.79 @ U_1 ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_636_evaln__max2,axiom,
% 0.34/0.79 ! [C2: com,S2: state,N2: nat,T2: state,C1: com,S1: state,N1: nat,T1: state] :
% 0.34/0.79 ( ( evaln @ C1 @ S1 @ N1 @ T1 )
% 0.34/0.79 => ( ( evaln @ C2 @ S2 @ N2 @ T2 )
% 0.34/0.79 => ? [N: nat] :
% 0.34/0.79 ( ( evaln @ C1 @ S1 @ N @ T1 )
% 0.34/0.79 & ( evaln @ C2 @ S2 @ N @ T2 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_637_mk__disjoint__insert,axiom,
% 0.34/0.79 ! [A_53: nat,A_52: nat > $o] :
% 0.34/0.79 ( ( member_nat @ A_53 @ A_52 )
% 0.34/0.79 => ? [B_26: nat > $o] :
% 0.34/0.79 ( ( A_52
% 0.34/0.79 = ( insert_nat @ A_53 @ B_26 ) )
% 0.34/0.79 & ~ ( member_nat @ A_53 @ B_26 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_638_mk__disjoint__insert,axiom,
% 0.34/0.79 ! [A_53: hoare_2091234717iple_a > $o,A_52: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( member99268621le_a_o @ A_53 @ A_52 )
% 0.34/0.79 => ? [B_26: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( A_52
% 0.34/0.79 = ( insert102003750le_a_o @ A_53 @ B_26 ) )
% 0.34/0.79 & ~ ( member99268621le_a_o @ A_53 @ B_26 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_639_mk__disjoint__insert,axiom,
% 0.34/0.79 ! [A_53: hoare_2091234717iple_a,A_52: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( member290856304iple_a @ A_53 @ A_52 )
% 0.34/0.79 => ? [B_26: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( A_52
% 0.34/0.79 = ( insert1597628439iple_a @ A_53 @ B_26 ) )
% 0.34/0.79 & ~ ( member290856304iple_a @ A_53 @ B_26 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_640_mk__disjoint__insert,axiom,
% 0.34/0.79 ! [A_53: hoare_1708887482_state,A_52: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( member451959335_state @ A_53 @ A_52 )
% 0.34/0.79 => ? [B_26: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( A_52
% 0.34/0.79 = ( insert528405184_state @ A_53 @ B_26 ) )
% 0.34/0.79 & ~ ( member451959335_state @ A_53 @ B_26 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_641_mk__disjoint__insert,axiom,
% 0.34/0.79 ! [A_53: pname,A_52: pname > $o] :
% 0.34/0.79 ( ( member_pname @ A_53 @ A_52 )
% 0.34/0.79 => ? [B_26: pname > $o] :
% 0.34/0.79 ( ( A_52
% 0.34/0.79 = ( insert_pname @ A_53 @ B_26 ) )
% 0.34/0.79 & ~ ( member_pname @ A_53 @ B_26 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_642_evaln_OSemi,axiom,
% 0.34/0.79 ! [C1: com,S2: state,C0: com,S0: state,N_1: nat,S1: state] :
% 0.34/0.79 ( ( evaln @ C0 @ S0 @ N_1 @ S1 )
% 0.34/0.79 => ( ( evaln @ C1 @ S1 @ N_1 @ S2 )
% 0.34/0.79 => ( evaln @ ( semi @ C0 @ C1 ) @ S0 @ N_1 @ S2 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_643_evalc_OSemi,axiom,
% 0.34/0.79 ! [C1: com,S2: state,C0: com,S0: state,S1: state] :
% 0.34/0.79 ( ( evalc @ C0 @ S0 @ S1 )
% 0.34/0.79 => ( ( evalc @ C1 @ S1 @ S2 )
% 0.34/0.79 => ( evalc @ ( semi @ C0 @ C1 ) @ S0 @ S2 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_644_com_Osimps_I3_J,axiom,
% 0.34/0.79 ! [Com1_1: com,Com2_1: com,Com1: com,Com2: com] :
% 0.34/0.79 ( ( ( semi @ Com1_1 @ Com2_1 )
% 0.34/0.79 = ( semi @ Com1 @ Com2 ) )
% 0.34/0.79 <=> ( ( Com1_1 = Com1 )
% 0.34/0.79 & ( Com2_1 = Com2 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_645_com_Osimps_I48_J,axiom,
% 0.34/0.79 ! [Com1_1: com,Com2_1: com,Pname: pname] :
% 0.34/0.79 ( ( semi @ Com1_1 @ Com2_1 )
% 0.34/0.79 != ( body @ Pname ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_646_com_Osimps_I49_J,axiom,
% 0.34/0.79 ! [Pname: pname,Com1_1: com,Com2_1: com] :
% 0.34/0.79 ( ( body @ Pname )
% 0.34/0.79 != ( semi @ Com1_1 @ Com2_1 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_647_com_Osimps_I47_J,axiom,
% 0.34/0.79 ! [Fun: state > $o,Com: com,Com1_1: com,Com2_1: com] :
% 0.34/0.79 ( ( while @ Fun @ Com )
% 0.34/0.79 != ( semi @ Com1_1 @ Com2_1 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_648_com_Osimps_I46_J,axiom,
% 0.34/0.79 ! [Com1_1: com,Com2_1: com,Fun: state > $o,Com: com] :
% 0.34/0.79 ( ( semi @ Com1_1 @ Com2_1 )
% 0.34/0.79 != ( while @ Fun @ Com ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_649_com_Osimps_I13_J,axiom,
% 0.34/0.79 ! [Com1: com,Com2: com] :
% 0.34/0.79 ( ( semi @ Com1 @ Com2 )
% 0.34/0.79 != skip ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_650_com_Osimps_I12_J,axiom,
% 0.34/0.79 ! [Com1: com,Com2: com] :
% 0.34/0.79 ( skip
% 0.34/0.79 != ( semi @ Com1 @ Com2 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_651_evalc__elim__cases_I4_J,axiom,
% 0.34/0.79 ! [C1: com,C2: com,S: state,T: state] :
% 0.34/0.79 ( ( evalc @ ( semi @ C1 @ C2 ) @ S @ T )
% 0.34/0.79 => ~ ! [S1_1: state] :
% 0.34/0.79 ( ( evalc @ C1 @ S @ S1_1 )
% 0.34/0.79 => ~ ( evalc @ C2 @ S1_1 @ T ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_652_evaln__elim__cases_I4_J,axiom,
% 0.34/0.79 ! [C1: com,C2: com,S: state,N_1: nat,T: state] :
% 0.34/0.79 ( ( evaln @ ( semi @ C1 @ C2 ) @ S @ N_1 @ T )
% 0.34/0.79 => ~ ! [S1_1: state] :
% 0.34/0.79 ( ( evaln @ C1 @ S @ N_1 @ S1_1 )
% 0.34/0.79 => ~ ( evaln @ C2 @ S1_1 @ N_1 @ T ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_653_finite__imageI,axiom,
% 0.34/0.79 ! [H_1: pname > hoare_1708887482_state,F_35: pname > $o] :
% 0.34/0.79 ( ( finite_finite_pname @ F_35 )
% 0.34/0.79 => ( finite1625599783_state @ ( image_1116629049_state @ H_1 @ F_35 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_654_finite__imageI,axiom,
% 0.34/0.79 ! [H_1: nat > hoare_2091234717iple_a,F_35: nat > $o] :
% 0.34/0.79 ( ( finite_finite_nat @ F_35 )
% 0.34/0.79 => ( finite232261744iple_a @ ( image_359186840iple_a @ H_1 @ F_35 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_655_finite__imageI,axiom,
% 0.34/0.79 ! [H_1: nat > hoare_2091234717iple_a > $o,F_35: nat > $o] :
% 0.34/0.79 ( ( finite_finite_nat @ F_35 )
% 0.34/0.79 => ( finite1829014797le_a_o @ ( image_1995609573le_a_o @ H_1 @ F_35 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_656_finite__imageI,axiom,
% 0.34/0.79 ! [H_1: nat > pname,F_35: nat > $o] :
% 0.34/0.79 ( ( finite_finite_nat @ F_35 )
% 0.34/0.79 => ( finite_finite_pname @ ( image_nat_pname @ H_1 @ F_35 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_657_finite__imageI,axiom,
% 0.34/0.79 ! [H_1: nat > nat,F_35: nat > $o] :
% 0.34/0.79 ( ( finite_finite_nat @ F_35 )
% 0.34/0.79 => ( finite_finite_nat @ ( image_nat_nat @ H_1 @ F_35 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_658_finite__imageI,axiom,
% 0.34/0.79 ! [H_1: hoare_2091234717iple_a > nat,F_35: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( finite232261744iple_a @ F_35 )
% 0.34/0.79 => ( finite_finite_nat @ ( image_1773322034_a_nat @ H_1 @ F_35 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_659_finite__imageI,axiom,
% 0.34/0.79 ! [H_1: ( hoare_2091234717iple_a > $o ) > nat,F_35: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( finite1829014797le_a_o @ F_35 )
% 0.34/0.79 => ( finite_finite_nat @ ( image_75520503_o_nat @ H_1 @ F_35 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_660_finite__imageI,axiom,
% 0.34/0.79 ! [H_1: pname > nat,F_35: pname > $o] :
% 0.34/0.79 ( ( finite_finite_pname @ F_35 )
% 0.34/0.79 => ( finite_finite_nat @ ( image_pname_nat @ H_1 @ F_35 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_661_finite__imageI,axiom,
% 0.34/0.79 ! [H_1: pname > hoare_2091234717iple_a,F_35: pname > $o] :
% 0.34/0.79 ( ( finite_finite_pname @ F_35 )
% 0.34/0.79 => ( finite232261744iple_a @ ( image_231808478iple_a @ H_1 @ F_35 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_662_finite_OinsertI,axiom,
% 0.34/0.79 ! [A_51: hoare_2091234717iple_a > $o,A_50: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( finite1829014797le_a_o @ A_50 )
% 0.34/0.79 => ( finite1829014797le_a_o @ ( insert102003750le_a_o @ A_51 @ A_50 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_663_finite_OinsertI,axiom,
% 0.34/0.79 ! [A_51: pname,A_50: pname > $o] :
% 0.34/0.79 ( ( finite_finite_pname @ A_50 )
% 0.34/0.79 => ( finite_finite_pname @ ( insert_pname @ A_51 @ A_50 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_664_finite_OinsertI,axiom,
% 0.34/0.79 ! [A_51: hoare_2091234717iple_a,A_50: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( finite232261744iple_a @ A_50 )
% 0.34/0.79 => ( finite232261744iple_a @ ( insert1597628439iple_a @ A_51 @ A_50 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_665_finite_OinsertI,axiom,
% 0.34/0.79 ! [A_51: hoare_1708887482_state,A_50: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( finite1625599783_state @ A_50 )
% 0.34/0.79 => ( finite1625599783_state @ ( insert528405184_state @ A_51 @ A_50 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_666_finite_OinsertI,axiom,
% 0.34/0.79 ! [A_51: nat,A_50: nat > $o] :
% 0.34/0.79 ( ( finite_finite_nat @ A_50 )
% 0.34/0.79 => ( finite_finite_nat @ ( insert_nat @ A_51 @ A_50 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_667_finite_OemptyI,axiom,
% 0.34/0.79 finite232261744iple_a @ bot_bo1791335050le_a_o ).
% 0.34/0.79
% 0.34/0.79 thf(fact_668_finite_OemptyI,axiom,
% 0.34/0.79 finite1829014797le_a_o @ bot_bo1957696069_a_o_o ).
% 0.34/0.79
% 0.34/0.79 thf(fact_669_finite_OemptyI,axiom,
% 0.34/0.79 finite_finite_pname @ bot_bot_pname_o ).
% 0.34/0.79
% 0.34/0.79 thf(fact_670_finite_OemptyI,axiom,
% 0.34/0.79 finite1625599783_state @ bot_bo19817387tate_o ).
% 0.34/0.79
% 0.34/0.79 thf(fact_671_finite_OemptyI,axiom,
% 0.34/0.79 finite_finite_nat @ bot_bot_nat_o ).
% 0.34/0.79
% 0.34/0.79 thf(fact_672_finite__Collect__conjI,axiom,
% 0.34/0.79 ! [Q_2: pname > $o,P_6: pname > $o] :
% 0.34/0.79 ( ( ( finite_finite_pname @ ( collect_pname @ P_6 ) )
% 0.34/0.79 | ( finite_finite_pname @ ( collect_pname @ Q_2 ) ) )
% 0.34/0.79 => ( finite_finite_pname
% 0.34/0.79 @ ( collect_pname
% 0.34/0.79 @ ^ [X: pname] : ( (&) @ ( P_6 @ X ) @ ( Q_2 @ X ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_673_finite__Collect__conjI,axiom,
% 0.34/0.79 ! [Q_2: hoare_2091234717iple_a > $o,P_6: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( ( finite232261744iple_a @ ( collec992574898iple_a @ P_6 ) )
% 0.34/0.79 | ( finite232261744iple_a @ ( collec992574898iple_a @ Q_2 ) ) )
% 0.34/0.79 => ( finite232261744iple_a
% 0.34/0.79 @ ( collec992574898iple_a
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a] : ( (&) @ ( P_6 @ X ) @ ( Q_2 @ X ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_674_finite__Collect__conjI,axiom,
% 0.34/0.79 ! [Q_2: ( hoare_2091234717iple_a > $o ) > $o,P_6: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( ( finite1829014797le_a_o @ ( collec1008234059le_a_o @ P_6 ) )
% 0.34/0.79 | ( finite1829014797le_a_o @ ( collec1008234059le_a_o @ Q_2 ) ) )
% 0.34/0.79 => ( finite1829014797le_a_o
% 0.34/0.79 @ ( collec1008234059le_a_o
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a > $o] : ( (&) @ ( P_6 @ X ) @ ( Q_2 @ X ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_675_finite__Collect__conjI,axiom,
% 0.34/0.79 ! [Q_2: nat > $o,P_6: nat > $o] :
% 0.34/0.79 ( ( ( finite_finite_nat @ ( collect_nat @ P_6 ) )
% 0.34/0.79 | ( finite_finite_nat @ ( collect_nat @ Q_2 ) ) )
% 0.34/0.79 => ( finite_finite_nat
% 0.34/0.79 @ ( collect_nat
% 0.34/0.79 @ ^ [X: nat] : ( (&) @ ( P_6 @ X ) @ ( Q_2 @ X ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_676_finite__Un,axiom,
% 0.34/0.79 ! [F_34: ( hoare_2091234717iple_a > $o ) > $o,G_5: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( finite1829014797le_a_o @ ( semila2050116131_a_o_o @ F_34 @ G_5 ) )
% 0.34/0.79 <=> ( ( finite1829014797le_a_o @ F_34 )
% 0.34/0.79 & ( finite1829014797le_a_o @ G_5 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_677_finite__Un,axiom,
% 0.34/0.79 ! [F_34: pname > $o,G_5: pname > $o] :
% 0.34/0.79 ( ( finite_finite_pname @ ( semila1780557381name_o @ F_34 @ G_5 ) )
% 0.34/0.79 <=> ( ( finite_finite_pname @ F_34 )
% 0.34/0.79 & ( finite_finite_pname @ G_5 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_678_finite__Un,axiom,
% 0.34/0.79 ! [F_34: hoare_1708887482_state > $o,G_5: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( finite1625599783_state @ ( semila1122118281tate_o @ F_34 @ G_5 ) )
% 0.34/0.79 <=> ( ( finite1625599783_state @ F_34 )
% 0.34/0.79 & ( finite1625599783_state @ G_5 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_679_finite__Un,axiom,
% 0.34/0.79 ! [F_34: hoare_2091234717iple_a > $o,G_5: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( finite232261744iple_a @ ( semila1052848428le_a_o @ F_34 @ G_5 ) )
% 0.34/0.79 <=> ( ( finite232261744iple_a @ F_34 )
% 0.34/0.79 & ( finite232261744iple_a @ G_5 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_680_finite__Un,axiom,
% 0.34/0.79 ! [F_34: nat > $o,G_5: nat > $o] :
% 0.34/0.79 ( ( finite_finite_nat @ ( semila848761471_nat_o @ F_34 @ G_5 ) )
% 0.34/0.79 <=> ( ( finite_finite_nat @ F_34 )
% 0.34/0.79 & ( finite_finite_nat @ G_5 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_681_finite__UnI,axiom,
% 0.34/0.79 ! [G_4: ( hoare_2091234717iple_a > $o ) > $o,F_33: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( finite1829014797le_a_o @ F_33 )
% 0.34/0.79 => ( ( finite1829014797le_a_o @ G_4 )
% 0.34/0.79 => ( finite1829014797le_a_o @ ( semila2050116131_a_o_o @ F_33 @ G_4 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_682_finite__UnI,axiom,
% 0.34/0.79 ! [G_4: pname > $o,F_33: pname > $o] :
% 0.34/0.79 ( ( finite_finite_pname @ F_33 )
% 0.34/0.79 => ( ( finite_finite_pname @ G_4 )
% 0.34/0.79 => ( finite_finite_pname @ ( semila1780557381name_o @ F_33 @ G_4 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_683_finite__UnI,axiom,
% 0.34/0.79 ! [G_4: hoare_1708887482_state > $o,F_33: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( finite1625599783_state @ F_33 )
% 0.34/0.79 => ( ( finite1625599783_state @ G_4 )
% 0.34/0.79 => ( finite1625599783_state @ ( semila1122118281tate_o @ F_33 @ G_4 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_684_finite__UnI,axiom,
% 0.34/0.79 ! [G_4: hoare_2091234717iple_a > $o,F_33: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( finite232261744iple_a @ F_33 )
% 0.34/0.79 => ( ( finite232261744iple_a @ G_4 )
% 0.34/0.79 => ( finite232261744iple_a @ ( semila1052848428le_a_o @ F_33 @ G_4 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_685_finite__UnI,axiom,
% 0.34/0.79 ! [G_4: nat > $o,F_33: nat > $o] :
% 0.34/0.79 ( ( finite_finite_nat @ F_33 )
% 0.34/0.79 => ( ( finite_finite_nat @ G_4 )
% 0.34/0.79 => ( finite_finite_nat @ ( semila848761471_nat_o @ F_33 @ G_4 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_686_finite__Collect__disjI,axiom,
% 0.34/0.79 ! [P_5: pname > $o,Q_1: pname > $o] :
% 0.34/0.79 ( ( finite_finite_pname
% 0.34/0.79 @ ( collect_pname
% 0.34/0.79 @ ^ [X: pname] : ( (|) @ ( P_5 @ X ) @ ( Q_1 @ X ) ) ) )
% 0.34/0.79 <=> ( ( finite_finite_pname @ ( collect_pname @ P_5 ) )
% 0.34/0.79 & ( finite_finite_pname @ ( collect_pname @ Q_1 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_687_finite__Collect__disjI,axiom,
% 0.34/0.79 ! [P_5: hoare_2091234717iple_a > $o,Q_1: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( finite232261744iple_a
% 0.34/0.79 @ ( collec992574898iple_a
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a] : ( (|) @ ( P_5 @ X ) @ ( Q_1 @ X ) ) ) )
% 0.34/0.79 <=> ( ( finite232261744iple_a @ ( collec992574898iple_a @ P_5 ) )
% 0.34/0.79 & ( finite232261744iple_a @ ( collec992574898iple_a @ Q_1 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_688_finite__Collect__disjI,axiom,
% 0.34/0.79 ! [P_5: ( hoare_2091234717iple_a > $o ) > $o,Q_1: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( finite1829014797le_a_o
% 0.34/0.79 @ ( collec1008234059le_a_o
% 0.34/0.79 @ ^ [X: hoare_2091234717iple_a > $o] : ( (|) @ ( P_5 @ X ) @ ( Q_1 @ X ) ) ) )
% 0.34/0.79 <=> ( ( finite1829014797le_a_o @ ( collec1008234059le_a_o @ P_5 ) )
% 0.34/0.79 & ( finite1829014797le_a_o @ ( collec1008234059le_a_o @ Q_1 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_689_finite__Collect__disjI,axiom,
% 0.34/0.79 ! [P_5: nat > $o,Q_1: nat > $o] :
% 0.34/0.79 ( ( finite_finite_nat
% 0.34/0.79 @ ( collect_nat
% 0.34/0.79 @ ^ [X: nat] : ( (|) @ ( P_5 @ X ) @ ( Q_1 @ X ) ) ) )
% 0.34/0.79 <=> ( ( finite_finite_nat @ ( collect_nat @ P_5 ) )
% 0.34/0.79 & ( finite_finite_nat @ ( collect_nat @ Q_1 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_690_finite__insert,axiom,
% 0.34/0.79 ! [A_49: hoare_2091234717iple_a > $o,A_48: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( finite1829014797le_a_o @ ( insert102003750le_a_o @ A_49 @ A_48 ) )
% 0.34/0.79 <=> ( finite1829014797le_a_o @ A_48 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_691_finite__insert,axiom,
% 0.34/0.79 ! [A_49: pname,A_48: pname > $o] :
% 0.34/0.79 ( ( finite_finite_pname @ ( insert_pname @ A_49 @ A_48 ) )
% 0.34/0.79 <=> ( finite_finite_pname @ A_48 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_692_finite__insert,axiom,
% 0.34/0.79 ! [A_49: hoare_2091234717iple_a,A_48: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( finite232261744iple_a @ ( insert1597628439iple_a @ A_49 @ A_48 ) )
% 0.34/0.79 <=> ( finite232261744iple_a @ A_48 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_693_finite__insert,axiom,
% 0.34/0.79 ! [A_49: hoare_1708887482_state,A_48: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( finite1625599783_state @ ( insert528405184_state @ A_49 @ A_48 ) )
% 0.34/0.79 <=> ( finite1625599783_state @ A_48 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_694_finite__insert,axiom,
% 0.34/0.79 ! [A_49: nat,A_48: nat > $o] :
% 0.34/0.79 ( ( finite_finite_nat @ ( insert_nat @ A_49 @ A_48 ) )
% 0.34/0.79 <=> ( finite_finite_nat @ A_48 ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_695_finite__induct,axiom,
% 0.34/0.79 ! [P_4: ( ( hoare_2091234717iple_a > $o ) > $o ) > $o,F_32: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( finite1829014797le_a_o @ F_32 )
% 0.34/0.79 => ( ( P_4 @ bot_bo1957696069_a_o_o )
% 0.34/0.79 => ( ! [X: hoare_2091234717iple_a > $o,F_25: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( finite1829014797le_a_o @ F_25 )
% 0.34/0.79 => ( ~ ( member99268621le_a_o @ X @ F_25 )
% 0.34/0.79 => ( ( P_4 @ F_25 )
% 0.34/0.79 => ( P_4 @ ( insert102003750le_a_o @ X @ F_25 ) ) ) ) )
% 0.34/0.79 => ( P_4 @ F_32 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_696_finite__induct,axiom,
% 0.34/0.79 ! [P_4: ( hoare_2091234717iple_a > $o ) > $o,F_32: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( finite232261744iple_a @ F_32 )
% 0.34/0.79 => ( ( P_4 @ bot_bo1791335050le_a_o )
% 0.34/0.79 => ( ! [X: hoare_2091234717iple_a,F_25: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( finite232261744iple_a @ F_25 )
% 0.34/0.79 => ( ~ ( member290856304iple_a @ X @ F_25 )
% 0.34/0.79 => ( ( P_4 @ F_25 )
% 0.34/0.79 => ( P_4 @ ( insert1597628439iple_a @ X @ F_25 ) ) ) ) )
% 0.34/0.79 => ( P_4 @ F_32 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_697_finite__induct,axiom,
% 0.34/0.79 ! [P_4: ( hoare_1708887482_state > $o ) > $o,F_32: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( finite1625599783_state @ F_32 )
% 0.34/0.79 => ( ( P_4 @ bot_bo19817387tate_o )
% 0.34/0.79 => ( ! [X: hoare_1708887482_state,F_25: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( finite1625599783_state @ F_25 )
% 0.34/0.79 => ( ~ ( member451959335_state @ X @ F_25 )
% 0.34/0.79 => ( ( P_4 @ F_25 )
% 0.34/0.79 => ( P_4 @ ( insert528405184_state @ X @ F_25 ) ) ) ) )
% 0.34/0.79 => ( P_4 @ F_32 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_698_finite__induct,axiom,
% 0.34/0.79 ! [P_4: ( nat > $o ) > $o,F_32: nat > $o] :
% 0.34/0.79 ( ( finite_finite_nat @ F_32 )
% 0.34/0.79 => ( ( P_4 @ bot_bot_nat_o )
% 0.34/0.79 => ( ! [X: nat,F_25: nat > $o] :
% 0.34/0.79 ( ( finite_finite_nat @ F_25 )
% 0.34/0.79 => ( ~ ( member_nat @ X @ F_25 )
% 0.34/0.79 => ( ( P_4 @ F_25 )
% 0.34/0.79 => ( P_4 @ ( insert_nat @ X @ F_25 ) ) ) ) )
% 0.34/0.79 => ( P_4 @ F_32 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_699_finite__induct,axiom,
% 0.34/0.79 ! [P_4: ( pname > $o ) > $o,F_32: pname > $o] :
% 0.34/0.79 ( ( finite_finite_pname @ F_32 )
% 0.34/0.79 => ( ( P_4 @ bot_bot_pname_o )
% 0.34/0.79 => ( ! [X: pname,F_25: pname > $o] :
% 0.34/0.79 ( ( finite_finite_pname @ F_25 )
% 0.34/0.79 => ( ~ ( member_pname @ X @ F_25 )
% 0.34/0.79 => ( ( P_4 @ F_25 )
% 0.34/0.79 => ( P_4 @ ( insert_pname @ X @ F_25 ) ) ) ) )
% 0.34/0.79 => ( P_4 @ F_32 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_700_finite_Osimps,axiom,
% 0.34/0.79 ! [A_46: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( finite1829014797le_a_o @ A_46 )
% 0.34/0.79 <=> ( ( A_46 = bot_bo1957696069_a_o_o )
% 0.34/0.79 | ? [A_47: ( hoare_2091234717iple_a > $o ) > $o,A_45: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( A_46
% 0.34/0.79 = ( insert102003750le_a_o @ A_45 @ A_47 ) )
% 0.34/0.79 & ( finite1829014797le_a_o @ A_47 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_701_finite_Osimps,axiom,
% 0.34/0.79 ! [A_46: pname > $o] :
% 0.34/0.79 ( ( finite_finite_pname @ A_46 )
% 0.34/0.79 <=> ( ( A_46 = bot_bot_pname_o )
% 0.34/0.79 | ? [A_47: pname > $o,A_45: pname] :
% 0.34/0.79 ( ( A_46
% 0.34/0.79 = ( insert_pname @ A_45 @ A_47 ) )
% 0.34/0.79 & ( finite_finite_pname @ A_47 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_702_finite_Osimps,axiom,
% 0.34/0.79 ! [A_46: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( finite232261744iple_a @ A_46 )
% 0.34/0.79 <=> ( ( A_46 = bot_bo1791335050le_a_o )
% 0.34/0.79 | ? [A_47: hoare_2091234717iple_a > $o,A_45: hoare_2091234717iple_a] :
% 0.34/0.79 ( ( A_46
% 0.34/0.79 = ( insert1597628439iple_a @ A_45 @ A_47 ) )
% 0.34/0.79 & ( finite232261744iple_a @ A_47 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_703_finite_Osimps,axiom,
% 0.34/0.79 ! [A_46: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( finite1625599783_state @ A_46 )
% 0.34/0.79 <=> ( ( A_46 = bot_bo19817387tate_o )
% 0.34/0.79 | ? [A_47: hoare_1708887482_state > $o,A_45: hoare_1708887482_state] :
% 0.34/0.79 ( ( A_46
% 0.34/0.79 = ( insert528405184_state @ A_45 @ A_47 ) )
% 0.34/0.79 & ( finite1625599783_state @ A_47 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_704_finite_Osimps,axiom,
% 0.34/0.79 ! [A_46: nat > $o] :
% 0.34/0.79 ( ( finite_finite_nat @ A_46 )
% 0.34/0.79 <=> ( ( A_46 = bot_bot_nat_o )
% 0.34/0.79 | ? [A_47: nat > $o,A_45: nat] :
% 0.34/0.79 ( ( A_46
% 0.34/0.79 = ( insert_nat @ A_45 @ A_47 ) )
% 0.34/0.79 & ( finite_finite_nat @ A_47 ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_705_pigeonhole__infinite,axiom,
% 0.34/0.79 ! [F_31: ( hoare_2091234717iple_a > $o ) > nat,A_44: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ~ ( finite1829014797le_a_o @ A_44 )
% 0.34/0.79 => ( ( finite_finite_nat @ ( image_75520503_o_nat @ F_31 @ A_44 ) )
% 0.34/0.79 => ? [X: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( member99268621le_a_o @ X @ A_44 )
% 0.34/0.79 & ~ ( finite1829014797le_a_o
% 0.34/0.79 @ ( collec1008234059le_a_o
% 0.34/0.79 @ ^ [A_45: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( (&) @ ( member99268621le_a_o @ A_45 @ A_44 )
% 0.34/0.79 @ ( ( F_31 @ A_45 )
% 0.34/0.79 = ( F_31 @ X ) ) ) ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_706_pigeonhole__infinite,axiom,
% 0.34/0.79 ! [F_31: hoare_2091234717iple_a > nat,A_44: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ~ ( finite232261744iple_a @ A_44 )
% 0.34/0.79 => ( ( finite_finite_nat @ ( image_1773322034_a_nat @ F_31 @ A_44 ) )
% 0.34/0.79 => ? [X: hoare_2091234717iple_a] :
% 0.34/0.79 ( ( member290856304iple_a @ X @ A_44 )
% 0.34/0.79 & ~ ( finite232261744iple_a
% 0.34/0.79 @ ( collec992574898iple_a
% 0.34/0.79 @ ^ [A_45: hoare_2091234717iple_a] :
% 0.34/0.79 ( (&) @ ( member290856304iple_a @ A_45 @ A_44 )
% 0.34/0.79 @ ( ( F_31 @ A_45 )
% 0.34/0.79 = ( F_31 @ X ) ) ) ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_707_pigeonhole__infinite,axiom,
% 0.34/0.79 ! [F_31: pname > nat,A_44: pname > $o] :
% 0.34/0.79 ( ~ ( finite_finite_pname @ A_44 )
% 0.34/0.79 => ( ( finite_finite_nat @ ( image_pname_nat @ F_31 @ A_44 ) )
% 0.34/0.79 => ? [X: pname] :
% 0.34/0.79 ( ( member_pname @ X @ A_44 )
% 0.34/0.79 & ~ ( finite_finite_pname
% 0.34/0.79 @ ( collect_pname
% 0.34/0.79 @ ^ [A_45: pname] :
% 0.34/0.79 ( (&) @ ( member_pname @ A_45 @ A_44 )
% 0.34/0.79 @ ( ( F_31 @ A_45 )
% 0.34/0.79 = ( F_31 @ X ) ) ) ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_708_pigeonhole__infinite,axiom,
% 0.34/0.79 ! [F_31: nat > nat,A_44: nat > $o] :
% 0.34/0.79 ( ~ ( finite_finite_nat @ A_44 )
% 0.34/0.79 => ( ( finite_finite_nat @ ( image_nat_nat @ F_31 @ A_44 ) )
% 0.34/0.79 => ? [X: nat] :
% 0.34/0.79 ( ( member_nat @ X @ A_44 )
% 0.34/0.79 & ~ ( finite_finite_nat
% 0.34/0.79 @ ( collect_nat
% 0.34/0.79 @ ^ [A_45: nat] :
% 0.34/0.79 ( (&) @ ( member_nat @ A_45 @ A_44 )
% 0.34/0.79 @ ( ( F_31 @ A_45 )
% 0.34/0.79 = ( F_31 @ X ) ) ) ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_709_pigeonhole__infinite,axiom,
% 0.34/0.79 ! [F_31: nat > hoare_2091234717iple_a,A_44: nat > $o] :
% 0.34/0.79 ( ~ ( finite_finite_nat @ A_44 )
% 0.34/0.79 => ( ( finite232261744iple_a @ ( image_359186840iple_a @ F_31 @ A_44 ) )
% 0.34/0.79 => ? [X: nat] :
% 0.34/0.79 ( ( member_nat @ X @ A_44 )
% 0.34/0.79 & ~ ( finite_finite_nat
% 0.34/0.79 @ ( collect_nat
% 0.34/0.79 @ ^ [A_45: nat] :
% 0.34/0.79 ( (&) @ ( member_nat @ A_45 @ A_44 )
% 0.34/0.79 @ ( ( F_31 @ A_45 )
% 0.34/0.79 = ( F_31 @ X ) ) ) ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_710_pigeonhole__infinite,axiom,
% 0.34/0.79 ! [F_31: nat > hoare_2091234717iple_a > $o,A_44: nat > $o] :
% 0.34/0.79 ( ~ ( finite_finite_nat @ A_44 )
% 0.34/0.79 => ( ( finite1829014797le_a_o @ ( image_1995609573le_a_o @ F_31 @ A_44 ) )
% 0.34/0.79 => ? [X: nat] :
% 0.34/0.79 ( ( member_nat @ X @ A_44 )
% 0.34/0.79 & ~ ( finite_finite_nat
% 0.34/0.79 @ ( collect_nat
% 0.34/0.79 @ ^ [A_45: nat] :
% 0.34/0.79 ( (&) @ ( member_nat @ A_45 @ A_44 )
% 0.34/0.79 @ ( ( F_31 @ A_45 )
% 0.34/0.79 = ( F_31 @ X ) ) ) ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_711_pigeonhole__infinite,axiom,
% 0.34/0.79 ! [F_31: nat > pname,A_44: nat > $o] :
% 0.34/0.79 ( ~ ( finite_finite_nat @ A_44 )
% 0.34/0.79 => ( ( finite_finite_pname @ ( image_nat_pname @ F_31 @ A_44 ) )
% 0.34/0.79 => ? [X: nat] :
% 0.34/0.79 ( ( member_nat @ X @ A_44 )
% 0.34/0.79 & ~ ( finite_finite_nat
% 0.34/0.79 @ ( collect_nat
% 0.34/0.79 @ ^ [A_45: nat] :
% 0.34/0.79 ( (&) @ ( member_nat @ A_45 @ A_44 )
% 0.34/0.79 @ ( ( F_31 @ A_45 )
% 0.34/0.79 = ( F_31 @ X ) ) ) ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_712_pigeonhole__infinite,axiom,
% 0.34/0.79 ! [F_31: pname > hoare_1708887482_state,A_44: pname > $o] :
% 0.34/0.79 ( ~ ( finite_finite_pname @ A_44 )
% 0.34/0.79 => ( ( finite1625599783_state @ ( image_1116629049_state @ F_31 @ A_44 ) )
% 0.34/0.79 => ? [X: pname] :
% 0.34/0.79 ( ( member_pname @ X @ A_44 )
% 0.34/0.79 & ~ ( finite_finite_pname
% 0.34/0.79 @ ( collect_pname
% 0.34/0.79 @ ^ [A_45: pname] :
% 0.34/0.79 ( (&) @ ( member_pname @ A_45 @ A_44 )
% 0.34/0.79 @ ( ( F_31 @ A_45 )
% 0.34/0.79 = ( F_31 @ X ) ) ) ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_713_pigeonhole__infinite,axiom,
% 0.34/0.79 ! [F_31: pname > hoare_2091234717iple_a > $o,A_44: pname > $o] :
% 0.34/0.79 ( ~ ( finite_finite_pname @ A_44 )
% 0.34/0.79 => ( ( finite1829014797le_a_o @ ( image_742317343le_a_o @ F_31 @ A_44 ) )
% 0.34/0.79 => ? [X: pname] :
% 0.34/0.79 ( ( member_pname @ X @ A_44 )
% 0.34/0.79 & ~ ( finite_finite_pname
% 0.34/0.79 @ ( collect_pname
% 0.34/0.79 @ ^ [A_45: pname] :
% 0.34/0.79 ( (&) @ ( member_pname @ A_45 @ A_44 )
% 0.34/0.79 @ ( ( F_31 @ A_45 )
% 0.34/0.79 = ( F_31 @ X ) ) ) ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_714_pigeonhole__infinite,axiom,
% 0.34/0.79 ! [F_31: pname > pname,A_44: pname > $o] :
% 0.34/0.79 ( ~ ( finite_finite_pname @ A_44 )
% 0.34/0.79 => ( ( finite_finite_pname @ ( image_pname_pname @ F_31 @ A_44 ) )
% 0.34/0.79 => ? [X: pname] :
% 0.34/0.79 ( ( member_pname @ X @ A_44 )
% 0.34/0.79 & ~ ( finite_finite_pname
% 0.34/0.79 @ ( collect_pname
% 0.34/0.79 @ ^ [A_45: pname] :
% 0.34/0.79 ( (&) @ ( member_pname @ A_45 @ A_44 )
% 0.34/0.79 @ ( ( F_31 @ A_45 )
% 0.34/0.79 = ( F_31 @ X ) ) ) ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_715_pigeonhole__infinite,axiom,
% 0.34/0.79 ! [F_31: pname > hoare_2091234717iple_a,A_44: pname > $o] :
% 0.34/0.79 ( ~ ( finite_finite_pname @ A_44 )
% 0.34/0.79 => ( ( finite232261744iple_a @ ( image_231808478iple_a @ F_31 @ A_44 ) )
% 0.34/0.79 => ? [X: pname] :
% 0.34/0.79 ( ( member_pname @ X @ A_44 )
% 0.34/0.79 & ~ ( finite_finite_pname
% 0.34/0.79 @ ( collect_pname
% 0.34/0.79 @ ^ [A_45: pname] :
% 0.34/0.79 ( (&) @ ( member_pname @ A_45 @ A_44 )
% 0.34/0.79 @ ( ( F_31 @ A_45 )
% 0.34/0.79 = ( F_31 @ X ) ) ) ) ) ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_716_nonempty__iff,axiom,
% 0.34/0.79 ! [A_43: nat > $o] :
% 0.34/0.79 ( ( A_43 != bot_bot_nat_o )
% 0.34/0.79 <=> ? [X: nat,B_26: nat > $o] :
% 0.34/0.79 ( ( A_43
% 0.34/0.79 = ( insert_nat @ X @ B_26 ) )
% 0.34/0.79 & ~ ( member_nat @ X @ B_26 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_717_nonempty__iff,axiom,
% 0.34/0.79 ! [A_43: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( A_43 != bot_bo1957696069_a_o_o )
% 0.34/0.79 <=> ? [X: hoare_2091234717iple_a > $o,B_26: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.34/0.79 ( ( A_43
% 0.34/0.79 = ( insert102003750le_a_o @ X @ B_26 ) )
% 0.34/0.79 & ~ ( member99268621le_a_o @ X @ B_26 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_718_nonempty__iff,axiom,
% 0.34/0.79 ! [A_43: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( A_43 != bot_bo1791335050le_a_o )
% 0.34/0.79 <=> ? [X: hoare_2091234717iple_a,B_26: hoare_2091234717iple_a > $o] :
% 0.34/0.79 ( ( A_43
% 0.34/0.79 = ( insert1597628439iple_a @ X @ B_26 ) )
% 0.34/0.79 & ~ ( member290856304iple_a @ X @ B_26 ) ) ) ).
% 0.34/0.79
% 0.34/0.79 thf(fact_719_nonempty__iff,axiom,
% 0.34/0.79 ! [A_43: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( A_43 != bot_bo19817387tate_o )
% 0.34/0.79 <=> ? [X: hoare_1708887482_state,B_26: hoare_1708887482_state > $o] :
% 0.34/0.79 ( ( A_43
% 0.34/0.79 = ( insert528405184_state @ X @ B_26 ) )
% 0.61/0.79 & ~ ( member451959335_state @ X @ B_26 ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_720_nonempty__iff,axiom,
% 0.61/0.79 ! [A_43: pname > $o] :
% 0.61/0.79 ( ( A_43 != bot_bot_pname_o )
% 0.61/0.79 <=> ? [X: pname,B_26: pname > $o] :
% 0.61/0.79 ( ( A_43
% 0.61/0.79 = ( insert_pname @ X @ B_26 ) )
% 0.61/0.79 & ~ ( member_pname @ X @ B_26 ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_721_folding__one__idem_Ounion__idem,axiom,
% 0.61/0.79 ! [B_27: ( hoare_2091234717iple_a > $o ) > $o,A_42: ( hoare_2091234717iple_a > $o ) > $o,F_30: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o,F_29: ( ( hoare_2091234717iple_a > $o ) > $o ) > hoare_2091234717iple_a > $o] :
% 0.61/0.79 ( ( finite574580006le_a_o @ F_30 @ F_29 )
% 0.61/0.79 => ( ( finite1829014797le_a_o @ A_42 )
% 0.61/0.79 => ( ( A_42 != bot_bo1957696069_a_o_o )
% 0.61/0.79 => ( ( finite1829014797le_a_o @ B_27 )
% 0.61/0.79 => ( ( B_27 != bot_bo1957696069_a_o_o )
% 0.61/0.79 => ( ( F_29 @ ( semila2050116131_a_o_o @ A_42 @ B_27 ) )
% 0.61/0.79 = ( F_30 @ ( F_29 @ A_42 ) @ ( F_29 @ B_27 ) ) ) ) ) ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_722_folding__one__idem_Ounion__idem,axiom,
% 0.61/0.79 ! [B_27: pname > $o,A_42: pname > $o,F_30: pname > pname > pname,F_29: ( pname > $o ) > pname] :
% 0.61/0.79 ( ( finite89670078_pname @ F_30 @ F_29 )
% 0.61/0.79 => ( ( finite_finite_pname @ A_42 )
% 0.61/0.79 => ( ( A_42 != bot_bot_pname_o )
% 0.61/0.79 => ( ( finite_finite_pname @ B_27 )
% 0.61/0.79 => ( ( B_27 != bot_bot_pname_o )
% 0.61/0.79 => ( ( F_29 @ ( semila1780557381name_o @ A_42 @ B_27 ) )
% 0.61/0.79 = ( F_30 @ ( F_29 @ A_42 ) @ ( F_29 @ B_27 ) ) ) ) ) ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_723_folding__one__idem_Ounion__idem,axiom,
% 0.61/0.79 ! [B_27: hoare_1708887482_state > $o,A_42: hoare_1708887482_state > $o,F_30: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_29: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.61/0.79 ( ( finite1347568576_state @ F_30 @ F_29 )
% 0.61/0.79 => ( ( finite1625599783_state @ A_42 )
% 0.61/0.79 => ( ( A_42 != bot_bo19817387tate_o )
% 0.61/0.79 => ( ( finite1625599783_state @ B_27 )
% 0.61/0.79 => ( ( B_27 != bot_bo19817387tate_o )
% 0.61/0.79 => ( ( F_29 @ ( semila1122118281tate_o @ A_42 @ B_27 ) )
% 0.61/0.79 = ( F_30 @ ( F_29 @ A_42 ) @ ( F_29 @ B_27 ) ) ) ) ) ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_724_folding__one__idem_Ounion__idem,axiom,
% 0.61/0.79 ! [B_27: hoare_2091234717iple_a > $o,A_42: hoare_2091234717iple_a > $o,F_30: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,F_29: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
% 0.61/0.79 ( ( finite1674555159iple_a @ F_30 @ F_29 )
% 0.61/0.79 => ( ( finite232261744iple_a @ A_42 )
% 0.61/0.79 => ( ( A_42 != bot_bo1791335050le_a_o )
% 0.61/0.79 => ( ( finite232261744iple_a @ B_27 )
% 0.61/0.79 => ( ( B_27 != bot_bo1791335050le_a_o )
% 0.61/0.79 => ( ( F_29 @ ( semila1052848428le_a_o @ A_42 @ B_27 ) )
% 0.61/0.79 = ( F_30 @ ( F_29 @ A_42 ) @ ( F_29 @ B_27 ) ) ) ) ) ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_725_folding__one__idem_Ounion__idem,axiom,
% 0.61/0.79 ! [B_27: nat > $o,A_42: nat > $o,F_30: nat > nat > nat,F_29: ( nat > $o ) > nat] :
% 0.61/0.79 ( ( finite795500164em_nat @ F_30 @ F_29 )
% 0.61/0.79 => ( ( finite_finite_nat @ A_42 )
% 0.61/0.79 => ( ( A_42 != bot_bot_nat_o )
% 0.61/0.79 => ( ( finite_finite_nat @ B_27 )
% 0.61/0.79 => ( ( B_27 != bot_bot_nat_o )
% 0.61/0.79 => ( ( F_29 @ ( semila848761471_nat_o @ A_42 @ B_27 ) )
% 0.61/0.79 = ( F_30 @ ( F_29 @ A_42 ) @ ( F_29 @ B_27 ) ) ) ) ) ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_726_folding__one__idem_Oinsert__idem,axiom,
% 0.61/0.79 ! [X_20: hoare_2091234717iple_a > $o,A_41: ( hoare_2091234717iple_a > $o ) > $o,F_28: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o,F_27: ( ( hoare_2091234717iple_a > $o ) > $o ) > hoare_2091234717iple_a > $o] :
% 0.61/0.79 ( ( finite574580006le_a_o @ F_28 @ F_27 )
% 0.61/0.79 => ( ( finite1829014797le_a_o @ A_41 )
% 0.61/0.79 => ( ( A_41 != bot_bo1957696069_a_o_o )
% 0.61/0.79 => ( ( F_27 @ ( insert102003750le_a_o @ X_20 @ A_41 ) )
% 0.61/0.79 = ( F_28 @ X_20 @ ( F_27 @ A_41 ) ) ) ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_727_folding__one__idem_Oinsert__idem,axiom,
% 0.61/0.79 ! [X_20: pname,A_41: pname > $o,F_28: pname > pname > pname,F_27: ( pname > $o ) > pname] :
% 0.61/0.79 ( ( finite89670078_pname @ F_28 @ F_27 )
% 0.61/0.79 => ( ( finite_finite_pname @ A_41 )
% 0.61/0.79 => ( ( A_41 != bot_bot_pname_o )
% 0.61/0.79 => ( ( F_27 @ ( insert_pname @ X_20 @ A_41 ) )
% 0.61/0.79 = ( F_28 @ X_20 @ ( F_27 @ A_41 ) ) ) ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_728_folding__one__idem_Oinsert__idem,axiom,
% 0.61/0.79 ! [X_20: hoare_2091234717iple_a,A_41: hoare_2091234717iple_a > $o,F_28: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,F_27: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
% 0.61/0.79 ( ( finite1674555159iple_a @ F_28 @ F_27 )
% 0.61/0.79 => ( ( finite232261744iple_a @ A_41 )
% 0.61/0.79 => ( ( A_41 != bot_bo1791335050le_a_o )
% 0.61/0.79 => ( ( F_27 @ ( insert1597628439iple_a @ X_20 @ A_41 ) )
% 0.61/0.79 = ( F_28 @ X_20 @ ( F_27 @ A_41 ) ) ) ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_729_folding__one__idem_Oinsert__idem,axiom,
% 0.61/0.79 ! [X_20: hoare_1708887482_state,A_41: hoare_1708887482_state > $o,F_28: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_27: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.61/0.79 ( ( finite1347568576_state @ F_28 @ F_27 )
% 0.61/0.79 => ( ( finite1625599783_state @ A_41 )
% 0.61/0.79 => ( ( A_41 != bot_bo19817387tate_o )
% 0.61/0.79 => ( ( F_27 @ ( insert528405184_state @ X_20 @ A_41 ) )
% 0.61/0.79 = ( F_28 @ X_20 @ ( F_27 @ A_41 ) ) ) ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_730_folding__one__idem_Oinsert__idem,axiom,
% 0.61/0.79 ! [X_20: nat,A_41: nat > $o,F_28: nat > nat > nat,F_27: ( nat > $o ) > nat] :
% 0.61/0.79 ( ( finite795500164em_nat @ F_28 @ F_27 )
% 0.61/0.79 => ( ( finite_finite_nat @ A_41 )
% 0.61/0.79 => ( ( A_41 != bot_bot_nat_o )
% 0.61/0.79 => ( ( F_27 @ ( insert_nat @ X_20 @ A_41 ) )
% 0.61/0.79 = ( F_28 @ X_20 @ ( F_27 @ A_41 ) ) ) ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_731_image__eq__fold__image,axiom,
% 0.61/0.79 ! [F_26: pname > hoare_1708887482_state,A_40: pname > $o] :
% 0.61/0.79 ( ( finite_finite_pname @ A_40 )
% 0.61/0.79 => ( ( image_1116629049_state @ F_26 @ A_40 )
% 0.61/0.79 = ( finite2139561282_pname @ semila1122118281tate_o
% 0.61/0.79 @ ^ [X: pname] : ( insert528405184_state @ ( F_26 @ X ) @ bot_bo19817387tate_o )
% 0.61/0.79 @ bot_bo19817387tate_o
% 0.61/0.79 @ A_40 ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_732_image__eq__fold__image,axiom,
% 0.61/0.79 ! [F_26: hoare_2091234717iple_a > hoare_2091234717iple_a,A_40: hoare_2091234717iple_a > $o] :
% 0.61/0.79 ( ( finite232261744iple_a @ A_40 )
% 0.61/0.79 => ( ( image_1661191109iple_a @ F_26 @ A_40 )
% 0.61/0.79 = ( finite1481787452iple_a @ semila1052848428le_a_o
% 0.61/0.79 @ ^ [X: hoare_2091234717iple_a] : ( insert1597628439iple_a @ ( F_26 @ X ) @ bot_bo1791335050le_a_o )
% 0.61/0.79 @ bot_bo1791335050le_a_o
% 0.61/0.79 @ A_40 ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_733_image__eq__fold__image,axiom,
% 0.61/0.79 ! [F_26: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a,A_40: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.79 ( ( finite1829014797le_a_o @ A_40 )
% 0.61/0.79 => ( ( image_136408202iple_a @ F_26 @ A_40 )
% 0.61/0.79 = ( finite903029825le_a_o @ semila1052848428le_a_o
% 0.61/0.79 @ ^ [X: hoare_2091234717iple_a > $o] : ( insert1597628439iple_a @ ( F_26 @ X ) @ bot_bo1791335050le_a_o )
% 0.61/0.79 @ bot_bo1791335050le_a_o
% 0.61/0.79 @ A_40 ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_734_image__eq__fold__image,axiom,
% 0.61/0.79 ! [F_26: nat > nat,A_40: nat > $o] :
% 0.61/0.79 ( ( finite_finite_nat @ A_40 )
% 0.61/0.79 => ( ( image_nat_nat @ F_26 @ A_40 )
% 0.61/0.79 = ( finite141655318_o_nat @ semila848761471_nat_o
% 0.61/0.79 @ ^ [X: nat] : ( insert_nat @ ( F_26 @ X ) @ bot_bot_nat_o )
% 0.61/0.79 @ bot_bot_nat_o
% 0.61/0.79 @ A_40 ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_735_image__eq__fold__image,axiom,
% 0.61/0.79 ! [F_26: nat > hoare_2091234717iple_a > $o,A_40: nat > $o] :
% 0.61/0.79 ( ( finite_finite_nat @ A_40 )
% 0.61/0.79 => ( ( image_1995609573le_a_o @ F_26 @ A_40 )
% 0.61/0.79 = ( finite2009943022_o_nat @ semila2050116131_a_o_o
% 0.61/0.79 @ ^ [X: nat] : ( insert102003750le_a_o @ ( F_26 @ X ) @ bot_bo1957696069_a_o_o )
% 0.61/0.79 @ bot_bo1957696069_a_o_o
% 0.61/0.79 @ A_40 ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_736_image__eq__fold__image,axiom,
% 0.61/0.79 ! [F_26: nat > pname,A_40: nat > $o] :
% 0.61/0.79 ( ( finite_finite_nat @ A_40 )
% 0.61/0.79 => ( ( image_nat_pname @ F_26 @ A_40 )
% 0.61/0.79 = ( finite1427591632_o_nat @ semila1780557381name_o
% 0.61/0.79 @ ^ [X: nat] : ( insert_pname @ ( F_26 @ X ) @ bot_bot_pname_o )
% 0.61/0.79 @ bot_bot_pname_o
% 0.61/0.79 @ A_40 ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_737_image__eq__fold__image,axiom,
% 0.61/0.79 ! [F_26: nat > hoare_2091234717iple_a,A_40: nat > $o] :
% 0.61/0.79 ( ( finite_finite_nat @ A_40 )
% 0.61/0.79 => ( ( image_359186840iple_a @ F_26 @ A_40 )
% 0.61/0.79 = ( finite2100865449_o_nat @ semila1052848428le_a_o
% 0.61/0.79 @ ^ [X: nat] : ( insert1597628439iple_a @ ( F_26 @ X ) @ bot_bo1791335050le_a_o )
% 0.61/0.79 @ bot_bo1791335050le_a_o
% 0.61/0.79 @ A_40 ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_738_image__eq__fold__image,axiom,
% 0.61/0.79 ! [F_26: nat > hoare_1708887482_state,A_40: nat > $o] :
% 0.61/0.79 ( ( finite_finite_nat @ A_40 )
% 0.61/0.79 => ( ( image_514827263_state @ F_26 @ A_40 )
% 0.61/0.79 = ( finite1400355848_o_nat @ semila1122118281tate_o
% 0.61/0.79 @ ^ [X: nat] : ( insert528405184_state @ ( F_26 @ X ) @ bot_bo19817387tate_o )
% 0.61/0.79 @ bot_bo19817387tate_o
% 0.61/0.79 @ A_40 ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_739_image__eq__fold__image,axiom,
% 0.61/0.79 ! [F_26: pname > hoare_2091234717iple_a,A_40: pname > $o] :
% 0.61/0.79 ( ( finite_finite_pname @ A_40 )
% 0.61/0.79 => ( ( image_231808478iple_a @ F_26 @ A_40 )
% 0.61/0.79 = ( finite1290357347_pname @ semila1052848428le_a_o
% 0.61/0.79 @ ^ [X: pname] : ( insert1597628439iple_a @ ( F_26 @ X ) @ bot_bo1791335050le_a_o )
% 0.61/0.79 @ bot_bo1791335050le_a_o
% 0.61/0.79 @ A_40 ) ) ) ).
% 0.61/0.79
% 0.61/0.79 thf(fact_740_finite__ne__induct,axiom,
% 0.61/0.79 ! [P_3: ( ( hoare_2091234717iple_a > $o ) > $o ) > $o,F_24: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.79 ( ( finite1829014797le_a_o @ F_24 )
% 0.61/0.79 => ( ( F_24 != bot_bo1957696069_a_o_o )
% 0.61/0.79 => ( ! [X: hoare_2091234717iple_a > $o] : ( P_3 @ ( insert102003750le_a_o @ X @ bot_bo1957696069_a_o_o ) )
% 0.61/0.79 => ( ! [X: hoare_2091234717iple_a > $o,F_25: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.79 ( ( finite1829014797le_a_o @ F_25 )
% 0.61/0.79 => ( ( F_25 != bot_bo1957696069_a_o_o )
% 0.61/0.79 => ( ~ ( member99268621le_a_o @ X @ F_25 )
% 0.61/0.79 => ( ( P_3 @ F_25 )
% 0.61/0.79 => ( P_3 @ ( insert102003750le_a_o @ X @ F_25 ) ) ) ) ) )
% 0.61/0.79 => ( P_3 @ F_24 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_741_finite__ne__induct,axiom,
% 0.61/0.80 ! [P_3: ( hoare_2091234717iple_a > $o ) > $o,F_24: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( finite232261744iple_a @ F_24 )
% 0.61/0.80 => ( ( F_24 != bot_bo1791335050le_a_o )
% 0.61/0.80 => ( ! [X: hoare_2091234717iple_a] : ( P_3 @ ( insert1597628439iple_a @ X @ bot_bo1791335050le_a_o ) )
% 0.61/0.80 => ( ! [X: hoare_2091234717iple_a,F_25: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( finite232261744iple_a @ F_25 )
% 0.61/0.80 => ( ( F_25 != bot_bo1791335050le_a_o )
% 0.61/0.80 => ( ~ ( member290856304iple_a @ X @ F_25 )
% 0.61/0.80 => ( ( P_3 @ F_25 )
% 0.61/0.80 => ( P_3 @ ( insert1597628439iple_a @ X @ F_25 ) ) ) ) ) )
% 0.61/0.80 => ( P_3 @ F_24 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_742_finite__ne__induct,axiom,
% 0.61/0.80 ! [P_3: ( hoare_1708887482_state > $o ) > $o,F_24: hoare_1708887482_state > $o] :
% 0.61/0.80 ( ( finite1625599783_state @ F_24 )
% 0.61/0.80 => ( ( F_24 != bot_bo19817387tate_o )
% 0.61/0.80 => ( ! [X: hoare_1708887482_state] : ( P_3 @ ( insert528405184_state @ X @ bot_bo19817387tate_o ) )
% 0.61/0.80 => ( ! [X: hoare_1708887482_state,F_25: hoare_1708887482_state > $o] :
% 0.61/0.80 ( ( finite1625599783_state @ F_25 )
% 0.61/0.80 => ( ( F_25 != bot_bo19817387tate_o )
% 0.61/0.80 => ( ~ ( member451959335_state @ X @ F_25 )
% 0.61/0.80 => ( ( P_3 @ F_25 )
% 0.61/0.80 => ( P_3 @ ( insert528405184_state @ X @ F_25 ) ) ) ) ) )
% 0.61/0.80 => ( P_3 @ F_24 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_743_finite__ne__induct,axiom,
% 0.61/0.80 ! [P_3: ( nat > $o ) > $o,F_24: nat > $o] :
% 0.61/0.80 ( ( finite_finite_nat @ F_24 )
% 0.61/0.80 => ( ( F_24 != bot_bot_nat_o )
% 0.61/0.80 => ( ! [X: nat] : ( P_3 @ ( insert_nat @ X @ bot_bot_nat_o ) )
% 0.61/0.80 => ( ! [X: nat,F_25: nat > $o] :
% 0.61/0.80 ( ( finite_finite_nat @ F_25 )
% 0.61/0.80 => ( ( F_25 != bot_bot_nat_o )
% 0.61/0.80 => ( ~ ( member_nat @ X @ F_25 )
% 0.61/0.80 => ( ( P_3 @ F_25 )
% 0.61/0.80 => ( P_3 @ ( insert_nat @ X @ F_25 ) ) ) ) ) )
% 0.61/0.80 => ( P_3 @ F_24 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_744_finite__ne__induct,axiom,
% 0.61/0.80 ! [P_3: ( pname > $o ) > $o,F_24: pname > $o] :
% 0.61/0.80 ( ( finite_finite_pname @ F_24 )
% 0.61/0.80 => ( ( F_24 != bot_bot_pname_o )
% 0.61/0.80 => ( ! [X: pname] : ( P_3 @ ( insert_pname @ X @ bot_bot_pname_o ) )
% 0.61/0.80 => ( ! [X: pname,F_25: pname > $o] :
% 0.61/0.80 ( ( finite_finite_pname @ F_25 )
% 0.61/0.80 => ( ( F_25 != bot_bot_pname_o )
% 0.61/0.80 => ( ~ ( member_pname @ X @ F_25 )
% 0.61/0.80 => ( ( P_3 @ F_25 )
% 0.61/0.80 => ( P_3 @ ( insert_pname @ X @ F_25 ) ) ) ) ) )
% 0.61/0.80 => ( P_3 @ F_24 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_745_folding__one__idem_Oidem,axiom,
% 0.61/0.80 ! [X_19: nat,F_23: nat > nat > nat,F_22: ( nat > $o ) > nat] :
% 0.61/0.80 ( ( finite795500164em_nat @ F_23 @ F_22 )
% 0.61/0.80 => ( ( F_23 @ X_19 @ X_19 )
% 0.61/0.80 = X_19 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_746_folding__one__idem_Oidem,axiom,
% 0.61/0.80 ! [X_19: pname,F_23: pname > pname > pname,F_22: ( pname > $o ) > pname] :
% 0.61/0.80 ( ( finite89670078_pname @ F_23 @ F_22 )
% 0.61/0.80 => ( ( F_23 @ X_19 @ X_19 )
% 0.61/0.80 = X_19 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_747_folding__one__idem_Oidem,axiom,
% 0.61/0.80 ! [X_19: hoare_2091234717iple_a,F_23: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,F_22: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
% 0.61/0.80 ( ( finite1674555159iple_a @ F_23 @ F_22 )
% 0.61/0.80 => ( ( F_23 @ X_19 @ X_19 )
% 0.61/0.80 = X_19 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_748_fold__image__empty,axiom,
% 0.61/0.80 ! [F_21: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o,G_3: pname > hoare_2091234717iple_a > $o,Z_4: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( finite1290357347_pname @ F_21 @ G_3 @ Z_4 @ bot_bot_pname_o )
% 0.61/0.80 = Z_4 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_749_folding__one__idem_Oin__idem,axiom,
% 0.61/0.80 ! [X_18: hoare_2091234717iple_a > $o,A_39: ( hoare_2091234717iple_a > $o ) > $o,F_20: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o,F_19: ( ( hoare_2091234717iple_a > $o ) > $o ) > hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( finite574580006le_a_o @ F_20 @ F_19 )
% 0.61/0.80 => ( ( finite1829014797le_a_o @ A_39 )
% 0.61/0.80 => ( ( member99268621le_a_o @ X_18 @ A_39 )
% 0.61/0.80 => ( ( F_20 @ X_18 @ ( F_19 @ A_39 ) )
% 0.61/0.80 = ( F_19 @ A_39 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_750_folding__one__idem_Oin__idem,axiom,
% 0.61/0.80 ! [X_18: hoare_2091234717iple_a,A_39: hoare_2091234717iple_a > $o,F_20: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,F_19: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
% 0.61/0.80 ( ( finite1674555159iple_a @ F_20 @ F_19 )
% 0.61/0.80 => ( ( finite232261744iple_a @ A_39 )
% 0.61/0.80 => ( ( member290856304iple_a @ X_18 @ A_39 )
% 0.61/0.80 => ( ( F_20 @ X_18 @ ( F_19 @ A_39 ) )
% 0.61/0.80 = ( F_19 @ A_39 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_751_folding__one__idem_Oin__idem,axiom,
% 0.61/0.80 ! [X_18: nat,A_39: nat > $o,F_20: nat > nat > nat,F_19: ( nat > $o ) > nat] :
% 0.61/0.80 ( ( finite795500164em_nat @ F_20 @ F_19 )
% 0.61/0.80 => ( ( finite_finite_nat @ A_39 )
% 0.61/0.80 => ( ( member_nat @ X_18 @ A_39 )
% 0.61/0.80 => ( ( F_20 @ X_18 @ ( F_19 @ A_39 ) )
% 0.61/0.80 = ( F_19 @ A_39 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_752_folding__one__idem_Oin__idem,axiom,
% 0.61/0.80 ! [X_18: pname,A_39: pname > $o,F_20: pname > pname > pname,F_19: ( pname > $o ) > pname] :
% 0.61/0.80 ( ( finite89670078_pname @ F_20 @ F_19 )
% 0.61/0.80 => ( ( finite_finite_pname @ A_39 )
% 0.61/0.80 => ( ( member_pname @ X_18 @ A_39 )
% 0.61/0.80 => ( ( F_20 @ X_18 @ ( F_19 @ A_39 ) )
% 0.61/0.80 = ( F_19 @ A_39 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_753_folding__one__idem_Ohom__commute,axiom,
% 0.61/0.80 ! [N_3: hoare_2091234717iple_a > $o,H: hoare_2091234717iple_a > hoare_2091234717iple_a,F_18: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,F_17: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
% 0.61/0.80 ( ( finite1674555159iple_a @ F_18 @ F_17 )
% 0.61/0.80 => ( ! [X: hoare_2091234717iple_a,Y_7: hoare_2091234717iple_a] :
% 0.61/0.80 ( ( H @ ( F_18 @ X @ Y_7 ) )
% 0.61/0.80 = ( F_18 @ ( H @ X ) @ ( H @ Y_7 ) ) )
% 0.61/0.80 => ( ( finite232261744iple_a @ N_3 )
% 0.61/0.80 => ( ( N_3 != bot_bo1791335050le_a_o )
% 0.61/0.80 => ( ( H @ ( F_17 @ N_3 ) )
% 0.61/0.80 = ( F_17 @ ( image_1661191109iple_a @ H @ N_3 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_754_folding__one__idem_Ohom__commute,axiom,
% 0.61/0.80 ! [N_3: ( hoare_2091234717iple_a > $o ) > $o,H: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o,F_18: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o,F_17: ( ( hoare_2091234717iple_a > $o ) > $o ) > hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( finite574580006le_a_o @ F_18 @ F_17 )
% 0.61/0.80 => ( ! [X: hoare_2091234717iple_a > $o,Y_7: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( H @ ( F_18 @ X @ Y_7 ) )
% 0.61/0.80 = ( F_18 @ ( H @ X ) @ ( H @ Y_7 ) ) )
% 0.61/0.80 => ( ( finite1829014797le_a_o @ N_3 )
% 0.61/0.80 => ( ( N_3 != bot_bo1957696069_a_o_o )
% 0.61/0.80 => ( ( H @ ( F_17 @ N_3 ) )
% 0.61/0.80 = ( F_17 @ ( image_784579955le_a_o @ H @ N_3 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_755_folding__one__idem_Ohom__commute,axiom,
% 0.61/0.80 ! [N_3: pname > $o,H: pname > pname,F_18: pname > pname > pname,F_17: ( pname > $o ) > pname] :
% 0.61/0.80 ( ( finite89670078_pname @ F_18 @ F_17 )
% 0.61/0.80 => ( ! [X: pname,Y_7: pname] :
% 0.61/0.80 ( ( H @ ( F_18 @ X @ Y_7 ) )
% 0.61/0.80 = ( F_18 @ ( H @ X ) @ ( H @ Y_7 ) ) )
% 0.61/0.80 => ( ( finite_finite_pname @ N_3 )
% 0.61/0.80 => ( ( N_3 != bot_bot_pname_o )
% 0.61/0.80 => ( ( H @ ( F_17 @ N_3 ) )
% 0.61/0.80 = ( F_17 @ ( image_pname_pname @ H @ N_3 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_756_folding__one__idem_Ohom__commute,axiom,
% 0.61/0.80 ! [N_3: hoare_1708887482_state > $o,H: hoare_1708887482_state > hoare_1708887482_state,F_18: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_17: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.61/0.80 ( ( finite1347568576_state @ F_18 @ F_17 )
% 0.61/0.80 => ( ! [X: hoare_1708887482_state,Y_7: hoare_1708887482_state] :
% 0.61/0.80 ( ( H @ ( F_18 @ X @ Y_7 ) )
% 0.61/0.80 = ( F_18 @ ( H @ X ) @ ( H @ Y_7 ) ) )
% 0.61/0.80 => ( ( finite1625599783_state @ N_3 )
% 0.61/0.80 => ( ( N_3 != bot_bo19817387tate_o )
% 0.61/0.80 => ( ( H @ ( F_17 @ N_3 ) )
% 0.61/0.80 = ( F_17 @ ( image_757158439_state @ H @ N_3 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_757_folding__one__idem_Ohom__commute,axiom,
% 0.61/0.80 ! [N_3: nat > $o,H: nat > nat,F_18: nat > nat > nat,F_17: ( nat > $o ) > nat] :
% 0.61/0.80 ( ( finite795500164em_nat @ F_18 @ F_17 )
% 0.61/0.80 => ( ! [X: nat,Y_7: nat] :
% 0.61/0.80 ( ( H @ ( F_18 @ X @ Y_7 ) )
% 0.61/0.80 = ( F_18 @ ( H @ X ) @ ( H @ Y_7 ) ) )
% 0.61/0.80 => ( ( finite_finite_nat @ N_3 )
% 0.61/0.80 => ( ( N_3 != bot_bot_nat_o )
% 0.61/0.80 => ( ( H @ ( F_17 @ N_3 ) )
% 0.61/0.80 = ( F_17 @ ( image_nat_nat @ H @ N_3 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_758_comm__monoid__big_OF__eq,axiom,
% 0.61/0.80 ! [G_2: pname > hoare_2091234717iple_a > $o,A_38: pname > $o,F_16: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o,Z_3: hoare_2091234717iple_a > $o,F_15: ( pname > hoare_2091234717iple_a > $o ) > ( pname > $o ) > hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( big_co1924420859_pname @ F_16 @ Z_3 @ F_15 )
% 0.61/0.80 => ( ( ( finite_finite_pname @ A_38 )
% 0.61/0.80 => ( ( F_15 @ G_2 @ A_38 )
% 0.61/0.80 = ( finite1290357347_pname @ F_16 @ G_2 @ Z_3 @ A_38 ) ) )
% 0.61/0.80 & ( ~ ( finite_finite_pname @ A_38 )
% 0.61/0.80 => ( ( F_15 @ G_2 @ A_38 )
% 0.61/0.80 = Z_3 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_759_folding__one_Oinsert,axiom,
% 0.61/0.80 ! [X_17: hoare_2091234717iple_a > $o,A_37: ( hoare_2091234717iple_a > $o ) > $o,F_14: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o,F_13: ( ( hoare_2091234717iple_a > $o ) > $o ) > hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( finite14499299le_a_o @ F_14 @ F_13 )
% 0.61/0.80 => ( ( finite1829014797le_a_o @ A_37 )
% 0.61/0.80 => ( ~ ( member99268621le_a_o @ X_17 @ A_37 )
% 0.61/0.80 => ( ( A_37 != bot_bo1957696069_a_o_o )
% 0.61/0.80 => ( ( F_13 @ ( insert102003750le_a_o @ X_17 @ A_37 ) )
% 0.61/0.80 = ( F_14 @ X_17 @ ( F_13 @ A_37 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_760_folding__one_Oinsert,axiom,
% 0.61/0.80 ! [X_17: hoare_2091234717iple_a,A_37: hoare_2091234717iple_a > $o,F_14: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,F_13: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
% 0.61/0.80 ( ( finite247037978iple_a @ F_14 @ F_13 )
% 0.61/0.80 => ( ( finite232261744iple_a @ A_37 )
% 0.61/0.80 => ( ~ ( member290856304iple_a @ X_17 @ A_37 )
% 0.61/0.80 => ( ( A_37 != bot_bo1791335050le_a_o )
% 0.61/0.80 => ( ( F_13 @ ( insert1597628439iple_a @ X_17 @ A_37 ) )
% 0.61/0.80 = ( F_14 @ X_17 @ ( F_13 @ A_37 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_761_folding__one_Oinsert,axiom,
% 0.61/0.80 ! [X_17: hoare_1708887482_state,A_37: hoare_1708887482_state > $o,F_14: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_13: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.61/0.80 ( ( finite1615457021_state @ F_14 @ F_13 )
% 0.61/0.80 => ( ( finite1625599783_state @ A_37 )
% 0.61/0.80 => ( ~ ( member451959335_state @ X_17 @ A_37 )
% 0.61/0.80 => ( ( A_37 != bot_bo19817387tate_o )
% 0.61/0.80 => ( ( F_13 @ ( insert528405184_state @ X_17 @ A_37 ) )
% 0.61/0.80 = ( F_14 @ X_17 @ ( F_13 @ A_37 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_762_folding__one_Oinsert,axiom,
% 0.61/0.80 ! [X_17: nat,A_37: nat > $o,F_14: nat > nat > nat,F_13: ( nat > $o ) > nat] :
% 0.61/0.80 ( ( finite988810631ne_nat @ F_14 @ F_13 )
% 0.61/0.80 => ( ( finite_finite_nat @ A_37 )
% 0.61/0.80 => ( ~ ( member_nat @ X_17 @ A_37 )
% 0.61/0.80 => ( ( A_37 != bot_bot_nat_o )
% 0.61/0.80 => ( ( F_13 @ ( insert_nat @ X_17 @ A_37 ) )
% 0.61/0.80 = ( F_14 @ X_17 @ ( F_13 @ A_37 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_763_folding__one_Oinsert,axiom,
% 0.61/0.80 ! [X_17: pname,A_37: pname > $o,F_14: pname > pname > pname,F_13: ( pname > $o ) > pname] :
% 0.61/0.80 ( ( finite1282449217_pname @ F_14 @ F_13 )
% 0.61/0.80 => ( ( finite_finite_pname @ A_37 )
% 0.61/0.80 => ( ~ ( member_pname @ X_17 @ A_37 )
% 0.61/0.80 => ( ( A_37 != bot_bot_pname_o )
% 0.61/0.80 => ( ( F_13 @ ( insert_pname @ X_17 @ A_37 ) )
% 0.61/0.80 = ( F_14 @ X_17 @ ( F_13 @ A_37 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_764_folding__one_Osingleton,axiom,
% 0.61/0.80 ! [X_16: nat,F_12: nat > nat > nat,F_11: ( nat > $o ) > nat] :
% 0.61/0.80 ( ( finite988810631ne_nat @ F_12 @ F_11 )
% 0.61/0.80 => ( ( F_11 @ ( insert_nat @ X_16 @ bot_bot_nat_o ) )
% 0.61/0.80 = X_16 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_765_folding__one_Osingleton,axiom,
% 0.61/0.80 ! [X_16: hoare_2091234717iple_a > $o,F_12: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o,F_11: ( ( hoare_2091234717iple_a > $o ) > $o ) > hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( finite14499299le_a_o @ F_12 @ F_11 )
% 0.61/0.80 => ( ( F_11 @ ( insert102003750le_a_o @ X_16 @ bot_bo1957696069_a_o_o ) )
% 0.61/0.80 = X_16 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_766_folding__one_Osingleton,axiom,
% 0.61/0.80 ! [X_16: pname,F_12: pname > pname > pname,F_11: ( pname > $o ) > pname] :
% 0.61/0.80 ( ( finite1282449217_pname @ F_12 @ F_11 )
% 0.61/0.80 => ( ( F_11 @ ( insert_pname @ X_16 @ bot_bot_pname_o ) )
% 0.61/0.80 = X_16 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_767_folding__one_Osingleton,axiom,
% 0.61/0.80 ! [X_16: hoare_2091234717iple_a,F_12: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,F_11: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
% 0.61/0.80 ( ( finite247037978iple_a @ F_12 @ F_11 )
% 0.61/0.80 => ( ( F_11 @ ( insert1597628439iple_a @ X_16 @ bot_bo1791335050le_a_o ) )
% 0.61/0.80 = X_16 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_768_folding__one_Osingleton,axiom,
% 0.61/0.80 ! [X_16: hoare_1708887482_state,F_12: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_11: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.61/0.80 ( ( finite1615457021_state @ F_12 @ F_11 )
% 0.61/0.80 => ( ( F_11 @ ( insert528405184_state @ X_16 @ bot_bo19817387tate_o ) )
% 0.61/0.80 = X_16 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_769_folding__one_Oclosed,axiom,
% 0.61/0.80 ! [A_36: ( hoare_2091234717iple_a > $o ) > $o,F_10: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o,F_9: ( ( hoare_2091234717iple_a > $o ) > $o ) > hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( finite14499299le_a_o @ F_10 @ F_9 )
% 0.61/0.80 => ( ( finite1829014797le_a_o @ A_36 )
% 0.61/0.80 => ( ( A_36 != bot_bo1957696069_a_o_o )
% 0.61/0.80 => ( ! [X: hoare_2091234717iple_a > $o,Y_7: hoare_2091234717iple_a > $o] : ( member99268621le_a_o @ ( F_10 @ X @ Y_7 ) @ ( insert102003750le_a_o @ X @ ( insert102003750le_a_o @ Y_7 @ bot_bo1957696069_a_o_o ) ) )
% 0.61/0.80 => ( member99268621le_a_o @ ( F_9 @ A_36 ) @ A_36 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_770_folding__one_Oclosed,axiom,
% 0.61/0.80 ! [A_36: hoare_2091234717iple_a > $o,F_10: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,F_9: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
% 0.61/0.80 ( ( finite247037978iple_a @ F_10 @ F_9 )
% 0.61/0.80 => ( ( finite232261744iple_a @ A_36 )
% 0.61/0.80 => ( ( A_36 != bot_bo1791335050le_a_o )
% 0.61/0.80 => ( ! [X: hoare_2091234717iple_a,Y_7: hoare_2091234717iple_a] : ( member290856304iple_a @ ( F_10 @ X @ Y_7 ) @ ( insert1597628439iple_a @ X @ ( insert1597628439iple_a @ Y_7 @ bot_bo1791335050le_a_o ) ) )
% 0.61/0.80 => ( member290856304iple_a @ ( F_9 @ A_36 ) @ A_36 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_771_folding__one_Oclosed,axiom,
% 0.61/0.80 ! [A_36: hoare_1708887482_state > $o,F_10: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_9: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.61/0.80 ( ( finite1615457021_state @ F_10 @ F_9 )
% 0.61/0.80 => ( ( finite1625599783_state @ A_36 )
% 0.61/0.80 => ( ( A_36 != bot_bo19817387tate_o )
% 0.61/0.80 => ( ! [X: hoare_1708887482_state,Y_7: hoare_1708887482_state] : ( member451959335_state @ ( F_10 @ X @ Y_7 ) @ ( insert528405184_state @ X @ ( insert528405184_state @ Y_7 @ bot_bo19817387tate_o ) ) )
% 0.61/0.80 => ( member451959335_state @ ( F_9 @ A_36 ) @ A_36 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_772_folding__one_Oclosed,axiom,
% 0.61/0.80 ! [A_36: nat > $o,F_10: nat > nat > nat,F_9: ( nat > $o ) > nat] :
% 0.61/0.80 ( ( finite988810631ne_nat @ F_10 @ F_9 )
% 0.61/0.80 => ( ( finite_finite_nat @ A_36 )
% 0.61/0.80 => ( ( A_36 != bot_bot_nat_o )
% 0.61/0.80 => ( ! [X: nat,Y_7: nat] : ( member_nat @ ( F_10 @ X @ Y_7 ) @ ( insert_nat @ X @ ( insert_nat @ Y_7 @ bot_bot_nat_o ) ) )
% 0.61/0.80 => ( member_nat @ ( F_9 @ A_36 ) @ A_36 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_773_folding__one_Oclosed,axiom,
% 0.61/0.80 ! [A_36: pname > $o,F_10: pname > pname > pname,F_9: ( pname > $o ) > pname] :
% 0.61/0.80 ( ( finite1282449217_pname @ F_10 @ F_9 )
% 0.61/0.80 => ( ( finite_finite_pname @ A_36 )
% 0.61/0.80 => ( ( A_36 != bot_bot_pname_o )
% 0.61/0.80 => ( ! [X: pname,Y_7: pname] : ( member_pname @ ( F_10 @ X @ Y_7 ) @ ( insert_pname @ X @ ( insert_pname @ Y_7 @ bot_bot_pname_o ) ) )
% 0.61/0.80 => ( member_pname @ ( F_9 @ A_36 ) @ A_36 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_774_Set_Oset__insert,axiom,
% 0.61/0.80 ! [X_15: nat,A_35: nat > $o] :
% 0.61/0.80 ( ( member_nat @ X_15 @ A_35 )
% 0.61/0.80 => ~ ! [B_26: nat > $o] :
% 0.61/0.80 ( ( A_35
% 0.61/0.80 = ( insert_nat @ X_15 @ B_26 ) )
% 0.61/0.80 => ( member_nat @ X_15 @ B_26 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_775_Set_Oset__insert,axiom,
% 0.61/0.80 ! [X_15: hoare_2091234717iple_a > $o,A_35: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( member99268621le_a_o @ X_15 @ A_35 )
% 0.61/0.80 => ~ ! [B_26: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( A_35
% 0.61/0.80 = ( insert102003750le_a_o @ X_15 @ B_26 ) )
% 0.61/0.80 => ( member99268621le_a_o @ X_15 @ B_26 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_776_Set_Oset__insert,axiom,
% 0.61/0.80 ! [X_15: hoare_2091234717iple_a,A_35: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( member290856304iple_a @ X_15 @ A_35 )
% 0.61/0.80 => ~ ! [B_26: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( A_35
% 0.61/0.80 = ( insert1597628439iple_a @ X_15 @ B_26 ) )
% 0.61/0.80 => ( member290856304iple_a @ X_15 @ B_26 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_777_Set_Oset__insert,axiom,
% 0.61/0.80 ! [X_15: hoare_1708887482_state,A_35: hoare_1708887482_state > $o] :
% 0.61/0.80 ( ( member451959335_state @ X_15 @ A_35 )
% 0.61/0.80 => ~ ! [B_26: hoare_1708887482_state > $o] :
% 0.61/0.80 ( ( A_35
% 0.61/0.80 = ( insert528405184_state @ X_15 @ B_26 ) )
% 0.61/0.80 => ( member451959335_state @ X_15 @ B_26 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_778_Set_Oset__insert,axiom,
% 0.61/0.80 ! [X_15: pname,A_35: pname > $o] :
% 0.61/0.80 ( ( member_pname @ X_15 @ A_35 )
% 0.61/0.80 => ~ ! [B_26: pname > $o] :
% 0.61/0.80 ( ( A_35
% 0.61/0.80 = ( insert_pname @ X_15 @ B_26 ) )
% 0.61/0.80 => ( member_pname @ X_15 @ B_26 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_779_equals0I,axiom,
% 0.61/0.80 ! [A_34: nat > $o] :
% 0.61/0.80 ( ! [Y_7: nat] :
% 0.61/0.80 ~ ( member_nat @ Y_7 @ A_34 )
% 0.61/0.80 => ( A_34 = bot_bot_nat_o ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_780_equals0I,axiom,
% 0.61/0.80 ! [A_34: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ! [Y_7: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ~ ( member99268621le_a_o @ Y_7 @ A_34 )
% 0.61/0.80 => ( A_34 = bot_bo1957696069_a_o_o ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_781_equals0I,axiom,
% 0.61/0.80 ! [A_34: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ! [Y_7: hoare_2091234717iple_a] :
% 0.61/0.80 ~ ( member290856304iple_a @ Y_7 @ A_34 )
% 0.61/0.80 => ( A_34 = bot_bo1791335050le_a_o ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_782_equals0I,axiom,
% 0.61/0.80 ! [A_34: hoare_1708887482_state > $o] :
% 0.61/0.80 ( ! [Y_7: hoare_1708887482_state] :
% 0.61/0.80 ~ ( member451959335_state @ Y_7 @ A_34 )
% 0.61/0.80 => ( A_34 = bot_bo19817387tate_o ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_783_equals0I,axiom,
% 0.61/0.80 ! [A_34: pname > $o] :
% 0.61/0.80 ( ! [Y_7: pname] :
% 0.61/0.80 ~ ( member_pname @ Y_7 @ A_34 )
% 0.61/0.80 => ( A_34 = bot_bot_pname_o ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_784_Sup__fin_Ounion__idem,axiom,
% 0.61/0.80 ! [B_25: ( nat > $o ) > $o,A_33: ( nat > $o ) > $o] :
% 0.61/0.80 ( ( finite_finite_nat_o @ A_33 )
% 0.61/0.80 => ( ( A_33 != bot_bot_nat_o_o )
% 0.61/0.80 => ( ( finite_finite_nat_o @ B_25 )
% 0.61/0.80 => ( ( B_25 != bot_bot_nat_o_o )
% 0.61/0.80 => ( ( big_la1658356148_nat_o @ ( semila72246288at_o_o @ A_33 @ B_25 ) )
% 0.61/0.80 = ( semila848761471_nat_o @ ( big_la1658356148_nat_o @ A_33 ) @ ( big_la1658356148_nat_o @ B_25 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_785_Sup__fin_Ounion__idem,axiom,
% 0.61/0.80 ! [B_25: ( ( hoare_2091234717iple_a > $o ) > $o ) > $o,A_33: ( ( hoare_2091234717iple_a > $o ) > $o ) > $o] :
% 0.61/0.80 ( ( finite886417794_a_o_o @ A_33 )
% 0.61/0.80 => ( ( A_33 != bot_bo690906872_o_o_o )
% 0.61/0.80 => ( ( finite886417794_a_o_o @ B_25 )
% 0.61/0.80 => ( ( B_25 != bot_bo690906872_o_o_o )
% 0.61/0.80 => ( ( big_la1994307886_a_o_o @ ( semila484278426_o_o_o @ A_33 @ B_25 ) )
% 0.61/0.80 = ( semila2050116131_a_o_o @ ( big_la1994307886_a_o_o @ A_33 ) @ ( big_la1994307886_a_o_o @ B_25 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_786_Sup__fin_Ounion__idem,axiom,
% 0.61/0.80 ! [B_25: ( hoare_1708887482_state > $o ) > $o,A_33: ( hoare_1708887482_state > $o ) > $o] :
% 0.61/0.80 ( ( finite1329924456tate_o @ A_33 )
% 0.61/0.80 => ( ( A_33 != bot_bo1678742418te_o_o )
% 0.61/0.80 => ( ( finite1329924456tate_o @ B_25 )
% 0.61/0.80 => ( ( B_25 != bot_bo1678742418te_o_o )
% 0.61/0.80 => ( ( big_la1088302868tate_o @ ( semila1853742644te_o_o @ A_33 @ B_25 ) )
% 0.61/0.80 = ( semila1122118281tate_o @ ( big_la1088302868tate_o @ A_33 ) @ ( big_la1088302868tate_o @ B_25 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_787_Sup__fin_Ounion__idem,axiom,
% 0.61/0.80 ! [B_25: ( pname > $o ) > $o,A_33: ( pname > $o ) > $o] :
% 0.61/0.80 ( ( finite297249702name_o @ A_33 )
% 0.61/0.80 => ( ( A_33 != bot_bot_pname_o_o )
% 0.61/0.80 => ( ( finite297249702name_o @ B_25 )
% 0.61/0.80 => ( ( B_25 != bot_bot_pname_o_o )
% 0.61/0.80 => ( ( big_la1286884090name_o @ ( semila181081674me_o_o @ A_33 @ B_25 ) )
% 0.61/0.80 = ( semila1780557381name_o @ ( big_la1286884090name_o @ A_33 ) @ ( big_la1286884090name_o @ B_25 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_788_Sup__fin_Ounion__idem,axiom,
% 0.61/0.80 ! [B_25: $o > $o,A_33: $o > $o] :
% 0.61/0.80 ( ( finite_finite_o @ A_33 )
% 0.61/0.80 => ( ( A_33 != bot_bot_o_o )
% 0.61/0.80 => ( ( finite_finite_o @ B_25 )
% 0.61/0.80 => ( ( B_25 != bot_bot_o_o )
% 0.61/0.80 => ( ( big_la727467310_fin_o @ ( semila2062604954up_o_o @ A_33 @ B_25 ) )
% 0.61/0.80 <=> ( semila10642723_sup_o @ ( big_la727467310_fin_o @ A_33 ) @ ( big_la727467310_fin_o @ B_25 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_789_Sup__fin_Ounion__idem,axiom,
% 0.61/0.80 ! [B_25: ( hoare_2091234717iple_a > $o ) > $o,A_33: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( finite1829014797le_a_o @ A_33 )
% 0.61/0.80 => ( ( A_33 != bot_bo1957696069_a_o_o )
% 0.61/0.80 => ( ( finite1829014797le_a_o @ B_25 )
% 0.61/0.80 => ( ( B_25 != bot_bo1957696069_a_o_o )
% 0.61/0.80 => ( ( big_la735727201le_a_o @ ( semila2050116131_a_o_o @ A_33 @ B_25 ) )
% 0.61/0.80 = ( semila1052848428le_a_o @ ( big_la735727201le_a_o @ A_33 ) @ ( big_la735727201le_a_o @ B_25 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_790_Sup__fin_Ounion__idem,axiom,
% 0.61/0.80 ! [B_25: nat > $o,A_33: nat > $o] :
% 0.61/0.80 ( ( finite_finite_nat @ A_33 )
% 0.61/0.80 => ( ( A_33 != bot_bot_nat_o )
% 0.61/0.80 => ( ( finite_finite_nat @ B_25 )
% 0.61/0.80 => ( ( B_25 != bot_bot_nat_o )
% 0.61/0.80 => ( ( big_la43341705in_nat @ ( semila848761471_nat_o @ A_33 @ B_25 ) )
% 0.61/0.80 = ( semila972727038up_nat @ ( big_la43341705in_nat @ A_33 ) @ ( big_la43341705in_nat @ B_25 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_791_Sup__fin_Oinsert,axiom,
% 0.61/0.80 ! [X_14: nat > $o,A_32: ( nat > $o ) > $o] :
% 0.61/0.80 ( ( finite_finite_nat_o @ A_32 )
% 0.61/0.80 => ( ~ ( member_nat_o @ X_14 @ A_32 )
% 0.61/0.80 => ( ( A_32 != bot_bot_nat_o_o )
% 0.61/0.80 => ( ( big_la1658356148_nat_o @ ( insert_nat_o @ X_14 @ A_32 ) )
% 0.61/0.80 = ( semila848761471_nat_o @ X_14 @ ( big_la1658356148_nat_o @ A_32 ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_792_Sup__fin_Oinsert,axiom,
% 0.61/0.80 ! [X_14: ( hoare_2091234717iple_a > $o ) > $o,A_32: ( ( hoare_2091234717iple_a > $o ) > $o ) > $o] :
% 0.61/0.80 ( ( finite886417794_a_o_o @ A_32 )
% 0.61/0.80 => ( ~ ( member1297825410_a_o_o @ X_14 @ A_32 )
% 0.61/0.80 => ( ( A_32 != bot_bo690906872_o_o_o )
% 0.61/0.80 => ( ( big_la1994307886_a_o_o @ ( insert987231145_a_o_o @ X_14 @ A_32 ) )
% 0.61/0.80 = ( semila2050116131_a_o_o @ X_14 @ ( big_la1994307886_a_o_o @ A_32 ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_793_Sup__fin_Oinsert,axiom,
% 0.61/0.80 ! [X_14: hoare_1708887482_state > $o,A_32: ( hoare_1708887482_state > $o ) > $o] :
% 0.61/0.80 ( ( finite1329924456tate_o @ A_32 )
% 0.61/0.80 => ( ~ ( member814030440tate_o @ X_14 @ A_32 )
% 0.61/0.80 => ( ( A_32 != bot_bo1678742418te_o_o )
% 0.61/0.80 => ( ( big_la1088302868tate_o @ ( insert949073679tate_o @ X_14 @ A_32 ) )
% 0.61/0.80 = ( semila1122118281tate_o @ X_14 @ ( big_la1088302868tate_o @ A_32 ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_794_Sup__fin_Oinsert,axiom,
% 0.61/0.80 ! [X_14: pname > $o,A_32: ( pname > $o ) > $o] :
% 0.61/0.80 ( ( finite297249702name_o @ A_32 )
% 0.61/0.80 => ( ~ ( member_pname_o @ X_14 @ A_32 )
% 0.61/0.80 => ( ( A_32 != bot_bot_pname_o_o )
% 0.61/0.80 => ( ( big_la1286884090name_o @ ( insert_pname_o @ X_14 @ A_32 ) )
% 0.61/0.80 = ( semila1780557381name_o @ X_14 @ ( big_la1286884090name_o @ A_32 ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_795_Sup__fin_Oinsert,axiom,
% 0.61/0.80 ! [X_14: $o,A_32: $o > $o] :
% 0.61/0.80 ( ( finite_finite_o @ A_32 )
% 0.61/0.80 => ( ~ ( member_o @ X_14 @ A_32 )
% 0.61/0.80 => ( ( A_32 != bot_bot_o_o )
% 0.61/0.80 => ( ( big_la727467310_fin_o @ ( insert_o @ X_14 @ A_32 ) )
% 0.61/0.80 <=> ( semila10642723_sup_o @ X_14 @ ( big_la727467310_fin_o @ A_32 ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_796_Sup__fin_Oinsert,axiom,
% 0.61/0.80 ! [X_14: hoare_2091234717iple_a > $o,A_32: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( finite1829014797le_a_o @ A_32 )
% 0.61/0.80 => ( ~ ( member99268621le_a_o @ X_14 @ A_32 )
% 0.61/0.80 => ( ( A_32 != bot_bo1957696069_a_o_o )
% 0.61/0.80 => ( ( big_la735727201le_a_o @ ( insert102003750le_a_o @ X_14 @ A_32 ) )
% 0.61/0.80 = ( semila1052848428le_a_o @ X_14 @ ( big_la735727201le_a_o @ A_32 ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_797_Sup__fin_Oinsert,axiom,
% 0.61/0.80 ! [X_14: nat,A_32: nat > $o] :
% 0.61/0.80 ( ( finite_finite_nat @ A_32 )
% 0.61/0.80 => ( ~ ( member_nat @ X_14 @ A_32 )
% 0.61/0.80 => ( ( A_32 != bot_bot_nat_o )
% 0.61/0.80 => ( ( big_la43341705in_nat @ ( insert_nat @ X_14 @ A_32 ) )
% 0.61/0.80 = ( semila972727038up_nat @ X_14 @ ( big_la43341705in_nat @ A_32 ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_798_Sup__fin_Oinsert__idem,axiom,
% 0.61/0.80 ! [X_13: nat > $o,A_31: ( nat > $o ) > $o] :
% 0.61/0.80 ( ( finite_finite_nat_o @ A_31 )
% 0.61/0.80 => ( ( A_31 != bot_bot_nat_o_o )
% 0.61/0.80 => ( ( big_la1658356148_nat_o @ ( insert_nat_o @ X_13 @ A_31 ) )
% 0.61/0.80 = ( semila848761471_nat_o @ X_13 @ ( big_la1658356148_nat_o @ A_31 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_799_Sup__fin_Oinsert__idem,axiom,
% 0.61/0.80 ! [X_13: ( hoare_2091234717iple_a > $o ) > $o,A_31: ( ( hoare_2091234717iple_a > $o ) > $o ) > $o] :
% 0.61/0.80 ( ( finite886417794_a_o_o @ A_31 )
% 0.61/0.80 => ( ( A_31 != bot_bo690906872_o_o_o )
% 0.61/0.80 => ( ( big_la1994307886_a_o_o @ ( insert987231145_a_o_o @ X_13 @ A_31 ) )
% 0.61/0.80 = ( semila2050116131_a_o_o @ X_13 @ ( big_la1994307886_a_o_o @ A_31 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_800_Sup__fin_Oinsert__idem,axiom,
% 0.61/0.80 ! [X_13: hoare_1708887482_state > $o,A_31: ( hoare_1708887482_state > $o ) > $o] :
% 0.61/0.80 ( ( finite1329924456tate_o @ A_31 )
% 0.61/0.80 => ( ( A_31 != bot_bo1678742418te_o_o )
% 0.61/0.80 => ( ( big_la1088302868tate_o @ ( insert949073679tate_o @ X_13 @ A_31 ) )
% 0.61/0.80 = ( semila1122118281tate_o @ X_13 @ ( big_la1088302868tate_o @ A_31 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_801_Sup__fin_Oinsert__idem,axiom,
% 0.61/0.80 ! [X_13: pname > $o,A_31: ( pname > $o ) > $o] :
% 0.61/0.80 ( ( finite297249702name_o @ A_31 )
% 0.61/0.80 => ( ( A_31 != bot_bot_pname_o_o )
% 0.61/0.80 => ( ( big_la1286884090name_o @ ( insert_pname_o @ X_13 @ A_31 ) )
% 0.61/0.80 = ( semila1780557381name_o @ X_13 @ ( big_la1286884090name_o @ A_31 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_802_Sup__fin_Oinsert__idem,axiom,
% 0.61/0.80 ! [X_13: $o,A_31: $o > $o] :
% 0.61/0.80 ( ( finite_finite_o @ A_31 )
% 0.61/0.80 => ( ( A_31 != bot_bot_o_o )
% 0.61/0.80 => ( ( big_la727467310_fin_o @ ( insert_o @ X_13 @ A_31 ) )
% 0.61/0.80 <=> ( semila10642723_sup_o @ X_13 @ ( big_la727467310_fin_o @ A_31 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_803_Sup__fin_Oinsert__idem,axiom,
% 0.61/0.80 ! [X_13: hoare_2091234717iple_a > $o,A_31: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( finite1829014797le_a_o @ A_31 )
% 0.61/0.80 => ( ( A_31 != bot_bo1957696069_a_o_o )
% 0.61/0.80 => ( ( big_la735727201le_a_o @ ( insert102003750le_a_o @ X_13 @ A_31 ) )
% 0.61/0.80 = ( semila1052848428le_a_o @ X_13 @ ( big_la735727201le_a_o @ A_31 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_804_Sup__fin_Oinsert__idem,axiom,
% 0.61/0.80 ! [X_13: nat,A_31: nat > $o] :
% 0.61/0.80 ( ( finite_finite_nat @ A_31 )
% 0.61/0.80 => ( ( A_31 != bot_bot_nat_o )
% 0.61/0.80 => ( ( big_la43341705in_nat @ ( insert_nat @ X_13 @ A_31 ) )
% 0.61/0.80 = ( semila972727038up_nat @ X_13 @ ( big_la43341705in_nat @ A_31 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_805_folding__one_Ounion__disjoint,axiom,
% 0.61/0.80 ! [B_24: ( hoare_2091234717iple_a > $o ) > $o,A_30: ( hoare_2091234717iple_a > $o ) > $o,F_8: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o,F_7: ( ( hoare_2091234717iple_a > $o ) > $o ) > hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( finite14499299le_a_o @ F_8 @ F_7 )
% 0.61/0.80 => ( ( finite1829014797le_a_o @ A_30 )
% 0.61/0.80 => ( ( A_30 != bot_bo1957696069_a_o_o )
% 0.61/0.80 => ( ( finite1829014797le_a_o @ B_24 )
% 0.61/0.80 => ( ( B_24 != bot_bo1957696069_a_o_o )
% 0.61/0.80 => ( ( ( semila1672913213_a_o_o @ A_30 @ B_24 )
% 0.61/0.80 = bot_bo1957696069_a_o_o )
% 0.61/0.80 => ( ( F_7 @ ( semila2050116131_a_o_o @ A_30 @ B_24 ) )
% 0.61/0.80 = ( F_8 @ ( F_7 @ A_30 ) @ ( F_7 @ B_24 ) ) ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_806_folding__one_Ounion__disjoint,axiom,
% 0.61/0.80 ! [B_24: pname > $o,A_30: pname > $o,F_8: pname > pname > pname,F_7: ( pname > $o ) > pname] :
% 0.61/0.80 ( ( finite1282449217_pname @ F_8 @ F_7 )
% 0.61/0.80 => ( ( finite_finite_pname @ A_30 )
% 0.61/0.80 => ( ( A_30 != bot_bot_pname_o )
% 0.61/0.80 => ( ( finite_finite_pname @ B_24 )
% 0.61/0.80 => ( ( B_24 != bot_bot_pname_o )
% 0.61/0.80 => ( ( ( semila1673364395name_o @ A_30 @ B_24 )
% 0.61/0.80 = bot_bot_pname_o )
% 0.61/0.80 => ( ( F_7 @ ( semila1780557381name_o @ A_30 @ B_24 ) )
% 0.61/0.80 = ( F_8 @ ( F_7 @ A_30 ) @ ( F_7 @ B_24 ) ) ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_807_folding__one_Ounion__disjoint,axiom,
% 0.61/0.80 ! [B_24: hoare_1708887482_state > $o,A_30: hoare_1708887482_state > $o,F_8: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_7: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.61/0.80 ( ( finite1615457021_state @ F_8 @ F_7 )
% 0.61/0.80 => ( ( finite1625599783_state @ A_30 )
% 0.61/0.80 => ( ( A_30 != bot_bo19817387tate_o )
% 0.61/0.80 => ( ( finite1625599783_state @ B_24 )
% 0.61/0.80 => ( ( B_24 != bot_bo19817387tate_o )
% 0.61/0.80 => ( ( ( semila129691299tate_o @ A_30 @ B_24 )
% 0.61/0.80 = bot_bo19817387tate_o )
% 0.61/0.80 => ( ( F_7 @ ( semila1122118281tate_o @ A_30 @ B_24 ) )
% 0.61/0.80 = ( F_8 @ ( F_7 @ A_30 ) @ ( F_7 @ B_24 ) ) ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_808_folding__one_Ounion__disjoint,axiom,
% 0.61/0.80 ! [B_24: hoare_2091234717iple_a > $o,A_30: hoare_2091234717iple_a > $o,F_8: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,F_7: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
% 0.61/0.80 ( ( finite247037978iple_a @ F_8 @ F_7 )
% 0.61/0.80 => ( ( finite232261744iple_a @ A_30 )
% 0.61/0.80 => ( ( A_30 != bot_bo1791335050le_a_o )
% 0.61/0.80 => ( ( finite232261744iple_a @ B_24 )
% 0.61/0.80 => ( ( B_24 != bot_bo1791335050le_a_o )
% 0.61/0.80 => ( ( ( semila2006181266le_a_o @ A_30 @ B_24 )
% 0.61/0.80 = bot_bo1791335050le_a_o )
% 0.61/0.80 => ( ( F_7 @ ( semila1052848428le_a_o @ A_30 @ B_24 ) )
% 0.61/0.80 = ( F_8 @ ( F_7 @ A_30 ) @ ( F_7 @ B_24 ) ) ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_809_folding__one_Ounion__disjoint,axiom,
% 0.61/0.80 ! [B_24: nat > $o,A_30: nat > $o,F_8: nat > nat > nat,F_7: ( nat > $o ) > nat] :
% 0.61/0.80 ( ( finite988810631ne_nat @ F_8 @ F_7 )
% 0.61/0.80 => ( ( finite_finite_nat @ A_30 )
% 0.61/0.80 => ( ( A_30 != bot_bot_nat_o )
% 0.61/0.80 => ( ( finite_finite_nat @ B_24 )
% 0.61/0.80 => ( ( B_24 != bot_bot_nat_o )
% 0.61/0.80 => ( ( ( semila1947288293_nat_o @ A_30 @ B_24 )
% 0.61/0.80 = bot_bot_nat_o )
% 0.61/0.80 => ( ( F_7 @ ( semila848761471_nat_o @ A_30 @ B_24 ) )
% 0.61/0.80 = ( F_8 @ ( F_7 @ A_30 ) @ ( F_7 @ B_24 ) ) ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_810_folding__one_Ounion__inter,axiom,
% 0.61/0.80 ! [B_23: ( hoare_2091234717iple_a > $o ) > $o,A_29: ( hoare_2091234717iple_a > $o ) > $o,F_6: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o,F_5: ( ( hoare_2091234717iple_a > $o ) > $o ) > hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( finite14499299le_a_o @ F_6 @ F_5 )
% 0.61/0.80 => ( ( finite1829014797le_a_o @ A_29 )
% 0.61/0.80 => ( ( finite1829014797le_a_o @ B_23 )
% 0.61/0.80 => ( ( ( semila1672913213_a_o_o @ A_29 @ B_23 )
% 0.61/0.80 != bot_bo1957696069_a_o_o )
% 0.61/0.80 => ( ( F_6 @ ( F_5 @ ( semila2050116131_a_o_o @ A_29 @ B_23 ) ) @ ( F_5 @ ( semila1672913213_a_o_o @ A_29 @ B_23 ) ) )
% 0.61/0.80 = ( F_6 @ ( F_5 @ A_29 ) @ ( F_5 @ B_23 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_811_folding__one_Ounion__inter,axiom,
% 0.61/0.80 ! [B_23: pname > $o,A_29: pname > $o,F_6: pname > pname > pname,F_5: ( pname > $o ) > pname] :
% 0.61/0.80 ( ( finite1282449217_pname @ F_6 @ F_5 )
% 0.61/0.80 => ( ( finite_finite_pname @ A_29 )
% 0.61/0.80 => ( ( finite_finite_pname @ B_23 )
% 0.61/0.80 => ( ( ( semila1673364395name_o @ A_29 @ B_23 )
% 0.61/0.80 != bot_bot_pname_o )
% 0.61/0.80 => ( ( F_6 @ ( F_5 @ ( semila1780557381name_o @ A_29 @ B_23 ) ) @ ( F_5 @ ( semila1673364395name_o @ A_29 @ B_23 ) ) )
% 0.61/0.80 = ( F_6 @ ( F_5 @ A_29 ) @ ( F_5 @ B_23 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_812_folding__one_Ounion__inter,axiom,
% 0.61/0.80 ! [B_23: hoare_1708887482_state > $o,A_29: hoare_1708887482_state > $o,F_6: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_5: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.61/0.80 ( ( finite1615457021_state @ F_6 @ F_5 )
% 0.61/0.80 => ( ( finite1625599783_state @ A_29 )
% 0.61/0.80 => ( ( finite1625599783_state @ B_23 )
% 0.61/0.80 => ( ( ( semila129691299tate_o @ A_29 @ B_23 )
% 0.61/0.80 != bot_bo19817387tate_o )
% 0.61/0.80 => ( ( F_6 @ ( F_5 @ ( semila1122118281tate_o @ A_29 @ B_23 ) ) @ ( F_5 @ ( semila129691299tate_o @ A_29 @ B_23 ) ) )
% 0.61/0.80 = ( F_6 @ ( F_5 @ A_29 ) @ ( F_5 @ B_23 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_813_folding__one_Ounion__inter,axiom,
% 0.61/0.80 ! [B_23: hoare_2091234717iple_a > $o,A_29: hoare_2091234717iple_a > $o,F_6: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,F_5: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
% 0.61/0.80 ( ( finite247037978iple_a @ F_6 @ F_5 )
% 0.61/0.80 => ( ( finite232261744iple_a @ A_29 )
% 0.61/0.80 => ( ( finite232261744iple_a @ B_23 )
% 0.61/0.80 => ( ( ( semila2006181266le_a_o @ A_29 @ B_23 )
% 0.61/0.80 != bot_bo1791335050le_a_o )
% 0.61/0.80 => ( ( F_6 @ ( F_5 @ ( semila1052848428le_a_o @ A_29 @ B_23 ) ) @ ( F_5 @ ( semila2006181266le_a_o @ A_29 @ B_23 ) ) )
% 0.61/0.80 = ( F_6 @ ( F_5 @ A_29 ) @ ( F_5 @ B_23 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_814_folding__one_Ounion__inter,axiom,
% 0.61/0.80 ! [B_23: nat > $o,A_29: nat > $o,F_6: nat > nat > nat,F_5: ( nat > $o ) > nat] :
% 0.61/0.80 ( ( finite988810631ne_nat @ F_6 @ F_5 )
% 0.61/0.80 => ( ( finite_finite_nat @ A_29 )
% 0.61/0.80 => ( ( finite_finite_nat @ B_23 )
% 0.61/0.80 => ( ( ( semila1947288293_nat_o @ A_29 @ B_23 )
% 0.61/0.80 != bot_bot_nat_o )
% 0.61/0.80 => ( ( F_6 @ ( F_5 @ ( semila848761471_nat_o @ A_29 @ B_23 ) ) @ ( F_5 @ ( semila1947288293_nat_o @ A_29 @ B_23 ) ) )
% 0.61/0.80 = ( F_6 @ ( F_5 @ A_29 ) @ ( F_5 @ B_23 ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_815_folding__one_Oinsert__remove,axiom,
% 0.61/0.80 ! [X_12: hoare_2091234717iple_a > $o,A_28: ( hoare_2091234717iple_a > $o ) > $o,F_4: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o,F_3: ( ( hoare_2091234717iple_a > $o ) > $o ) > hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( finite14499299le_a_o @ F_4 @ F_3 )
% 0.61/0.80 => ( ( finite1829014797le_a_o @ A_28 )
% 0.61/0.80 => ( ( ( ( minus_1746272704_a_o_o @ A_28 @ ( insert102003750le_a_o @ X_12 @ bot_bo1957696069_a_o_o ) )
% 0.61/0.80 = bot_bo1957696069_a_o_o )
% 0.61/0.80 => ( ( F_3 @ ( insert102003750le_a_o @ X_12 @ A_28 ) )
% 0.61/0.80 = X_12 ) )
% 0.61/0.80 & ( ( ( minus_1746272704_a_o_o @ A_28 @ ( insert102003750le_a_o @ X_12 @ bot_bo1957696069_a_o_o ) )
% 0.61/0.80 != bot_bo1957696069_a_o_o )
% 0.61/0.80 => ( ( F_3 @ ( insert102003750le_a_o @ X_12 @ A_28 ) )
% 0.61/0.80 = ( F_4 @ X_12 @ ( F_3 @ ( minus_1746272704_a_o_o @ A_28 @ ( insert102003750le_a_o @ X_12 @ bot_bo1957696069_a_o_o ) ) ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_816_folding__one_Oinsert__remove,axiom,
% 0.61/0.80 ! [X_12: pname,A_28: pname > $o,F_4: pname > pname > pname,F_3: ( pname > $o ) > pname] :
% 0.61/0.80 ( ( finite1282449217_pname @ F_4 @ F_3 )
% 0.61/0.80 => ( ( finite_finite_pname @ A_28 )
% 0.61/0.80 => ( ( ( ( minus_minus_pname_o @ A_28 @ ( insert_pname @ X_12 @ bot_bot_pname_o ) )
% 0.61/0.80 = bot_bot_pname_o )
% 0.61/0.80 => ( ( F_3 @ ( insert_pname @ X_12 @ A_28 ) )
% 0.61/0.80 = X_12 ) )
% 0.61/0.80 & ( ( ( minus_minus_pname_o @ A_28 @ ( insert_pname @ X_12 @ bot_bot_pname_o ) )
% 0.61/0.80 != bot_bot_pname_o )
% 0.61/0.80 => ( ( F_3 @ ( insert_pname @ X_12 @ A_28 ) )
% 0.61/0.80 = ( F_4 @ X_12 @ ( F_3 @ ( minus_minus_pname_o @ A_28 @ ( insert_pname @ X_12 @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_817_folding__one_Oinsert__remove,axiom,
% 0.61/0.80 ! [X_12: hoare_2091234717iple_a,A_28: hoare_2091234717iple_a > $o,F_4: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,F_3: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
% 0.61/0.80 ( ( finite247037978iple_a @ F_4 @ F_3 )
% 0.61/0.80 => ( ( finite232261744iple_a @ A_28 )
% 0.61/0.80 => ( ( ( ( minus_836160335le_a_o @ A_28 @ ( insert1597628439iple_a @ X_12 @ bot_bo1791335050le_a_o ) )
% 0.61/0.80 = bot_bo1791335050le_a_o )
% 0.61/0.80 => ( ( F_3 @ ( insert1597628439iple_a @ X_12 @ A_28 ) )
% 0.61/0.80 = X_12 ) )
% 0.61/0.80 & ( ( ( minus_836160335le_a_o @ A_28 @ ( insert1597628439iple_a @ X_12 @ bot_bo1791335050le_a_o ) )
% 0.61/0.80 != bot_bo1791335050le_a_o )
% 0.61/0.80 => ( ( F_3 @ ( insert1597628439iple_a @ X_12 @ A_28 ) )
% 0.61/0.80 = ( F_4 @ X_12 @ ( F_3 @ ( minus_836160335le_a_o @ A_28 @ ( insert1597628439iple_a @ X_12 @ bot_bo1791335050le_a_o ) ) ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_818_folding__one_Oinsert__remove,axiom,
% 0.61/0.80 ! [X_12: hoare_1708887482_state,A_28: hoare_1708887482_state > $o,F_4: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_3: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.61/0.80 ( ( finite1615457021_state @ F_4 @ F_3 )
% 0.61/0.80 => ( ( finite1625599783_state @ A_28 )
% 0.61/0.80 => ( ( ( ( minus_2056855718tate_o @ A_28 @ ( insert528405184_state @ X_12 @ bot_bo19817387tate_o ) )
% 0.61/0.80 = bot_bo19817387tate_o )
% 0.61/0.80 => ( ( F_3 @ ( insert528405184_state @ X_12 @ A_28 ) )
% 0.61/0.80 = X_12 ) )
% 0.61/0.80 & ( ( ( minus_2056855718tate_o @ A_28 @ ( insert528405184_state @ X_12 @ bot_bo19817387tate_o ) )
% 0.61/0.80 != bot_bo19817387tate_o )
% 0.61/0.80 => ( ( F_3 @ ( insert528405184_state @ X_12 @ A_28 ) )
% 0.61/0.80 = ( F_4 @ X_12 @ ( F_3 @ ( minus_2056855718tate_o @ A_28 @ ( insert528405184_state @ X_12 @ bot_bo19817387tate_o ) ) ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_819_folding__one_Oinsert__remove,axiom,
% 0.61/0.80 ! [X_12: nat,A_28: nat > $o,F_4: nat > nat > nat,F_3: ( nat > $o ) > nat] :
% 0.61/0.80 ( ( finite988810631ne_nat @ F_4 @ F_3 )
% 0.61/0.80 => ( ( finite_finite_nat @ A_28 )
% 0.61/0.80 => ( ( ( ( minus_minus_nat_o @ A_28 @ ( insert_nat @ X_12 @ bot_bot_nat_o ) )
% 0.61/0.80 = bot_bot_nat_o )
% 0.61/0.80 => ( ( F_3 @ ( insert_nat @ X_12 @ A_28 ) )
% 0.61/0.80 = X_12 ) )
% 0.61/0.80 & ( ( ( minus_minus_nat_o @ A_28 @ ( insert_nat @ X_12 @ bot_bot_nat_o ) )
% 0.61/0.80 != bot_bot_nat_o )
% 0.61/0.80 => ( ( F_3 @ ( insert_nat @ X_12 @ A_28 ) )
% 0.61/0.80 = ( F_4 @ X_12 @ ( F_3 @ ( minus_minus_nat_o @ A_28 @ ( insert_nat @ X_12 @ bot_bot_nat_o ) ) ) ) ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_820_inf1I,axiom,
% 0.61/0.80 ! [B_22: nat > $o,A_27: nat > $o,X_11: nat] :
% 0.61/0.80 ( ( A_27 @ X_11 )
% 0.61/0.80 => ( ( B_22 @ X_11 )
% 0.61/0.80 => ( semila1947288293_nat_o @ A_27 @ B_22 @ X_11 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_821_inf1I,axiom,
% 0.61/0.80 ! [B_22: hoare_2091234717iple_a > $o,A_27: hoare_2091234717iple_a > $o,X_11: hoare_2091234717iple_a] :
% 0.61/0.80 ( ( A_27 @ X_11 )
% 0.61/0.80 => ( ( B_22 @ X_11 )
% 0.61/0.80 => ( semila2006181266le_a_o @ A_27 @ B_22 @ X_11 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_822_inf1I,axiom,
% 0.61/0.80 ! [B_22: pname > $o,A_27: pname > $o,X_11: pname] :
% 0.61/0.80 ( ( A_27 @ X_11 )
% 0.61/0.80 => ( ( B_22 @ X_11 )
% 0.61/0.80 => ( semila1673364395name_o @ A_27 @ B_22 @ X_11 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_823_IntI,axiom,
% 0.61/0.80 ! [B_21: nat > $o,C_11: nat,A_26: nat > $o] :
% 0.61/0.80 ( ( member_nat @ C_11 @ A_26 )
% 0.61/0.80 => ( ( member_nat @ C_11 @ B_21 )
% 0.61/0.80 => ( member_nat @ C_11 @ ( semila1947288293_nat_o @ A_26 @ B_21 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_824_IntI,axiom,
% 0.61/0.80 ! [B_21: ( hoare_2091234717iple_a > $o ) > $o,C_11: hoare_2091234717iple_a > $o,A_26: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( member99268621le_a_o @ C_11 @ A_26 )
% 0.61/0.80 => ( ( member99268621le_a_o @ C_11 @ B_21 )
% 0.61/0.80 => ( member99268621le_a_o @ C_11 @ ( semila1672913213_a_o_o @ A_26 @ B_21 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_825_IntI,axiom,
% 0.61/0.80 ! [B_21: hoare_2091234717iple_a > $o,C_11: hoare_2091234717iple_a,A_26: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( member290856304iple_a @ C_11 @ A_26 )
% 0.61/0.80 => ( ( member290856304iple_a @ C_11 @ B_21 )
% 0.61/0.80 => ( member290856304iple_a @ C_11 @ ( semila2006181266le_a_o @ A_26 @ B_21 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_826_IntI,axiom,
% 0.61/0.80 ! [B_21: pname > $o,C_11: pname,A_26: pname > $o] :
% 0.61/0.80 ( ( member_pname @ C_11 @ A_26 )
% 0.61/0.80 => ( ( member_pname @ C_11 @ B_21 )
% 0.61/0.80 => ( member_pname @ C_11 @ ( semila1673364395name_o @ A_26 @ B_21 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_827_IntE,axiom,
% 0.61/0.80 ! [C_10: nat,A_25: nat > $o,B_20: nat > $o] :
% 0.61/0.80 ( ( member_nat @ C_10 @ ( semila1947288293_nat_o @ A_25 @ B_20 ) )
% 0.61/0.80 => ~ ( ( member_nat @ C_10 @ A_25 )
% 0.61/0.80 => ~ ( member_nat @ C_10 @ B_20 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_828_IntE,axiom,
% 0.61/0.80 ! [C_10: hoare_2091234717iple_a > $o,A_25: ( hoare_2091234717iple_a > $o ) > $o,B_20: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( member99268621le_a_o @ C_10 @ ( semila1672913213_a_o_o @ A_25 @ B_20 ) )
% 0.61/0.80 => ~ ( ( member99268621le_a_o @ C_10 @ A_25 )
% 0.61/0.80 => ~ ( member99268621le_a_o @ C_10 @ B_20 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_829_IntE,axiom,
% 0.61/0.80 ! [C_10: hoare_2091234717iple_a,A_25: hoare_2091234717iple_a > $o,B_20: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( member290856304iple_a @ C_10 @ ( semila2006181266le_a_o @ A_25 @ B_20 ) )
% 0.61/0.80 => ~ ( ( member290856304iple_a @ C_10 @ A_25 )
% 0.61/0.80 => ~ ( member290856304iple_a @ C_10 @ B_20 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_830_IntE,axiom,
% 0.61/0.80 ! [C_10: pname,A_25: pname > $o,B_20: pname > $o] :
% 0.61/0.80 ( ( member_pname @ C_10 @ ( semila1673364395name_o @ A_25 @ B_20 ) )
% 0.61/0.80 => ~ ( ( member_pname @ C_10 @ A_25 )
% 0.61/0.80 => ~ ( member_pname @ C_10 @ B_20 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_831_inf1E,axiom,
% 0.61/0.80 ! [A_24: nat > $o,B_19: nat > $o,X_10: nat] :
% 0.61/0.80 ( ( semila1947288293_nat_o @ A_24 @ B_19 @ X_10 )
% 0.61/0.80 => ~ ( ( A_24 @ X_10 )
% 0.61/0.80 => ~ ( B_19 @ X_10 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_832_inf1E,axiom,
% 0.61/0.80 ! [A_24: hoare_2091234717iple_a > $o,B_19: hoare_2091234717iple_a > $o,X_10: hoare_2091234717iple_a] :
% 0.61/0.80 ( ( semila2006181266le_a_o @ A_24 @ B_19 @ X_10 )
% 0.61/0.80 => ~ ( ( A_24 @ X_10 )
% 0.61/0.80 => ~ ( B_19 @ X_10 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_833_inf1E,axiom,
% 0.61/0.80 ! [A_24: pname > $o,B_19: pname > $o,X_10: pname] :
% 0.61/0.80 ( ( semila1673364395name_o @ A_24 @ B_19 @ X_10 )
% 0.61/0.80 => ~ ( ( A_24 @ X_10 )
% 0.61/0.80 => ~ ( B_19 @ X_10 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_834_DiffI,axiom,
% 0.61/0.80 ! [B_18: nat > $o,C_9: nat,A_23: nat > $o] :
% 0.61/0.80 ( ( member_nat @ C_9 @ A_23 )
% 0.61/0.80 => ( ~ ( member_nat @ C_9 @ B_18 )
% 0.61/0.80 => ( member_nat @ C_9 @ ( minus_minus_nat_o @ A_23 @ B_18 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_835_DiffI,axiom,
% 0.61/0.80 ! [B_18: ( hoare_2091234717iple_a > $o ) > $o,C_9: hoare_2091234717iple_a > $o,A_23: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( member99268621le_a_o @ C_9 @ A_23 )
% 0.61/0.80 => ( ~ ( member99268621le_a_o @ C_9 @ B_18 )
% 0.61/0.80 => ( member99268621le_a_o @ C_9 @ ( minus_1746272704_a_o_o @ A_23 @ B_18 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_836_DiffI,axiom,
% 0.61/0.80 ! [B_18: hoare_2091234717iple_a > $o,C_9: hoare_2091234717iple_a,A_23: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( member290856304iple_a @ C_9 @ A_23 )
% 0.61/0.80 => ( ~ ( member290856304iple_a @ C_9 @ B_18 )
% 0.61/0.80 => ( member290856304iple_a @ C_9 @ ( minus_836160335le_a_o @ A_23 @ B_18 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_837_DiffI,axiom,
% 0.61/0.80 ! [B_18: pname > $o,C_9: pname,A_23: pname > $o] :
% 0.61/0.80 ( ( member_pname @ C_9 @ A_23 )
% 0.61/0.80 => ( ~ ( member_pname @ C_9 @ B_18 )
% 0.61/0.80 => ( member_pname @ C_9 @ ( minus_minus_pname_o @ A_23 @ B_18 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_838_DiffE,axiom,
% 0.61/0.80 ! [C_8: nat,A_22: nat > $o,B_17: nat > $o] :
% 0.61/0.80 ( ( member_nat @ C_8 @ ( minus_minus_nat_o @ A_22 @ B_17 ) )
% 0.61/0.80 => ~ ( ( member_nat @ C_8 @ A_22 )
% 0.61/0.80 => ( member_nat @ C_8 @ B_17 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_839_DiffE,axiom,
% 0.61/0.80 ! [C_8: hoare_2091234717iple_a > $o,A_22: ( hoare_2091234717iple_a > $o ) > $o,B_17: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( member99268621le_a_o @ C_8 @ ( minus_1746272704_a_o_o @ A_22 @ B_17 ) )
% 0.61/0.80 => ~ ( ( member99268621le_a_o @ C_8 @ A_22 )
% 0.61/0.80 => ( member99268621le_a_o @ C_8 @ B_17 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_840_DiffE,axiom,
% 0.61/0.80 ! [C_8: hoare_2091234717iple_a,A_22: hoare_2091234717iple_a > $o,B_17: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( member290856304iple_a @ C_8 @ ( minus_836160335le_a_o @ A_22 @ B_17 ) )
% 0.61/0.80 => ~ ( ( member290856304iple_a @ C_8 @ A_22 )
% 0.61/0.80 => ( member290856304iple_a @ C_8 @ B_17 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_841_DiffE,axiom,
% 0.61/0.80 ! [C_8: pname,A_22: pname > $o,B_17: pname > $o] :
% 0.61/0.80 ( ( member_pname @ C_8 @ ( minus_minus_pname_o @ A_22 @ B_17 ) )
% 0.61/0.80 => ~ ( ( member_pname @ C_8 @ A_22 )
% 0.61/0.80 => ( member_pname @ C_8 @ B_17 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_842_finite__Int,axiom,
% 0.61/0.80 ! [G_1: hoare_2091234717iple_a > $o,F_2: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( ( finite232261744iple_a @ F_2 )
% 0.61/0.80 | ( finite232261744iple_a @ G_1 ) )
% 0.61/0.80 => ( finite232261744iple_a @ ( semila2006181266le_a_o @ F_2 @ G_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_843_finite__Int,axiom,
% 0.61/0.80 ! [G_1: ( hoare_2091234717iple_a > $o ) > $o,F_2: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( ( finite1829014797le_a_o @ F_2 )
% 0.61/0.80 | ( finite1829014797le_a_o @ G_1 ) )
% 0.61/0.80 => ( finite1829014797le_a_o @ ( semila1672913213_a_o_o @ F_2 @ G_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_844_finite__Int,axiom,
% 0.61/0.80 ! [G_1: pname > $o,F_2: pname > $o] :
% 0.61/0.80 ( ( ( finite_finite_pname @ F_2 )
% 0.61/0.80 | ( finite_finite_pname @ G_1 ) )
% 0.61/0.80 => ( finite_finite_pname @ ( semila1673364395name_o @ F_2 @ G_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_845_finite__Int,axiom,
% 0.61/0.80 ! [G_1: nat > $o,F_2: nat > $o] :
% 0.61/0.80 ( ( ( finite_finite_nat @ F_2 )
% 0.61/0.80 | ( finite_finite_nat @ G_1 ) )
% 0.61/0.80 => ( finite_finite_nat @ ( semila1947288293_nat_o @ F_2 @ G_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_846_finite__Diff,axiom,
% 0.61/0.80 ! [B_16: hoare_2091234717iple_a > $o,A_21: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( finite232261744iple_a @ A_21 )
% 0.61/0.80 => ( finite232261744iple_a @ ( minus_836160335le_a_o @ A_21 @ B_16 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_847_finite__Diff,axiom,
% 0.61/0.80 ! [B_16: ( hoare_2091234717iple_a > $o ) > $o,A_21: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( finite1829014797le_a_o @ A_21 )
% 0.61/0.80 => ( finite1829014797le_a_o @ ( minus_1746272704_a_o_o @ A_21 @ B_16 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_848_finite__Diff,axiom,
% 0.61/0.80 ! [B_16: pname > $o,A_21: pname > $o] :
% 0.61/0.80 ( ( finite_finite_pname @ A_21 )
% 0.61/0.80 => ( finite_finite_pname @ ( minus_minus_pname_o @ A_21 @ B_16 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_849_finite__Diff,axiom,
% 0.61/0.80 ! [B_16: nat > $o,A_21: nat > $o] :
% 0.61/0.80 ( ( finite_finite_nat @ A_21 )
% 0.61/0.80 => ( finite_finite_nat @ ( minus_minus_nat_o @ A_21 @ B_16 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_850_inf__Sup__absorb,axiom,
% 0.61/0.80 ! [A_20: hoare_2091234717iple_a > $o,A_19: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( finite1829014797le_a_o @ A_19 )
% 0.61/0.80 => ( ( member99268621le_a_o @ A_20 @ A_19 )
% 0.61/0.80 => ( ( semila2006181266le_a_o @ A_20 @ ( big_la735727201le_a_o @ A_19 ) )
% 0.61/0.80 = A_20 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_851_inf__Sup__absorb,axiom,
% 0.61/0.80 ! [A_20: nat > $o,A_19: ( nat > $o ) > $o] :
% 0.61/0.80 ( ( finite_finite_nat_o @ A_19 )
% 0.61/0.80 => ( ( member_nat_o @ A_20 @ A_19 )
% 0.61/0.80 => ( ( semila1947288293_nat_o @ A_20 @ ( big_la1658356148_nat_o @ A_19 ) )
% 0.61/0.80 = A_20 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_852_inf__Sup__absorb,axiom,
% 0.61/0.80 ! [A_20: pname > $o,A_19: ( pname > $o ) > $o] :
% 0.61/0.80 ( ( finite297249702name_o @ A_19 )
% 0.61/0.80 => ( ( member_pname_o @ A_20 @ A_19 )
% 0.61/0.80 => ( ( semila1673364395name_o @ A_20 @ ( big_la1286884090name_o @ A_19 ) )
% 0.61/0.80 = A_20 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_853_inf__Sup__absorb,axiom,
% 0.61/0.80 ! [A_20: nat,A_19: nat > $o] :
% 0.61/0.80 ( ( finite_finite_nat @ A_19 )
% 0.61/0.80 => ( ( member_nat @ A_20 @ A_19 )
% 0.61/0.80 => ( ( semila80283416nf_nat @ A_20 @ ( big_la43341705in_nat @ A_19 ) )
% 0.61/0.80 = A_20 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_854_Diff__Int,axiom,
% 0.61/0.80 ! [A_18: nat > $o,B_15: nat > $o,C_7: nat > $o] :
% 0.61/0.80 ( ( minus_minus_nat_o @ A_18 @ ( semila1947288293_nat_o @ B_15 @ C_7 ) )
% 0.61/0.80 = ( semila848761471_nat_o @ ( minus_minus_nat_o @ A_18 @ B_15 ) @ ( minus_minus_nat_o @ A_18 @ C_7 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_855_Diff__Int,axiom,
% 0.61/0.80 ! [A_18: pname > $o,B_15: pname > $o,C_7: pname > $o] :
% 0.61/0.80 ( ( minus_minus_pname_o @ A_18 @ ( semila1673364395name_o @ B_15 @ C_7 ) )
% 0.61/0.80 = ( semila1780557381name_o @ ( minus_minus_pname_o @ A_18 @ B_15 ) @ ( minus_minus_pname_o @ A_18 @ C_7 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_856_Diff__Int,axiom,
% 0.61/0.80 ! [A_18: ( hoare_2091234717iple_a > $o ) > $o,B_15: ( hoare_2091234717iple_a > $o ) > $o,C_7: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( minus_1746272704_a_o_o @ A_18 @ ( semila1672913213_a_o_o @ B_15 @ C_7 ) )
% 0.61/0.80 = ( semila2050116131_a_o_o @ ( minus_1746272704_a_o_o @ A_18 @ B_15 ) @ ( minus_1746272704_a_o_o @ A_18 @ C_7 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_857_Diff__Int,axiom,
% 0.61/0.80 ! [A_18: hoare_1708887482_state > $o,B_15: hoare_1708887482_state > $o,C_7: hoare_1708887482_state > $o] :
% 0.61/0.80 ( ( minus_2056855718tate_o @ A_18 @ ( semila129691299tate_o @ B_15 @ C_7 ) )
% 0.61/0.80 = ( semila1122118281tate_o @ ( minus_2056855718tate_o @ A_18 @ B_15 ) @ ( minus_2056855718tate_o @ A_18 @ C_7 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_858_Diff__Int,axiom,
% 0.61/0.80 ! [A_18: hoare_2091234717iple_a > $o,B_15: hoare_2091234717iple_a > $o,C_7: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( minus_836160335le_a_o @ A_18 @ ( semila2006181266le_a_o @ B_15 @ C_7 ) )
% 0.61/0.80 = ( semila1052848428le_a_o @ ( minus_836160335le_a_o @ A_18 @ B_15 ) @ ( minus_836160335le_a_o @ A_18 @ C_7 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_859_Diff__Un,axiom,
% 0.61/0.80 ! [A_17: nat > $o,B_14: nat > $o,C_6: nat > $o] :
% 0.61/0.80 ( ( minus_minus_nat_o @ A_17 @ ( semila848761471_nat_o @ B_14 @ C_6 ) )
% 0.61/0.80 = ( semila1947288293_nat_o @ ( minus_minus_nat_o @ A_17 @ B_14 ) @ ( minus_minus_nat_o @ A_17 @ C_6 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_860_Diff__Un,axiom,
% 0.61/0.80 ! [A_17: pname > $o,B_14: pname > $o,C_6: pname > $o] :
% 0.61/0.80 ( ( minus_minus_pname_o @ A_17 @ ( semila1780557381name_o @ B_14 @ C_6 ) )
% 0.61/0.80 = ( semila1673364395name_o @ ( minus_minus_pname_o @ A_17 @ B_14 ) @ ( minus_minus_pname_o @ A_17 @ C_6 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_861_Diff__Un,axiom,
% 0.61/0.80 ! [A_17: ( hoare_2091234717iple_a > $o ) > $o,B_14: ( hoare_2091234717iple_a > $o ) > $o,C_6: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( minus_1746272704_a_o_o @ A_17 @ ( semila2050116131_a_o_o @ B_14 @ C_6 ) )
% 0.61/0.80 = ( semila1672913213_a_o_o @ ( minus_1746272704_a_o_o @ A_17 @ B_14 ) @ ( minus_1746272704_a_o_o @ A_17 @ C_6 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_862_Diff__Un,axiom,
% 0.61/0.80 ! [A_17: hoare_1708887482_state > $o,B_14: hoare_1708887482_state > $o,C_6: hoare_1708887482_state > $o] :
% 0.61/0.80 ( ( minus_2056855718tate_o @ A_17 @ ( semila1122118281tate_o @ B_14 @ C_6 ) )
% 0.61/0.80 = ( semila129691299tate_o @ ( minus_2056855718tate_o @ A_17 @ B_14 ) @ ( minus_2056855718tate_o @ A_17 @ C_6 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_863_Diff__Un,axiom,
% 0.61/0.80 ! [A_17: hoare_2091234717iple_a > $o,B_14: hoare_2091234717iple_a > $o,C_6: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( minus_836160335le_a_o @ A_17 @ ( semila1052848428le_a_o @ B_14 @ C_6 ) )
% 0.61/0.80 = ( semila2006181266le_a_o @ ( minus_836160335le_a_o @ A_17 @ B_14 ) @ ( minus_836160335le_a_o @ A_17 @ C_6 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_864_Un__Diff__Int,axiom,
% 0.61/0.80 ! [A_16: nat > $o,B_13: nat > $o] :
% 0.61/0.80 ( ( semila848761471_nat_o @ ( minus_minus_nat_o @ A_16 @ B_13 ) @ ( semila1947288293_nat_o @ A_16 @ B_13 ) )
% 0.61/0.80 = A_16 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_865_Un__Diff__Int,axiom,
% 0.61/0.80 ! [A_16: pname > $o,B_13: pname > $o] :
% 0.61/0.80 ( ( semila1780557381name_o @ ( minus_minus_pname_o @ A_16 @ B_13 ) @ ( semila1673364395name_o @ A_16 @ B_13 ) )
% 0.61/0.80 = A_16 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_866_Un__Diff__Int,axiom,
% 0.61/0.80 ! [A_16: ( hoare_2091234717iple_a > $o ) > $o,B_13: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( semila2050116131_a_o_o @ ( minus_1746272704_a_o_o @ A_16 @ B_13 ) @ ( semila1672913213_a_o_o @ A_16 @ B_13 ) )
% 0.61/0.80 = A_16 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_867_Un__Diff__Int,axiom,
% 0.61/0.80 ! [A_16: hoare_1708887482_state > $o,B_13: hoare_1708887482_state > $o] :
% 0.61/0.80 ( ( semila1122118281tate_o @ ( minus_2056855718tate_o @ A_16 @ B_13 ) @ ( semila129691299tate_o @ A_16 @ B_13 ) )
% 0.61/0.80 = A_16 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_868_Un__Diff__Int,axiom,
% 0.61/0.80 ! [A_16: hoare_2091234717iple_a > $o,B_13: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( semila1052848428le_a_o @ ( minus_836160335le_a_o @ A_16 @ B_13 ) @ ( semila2006181266le_a_o @ A_16 @ B_13 ) )
% 0.61/0.80 = A_16 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_869_Collect__conj__eq,axiom,
% 0.61/0.80 ! [P_2: pname > $o,Q: pname > $o] :
% 0.61/0.80 ( ( collect_pname
% 0.61/0.80 @ ^ [X: pname] : ( (&) @ ( P_2 @ X ) @ ( Q @ X ) ) )
% 0.61/0.80 = ( semila1673364395name_o @ ( collect_pname @ P_2 ) @ ( collect_pname @ Q ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_870_Collect__conj__eq,axiom,
% 0.61/0.80 ! [P_2: hoare_2091234717iple_a > $o,Q: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( collec992574898iple_a
% 0.61/0.80 @ ^ [X: hoare_2091234717iple_a] : ( (&) @ ( P_2 @ X ) @ ( Q @ X ) ) )
% 0.61/0.80 = ( semila2006181266le_a_o @ ( collec992574898iple_a @ P_2 ) @ ( collec992574898iple_a @ Q ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_871_Collect__conj__eq,axiom,
% 0.61/0.80 ! [P_2: nat > $o,Q: nat > $o] :
% 0.61/0.80 ( ( collect_nat
% 0.61/0.80 @ ^ [X: nat] : ( (&) @ ( P_2 @ X ) @ ( Q @ X ) ) )
% 0.61/0.80 = ( semila1947288293_nat_o @ ( collect_nat @ P_2 ) @ ( collect_nat @ Q ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_872_Int__Collect,axiom,
% 0.61/0.80 ! [X_9: hoare_2091234717iple_a > $o,A_15: ( hoare_2091234717iple_a > $o ) > $o,P_1: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( member99268621le_a_o @ X_9 @ ( semila1672913213_a_o_o @ A_15 @ ( collec1008234059le_a_o @ P_1 ) ) )
% 0.61/0.80 <=> ( ( member99268621le_a_o @ X_9 @ A_15 )
% 0.61/0.80 & ( P_1 @ X_9 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_873_Int__Collect,axiom,
% 0.61/0.80 ! [X_9: nat,A_15: nat > $o,P_1: nat > $o] :
% 0.61/0.80 ( ( member_nat @ X_9 @ ( semila1947288293_nat_o @ A_15 @ ( collect_nat @ P_1 ) ) )
% 0.61/0.80 <=> ( ( member_nat @ X_9 @ A_15 )
% 0.61/0.80 & ( P_1 @ X_9 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_874_Int__Collect,axiom,
% 0.61/0.80 ! [X_9: hoare_2091234717iple_a,A_15: hoare_2091234717iple_a > $o,P_1: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( member290856304iple_a @ X_9 @ ( semila2006181266le_a_o @ A_15 @ ( collec992574898iple_a @ P_1 ) ) )
% 0.61/0.80 <=> ( ( member290856304iple_a @ X_9 @ A_15 )
% 0.61/0.80 & ( P_1 @ X_9 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_875_Int__Collect,axiom,
% 0.61/0.80 ! [X_9: pname,A_15: pname > $o,P_1: pname > $o] :
% 0.61/0.80 ( ( member_pname @ X_9 @ ( semila1673364395name_o @ A_15 @ ( collect_pname @ P_1 ) ) )
% 0.61/0.80 <=> ( ( member_pname @ X_9 @ A_15 )
% 0.61/0.80 & ( P_1 @ X_9 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_876_inf__Int__eq,axiom,
% 0.61/0.80 ! [R: ( hoare_2091234717iple_a > $o ) > $o,S_1: ( hoare_2091234717iple_a > $o ) > $o,X: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( semila1672913213_a_o_o
% 0.61/0.80 @ ^ [Y_7: hoare_2091234717iple_a > $o] : ( member99268621le_a_o @ Y_7 @ R )
% 0.61/0.80 @ ^ [Y_7: hoare_2091234717iple_a > $o] : ( member99268621le_a_o @ Y_7 @ S_1 )
% 0.61/0.80 @ X )
% 0.61/0.80 <=> ( member99268621le_a_o @ X @ ( semila1672913213_a_o_o @ R @ S_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_877_inf__Int__eq,axiom,
% 0.61/0.80 ! [R: nat > $o,S_1: nat > $o,X: nat] :
% 0.61/0.80 ( ( semila1947288293_nat_o
% 0.61/0.80 @ ^ [Y_7: nat] : ( member_nat @ Y_7 @ R )
% 0.61/0.80 @ ^ [Y_7: nat] : ( member_nat @ Y_7 @ S_1 )
% 0.61/0.80 @ X )
% 0.61/0.80 <=> ( member_nat @ X @ ( semila1947288293_nat_o @ R @ S_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_878_inf__Int__eq,axiom,
% 0.61/0.80 ! [R: hoare_2091234717iple_a > $o,S_1: hoare_2091234717iple_a > $o,X: hoare_2091234717iple_a] :
% 0.61/0.80 ( ( semila2006181266le_a_o
% 0.61/0.80 @ ^ [Y_7: hoare_2091234717iple_a] : ( member290856304iple_a @ Y_7 @ R )
% 0.61/0.80 @ ^ [Y_7: hoare_2091234717iple_a] : ( member290856304iple_a @ Y_7 @ S_1 )
% 0.61/0.80 @ X )
% 0.61/0.80 <=> ( member290856304iple_a @ X @ ( semila2006181266le_a_o @ R @ S_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_879_inf__Int__eq,axiom,
% 0.61/0.80 ! [R: pname > $o,S_1: pname > $o,X: pname] :
% 0.61/0.80 ( ( semila1673364395name_o
% 0.61/0.80 @ ^ [Y_7: pname] : ( member_pname @ Y_7 @ R )
% 0.61/0.80 @ ^ [Y_7: pname] : ( member_pname @ Y_7 @ S_1 )
% 0.61/0.80 @ X )
% 0.61/0.80 <=> ( member_pname @ X @ ( semila1673364395name_o @ R @ S_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_880_Int__absorb,axiom,
% 0.61/0.80 ! [A_14: nat > $o] :
% 0.61/0.80 ( ( semila1947288293_nat_o @ A_14 @ A_14 )
% 0.61/0.80 = A_14 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_881_Int__absorb,axiom,
% 0.61/0.80 ! [A_14: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( semila2006181266le_a_o @ A_14 @ A_14 )
% 0.61/0.80 = A_14 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_882_Int__absorb,axiom,
% 0.61/0.80 ! [A_14: pname > $o] :
% 0.61/0.80 ( ( semila1673364395name_o @ A_14 @ A_14 )
% 0.61/0.80 = A_14 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_883_inf_Oidem,axiom,
% 0.61/0.80 ! [A_13: nat > $o] :
% 0.61/0.80 ( ( semila1947288293_nat_o @ A_13 @ A_13 )
% 0.61/0.80 = A_13 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_884_inf_Oidem,axiom,
% 0.61/0.80 ! [A_13: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( semila2006181266le_a_o @ A_13 @ A_13 )
% 0.61/0.80 = A_13 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_885_inf_Oidem,axiom,
% 0.61/0.80 ! [A_13: nat] :
% 0.61/0.80 ( ( semila80283416nf_nat @ A_13 @ A_13 )
% 0.61/0.80 = A_13 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_886_inf_Oidem,axiom,
% 0.61/0.80 ! [A_13: pname > $o] :
% 0.61/0.80 ( ( semila1673364395name_o @ A_13 @ A_13 )
% 0.61/0.80 = A_13 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_887_inf__idem,axiom,
% 0.61/0.80 ! [X_8: nat > $o] :
% 0.61/0.80 ( ( semila1947288293_nat_o @ X_8 @ X_8 )
% 0.61/0.80 = X_8 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_888_inf__idem,axiom,
% 0.61/0.80 ! [X_8: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( semila2006181266le_a_o @ X_8 @ X_8 )
% 0.61/0.80 = X_8 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_889_inf__idem,axiom,
% 0.61/0.80 ! [X_8: nat] :
% 0.61/0.80 ( ( semila80283416nf_nat @ X_8 @ X_8 )
% 0.61/0.80 = X_8 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_890_inf__idem,axiom,
% 0.61/0.80 ! [X_8: pname > $o] :
% 0.61/0.80 ( ( semila1673364395name_o @ X_8 @ X_8 )
% 0.61/0.80 = X_8 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_891_fun__diff__def,axiom,
% 0.61/0.80 ! [A_12: hoare_2091234717iple_a > $o,B_12: hoare_2091234717iple_a > $o,X: hoare_2091234717iple_a] :
% 0.61/0.80 ( ( minus_836160335le_a_o @ A_12 @ B_12 @ X )
% 0.61/0.80 <=> ( minus_minus_o @ ( A_12 @ X ) @ ( B_12 @ X ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_892_fun__diff__def,axiom,
% 0.61/0.80 ! [A_12: pname > $o,B_12: pname > $o,X: pname] :
% 0.61/0.80 ( ( minus_minus_pname_o @ A_12 @ B_12 @ X )
% 0.61/0.80 <=> ( minus_minus_o @ ( A_12 @ X ) @ ( B_12 @ X ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_893_fun__diff__def,axiom,
% 0.61/0.80 ! [A_12: nat > $o,B_12: nat > $o,X: nat] :
% 0.61/0.80 ( ( minus_minus_nat_o @ A_12 @ B_12 @ X )
% 0.61/0.80 <=> ( minus_minus_o @ ( A_12 @ X ) @ ( B_12 @ X ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_894_inf__fun__def,axiom,
% 0.61/0.80 ! [F_1: nat > $o,G: nat > $o,X: nat] :
% 0.61/0.80 ( ( semila1947288293_nat_o @ F_1 @ G @ X )
% 0.61/0.80 <=> ( semila854092349_inf_o @ ( F_1 @ X ) @ ( G @ X ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_895_inf__fun__def,axiom,
% 0.61/0.80 ! [F_1: hoare_2091234717iple_a > $o,G: hoare_2091234717iple_a > $o,X: hoare_2091234717iple_a] :
% 0.61/0.80 ( ( semila2006181266le_a_o @ F_1 @ G @ X )
% 0.61/0.80 <=> ( semila854092349_inf_o @ ( F_1 @ X ) @ ( G @ X ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_896_inf__fun__def,axiom,
% 0.61/0.80 ! [F_1: pname > $o,G: pname > $o,X: pname] :
% 0.61/0.80 ( ( semila1673364395name_o @ F_1 @ G @ X )
% 0.61/0.80 <=> ( semila854092349_inf_o @ ( F_1 @ X ) @ ( G @ X ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_897_set__diff__eq,axiom,
% 0.61/0.80 ! [A_11: ( hoare_2091234717iple_a > $o ) > $o,B_11: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( minus_1746272704_a_o_o @ A_11 @ B_11 )
% 0.61/0.80 = ( collec1008234059le_a_o
% 0.61/0.80 @ ^ [X: hoare_2091234717iple_a > $o] : ( (&) @ ( member99268621le_a_o @ X @ A_11 ) @ ( (~) @ ( member99268621le_a_o @ X @ B_11 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_898_set__diff__eq,axiom,
% 0.61/0.80 ! [A_11: nat > $o,B_11: nat > $o] :
% 0.61/0.80 ( ( minus_minus_nat_o @ A_11 @ B_11 )
% 0.61/0.80 = ( collect_nat
% 0.61/0.80 @ ^ [X: nat] : ( (&) @ ( member_nat @ X @ A_11 ) @ ( (~) @ ( member_nat @ X @ B_11 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_899_set__diff__eq,axiom,
% 0.61/0.80 ! [A_11: hoare_2091234717iple_a > $o,B_11: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( minus_836160335le_a_o @ A_11 @ B_11 )
% 0.61/0.80 = ( collec992574898iple_a
% 0.61/0.80 @ ^ [X: hoare_2091234717iple_a] : ( (&) @ ( member290856304iple_a @ X @ A_11 ) @ ( (~) @ ( member290856304iple_a @ X @ B_11 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_900_set__diff__eq,axiom,
% 0.61/0.80 ! [A_11: pname > $o,B_11: pname > $o] :
% 0.61/0.80 ( ( minus_minus_pname_o @ A_11 @ B_11 )
% 0.61/0.80 = ( collect_pname
% 0.61/0.80 @ ^ [X: pname] : ( (&) @ ( member_pname @ X @ A_11 ) @ ( (~) @ ( member_pname @ X @ B_11 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_901_Int__def,axiom,
% 0.61/0.80 ! [A_10: ( hoare_2091234717iple_a > $o ) > $o,B_10: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( semila1672913213_a_o_o @ A_10 @ B_10 )
% 0.61/0.80 = ( collec1008234059le_a_o
% 0.61/0.80 @ ^ [X: hoare_2091234717iple_a > $o] : ( (&) @ ( member99268621le_a_o @ X @ A_10 ) @ ( member99268621le_a_o @ X @ B_10 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_902_Int__def,axiom,
% 0.61/0.80 ! [A_10: nat > $o,B_10: nat > $o] :
% 0.61/0.80 ( ( semila1947288293_nat_o @ A_10 @ B_10 )
% 0.61/0.80 = ( collect_nat
% 0.61/0.80 @ ^ [X: nat] : ( (&) @ ( member_nat @ X @ A_10 ) @ ( member_nat @ X @ B_10 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_903_Int__def,axiom,
% 0.61/0.80 ! [A_10: hoare_2091234717iple_a > $o,B_10: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( semila2006181266le_a_o @ A_10 @ B_10 )
% 0.61/0.80 = ( collec992574898iple_a
% 0.61/0.80 @ ^ [X: hoare_2091234717iple_a] : ( (&) @ ( member290856304iple_a @ X @ A_10 ) @ ( member290856304iple_a @ X @ B_10 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_904_Int__def,axiom,
% 0.61/0.80 ! [A_10: pname > $o,B_10: pname > $o] :
% 0.61/0.80 ( ( semila1673364395name_o @ A_10 @ B_10 )
% 0.61/0.80 = ( collect_pname
% 0.61/0.80 @ ^ [X: pname] : ( (&) @ ( member_pname @ X @ A_10 ) @ ( member_pname @ X @ B_10 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_905_Int__commute,axiom,
% 0.61/0.80 ! [A_9: nat > $o,B_9: nat > $o] :
% 0.61/0.80 ( ( semila1947288293_nat_o @ A_9 @ B_9 )
% 0.61/0.80 = ( semila1947288293_nat_o @ B_9 @ A_9 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_906_Int__commute,axiom,
% 0.61/0.80 ! [A_9: hoare_2091234717iple_a > $o,B_9: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( semila2006181266le_a_o @ A_9 @ B_9 )
% 0.61/0.80 = ( semila2006181266le_a_o @ B_9 @ A_9 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_907_Int__commute,axiom,
% 0.61/0.80 ! [A_9: pname > $o,B_9: pname > $o] :
% 0.61/0.80 ( ( semila1673364395name_o @ A_9 @ B_9 )
% 0.61/0.80 = ( semila1673364395name_o @ B_9 @ A_9 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_908_inf_Ocommute,axiom,
% 0.61/0.80 ! [A_8: nat > $o,B_8: nat > $o] :
% 0.61/0.80 ( ( semila1947288293_nat_o @ A_8 @ B_8 )
% 0.61/0.80 = ( semila1947288293_nat_o @ B_8 @ A_8 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_909_inf_Ocommute,axiom,
% 0.61/0.80 ! [A_8: hoare_2091234717iple_a > $o,B_8: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( semila2006181266le_a_o @ A_8 @ B_8 )
% 0.61/0.80 = ( semila2006181266le_a_o @ B_8 @ A_8 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_910_inf_Ocommute,axiom,
% 0.61/0.80 ! [A_8: nat,B_8: nat] :
% 0.61/0.80 ( ( semila80283416nf_nat @ A_8 @ B_8 )
% 0.61/0.80 = ( semila80283416nf_nat @ B_8 @ A_8 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_911_inf_Ocommute,axiom,
% 0.61/0.80 ! [A_8: pname > $o,B_8: pname > $o] :
% 0.61/0.80 ( ( semila1673364395name_o @ A_8 @ B_8 )
% 0.61/0.80 = ( semila1673364395name_o @ B_8 @ A_8 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_912_inf__sup__aci_I1_J,axiom,
% 0.61/0.80 ! [X_7: nat > $o,Y_6: nat > $o] :
% 0.61/0.80 ( ( semila1947288293_nat_o @ X_7 @ Y_6 )
% 0.61/0.80 = ( semila1947288293_nat_o @ Y_6 @ X_7 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_913_inf__sup__aci_I1_J,axiom,
% 0.61/0.80 ! [X_7: hoare_2091234717iple_a > $o,Y_6: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( semila2006181266le_a_o @ X_7 @ Y_6 )
% 0.61/0.80 = ( semila2006181266le_a_o @ Y_6 @ X_7 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_914_inf__sup__aci_I1_J,axiom,
% 0.61/0.80 ! [X_7: nat,Y_6: nat] :
% 0.61/0.80 ( ( semila80283416nf_nat @ X_7 @ Y_6 )
% 0.61/0.80 = ( semila80283416nf_nat @ Y_6 @ X_7 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_915_inf__sup__aci_I1_J,axiom,
% 0.61/0.80 ! [X_7: pname > $o,Y_6: pname > $o] :
% 0.61/0.80 ( ( semila1673364395name_o @ X_7 @ Y_6 )
% 0.61/0.80 = ( semila1673364395name_o @ Y_6 @ X_7 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_916_inf__commute,axiom,
% 0.61/0.80 ! [X_6: nat > $o,Y_5: nat > $o] :
% 0.61/0.80 ( ( semila1947288293_nat_o @ X_6 @ Y_5 )
% 0.61/0.80 = ( semila1947288293_nat_o @ Y_5 @ X_6 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_917_inf__commute,axiom,
% 0.61/0.80 ! [X_6: hoare_2091234717iple_a > $o,Y_5: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( semila2006181266le_a_o @ X_6 @ Y_5 )
% 0.61/0.80 = ( semila2006181266le_a_o @ Y_5 @ X_6 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_918_inf__commute,axiom,
% 0.61/0.80 ! [X_6: nat,Y_5: nat] :
% 0.61/0.80 ( ( semila80283416nf_nat @ X_6 @ Y_5 )
% 0.61/0.80 = ( semila80283416nf_nat @ Y_5 @ X_6 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_919_inf__commute,axiom,
% 0.61/0.80 ! [X_6: pname > $o,Y_5: pname > $o] :
% 0.61/0.80 ( ( semila1673364395name_o @ X_6 @ Y_5 )
% 0.61/0.80 = ( semila1673364395name_o @ Y_5 @ X_6 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_920_Int__left__absorb,axiom,
% 0.61/0.80 ! [A_7: nat > $o,B_7: nat > $o] :
% 0.61/0.80 ( ( semila1947288293_nat_o @ A_7 @ ( semila1947288293_nat_o @ A_7 @ B_7 ) )
% 0.61/0.80 = ( semila1947288293_nat_o @ A_7 @ B_7 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_921_Int__left__absorb,axiom,
% 0.61/0.80 ! [A_7: hoare_2091234717iple_a > $o,B_7: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( semila2006181266le_a_o @ A_7 @ ( semila2006181266le_a_o @ A_7 @ B_7 ) )
% 0.61/0.80 = ( semila2006181266le_a_o @ A_7 @ B_7 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_922_Int__left__absorb,axiom,
% 0.61/0.80 ! [A_7: pname > $o,B_7: pname > $o] :
% 0.61/0.80 ( ( semila1673364395name_o @ A_7 @ ( semila1673364395name_o @ A_7 @ B_7 ) )
% 0.61/0.80 = ( semila1673364395name_o @ A_7 @ B_7 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_923_inf_Oleft__idem,axiom,
% 0.61/0.80 ! [A_6: nat > $o,B_6: nat > $o] :
% 0.61/0.80 ( ( semila1947288293_nat_o @ A_6 @ ( semila1947288293_nat_o @ A_6 @ B_6 ) )
% 0.61/0.80 = ( semila1947288293_nat_o @ A_6 @ B_6 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_924_inf_Oleft__idem,axiom,
% 0.61/0.80 ! [A_6: hoare_2091234717iple_a > $o,B_6: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( semila2006181266le_a_o @ A_6 @ ( semila2006181266le_a_o @ A_6 @ B_6 ) )
% 0.61/0.80 = ( semila2006181266le_a_o @ A_6 @ B_6 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_925_inf_Oleft__idem,axiom,
% 0.61/0.80 ! [A_6: nat,B_6: nat] :
% 0.61/0.80 ( ( semila80283416nf_nat @ A_6 @ ( semila80283416nf_nat @ A_6 @ B_6 ) )
% 0.61/0.80 = ( semila80283416nf_nat @ A_6 @ B_6 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_926_inf_Oleft__idem,axiom,
% 0.61/0.80 ! [A_6: pname > $o,B_6: pname > $o] :
% 0.61/0.80 ( ( semila1673364395name_o @ A_6 @ ( semila1673364395name_o @ A_6 @ B_6 ) )
% 0.61/0.80 = ( semila1673364395name_o @ A_6 @ B_6 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_927_inf__sup__aci_I4_J,axiom,
% 0.61/0.80 ! [X_5: nat > $o,Y_4: nat > $o] :
% 0.61/0.80 ( ( semila1947288293_nat_o @ X_5 @ ( semila1947288293_nat_o @ X_5 @ Y_4 ) )
% 0.61/0.80 = ( semila1947288293_nat_o @ X_5 @ Y_4 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_928_inf__sup__aci_I4_J,axiom,
% 0.61/0.80 ! [X_5: hoare_2091234717iple_a > $o,Y_4: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( semila2006181266le_a_o @ X_5 @ ( semila2006181266le_a_o @ X_5 @ Y_4 ) )
% 0.61/0.80 = ( semila2006181266le_a_o @ X_5 @ Y_4 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_929_inf__sup__aci_I4_J,axiom,
% 0.61/0.80 ! [X_5: nat,Y_4: nat] :
% 0.61/0.80 ( ( semila80283416nf_nat @ X_5 @ ( semila80283416nf_nat @ X_5 @ Y_4 ) )
% 0.61/0.80 = ( semila80283416nf_nat @ X_5 @ Y_4 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_930_inf__sup__aci_I4_J,axiom,
% 0.61/0.80 ! [X_5: pname > $o,Y_4: pname > $o] :
% 0.61/0.80 ( ( semila1673364395name_o @ X_5 @ ( semila1673364395name_o @ X_5 @ Y_4 ) )
% 0.61/0.80 = ( semila1673364395name_o @ X_5 @ Y_4 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_931_inf__left__idem,axiom,
% 0.61/0.80 ! [X_4: nat > $o,Y_3: nat > $o] :
% 0.61/0.80 ( ( semila1947288293_nat_o @ X_4 @ ( semila1947288293_nat_o @ X_4 @ Y_3 ) )
% 0.61/0.80 = ( semila1947288293_nat_o @ X_4 @ Y_3 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_932_inf__left__idem,axiom,
% 0.61/0.80 ! [X_4: hoare_2091234717iple_a > $o,Y_3: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( semila2006181266le_a_o @ X_4 @ ( semila2006181266le_a_o @ X_4 @ Y_3 ) )
% 0.61/0.80 = ( semila2006181266le_a_o @ X_4 @ Y_3 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_933_inf__left__idem,axiom,
% 0.61/0.80 ! [X_4: nat,Y_3: nat] :
% 0.61/0.80 ( ( semila80283416nf_nat @ X_4 @ ( semila80283416nf_nat @ X_4 @ Y_3 ) )
% 0.61/0.80 = ( semila80283416nf_nat @ X_4 @ Y_3 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_934_inf__left__idem,axiom,
% 0.61/0.80 ! [X_4: pname > $o,Y_3: pname > $o] :
% 0.61/0.80 ( ( semila1673364395name_o @ X_4 @ ( semila1673364395name_o @ X_4 @ Y_3 ) )
% 0.61/0.80 = ( semila1673364395name_o @ X_4 @ Y_3 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_935_Int__left__commute,axiom,
% 0.61/0.80 ! [A_5: nat > $o,B_5: nat > $o,C_5: nat > $o] :
% 0.61/0.80 ( ( semila1947288293_nat_o @ A_5 @ ( semila1947288293_nat_o @ B_5 @ C_5 ) )
% 0.61/0.80 = ( semila1947288293_nat_o @ B_5 @ ( semila1947288293_nat_o @ A_5 @ C_5 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_936_Int__left__commute,axiom,
% 0.61/0.80 ! [A_5: hoare_2091234717iple_a > $o,B_5: hoare_2091234717iple_a > $o,C_5: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( semila2006181266le_a_o @ A_5 @ ( semila2006181266le_a_o @ B_5 @ C_5 ) )
% 0.61/0.80 = ( semila2006181266le_a_o @ B_5 @ ( semila2006181266le_a_o @ A_5 @ C_5 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_937_Int__left__commute,axiom,
% 0.61/0.80 ! [A_5: pname > $o,B_5: pname > $o,C_5: pname > $o] :
% 0.61/0.80 ( ( semila1673364395name_o @ A_5 @ ( semila1673364395name_o @ B_5 @ C_5 ) )
% 0.61/0.80 = ( semila1673364395name_o @ B_5 @ ( semila1673364395name_o @ A_5 @ C_5 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_938_inf_Oleft__commute,axiom,
% 0.61/0.80 ! [B_4: nat > $o,A_4: nat > $o,C_4: nat > $o] :
% 0.61/0.80 ( ( semila1947288293_nat_o @ B_4 @ ( semila1947288293_nat_o @ A_4 @ C_4 ) )
% 0.61/0.80 = ( semila1947288293_nat_o @ A_4 @ ( semila1947288293_nat_o @ B_4 @ C_4 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_939_inf_Oleft__commute,axiom,
% 0.61/0.80 ! [B_4: hoare_2091234717iple_a > $o,A_4: hoare_2091234717iple_a > $o,C_4: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( semila2006181266le_a_o @ B_4 @ ( semila2006181266le_a_o @ A_4 @ C_4 ) )
% 0.61/0.80 = ( semila2006181266le_a_o @ A_4 @ ( semila2006181266le_a_o @ B_4 @ C_4 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_940_inf_Oleft__commute,axiom,
% 0.61/0.80 ! [B_4: nat,A_4: nat,C_4: nat] :
% 0.61/0.80 ( ( semila80283416nf_nat @ B_4 @ ( semila80283416nf_nat @ A_4 @ C_4 ) )
% 0.61/0.80 = ( semila80283416nf_nat @ A_4 @ ( semila80283416nf_nat @ B_4 @ C_4 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_941_inf_Oleft__commute,axiom,
% 0.61/0.80 ! [B_4: pname > $o,A_4: pname > $o,C_4: pname > $o] :
% 0.61/0.80 ( ( semila1673364395name_o @ B_4 @ ( semila1673364395name_o @ A_4 @ C_4 ) )
% 0.61/0.80 = ( semila1673364395name_o @ A_4 @ ( semila1673364395name_o @ B_4 @ C_4 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_942_inf__sup__aci_I3_J,axiom,
% 0.61/0.80 ! [X_3: nat > $o,Y_2: nat > $o,Z_2: nat > $o] :
% 0.61/0.80 ( ( semila1947288293_nat_o @ X_3 @ ( semila1947288293_nat_o @ Y_2 @ Z_2 ) )
% 0.61/0.80 = ( semila1947288293_nat_o @ Y_2 @ ( semila1947288293_nat_o @ X_3 @ Z_2 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_943_inf__sup__aci_I3_J,axiom,
% 0.61/0.80 ! [X_3: hoare_2091234717iple_a > $o,Y_2: hoare_2091234717iple_a > $o,Z_2: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( semila2006181266le_a_o @ X_3 @ ( semila2006181266le_a_o @ Y_2 @ Z_2 ) )
% 0.61/0.80 = ( semila2006181266le_a_o @ Y_2 @ ( semila2006181266le_a_o @ X_3 @ Z_2 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_944_inf__sup__aci_I3_J,axiom,
% 0.61/0.80 ! [X_3: nat,Y_2: nat,Z_2: nat] :
% 0.61/0.80 ( ( semila80283416nf_nat @ X_3 @ ( semila80283416nf_nat @ Y_2 @ Z_2 ) )
% 0.61/0.80 = ( semila80283416nf_nat @ Y_2 @ ( semila80283416nf_nat @ X_3 @ Z_2 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_945_inf__sup__aci_I3_J,axiom,
% 0.61/0.80 ! [X_3: pname > $o,Y_2: pname > $o,Z_2: pname > $o] :
% 0.61/0.80 ( ( semila1673364395name_o @ X_3 @ ( semila1673364395name_o @ Y_2 @ Z_2 ) )
% 0.61/0.80 = ( semila1673364395name_o @ Y_2 @ ( semila1673364395name_o @ X_3 @ Z_2 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_946_inf__left__commute,axiom,
% 0.61/0.80 ! [X_2: nat > $o,Y_1: nat > $o,Z_1: nat > $o] :
% 0.61/0.80 ( ( semila1947288293_nat_o @ X_2 @ ( semila1947288293_nat_o @ Y_1 @ Z_1 ) )
% 0.61/0.80 = ( semila1947288293_nat_o @ Y_1 @ ( semila1947288293_nat_o @ X_2 @ Z_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_947_inf__left__commute,axiom,
% 0.61/0.80 ! [X_2: hoare_2091234717iple_a > $o,Y_1: hoare_2091234717iple_a > $o,Z_1: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( semila2006181266le_a_o @ X_2 @ ( semila2006181266le_a_o @ Y_1 @ Z_1 ) )
% 0.61/0.80 = ( semila2006181266le_a_o @ Y_1 @ ( semila2006181266le_a_o @ X_2 @ Z_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_948_inf__left__commute,axiom,
% 0.61/0.80 ! [X_2: nat,Y_1: nat,Z_1: nat] :
% 0.61/0.80 ( ( semila80283416nf_nat @ X_2 @ ( semila80283416nf_nat @ Y_1 @ Z_1 ) )
% 0.61/0.80 = ( semila80283416nf_nat @ Y_1 @ ( semila80283416nf_nat @ X_2 @ Z_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_949_inf__left__commute,axiom,
% 0.61/0.80 ! [X_2: pname > $o,Y_1: pname > $o,Z_1: pname > $o] :
% 0.61/0.80 ( ( semila1673364395name_o @ X_2 @ ( semila1673364395name_o @ Y_1 @ Z_1 ) )
% 0.61/0.80 = ( semila1673364395name_o @ Y_1 @ ( semila1673364395name_o @ X_2 @ Z_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_950_Diff__iff,axiom,
% 0.61/0.80 ! [C_3: hoare_2091234717iple_a > $o,A_3: ( hoare_2091234717iple_a > $o ) > $o,B_3: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( member99268621le_a_o @ C_3 @ ( minus_1746272704_a_o_o @ A_3 @ B_3 ) )
% 0.61/0.80 <=> ( ( member99268621le_a_o @ C_3 @ A_3 )
% 0.61/0.80 & ~ ( member99268621le_a_o @ C_3 @ B_3 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_951_Diff__iff,axiom,
% 0.61/0.80 ! [C_3: nat,A_3: nat > $o,B_3: nat > $o] :
% 0.61/0.80 ( ( member_nat @ C_3 @ ( minus_minus_nat_o @ A_3 @ B_3 ) )
% 0.61/0.80 <=> ( ( member_nat @ C_3 @ A_3 )
% 0.61/0.80 & ~ ( member_nat @ C_3 @ B_3 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_952_Diff__iff,axiom,
% 0.61/0.80 ! [C_3: hoare_2091234717iple_a,A_3: hoare_2091234717iple_a > $o,B_3: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( member290856304iple_a @ C_3 @ ( minus_836160335le_a_o @ A_3 @ B_3 ) )
% 0.61/0.80 <=> ( ( member290856304iple_a @ C_3 @ A_3 )
% 0.61/0.80 & ~ ( member290856304iple_a @ C_3 @ B_3 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_953_Diff__iff,axiom,
% 0.61/0.80 ! [C_3: pname,A_3: pname > $o,B_3: pname > $o] :
% 0.61/0.80 ( ( member_pname @ C_3 @ ( minus_minus_pname_o @ A_3 @ B_3 ) )
% 0.61/0.80 <=> ( ( member_pname @ C_3 @ A_3 )
% 0.61/0.80 & ~ ( member_pname @ C_3 @ B_3 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_954_Int__iff,axiom,
% 0.61/0.80 ! [C_2: hoare_2091234717iple_a > $o,A_2: ( hoare_2091234717iple_a > $o ) > $o,B_2: ( hoare_2091234717iple_a > $o ) > $o] :
% 0.61/0.80 ( ( member99268621le_a_o @ C_2 @ ( semila1672913213_a_o_o @ A_2 @ B_2 ) )
% 0.61/0.80 <=> ( ( member99268621le_a_o @ C_2 @ A_2 )
% 0.61/0.80 & ( member99268621le_a_o @ C_2 @ B_2 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_955_Int__iff,axiom,
% 0.61/0.80 ! [C_2: nat,A_2: nat > $o,B_2: nat > $o] :
% 0.61/0.80 ( ( member_nat @ C_2 @ ( semila1947288293_nat_o @ A_2 @ B_2 ) )
% 0.61/0.80 <=> ( ( member_nat @ C_2 @ A_2 )
% 0.61/0.80 & ( member_nat @ C_2 @ B_2 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_956_Int__iff,axiom,
% 0.61/0.80 ! [C_2: hoare_2091234717iple_a,A_2: hoare_2091234717iple_a > $o,B_2: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( member290856304iple_a @ C_2 @ ( semila2006181266le_a_o @ A_2 @ B_2 ) )
% 0.61/0.80 <=> ( ( member290856304iple_a @ C_2 @ A_2 )
% 0.61/0.80 & ( member290856304iple_a @ C_2 @ B_2 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_957_Int__iff,axiom,
% 0.61/0.80 ! [C_2: pname,A_2: pname > $o,B_2: pname > $o] :
% 0.61/0.80 ( ( member_pname @ C_2 @ ( semila1673364395name_o @ A_2 @ B_2 ) )
% 0.61/0.80 <=> ( ( member_pname @ C_2 @ A_2 )
% 0.61/0.80 & ( member_pname @ C_2 @ B_2 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_958_Diff__Int__distrib,axiom,
% 0.61/0.80 ! [C_1: hoare_2091234717iple_a > $o,A_1: hoare_2091234717iple_a > $o,B_1: hoare_2091234717iple_a > $o] :
% 0.61/0.80 ( ( semila2006181266le_a_o @ C_1 @ ( minus_836160335le_a_o @ A_1 @ B_1 ) )
% 0.61/0.80 = ( minus_836160335le_a_o @ ( semila2006181266le_a_o @ C_1 @ A_1 ) @ ( semila2006181266le_a_o @ C_1 @ B_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_959_Diff__Int__distrib,axiom,
% 0.61/0.80 ! [C_1: pname > $o,A_1: pname > $o,B_1: pname > $o] :
% 0.61/0.80 ( ( semila1673364395name_o @ C_1 @ ( minus_minus_pname_o @ A_1 @ B_1 ) )
% 0.61/0.80 = ( minus_minus_pname_o @ ( semila1673364395name_o @ C_1 @ A_1 ) @ ( semila1673364395name_o @ C_1 @ B_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_960_Diff__Int__distrib,axiom,
% 0.61/0.80 ! [C_1: nat > $o,A_1: nat > $o,B_1: nat > $o] :
% 0.61/0.80 ( ( semila1947288293_nat_o @ C_1 @ ( minus_minus_nat_o @ A_1 @ B_1 ) )
% 0.61/0.80 = ( minus_minus_nat_o @ ( semila1947288293_nat_o @ C_1 @ A_1 ) @ ( semila1947288293_nat_o @ C_1 @ B_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_961_diff__0__eq__0,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ( ( minus_minus_nat @ zero_zero_nat @ N_1 )
% 0.61/0.80 = zero_zero_nat ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_962_minus__nat_Odiff__0,axiom,
% 0.61/0.80 ! [M: nat] :
% 0.61/0.80 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.61/0.80 = M ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_963_diff__self__eq__0,axiom,
% 0.61/0.80 ! [M: nat] :
% 0.61/0.80 ( ( minus_minus_nat @ M @ M )
% 0.61/0.80 = zero_zero_nat ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_964_diffs0__imp__equal,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ( minus_minus_nat @ M @ N_1 )
% 0.61/0.80 = zero_zero_nat )
% 0.61/0.80 => ( ( ( minus_minus_nat @ N_1 @ M )
% 0.61/0.80 = zero_zero_nat )
% 0.61/0.80 => ( M = N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_965_diff__Suc__Suc,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N_1 ) )
% 0.61/0.80 = ( minus_minus_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_966_Suc__diff__diff,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat,K_1: nat] :
% 0.61/0.80 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N_1 ) @ ( suc @ K_1 ) )
% 0.61/0.80 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N_1 ) @ K_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_967_diff__commute,axiom,
% 0.61/0.80 ! [I_1: nat,J_1: nat,K_1: nat] :
% 0.61/0.80 ( ( minus_minus_nat @ ( minus_minus_nat @ I_1 @ J_1 ) @ K_1 )
% 0.61/0.80 = ( minus_minus_nat @ ( minus_minus_nat @ I_1 @ K_1 ) @ J_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_968_zero__induct__lemma,axiom,
% 0.61/0.80 ! [I_1: nat,P: nat > $o,K_1: nat] :
% 0.61/0.80 ( ( P @ K_1 )
% 0.61/0.80 => ( ! [N: nat] :
% 0.61/0.80 ( ( P @ ( suc @ N ) )
% 0.61/0.80 => ( P @ N ) )
% 0.61/0.80 => ( P @ ( minus_minus_nat @ K_1 @ I_1 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_969_diff__Suc,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( minus_minus_nat @ M @ ( suc @ N_1 ) )
% 0.61/0.80 = ( nat_case_nat @ zero_zero_nat
% 0.61/0.80 @ ^ [K: nat] : K
% 0.61/0.80 @ ( minus_minus_nat @ M @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_970_One__nat__def,axiom,
% 0.61/0.80 ( one_one_nat
% 0.61/0.80 = ( suc @ zero_zero_nat ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_971_diff__Suc__1,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ( ( minus_minus_nat @ ( suc @ N_1 ) @ one_one_nat )
% 0.61/0.80 = N_1 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_972_diff__Suc__eq__diff__pred,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( minus_minus_nat @ M @ ( suc @ N_1 ) )
% 0.61/0.80 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_973_plus__nat_Oadd__0,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ( ( plus_plus_nat @ zero_zero_nat @ N_1 )
% 0.61/0.80 = N_1 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_974_Nat_Oadd__0__right,axiom,
% 0.61/0.80 ! [M: nat] :
% 0.61/0.80 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 0.61/0.80 = M ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_975_add__is__0,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ( plus_plus_nat @ M @ N_1 )
% 0.61/0.80 = zero_zero_nat )
% 0.61/0.80 <=> ( ( M = zero_zero_nat )
% 0.61/0.80 & ( N_1 = zero_zero_nat ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_976_add__eq__self__zero,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ( plus_plus_nat @ M @ N_1 )
% 0.61/0.80 = M )
% 0.61/0.80 => ( N_1 = zero_zero_nat ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_977_add__Suc__right,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( plus_plus_nat @ M @ ( suc @ N_1 ) )
% 0.61/0.80 = ( suc @ ( plus_plus_nat @ M @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_978_add__Suc,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( plus_plus_nat @ ( suc @ M ) @ N_1 )
% 0.61/0.80 = ( suc @ ( plus_plus_nat @ M @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_979_add__Suc__shift,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( plus_plus_nat @ ( suc @ M ) @ N_1 )
% 0.61/0.80 = ( plus_plus_nat @ M @ ( suc @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_980_nat__add__commute,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( plus_plus_nat @ M @ N_1 )
% 0.61/0.80 = ( plus_plus_nat @ N_1 @ M ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_981_nat__add__left__commute,axiom,
% 0.61/0.80 ! [X_1: nat,Y: nat,Z: nat] :
% 0.61/0.80 ( ( plus_plus_nat @ X_1 @ ( plus_plus_nat @ Y @ Z ) )
% 0.61/0.80 = ( plus_plus_nat @ Y @ ( plus_plus_nat @ X_1 @ Z ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_982_nat__add__assoc,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat,K_1: nat] :
% 0.61/0.80 ( ( plus_plus_nat @ ( plus_plus_nat @ M @ N_1 ) @ K_1 )
% 0.61/0.80 = ( plus_plus_nat @ M @ ( plus_plus_nat @ N_1 @ K_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_983_nat__add__left__cancel,axiom,
% 0.61/0.80 ! [K_1: nat,M: nat,N_1: nat] :
% 0.61/0.80 ( ( ( plus_plus_nat @ K_1 @ M )
% 0.61/0.80 = ( plus_plus_nat @ K_1 @ N_1 ) )
% 0.61/0.80 <=> ( M = N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_984_nat__add__right__cancel,axiom,
% 0.61/0.80 ! [M: nat,K_1: nat,N_1: nat] :
% 0.61/0.80 ( ( ( plus_plus_nat @ M @ K_1 )
% 0.61/0.80 = ( plus_plus_nat @ N_1 @ K_1 ) )
% 0.61/0.80 <=> ( M = N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_985_diff__add__inverse2,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N_1 ) @ N_1 )
% 0.61/0.80 = M ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_986_diff__add__inverse,axiom,
% 0.61/0.80 ! [N_1: nat,M: nat] :
% 0.61/0.80 ( ( minus_minus_nat @ ( plus_plus_nat @ N_1 @ M ) @ N_1 )
% 0.61/0.80 = M ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_987_diff__diff__left,axiom,
% 0.61/0.80 ! [I_1: nat,J_1: nat,K_1: nat] :
% 0.61/0.80 ( ( minus_minus_nat @ ( minus_minus_nat @ I_1 @ J_1 ) @ K_1 )
% 0.61/0.80 = ( minus_minus_nat @ I_1 @ ( plus_plus_nat @ J_1 @ K_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_988_diff__cancel,axiom,
% 0.61/0.80 ! [K_1: nat,M: nat,N_1: nat] :
% 0.61/0.80 ( ( minus_minus_nat @ ( plus_plus_nat @ K_1 @ M ) @ ( plus_plus_nat @ K_1 @ N_1 ) )
% 0.61/0.80 = ( minus_minus_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_989_diff__cancel2,axiom,
% 0.61/0.80 ! [M: nat,K_1: nat,N_1: nat] :
% 0.61/0.80 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K_1 ) @ ( plus_plus_nat @ N_1 @ K_1 ) )
% 0.61/0.80 = ( minus_minus_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_990_add__is__1,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ( plus_plus_nat @ M @ N_1 )
% 0.61/0.80 = ( suc @ zero_zero_nat ) )
% 0.61/0.80 <=> ( ( ( M
% 0.61/0.80 = ( suc @ zero_zero_nat ) )
% 0.61/0.80 & ( N_1 = zero_zero_nat ) )
% 0.61/0.80 | ( ( M = zero_zero_nat )
% 0.61/0.80 & ( N_1
% 0.61/0.80 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_991_one__is__add,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ( suc @ zero_zero_nat )
% 0.61/0.80 = ( plus_plus_nat @ M @ N_1 ) )
% 0.61/0.80 <=> ( ( ( M
% 0.61/0.80 = ( suc @ zero_zero_nat ) )
% 0.61/0.80 & ( N_1 = zero_zero_nat ) )
% 0.61/0.80 | ( ( M = zero_zero_nat )
% 0.61/0.80 & ( N_1
% 0.61/0.80 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_992_diff__add__0,axiom,
% 0.61/0.80 ! [N_1: nat,M: nat] :
% 0.61/0.80 ( ( minus_minus_nat @ N_1 @ ( plus_plus_nat @ N_1 @ M ) )
% 0.61/0.80 = zero_zero_nat ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_993_Suc__eq__plus1,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ( ( suc @ N_1 )
% 0.61/0.80 = ( plus_plus_nat @ N_1 @ one_one_nat ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_994_Suc__eq__plus1__left,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ( ( suc @ N_1 )
% 0.61/0.80 = ( plus_plus_nat @ one_one_nat @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_995_add__eq__if,axiom,
% 0.61/0.80 ! [N_1: nat,M: nat] :
% 0.61/0.80 ( ( ( M = zero_zero_nat )
% 0.61/0.80 => ( ( plus_plus_nat @ M @ N_1 )
% 0.61/0.80 = N_1 ) )
% 0.61/0.80 & ( ( M != zero_zero_nat )
% 0.61/0.80 => ( ( plus_plus_nat @ M @ N_1 )
% 0.61/0.80 = ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N_1 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_996_com_Osize_I4_J,axiom,
% 0.61/0.80 ! [Com1_1: com,Com2_1: com] :
% 0.61/0.80 ( ( com_size @ ( semi @ Com1_1 @ Com2_1 ) )
% 0.61/0.80 = ( plus_plus_nat @ ( plus_plus_nat @ ( com_size @ Com1_1 ) @ ( com_size @ Com2_1 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_997_com_Osize_I6_J,axiom,
% 0.61/0.80 ! [Fun_1: state > $o,Com_1: com] :
% 0.61/0.80 ( ( com_size @ ( while @ Fun_1 @ Com_1 ) )
% 0.61/0.80 = ( plus_plus_nat @ ( com_size @ Com_1 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_998_com_Osize_I7_J,axiom,
% 0.61/0.80 ! [Pname_1: pname] :
% 0.61/0.80 ( ( com_size @ ( body @ Pname_1 ) )
% 0.61/0.80 = zero_zero_nat ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_999_com_Osize_I1_J,axiom,
% 0.61/0.80 ( ( com_size @ skip )
% 0.61/0.80 = zero_zero_nat ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1000_com_Osize_I12_J,axiom,
% 0.61/0.80 ! [Com1_1: com,Com2_1: com] :
% 0.61/0.80 ( ( size_size_com @ ( semi @ Com1_1 @ Com2_1 ) )
% 0.61/0.80 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_size_com @ Com1_1 ) @ ( size_size_com @ Com2_1 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1001_com_Osize_I14_J,axiom,
% 0.61/0.80 ! [Fun_1: state > $o,Com_1: com] :
% 0.61/0.80 ( ( size_size_com @ ( while @ Fun_1 @ Com_1 ) )
% 0.61/0.80 = ( plus_plus_nat @ ( size_size_com @ Com_1 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1002_add__mult__distrib2,axiom,
% 0.61/0.80 ! [K_1: nat,M: nat,N_1: nat] :
% 0.61/0.80 ( ( times_times_nat @ K_1 @ ( plus_plus_nat @ M @ N_1 ) )
% 0.61/0.80 = ( plus_plus_nat @ ( times_times_nat @ K_1 @ M ) @ ( times_times_nat @ K_1 @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1003_add__mult__distrib,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat,K_1: nat] :
% 0.61/0.80 ( ( times_times_nat @ ( plus_plus_nat @ M @ N_1 ) @ K_1 )
% 0.61/0.80 = ( plus_plus_nat @ ( times_times_nat @ M @ K_1 ) @ ( times_times_nat @ N_1 @ K_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1004_nat__mult__eq__1__iff,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ( times_times_nat @ M @ N_1 )
% 0.61/0.80 = one_one_nat )
% 0.61/0.80 <=> ( ( M = one_one_nat )
% 0.61/0.80 & ( N_1 = one_one_nat ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1005_nat__mult__1__right,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ( ( times_times_nat @ N_1 @ one_one_nat )
% 0.61/0.80 = N_1 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1006_nat__1__eq__mult__iff,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( one_one_nat
% 0.61/0.80 = ( times_times_nat @ M @ N_1 ) )
% 0.61/0.80 <=> ( ( M = one_one_nat )
% 0.61/0.80 & ( N_1 = one_one_nat ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1007_nat__mult__1,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ( ( times_times_nat @ one_one_nat @ N_1 )
% 0.61/0.80 = N_1 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1008_mult__0,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ( ( times_times_nat @ zero_zero_nat @ N_1 )
% 0.61/0.80 = zero_zero_nat ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1009_mult__0__right,axiom,
% 0.61/0.80 ! [M: nat] :
% 0.61/0.80 ( ( times_times_nat @ M @ zero_zero_nat )
% 0.61/0.80 = zero_zero_nat ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1010_mult__is__0,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ( times_times_nat @ M @ N_1 )
% 0.61/0.80 = zero_zero_nat )
% 0.61/0.80 <=> ( ( M = zero_zero_nat )
% 0.61/0.80 | ( N_1 = zero_zero_nat ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1011_mult__cancel1,axiom,
% 0.61/0.80 ! [K_1: nat,M: nat,N_1: nat] :
% 0.61/0.80 ( ( ( times_times_nat @ K_1 @ M )
% 0.61/0.80 = ( times_times_nat @ K_1 @ N_1 ) )
% 0.61/0.80 <=> ( ( M = N_1 )
% 0.61/0.80 | ( K_1 = zero_zero_nat ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1012_mult__cancel2,axiom,
% 0.61/0.80 ! [M: nat,K_1: nat,N_1: nat] :
% 0.61/0.80 ( ( ( times_times_nat @ M @ K_1 )
% 0.61/0.80 = ( times_times_nat @ N_1 @ K_1 ) )
% 0.61/0.80 <=> ( ( M = N_1 )
% 0.61/0.80 | ( K_1 = zero_zero_nat ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1013_Suc__mult__cancel1,axiom,
% 0.61/0.80 ! [K_1: nat,M: nat,N_1: nat] :
% 0.61/0.80 ( ( ( times_times_nat @ ( suc @ K_1 ) @ M )
% 0.61/0.80 = ( times_times_nat @ ( suc @ K_1 ) @ N_1 ) )
% 0.61/0.80 <=> ( M = N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1014_diff__mult__distrib,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat,K_1: nat] :
% 0.61/0.80 ( ( times_times_nat @ ( minus_minus_nat @ M @ N_1 ) @ K_1 )
% 0.61/0.80 = ( minus_minus_nat @ ( times_times_nat @ M @ K_1 ) @ ( times_times_nat @ N_1 @ K_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1015_diff__mult__distrib2,axiom,
% 0.61/0.80 ! [K_1: nat,M: nat,N_1: nat] :
% 0.61/0.80 ( ( times_times_nat @ K_1 @ ( minus_minus_nat @ M @ N_1 ) )
% 0.61/0.80 = ( minus_minus_nat @ ( times_times_nat @ K_1 @ M ) @ ( times_times_nat @ K_1 @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1016_mult__eq__1__iff,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ( times_times_nat @ M @ N_1 )
% 0.61/0.80 = ( suc @ zero_zero_nat ) )
% 0.61/0.80 <=> ( ( M
% 0.61/0.80 = ( suc @ zero_zero_nat ) )
% 0.61/0.80 & ( N_1
% 0.61/0.80 = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1017_mult__Suc,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( times_times_nat @ ( suc @ M ) @ N_1 )
% 0.61/0.80 = ( plus_plus_nat @ N_1 @ ( times_times_nat @ M @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1018_mult__Suc__right,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( times_times_nat @ M @ ( suc @ N_1 ) )
% 0.61/0.80 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1019_mult__eq__self__implies__10,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( M
% 0.61/0.80 = ( times_times_nat @ M @ N_1 ) )
% 0.61/0.80 => ( ( N_1 = one_one_nat )
% 0.61/0.80 | ( M = zero_zero_nat ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1020_com_Osize_I15_J,axiom,
% 0.61/0.80 ! [Pname_1: pname] :
% 0.61/0.80 ( ( size_size_com @ ( body @ Pname_1 ) )
% 0.61/0.80 = zero_zero_nat ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1021_com_Osize_I9_J,axiom,
% 0.61/0.80 ( ( size_size_com @ skip )
% 0.61/0.80 = zero_zero_nat ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1022_mult__eq__if,axiom,
% 0.61/0.80 ! [N_1: nat,M: nat] :
% 0.61/0.80 ( ( ( M = zero_zero_nat )
% 0.61/0.80 => ( ( times_times_nat @ M @ N_1 )
% 0.61/0.80 = zero_zero_nat ) )
% 0.61/0.80 & ( ( M != zero_zero_nat )
% 0.61/0.80 => ( ( times_times_nat @ M @ N_1 )
% 0.61/0.80 = ( plus_plus_nat @ N_1 @ ( times_times_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N_1 ) ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1023_nat__mult__commute,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( times_times_nat @ M @ N_1 )
% 0.61/0.80 = ( times_times_nat @ N_1 @ M ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1024_nat__mult__assoc,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat,K_1: nat] :
% 0.61/0.80 ( ( times_times_nat @ ( times_times_nat @ M @ N_1 ) @ K_1 )
% 0.61/0.80 = ( times_times_nat @ M @ ( times_times_nat @ N_1 @ K_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1025_left__add__mult__distrib,axiom,
% 0.61/0.80 ! [I_1: nat,U: nat,J_1: nat,K_1: nat] :
% 0.61/0.80 ( ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J_1 @ U ) @ K_1 ) )
% 0.61/0.80 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I_1 @ J_1 ) @ U ) @ K_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1026_nat__mult__eq__cancel__disj,axiom,
% 0.61/0.80 ! [K_1: nat,M: nat,N_1: nat] :
% 0.61/0.80 ( ( ( times_times_nat @ K_1 @ M )
% 0.61/0.80 = ( times_times_nat @ K_1 @ N_1 ) )
% 0.61/0.80 <=> ( ( K_1 = zero_zero_nat )
% 0.61/0.80 | ( M = N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1027_com_Osize_I13_J,axiom,
% 0.61/0.80 ! [Fun_1: state > $o,Com1_1: com,Com2_1: com] :
% 0.61/0.80 ( ( size_size_com @ ( cond @ Fun_1 @ Com1_1 @ Com2_1 ) )
% 0.61/0.80 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_size_com @ Com1_1 ) @ ( size_size_com @ Com2_1 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1028_com_Osize_I5_J,axiom,
% 0.61/0.80 ! [Fun_1: state > $o,Com1_1: com,Com2_1: com] :
% 0.61/0.80 ( ( com_size @ ( cond @ Fun_1 @ Com1_1 @ Com2_1 ) )
% 0.61/0.80 = ( plus_plus_nat @ ( plus_plus_nat @ ( com_size @ Com1_1 ) @ ( com_size @ Com2_1 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1029_finite__Collect__le__nat,axiom,
% 0.61/0.80 ! [K_1: nat] :
% 0.61/0.80 ( finite_finite_nat
% 0.61/0.80 @ ( collect_nat
% 0.61/0.80 @ ^ [N: nat] : ( ord_less_eq_nat @ N @ K_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1030_le0,axiom,
% 0.61/0.80 ! [N_1: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N_1 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1031_evaln__elim__cases_I5_J,axiom,
% 0.61/0.80 ! [B: state > $o,C1: com,C2: com,S: state,N_1: nat,T: state] :
% 0.61/0.80 ( ( evaln @ ( cond @ B @ C1 @ C2 ) @ S @ N_1 @ T )
% 0.61/0.80 => ( ( ( B @ S )
% 0.61/0.80 => ~ ( evaln @ C1 @ S @ N_1 @ T ) )
% 0.61/0.80 => ~ ( ~ ( B @ S )
% 0.61/0.80 => ~ ( evaln @ C2 @ S @ N_1 @ T ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1032_evaln_OIfTrue,axiom,
% 0.61/0.80 ! [C1: com,C0: com,N_1: nat,S1: state,B: state > $o,S: state] :
% 0.61/0.80 ( ( B @ S )
% 0.61/0.80 => ( ( evaln @ C0 @ S @ N_1 @ S1 )
% 0.61/0.80 => ( evaln @ ( cond @ B @ C0 @ C1 ) @ S @ N_1 @ S1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1033_evaln_OIfFalse,axiom,
% 0.61/0.80 ! [C0: com,C1: com,N_1: nat,S1: state,B: state > $o,S: state] :
% 0.61/0.80 ( ~ ( B @ S )
% 0.61/0.80 => ( ( evaln @ C1 @ S @ N_1 @ S1 )
% 0.61/0.80 => ( evaln @ ( cond @ B @ C0 @ C1 ) @ S @ N_1 @ S1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1034_evalc_OIfFalse,axiom,
% 0.61/0.80 ! [C0: com,C1: com,S1: state,B: state > $o,S: state] :
% 0.61/0.80 ( ~ ( B @ S )
% 0.61/0.80 => ( ( evalc @ C1 @ S @ S1 )
% 0.61/0.80 => ( evalc @ ( cond @ B @ C0 @ C1 ) @ S @ S1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1035_evalc_OIfTrue,axiom,
% 0.61/0.80 ! [C1: com,C0: com,S1: state,B: state > $o,S: state] :
% 0.61/0.80 ( ( B @ S )
% 0.61/0.80 => ( ( evalc @ C0 @ S @ S1 )
% 0.61/0.80 => ( evalc @ ( cond @ B @ C0 @ C1 ) @ S @ S1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1036_evalc__elim__cases_I5_J,axiom,
% 0.61/0.80 ! [B: state > $o,C1: com,C2: com,S: state,T: state] :
% 0.61/0.80 ( ( evalc @ ( cond @ B @ C1 @ C2 ) @ S @ T )
% 0.61/0.80 => ( ( ( B @ S )
% 0.61/0.80 => ~ ( evalc @ C1 @ S @ T ) )
% 0.61/0.80 => ~ ( ~ ( B @ S )
% 0.61/0.80 => ~ ( evalc @ C2 @ S @ T ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1037_com_Osimps_I55_J,axiom,
% 0.61/0.80 ! [Pname: pname,Fun_1: state > $o,Com1_1: com,Com2_1: com] :
% 0.61/0.80 ( ( body @ Pname )
% 0.61/0.80 != ( cond @ Fun_1 @ Com1_1 @ Com2_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1038_com_Osimps_I54_J,axiom,
% 0.61/0.80 ! [Fun_1: state > $o,Com1_1: com,Com2_1: com,Pname: pname] :
% 0.61/0.80 ( ( cond @ Fun_1 @ Com1_1 @ Com2_1 )
% 0.61/0.80 != ( body @ Pname ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1039_com_Osimps_I4_J,axiom,
% 0.61/0.80 ! [Fun_1: state > $o,Com1_1: com,Com2_1: com,Fun: state > $o,Com1: com,Com2: com] :
% 0.61/0.80 ( ( ( cond @ Fun_1 @ Com1_1 @ Com2_1 )
% 0.61/0.80 = ( cond @ Fun @ Com1 @ Com2 ) )
% 0.61/0.80 <=> ( ( Fun_1 = Fun )
% 0.61/0.80 & ( Com1_1 = Com1 )
% 0.61/0.80 & ( Com2_1 = Com2 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1040_le__antisym,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ M @ N_1 )
% 0.61/0.80 => ( ( ord_less_eq_nat @ N_1 @ M )
% 0.61/0.80 => ( M = N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1041_le__trans,axiom,
% 0.61/0.80 ! [K_1: nat,I_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.61/0.80 => ( ( ord_less_eq_nat @ J_1 @ K_1 )
% 0.61/0.80 => ( ord_less_eq_nat @ I_1 @ K_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1042_eq__imp__le,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( M = N_1 )
% 0.61/0.80 => ( ord_less_eq_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1043_nat__le__linear,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ M @ N_1 )
% 0.61/0.80 | ( ord_less_eq_nat @ N_1 @ M ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1044_le__refl,axiom,
% 0.61/0.80 ! [N_1: nat] : ( ord_less_eq_nat @ N_1 @ N_1 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1045_Suc__leD,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ ( suc @ M ) @ N_1 )
% 0.61/0.80 => ( ord_less_eq_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1046_le__SucE,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ M @ ( suc @ N_1 ) )
% 0.61/0.80 => ( ~ ( ord_less_eq_nat @ M @ N_1 )
% 0.61/0.80 => ( M
% 0.61/0.80 = ( suc @ N_1 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1047_le__SucI,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ M @ N_1 )
% 0.61/0.80 => ( ord_less_eq_nat @ M @ ( suc @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1048_Suc__le__mono,axiom,
% 0.61/0.80 ! [N_1: nat,M: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ ( suc @ N_1 ) @ ( suc @ M ) )
% 0.61/0.80 <=> ( ord_less_eq_nat @ N_1 @ M ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1049_le__Suc__eq,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ M @ ( suc @ N_1 ) )
% 0.61/0.80 <=> ( ( ord_less_eq_nat @ M @ N_1 )
% 0.61/0.80 | ( M
% 0.61/0.80 = ( suc @ N_1 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1050_not__less__eq__eq,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ~ ( ord_less_eq_nat @ M @ N_1 )
% 0.61/0.80 <=> ( ord_less_eq_nat @ ( suc @ N_1 ) @ M ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1051_Suc__n__not__le__n,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ~ ( ord_less_eq_nat @ ( suc @ N_1 ) @ N_1 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1052_le__0__eq,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ N_1 @ zero_zero_nat )
% 0.61/0.80 <=> ( N_1 = zero_zero_nat ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1053_less__eq__nat_Osimps_I1_J,axiom,
% 0.61/0.80 ! [N_1: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N_1 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1054_evaln__nonstrict,axiom,
% 0.61/0.80 ! [M: nat,C: com,S: state,N_1: nat,T: state] :
% 0.61/0.80 ( ( evaln @ C @ S @ N_1 @ T )
% 0.61/0.80 => ( ( ord_less_eq_nat @ N_1 @ M )
% 0.61/0.80 => ( evaln @ C @ S @ M @ T ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1055_diff__le__self,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N_1 ) @ M ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1056_diff__le__mono2,axiom,
% 0.61/0.80 ! [L: nat,M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ M @ N_1 )
% 0.61/0.80 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N_1 ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1057_diff__le__mono,axiom,
% 0.61/0.80 ! [L: nat,M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ M @ N_1 )
% 0.61/0.80 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N_1 @ L ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1058_diff__diff__cancel,axiom,
% 0.61/0.80 ! [I_1: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ I_1 @ N_1 )
% 0.61/0.80 => ( ( minus_minus_nat @ N_1 @ ( minus_minus_nat @ N_1 @ I_1 ) )
% 0.61/0.80 = I_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1059_eq__diff__iff,axiom,
% 0.61/0.80 ! [N_1: nat,K_1: nat,M: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ K_1 @ M )
% 0.61/0.80 => ( ( ord_less_eq_nat @ K_1 @ N_1 )
% 0.61/0.80 => ( ( ( minus_minus_nat @ M @ K_1 )
% 0.61/0.80 = ( minus_minus_nat @ N_1 @ K_1 ) )
% 0.61/0.80 <=> ( M = N_1 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1060_Nat_Odiff__diff__eq,axiom,
% 0.61/0.80 ! [N_1: nat,K_1: nat,M: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ K_1 @ M )
% 0.61/0.80 => ( ( ord_less_eq_nat @ K_1 @ N_1 )
% 0.61/0.80 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K_1 ) @ ( minus_minus_nat @ N_1 @ K_1 ) )
% 0.61/0.80 = ( minus_minus_nat @ M @ N_1 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1061_le__diff__iff,axiom,
% 0.61/0.80 ! [N_1: nat,K_1: nat,M: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ K_1 @ M )
% 0.61/0.80 => ( ( ord_less_eq_nat @ K_1 @ N_1 )
% 0.61/0.80 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K_1 ) @ ( minus_minus_nat @ N_1 @ K_1 ) )
% 0.61/0.80 <=> ( ord_less_eq_nat @ M @ N_1 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1062_add__leE,axiom,
% 0.61/0.80 ! [M: nat,K_1: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K_1 ) @ N_1 )
% 0.61/0.80 => ~ ( ( ord_less_eq_nat @ M @ N_1 )
% 0.61/0.80 => ~ ( ord_less_eq_nat @ K_1 @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1063_add__leD1,axiom,
% 0.61/0.80 ! [M: nat,K_1: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K_1 ) @ N_1 )
% 0.61/0.80 => ( ord_less_eq_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1064_add__leD2,axiom,
% 0.61/0.80 ! [M: nat,K_1: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K_1 ) @ N_1 )
% 0.61/0.80 => ( ord_less_eq_nat @ K_1 @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1065_add__le__mono,axiom,
% 0.61/0.80 ! [K_1: nat,L: nat,I_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.61/0.80 => ( ( ord_less_eq_nat @ K_1 @ L )
% 0.61/0.80 => ( ord_less_eq_nat @ ( plus_plus_nat @ I_1 @ K_1 ) @ ( plus_plus_nat @ J_1 @ L ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1066_add__le__mono1,axiom,
% 0.61/0.80 ! [K_1: nat,I_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.61/0.80 => ( ord_less_eq_nat @ ( plus_plus_nat @ I_1 @ K_1 ) @ ( plus_plus_nat @ J_1 @ K_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1067_trans__le__add2,axiom,
% 0.61/0.80 ! [M: nat,I_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.61/0.80 => ( ord_less_eq_nat @ I_1 @ ( plus_plus_nat @ M @ J_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1068_trans__le__add1,axiom,
% 0.61/0.80 ! [M: nat,I_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.61/0.80 => ( ord_less_eq_nat @ I_1 @ ( plus_plus_nat @ J_1 @ M ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1069_nat__add__left__cancel__le,axiom,
% 0.61/0.80 ! [K_1: nat,M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K_1 @ M ) @ ( plus_plus_nat @ K_1 @ N_1 ) )
% 0.61/0.80 <=> ( ord_less_eq_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1070_le__iff__add,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ M @ N_1 )
% 0.61/0.80 <=> ? [K: nat] :
% 0.61/0.80 ( N_1
% 0.61/0.80 = ( plus_plus_nat @ M @ K ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1071_le__add1,axiom,
% 0.61/0.80 ! [N_1: nat,M: nat] : ( ord_less_eq_nat @ N_1 @ ( plus_plus_nat @ N_1 @ M ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1072_le__add2,axiom,
% 0.61/0.80 ! [N_1: nat,M: nat] : ( ord_less_eq_nat @ N_1 @ ( plus_plus_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1073_card__Collect__le__nat,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ( ( finite_card_nat
% 0.61/0.80 @ ( collect_nat
% 0.61/0.80 @ ^ [I: nat] : ( ord_less_eq_nat @ I @ N_1 ) ) )
% 0.61/0.80 = ( suc @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1074_less__eq__nat_Osimps_I2_J,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ ( suc @ M ) @ N_1 )
% 0.61/0.80 <=> ( nat_case_o @ $false @ ( ord_less_eq_nat @ M ) @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1075_mult__le__mono,axiom,
% 0.61/0.80 ! [K_1: nat,L: nat,I_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.61/0.80 => ( ( ord_less_eq_nat @ K_1 @ L )
% 0.61/0.80 => ( ord_less_eq_nat @ ( times_times_nat @ I_1 @ K_1 ) @ ( times_times_nat @ J_1 @ L ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1076_mult__le__mono2,axiom,
% 0.61/0.80 ! [K_1: nat,I_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.61/0.80 => ( ord_less_eq_nat @ ( times_times_nat @ K_1 @ I_1 ) @ ( times_times_nat @ K_1 @ J_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1077_mult__le__mono1,axiom,
% 0.61/0.80 ! [K_1: nat,I_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.61/0.80 => ( ord_less_eq_nat @ ( times_times_nat @ I_1 @ K_1 ) @ ( times_times_nat @ J_1 @ K_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1078_le__cube,axiom,
% 0.61/0.80 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1079_le__square,axiom,
% 0.61/0.80 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1080_com_Osimps_I52_J,axiom,
% 0.61/0.80 ! [Fun_1: state > $o,Com1_1: com,Com2_1: com,Fun: state > $o,Com: com] :
% 0.61/0.80 ( ( cond @ Fun_1 @ Com1_1 @ Com2_1 )
% 0.61/0.80 != ( while @ Fun @ Com ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1081_com_Osimps_I53_J,axiom,
% 0.61/0.80 ! [Fun: state > $o,Com: com,Fun_1: state > $o,Com1_1: com,Com2_1: com] :
% 0.61/0.80 ( ( while @ Fun @ Com )
% 0.61/0.80 != ( cond @ Fun_1 @ Com1_1 @ Com2_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1082_com_Osimps_I45_J,axiom,
% 0.61/0.80 ! [Fun: state > $o,Com1: com,Com2: com,Com1_1: com,Com2_1: com] :
% 0.61/0.80 ( ( cond @ Fun @ Com1 @ Com2 )
% 0.61/0.80 != ( semi @ Com1_1 @ Com2_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1083_com_Osimps_I44_J,axiom,
% 0.61/0.80 ! [Com1_1: com,Com2_1: com,Fun: state > $o,Com1: com,Com2: com] :
% 0.61/0.80 ( ( semi @ Com1_1 @ Com2_1 )
% 0.61/0.80 != ( cond @ Fun @ Com1 @ Com2 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1084_com_Osimps_I15_J,axiom,
% 0.61/0.80 ! [Fun: state > $o,Com1: com,Com2: com] :
% 0.61/0.80 ( ( cond @ Fun @ Com1 @ Com2 )
% 0.61/0.80 != skip ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1085_com_Osimps_I14_J,axiom,
% 0.61/0.80 ! [Fun: state > $o,Com1: com,Com2: com] :
% 0.61/0.80 ( skip
% 0.61/0.80 != ( cond @ Fun @ Com1 @ Com2 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1086_diff__is__0__eq_H,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ M @ N_1 )
% 0.61/0.80 => ( ( minus_minus_nat @ M @ N_1 )
% 0.61/0.80 = zero_zero_nat ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1087_diff__is__0__eq,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ( minus_minus_nat @ M @ N_1 )
% 0.61/0.80 = zero_zero_nat )
% 0.61/0.80 <=> ( ord_less_eq_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1088_Suc__diff__le,axiom,
% 0.61/0.80 ! [N_1: nat,M: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ N_1 @ M )
% 0.61/0.80 => ( ( minus_minus_nat @ ( suc @ M ) @ N_1 )
% 0.61/0.80 = ( suc @ ( minus_minus_nat @ M @ N_1 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1089_Suc__mult__le__cancel1,axiom,
% 0.61/0.80 ! [K_1: nat,M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K_1 ) @ M ) @ ( times_times_nat @ ( suc @ K_1 ) @ N_1 ) )
% 0.61/0.80 <=> ( ord_less_eq_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1090_diff__diff__right,axiom,
% 0.61/0.80 ! [I_1: nat,K_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ K_1 @ J_1 )
% 0.61/0.80 => ( ( minus_minus_nat @ I_1 @ ( minus_minus_nat @ J_1 @ K_1 ) )
% 0.61/0.80 = ( minus_minus_nat @ ( plus_plus_nat @ I_1 @ K_1 ) @ J_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1091_le__diff__conv,axiom,
% 0.61/0.80 ! [J_1: nat,K_1: nat,I_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J_1 @ K_1 ) @ I_1 )
% 0.61/0.80 <=> ( ord_less_eq_nat @ J_1 @ ( plus_plus_nat @ I_1 @ K_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1092_le__add__diff,axiom,
% 0.61/0.80 ! [M: nat,K_1: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ K_1 @ N_1 )
% 0.61/0.80 => ( ord_less_eq_nat @ M @ ( minus_minus_nat @ ( plus_plus_nat @ N_1 @ M ) @ K_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1093_le__add__diff__inverse,axiom,
% 0.61/0.80 ! [N_1: nat,M: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ N_1 @ M )
% 0.61/0.80 => ( ( plus_plus_nat @ N_1 @ ( minus_minus_nat @ M @ N_1 ) )
% 0.61/0.80 = M ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1094_add__diff__assoc,axiom,
% 0.61/0.80 ! [I_1: nat,K_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ K_1 @ J_1 )
% 0.61/0.80 => ( ( plus_plus_nat @ I_1 @ ( minus_minus_nat @ J_1 @ K_1 ) )
% 0.61/0.80 = ( minus_minus_nat @ ( plus_plus_nat @ I_1 @ J_1 ) @ K_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1095_le__diff__conv2,axiom,
% 0.61/0.80 ! [I_1: nat,K_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ K_1 @ J_1 )
% 0.61/0.80 => ( ( ord_less_eq_nat @ I_1 @ ( minus_minus_nat @ J_1 @ K_1 ) )
% 0.61/0.80 <=> ( ord_less_eq_nat @ ( plus_plus_nat @ I_1 @ K_1 ) @ J_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1096_le__add__diff__inverse2,axiom,
% 0.61/0.80 ! [N_1: nat,M: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ N_1 @ M )
% 0.61/0.80 => ( ( plus_plus_nat @ ( minus_minus_nat @ M @ N_1 ) @ N_1 )
% 0.61/0.80 = M ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1097_le__imp__diff__is__add,axiom,
% 0.61/0.80 ! [K_1: nat,I_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.61/0.80 => ( ( ( minus_minus_nat @ J_1 @ I_1 )
% 0.61/0.80 = K_1 )
% 0.61/0.80 <=> ( J_1
% 0.61/0.80 = ( plus_plus_nat @ K_1 @ I_1 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1098_diff__add__assoc,axiom,
% 0.61/0.80 ! [I_1: nat,K_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ K_1 @ J_1 )
% 0.61/0.80 => ( ( minus_minus_nat @ ( plus_plus_nat @ I_1 @ J_1 ) @ K_1 )
% 0.61/0.80 = ( plus_plus_nat @ I_1 @ ( minus_minus_nat @ J_1 @ K_1 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1099_add__diff__assoc2,axiom,
% 0.61/0.80 ! [I_1: nat,K_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ K_1 @ J_1 )
% 0.61/0.80 => ( ( plus_plus_nat @ ( minus_minus_nat @ J_1 @ K_1 ) @ I_1 )
% 0.61/0.80 = ( minus_minus_nat @ ( plus_plus_nat @ J_1 @ I_1 ) @ K_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1100_diff__add__assoc2,axiom,
% 0.61/0.80 ! [I_1: nat,K_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ K_1 @ J_1 )
% 0.61/0.80 => ( ( minus_minus_nat @ ( plus_plus_nat @ J_1 @ I_1 ) @ K_1 )
% 0.61/0.80 = ( plus_plus_nat @ ( minus_minus_nat @ J_1 @ K_1 ) @ I_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1101_one__le__mult__iff,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N_1 ) )
% 0.61/0.80 <=> ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.61/0.80 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1102_diff__Suc__diff__eq2,axiom,
% 0.61/0.80 ! [M: nat,K_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ K_1 @ J_1 )
% 0.61/0.80 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J_1 @ K_1 ) ) @ M )
% 0.61/0.80 = ( minus_minus_nat @ ( suc @ J_1 ) @ ( plus_plus_nat @ K_1 @ M ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1103_diff__Suc__diff__eq1,axiom,
% 0.61/0.80 ! [M: nat,K_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ K_1 @ J_1 )
% 0.61/0.80 => ( ( minus_minus_nat @ M @ ( suc @ ( minus_minus_nat @ J_1 @ K_1 ) ) )
% 0.61/0.80 = ( minus_minus_nat @ ( plus_plus_nat @ M @ K_1 ) @ ( suc @ J_1 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1104_nat__le__add__iff1,axiom,
% 0.61/0.80 ! [U: nat,M: nat,N_1: nat,J_1: nat,I_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ J_1 @ I_1 )
% 0.61/0.80 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J_1 @ U ) @ N_1 ) )
% 0.61/0.80 <=> ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I_1 @ J_1 ) @ U ) @ M ) @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1105_nat__diff__add__eq1,axiom,
% 0.61/0.80 ! [U: nat,M: nat,N_1: nat,J_1: nat,I_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ J_1 @ I_1 )
% 0.61/0.80 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J_1 @ U ) @ N_1 ) )
% 0.61/0.80 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I_1 @ J_1 ) @ U ) @ M ) @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1106_nat__eq__add__iff1,axiom,
% 0.61/0.80 ! [U: nat,M: nat,N_1: nat,J_1: nat,I_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ J_1 @ I_1 )
% 0.61/0.80 => ( ( ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M )
% 0.61/0.80 = ( plus_plus_nat @ ( times_times_nat @ J_1 @ U ) @ N_1 ) )
% 0.61/0.80 <=> ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I_1 @ J_1 ) @ U ) @ M )
% 0.61/0.80 = N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1107_nat__le__add__iff2,axiom,
% 0.61/0.80 ! [U: nat,M: nat,N_1: nat,I_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.61/0.80 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J_1 @ U ) @ N_1 ) )
% 0.61/0.80 <=> ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J_1 @ I_1 ) @ U ) @ N_1 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1108_nat__diff__add__eq2,axiom,
% 0.61/0.80 ! [U: nat,M: nat,N_1: nat,I_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.61/0.80 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J_1 @ U ) @ N_1 ) )
% 0.61/0.80 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J_1 @ I_1 ) @ U ) @ N_1 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1109_nat__eq__add__iff2,axiom,
% 0.61/0.80 ! [U: nat,M: nat,N_1: nat,I_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.61/0.80 => ( ( ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M )
% 0.61/0.80 = ( plus_plus_nat @ ( times_times_nat @ J_1 @ U ) @ N_1 ) )
% 0.61/0.80 <=> ( M
% 0.61/0.80 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J_1 @ I_1 ) @ U ) @ N_1 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1110_Suc__le__D,axiom,
% 0.61/0.80 ! [N_1: nat,M_2: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ ( suc @ N_1 ) @ M_2 )
% 0.61/0.80 => ? [M_1: nat] :
% 0.61/0.80 ( M_2
% 0.61/0.80 = ( suc @ M_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1111_Suc__le__D__lemma,axiom,
% 0.61/0.80 ! [P: nat > $o,N_1: nat,M_2: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ ( suc @ N_1 ) @ M_2 )
% 0.61/0.80 => ( ! [M_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ N_1 @ M_1 )
% 0.61/0.80 => ( P @ ( suc @ M_1 ) ) )
% 0.61/0.80 => ( P @ M_2 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1112_finite__nat__set__iff__bounded__le,axiom,
% 0.61/0.80 ! [N_2: nat > $o] :
% 0.61/0.80 ( ( finite_finite_nat @ N_2 )
% 0.61/0.80 <=> ? [M_1: nat] :
% 0.61/0.80 ! [X: nat] :
% 0.61/0.80 ( ( member_nat @ X @ N_2 )
% 0.61/0.80 => ( ord_less_eq_nat @ X @ M_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1113_finite__less__ub,axiom,
% 0.61/0.80 ! [U: nat,F: nat > nat] :
% 0.61/0.80 ( ! [N: nat] : ( ord_less_eq_nat @ N @ ( F @ N ) )
% 0.61/0.80 => ( finite_finite_nat
% 0.61/0.80 @ ( collect_nat
% 0.61/0.80 @ ^ [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ U ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1114_termination__basic__simps_I3_J,axiom,
% 0.61/0.80 ! [Z: nat,X_1: nat,Y: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ X_1 @ Y )
% 0.61/0.80 => ( ord_less_eq_nat @ X_1 @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1115_termination__basic__simps_I4_J,axiom,
% 0.61/0.80 ! [Y: nat,X_1: nat,Z: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ X_1 @ Z )
% 0.61/0.80 => ( ord_less_eq_nat @ X_1 @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1116_less__zeroE,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ~ ( ord_less_nat @ N_1 @ zero_zero_nat ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1117_lessI,axiom,
% 0.61/0.80 ! [N_1: nat] : ( ord_less_nat @ N_1 @ ( suc @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1118_Suc__mono,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ M @ N_1 )
% 0.61/0.80 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1119_finite__Collect__less__nat,axiom,
% 0.61/0.80 ! [K_1: nat] :
% 0.61/0.80 ( finite_finite_nat
% 0.61/0.80 @ ( collect_nat
% 0.61/0.80 @ ^ [N: nat] : ( ord_less_nat @ N @ K_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1120_zero__less__Suc,axiom,
% 0.61/0.80 ! [N_1: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1121_finite__M__bounded__by__nat,axiom,
% 0.61/0.80 ! [P: nat > $o,I_1: nat] :
% 0.61/0.80 ( finite_finite_nat
% 0.61/0.80 @ ( collect_nat
% 0.61/0.80 @ ^ [K: nat] : ( (&) @ ( P @ K ) @ ( ord_less_nat @ K @ I_1 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1122_finite__nat__set__iff__bounded,axiom,
% 0.61/0.80 ! [N_2: nat > $o] :
% 0.61/0.80 ( ( finite_finite_nat @ N_2 )
% 0.61/0.80 <=> ? [M_1: nat] :
% 0.61/0.80 ! [X: nat] :
% 0.61/0.80 ( ( member_nat @ X @ N_2 )
% 0.61/0.80 => ( ord_less_nat @ X @ M_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1123_less__or__eq__imp__le,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ( ord_less_nat @ M @ N_1 )
% 0.61/0.80 | ( M = N_1 ) )
% 0.61/0.80 => ( ord_less_eq_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1124_le__neq__implies__less,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ M @ N_1 )
% 0.61/0.80 => ( ( M != N_1 )
% 0.61/0.80 => ( ord_less_nat @ M @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1125_less__imp__le__nat,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ M @ N_1 )
% 0.61/0.80 => ( ord_less_eq_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1126_le__eq__less__or__eq,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ M @ N_1 )
% 0.61/0.80 <=> ( ( ord_less_nat @ M @ N_1 )
% 0.61/0.80 | ( M = N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1127_nat__less__le,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ M @ N_1 )
% 0.61/0.80 <=> ( ( ord_less_eq_nat @ M @ N_1 )
% 0.61/0.80 & ( M != N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1128_Suc__le__lessD,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ ( suc @ M ) @ N_1 )
% 0.61/0.80 => ( ord_less_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1129_le__less__Suc__eq,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ M @ N_1 )
% 0.61/0.80 => ( ( ord_less_nat @ N_1 @ ( suc @ M ) )
% 0.61/0.80 <=> ( N_1 = M ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1130_Suc__leI,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ M @ N_1 )
% 0.61/0.80 => ( ord_less_eq_nat @ ( suc @ M ) @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1131_le__imp__less__Suc,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ M @ N_1 )
% 0.61/0.80 => ( ord_less_nat @ M @ ( suc @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1132_Suc__le__eq,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ ( suc @ M ) @ N_1 )
% 0.61/0.80 <=> ( ord_less_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1133_less__Suc__eq__le,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ M @ ( suc @ N_1 ) )
% 0.61/0.80 <=> ( ord_less_eq_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1134_less__eq__Suc__le,axiom,
% 0.61/0.80 ! [N_1: nat,M: nat] :
% 0.61/0.80 ( ( ord_less_nat @ N_1 @ M )
% 0.61/0.80 <=> ( ord_less_eq_nat @ ( suc @ N_1 ) @ M ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1135_less__diff__iff,axiom,
% 0.61/0.80 ! [N_1: nat,K_1: nat,M: nat] :
% 0.61/0.80 ( ( ord_less_eq_nat @ K_1 @ M )
% 0.61/0.80 => ( ( ord_less_eq_nat @ K_1 @ N_1 )
% 0.61/0.80 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K_1 ) @ ( minus_minus_nat @ N_1 @ K_1 ) )
% 0.61/0.80 <=> ( ord_less_nat @ M @ N_1 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1136_diff__less__mono,axiom,
% 0.61/0.80 ! [C: nat,A: nat,B: nat] :
% 0.61/0.80 ( ( ord_less_nat @ A @ B )
% 0.61/0.80 => ( ( ord_less_eq_nat @ C @ A )
% 0.61/0.80 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1137_not__add__less1,axiom,
% 0.61/0.80 ! [I_1: nat,J_1: nat] :
% 0.61/0.80 ~ ( ord_less_nat @ ( plus_plus_nat @ I_1 @ J_1 ) @ I_1 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1138_not__add__less2,axiom,
% 0.61/0.80 ! [J_1: nat,I_1: nat] :
% 0.61/0.80 ~ ( ord_less_nat @ ( plus_plus_nat @ J_1 @ I_1 ) @ I_1 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1139_nat__add__left__cancel__less,axiom,
% 0.61/0.80 ! [K_1: nat,M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ ( plus_plus_nat @ K_1 @ M ) @ ( plus_plus_nat @ K_1 @ N_1 ) )
% 0.61/0.80 <=> ( ord_less_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1140_trans__less__add1,axiom,
% 0.61/0.80 ! [M: nat,I_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ I_1 @ J_1 )
% 0.61/0.80 => ( ord_less_nat @ I_1 @ ( plus_plus_nat @ J_1 @ M ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1141_trans__less__add2,axiom,
% 0.61/0.80 ! [M: nat,I_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ I_1 @ J_1 )
% 0.61/0.80 => ( ord_less_nat @ I_1 @ ( plus_plus_nat @ M @ J_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1142_add__less__mono1,axiom,
% 0.61/0.80 ! [K_1: nat,I_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ I_1 @ J_1 )
% 0.61/0.80 => ( ord_less_nat @ ( plus_plus_nat @ I_1 @ K_1 ) @ ( plus_plus_nat @ J_1 @ K_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1143_add__less__mono,axiom,
% 0.61/0.80 ! [K_1: nat,L: nat,I_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ I_1 @ J_1 )
% 0.61/0.80 => ( ( ord_less_nat @ K_1 @ L )
% 0.61/0.80 => ( ord_less_nat @ ( plus_plus_nat @ I_1 @ K_1 ) @ ( plus_plus_nat @ J_1 @ L ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1144_less__add__eq__less,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat,K_1: nat,L: nat] :
% 0.61/0.80 ( ( ord_less_nat @ K_1 @ L )
% 0.61/0.80 => ( ( ( plus_plus_nat @ M @ L )
% 0.61/0.80 = ( plus_plus_nat @ K_1 @ N_1 ) )
% 0.61/0.80 => ( ord_less_nat @ M @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1145_add__lessD1,axiom,
% 0.61/0.80 ! [I_1: nat,J_1: nat,K_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ ( plus_plus_nat @ I_1 @ J_1 ) @ K_1 )
% 0.61/0.80 => ( ord_less_nat @ I_1 @ K_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1146_diff__less__mono2,axiom,
% 0.61/0.80 ! [L: nat,M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ M @ N_1 )
% 0.61/0.80 => ( ( ord_less_nat @ M @ L )
% 0.61/0.80 => ( ord_less_nat @ ( minus_minus_nat @ L @ N_1 ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1147_less__imp__diff__less,axiom,
% 0.61/0.80 ! [N_1: nat,J_1: nat,K_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ J_1 @ K_1 )
% 0.61/0.80 => ( ord_less_nat @ ( minus_minus_nat @ J_1 @ N_1 ) @ K_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1148_not__less0,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ~ ( ord_less_nat @ N_1 @ zero_zero_nat ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1149_neq0__conv,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ( ( N_1 != zero_zero_nat )
% 0.61/0.80 <=> ( ord_less_nat @ zero_zero_nat @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1150_less__nat__zero__code,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ~ ( ord_less_nat @ N_1 @ zero_zero_nat ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1151_gr__implies__not0,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ M @ N_1 )
% 0.61/0.80 => ( N_1 != zero_zero_nat ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1152_gr0I,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ( ( N_1 != zero_zero_nat )
% 0.61/0.80 => ( ord_less_nat @ zero_zero_nat @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1153_not__less__eq,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ~ ( ord_less_nat @ M @ N_1 )
% 0.61/0.80 <=> ( ord_less_nat @ N_1 @ ( suc @ M ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1154_less__Suc__eq,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ M @ ( suc @ N_1 ) )
% 0.61/0.80 <=> ( ( ord_less_nat @ M @ N_1 )
% 0.61/0.80 | ( M = N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1155_Suc__less__eq,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N_1 ) )
% 0.61/0.80 <=> ( ord_less_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1156_not__less__less__Suc__eq,axiom,
% 0.61/0.80 ! [N_1: nat,M: nat] :
% 0.61/0.80 ( ~ ( ord_less_nat @ N_1 @ M )
% 0.61/0.80 => ( ( ord_less_nat @ N_1 @ ( suc @ M ) )
% 0.61/0.80 <=> ( N_1 = M ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1157_less__antisym,axiom,
% 0.61/0.80 ! [N_1: nat,M: nat] :
% 0.61/0.80 ( ~ ( ord_less_nat @ N_1 @ M )
% 0.61/0.80 => ( ( ord_less_nat @ N_1 @ ( suc @ M ) )
% 0.61/0.80 => ( M = N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1158_less__SucI,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ M @ N_1 )
% 0.61/0.80 => ( ord_less_nat @ M @ ( suc @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1159_Suc__lessI,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ M @ N_1 )
% 0.61/0.80 => ( ( ( suc @ M )
% 0.61/0.80 != N_1 )
% 0.61/0.80 => ( ord_less_nat @ ( suc @ M ) @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1160_less__trans__Suc,axiom,
% 0.61/0.80 ! [K_1: nat,I_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ I_1 @ J_1 )
% 0.61/0.80 => ( ( ord_less_nat @ J_1 @ K_1 )
% 0.61/0.80 => ( ord_less_nat @ ( suc @ I_1 ) @ K_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1161_less__SucE,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ M @ ( suc @ N_1 ) )
% 0.61/0.80 => ( ~ ( ord_less_nat @ M @ N_1 )
% 0.61/0.80 => ( M = N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1162_Suc__lessD,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ ( suc @ M ) @ N_1 )
% 0.61/0.80 => ( ord_less_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1163_Suc__less__SucD,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N_1 ) )
% 0.61/0.80 => ( ord_less_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1164_less__not__refl,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ~ ( ord_less_nat @ N_1 @ N_1 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1165_nat__neq__iff,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( M != N_1 )
% 0.61/0.80 <=> ( ( ord_less_nat @ M @ N_1 )
% 0.61/0.80 | ( ord_less_nat @ N_1 @ M ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1166_linorder__neqE__nat,axiom,
% 0.61/0.80 ! [X_1: nat,Y: nat] :
% 0.61/0.80 ( ( X_1 != Y )
% 0.61/0.80 => ( ~ ( ord_less_nat @ X_1 @ Y )
% 0.61/0.80 => ( ord_less_nat @ Y @ X_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1167_less__irrefl__nat,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ~ ( ord_less_nat @ N_1 @ N_1 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1168_less__not__refl2,axiom,
% 0.61/0.80 ! [N_1: nat,M: nat] :
% 0.61/0.80 ( ( ord_less_nat @ N_1 @ M )
% 0.61/0.80 => ( M != N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1169_less__not__refl3,axiom,
% 0.61/0.80 ! [S: nat,T: nat] :
% 0.61/0.80 ( ( ord_less_nat @ S @ T )
% 0.61/0.80 => ( S != T ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1170_nat__less__cases,axiom,
% 0.61/0.80 ! [P: nat > nat > $o,M: nat,N_1: nat] :
% 0.61/0.80 ( ( ( ord_less_nat @ M @ N_1 )
% 0.61/0.80 => ( P @ N_1 @ M ) )
% 0.61/0.80 => ( ( ( M = N_1 )
% 0.61/0.80 => ( P @ N_1 @ M ) )
% 0.61/0.80 => ( ( ( ord_less_nat @ N_1 @ M )
% 0.61/0.80 => ( P @ N_1 @ M ) )
% 0.61/0.80 => ( P @ N_1 @ M ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1171_less__diff__conv,axiom,
% 0.61/0.80 ! [I_1: nat,J_1: nat,K_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ I_1 @ ( minus_minus_nat @ J_1 @ K_1 ) )
% 0.61/0.80 <=> ( ord_less_nat @ ( plus_plus_nat @ I_1 @ K_1 ) @ J_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1172_add__diff__inverse,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ~ ( ord_less_nat @ M @ N_1 )
% 0.61/0.80 => ( ( plus_plus_nat @ N_1 @ ( minus_minus_nat @ M @ N_1 ) )
% 0.61/0.80 = M ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1173_Suc__mult__less__cancel1,axiom,
% 0.61/0.80 ! [K_1: nat,M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K_1 ) @ M ) @ ( times_times_nat @ ( suc @ K_1 ) @ N_1 ) )
% 0.61/0.80 <=> ( ord_less_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1174_diff__less__Suc,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N_1 ) @ ( suc @ M ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1175_nat__0__less__mult__iff,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N_1 ) )
% 0.61/0.80 <=> ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.61/0.80 & ( ord_less_nat @ zero_zero_nat @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1176_mult__less__cancel1,axiom,
% 0.61/0.80 ! [K_1: nat,M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ ( times_times_nat @ K_1 @ M ) @ ( times_times_nat @ K_1 @ N_1 ) )
% 0.61/0.80 <=> ( ( ord_less_nat @ zero_zero_nat @ K_1 )
% 0.61/0.80 & ( ord_less_nat @ M @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1177_mult__less__cancel2,axiom,
% 0.61/0.80 ! [M: nat,K_1: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ ( times_times_nat @ M @ K_1 ) @ ( times_times_nat @ N_1 @ K_1 ) )
% 0.61/0.80 <=> ( ( ord_less_nat @ zero_zero_nat @ K_1 )
% 0.61/0.80 & ( ord_less_nat @ M @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1178_mult__less__mono1,axiom,
% 0.61/0.80 ! [K_1: nat,I_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ I_1 @ J_1 )
% 0.61/0.80 => ( ( ord_less_nat @ zero_zero_nat @ K_1 )
% 0.61/0.80 => ( ord_less_nat @ ( times_times_nat @ I_1 @ K_1 ) @ ( times_times_nat @ J_1 @ K_1 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1179_mult__less__mono2,axiom,
% 0.61/0.80 ! [K_1: nat,I_1: nat,J_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ I_1 @ J_1 )
% 0.61/0.80 => ( ( ord_less_nat @ zero_zero_nat @ K_1 )
% 0.61/0.80 => ( ord_less_nat @ ( times_times_nat @ K_1 @ I_1 ) @ ( times_times_nat @ K_1 @ J_1 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1180_nat__mult__eq__cancel1,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat,K_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ zero_zero_nat @ K_1 )
% 0.61/0.80 => ( ( ( times_times_nat @ K_1 @ M )
% 0.61/0.80 = ( times_times_nat @ K_1 @ N_1 ) )
% 0.61/0.80 <=> ( M = N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1181_nat__mult__less__cancel1,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat,K_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ zero_zero_nat @ K_1 )
% 0.61/0.80 => ( ( ord_less_nat @ ( times_times_nat @ K_1 @ M ) @ ( times_times_nat @ K_1 @ N_1 ) )
% 0.61/0.80 <=> ( ord_less_nat @ M @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1182_diff__less,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ zero_zero_nat @ N_1 )
% 0.61/0.80 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.61/0.80 => ( ord_less_nat @ ( minus_minus_nat @ M @ N_1 ) @ M ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1183_zero__less__diff,axiom,
% 0.61/0.80 ! [N_1: nat,M: nat] :
% 0.61/0.80 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N_1 @ M ) )
% 0.61/0.80 <=> ( ord_less_nat @ M @ N_1 ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1184_less__add__Suc1,axiom,
% 0.61/0.80 ! [I_1: nat,M: nat] : ( ord_less_nat @ I_1 @ ( suc @ ( plus_plus_nat @ I_1 @ M ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1185_less__add__Suc2,axiom,
% 0.61/0.80 ! [I_1: nat,M: nat] : ( ord_less_nat @ I_1 @ ( suc @ ( plus_plus_nat @ M @ I_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1186_less__iff__Suc__add,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ M @ N_1 )
% 0.61/0.80 <=> ? [K: nat] :
% 0.61/0.80 ( N_1
% 0.61/0.80 = ( suc @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1187_add__gr__0,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N_1 ) )
% 0.61/0.80 <=> ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.61/0.80 | ( ord_less_nat @ zero_zero_nat @ N_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1188_gr0__conv__Suc,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ zero_zero_nat @ N_1 )
% 0.61/0.80 <=> ? [M_1: nat] :
% 0.61/0.80 ( N_1
% 0.61/0.80 = ( suc @ M_1 ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1189_less__Suc0,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ N_1 @ ( suc @ zero_zero_nat ) )
% 0.61/0.80 <=> ( N_1 = zero_zero_nat ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1190_less__Suc__eq__0__disj,axiom,
% 0.61/0.80 ! [M: nat,N_1: nat] :
% 0.61/0.80 ( ( ord_less_nat @ M @ ( suc @ N_1 ) )
% 0.61/0.80 <=> ( ( M = zero_zero_nat )
% 0.61/0.80 | ? [J: nat] :
% 0.61/0.80 ( ( M
% 0.61/0.80 = ( suc @ J ) )
% 0.61/0.80 & ( ord_less_nat @ J @ N_1 ) ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1191_card__Collect__less__nat,axiom,
% 0.61/0.80 ! [N_1: nat] :
% 0.61/0.80 ( ( finite_card_nat
% 0.61/0.80 @ ( collect_nat
% 0.61/0.80 @ ^ [I: nat] : ( ord_less_nat @ I @ N_1 ) ) )
% 0.61/0.80 = N_1 ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1192_less__eq__Suc__le__raw,axiom,
% 0.61/0.80 ! [X: nat] :
% 0.61/0.80 ( ( ord_less_nat @ X )
% 0.61/0.80 = ( ord_less_eq_nat @ ( suc @ X ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1193_termination__basic__simps_I1_J,axiom,
% 0.61/0.80 ! [Z: nat,X_1: nat,Y: nat] :
% 0.61/0.80 ( ( ord_less_nat @ X_1 @ Y )
% 0.61/0.80 => ( ord_less_nat @ X_1 @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1194_termination__basic__simps_I2_J,axiom,
% 0.61/0.80 ! [Y: nat,X_1: nat,Z: nat] :
% 0.61/0.80 ( ( ord_less_nat @ X_1 @ Z )
% 0.61/0.80 => ( ord_less_nat @ X_1 @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(fact_1195_termination__basic__simps_I5_J,axiom,
% 0.61/0.80 ! [X_1: nat,Y: nat] :
% 0.61/0.80 ( ( ord_less_nat @ X_1 @ Y )
% 0.61/0.80 => ( ord_less_eq_nat @ X_1 @ Y ) ) ).
% 0.61/0.80
% 0.61/0.80 %----Helper facts (12)
% 0.61/0.80 thf(help_fequal_1_1_fequal_000tc__Nat__Onat_T,axiom,
% 0.61/0.80 ! [X_1: nat,Y: nat] :
% 0.61/0.80 ( ~ ( fequal_nat @ X_1 @ Y )
% 0.61/0.80 | ( X_1 = Y ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(help_fequal_2_1_fequal_000tc__Nat__Onat_T,axiom,
% 0.61/0.80 ! [X_1: nat,Y: nat] :
% 0.61/0.80 ( ( X_1 != Y )
% 0.61/0.80 | ( fequal_nat @ X_1 @ Y ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,
% 0.61/0.80 ! [X_1: pname,Y: pname] :
% 0.61/0.80 ( ~ ( fequal_pname @ X_1 @ Y )
% 0.61/0.80 | ( X_1 = Y ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,
% 0.61/0.80 ! [X_1: pname,Y: pname] :
% 0.61/0.80 ( ( X_1 != Y )
% 0.61/0.80 | ( fequal_pname @ X_1 @ Y ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(help_fequal_1_1_fequal_000tc__Com__Ostate_T,axiom,
% 0.61/0.80 ! [X_1: state,Y: state] :
% 0.61/0.80 ( ~ ( fequal_state @ X_1 @ Y )
% 0.61/0.80 | ( X_1 = Y ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(help_fequal_2_1_fequal_000tc__Com__Ostate_T,axiom,
% 0.61/0.80 ! [X_1: state,Y: state] :
% 0.61/0.80 ( ( X_1 != Y )
% 0.61/0.80 | ( fequal_state @ X_1 @ Y ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_,axiom,
% 0.61/0.80 ! [X_1: hoare_2091234717iple_a,Y: hoare_2091234717iple_a] :
% 0.61/0.80 ( ~ ( fequal1604381340iple_a @ X_1 @ Y )
% 0.61/0.80 | ( X_1 = Y ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_,axiom,
% 0.61/0.80 ! [X_1: hoare_2091234717iple_a,Y: hoare_2091234717iple_a] :
% 0.61/0.80 ( ( X_1 != Y )
% 0.61/0.80 | ( fequal1604381340iple_a @ X_1 @ Y ) ) ).
% 0.61/0.80
% 0.61/0.80 thf(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com,axiom,
% 0.61/0.80 ! [X_1: hoare_1708887482_state,Y: hoare_1708887482_state] :
% 0.61/0.80 ( ~ ( fequal224822779_state @ X_1 @ Y )
% 0.62/0.95 | ( X_1 = Y ) ) ).
% 0.62/0.95
% 0.62/0.95 thf(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com,axiom,
% 0.62/0.95 ! [X_1: hoare_1708887482_state,Y: hoare_1708887482_state] :
% 0.62/0.95 ( ( X_1 != Y )
% 0.62/0.95 | ( fequal224822779_state @ X_1 @ Y ) ) ).
% 0.62/0.95
% 0.62/0.95 thf(help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It,axiom,
% 0.62/0.95 ! [X_1: hoare_2091234717iple_a > $o,Y: hoare_2091234717iple_a > $o] :
% 0.62/0.95 ( ~ ( fequal845167073le_a_o @ X_1 @ Y )
% 0.62/0.95 | ( X_1 = Y ) ) ).
% 0.62/0.95
% 0.62/0.95 thf(help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It,axiom,
% 0.62/0.95 ! [X_1: hoare_2091234717iple_a > $o,Y: hoare_2091234717iple_a > $o] :
% 0.62/0.95 ( ( X_1 != Y )
% 0.62/0.95 | ( fequal845167073le_a_o @ X_1 @ Y ) ) ).
% 0.62/0.95
% 0.62/0.95 %----Conjectures (2)
% 0.62/0.95 thf(conj_0,hypothesis,
% 0.62/0.95 ! [N: nat] :
% 0.62/0.95 ( ! [X: hoare_2091234717iple_a] :
% 0.62/0.95 ( ( member290856304iple_a @ X
% 0.62/0.95 @ ( semila1052848428le_a_o @ g
% 0.62/0.95 @ ( image_231808478iple_a
% 0.62/0.95 @ ^ [Pn: pname] : ( hoare_657976383iple_a @ ( p @ Pn ) @ ( body @ Pn ) @ ( q @ Pn ) )
% 0.62/0.95 @ procs ) ) )
% 0.62/0.95 => ( hoare_1421888935alid_a @ N @ X ) )
% 0.62/0.95 => ! [X: hoare_2091234717iple_a] :
% 0.62/0.95 ( ( member290856304iple_a @ X
% 0.62/0.95 @ ( image_231808478iple_a
% 0.62/0.95 @ ^ [Pn: pname] : ( hoare_657976383iple_a @ ( p @ Pn ) @ ( the_com @ ( body_1 @ Pn ) ) @ ( q @ Pn ) )
% 0.62/0.95 @ procs ) )
% 0.62/0.95 => ( hoare_1421888935alid_a @ N @ X ) ) ) ).
% 0.62/0.95
% 0.62/0.95 thf(conj_1,conjecture,
% 0.62/0.95 ( ! [X: hoare_2091234717iple_a] :
% 0.62/0.95 ( ( member290856304iple_a @ X @ g )
% 0.62/0.95 => ( hoare_1421888935alid_a @ n @ X ) )
% 0.62/0.95 => ! [X: hoare_2091234717iple_a] :
% 0.62/0.95 ( ( member290856304iple_a @ X
% 0.62/0.95 @ ( image_231808478iple_a
% 0.62/0.95 @ ^ [Pn: pname] : ( hoare_657976383iple_a @ ( p @ Pn ) @ ( body @ Pn ) @ ( q @ Pn ) )
% 0.62/0.95 @ procs ) )
% 0.62/0.95 => ( hoare_1421888935alid_a @ n @ X ) ) ) ).
% 0.62/0.95
% 0.62/0.95 %------------------------------------------------------------------------------
% 0.62/0.95 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.HpU680UFcj/cvc5---1.0.5_25055.p...
% 0.62/0.95 (declare-sort $$unsorted 0)
% 0.62/0.95 (declare-sort tptp.x_a 0)
% 0.62/0.95 (declare-sort tptp.com 0)
% 0.62/0.95 (declare-sort tptp.pname 0)
% 0.62/0.95 (declare-sort tptp.state 0)
% 0.62/0.95 (declare-sort tptp.hoare_2091234717iple_a 0)
% 0.62/0.95 (declare-sort tptp.hoare_1708887482_state 0)
% 0.62/0.95 (declare-sort tptp.nat 0)
% 0.62/0.95 (declare-sort tptp.option_com 0)
% 0.62/0.95 (declare-fun tptp.big_co1924420859_pname ((-> (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) (-> (-> tptp.pname tptp.hoare_2091234717iple_a Bool) (-> tptp.pname Bool) tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.big_la1994307886_a_o_o ((-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) Bool) (-> tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.big_la1286884090name_o ((-> (-> tptp.pname Bool) Bool) tptp.pname) Bool)
% 0.62/0.95 (declare-fun tptp.big_la735727201le_a_o ((-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.big_la1088302868tate_o ((-> (-> tptp.hoare_1708887482_state Bool) Bool) tptp.hoare_1708887482_state) Bool)
% 0.62/0.95 (declare-fun tptp.big_la1658356148_nat_o ((-> (-> tptp.nat Bool) Bool) tptp.nat) Bool)
% 0.62/0.95 (declare-fun tptp.big_la727467310_fin_o ((-> Bool Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.big_la43341705in_nat ((-> tptp.nat Bool)) tptp.nat)
% 0.62/0.95 (declare-fun tptp.body_1 (tptp.pname) tptp.option_com)
% 0.62/0.95 (declare-fun tptp.body (tptp.pname) tptp.com)
% 0.62/0.95 (declare-fun tptp.cond ((-> tptp.state Bool) tptp.com tptp.com) tptp.com)
% 0.62/0.95 (declare-fun tptp.skip () tptp.com)
% 0.62/0.95 (declare-fun tptp.semi (tptp.com tptp.com) tptp.com)
% 0.62/0.95 (declare-fun tptp.while ((-> tptp.state Bool) tptp.com) tptp.com)
% 0.62/0.95 (declare-fun tptp.com_size (tptp.com) tptp.nat)
% 0.62/0.95 (declare-fun tptp.finite_card_nat ((-> tptp.nat Bool)) tptp.nat)
% 0.62/0.95 (declare-fun tptp.finite886417794_a_o_o ((-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.finite297249702name_o ((-> (-> tptp.pname Bool) Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.finite1829014797le_a_o ((-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.finite1329924456tate_o ((-> (-> tptp.hoare_1708887482_state Bool) Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.finite_finite_nat_o ((-> (-> tptp.nat Bool) Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.finite_finite_o ((-> Bool Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.finite_finite_pname ((-> tptp.pname Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.finite232261744iple_a ((-> tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.finite1625599783_state ((-> tptp.hoare_1708887482_state Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.finite_finite_nat ((-> tptp.nat Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.finite2009943022_o_nat ((-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) (-> tptp.hoare_2091234717iple_a Bool) Bool) (-> tptp.nat (-> tptp.hoare_2091234717iple_a Bool) Bool) (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) (-> tptp.nat Bool) (-> tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.finite1427591632_o_nat ((-> (-> tptp.pname Bool) (-> tptp.pname Bool) tptp.pname Bool) (-> tptp.nat tptp.pname Bool) (-> tptp.pname Bool) (-> tptp.nat Bool) tptp.pname) Bool)
% 0.62/0.95 (declare-fun tptp.finite903029825le_a_o ((-> (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool) (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.finite1290357347_pname ((-> (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool) (-> tptp.pname tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.pname Bool) tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.finite1481787452iple_a ((-> (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.finite2100865449_o_nat ((-> (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool) (-> tptp.nat tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.nat Bool) tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.finite2139561282_pname ((-> (-> tptp.hoare_1708887482_state Bool) (-> tptp.hoare_1708887482_state Bool) tptp.hoare_1708887482_state Bool) (-> tptp.pname tptp.hoare_1708887482_state Bool) (-> tptp.hoare_1708887482_state Bool) (-> tptp.pname Bool) tptp.hoare_1708887482_state) Bool)
% 0.62/0.95 (declare-fun tptp.finite1400355848_o_nat ((-> (-> tptp.hoare_1708887482_state Bool) (-> tptp.hoare_1708887482_state Bool) tptp.hoare_1708887482_state Bool) (-> tptp.nat tptp.hoare_1708887482_state Bool) (-> tptp.hoare_1708887482_state Bool) (-> tptp.nat Bool) tptp.hoare_1708887482_state) Bool)
% 0.62/0.95 (declare-fun tptp.finite141655318_o_nat ((-> (-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 0.62/0.95 (declare-fun tptp.finite14499299le_a_o ((-> (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool) (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.finite1282449217_pname ((-> tptp.pname tptp.pname tptp.pname) (-> (-> tptp.pname Bool) tptp.pname)) Bool)
% 0.62/0.95 (declare-fun tptp.finite247037978iple_a ((-> tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a) (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a)) Bool)
% 0.62/0.95 (declare-fun tptp.finite1615457021_state ((-> tptp.hoare_1708887482_state tptp.hoare_1708887482_state tptp.hoare_1708887482_state) (-> (-> tptp.hoare_1708887482_state Bool) tptp.hoare_1708887482_state)) Bool)
% 0.62/0.95 (declare-fun tptp.finite988810631ne_nat ((-> tptp.nat tptp.nat tptp.nat) (-> (-> tptp.nat Bool) tptp.nat)) Bool)
% 0.62/0.95 (declare-fun tptp.finite574580006le_a_o ((-> (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool) (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.finite89670078_pname ((-> tptp.pname tptp.pname tptp.pname) (-> (-> tptp.pname Bool) tptp.pname)) Bool)
% 0.62/0.95 (declare-fun tptp.finite1674555159iple_a ((-> tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a) (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a)) Bool)
% 0.62/0.95 (declare-fun tptp.finite1347568576_state ((-> tptp.hoare_1708887482_state tptp.hoare_1708887482_state tptp.hoare_1708887482_state) (-> (-> tptp.hoare_1708887482_state Bool) tptp.hoare_1708887482_state)) Bool)
% 0.62/0.95 (declare-fun tptp.finite795500164em_nat ((-> tptp.nat tptp.nat tptp.nat) (-> (-> tptp.nat Bool) tptp.nat)) Bool)
% 0.62/0.95 (declare-fun tptp.minus_1746272704_a_o_o ((-> (-> tptp.hoare_2091234717iple_a Bool) Bool) (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) (-> tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.minus_minus_pname_o ((-> tptp.pname Bool) (-> tptp.pname Bool) tptp.pname) Bool)
% 0.62/0.95 (declare-fun tptp.minus_836160335le_a_o ((-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.minus_2056855718tate_o ((-> tptp.hoare_1708887482_state Bool) (-> tptp.hoare_1708887482_state Bool) tptp.hoare_1708887482_state) Bool)
% 0.62/0.95 (declare-fun tptp.minus_minus_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 0.62/0.95 (declare-fun tptp.minus_minus_o (Bool Bool) Bool)
% 0.62/0.95 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.62/0.95 (declare-fun tptp.one_one_nat () tptp.nat)
% 0.62/0.95 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.62/0.95 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 0.62/0.95 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 0.62/0.95 (declare-fun tptp.the_Ho2077879471le_a_o ((-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.the_pname ((-> tptp.pname Bool)) tptp.pname)
% 0.62/0.95 (declare-fun tptp.the_Ho1471183438iple_a ((-> tptp.hoare_2091234717iple_a Bool)) tptp.hoare_2091234717iple_a)
% 0.62/0.95 (declare-fun tptp.the_Ho851197897_state ((-> tptp.hoare_1708887482_state Bool)) tptp.hoare_1708887482_state)
% 0.62/0.95 (declare-fun tptp.the_nat ((-> tptp.nat Bool)) tptp.nat)
% 0.62/0.95 (declare-fun tptp.hoare_Mirabelle_MGT (tptp.com) tptp.hoare_1708887482_state)
% 0.62/0.95 (declare-fun tptp.hoare_1467856363rivs_a ((-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.hoare_90032982_state ((-> tptp.hoare_1708887482_state Bool) (-> tptp.hoare_1708887482_state Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.hoare_1805689709lids_a ((-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.hoare_496444244_state ((-> tptp.hoare_1708887482_state Bool) (-> tptp.hoare_1708887482_state Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.hoare_657976383iple_a ((-> tptp.x_a tptp.state Bool) tptp.com (-> tptp.x_a tptp.state Bool)) tptp.hoare_2091234717iple_a)
% 0.62/0.95 (declare-fun tptp.hoare_858012674_state ((-> tptp.state tptp.state Bool) tptp.com (-> tptp.state tptp.state Bool)) tptp.hoare_1708887482_state)
% 0.62/0.95 (declare-fun tptp.hoare_1169027232size_a ((-> tptp.x_a tptp.nat) tptp.hoare_2091234717iple_a) tptp.nat)
% 0.62/0.95 (declare-fun tptp.hoare_518771297_state ((-> tptp.state tptp.nat) tptp.hoare_1708887482_state) tptp.nat)
% 0.62/0.95 (declare-fun tptp.hoare_1421888935alid_a (tptp.nat tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.hoare_23738522_state (tptp.nat tptp.hoare_1708887482_state) Bool)
% 0.62/0.95 (declare-fun tptp.semila1672913213_a_o_o ((-> (-> tptp.hoare_2091234717iple_a Bool) Bool) (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) (-> tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.semila1673364395name_o ((-> tptp.pname Bool) (-> tptp.pname Bool) tptp.pname) Bool)
% 0.62/0.95 (declare-fun tptp.semila2006181266le_a_o ((-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.semila129691299tate_o ((-> tptp.hoare_1708887482_state Bool) (-> tptp.hoare_1708887482_state Bool) tptp.hoare_1708887482_state) Bool)
% 0.62/0.95 (declare-fun tptp.semila1947288293_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 0.62/0.95 (declare-fun tptp.semila854092349_inf_o (Bool Bool) Bool)
% 0.62/0.95 (declare-fun tptp.semila80283416nf_nat (tptp.nat tptp.nat) tptp.nat)
% 0.62/0.95 (declare-fun tptp.semila484278426_o_o_o ((-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) Bool) (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) Bool) (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.semila181081674me_o_o ((-> (-> tptp.pname Bool) Bool) (-> (-> tptp.pname Bool) Bool) (-> tptp.pname Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.semila2050116131_a_o_o ((-> (-> tptp.hoare_2091234717iple_a Bool) Bool) (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) (-> tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.semila1853742644te_o_o ((-> (-> tptp.hoare_1708887482_state Bool) Bool) (-> (-> tptp.hoare_1708887482_state Bool) Bool) (-> tptp.hoare_1708887482_state Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.semila72246288at_o_o ((-> (-> tptp.nat Bool) Bool) (-> (-> tptp.nat Bool) Bool) (-> tptp.nat Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.semila2062604954up_o_o ((-> Bool Bool) (-> Bool Bool) Bool) Bool)
% 0.62/0.95 (declare-fun tptp.semila1780557381name_o ((-> tptp.pname Bool) (-> tptp.pname Bool) tptp.pname) Bool)
% 0.62/0.95 (declare-fun tptp.semila1052848428le_a_o ((-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.semila1122118281tate_o ((-> tptp.hoare_1708887482_state Bool) (-> tptp.hoare_1708887482_state Bool) tptp.hoare_1708887482_state) Bool)
% 0.62/0.95 (declare-fun tptp.semila848761471_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 0.62/0.95 (declare-fun tptp.semila10642723_sup_o (Bool Bool) Bool)
% 0.62/0.95 (declare-fun tptp.semila972727038up_nat (tptp.nat tptp.nat) tptp.nat)
% 0.62/0.95 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 0.62/0.95 (declare-fun tptp.nat_case_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 0.62/0.95 (declare-fun tptp.nat_case_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 0.62/0.95 (declare-fun tptp.size_size_com (tptp.com) tptp.nat)
% 0.62/0.95 (declare-fun tptp.size_s1040486067iple_a (tptp.hoare_2091234717iple_a) tptp.nat)
% 0.62/0.95 (declare-fun tptp.size_s1186992420_state (tptp.hoare_1708887482_state) tptp.nat)
% 0.62/0.95 (declare-fun tptp.evalc (tptp.com tptp.state tptp.state) Bool)
% 0.62/0.95 (declare-fun tptp.evaln (tptp.com tptp.state tptp.nat tptp.state) Bool)
% 0.62/0.95 (declare-fun tptp.the_com (tptp.option_com) tptp.com)
% 0.62/0.95 (declare-fun tptp.bot_bo690906872_o_o_o ((-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.bot_bot_pname_o_o ((-> tptp.pname Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.bot_bo1957696069_a_o_o ((-> tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.bot_bo1678742418te_o_o ((-> tptp.hoare_1708887482_state Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.bot_bot_nat_o_o ((-> tptp.nat Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.bot_bot_o_o (Bool) Bool)
% 0.62/0.95 (declare-fun tptp.bot_bot_pname_o (tptp.pname) Bool)
% 0.62/0.95 (declare-fun tptp.bot_bo1791335050le_a_o (tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.bot_bo19817387tate_o (tptp.hoare_1708887482_state) Bool)
% 0.62/0.95 (declare-fun tptp.bot_bot_nat_o (tptp.nat) Bool)
% 0.62/0.95 (declare-fun tptp.bot_bot_o () Bool)
% 0.62/0.95 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 0.62/0.95 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.62/0.95 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.62/0.95 (declare-fun tptp.collec1008234059le_a_o ((-> (-> tptp.hoare_2091234717iple_a Bool) Bool) (-> tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.collect_pname ((-> tptp.pname Bool) tptp.pname) Bool)
% 0.62/0.95 (declare-fun tptp.collec992574898iple_a ((-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.collec1568722789_state ((-> tptp.hoare_1708887482_state Bool) tptp.hoare_1708887482_state) Bool)
% 0.62/0.95 (declare-fun tptp.collect_nat ((-> tptp.nat Bool) tptp.nat) Bool)
% 0.62/0.95 (declare-fun tptp.image_784579955le_a_o ((-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool) (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) (-> tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.image_1908519857_pname ((-> (-> tptp.hoare_2091234717iple_a Bool) tptp.pname) (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.pname) Bool)
% 0.62/0.95 (declare-fun tptp.image_136408202iple_a ((-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a) (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.image_1501246093_state ((-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_1708887482_state) (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.hoare_1708887482_state) Bool)
% 0.62/0.95 (declare-fun tptp.image_75520503_o_nat ((-> (-> tptp.hoare_2091234717iple_a Bool) tptp.nat) (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.nat) Bool)
% 0.62/0.95 (declare-fun tptp.image_742317343le_a_o ((-> tptp.pname tptp.hoare_2091234717iple_a Bool) (-> tptp.pname Bool) (-> tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.image_pname_pname ((-> tptp.pname tptp.pname) (-> tptp.pname Bool) tptp.pname) Bool)
% 0.62/0.95 (declare-fun tptp.image_231808478iple_a ((-> tptp.pname tptp.hoare_2091234717iple_a) (-> tptp.pname Bool) tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.image_1116629049_state ((-> tptp.pname tptp.hoare_1708887482_state) (-> tptp.pname Bool) tptp.hoare_1708887482_state) Bool)
% 0.62/0.95 (declare-fun tptp.image_pname_nat ((-> tptp.pname tptp.nat) (-> tptp.pname Bool) tptp.nat) Bool)
% 0.62/0.95 (declare-fun tptp.image_1642350072le_a_o ((-> tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.image_924789612_pname ((-> tptp.hoare_2091234717iple_a tptp.pname) (-> tptp.hoare_2091234717iple_a Bool) tptp.pname) Bool)
% 0.62/0.95 (declare-fun tptp.image_1661191109iple_a ((-> tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.image_1884482962_state ((-> tptp.hoare_2091234717iple_a tptp.hoare_1708887482_state) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_1708887482_state) Bool)
% 0.62/0.95 (declare-fun tptp.image_1773322034_a_nat ((-> tptp.hoare_2091234717iple_a tptp.nat) (-> tptp.hoare_2091234717iple_a Bool) tptp.nat) Bool)
% 0.62/0.95 (declare-fun tptp.image_293283184iple_a ((-> tptp.hoare_1708887482_state tptp.hoare_2091234717iple_a) (-> tptp.hoare_1708887482_state Bool) tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.image_757158439_state ((-> tptp.hoare_1708887482_state tptp.hoare_1708887482_state) (-> tptp.hoare_1708887482_state Bool) tptp.hoare_1708887482_state) Bool)
% 0.62/0.95 (declare-fun tptp.image_1995609573le_a_o ((-> tptp.nat tptp.hoare_2091234717iple_a Bool) (-> tptp.nat Bool) (-> tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.image_nat_pname ((-> tptp.nat tptp.pname) (-> tptp.nat Bool) tptp.pname) Bool)
% 0.62/0.95 (declare-fun tptp.image_359186840iple_a ((-> tptp.nat tptp.hoare_2091234717iple_a) (-> tptp.nat Bool) tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.image_514827263_state ((-> tptp.nat tptp.hoare_1708887482_state) (-> tptp.nat Bool) tptp.hoare_1708887482_state) Bool)
% 0.62/0.95 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat Bool) tptp.nat) Bool)
% 0.62/0.95 (declare-fun tptp.insert987231145_a_o_o ((-> (-> tptp.hoare_2091234717iple_a Bool) Bool) (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) Bool) (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.insert_pname_o ((-> tptp.pname Bool) (-> (-> tptp.pname Bool) Bool) (-> tptp.pname Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.insert102003750le_a_o ((-> tptp.hoare_2091234717iple_a Bool) (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) (-> tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.insert949073679tate_o ((-> tptp.hoare_1708887482_state Bool) (-> (-> tptp.hoare_1708887482_state Bool) Bool) (-> tptp.hoare_1708887482_state Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.insert_nat_o ((-> tptp.nat Bool) (-> (-> tptp.nat Bool) Bool) (-> tptp.nat Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.insert_o (Bool (-> Bool Bool) Bool) Bool)
% 0.62/0.95 (declare-fun tptp.insert_pname (tptp.pname (-> tptp.pname Bool) tptp.pname) Bool)
% 0.62/0.95 (declare-fun tptp.insert1597628439iple_a (tptp.hoare_2091234717iple_a (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.insert528405184_state (tptp.hoare_1708887482_state (-> tptp.hoare_1708887482_state Bool) tptp.hoare_1708887482_state) Bool)
% 0.62/0.95 (declare-fun tptp.insert_nat (tptp.nat (-> tptp.nat Bool) tptp.nat) Bool)
% 0.62/0.95 (declare-fun tptp.the_el1618277441le_a_o ((-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.the_elem_pname ((-> tptp.pname Bool)) tptp.pname)
% 0.62/0.95 (declare-fun tptp.the_el13400124iple_a ((-> tptp.hoare_2091234717iple_a Bool)) tptp.hoare_2091234717iple_a)
% 0.62/0.95 (declare-fun tptp.the_el864710747_state ((-> tptp.hoare_1708887482_state Bool)) tptp.hoare_1708887482_state)
% 0.62/0.95 (declare-fun tptp.the_elem_nat ((-> tptp.nat Bool)) tptp.nat)
% 0.62/0.95 (declare-fun tptp.fequal845167073le_a_o ((-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.fequal_pname (tptp.pname tptp.pname) Bool)
% 0.62/0.95 (declare-fun tptp.fequal_state (tptp.state tptp.state) Bool)
% 0.62/0.95 (declare-fun tptp.fequal1604381340iple_a (tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.fequal224822779_state (tptp.hoare_1708887482_state tptp.hoare_1708887482_state) Bool)
% 0.62/0.95 (declare-fun tptp.fequal_nat (tptp.nat tptp.nat) Bool)
% 0.62/0.95 (declare-fun tptp.member1297825410_a_o_o ((-> (-> tptp.hoare_2091234717iple_a Bool) Bool) (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.member_pname_o ((-> tptp.pname Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.member99268621le_a_o ((-> tptp.hoare_2091234717iple_a Bool) (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.member814030440tate_o ((-> tptp.hoare_1708887482_state Bool) (-> (-> tptp.hoare_1708887482_state Bool) Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.member_nat_o ((-> tptp.nat Bool) (-> (-> tptp.nat Bool) Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.member_o (Bool (-> Bool Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.member_pname (tptp.pname (-> tptp.pname Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.member290856304iple_a (tptp.hoare_2091234717iple_a (-> tptp.hoare_2091234717iple_a Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.member451959335_state (tptp.hoare_1708887482_state (-> tptp.hoare_1708887482_state Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.member_nat (tptp.nat (-> tptp.nat Bool)) Bool)
% 0.62/0.95 (declare-fun tptp.g (tptp.hoare_2091234717iple_a) Bool)
% 0.62/0.95 (declare-fun tptp.p (tptp.pname tptp.x_a tptp.state) Bool)
% 0.62/0.95 (declare-fun tptp.procs (tptp.pname) Bool)
% 0.62/0.95 (declare-fun tptp.q (tptp.pname tptp.x_a tptp.state) Bool)
% 0.62/0.95 (declare-fun tptp.n () tptp.nat)
% 0.62/0.95 (assert (forall ((Fun1_4 (-> tptp.x_a tptp.state Bool)) (Com_1 tptp.com) (Fun2_4 (-> tptp.x_a tptp.state Bool)) (Fun1_3 (-> tptp.x_a tptp.state Bool)) (Com tptp.com) (Fun2_3 (-> tptp.x_a tptp.state Bool))) (= (= (@ (@ (@ tptp.hoare_657976383iple_a Fun1_4) Com_1) Fun2_4) (@ (@ (@ tptp.hoare_657976383iple_a Fun1_3) Com) Fun2_3)) (and (= Fun1_4 Fun1_3) (= Com_1 Com) (= Fun2_4 Fun2_3)))))
% 0.62/0.95 (assert (forall ((Fun1_4 (-> tptp.state tptp.state Bool)) (Com_1 tptp.com) (Fun2_4 (-> tptp.state tptp.state Bool)) (Fun1_3 (-> tptp.state tptp.state Bool)) (Com tptp.com) (Fun2_3 (-> tptp.state tptp.state Bool))) (= (= (@ (@ (@ tptp.hoare_858012674_state Fun1_4) Com_1) Fun2_4) (@ (@ (@ tptp.hoare_858012674_state Fun1_3) Com) Fun2_3)) (and (= Fun1_4 Fun1_3) (= Com_1 Com) (= Fun2_4 Fun2_3)))))
% 0.62/0.95 (assert (forall ((G_28 (-> tptp.hoare_1708887482_state Bool)) (Ts_4 (-> tptp.hoare_1708887482_state Bool))) (= (@ (@ tptp.hoare_496444244_state G_28) Ts_4) (forall ((N tptp.nat)) (=> (forall ((X tptp.hoare_1708887482_state)) (=> (@ (@ tptp.member451959335_state X) G_28) (@ (@ tptp.hoare_23738522_state N) X))) (forall ((X tptp.hoare_1708887482_state)) (=> (@ (@ tptp.member451959335_state X) Ts_4) (@ (@ tptp.hoare_23738522_state N) X))))))))
% 0.62/0.95 (assert (forall ((G_28 (-> tptp.hoare_2091234717iple_a Bool)) (Ts_4 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.hoare_1805689709lids_a G_28) Ts_4) (forall ((N tptp.nat)) (=> (forall ((X tptp.hoare_2091234717iple_a)) (=> (@ (@ tptp.member290856304iple_a X) G_28) (@ (@ tptp.hoare_1421888935alid_a N) X))) (forall ((X tptp.hoare_2091234717iple_a)) (=> (@ (@ tptp.member290856304iple_a X) Ts_4) (@ (@ tptp.hoare_1421888935alid_a N) X))))))))
% 0.62/0.95 (assert (forall ((G_27 (-> tptp.hoare_1708887482_state Bool)) (P_36 (-> tptp.pname tptp.state tptp.state Bool)) (Q_20 (-> tptp.pname tptp.state tptp.state Bool)) (Procs_1 (-> tptp.pname Bool))) (=> (@ (@ tptp.hoare_90032982_state (@ (@ tptp.semila1122118281tate_o G_27) (@ (@ tptp.image_1116629049_state (lambda ((P_9 tptp.pname)) (@ (@ (@ tptp.hoare_858012674_state (@ P_36 P_9)) (@ tptp.body P_9)) (@ Q_20 P_9)))) Procs_1))) (@ (@ tptp.image_1116629049_state (lambda ((P_9 tptp.pname)) (@ (@ (@ tptp.hoare_858012674_state (@ P_36 P_9)) (@ tptp.the_com (@ tptp.body_1 P_9))) (@ Q_20 P_9)))) Procs_1)) (@ (@ tptp.hoare_90032982_state G_27) (@ (@ tptp.image_1116629049_state (lambda ((P_9 tptp.pname)) (@ (@ (@ tptp.hoare_858012674_state (@ P_36 P_9)) (@ tptp.body P_9)) (@ Q_20 P_9)))) Procs_1)))))
% 0.62/0.95 (assert (forall ((G_27 (-> tptp.hoare_2091234717iple_a Bool)) (P_36 (-> 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_1467856363rivs_a (@ (@ tptp.semila1052848428le_a_o G_27) (@ (@ tptp.image_231808478iple_a (lambda ((P_9 tptp.pname)) (@ (@ (@ tptp.hoare_657976383iple_a (@ P_36 P_9)) (@ tptp.body P_9)) (@ Q_20 P_9)))) Procs_1))) (@ (@ tptp.image_231808478iple_a (lambda ((P_9 tptp.pname)) (@ (@ (@ tptp.hoare_657976383iple_a (@ P_36 P_9)) (@ tptp.the_com (@ tptp.body_1 P_9))) (@ Q_20 P_9)))) Procs_1)) (@ (@ tptp.hoare_1467856363rivs_a G_27) (@ (@ tptp.image_231808478iple_a (lambda ((P_9 tptp.pname)) (@ (@ (@ tptp.hoare_657976383iple_a (@ P_36 P_9)) (@ tptp.body P_9)) (@ Q_20 P_9)))) Procs_1)))))
% 0.62/0.95 (assert (forall ((C_34 tptp.nat) (A_129 (-> tptp.nat Bool)) (B_71 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_34))) (=> (@ _let_1 (@ (@ tptp.semila848761471_nat_o A_129) B_71)) (=> (not (@ _let_1 A_129)) (@ _let_1 B_71))))))
% 0.62/0.95 (assert (forall ((C_34 (-> tptp.hoare_2091234717iple_a Bool)) (A_129 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_71 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.member99268621le_a_o C_34))) (=> (@ _let_1 (@ (@ tptp.semila2050116131_a_o_o A_129) B_71)) (=> (not (@ _let_1 A_129)) (@ _let_1 B_71))))))
% 0.62/0.95 (assert (forall ((C_34 tptp.hoare_1708887482_state) (A_129 (-> tptp.hoare_1708887482_state Bool)) (B_71 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.member451959335_state C_34))) (=> (@ _let_1 (@ (@ tptp.semila1122118281tate_o A_129) B_71)) (=> (not (@ _let_1 A_129)) (@ _let_1 B_71))))))
% 0.62/0.95 (assert (forall ((C_34 tptp.hoare_2091234717iple_a) (A_129 (-> tptp.hoare_2091234717iple_a Bool)) (B_71 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.member290856304iple_a C_34))) (=> (@ _let_1 (@ (@ tptp.semila1052848428le_a_o A_129) B_71)) (=> (not (@ _let_1 A_129)) (@ _let_1 B_71))))))
% 0.62/0.95 (assert (forall ((C_34 tptp.pname) (A_129 (-> tptp.pname Bool)) (B_71 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_34))) (=> (@ _let_1 (@ (@ tptp.semila1780557381name_o A_129) B_71)) (=> (not (@ _let_1 A_129)) (@ _let_1 B_71))))))
% 0.62/0.95 (assert (forall ((A_128 (-> tptp.nat Bool)) (B_70 (-> tptp.nat Bool)) (X_51 tptp.nat)) (=> (@ (@ (@ tptp.semila848761471_nat_o A_128) B_70) X_51) (=> (not (@ A_128 X_51)) (@ B_70 X_51)))))
% 0.62/0.95 (assert (forall ((A_128 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_70 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (X_51 (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ (@ (@ tptp.semila2050116131_a_o_o A_128) B_70) X_51) (=> (not (@ A_128 X_51)) (@ B_70 X_51)))))
% 0.62/0.95 (assert (forall ((A_128 (-> tptp.hoare_1708887482_state Bool)) (B_70 (-> tptp.hoare_1708887482_state Bool)) (X_51 tptp.hoare_1708887482_state)) (=> (@ (@ (@ tptp.semila1122118281tate_o A_128) B_70) X_51) (=> (not (@ A_128 X_51)) (@ B_70 X_51)))))
% 0.62/0.95 (assert (forall ((A_128 (-> tptp.pname Bool)) (B_70 (-> tptp.pname Bool)) (X_51 tptp.pname)) (=> (@ (@ (@ tptp.semila1780557381name_o A_128) B_70) X_51) (=> (not (@ A_128 X_51)) (@ B_70 X_51)))))
% 0.62/0.95 (assert (forall ((A_128 (-> tptp.hoare_2091234717iple_a Bool)) (B_70 (-> tptp.hoare_2091234717iple_a Bool)) (X_51 tptp.hoare_2091234717iple_a)) (=> (@ (@ (@ tptp.semila1052848428le_a_o A_128) B_70) X_51) (=> (not (@ A_128 X_51)) (@ B_70 X_51)))))
% 0.62/0.95 (assert (forall ((A_127 (-> tptp.nat Bool)) (B_69 (-> tptp.nat Bool)) (X_50 tptp.nat)) (=> (=> (not (@ B_69 X_50)) (@ A_127 X_50)) (@ (@ (@ tptp.semila848761471_nat_o A_127) B_69) X_50))))
% 0.62/0.95 (assert (forall ((A_127 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_69 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (X_50 (-> tptp.hoare_2091234717iple_a Bool))) (=> (=> (not (@ B_69 X_50)) (@ A_127 X_50)) (@ (@ (@ tptp.semila2050116131_a_o_o A_127) B_69) X_50))))
% 0.62/0.95 (assert (forall ((A_127 (-> tptp.hoare_1708887482_state Bool)) (B_69 (-> tptp.hoare_1708887482_state Bool)) (X_50 tptp.hoare_1708887482_state)) (=> (=> (not (@ B_69 X_50)) (@ A_127 X_50)) (@ (@ (@ tptp.semila1122118281tate_o A_127) B_69) X_50))))
% 0.62/0.95 (assert (forall ((A_127 (-> tptp.pname Bool)) (B_69 (-> tptp.pname Bool)) (X_50 tptp.pname)) (=> (=> (not (@ B_69 X_50)) (@ A_127 X_50)) (@ (@ (@ tptp.semila1780557381name_o A_127) B_69) X_50))))
% 0.62/0.95 (assert (forall ((A_127 (-> tptp.hoare_2091234717iple_a Bool)) (B_69 (-> tptp.hoare_2091234717iple_a Bool)) (X_50 tptp.hoare_2091234717iple_a)) (=> (=> (not (@ B_69 X_50)) (@ A_127 X_50)) (@ (@ (@ tptp.semila1052848428le_a_o A_127) B_69) X_50))))
% 0.62/0.95 (assert (forall ((A_126 (-> tptp.nat Bool)) (C_33 tptp.nat) (B_68 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_33))) (=> (=> (not (@ _let_1 B_68)) (@ _let_1 A_126)) (@ _let_1 (@ (@ tptp.semila848761471_nat_o A_126) B_68))))))
% 0.62/0.95 (assert (forall ((A_126 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (C_33 (-> tptp.hoare_2091234717iple_a Bool)) (B_68 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.member99268621le_a_o C_33))) (=> (=> (not (@ _let_1 B_68)) (@ _let_1 A_126)) (@ _let_1 (@ (@ tptp.semila2050116131_a_o_o A_126) B_68))))))
% 0.62/0.95 (assert (forall ((A_126 (-> tptp.hoare_1708887482_state Bool)) (C_33 tptp.hoare_1708887482_state) (B_68 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.member451959335_state C_33))) (=> (=> (not (@ _let_1 B_68)) (@ _let_1 A_126)) (@ _let_1 (@ (@ tptp.semila1122118281tate_o A_126) B_68))))))
% 0.62/0.95 (assert (forall ((A_126 (-> tptp.hoare_2091234717iple_a Bool)) (C_33 tptp.hoare_2091234717iple_a) (B_68 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.member290856304iple_a C_33))) (=> (=> (not (@ _let_1 B_68)) (@ _let_1 A_126)) (@ _let_1 (@ (@ tptp.semila1052848428le_a_o A_126) B_68))))))
% 0.62/0.95 (assert (forall ((A_126 (-> tptp.pname Bool)) (C_33 tptp.pname) (B_68 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_33))) (=> (=> (not (@ _let_1 B_68)) (@ _let_1 A_126)) (@ _let_1 (@ (@ tptp.semila1780557381name_o A_126) B_68))))))
% 0.62/0.95 (assert (forall ((A_125 (-> tptp.nat Bool)) (B_67 tptp.nat) (F_50 (-> tptp.nat tptp.nat)) (X_49 tptp.nat)) (=> (= B_67 (@ F_50 X_49)) (=> (@ (@ tptp.member_nat X_49) A_125) (@ (@ tptp.member_nat B_67) (@ (@ tptp.image_nat_nat F_50) A_125))))))
% 0.62/0.95 (assert (forall ((A_125 (-> tptp.pname Bool)) (B_67 tptp.hoare_1708887482_state) (F_50 (-> tptp.pname tptp.hoare_1708887482_state)) (X_49 tptp.pname)) (=> (= B_67 (@ F_50 X_49)) (=> (@ (@ tptp.member_pname X_49) A_125) (@ (@ tptp.member451959335_state B_67) (@ (@ tptp.image_1116629049_state F_50) A_125))))))
% 0.62/0.95 (assert (forall ((A_125 (-> tptp.pname Bool)) (B_67 tptp.nat) (F_50 (-> tptp.pname tptp.nat)) (X_49 tptp.pname)) (=> (= B_67 (@ F_50 X_49)) (=> (@ (@ tptp.member_pname X_49) A_125) (@ (@ tptp.member_nat B_67) (@ (@ tptp.image_pname_nat F_50) A_125))))))
% 0.62/0.95 (assert (forall ((A_125 (-> tptp.pname Bool)) (B_67 (-> tptp.hoare_2091234717iple_a Bool)) (F_50 (-> tptp.pname tptp.hoare_2091234717iple_a Bool)) (X_49 tptp.pname)) (=> (= B_67 (@ F_50 X_49)) (=> (@ (@ tptp.member_pname X_49) A_125) (@ (@ tptp.member99268621le_a_o B_67) (@ (@ tptp.image_742317343le_a_o F_50) A_125))))))
% 0.62/0.95 (assert (forall ((A_125 (-> tptp.nat Bool)) (B_67 tptp.pname) (F_50 (-> tptp.nat tptp.pname)) (X_49 tptp.nat)) (=> (= B_67 (@ F_50 X_49)) (=> (@ (@ tptp.member_nat X_49) A_125) (@ (@ tptp.member_pname B_67) (@ (@ tptp.image_nat_pname F_50) A_125))))))
% 0.62/0.95 (assert (forall ((A_125 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_67 tptp.pname) (F_50 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.pname)) (X_49 (-> tptp.hoare_2091234717iple_a Bool))) (=> (= B_67 (@ F_50 X_49)) (=> (@ (@ tptp.member99268621le_a_o X_49) A_125) (@ (@ tptp.member_pname B_67) (@ (@ tptp.image_1908519857_pname F_50) A_125))))))
% 0.62/0.95 (assert (forall ((A_125 (-> tptp.hoare_2091234717iple_a Bool)) (B_67 tptp.pname) (F_50 (-> tptp.hoare_2091234717iple_a tptp.pname)) (X_49 tptp.hoare_2091234717iple_a)) (=> (= B_67 (@ F_50 X_49)) (=> (@ (@ tptp.member290856304iple_a X_49) A_125) (@ (@ tptp.member_pname B_67) (@ (@ tptp.image_924789612_pname F_50) A_125))))))
% 0.62/0.95 (assert (forall ((A_125 (-> tptp.pname Bool)) (B_67 tptp.hoare_2091234717iple_a) (F_50 (-> tptp.pname tptp.hoare_2091234717iple_a)) (X_49 tptp.pname)) (=> (= B_67 (@ F_50 X_49)) (=> (@ (@ tptp.member_pname X_49) A_125) (@ (@ tptp.member290856304iple_a B_67) (@ (@ tptp.image_231808478iple_a F_50) A_125))))))
% 0.62/0.95 (assert (forall ((F_49 (-> tptp.nat tptp.nat)) (A_124 (-> tptp.nat Bool)) (B_66 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.image_nat_nat F_49))) (= (@ _let_1 (@ (@ tptp.semila848761471_nat_o A_124) B_66)) (@ (@ tptp.semila848761471_nat_o (@ _let_1 A_124)) (@ _let_1 B_66))))))
% 0.62/0.95 (assert (forall ((F_49 (-> tptp.pname tptp.hoare_1708887482_state)) (A_124 (-> tptp.pname Bool)) (B_66 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_1116629049_state F_49))) (= (@ _let_1 (@ (@ tptp.semila1780557381name_o A_124) B_66)) (@ (@ tptp.semila1122118281tate_o (@ _let_1 A_124)) (@ _let_1 B_66))))))
% 0.62/0.95 (assert (forall ((F_49 (-> tptp.hoare_2091234717iple_a tptp.nat)) (A_124 (-> tptp.hoare_2091234717iple_a Bool)) (B_66 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.image_1773322034_a_nat F_49))) (= (@ _let_1 (@ (@ tptp.semila1052848428le_a_o A_124) B_66)) (@ (@ tptp.semila848761471_nat_o (@ _let_1 A_124)) (@ _let_1 B_66))))))
% 0.62/0.95 (assert (forall ((F_49 (-> tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a Bool)) (A_124 (-> tptp.hoare_2091234717iple_a Bool)) (B_66 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.image_1642350072le_a_o F_49))) (= (@ _let_1 (@ (@ tptp.semila1052848428le_a_o A_124) B_66)) (@ (@ tptp.semila2050116131_a_o_o (@ _let_1 A_124)) (@ _let_1 B_66))))))
% 0.62/0.95 (assert (forall ((F_49 (-> tptp.hoare_2091234717iple_a tptp.hoare_1708887482_state)) (A_124 (-> tptp.hoare_2091234717iple_a Bool)) (B_66 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.image_1884482962_state F_49))) (= (@ _let_1 (@ (@ tptp.semila1052848428le_a_o A_124) B_66)) (@ (@ tptp.semila1122118281tate_o (@ _let_1 A_124)) (@ _let_1 B_66))))))
% 0.62/0.95 (assert (forall ((F_49 (-> tptp.hoare_2091234717iple_a tptp.pname)) (A_124 (-> tptp.hoare_2091234717iple_a Bool)) (B_66 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.image_924789612_pname F_49))) (= (@ _let_1 (@ (@ tptp.semila1052848428le_a_o A_124) B_66)) (@ (@ tptp.semila1780557381name_o (@ _let_1 A_124)) (@ _let_1 B_66))))))
% 0.62/0.95 (assert (forall ((F_49 (-> tptp.nat tptp.hoare_2091234717iple_a)) (A_124 (-> tptp.nat Bool)) (B_66 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.image_359186840iple_a F_49))) (= (@ _let_1 (@ (@ tptp.semila848761471_nat_o A_124) B_66)) (@ (@ tptp.semila1052848428le_a_o (@ _let_1 A_124)) (@ _let_1 B_66))))))
% 0.62/0.95 (assert (forall ((F_49 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a)) (A_124 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_66 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.image_136408202iple_a F_49))) (= (@ _let_1 (@ (@ tptp.semila2050116131_a_o_o A_124) B_66)) (@ (@ tptp.semila1052848428le_a_o (@ _let_1 A_124)) (@ _let_1 B_66))))))
% 0.62/0.95 (assert (forall ((F_49 (-> tptp.hoare_1708887482_state tptp.hoare_2091234717iple_a)) (A_124 (-> tptp.hoare_1708887482_state Bool)) (B_66 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.image_293283184iple_a F_49))) (= (@ _let_1 (@ (@ tptp.semila1122118281tate_o A_124) B_66)) (@ (@ tptp.semila1052848428le_a_o (@ _let_1 A_124)) (@ _let_1 B_66))))))
% 0.62/0.95 (assert (forall ((F_49 (-> tptp.pname tptp.hoare_2091234717iple_a)) (A_124 (-> tptp.pname Bool)) (B_66 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_231808478iple_a F_49))) (= (@ _let_1 (@ (@ tptp.semila1780557381name_o A_124) B_66)) (@ (@ tptp.semila1052848428le_a_o (@ _let_1 A_124)) (@ _let_1 B_66))))))
% 0.62/0.95 (assert (forall ((F_48 (-> tptp.nat Bool)) (G_26 (-> tptp.nat Bool)) (X tptp.nat)) (= (@ (@ (@ tptp.semila848761471_nat_o F_48) G_26) X) (@ (@ tptp.semila10642723_sup_o (@ F_48 X)) (@ G_26 X)))))
% 0.62/0.95 (assert (forall ((F_48 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (G_26 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (X (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ (@ tptp.semila2050116131_a_o_o F_48) G_26) X) (@ (@ tptp.semila10642723_sup_o (@ F_48 X)) (@ G_26 X)))))
% 0.62/0.95 (assert (forall ((F_48 (-> tptp.hoare_1708887482_state Bool)) (G_26 (-> tptp.hoare_1708887482_state Bool)) (X tptp.hoare_1708887482_state)) (= (@ (@ (@ tptp.semila1122118281tate_o F_48) G_26) X) (@ (@ tptp.semila10642723_sup_o (@ F_48 X)) (@ G_26 X)))))
% 0.62/0.95 (assert (forall ((F_48 (-> tptp.pname Bool)) (G_26 (-> tptp.pname Bool)) (X tptp.pname)) (= (@ (@ (@ tptp.semila1780557381name_o F_48) G_26) X) (@ (@ tptp.semila10642723_sup_o (@ F_48 X)) (@ G_26 X)))))
% 0.62/0.95 (assert (forall ((F_48 (-> tptp.hoare_2091234717iple_a Bool)) (G_26 (-> tptp.hoare_2091234717iple_a Bool)) (X tptp.hoare_2091234717iple_a)) (= (@ (@ (@ tptp.semila1052848428le_a_o F_48) G_26) X) (@ (@ tptp.semila10642723_sup_o (@ F_48 X)) (@ G_26 X)))))
% 0.62/0.95 (assert (forall ((F_47 (-> tptp.nat Bool)) (G_25 (-> tptp.nat Bool)) (X_48 tptp.nat)) (= (@ (@ (@ tptp.semila848761471_nat_o F_47) G_25) X_48) (@ (@ tptp.semila10642723_sup_o (@ F_47 X_48)) (@ G_25 X_48)))))
% 0.62/0.95 (assert (forall ((F_47 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (G_25 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (X_48 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ (@ tptp.semila2050116131_a_o_o F_47) G_25) X_48) (@ (@ tptp.semila10642723_sup_o (@ F_47 X_48)) (@ G_25 X_48)))))
% 0.62/0.95 (assert (forall ((F_47 (-> tptp.hoare_1708887482_state Bool)) (G_25 (-> tptp.hoare_1708887482_state Bool)) (X_48 tptp.hoare_1708887482_state)) (= (@ (@ (@ tptp.semila1122118281tate_o F_47) G_25) X_48) (@ (@ tptp.semila10642723_sup_o (@ F_47 X_48)) (@ G_25 X_48)))))
% 0.62/0.95 (assert (forall ((F_47 (-> tptp.pname Bool)) (G_25 (-> tptp.pname Bool)) (X_48 tptp.pname)) (= (@ (@ (@ tptp.semila1780557381name_o F_47) G_25) X_48) (@ (@ tptp.semila10642723_sup_o (@ F_47 X_48)) (@ G_25 X_48)))))
% 0.62/0.95 (assert (forall ((F_47 (-> tptp.hoare_2091234717iple_a Bool)) (G_25 (-> tptp.hoare_2091234717iple_a Bool)) (X_48 tptp.hoare_2091234717iple_a)) (= (@ (@ (@ tptp.semila1052848428le_a_o F_47) G_25) X_48) (@ (@ tptp.semila10642723_sup_o (@ F_47 X_48)) (@ G_25 X_48)))))
% 0.62/0.95 (assert (forall ((G_24 (-> tptp.hoare_2091234717iple_a Bool)) (G_23 (-> tptp.hoare_2091234717iple_a Bool)) (Ts_3 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.hoare_1467856363rivs_a G_24))) (=> (@ (@ tptp.hoare_1467856363rivs_a G_23) Ts_3) (=> (@ _let_1 G_23) (@ _let_1 Ts_3))))))
% 0.62/0.95 (assert (forall ((G_24 (-> tptp.hoare_1708887482_state Bool)) (G_23 (-> tptp.hoare_1708887482_state Bool)) (Ts_3 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.hoare_90032982_state G_24))) (=> (@ (@ tptp.hoare_90032982_state G_23) Ts_3) (=> (@ _let_1 G_23) (@ _let_1 Ts_3))))))
% 0.62/0.95 (assert (forall ((X_47 (-> tptp.nat Bool)) (Y_20 (-> tptp.nat Bool)) (Z_11 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila848761471_nat_o X_47))) (= (@ (@ tptp.semila848761471_nat_o (@ _let_1 Y_20)) Z_11) (@ _let_1 (@ (@ tptp.semila848761471_nat_o Y_20) Z_11))))))
% 0.62/0.95 (assert (forall ((X_47 tptp.nat) (Y_20 tptp.nat) (Z_11 tptp.nat)) (let ((_let_1 (@ tptp.semila972727038up_nat X_47))) (= (@ (@ tptp.semila972727038up_nat (@ _let_1 Y_20)) Z_11) (@ _let_1 (@ (@ tptp.semila972727038up_nat Y_20) Z_11))))))
% 0.62/0.95 (assert (forall ((X_47 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (Y_20 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (Z_11 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.semila2050116131_a_o_o X_47))) (= (@ (@ tptp.semila2050116131_a_o_o (@ _let_1 Y_20)) Z_11) (@ _let_1 (@ (@ tptp.semila2050116131_a_o_o Y_20) Z_11))))))
% 0.62/0.95 (assert (forall ((X_47 (-> tptp.hoare_1708887482_state Bool)) (Y_20 (-> tptp.hoare_1708887482_state Bool)) (Z_11 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.semila1122118281tate_o X_47))) (= (@ (@ tptp.semila1122118281tate_o (@ _let_1 Y_20)) Z_11) (@ _let_1 (@ (@ tptp.semila1122118281tate_o Y_20) Z_11))))))
% 0.62/0.95 (assert (forall ((X_47 (-> tptp.pname Bool)) (Y_20 (-> tptp.pname Bool)) (Z_11 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o X_47))) (= (@ (@ tptp.semila1780557381name_o (@ _let_1 Y_20)) Z_11) (@ _let_1 (@ (@ tptp.semila1780557381name_o Y_20) Z_11))))))
% 0.62/0.95 (assert (forall ((X_47 Bool) (Y_20 Bool) (Z_11 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o X_47))) (= (@ (@ tptp.semila10642723_sup_o (@ _let_1 Y_20)) Z_11) (@ _let_1 (@ (@ tptp.semila10642723_sup_o Y_20) Z_11))))))
% 0.62/0.95 (assert (forall ((X_47 (-> tptp.hoare_2091234717iple_a Bool)) (Y_20 (-> tptp.hoare_2091234717iple_a Bool)) (Z_11 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila1052848428le_a_o X_47))) (= (@ (@ tptp.semila1052848428le_a_o (@ _let_1 Y_20)) Z_11) (@ _let_1 (@ (@ tptp.semila1052848428le_a_o Y_20) Z_11))))))
% 0.62/0.95 (assert (forall ((X_46 (-> tptp.nat Bool)) (Y_19 (-> tptp.nat Bool)) (Z_10 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila848761471_nat_o X_46))) (= (@ (@ tptp.semila848761471_nat_o (@ _let_1 Y_19)) Z_10) (@ _let_1 (@ (@ tptp.semila848761471_nat_o Y_19) Z_10))))))
% 0.62/0.95 (assert (forall ((X_46 tptp.nat) (Y_19 tptp.nat) (Z_10 tptp.nat)) (let ((_let_1 (@ tptp.semila972727038up_nat X_46))) (= (@ (@ tptp.semila972727038up_nat (@ _let_1 Y_19)) Z_10) (@ _let_1 (@ (@ tptp.semila972727038up_nat Y_19) Z_10))))))
% 0.62/0.95 (assert (forall ((X_46 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (Y_19 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (Z_10 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.semila2050116131_a_o_o X_46))) (= (@ (@ tptp.semila2050116131_a_o_o (@ _let_1 Y_19)) Z_10) (@ _let_1 (@ (@ tptp.semila2050116131_a_o_o Y_19) Z_10))))))
% 0.62/0.96 (assert (forall ((X_46 (-> tptp.hoare_1708887482_state Bool)) (Y_19 (-> tptp.hoare_1708887482_state Bool)) (Z_10 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.semila1122118281tate_o X_46))) (= (@ (@ tptp.semila1122118281tate_o (@ _let_1 Y_19)) Z_10) (@ _let_1 (@ (@ tptp.semila1122118281tate_o Y_19) Z_10))))))
% 0.62/0.96 (assert (forall ((X_46 (-> tptp.pname Bool)) (Y_19 (-> tptp.pname Bool)) (Z_10 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o X_46))) (= (@ (@ tptp.semila1780557381name_o (@ _let_1 Y_19)) Z_10) (@ _let_1 (@ (@ tptp.semila1780557381name_o Y_19) Z_10))))))
% 0.62/0.96 (assert (forall ((X_46 Bool) (Y_19 Bool) (Z_10 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o X_46))) (= (@ (@ tptp.semila10642723_sup_o (@ _let_1 Y_19)) Z_10) (@ _let_1 (@ (@ tptp.semila10642723_sup_o Y_19) Z_10))))))
% 0.62/0.96 (assert (forall ((X_46 (-> tptp.hoare_2091234717iple_a Bool)) (Y_19 (-> tptp.hoare_2091234717iple_a Bool)) (Z_10 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila1052848428le_a_o X_46))) (= (@ (@ tptp.semila1052848428le_a_o (@ _let_1 Y_19)) Z_10) (@ _let_1 (@ (@ tptp.semila1052848428le_a_o Y_19) Z_10))))))
% 0.62/0.96 (assert (forall ((A_123 (-> tptp.nat Bool)) (B_65 (-> tptp.nat Bool)) (C_32 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila848761471_nat_o A_123))) (= (@ (@ tptp.semila848761471_nat_o (@ _let_1 B_65)) C_32) (@ _let_1 (@ (@ tptp.semila848761471_nat_o B_65) C_32))))))
% 0.62/0.96 (assert (forall ((A_123 tptp.nat) (B_65 tptp.nat) (C_32 tptp.nat)) (let ((_let_1 (@ tptp.semila972727038up_nat A_123))) (= (@ (@ tptp.semila972727038up_nat (@ _let_1 B_65)) C_32) (@ _let_1 (@ (@ tptp.semila972727038up_nat B_65) C_32))))))
% 0.62/0.96 (assert (forall ((A_123 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_65 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (C_32 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.semila2050116131_a_o_o A_123))) (= (@ (@ tptp.semila2050116131_a_o_o (@ _let_1 B_65)) C_32) (@ _let_1 (@ (@ tptp.semila2050116131_a_o_o B_65) C_32))))))
% 0.62/0.96 (assert (forall ((A_123 (-> tptp.hoare_1708887482_state Bool)) (B_65 (-> tptp.hoare_1708887482_state Bool)) (C_32 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.semila1122118281tate_o A_123))) (= (@ (@ tptp.semila1122118281tate_o (@ _let_1 B_65)) C_32) (@ _let_1 (@ (@ tptp.semila1122118281tate_o B_65) C_32))))))
% 0.62/0.96 (assert (forall ((A_123 (-> tptp.pname Bool)) (B_65 (-> tptp.pname Bool)) (C_32 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o A_123))) (= (@ (@ tptp.semila1780557381name_o (@ _let_1 B_65)) C_32) (@ _let_1 (@ (@ tptp.semila1780557381name_o B_65) C_32))))))
% 0.62/0.96 (assert (forall ((A_123 Bool) (B_65 Bool) (C_32 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o A_123))) (= (@ (@ tptp.semila10642723_sup_o (@ _let_1 B_65)) C_32) (@ _let_1 (@ (@ tptp.semila10642723_sup_o B_65) C_32))))))
% 0.62/0.96 (assert (forall ((A_123 (-> tptp.hoare_2091234717iple_a Bool)) (B_65 (-> tptp.hoare_2091234717iple_a Bool)) (C_32 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila1052848428le_a_o A_123))) (= (@ (@ tptp.semila1052848428le_a_o (@ _let_1 B_65)) C_32) (@ _let_1 (@ (@ tptp.semila1052848428le_a_o B_65) C_32))))))
% 0.62/0.96 (assert (forall ((X_45 (-> tptp.nat Bool)) (Y_18 (-> tptp.nat Bool)) (Z_9 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila848761471_nat_o X_45))) (let ((_let_2 (@ tptp.semila848761471_nat_o Y_18))) (= (@ _let_1 (@ _let_2 Z_9)) (@ _let_2 (@ _let_1 Z_9)))))))
% 0.62/0.96 (assert (forall ((X_45 tptp.nat) (Y_18 tptp.nat) (Z_9 tptp.nat)) (let ((_let_1 (@ tptp.semila972727038up_nat X_45))) (let ((_let_2 (@ tptp.semila972727038up_nat Y_18))) (= (@ _let_1 (@ _let_2 Z_9)) (@ _let_2 (@ _let_1 Z_9)))))))
% 0.62/0.96 (assert (forall ((X_45 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (Y_18 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (Z_9 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.semila2050116131_a_o_o X_45))) (let ((_let_2 (@ tptp.semila2050116131_a_o_o Y_18))) (= (@ _let_1 (@ _let_2 Z_9)) (@ _let_2 (@ _let_1 Z_9)))))))
% 0.62/0.96 (assert (forall ((X_45 (-> tptp.hoare_1708887482_state Bool)) (Y_18 (-> tptp.hoare_1708887482_state Bool)) (Z_9 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.semila1122118281tate_o X_45))) (let ((_let_2 (@ tptp.semila1122118281tate_o Y_18))) (= (@ _let_1 (@ _let_2 Z_9)) (@ _let_2 (@ _let_1 Z_9)))))))
% 0.62/0.96 (assert (forall ((X_45 (-> tptp.pname Bool)) (Y_18 (-> tptp.pname Bool)) (Z_9 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o X_45))) (let ((_let_2 (@ tptp.semila1780557381name_o Y_18))) (= (@ _let_1 (@ _let_2 Z_9)) (@ _let_2 (@ _let_1 Z_9)))))))
% 0.62/0.96 (assert (forall ((X_45 Bool) (Y_18 Bool) (Z_9 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o X_45))) (let ((_let_2 (@ tptp.semila10642723_sup_o Y_18))) (= (@ _let_1 (@ _let_2 Z_9)) (@ _let_2 (@ _let_1 Z_9)))))))
% 0.62/0.96 (assert (forall ((X_45 (-> tptp.hoare_2091234717iple_a Bool)) (Y_18 (-> tptp.hoare_2091234717iple_a Bool)) (Z_9 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila1052848428le_a_o X_45))) (let ((_let_2 (@ tptp.semila1052848428le_a_o Y_18))) (= (@ _let_1 (@ _let_2 Z_9)) (@ _let_2 (@ _let_1 Z_9)))))))
% 0.62/0.96 (assert (forall ((X_44 (-> tptp.nat Bool)) (Y_17 (-> tptp.nat Bool)) (Z_8 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila848761471_nat_o X_44))) (let ((_let_2 (@ tptp.semila848761471_nat_o Y_17))) (= (@ _let_1 (@ _let_2 Z_8)) (@ _let_2 (@ _let_1 Z_8)))))))
% 0.62/0.96 (assert (forall ((X_44 tptp.nat) (Y_17 tptp.nat) (Z_8 tptp.nat)) (let ((_let_1 (@ tptp.semila972727038up_nat X_44))) (let ((_let_2 (@ tptp.semila972727038up_nat Y_17))) (= (@ _let_1 (@ _let_2 Z_8)) (@ _let_2 (@ _let_1 Z_8)))))))
% 0.62/0.96 (assert (forall ((X_44 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (Y_17 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (Z_8 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.semila2050116131_a_o_o X_44))) (let ((_let_2 (@ tptp.semila2050116131_a_o_o Y_17))) (= (@ _let_1 (@ _let_2 Z_8)) (@ _let_2 (@ _let_1 Z_8)))))))
% 0.62/0.96 (assert (forall ((X_44 (-> tptp.hoare_1708887482_state Bool)) (Y_17 (-> tptp.hoare_1708887482_state Bool)) (Z_8 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.semila1122118281tate_o X_44))) (let ((_let_2 (@ tptp.semila1122118281tate_o Y_17))) (= (@ _let_1 (@ _let_2 Z_8)) (@ _let_2 (@ _let_1 Z_8)))))))
% 0.62/0.96 (assert (forall ((X_44 (-> tptp.pname Bool)) (Y_17 (-> tptp.pname Bool)) (Z_8 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o X_44))) (let ((_let_2 (@ tptp.semila1780557381name_o Y_17))) (= (@ _let_1 (@ _let_2 Z_8)) (@ _let_2 (@ _let_1 Z_8)))))))
% 0.62/0.96 (assert (forall ((X_44 Bool) (Y_17 Bool) (Z_8 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o X_44))) (let ((_let_2 (@ tptp.semila10642723_sup_o Y_17))) (= (@ _let_1 (@ _let_2 Z_8)) (@ _let_2 (@ _let_1 Z_8)))))))
% 0.62/0.96 (assert (forall ((X_44 (-> tptp.hoare_2091234717iple_a Bool)) (Y_17 (-> tptp.hoare_2091234717iple_a Bool)) (Z_8 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila1052848428le_a_o X_44))) (let ((_let_2 (@ tptp.semila1052848428le_a_o Y_17))) (= (@ _let_1 (@ _let_2 Z_8)) (@ _let_2 (@ _let_1 Z_8)))))))
% 0.62/0.96 (assert (forall ((B_64 (-> tptp.nat Bool)) (A_122 (-> tptp.nat Bool)) (C_31 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila848761471_nat_o B_64))) (let ((_let_2 (@ tptp.semila848761471_nat_o A_122))) (= (@ _let_1 (@ _let_2 C_31)) (@ _let_2 (@ _let_1 C_31)))))))
% 0.62/0.96 (assert (forall ((B_64 tptp.nat) (A_122 tptp.nat) (C_31 tptp.nat)) (let ((_let_1 (@ tptp.semila972727038up_nat B_64))) (let ((_let_2 (@ tptp.semila972727038up_nat A_122))) (= (@ _let_1 (@ _let_2 C_31)) (@ _let_2 (@ _let_1 C_31)))))))
% 0.62/0.96 (assert (forall ((B_64 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (A_122 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (C_31 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.semila2050116131_a_o_o B_64))) (let ((_let_2 (@ tptp.semila2050116131_a_o_o A_122))) (= (@ _let_1 (@ _let_2 C_31)) (@ _let_2 (@ _let_1 C_31)))))))
% 0.62/0.96 (assert (forall ((B_64 (-> tptp.hoare_1708887482_state Bool)) (A_122 (-> tptp.hoare_1708887482_state Bool)) (C_31 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.semila1122118281tate_o B_64))) (let ((_let_2 (@ tptp.semila1122118281tate_o A_122))) (= (@ _let_1 (@ _let_2 C_31)) (@ _let_2 (@ _let_1 C_31)))))))
% 0.62/0.96 (assert (forall ((B_64 (-> tptp.pname Bool)) (A_122 (-> tptp.pname Bool)) (C_31 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o B_64))) (let ((_let_2 (@ tptp.semila1780557381name_o A_122))) (= (@ _let_1 (@ _let_2 C_31)) (@ _let_2 (@ _let_1 C_31)))))))
% 0.62/0.96 (assert (forall ((B_64 Bool) (A_122 Bool) (C_31 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o B_64))) (let ((_let_2 (@ tptp.semila10642723_sup_o A_122))) (= (@ _let_1 (@ _let_2 C_31)) (@ _let_2 (@ _let_1 C_31)))))))
% 0.62/0.96 (assert (forall ((B_64 (-> tptp.hoare_2091234717iple_a Bool)) (A_122 (-> tptp.hoare_2091234717iple_a Bool)) (C_31 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila1052848428le_a_o B_64))) (let ((_let_2 (@ tptp.semila1052848428le_a_o A_122))) (= (@ _let_1 (@ _let_2 C_31)) (@ _let_2 (@ _let_1 C_31)))))))
% 0.62/0.96 (assert (forall ((X_43 (-> tptp.nat Bool)) (Y_16 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila848761471_nat_o X_43))) (let ((_let_2 (@ _let_1 Y_16))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_43 tptp.nat) (Y_16 tptp.nat)) (let ((_let_1 (@ tptp.semila972727038up_nat X_43))) (let ((_let_2 (@ _let_1 Y_16))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_43 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (Y_16 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.semila2050116131_a_o_o X_43))) (let ((_let_2 (@ _let_1 Y_16))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_43 (-> tptp.hoare_1708887482_state Bool)) (Y_16 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.semila1122118281tate_o X_43))) (let ((_let_2 (@ _let_1 Y_16))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_43 (-> tptp.pname Bool)) (Y_16 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o X_43))) (let ((_let_2 (@ _let_1 Y_16))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_43 Bool) (Y_16 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o X_43))) (let ((_let_2 (@ _let_1 Y_16))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_43 (-> tptp.hoare_2091234717iple_a Bool)) (Y_16 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila1052848428le_a_o X_43))) (let ((_let_2 (@ _let_1 Y_16))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_42 (-> tptp.nat Bool)) (Y_15 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila848761471_nat_o X_42))) (let ((_let_2 (@ _let_1 Y_15))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_42 tptp.nat) (Y_15 tptp.nat)) (let ((_let_1 (@ tptp.semila972727038up_nat X_42))) (let ((_let_2 (@ _let_1 Y_15))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_42 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (Y_15 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.semila2050116131_a_o_o X_42))) (let ((_let_2 (@ _let_1 Y_15))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_42 (-> tptp.hoare_1708887482_state Bool)) (Y_15 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.semila1122118281tate_o X_42))) (let ((_let_2 (@ _let_1 Y_15))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_42 (-> tptp.pname Bool)) (Y_15 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o X_42))) (let ((_let_2 (@ _let_1 Y_15))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_42 Bool) (Y_15 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o X_42))) (let ((_let_2 (@ _let_1 Y_15))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_42 (-> tptp.hoare_2091234717iple_a Bool)) (Y_15 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila1052848428le_a_o X_42))) (let ((_let_2 (@ _let_1 Y_15))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((A_121 (-> tptp.nat Bool)) (B_63 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila848761471_nat_o A_121))) (let ((_let_2 (@ _let_1 B_63))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((A_121 tptp.nat) (B_63 tptp.nat)) (let ((_let_1 (@ tptp.semila972727038up_nat A_121))) (let ((_let_2 (@ _let_1 B_63))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((A_121 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_63 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.semila2050116131_a_o_o A_121))) (let ((_let_2 (@ _let_1 B_63))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((A_121 (-> tptp.hoare_1708887482_state Bool)) (B_63 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.semila1122118281tate_o A_121))) (let ((_let_2 (@ _let_1 B_63))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((A_121 (-> tptp.pname Bool)) (B_63 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o A_121))) (let ((_let_2 (@ _let_1 B_63))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((A_121 Bool) (B_63 Bool)) (let ((_let_1 (@ tptp.semila10642723_sup_o A_121))) (let ((_let_2 (@ _let_1 B_63))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((A_121 (-> tptp.hoare_2091234717iple_a Bool)) (B_63 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila1052848428le_a_o A_121))) (let ((_let_2 (@ _let_1 B_63))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_41 (-> tptp.nat Bool)) (Y_14 (-> tptp.nat Bool))) (= (@ (@ tptp.semila848761471_nat_o X_41) Y_14) (@ (@ tptp.semila848761471_nat_o Y_14) X_41))))
% 0.62/0.96 (assert (forall ((X_41 tptp.nat) (Y_14 tptp.nat)) (= (@ (@ tptp.semila972727038up_nat X_41) Y_14) (@ (@ tptp.semila972727038up_nat Y_14) X_41))))
% 0.62/0.96 (assert (forall ((X_41 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (Y_14 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.semila2050116131_a_o_o X_41) Y_14) (@ (@ tptp.semila2050116131_a_o_o Y_14) X_41))))
% 0.62/0.96 (assert (forall ((X_41 (-> tptp.hoare_1708887482_state Bool)) (Y_14 (-> tptp.hoare_1708887482_state Bool))) (= (@ (@ tptp.semila1122118281tate_o X_41) Y_14) (@ (@ tptp.semila1122118281tate_o Y_14) X_41))))
% 0.62/0.96 (assert (forall ((X_41 (-> tptp.pname Bool)) (Y_14 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o X_41) Y_14) (@ (@ tptp.semila1780557381name_o Y_14) X_41))))
% 0.62/0.96 (assert (forall ((X_41 Bool) (Y_14 Bool)) (= (@ (@ tptp.semila10642723_sup_o X_41) Y_14) (@ (@ tptp.semila10642723_sup_o Y_14) X_41))))
% 0.62/0.96 (assert (forall ((X_41 (-> tptp.hoare_2091234717iple_a Bool)) (Y_14 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila1052848428le_a_o X_41) Y_14) (@ (@ tptp.semila1052848428le_a_o Y_14) X_41))))
% 0.62/0.96 (assert (forall ((X_40 (-> tptp.nat Bool)) (Y_13 (-> tptp.nat Bool))) (= (@ (@ tptp.semila848761471_nat_o X_40) Y_13) (@ (@ tptp.semila848761471_nat_o Y_13) X_40))))
% 0.62/0.96 (assert (forall ((X_40 tptp.nat) (Y_13 tptp.nat)) (= (@ (@ tptp.semila972727038up_nat X_40) Y_13) (@ (@ tptp.semila972727038up_nat Y_13) X_40))))
% 0.62/0.96 (assert (forall ((X_40 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (Y_13 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.semila2050116131_a_o_o X_40) Y_13) (@ (@ tptp.semila2050116131_a_o_o Y_13) X_40))))
% 0.62/0.96 (assert (forall ((X_40 (-> tptp.hoare_1708887482_state Bool)) (Y_13 (-> tptp.hoare_1708887482_state Bool))) (= (@ (@ tptp.semila1122118281tate_o X_40) Y_13) (@ (@ tptp.semila1122118281tate_o Y_13) X_40))))
% 0.62/0.96 (assert (forall ((X_40 (-> tptp.pname Bool)) (Y_13 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o X_40) Y_13) (@ (@ tptp.semila1780557381name_o Y_13) X_40))))
% 0.62/0.96 (assert (forall ((X_40 Bool) (Y_13 Bool)) (= (@ (@ tptp.semila10642723_sup_o X_40) Y_13) (@ (@ tptp.semila10642723_sup_o Y_13) X_40))))
% 0.62/0.96 (assert (forall ((X_40 (-> tptp.hoare_2091234717iple_a Bool)) (Y_13 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila1052848428le_a_o X_40) Y_13) (@ (@ tptp.semila1052848428le_a_o Y_13) X_40))))
% 0.62/0.96 (assert (forall ((A_120 (-> tptp.nat Bool)) (B_62 (-> tptp.nat Bool))) (= (@ (@ tptp.semila848761471_nat_o A_120) B_62) (@ (@ tptp.semila848761471_nat_o B_62) A_120))))
% 0.62/0.96 (assert (forall ((A_120 tptp.nat) (B_62 tptp.nat)) (= (@ (@ tptp.semila972727038up_nat A_120) B_62) (@ (@ tptp.semila972727038up_nat B_62) A_120))))
% 0.62/0.96 (assert (forall ((A_120 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_62 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.semila2050116131_a_o_o A_120) B_62) (@ (@ tptp.semila2050116131_a_o_o B_62) A_120))))
% 0.62/0.96 (assert (forall ((A_120 (-> tptp.hoare_1708887482_state Bool)) (B_62 (-> tptp.hoare_1708887482_state Bool))) (= (@ (@ tptp.semila1122118281tate_o A_120) B_62) (@ (@ tptp.semila1122118281tate_o B_62) A_120))))
% 0.62/0.96 (assert (forall ((A_120 (-> tptp.pname Bool)) (B_62 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o A_120) B_62) (@ (@ tptp.semila1780557381name_o B_62) A_120))))
% 0.62/0.96 (assert (forall ((A_120 Bool) (B_62 Bool)) (= (@ (@ tptp.semila10642723_sup_o A_120) B_62) (@ (@ tptp.semila10642723_sup_o B_62) A_120))))
% 0.62/0.96 (assert (forall ((A_120 (-> tptp.hoare_2091234717iple_a Bool)) (B_62 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila1052848428le_a_o A_120) B_62) (@ (@ tptp.semila1052848428le_a_o B_62) A_120))))
% 0.62/0.96 (assert (forall ((X_39 (-> tptp.nat Bool))) (= (@ (@ tptp.semila848761471_nat_o X_39) X_39) X_39)))
% 0.62/0.96 (assert (forall ((X_39 tptp.nat)) (= (@ (@ tptp.semila972727038up_nat X_39) X_39) X_39)))
% 0.62/0.96 (assert (forall ((X_39 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.semila2050116131_a_o_o X_39) X_39) X_39)))
% 0.62/0.96 (assert (forall ((X_39 (-> tptp.hoare_1708887482_state Bool))) (= (@ (@ tptp.semila1122118281tate_o X_39) X_39) X_39)))
% 0.62/0.96 (assert (forall ((X_39 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o X_39) X_39) X_39)))
% 0.62/0.96 (assert (forall ((X_39 Bool)) (= (@ (@ tptp.semila10642723_sup_o X_39) X_39) X_39)))
% 0.62/0.96 (assert (forall ((X_39 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila1052848428le_a_o X_39) X_39) X_39)))
% 0.62/0.96 (assert (forall ((A_119 (-> tptp.nat Bool))) (= (@ (@ tptp.semila848761471_nat_o A_119) A_119) A_119)))
% 0.62/0.96 (assert (forall ((A_119 tptp.nat)) (= (@ (@ tptp.semila972727038up_nat A_119) A_119) A_119)))
% 0.62/0.96 (assert (forall ((A_119 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.semila2050116131_a_o_o A_119) A_119) A_119)))
% 0.62/0.96 (assert (forall ((A_119 (-> tptp.hoare_1708887482_state Bool))) (= (@ (@ tptp.semila1122118281tate_o A_119) A_119) A_119)))
% 0.62/0.96 (assert (forall ((A_119 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o A_119) A_119) A_119)))
% 0.62/0.96 (assert (forall ((A_119 Bool)) (= (@ (@ tptp.semila10642723_sup_o A_119) A_119) A_119)))
% 0.62/0.96 (assert (forall ((A_119 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila1052848428le_a_o A_119) A_119) A_119)))
% 0.62/0.96 (assert (forall ((B_61 tptp.nat) (F_46 (-> tptp.nat tptp.nat)) (X_38 tptp.nat) (A_118 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_38) A_118) (=> (= B_61 (@ F_46 X_38)) (@ (@ tptp.member_nat B_61) (@ (@ tptp.image_nat_nat F_46) A_118))))))
% 0.62/0.96 (assert (forall ((B_61 tptp.hoare_1708887482_state) (F_46 (-> tptp.pname tptp.hoare_1708887482_state)) (X_38 tptp.pname) (A_118 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_38) A_118) (=> (= B_61 (@ F_46 X_38)) (@ (@ tptp.member451959335_state B_61) (@ (@ tptp.image_1116629049_state F_46) A_118))))))
% 0.62/0.96 (assert (forall ((B_61 tptp.nat) (F_46 (-> tptp.pname tptp.nat)) (X_38 tptp.pname) (A_118 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_38) A_118) (=> (= B_61 (@ F_46 X_38)) (@ (@ tptp.member_nat B_61) (@ (@ tptp.image_pname_nat F_46) A_118))))))
% 0.62/0.96 (assert (forall ((B_61 (-> tptp.hoare_2091234717iple_a Bool)) (F_46 (-> tptp.pname tptp.hoare_2091234717iple_a Bool)) (X_38 tptp.pname) (A_118 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_38) A_118) (=> (= B_61 (@ F_46 X_38)) (@ (@ tptp.member99268621le_a_o B_61) (@ (@ tptp.image_742317343le_a_o F_46) A_118))))))
% 0.62/0.96 (assert (forall ((B_61 tptp.pname) (F_46 (-> tptp.nat tptp.pname)) (X_38 tptp.nat) (A_118 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_38) A_118) (=> (= B_61 (@ F_46 X_38)) (@ (@ tptp.member_pname B_61) (@ (@ tptp.image_nat_pname F_46) A_118))))))
% 0.62/0.96 (assert (forall ((B_61 tptp.pname) (F_46 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.pname)) (X_38 (-> tptp.hoare_2091234717iple_a Bool)) (A_118 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (@ (@ tptp.member99268621le_a_o X_38) A_118) (=> (= B_61 (@ F_46 X_38)) (@ (@ tptp.member_pname B_61) (@ (@ tptp.image_1908519857_pname F_46) A_118))))))
% 0.62/0.96 (assert (forall ((B_61 tptp.pname) (F_46 (-> tptp.hoare_2091234717iple_a tptp.pname)) (X_38 tptp.hoare_2091234717iple_a) (A_118 (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ (@ tptp.member290856304iple_a X_38) A_118) (=> (= B_61 (@ F_46 X_38)) (@ (@ tptp.member_pname B_61) (@ (@ tptp.image_924789612_pname F_46) A_118))))))
% 0.62/0.96 (assert (forall ((B_61 tptp.hoare_2091234717iple_a) (F_46 (-> tptp.pname tptp.hoare_2091234717iple_a)) (X_38 tptp.pname) (A_118 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_38) A_118) (=> (= B_61 (@ F_46 X_38)) (@ (@ tptp.member290856304iple_a B_61) (@ (@ tptp.image_231808478iple_a F_46) A_118))))))
% 0.62/0.96 (assert (forall ((F_45 (-> tptp.nat tptp.nat)) (X_37 tptp.nat) (A_117 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_37) A_117) (@ (@ tptp.member_nat (@ F_45 X_37)) (@ (@ tptp.image_nat_nat F_45) A_117)))))
% 0.62/0.96 (assert (forall ((F_45 (-> tptp.pname tptp.hoare_1708887482_state)) (X_37 tptp.pname) (A_117 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_37) A_117) (@ (@ tptp.member451959335_state (@ F_45 X_37)) (@ (@ tptp.image_1116629049_state F_45) A_117)))))
% 0.62/0.96 (assert (forall ((F_45 (-> tptp.pname tptp.nat)) (X_37 tptp.pname) (A_117 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_37) A_117) (@ (@ tptp.member_nat (@ F_45 X_37)) (@ (@ tptp.image_pname_nat F_45) A_117)))))
% 0.62/0.96 (assert (forall ((F_45 (-> tptp.pname tptp.hoare_2091234717iple_a Bool)) (X_37 tptp.pname) (A_117 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_37) A_117) (@ (@ tptp.member99268621le_a_o (@ F_45 X_37)) (@ (@ tptp.image_742317343le_a_o F_45) A_117)))))
% 0.62/0.96 (assert (forall ((F_45 (-> tptp.nat tptp.pname)) (X_37 tptp.nat) (A_117 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_37) A_117) (@ (@ tptp.member_pname (@ F_45 X_37)) (@ (@ tptp.image_nat_pname F_45) A_117)))))
% 0.62/0.96 (assert (forall ((F_45 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.pname)) (X_37 (-> tptp.hoare_2091234717iple_a Bool)) (A_117 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (@ (@ tptp.member99268621le_a_o X_37) A_117) (@ (@ tptp.member_pname (@ F_45 X_37)) (@ (@ tptp.image_1908519857_pname F_45) A_117)))))
% 0.62/0.96 (assert (forall ((F_45 (-> tptp.hoare_2091234717iple_a tptp.pname)) (X_37 tptp.hoare_2091234717iple_a) (A_117 (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ (@ tptp.member290856304iple_a X_37) A_117) (@ (@ tptp.member_pname (@ F_45 X_37)) (@ (@ tptp.image_924789612_pname F_45) A_117)))))
% 0.62/0.96 (assert (forall ((F_45 (-> tptp.pname tptp.hoare_2091234717iple_a)) (X_37 tptp.pname) (A_117 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_37) A_117) (@ (@ tptp.member290856304iple_a (@ F_45 X_37)) (@ (@ tptp.image_231808478iple_a F_45) A_117)))))
% 0.62/0.96 (assert (forall ((Z_7 tptp.nat) (F_44 (-> tptp.nat tptp.nat)) (A_116 (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat Z_7) (@ (@ tptp.image_nat_nat F_44) A_116)) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A_116) (= Z_7 (@ F_44 X)))))))
% 0.62/0.96 (assert (forall ((Z_7 tptp.hoare_1708887482_state) (F_44 (-> tptp.pname tptp.hoare_1708887482_state)) (A_116 (-> tptp.pname Bool))) (= (@ (@ tptp.member451959335_state Z_7) (@ (@ tptp.image_1116629049_state F_44) A_116)) (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) A_116) (= Z_7 (@ F_44 X)))))))
% 0.62/0.96 (assert (forall ((Z_7 tptp.hoare_2091234717iple_a) (F_44 (-> tptp.pname tptp.hoare_2091234717iple_a)) (A_116 (-> tptp.pname Bool))) (= (@ (@ tptp.member290856304iple_a Z_7) (@ (@ tptp.image_231808478iple_a F_44) A_116)) (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) A_116) (= Z_7 (@ F_44 X)))))))
% 0.62/0.96 (assert (forall ((A_115 (-> tptp.nat Bool)) (C_30 tptp.nat) (B_60 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_30))) (=> (@ _let_1 B_60) (@ _let_1 (@ (@ tptp.semila848761471_nat_o A_115) B_60))))))
% 0.62/0.96 (assert (forall ((A_115 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (C_30 (-> tptp.hoare_2091234717iple_a Bool)) (B_60 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.member99268621le_a_o C_30))) (=> (@ _let_1 B_60) (@ _let_1 (@ (@ tptp.semila2050116131_a_o_o A_115) B_60))))))
% 0.62/0.96 (assert (forall ((A_115 (-> tptp.hoare_1708887482_state Bool)) (C_30 tptp.hoare_1708887482_state) (B_60 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.member451959335_state C_30))) (=> (@ _let_1 B_60) (@ _let_1 (@ (@ tptp.semila1122118281tate_o A_115) B_60))))))
% 0.62/0.96 (assert (forall ((A_115 (-> tptp.hoare_2091234717iple_a Bool)) (C_30 tptp.hoare_2091234717iple_a) (B_60 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.member290856304iple_a C_30))) (=> (@ _let_1 B_60) (@ _let_1 (@ (@ tptp.semila1052848428le_a_o A_115) B_60))))))
% 0.62/0.96 (assert (forall ((A_115 (-> tptp.pname Bool)) (C_30 tptp.pname) (B_60 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_30))) (=> (@ _let_1 B_60) (@ _let_1 (@ (@ tptp.semila1780557381name_o A_115) B_60))))))
% 0.62/0.96 (assert (forall ((B_59 (-> tptp.nat Bool)) (C_29 tptp.nat) (A_114 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_29))) (=> (@ _let_1 A_114) (@ _let_1 (@ (@ tptp.semila848761471_nat_o A_114) B_59))))))
% 0.62/0.96 (assert (forall ((B_59 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (C_29 (-> tptp.hoare_2091234717iple_a Bool)) (A_114 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.member99268621le_a_o C_29))) (=> (@ _let_1 A_114) (@ _let_1 (@ (@ tptp.semila2050116131_a_o_o A_114) B_59))))))
% 0.62/0.96 (assert (forall ((B_59 (-> tptp.hoare_1708887482_state Bool)) (C_29 tptp.hoare_1708887482_state) (A_114 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.member451959335_state C_29))) (=> (@ _let_1 A_114) (@ _let_1 (@ (@ tptp.semila1122118281tate_o A_114) B_59))))))
% 0.62/0.96 (assert (forall ((B_59 (-> tptp.hoare_2091234717iple_a Bool)) (C_29 tptp.hoare_2091234717iple_a) (A_114 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.member290856304iple_a C_29))) (=> (@ _let_1 A_114) (@ _let_1 (@ (@ tptp.semila1052848428le_a_o A_114) B_59))))))
% 0.62/0.96 (assert (forall ((B_59 (-> tptp.pname Bool)) (C_29 tptp.pname) (A_114 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_29))) (=> (@ _let_1 A_114) (@ _let_1 (@ (@ tptp.semila1780557381name_o A_114) B_59))))))
% 0.62/0.96 (assert (forall ((A_113 (-> tptp.nat Bool)) (B_58 (-> tptp.nat Bool)) (X_36 tptp.nat)) (=> (@ B_58 X_36) (@ (@ (@ tptp.semila848761471_nat_o A_113) B_58) X_36))))
% 0.62/0.96 (assert (forall ((A_113 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_58 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (X_36 (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ B_58 X_36) (@ (@ (@ tptp.semila2050116131_a_o_o A_113) B_58) X_36))))
% 0.62/0.96 (assert (forall ((A_113 (-> tptp.hoare_1708887482_state Bool)) (B_58 (-> tptp.hoare_1708887482_state Bool)) (X_36 tptp.hoare_1708887482_state)) (=> (@ B_58 X_36) (@ (@ (@ tptp.semila1122118281tate_o A_113) B_58) X_36))))
% 0.62/0.96 (assert (forall ((A_113 (-> tptp.pname Bool)) (B_58 (-> tptp.pname Bool)) (X_36 tptp.pname)) (=> (@ B_58 X_36) (@ (@ (@ tptp.semila1780557381name_o A_113) B_58) X_36))))
% 0.62/0.96 (assert (forall ((A_113 (-> tptp.hoare_2091234717iple_a Bool)) (B_58 (-> tptp.hoare_2091234717iple_a Bool)) (X_36 tptp.hoare_2091234717iple_a)) (=> (@ B_58 X_36) (@ (@ (@ tptp.semila1052848428le_a_o A_113) B_58) X_36))))
% 0.62/0.96 (assert (forall ((B_57 (-> tptp.nat Bool)) (A_112 (-> tptp.nat Bool)) (X_35 tptp.nat)) (=> (@ A_112 X_35) (@ (@ (@ tptp.semila848761471_nat_o A_112) B_57) X_35))))
% 0.62/0.96 (assert (forall ((B_57 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (A_112 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (X_35 (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ A_112 X_35) (@ (@ (@ tptp.semila2050116131_a_o_o A_112) B_57) X_35))))
% 0.62/0.96 (assert (forall ((B_57 (-> tptp.hoare_1708887482_state Bool)) (A_112 (-> tptp.hoare_1708887482_state Bool)) (X_35 tptp.hoare_1708887482_state)) (=> (@ A_112 X_35) (@ (@ (@ tptp.semila1122118281tate_o A_112) B_57) X_35))))
% 0.62/0.96 (assert (forall ((B_57 (-> tptp.pname Bool)) (A_112 (-> tptp.pname Bool)) (X_35 tptp.pname)) (=> (@ A_112 X_35) (@ (@ (@ tptp.semila1780557381name_o A_112) B_57) X_35))))
% 0.62/0.96 (assert (forall ((B_57 (-> tptp.hoare_2091234717iple_a Bool)) (A_112 (-> tptp.hoare_2091234717iple_a Bool)) (X_35 tptp.hoare_2091234717iple_a)) (=> (@ A_112 X_35) (@ (@ (@ tptp.semila1052848428le_a_o A_112) B_57) X_35))))
% 0.62/0.96 (assert (forall ((P_35 (-> tptp.nat Bool)) (A_111 (-> tptp.nat Bool)) (B_56 (-> tptp.nat Bool))) (= (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.semila848761471_nat_o A_111) B_56)) (@ P_35 X))) (and (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A_111) (@ P_35 X))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) B_56) (@ P_35 X)))))))
% 0.62/0.96 (assert (forall ((P_35 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (A_111 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_56 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (forall ((X (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ (@ tptp.member99268621le_a_o X) (@ (@ tptp.semila2050116131_a_o_o A_111) B_56)) (@ P_35 X))) (and (forall ((X (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ (@ tptp.member99268621le_a_o X) A_111) (@ P_35 X))) (forall ((X (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ (@ tptp.member99268621le_a_o X) B_56) (@ P_35 X)))))))
% 0.62/0.96 (assert (forall ((P_35 (-> tptp.hoare_1708887482_state Bool)) (A_111 (-> tptp.hoare_1708887482_state Bool)) (B_56 (-> tptp.hoare_1708887482_state Bool))) (= (forall ((X tptp.hoare_1708887482_state)) (=> (@ (@ tptp.member451959335_state X) (@ (@ tptp.semila1122118281tate_o A_111) B_56)) (@ P_35 X))) (and (forall ((X tptp.hoare_1708887482_state)) (=> (@ (@ tptp.member451959335_state X) A_111) (@ P_35 X))) (forall ((X tptp.hoare_1708887482_state)) (=> (@ (@ tptp.member451959335_state X) B_56) (@ P_35 X)))))))
% 0.62/0.96 (assert (forall ((P_35 (-> tptp.pname Bool)) (A_111 (-> tptp.pname Bool)) (B_56 (-> tptp.pname Bool))) (= (forall ((X tptp.pname)) (=> (@ (@ tptp.member_pname X) (@ (@ tptp.semila1780557381name_o A_111) B_56)) (@ P_35 X))) (and (forall ((X tptp.pname)) (=> (@ (@ tptp.member_pname X) A_111) (@ P_35 X))) (forall ((X tptp.pname)) (=> (@ (@ tptp.member_pname X) B_56) (@ P_35 X)))))))
% 0.62/0.96 (assert (forall ((P_35 (-> tptp.hoare_2091234717iple_a Bool)) (A_111 (-> tptp.hoare_2091234717iple_a Bool)) (B_56 (-> tptp.hoare_2091234717iple_a Bool))) (= (forall ((X tptp.hoare_2091234717iple_a)) (=> (@ (@ tptp.member290856304iple_a X) (@ (@ tptp.semila1052848428le_a_o A_111) B_56)) (@ P_35 X))) (and (forall ((X tptp.hoare_2091234717iple_a)) (=> (@ (@ tptp.member290856304iple_a X) A_111) (@ P_35 X))) (forall ((X tptp.hoare_2091234717iple_a)) (=> (@ (@ tptp.member290856304iple_a X) B_56) (@ P_35 X)))))))
% 0.62/0.96 (assert (forall ((P_34 (-> tptp.nat Bool)) (A_110 (-> tptp.nat Bool)) (B_55 (-> tptp.nat Bool))) (= (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ (@ tptp.semila848761471_nat_o A_110) B_55)) (@ P_34 X))) (or (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A_110) (@ P_34 X))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) B_55) (@ P_34 X)))))))
% 0.62/0.96 (assert (forall ((P_34 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (A_110 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_55 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (exists ((X (-> tptp.hoare_2091234717iple_a Bool))) (and (@ (@ tptp.member99268621le_a_o X) (@ (@ tptp.semila2050116131_a_o_o A_110) B_55)) (@ P_34 X))) (or (exists ((X (-> tptp.hoare_2091234717iple_a Bool))) (and (@ (@ tptp.member99268621le_a_o X) A_110) (@ P_34 X))) (exists ((X (-> tptp.hoare_2091234717iple_a Bool))) (and (@ (@ tptp.member99268621le_a_o X) B_55) (@ P_34 X)))))))
% 0.62/0.96 (assert (forall ((P_34 (-> tptp.hoare_1708887482_state Bool)) (A_110 (-> tptp.hoare_1708887482_state Bool)) (B_55 (-> tptp.hoare_1708887482_state Bool))) (= (exists ((X tptp.hoare_1708887482_state)) (and (@ (@ tptp.member451959335_state X) (@ (@ tptp.semila1122118281tate_o A_110) B_55)) (@ P_34 X))) (or (exists ((X tptp.hoare_1708887482_state)) (and (@ (@ tptp.member451959335_state X) A_110) (@ P_34 X))) (exists ((X tptp.hoare_1708887482_state)) (and (@ (@ tptp.member451959335_state X) B_55) (@ P_34 X)))))))
% 0.62/0.96 (assert (forall ((P_34 (-> tptp.pname Bool)) (A_110 (-> tptp.pname Bool)) (B_55 (-> tptp.pname Bool))) (= (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) (@ (@ tptp.semila1780557381name_o A_110) B_55)) (@ P_34 X))) (or (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) A_110) (@ P_34 X))) (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) B_55) (@ P_34 X)))))))
% 0.62/0.96 (assert (forall ((P_34 (-> tptp.hoare_2091234717iple_a Bool)) (A_110 (-> tptp.hoare_2091234717iple_a Bool)) (B_55 (-> tptp.hoare_2091234717iple_a Bool))) (= (exists ((X tptp.hoare_2091234717iple_a)) (and (@ (@ tptp.member290856304iple_a X) (@ (@ tptp.semila1052848428le_a_o A_110) B_55)) (@ P_34 X))) (or (exists ((X tptp.hoare_2091234717iple_a)) (and (@ (@ tptp.member290856304iple_a X) A_110) (@ P_34 X))) (exists ((X tptp.hoare_2091234717iple_a)) (and (@ (@ tptp.member290856304iple_a X) B_55) (@ P_34 X)))))))
% 0.62/0.96 (assert (forall ((A_109 (-> tptp.nat Bool)) (B_54 (-> tptp.nat Bool)) (C_28 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila848761471_nat_o A_109))) (= (@ (@ tptp.semila848761471_nat_o (@ _let_1 B_54)) C_28) (@ _let_1 (@ (@ tptp.semila848761471_nat_o B_54) C_28))))))
% 0.62/0.96 (assert (forall ((A_109 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_54 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (C_28 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.semila2050116131_a_o_o A_109))) (= (@ (@ tptp.semila2050116131_a_o_o (@ _let_1 B_54)) C_28) (@ _let_1 (@ (@ tptp.semila2050116131_a_o_o B_54) C_28))))))
% 0.62/0.96 (assert (forall ((A_109 (-> tptp.hoare_1708887482_state Bool)) (B_54 (-> tptp.hoare_1708887482_state Bool)) (C_28 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.semila1122118281tate_o A_109))) (= (@ (@ tptp.semila1122118281tate_o (@ _let_1 B_54)) C_28) (@ _let_1 (@ (@ tptp.semila1122118281tate_o B_54) C_28))))))
% 0.62/0.96 (assert (forall ((A_109 (-> tptp.pname Bool)) (B_54 (-> tptp.pname Bool)) (C_28 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o A_109))) (= (@ (@ tptp.semila1780557381name_o (@ _let_1 B_54)) C_28) (@ _let_1 (@ (@ tptp.semila1780557381name_o B_54) C_28))))))
% 0.62/0.96 (assert (forall ((A_109 (-> tptp.hoare_2091234717iple_a Bool)) (B_54 (-> tptp.hoare_2091234717iple_a Bool)) (C_28 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila1052848428le_a_o A_109))) (= (@ (@ tptp.semila1052848428le_a_o (@ _let_1 B_54)) C_28) (@ _let_1 (@ (@ tptp.semila1052848428le_a_o B_54) C_28))))))
% 0.62/0.96 (assert (forall ((C_27 tptp.nat) (A_108 (-> tptp.nat Bool)) (B_53 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_27))) (= (@ _let_1 (@ (@ tptp.semila848761471_nat_o A_108) B_53)) (or (@ _let_1 A_108) (@ _let_1 B_53))))))
% 0.62/0.96 (assert (forall ((C_27 (-> tptp.hoare_2091234717iple_a Bool)) (A_108 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_53 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.member99268621le_a_o C_27))) (= (@ _let_1 (@ (@ tptp.semila2050116131_a_o_o A_108) B_53)) (or (@ _let_1 A_108) (@ _let_1 B_53))))))
% 0.62/0.96 (assert (forall ((C_27 tptp.hoare_1708887482_state) (A_108 (-> tptp.hoare_1708887482_state Bool)) (B_53 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.member451959335_state C_27))) (= (@ _let_1 (@ (@ tptp.semila1122118281tate_o A_108) B_53)) (or (@ _let_1 A_108) (@ _let_1 B_53))))))
% 0.62/0.96 (assert (forall ((C_27 tptp.hoare_2091234717iple_a) (A_108 (-> tptp.hoare_2091234717iple_a Bool)) (B_53 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.member290856304iple_a C_27))) (= (@ _let_1 (@ (@ tptp.semila1052848428le_a_o A_108) B_53)) (or (@ _let_1 A_108) (@ _let_1 B_53))))))
% 0.62/0.96 (assert (forall ((C_27 tptp.pname) (A_108 (-> tptp.pname Bool)) (B_53 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_27))) (= (@ _let_1 (@ (@ tptp.semila1780557381name_o A_108) B_53)) (or (@ _let_1 A_108) (@ _let_1 B_53))))))
% 0.62/0.96 (assert (forall ((A_107 (-> tptp.nat Bool)) (B_52 (-> tptp.nat Bool)) (C_26 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila848761471_nat_o A_107))) (let ((_let_2 (@ tptp.semila848761471_nat_o B_52))) (= (@ _let_1 (@ _let_2 C_26)) (@ _let_2 (@ _let_1 C_26)))))))
% 0.62/0.96 (assert (forall ((A_107 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_52 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (C_26 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.semila2050116131_a_o_o A_107))) (let ((_let_2 (@ tptp.semila2050116131_a_o_o B_52))) (= (@ _let_1 (@ _let_2 C_26)) (@ _let_2 (@ _let_1 C_26)))))))
% 0.62/0.96 (assert (forall ((A_107 (-> tptp.hoare_1708887482_state Bool)) (B_52 (-> tptp.hoare_1708887482_state Bool)) (C_26 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.semila1122118281tate_o A_107))) (let ((_let_2 (@ tptp.semila1122118281tate_o B_52))) (= (@ _let_1 (@ _let_2 C_26)) (@ _let_2 (@ _let_1 C_26)))))))
% 0.62/0.96 (assert (forall ((A_107 (-> tptp.pname Bool)) (B_52 (-> tptp.pname Bool)) (C_26 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o A_107))) (let ((_let_2 (@ tptp.semila1780557381name_o B_52))) (= (@ _let_1 (@ _let_2 C_26)) (@ _let_2 (@ _let_1 C_26)))))))
% 0.62/0.96 (assert (forall ((A_107 (-> tptp.hoare_2091234717iple_a Bool)) (B_52 (-> tptp.hoare_2091234717iple_a Bool)) (C_26 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila1052848428le_a_o A_107))) (let ((_let_2 (@ tptp.semila1052848428le_a_o B_52))) (= (@ _let_1 (@ _let_2 C_26)) (@ _let_2 (@ _let_1 C_26)))))))
% 0.62/0.96 (assert (forall ((A_106 (-> tptp.nat Bool)) (B_51 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila848761471_nat_o A_106))) (let ((_let_2 (@ _let_1 B_51))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((A_106 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_51 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.semila2050116131_a_o_o A_106))) (let ((_let_2 (@ _let_1 B_51))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((A_106 (-> tptp.hoare_1708887482_state Bool)) (B_51 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.semila1122118281tate_o A_106))) (let ((_let_2 (@ _let_1 B_51))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((A_106 (-> tptp.pname Bool)) (B_51 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o A_106))) (let ((_let_2 (@ _let_1 B_51))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((A_106 (-> tptp.hoare_2091234717iple_a Bool)) (B_51 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila1052848428le_a_o A_106))) (let ((_let_2 (@ _let_1 B_51))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((A_105 (-> tptp.nat Bool)) (B_50 (-> tptp.nat Bool))) (= (@ (@ tptp.semila848761471_nat_o A_105) B_50) (@ (@ tptp.semila848761471_nat_o B_50) A_105))))
% 0.62/0.96 (assert (forall ((A_105 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_50 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.semila2050116131_a_o_o A_105) B_50) (@ (@ tptp.semila2050116131_a_o_o B_50) A_105))))
% 0.62/0.96 (assert (forall ((A_105 (-> tptp.hoare_1708887482_state Bool)) (B_50 (-> tptp.hoare_1708887482_state Bool))) (= (@ (@ tptp.semila1122118281tate_o A_105) B_50) (@ (@ tptp.semila1122118281tate_o B_50) A_105))))
% 0.62/0.96 (assert (forall ((A_105 (-> tptp.pname Bool)) (B_50 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o A_105) B_50) (@ (@ tptp.semila1780557381name_o B_50) A_105))))
% 0.62/0.96 (assert (forall ((A_105 (-> tptp.hoare_2091234717iple_a Bool)) (B_50 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila1052848428le_a_o A_105) B_50) (@ (@ tptp.semila1052848428le_a_o B_50) A_105))))
% 0.62/0.96 (assert (forall ((A_104 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_49 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.semila2050116131_a_o_o A_104) B_49) (@ tptp.collec1008234059le_a_o (lambda ((X (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.member99268621le_a_o X))) (or (@ _let_1 A_104) (@ _let_1 B_49))))))))
% 0.62/0.96 (assert (forall ((A_104 (-> tptp.hoare_1708887482_state Bool)) (B_49 (-> tptp.hoare_1708887482_state Bool))) (= (@ (@ tptp.semila1122118281tate_o A_104) B_49) (@ tptp.collec1568722789_state (lambda ((X tptp.hoare_1708887482_state)) (let ((_let_1 (@ tptp.member451959335_state X))) (or (@ _let_1 A_104) (@ _let_1 B_49))))))))
% 0.62/0.96 (assert (forall ((A_104 (-> tptp.hoare_2091234717iple_a Bool)) (B_49 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila1052848428le_a_o A_104) B_49) (@ tptp.collec992574898iple_a (lambda ((X tptp.hoare_2091234717iple_a)) (let ((_let_1 (@ tptp.member290856304iple_a X))) (or (@ _let_1 A_104) (@ _let_1 B_49))))))))
% 0.62/0.96 (assert (forall ((A_104 (-> tptp.nat Bool)) (B_49 (-> tptp.nat Bool))) (= (@ (@ tptp.semila848761471_nat_o A_104) B_49) (@ tptp.collect_nat (lambda ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (or (@ _let_1 A_104) (@ _let_1 B_49))))))))
% 0.62/0.96 (assert (forall ((A_104 (-> tptp.pname Bool)) (B_49 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o A_104) B_49) (@ tptp.collect_pname (lambda ((X tptp.pname)) (let ((_let_1 (@ tptp.member_pname X))) (or (@ _let_1 A_104) (@ _let_1 B_49))))))))
% 0.62/0.96 (assert (forall ((A_103 (-> tptp.nat Bool))) (= (@ (@ tptp.semila848761471_nat_o A_103) A_103) A_103)))
% 0.62/0.96 (assert (forall ((A_103 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.semila2050116131_a_o_o A_103) A_103) A_103)))
% 0.62/0.96 (assert (forall ((A_103 (-> tptp.hoare_1708887482_state Bool))) (= (@ (@ tptp.semila1122118281tate_o A_103) A_103) A_103)))
% 0.62/0.96 (assert (forall ((A_103 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o A_103) A_103) A_103)))
% 0.62/0.96 (assert (forall ((A_103 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila1052848428le_a_o A_103) A_103) A_103)))
% 0.62/0.96 (assert (forall ((Y_12 (-> tptp.nat Bool))) (= (@ (@ tptp.image_nat_nat (lambda ((X tptp.nat)) X)) Y_12) Y_12)))
% 0.62/0.96 (assert (forall ((F_43 (-> tptp.hoare_2091234717iple_a tptp.hoare_1708887482_state)) (G_22 (-> tptp.pname tptp.hoare_2091234717iple_a)) (A_102 (-> tptp.pname Bool))) (= (@ (@ tptp.image_1884482962_state F_43) (@ (@ tptp.image_231808478iple_a G_22) A_102)) (@ (@ tptp.image_1116629049_state (lambda ((X tptp.pname)) (@ F_43 (@ G_22 X)))) A_102))))
% 0.62/0.96 (assert (forall ((F_43 (-> tptp.hoare_1708887482_state tptp.hoare_2091234717iple_a)) (G_22 (-> tptp.pname tptp.hoare_1708887482_state)) (A_102 (-> tptp.pname Bool))) (= (@ (@ tptp.image_293283184iple_a F_43) (@ (@ tptp.image_1116629049_state G_22) A_102)) (@ (@ tptp.image_231808478iple_a (lambda ((X tptp.pname)) (@ F_43 (@ G_22 X)))) A_102))))
% 0.62/0.96 (assert (forall ((R_2 (-> tptp.nat Bool)) (S_5 (-> tptp.nat Bool)) (X tptp.nat)) (= (@ (@ (@ tptp.semila848761471_nat_o (lambda ((Y_7 tptp.nat)) (@ (@ tptp.member_nat Y_7) R_2))) (lambda ((Y_7 tptp.nat)) (@ (@ tptp.member_nat Y_7) S_5))) X) (@ (@ tptp.member_nat X) (@ (@ tptp.semila848761471_nat_o R_2) S_5)))))
% 0.62/0.96 (assert (forall ((R_2 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (S_5 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (X (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ (@ tptp.semila2050116131_a_o_o (lambda ((Y_7 (-> tptp.hoare_2091234717iple_a Bool))) (@ (@ tptp.member99268621le_a_o Y_7) R_2))) (lambda ((Y_7 (-> tptp.hoare_2091234717iple_a Bool))) (@ (@ tptp.member99268621le_a_o Y_7) S_5))) X) (@ (@ tptp.member99268621le_a_o X) (@ (@ tptp.semila2050116131_a_o_o R_2) S_5)))))
% 0.62/0.96 (assert (forall ((R_2 (-> tptp.hoare_1708887482_state Bool)) (S_5 (-> tptp.hoare_1708887482_state Bool)) (X tptp.hoare_1708887482_state)) (= (@ (@ (@ tptp.semila1122118281tate_o (lambda ((Y_7 tptp.hoare_1708887482_state)) (@ (@ tptp.member451959335_state Y_7) R_2))) (lambda ((Y_7 tptp.hoare_1708887482_state)) (@ (@ tptp.member451959335_state Y_7) S_5))) X) (@ (@ tptp.member451959335_state X) (@ (@ tptp.semila1122118281tate_o R_2) S_5)))))
% 0.62/0.96 (assert (forall ((R_2 (-> tptp.hoare_2091234717iple_a Bool)) (S_5 (-> tptp.hoare_2091234717iple_a Bool)) (X tptp.hoare_2091234717iple_a)) (= (@ (@ (@ tptp.semila1052848428le_a_o (lambda ((Y_7 tptp.hoare_2091234717iple_a)) (@ (@ tptp.member290856304iple_a Y_7) R_2))) (lambda ((Y_7 tptp.hoare_2091234717iple_a)) (@ (@ tptp.member290856304iple_a Y_7) S_5))) X) (@ (@ tptp.member290856304iple_a X) (@ (@ tptp.semila1052848428le_a_o R_2) S_5)))))
% 0.62/0.96 (assert (forall ((R_2 (-> tptp.pname Bool)) (S_5 (-> tptp.pname Bool)) (X tptp.pname)) (= (@ (@ (@ tptp.semila1780557381name_o (lambda ((Y_7 tptp.pname)) (@ (@ tptp.member_pname Y_7) R_2))) (lambda ((Y_7 tptp.pname)) (@ (@ tptp.member_pname Y_7) S_5))) X) (@ (@ tptp.member_pname X) (@ (@ tptp.semila1780557381name_o R_2) S_5)))))
% 0.62/0.96 (assert (forall ((P_33 (-> tptp.pname Bool)) (Q_19 (-> tptp.pname Bool))) (= (@ tptp.collect_pname (lambda ((X tptp.pname)) (or (@ P_33 X) (@ Q_19 X)))) (@ (@ tptp.semila1780557381name_o (@ tptp.collect_pname P_33)) (@ tptp.collect_pname Q_19)))))
% 0.62/0.96 (assert (forall ((P_33 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (Q_19 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ tptp.collec1008234059le_a_o (lambda ((X (-> tptp.hoare_2091234717iple_a Bool))) (or (@ P_33 X) (@ Q_19 X)))) (@ (@ tptp.semila2050116131_a_o_o (@ tptp.collec1008234059le_a_o P_33)) (@ tptp.collec1008234059le_a_o Q_19)))))
% 0.62/0.96 (assert (forall ((P_33 (-> tptp.hoare_1708887482_state Bool)) (Q_19 (-> tptp.hoare_1708887482_state Bool))) (= (@ tptp.collec1568722789_state (lambda ((X tptp.hoare_1708887482_state)) (or (@ P_33 X) (@ Q_19 X)))) (@ (@ tptp.semila1122118281tate_o (@ tptp.collec1568722789_state P_33)) (@ tptp.collec1568722789_state Q_19)))))
% 0.62/0.96 (assert (forall ((P_33 (-> tptp.hoare_2091234717iple_a Bool)) (Q_19 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ tptp.collec992574898iple_a (lambda ((X tptp.hoare_2091234717iple_a)) (or (@ P_33 X) (@ Q_19 X)))) (@ (@ tptp.semila1052848428le_a_o (@ tptp.collec992574898iple_a P_33)) (@ tptp.collec992574898iple_a Q_19)))))
% 0.62/0.96 (assert (forall ((P_33 (-> tptp.nat Bool)) (Q_19 (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (or (@ P_33 X) (@ Q_19 X)))) (@ (@ tptp.semila848761471_nat_o (@ tptp.collect_nat P_33)) (@ tptp.collect_nat Q_19)))))
% 0.62/0.96 (assert (forall ((B_48 tptp.nat) (F_42 (-> tptp.nat tptp.nat)) (A_101 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat B_48) (@ (@ tptp.image_nat_nat F_42) A_101)) (not (forall ((X tptp.nat)) (=> (= B_48 (@ F_42 X)) (not (@ (@ tptp.member_nat X) A_101))))))))
% 0.62/0.96 (assert (forall ((B_48 tptp.pname) (F_42 (-> tptp.nat tptp.pname)) (A_101 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_pname B_48) (@ (@ tptp.image_nat_pname F_42) A_101)) (not (forall ((X tptp.nat)) (=> (= B_48 (@ F_42 X)) (not (@ (@ tptp.member_nat X) A_101))))))))
% 0.62/0.96 (assert (forall ((B_48 tptp.pname) (F_42 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.pname)) (A_101 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (@ (@ tptp.member_pname B_48) (@ (@ tptp.image_1908519857_pname F_42) A_101)) (not (forall ((X (-> tptp.hoare_2091234717iple_a Bool))) (=> (= B_48 (@ F_42 X)) (not (@ (@ tptp.member99268621le_a_o X) A_101))))))))
% 0.62/0.96 (assert (forall ((B_48 tptp.pname) (F_42 (-> tptp.hoare_2091234717iple_a tptp.pname)) (A_101 (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ (@ tptp.member_pname B_48) (@ (@ tptp.image_924789612_pname F_42) A_101)) (not (forall ((X tptp.hoare_2091234717iple_a)) (=> (= B_48 (@ F_42 X)) (not (@ (@ tptp.member290856304iple_a X) A_101))))))))
% 0.62/0.96 (assert (forall ((B_48 tptp.hoare_1708887482_state) (F_42 (-> tptp.pname tptp.hoare_1708887482_state)) (A_101 (-> tptp.pname Bool))) (=> (@ (@ tptp.member451959335_state B_48) (@ (@ tptp.image_1116629049_state F_42) A_101)) (not (forall ((X tptp.pname)) (=> (= B_48 (@ F_42 X)) (not (@ (@ tptp.member_pname X) A_101))))))))
% 0.62/0.96 (assert (forall ((B_48 tptp.nat) (F_42 (-> tptp.pname tptp.nat)) (A_101 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_nat B_48) (@ (@ tptp.image_pname_nat F_42) A_101)) (not (forall ((X tptp.pname)) (=> (= B_48 (@ F_42 X)) (not (@ (@ tptp.member_pname X) A_101))))))))
% 0.62/0.96 (assert (forall ((B_48 (-> tptp.hoare_2091234717iple_a Bool)) (F_42 (-> tptp.pname tptp.hoare_2091234717iple_a Bool)) (A_101 (-> tptp.pname Bool))) (=> (@ (@ tptp.member99268621le_a_o B_48) (@ (@ tptp.image_742317343le_a_o F_42) A_101)) (not (forall ((X tptp.pname)) (=> (= B_48 (@ F_42 X)) (not (@ (@ tptp.member_pname X) A_101))))))))
% 0.62/0.96 (assert (forall ((B_48 tptp.hoare_2091234717iple_a) (F_42 (-> tptp.pname tptp.hoare_2091234717iple_a)) (A_101 (-> tptp.pname Bool))) (=> (@ (@ tptp.member290856304iple_a B_48) (@ (@ tptp.image_231808478iple_a F_42) A_101)) (not (forall ((X tptp.pname)) (=> (= B_48 (@ F_42 X)) (not (@ (@ tptp.member_pname X) A_101))))))))
% 0.62/0.96 (assert (forall ((N_8 tptp.nat) (P_32 (-> tptp.state tptp.state Bool)) (Pn_6 tptp.pname) (Q_18 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_858012674_state P_32))) (= (@ (@ tptp.hoare_23738522_state N_8) (@ (@ _let_1 (@ tptp.the_com (@ tptp.body_1 Pn_6))) Q_18)) (@ (@ tptp.hoare_23738522_state (@ tptp.suc N_8)) (@ (@ _let_1 (@ tptp.body Pn_6)) Q_18))))))
% 0.62/0.96 (assert (forall ((N_8 tptp.nat) (P_32 (-> tptp.x_a tptp.state Bool)) (Pn_6 tptp.pname) (Q_18 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_657976383iple_a P_32))) (= (@ (@ tptp.hoare_1421888935alid_a N_8) (@ (@ _let_1 (@ tptp.the_com (@ tptp.body_1 Pn_6))) Q_18)) (@ (@ tptp.hoare_1421888935alid_a (@ tptp.suc N_8)) (@ (@ _let_1 (@ tptp.body Pn_6)) Q_18))))))
% 0.62/0.96 (assert (forall ((Y_11 tptp.hoare_2091234717iple_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_11 (@ (@ (@ tptp.hoare_657976383iple_a Fun1_2) Com_4) Fun2_2)))))))
% 0.62/0.96 (assert (forall ((Y_11 tptp.hoare_1708887482_state)) (not (forall ((Fun1_2 (-> tptp.state tptp.state Bool)) (Com_4 tptp.com) (Fun2_2 (-> tptp.state tptp.state Bool))) (not (= Y_11 (@ (@ (@ tptp.hoare_858012674_state Fun1_2) Com_4) Fun2_2)))))))
% 0.62/0.96 (assert (forall ((Pn_5 tptp.pname) (G_21 (-> tptp.hoare_1708887482_state Bool)) (P_31 (-> tptp.pname tptp.state tptp.state Bool)) (Q_17 (-> tptp.pname tptp.state tptp.state Bool)) (Procs (-> tptp.pname Bool))) (=> (@ (@ tptp.hoare_90032982_state (@ (@ tptp.semila1122118281tate_o G_21) (@ (@ tptp.image_1116629049_state (lambda ((P_9 tptp.pname)) (@ (@ (@ tptp.hoare_858012674_state (@ P_31 P_9)) (@ tptp.body P_9)) (@ Q_17 P_9)))) Procs))) (@ (@ tptp.image_1116629049_state (lambda ((P_9 tptp.pname)) (@ (@ (@ tptp.hoare_858012674_state (@ P_31 P_9)) (@ tptp.the_com (@ tptp.body_1 P_9))) (@ Q_17 P_9)))) Procs)) (=> (@ (@ tptp.member_pname Pn_5) Procs) (@ (@ tptp.hoare_90032982_state G_21) (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state (@ P_31 Pn_5)) (@ tptp.body Pn_5)) (@ Q_17 Pn_5))) tptp.bot_bo19817387tate_o))))))
% 0.62/0.96 (assert (forall ((Pn_5 tptp.pname) (G_21 (-> tptp.hoare_2091234717iple_a Bool)) (P_31 (-> tptp.pname tptp.x_a tptp.state Bool)) (Q_17 (-> tptp.pname tptp.x_a tptp.state Bool)) (Procs (-> tptp.pname Bool))) (=> (@ (@ tptp.hoare_1467856363rivs_a (@ (@ tptp.semila1052848428le_a_o G_21) (@ (@ tptp.image_231808478iple_a (lambda ((P_9 tptp.pname)) (@ (@ (@ tptp.hoare_657976383iple_a (@ P_31 P_9)) (@ tptp.body P_9)) (@ Q_17 P_9)))) Procs))) (@ (@ tptp.image_231808478iple_a (lambda ((P_9 tptp.pname)) (@ (@ (@ tptp.hoare_657976383iple_a (@ P_31 P_9)) (@ tptp.the_com (@ tptp.body_1 P_9))) (@ Q_17 P_9)))) Procs)) (=> (@ (@ tptp.member_pname Pn_5) Procs) (@ (@ tptp.hoare_1467856363rivs_a G_21) (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a (@ P_31 Pn_5)) (@ tptp.body Pn_5)) (@ Q_17 Pn_5))) tptp.bot_bo1791335050le_a_o))))))
% 0.62/0.96 (assert (forall ((F_41 (-> tptp.nat tptp.nat)) (G_20 (-> tptp.nat tptp.nat)) (M_3 (-> tptp.nat Bool)) (N_7 (-> tptp.nat Bool))) (=> (= M_3 N_7) (=> (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N_7) (= (@ F_41 X) (@ G_20 X)))) (= (@ (@ tptp.image_nat_nat F_41) M_3) (@ (@ tptp.image_nat_nat G_20) N_7))))))
% 0.62/0.96 (assert (forall ((F_41 (-> tptp.pname tptp.hoare_1708887482_state)) (G_20 (-> tptp.pname tptp.hoare_1708887482_state)) (M_3 (-> tptp.pname Bool)) (N_7 (-> tptp.pname Bool))) (=> (= M_3 N_7) (=> (forall ((X tptp.pname)) (=> (@ (@ tptp.member_pname X) N_7) (= (@ F_41 X) (@ G_20 X)))) (= (@ (@ tptp.image_1116629049_state F_41) M_3) (@ (@ tptp.image_1116629049_state G_20) N_7))))))
% 0.62/0.96 (assert (forall ((F_41 (-> tptp.pname tptp.hoare_2091234717iple_a)) (G_20 (-> tptp.pname tptp.hoare_2091234717iple_a)) (M_3 (-> tptp.pname Bool)) (N_7 (-> tptp.pname Bool))) (=> (= M_3 N_7) (=> (forall ((X tptp.pname)) (=> (@ (@ tptp.member_pname X) N_7) (= (@ F_41 X) (@ G_20 X)))) (= (@ (@ tptp.image_231808478iple_a F_41) M_3) (@ (@ tptp.image_231808478iple_a G_20) N_7))))))
% 0.62/0.96 (assert (forall ((P_30 (-> tptp.state tptp.state Bool)) (Pn_4 tptp.pname) (Q_16 (-> tptp.state tptp.state Bool))) (@ (@ tptp.hoare_23738522_state tptp.zero_zero_nat) (@ (@ (@ tptp.hoare_858012674_state P_30) (@ tptp.body Pn_4)) Q_16))))
% 0.62/0.96 (assert (forall ((P_30 (-> tptp.x_a tptp.state Bool)) (Pn_4 tptp.pname) (Q_16 (-> tptp.x_a tptp.state Bool))) (@ (@ tptp.hoare_1421888935alid_a tptp.zero_zero_nat) (@ (@ (@ tptp.hoare_657976383iple_a P_30) (@ tptp.body Pn_4)) Q_16))))
% 0.62/0.96 (assert (forall ((Pname_1 tptp.pname) (Pname tptp.pname)) (= (= (@ tptp.body Pname_1) (@ tptp.body Pname)) (= Pname_1 Pname))))
% 0.62/0.96 (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))))
% 0.62/0.96 (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))))
% 0.62/0.96 (assert (forall ((X_34 (-> tptp.nat Bool))) (= (@ (@ tptp.semila848761471_nat_o X_34) X_34) X_34)))
% 0.62/0.96 (assert (forall ((X_34 tptp.nat)) (= (@ (@ tptp.semila972727038up_nat X_34) X_34) X_34)))
% 0.62/0.96 (assert (forall ((X_34 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.semila2050116131_a_o_o X_34) X_34) X_34)))
% 0.62/0.96 (assert (forall ((X_34 (-> tptp.hoare_1708887482_state Bool))) (= (@ (@ tptp.semila1122118281tate_o X_34) X_34) X_34)))
% 0.62/0.96 (assert (forall ((X_34 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o X_34) X_34) X_34)))
% 0.62/0.96 (assert (forall ((X_34 Bool)) (= (@ (@ tptp.semila10642723_sup_o X_34) X_34) X_34)))
% 0.62/0.96 (assert (forall ((X_34 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila1052848428le_a_o X_34) X_34) X_34)))
% 0.62/0.96 (assert (forall ((N_6 tptp.nat) (Ts_2 (-> tptp.hoare_1708887482_state Bool))) (=> (forall ((X tptp.hoare_1708887482_state)) (=> (@ (@ tptp.member451959335_state X) Ts_2) (@ (@ tptp.hoare_23738522_state (@ tptp.suc N_6)) X))) (forall ((X tptp.hoare_1708887482_state)) (=> (@ (@ tptp.member451959335_state X) Ts_2) (@ (@ tptp.hoare_23738522_state N_6) X))))))
% 0.62/0.96 (assert (forall ((N_6 tptp.nat) (Ts_2 (-> tptp.hoare_2091234717iple_a Bool))) (=> (forall ((X tptp.hoare_2091234717iple_a)) (=> (@ (@ tptp.member290856304iple_a X) Ts_2) (@ (@ tptp.hoare_1421888935alid_a (@ tptp.suc N_6)) X))) (forall ((X tptp.hoare_2091234717iple_a)) (=> (@ (@ tptp.member290856304iple_a X) Ts_2) (@ (@ tptp.hoare_1421888935alid_a N_6) X))))))
% 0.62/0.96 (assert (forall ((A_100 tptp.nat)) (not (@ (@ tptp.member_nat A_100) tptp.bot_bot_nat_o))))
% 0.62/0.96 (assert (forall ((A_100 (-> tptp.hoare_2091234717iple_a Bool))) (not (@ (@ tptp.member99268621le_a_o A_100) tptp.bot_bo1957696069_a_o_o))))
% 0.62/0.96 (assert (forall ((A_100 tptp.hoare_2091234717iple_a)) (not (@ (@ tptp.member290856304iple_a A_100) tptp.bot_bo1791335050le_a_o))))
% 0.62/0.96 (assert (forall ((A_100 tptp.hoare_1708887482_state)) (not (@ (@ tptp.member451959335_state A_100) tptp.bot_bo19817387tate_o))))
% 0.62/0.96 (assert (forall ((A_100 tptp.pname)) (not (@ (@ tptp.member_pname A_100) tptp.bot_bot_pname_o))))
% 0.62/0.96 (assert (forall ((A_99 tptp.nat) (B_47 tptp.nat) (A_98 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_99))) (=> (@ _let_1 (@ (@ tptp.insert_nat B_47) A_98)) (=> (not (= A_99 B_47)) (@ _let_1 A_98))))))
% 0.62/0.96 (assert (forall ((A_99 (-> tptp.hoare_2091234717iple_a Bool)) (B_47 (-> tptp.hoare_2091234717iple_a Bool)) (A_98 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.member99268621le_a_o A_99))) (=> (@ _let_1 (@ (@ tptp.insert102003750le_a_o B_47) A_98)) (=> (not (= A_99 B_47)) (@ _let_1 A_98))))))
% 0.62/0.96 (assert (forall ((A_99 tptp.hoare_2091234717iple_a) (B_47 tptp.hoare_2091234717iple_a) (A_98 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.member290856304iple_a A_99))) (=> (@ _let_1 (@ (@ tptp.insert1597628439iple_a B_47) A_98)) (=> (not (= A_99 B_47)) (@ _let_1 A_98))))))
% 0.62/0.96 (assert (forall ((A_99 tptp.hoare_1708887482_state) (B_47 tptp.hoare_1708887482_state) (A_98 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.member451959335_state A_99))) (=> (@ _let_1 (@ (@ tptp.insert528405184_state B_47) A_98)) (=> (not (= A_99 B_47)) (@ _let_1 A_98))))))
% 0.62/0.96 (assert (forall ((A_99 tptp.pname) (B_47 tptp.pname) (A_98 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_99))) (=> (@ _let_1 (@ (@ tptp.insert_pname B_47) A_98)) (=> (not (= A_99 B_47)) (@ _let_1 A_98))))))
% 0.62/0.96 (assert (forall ((B_46 tptp.nat) (A_97 tptp.nat) (B_45 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_97))) (=> (=> (not (@ _let_1 B_45)) (= A_97 B_46)) (@ _let_1 (@ (@ tptp.insert_nat B_46) B_45))))))
% 0.62/0.96 (assert (forall ((B_46 (-> tptp.hoare_2091234717iple_a Bool)) (A_97 (-> tptp.hoare_2091234717iple_a Bool)) (B_45 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.member99268621le_a_o A_97))) (=> (=> (not (@ _let_1 B_45)) (= A_97 B_46)) (@ _let_1 (@ (@ tptp.insert102003750le_a_o B_46) B_45))))))
% 0.62/0.96 (assert (forall ((B_46 tptp.hoare_2091234717iple_a) (A_97 tptp.hoare_2091234717iple_a) (B_45 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.member290856304iple_a A_97))) (=> (=> (not (@ _let_1 B_45)) (= A_97 B_46)) (@ _let_1 (@ (@ tptp.insert1597628439iple_a B_46) B_45))))))
% 0.62/0.96 (assert (forall ((B_46 tptp.hoare_1708887482_state) (A_97 tptp.hoare_1708887482_state) (B_45 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.member451959335_state A_97))) (=> (=> (not (@ _let_1 B_45)) (= A_97 B_46)) (@ _let_1 (@ (@ tptp.insert528405184_state B_46) B_45))))))
% 0.62/0.96 (assert (forall ((B_46 tptp.pname) (A_97 tptp.pname) (B_45 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_97))) (=> (=> (not (@ _let_1 B_45)) (= A_97 B_46)) (@ _let_1 (@ (@ tptp.insert_pname B_46) B_45))))))
% 0.62/0.96 (assert (forall ((A_96 tptp.nat) (A_95 (-> tptp.nat Bool))) (not (= tptp.bot_bot_nat_o (@ (@ tptp.insert_nat A_96) A_95)))))
% 0.62/0.96 (assert (forall ((A_96 (-> tptp.hoare_2091234717iple_a Bool)) (A_95 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (not (= tptp.bot_bo1957696069_a_o_o (@ (@ tptp.insert102003750le_a_o A_96) A_95)))))
% 0.62/0.96 (assert (forall ((A_96 tptp.pname) (A_95 (-> tptp.pname Bool))) (not (= tptp.bot_bot_pname_o (@ (@ tptp.insert_pname A_96) A_95)))))
% 0.62/0.96 (assert (forall ((A_96 tptp.hoare_2091234717iple_a) (A_95 (-> tptp.hoare_2091234717iple_a Bool))) (not (= tptp.bot_bo1791335050le_a_o (@ (@ tptp.insert1597628439iple_a A_96) A_95)))))
% 0.62/0.96 (assert (forall ((A_96 tptp.hoare_1708887482_state) (A_95 (-> tptp.hoare_1708887482_state Bool))) (not (= tptp.bot_bo19817387tate_o (@ (@ tptp.insert528405184_state A_96) A_95)))))
% 0.62/0.96 (assert (forall ((A_94 tptp.nat) (A_93 (-> tptp.nat Bool))) (not (= (@ (@ tptp.insert_nat A_94) A_93) tptp.bot_bot_nat_o))))
% 0.62/0.96 (assert (forall ((A_94 (-> tptp.hoare_2091234717iple_a Bool)) (A_93 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (not (= (@ (@ tptp.insert102003750le_a_o A_94) A_93) tptp.bot_bo1957696069_a_o_o))))
% 0.62/0.96 (assert (forall ((A_94 tptp.pname) (A_93 (-> tptp.pname Bool))) (not (= (@ (@ tptp.insert_pname A_94) A_93) tptp.bot_bot_pname_o))))
% 0.62/0.96 (assert (forall ((A_94 tptp.hoare_2091234717iple_a) (A_93 (-> tptp.hoare_2091234717iple_a Bool))) (not (= (@ (@ tptp.insert1597628439iple_a A_94) A_93) tptp.bot_bo1791335050le_a_o))))
% 0.62/0.96 (assert (forall ((A_94 tptp.hoare_1708887482_state) (A_93 (-> tptp.hoare_1708887482_state Bool))) (not (= (@ (@ tptp.insert528405184_state A_94) A_93) tptp.bot_bo19817387tate_o))))
% 0.62/0.96 (assert (forall ((X tptp.nat)) (= (@ tptp.bot_bot_nat_o X) (@ (@ tptp.member_nat X) tptp.bot_bot_nat_o))))
% 0.62/0.96 (assert (forall ((X (-> tptp.hoare_2091234717iple_a Bool))) (= (@ tptp.bot_bo1957696069_a_o_o X) (@ (@ tptp.member99268621le_a_o X) tptp.bot_bo1957696069_a_o_o))))
% 0.62/0.96 (assert (forall ((X tptp.hoare_2091234717iple_a)) (= (@ tptp.bot_bo1791335050le_a_o X) (@ (@ tptp.member290856304iple_a X) tptp.bot_bo1791335050le_a_o))))
% 0.62/0.96 (assert (forall ((X tptp.hoare_1708887482_state)) (= (@ tptp.bot_bo19817387tate_o X) (@ (@ tptp.member451959335_state X) tptp.bot_bo19817387tate_o))))
% 0.62/0.96 (assert (forall ((X tptp.pname)) (= (@ tptp.bot_bot_pname_o X) (@ (@ tptp.member_pname X) tptp.bot_bot_pname_o))))
% 0.62/0.96 (assert (= tptp.bot_bot_pname_o (@ tptp.collect_pname (lambda ((X tptp.pname)) false))))
% 0.62/0.96 (assert (= tptp.bot_bo1791335050le_a_o (@ tptp.collec992574898iple_a (lambda ((X tptp.hoare_2091234717iple_a)) false))))
% 0.62/0.96 (assert (= tptp.bot_bo1957696069_a_o_o (@ tptp.collec1008234059le_a_o (lambda ((X (-> tptp.hoare_2091234717iple_a Bool))) false))))
% 0.62/0.96 (assert (= tptp.bot_bo19817387tate_o (@ tptp.collec1568722789_state (lambda ((X tptp.hoare_1708887482_state)) false))))
% 0.62/0.96 (assert (= tptp.bot_bot_nat_o (@ tptp.collect_nat (lambda ((X tptp.nat)) false))))
% 0.62/0.96 (assert (forall ((A_92 tptp.nat) (B_44 (-> tptp.nat Bool))) (@ (@ tptp.member_nat A_92) (@ (@ tptp.insert_nat A_92) B_44))))
% 0.62/0.96 (assert (forall ((A_92 (-> tptp.hoare_2091234717iple_a Bool)) (B_44 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (@ (@ tptp.member99268621le_a_o A_92) (@ (@ tptp.insert102003750le_a_o A_92) B_44))))
% 0.62/0.96 (assert (forall ((A_92 tptp.hoare_2091234717iple_a) (B_44 (-> tptp.hoare_2091234717iple_a Bool))) (@ (@ tptp.member290856304iple_a A_92) (@ (@ tptp.insert1597628439iple_a A_92) B_44))))
% 0.62/0.96 (assert (forall ((A_92 tptp.hoare_1708887482_state) (B_44 (-> tptp.hoare_1708887482_state Bool))) (@ (@ tptp.member451959335_state A_92) (@ (@ tptp.insert528405184_state A_92) B_44))))
% 0.62/0.96 (assert (forall ((A_92 tptp.pname) (B_44 (-> tptp.pname Bool))) (@ (@ tptp.member_pname A_92) (@ (@ tptp.insert_pname A_92) B_44))))
% 0.62/0.96 (assert (forall ((A_91 (-> tptp.nat Bool))) (= (forall ((X tptp.nat)) (not (@ (@ tptp.member_nat X) A_91))) (= A_91 tptp.bot_bot_nat_o))))
% 0.62/0.96 (assert (forall ((A_91 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (forall ((X (-> tptp.hoare_2091234717iple_a Bool))) (not (@ (@ tptp.member99268621le_a_o X) A_91))) (= A_91 tptp.bot_bo1957696069_a_o_o))))
% 0.62/0.96 (assert (forall ((A_91 (-> tptp.hoare_2091234717iple_a Bool))) (= (forall ((X tptp.hoare_2091234717iple_a)) (not (@ (@ tptp.member290856304iple_a X) A_91))) (= A_91 tptp.bot_bo1791335050le_a_o))))
% 0.62/0.96 (assert (forall ((A_91 (-> tptp.hoare_1708887482_state Bool))) (= (forall ((X tptp.hoare_1708887482_state)) (not (@ (@ tptp.member451959335_state X) A_91))) (= A_91 tptp.bot_bo19817387tate_o))))
% 0.62/0.96 (assert (forall ((A_91 (-> tptp.pname Bool))) (= (forall ((X tptp.pname)) (not (@ (@ tptp.member_pname X) A_91))) (= A_91 tptp.bot_bot_pname_o))))
% 0.62/0.96 (assert (forall ((A_90 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ tptp.collec1008234059le_a_o (@ tptp.fequal845167073le_a_o A_90)) (@ (@ tptp.insert102003750le_a_o A_90) tptp.bot_bo1957696069_a_o_o))))
% 0.62/0.96 (assert (forall ((A_90 tptp.pname)) (= (@ tptp.collect_pname (@ tptp.fequal_pname A_90)) (@ (@ tptp.insert_pname A_90) tptp.bot_bot_pname_o))))
% 0.62/0.96 (assert (forall ((A_90 tptp.hoare_2091234717iple_a)) (= (@ tptp.collec992574898iple_a (@ tptp.fequal1604381340iple_a A_90)) (@ (@ tptp.insert1597628439iple_a A_90) tptp.bot_bo1791335050le_a_o))))
% 0.62/0.96 (assert (forall ((A_90 tptp.hoare_1708887482_state)) (= (@ tptp.collec1568722789_state (@ tptp.fequal224822779_state A_90)) (@ (@ tptp.insert528405184_state A_90) tptp.bot_bo19817387tate_o))))
% 0.62/0.96 (assert (forall ((A_90 tptp.nat)) (= (@ tptp.collect_nat (@ tptp.fequal_nat A_90)) (@ (@ tptp.insert_nat A_90) tptp.bot_bot_nat_o))))
% 0.62/0.96 (assert (forall ((A_89 (-> tptp.nat Bool))) (= (exists ((X tptp.nat)) (@ (@ tptp.member_nat X) A_89)) (not (= A_89 tptp.bot_bot_nat_o)))))
% 0.62/0.96 (assert (forall ((A_89 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (exists ((X (-> tptp.hoare_2091234717iple_a Bool))) (@ (@ tptp.member99268621le_a_o X) A_89)) (not (= A_89 tptp.bot_bo1957696069_a_o_o)))))
% 0.62/0.96 (assert (forall ((A_89 (-> tptp.hoare_2091234717iple_a Bool))) (= (exists ((X tptp.hoare_2091234717iple_a)) (@ (@ tptp.member290856304iple_a X) A_89)) (not (= A_89 tptp.bot_bo1791335050le_a_o)))))
% 0.62/0.96 (assert (forall ((A_89 (-> tptp.hoare_1708887482_state Bool))) (= (exists ((X tptp.hoare_1708887482_state)) (@ (@ tptp.member451959335_state X) A_89)) (not (= A_89 tptp.bot_bo19817387tate_o)))))
% 0.62/0.96 (assert (forall ((A_89 (-> tptp.pname Bool))) (= (exists ((X tptp.pname)) (@ (@ tptp.member_pname X) A_89)) (not (= A_89 tptp.bot_bot_pname_o)))))
% 0.62/0.96 (assert (forall ((A_88 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ tptp.collec1008234059le_a_o (lambda ((X (-> tptp.hoare_2091234717iple_a Bool))) (= X A_88))) (@ (@ tptp.insert102003750le_a_o A_88) tptp.bot_bo1957696069_a_o_o))))
% 0.62/0.96 (assert (forall ((A_88 tptp.pname)) (= (@ tptp.collect_pname (lambda ((X tptp.pname)) (= X A_88))) (@ (@ tptp.insert_pname A_88) tptp.bot_bot_pname_o))))
% 0.62/0.96 (assert (forall ((A_88 tptp.hoare_2091234717iple_a)) (= (@ tptp.collec992574898iple_a (lambda ((X tptp.hoare_2091234717iple_a)) (= X A_88))) (@ (@ tptp.insert1597628439iple_a A_88) tptp.bot_bo1791335050le_a_o))))
% 0.62/0.96 (assert (forall ((A_88 tptp.hoare_1708887482_state)) (= (@ tptp.collec1568722789_state (lambda ((X tptp.hoare_1708887482_state)) (= X A_88))) (@ (@ tptp.insert528405184_state A_88) tptp.bot_bo19817387tate_o))))
% 0.62/0.96 (assert (forall ((A_88 tptp.nat)) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (= X A_88))) (@ (@ tptp.insert_nat A_88) tptp.bot_bot_nat_o))))
% 0.62/0.96 (assert (forall ((P_29 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (A_87 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ P_29 A_87))) (and (=> _let_1 (= (@ tptp.collec1008234059le_a_o (lambda ((X (-> tptp.hoare_2091234717iple_a Bool))) (and (= A_87 X) (@ P_29 X)))) (@ (@ tptp.insert102003750le_a_o A_87) tptp.bot_bo1957696069_a_o_o))) (=> (not _let_1) (= (@ tptp.collec1008234059le_a_o (lambda ((X (-> tptp.hoare_2091234717iple_a Bool))) (and (= A_87 X) (@ P_29 X)))) tptp.bot_bo1957696069_a_o_o))))))
% 0.62/0.96 (assert (forall ((P_29 (-> tptp.pname Bool)) (A_87 tptp.pname)) (let ((_let_1 (@ P_29 A_87))) (and (=> _let_1 (= (@ tptp.collect_pname (lambda ((X tptp.pname)) (and (= A_87 X) (@ P_29 X)))) (@ (@ tptp.insert_pname A_87) tptp.bot_bot_pname_o))) (=> (not _let_1) (= (@ tptp.collect_pname (lambda ((X tptp.pname)) (and (= A_87 X) (@ P_29 X)))) tptp.bot_bot_pname_o))))))
% 0.62/0.96 (assert (forall ((P_29 (-> tptp.hoare_2091234717iple_a Bool)) (A_87 tptp.hoare_2091234717iple_a)) (let ((_let_1 (@ P_29 A_87))) (and (=> _let_1 (= (@ tptp.collec992574898iple_a (lambda ((X tptp.hoare_2091234717iple_a)) (and (= A_87 X) (@ P_29 X)))) (@ (@ tptp.insert1597628439iple_a A_87) tptp.bot_bo1791335050le_a_o))) (=> (not _let_1) (= (@ tptp.collec992574898iple_a (lambda ((X tptp.hoare_2091234717iple_a)) (and (= A_87 X) (@ P_29 X)))) tptp.bot_bo1791335050le_a_o))))))
% 0.62/0.96 (assert (forall ((P_29 (-> tptp.hoare_1708887482_state Bool)) (A_87 tptp.hoare_1708887482_state)) (let ((_let_1 (@ P_29 A_87))) (and (=> _let_1 (= (@ tptp.collec1568722789_state (lambda ((X tptp.hoare_1708887482_state)) (and (= A_87 X) (@ P_29 X)))) (@ (@ tptp.insert528405184_state A_87) tptp.bot_bo19817387tate_o))) (=> (not _let_1) (= (@ tptp.collec1568722789_state (lambda ((X tptp.hoare_1708887482_state)) (and (= A_87 X) (@ P_29 X)))) tptp.bot_bo19817387tate_o))))))
% 0.62/0.96 (assert (forall ((P_29 (-> tptp.nat Bool)) (A_87 tptp.nat)) (let ((_let_1 (@ P_29 A_87))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (= A_87 X) (@ P_29 X)))) (@ (@ tptp.insert_nat A_87) tptp.bot_bot_nat_o))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (= A_87 X) (@ P_29 X)))) tptp.bot_bot_nat_o))))))
% 0.62/0.96 (assert (forall ((P_28 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (A_86 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ P_28 A_86))) (and (=> _let_1 (= (@ tptp.collec1008234059le_a_o (lambda ((X (-> tptp.hoare_2091234717iple_a Bool))) (and (= X A_86) (@ P_28 X)))) (@ (@ tptp.insert102003750le_a_o A_86) tptp.bot_bo1957696069_a_o_o))) (=> (not _let_1) (= (@ tptp.collec1008234059le_a_o (lambda ((X (-> tptp.hoare_2091234717iple_a Bool))) (and (= X A_86) (@ P_28 X)))) tptp.bot_bo1957696069_a_o_o))))))
% 0.62/0.96 (assert (forall ((P_28 (-> tptp.pname Bool)) (A_86 tptp.pname)) (let ((_let_1 (@ P_28 A_86))) (and (=> _let_1 (= (@ tptp.collect_pname (lambda ((X tptp.pname)) (and (= X A_86) (@ P_28 X)))) (@ (@ tptp.insert_pname A_86) tptp.bot_bot_pname_o))) (=> (not _let_1) (= (@ tptp.collect_pname (lambda ((X tptp.pname)) (and (= X A_86) (@ P_28 X)))) tptp.bot_bot_pname_o))))))
% 0.62/0.96 (assert (forall ((P_28 (-> tptp.hoare_2091234717iple_a Bool)) (A_86 tptp.hoare_2091234717iple_a)) (let ((_let_1 (@ P_28 A_86))) (and (=> _let_1 (= (@ tptp.collec992574898iple_a (lambda ((X tptp.hoare_2091234717iple_a)) (and (= X A_86) (@ P_28 X)))) (@ (@ tptp.insert1597628439iple_a A_86) tptp.bot_bo1791335050le_a_o))) (=> (not _let_1) (= (@ tptp.collec992574898iple_a (lambda ((X tptp.hoare_2091234717iple_a)) (and (= X A_86) (@ P_28 X)))) tptp.bot_bo1791335050le_a_o))))))
% 0.62/0.96 (assert (forall ((P_28 (-> tptp.hoare_1708887482_state Bool)) (A_86 tptp.hoare_1708887482_state)) (let ((_let_1 (@ P_28 A_86))) (and (=> _let_1 (= (@ tptp.collec1568722789_state (lambda ((X tptp.hoare_1708887482_state)) (and (= X A_86) (@ P_28 X)))) (@ (@ tptp.insert528405184_state A_86) tptp.bot_bo19817387tate_o))) (=> (not _let_1) (= (@ tptp.collec1568722789_state (lambda ((X tptp.hoare_1708887482_state)) (and (= X A_86) (@ P_28 X)))) tptp.bot_bo19817387tate_o))))))
% 0.62/0.96 (assert (forall ((P_28 (-> tptp.nat Bool)) (A_86 tptp.nat)) (let ((_let_1 (@ P_28 A_86))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (= X A_86) (@ P_28 X)))) (@ (@ tptp.insert_nat A_86) tptp.bot_bot_nat_o))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (= X A_86) (@ P_28 X)))) tptp.bot_bot_nat_o))))))
% 0.62/0.96 (assert (forall ((X_33 tptp.nat) (A_85 (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat X_33) A_85) (@ A_85 X_33))))
% 0.62/0.96 (assert (forall ((X_33 (-> tptp.hoare_2091234717iple_a Bool)) (A_85 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.member99268621le_a_o X_33) A_85) (@ A_85 X_33))))
% 0.62/0.96 (assert (forall ((X_33 tptp.hoare_2091234717iple_a) (A_85 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.member290856304iple_a X_33) A_85) (@ A_85 X_33))))
% 0.62/0.96 (assert (forall ((X_33 tptp.pname) (A_85 (-> tptp.pname Bool))) (= (@ (@ tptp.member_pname X_33) A_85) (@ A_85 X_33))))
% 0.62/0.96 (assert (forall ((P_27 (-> tptp.pname Bool))) (= (@ tptp.collect_pname P_27) P_27)))
% 0.62/0.96 (assert (forall ((P_27 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ tptp.collec992574898iple_a P_27) P_27)))
% 0.62/0.96 (assert (forall ((P_27 (-> tptp.nat Bool))) (= (@ tptp.collect_nat P_27) P_27)))
% 0.62/0.96 (assert (forall ((P_26 (-> tptp.pname Bool))) (= (= tptp.bot_bot_pname_o (@ tptp.collect_pname P_26)) (forall ((X tptp.pname)) (not (@ P_26 X))))))
% 0.62/0.96 (assert (forall ((P_26 (-> tptp.hoare_2091234717iple_a Bool))) (= (= tptp.bot_bo1791335050le_a_o (@ tptp.collec992574898iple_a P_26)) (forall ((X tptp.hoare_2091234717iple_a)) (not (@ P_26 X))))))
% 0.62/0.96 (assert (forall ((P_26 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (= tptp.bot_bo1957696069_a_o_o (@ tptp.collec1008234059le_a_o P_26)) (forall ((X (-> tptp.hoare_2091234717iple_a Bool))) (not (@ P_26 X))))))
% 0.62/0.96 (assert (forall ((P_26 (-> tptp.hoare_1708887482_state Bool))) (= (= tptp.bot_bo19817387tate_o (@ tptp.collec1568722789_state P_26)) (forall ((X tptp.hoare_1708887482_state)) (not (@ P_26 X))))))
% 0.62/0.96 (assert (forall ((P_26 (-> tptp.nat Bool))) (= (= tptp.bot_bot_nat_o (@ tptp.collect_nat P_26)) (forall ((X tptp.nat)) (not (@ P_26 X))))))
% 0.62/0.96 (assert (forall ((C_25 tptp.nat)) (not (@ (@ tptp.member_nat C_25) tptp.bot_bot_nat_o))))
% 0.62/0.96 (assert (forall ((C_25 (-> tptp.hoare_2091234717iple_a Bool))) (not (@ (@ tptp.member99268621le_a_o C_25) tptp.bot_bo1957696069_a_o_o))))
% 0.62/0.96 (assert (forall ((C_25 tptp.hoare_2091234717iple_a)) (not (@ (@ tptp.member290856304iple_a C_25) tptp.bot_bo1791335050le_a_o))))
% 0.62/0.96 (assert (forall ((C_25 tptp.hoare_1708887482_state)) (not (@ (@ tptp.member451959335_state C_25) tptp.bot_bo19817387tate_o))))
% 0.62/0.96 (assert (forall ((C_25 tptp.pname)) (not (@ (@ tptp.member_pname C_25) tptp.bot_bot_pname_o))))
% 0.62/0.96 (assert (forall ((A_84 (-> tptp.hoare_2091234717iple_a Bool)) (B_43 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.insert102003750le_a_o A_84) B_43) (@ tptp.collec1008234059le_a_o (lambda ((X (-> tptp.hoare_2091234717iple_a Bool))) (or (= X A_84) (@ (@ tptp.member99268621le_a_o X) B_43)))))))
% 0.62/0.96 (assert (forall ((A_84 tptp.hoare_2091234717iple_a) (B_43 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.insert1597628439iple_a A_84) B_43) (@ tptp.collec992574898iple_a (lambda ((X tptp.hoare_2091234717iple_a)) (or (= X A_84) (@ (@ tptp.member290856304iple_a X) B_43)))))))
% 0.62/0.96 (assert (forall ((A_84 tptp.hoare_1708887482_state) (B_43 (-> tptp.hoare_1708887482_state Bool))) (= (@ (@ tptp.insert528405184_state A_84) B_43) (@ tptp.collec1568722789_state (lambda ((X tptp.hoare_1708887482_state)) (or (= X A_84) (@ (@ tptp.member451959335_state X) B_43)))))))
% 0.62/0.96 (assert (forall ((A_84 tptp.nat) (B_43 (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat A_84) B_43) (@ tptp.collect_nat (lambda ((X tptp.nat)) (or (= X A_84) (@ (@ tptp.member_nat X) B_43)))))))
% 0.62/0.96 (assert (forall ((A_84 tptp.pname) (B_43 (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname A_84) B_43) (@ tptp.collect_pname (lambda ((X tptp.pname)) (or (= X A_84) (@ (@ tptp.member_pname X) B_43)))))))
% 0.62/0.96 (assert (forall ((A_83 (-> tptp.hoare_2091234717iple_a Bool)) (P_25 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.insert102003750le_a_o A_83) (@ tptp.collec1008234059le_a_o P_25)) (@ tptp.collec1008234059le_a_o (lambda ((U_2 (-> tptp.hoare_2091234717iple_a Bool))) (=> (not (= U_2 A_83)) (@ P_25 U_2)))))))
% 0.62/0.96 (assert (forall ((A_83 tptp.pname) (P_25 (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname A_83) (@ tptp.collect_pname P_25)) (@ tptp.collect_pname (lambda ((U_2 tptp.pname)) (=> (not (= U_2 A_83)) (@ P_25 U_2)))))))
% 0.62/0.96 (assert (forall ((A_83 tptp.hoare_2091234717iple_a) (P_25 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.insert1597628439iple_a A_83) (@ tptp.collec992574898iple_a P_25)) (@ tptp.collec992574898iple_a (lambda ((U_2 tptp.hoare_2091234717iple_a)) (=> (not (= U_2 A_83)) (@ P_25 U_2)))))))
% 0.62/0.96 (assert (forall ((A_83 tptp.hoare_1708887482_state) (P_25 (-> tptp.hoare_1708887482_state Bool))) (= (@ (@ tptp.insert528405184_state A_83) (@ tptp.collec1568722789_state P_25)) (@ tptp.collec1568722789_state (lambda ((U_2 tptp.hoare_1708887482_state)) (=> (not (= U_2 A_83)) (@ P_25 U_2)))))))
% 0.62/0.96 (assert (forall ((A_83 tptp.nat) (P_25 (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat A_83) (@ tptp.collect_nat P_25)) (@ tptp.collect_nat (lambda ((U_2 tptp.nat)) (=> (not (= U_2 A_83)) (@ P_25 U_2)))))))
% 0.62/0.96 (assert (forall ((B_42 tptp.nat) (A_82 tptp.nat)) (= (@ (@ tptp.member_nat B_42) (@ (@ tptp.insert_nat A_82) tptp.bot_bot_nat_o)) (= B_42 A_82))))
% 0.62/0.96 (assert (forall ((B_42 (-> tptp.hoare_2091234717iple_a Bool)) (A_82 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.member99268621le_a_o B_42) (@ (@ tptp.insert102003750le_a_o A_82) tptp.bot_bo1957696069_a_o_o)) (= B_42 A_82))))
% 0.62/0.96 (assert (forall ((B_42 tptp.hoare_2091234717iple_a) (A_82 tptp.hoare_2091234717iple_a)) (= (@ (@ tptp.member290856304iple_a B_42) (@ (@ tptp.insert1597628439iple_a A_82) tptp.bot_bo1791335050le_a_o)) (= B_42 A_82))))
% 0.62/0.96 (assert (forall ((B_42 tptp.hoare_1708887482_state) (A_82 tptp.hoare_1708887482_state)) (= (@ (@ tptp.member451959335_state B_42) (@ (@ tptp.insert528405184_state A_82) tptp.bot_bo19817387tate_o)) (= B_42 A_82))))
% 0.62/0.96 (assert (forall ((B_42 tptp.pname) (A_82 tptp.pname)) (= (@ (@ tptp.member_pname B_42) (@ (@ tptp.insert_pname A_82) tptp.bot_bot_pname_o)) (= B_42 A_82))))
% 0.62/0.96 (assert (forall ((X_32 tptp.nat) (A_81 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_32))) (let ((_let_2 (@ _let_1 A_81))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_32 (-> tptp.hoare_2091234717iple_a Bool)) (A_81 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.insert102003750le_a_o X_32))) (let ((_let_2 (@ _let_1 A_81))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_32 tptp.pname) (A_81 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_32))) (let ((_let_2 (@ _let_1 A_81))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_32 tptp.hoare_2091234717iple_a) (A_81 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.insert1597628439iple_a X_32))) (let ((_let_2 (@ _let_1 A_81))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_32 tptp.hoare_1708887482_state) (A_81 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.insert528405184_state X_32))) (let ((_let_2 (@ _let_1 A_81))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_31 tptp.nat) (Y_10 tptp.nat) (A_80 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_31))) (let ((_let_2 (@ tptp.insert_nat Y_10))) (= (@ _let_1 (@ _let_2 A_80)) (@ _let_2 (@ _let_1 A_80)))))))
% 0.62/0.96 (assert (forall ((X_31 (-> tptp.hoare_2091234717iple_a Bool)) (Y_10 (-> tptp.hoare_2091234717iple_a Bool)) (A_80 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.insert102003750le_a_o X_31))) (let ((_let_2 (@ tptp.insert102003750le_a_o Y_10))) (= (@ _let_1 (@ _let_2 A_80)) (@ _let_2 (@ _let_1 A_80)))))))
% 0.62/0.96 (assert (forall ((X_31 tptp.pname) (Y_10 tptp.pname) (A_80 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_31))) (let ((_let_2 (@ tptp.insert_pname Y_10))) (= (@ _let_1 (@ _let_2 A_80)) (@ _let_2 (@ _let_1 A_80)))))))
% 0.62/0.96 (assert (forall ((X_31 tptp.hoare_2091234717iple_a) (Y_10 tptp.hoare_2091234717iple_a) (A_80 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.insert1597628439iple_a X_31))) (let ((_let_2 (@ tptp.insert1597628439iple_a Y_10))) (= (@ _let_1 (@ _let_2 A_80)) (@ _let_2 (@ _let_1 A_80)))))))
% 0.62/0.96 (assert (forall ((X_31 tptp.hoare_1708887482_state) (Y_10 tptp.hoare_1708887482_state) (A_80 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.insert528405184_state X_31))) (let ((_let_2 (@ tptp.insert528405184_state Y_10))) (= (@ _let_1 (@ _let_2 A_80)) (@ _let_2 (@ _let_1 A_80)))))))
% 0.62/0.96 (assert (forall ((A_79 tptp.nat) (B_41 tptp.nat) (A_78 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_79))) (= (@ _let_1 (@ (@ tptp.insert_nat B_41) A_78)) (or (= A_79 B_41) (@ _let_1 A_78))))))
% 0.62/0.96 (assert (forall ((A_79 (-> tptp.hoare_2091234717iple_a Bool)) (B_41 (-> tptp.hoare_2091234717iple_a Bool)) (A_78 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.member99268621le_a_o A_79))) (= (@ _let_1 (@ (@ tptp.insert102003750le_a_o B_41) A_78)) (or (= A_79 B_41) (@ _let_1 A_78))))))
% 0.62/0.96 (assert (forall ((A_79 tptp.hoare_2091234717iple_a) (B_41 tptp.hoare_2091234717iple_a) (A_78 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.member290856304iple_a A_79))) (= (@ _let_1 (@ (@ tptp.insert1597628439iple_a B_41) A_78)) (or (= A_79 B_41) (@ _let_1 A_78))))))
% 0.62/0.96 (assert (forall ((A_79 tptp.hoare_1708887482_state) (B_41 tptp.hoare_1708887482_state) (A_78 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.member451959335_state A_79))) (= (@ _let_1 (@ (@ tptp.insert528405184_state B_41) A_78)) (or (= A_79 B_41) (@ _let_1 A_78))))))
% 0.62/0.96 (assert (forall ((A_79 tptp.pname) (B_41 tptp.pname) (A_78 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_79))) (= (@ _let_1 (@ (@ tptp.insert_pname B_41) A_78)) (or (= A_79 B_41) (@ _let_1 A_78))))))
% 0.62/0.96 (assert (forall ((P_24 (-> tptp.pname Bool))) (= (= (@ tptp.collect_pname P_24) tptp.bot_bot_pname_o) (forall ((X tptp.pname)) (not (@ P_24 X))))))
% 0.62/0.96 (assert (forall ((P_24 (-> tptp.hoare_2091234717iple_a Bool))) (= (= (@ tptp.collec992574898iple_a P_24) tptp.bot_bo1791335050le_a_o) (forall ((X tptp.hoare_2091234717iple_a)) (not (@ P_24 X))))))
% 0.62/0.96 (assert (forall ((P_24 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (= (@ tptp.collec1008234059le_a_o P_24) tptp.bot_bo1957696069_a_o_o) (forall ((X (-> tptp.hoare_2091234717iple_a Bool))) (not (@ P_24 X))))))
% 0.62/0.96 (assert (forall ((P_24 (-> tptp.hoare_1708887482_state Bool))) (= (= (@ tptp.collec1568722789_state P_24) tptp.bot_bo19817387tate_o) (forall ((X tptp.hoare_1708887482_state)) (not (@ P_24 X))))))
% 0.62/0.96 (assert (forall ((P_24 (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P_24) tptp.bot_bot_nat_o) (forall ((X tptp.nat)) (not (@ P_24 X))))))
% 0.62/0.96 (assert (forall ((A_77 tptp.nat) (B_40 tptp.nat) (C_24 tptp.nat) (D_1 tptp.nat)) (= (= (@ (@ tptp.insert_nat A_77) (@ (@ tptp.insert_nat B_40) tptp.bot_bot_nat_o)) (@ (@ tptp.insert_nat C_24) (@ (@ tptp.insert_nat D_1) tptp.bot_bot_nat_o))) (or (and (= A_77 C_24) (= B_40 D_1)) (and (= A_77 D_1) (= B_40 C_24))))))
% 0.62/0.96 (assert (forall ((A_77 (-> tptp.hoare_2091234717iple_a Bool)) (B_40 (-> tptp.hoare_2091234717iple_a Bool)) (C_24 (-> tptp.hoare_2091234717iple_a Bool)) (D_1 (-> tptp.hoare_2091234717iple_a Bool))) (= (= (@ (@ tptp.insert102003750le_a_o A_77) (@ (@ tptp.insert102003750le_a_o B_40) tptp.bot_bo1957696069_a_o_o)) (@ (@ tptp.insert102003750le_a_o C_24) (@ (@ tptp.insert102003750le_a_o D_1) tptp.bot_bo1957696069_a_o_o))) (or (and (= A_77 C_24) (= B_40 D_1)) (and (= A_77 D_1) (= B_40 C_24))))))
% 0.62/0.96 (assert (forall ((A_77 tptp.pname) (B_40 tptp.pname) (C_24 tptp.pname) (D_1 tptp.pname)) (= (= (@ (@ tptp.insert_pname A_77) (@ (@ tptp.insert_pname B_40) tptp.bot_bot_pname_o)) (@ (@ tptp.insert_pname C_24) (@ (@ tptp.insert_pname D_1) tptp.bot_bot_pname_o))) (or (and (= A_77 C_24) (= B_40 D_1)) (and (= A_77 D_1) (= B_40 C_24))))))
% 0.62/0.96 (assert (forall ((A_77 tptp.hoare_2091234717iple_a) (B_40 tptp.hoare_2091234717iple_a) (C_24 tptp.hoare_2091234717iple_a) (D_1 tptp.hoare_2091234717iple_a)) (= (= (@ (@ tptp.insert1597628439iple_a A_77) (@ (@ tptp.insert1597628439iple_a B_40) tptp.bot_bo1791335050le_a_o)) (@ (@ tptp.insert1597628439iple_a C_24) (@ (@ tptp.insert1597628439iple_a D_1) tptp.bot_bo1791335050le_a_o))) (or (and (= A_77 C_24) (= B_40 D_1)) (and (= A_77 D_1) (= B_40 C_24))))))
% 0.62/0.96 (assert (forall ((A_77 tptp.hoare_1708887482_state) (B_40 tptp.hoare_1708887482_state) (C_24 tptp.hoare_1708887482_state) (D_1 tptp.hoare_1708887482_state)) (= (= (@ (@ tptp.insert528405184_state A_77) (@ (@ tptp.insert528405184_state B_40) tptp.bot_bo19817387tate_o)) (@ (@ tptp.insert528405184_state C_24) (@ (@ tptp.insert528405184_state D_1) tptp.bot_bo19817387tate_o))) (or (and (= A_77 C_24) (= B_40 D_1)) (and (= A_77 D_1) (= B_40 C_24))))))
% 0.62/0.96 (assert (forall ((Y_9 tptp.nat) (A_76 (-> tptp.nat Bool)) (X_30 tptp.nat)) (= (@ (@ (@ tptp.insert_nat Y_9) A_76) X_30) (or (= Y_9 X_30) (@ A_76 X_30)))))
% 0.62/0.96 (assert (forall ((Y_9 (-> tptp.hoare_2091234717iple_a Bool)) (A_76 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (X_30 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ (@ tptp.insert102003750le_a_o Y_9) A_76) X_30) (or (= Y_9 X_30) (@ A_76 X_30)))))
% 0.62/0.96 (assert (forall ((Y_9 tptp.pname) (A_76 (-> tptp.pname Bool)) (X_30 tptp.pname)) (= (@ (@ (@ tptp.insert_pname Y_9) A_76) X_30) (or (= Y_9 X_30) (@ A_76 X_30)))))
% 0.62/0.96 (assert (forall ((Y_9 tptp.hoare_2091234717iple_a) (A_76 (-> tptp.hoare_2091234717iple_a Bool)) (X_30 tptp.hoare_2091234717iple_a)) (= (@ (@ (@ tptp.insert1597628439iple_a Y_9) A_76) X_30) (or (= Y_9 X_30) (@ A_76 X_30)))))
% 0.62/0.96 (assert (forall ((Y_9 tptp.hoare_1708887482_state) (A_76 (-> tptp.hoare_1708887482_state Bool)) (X_30 tptp.hoare_1708887482_state)) (= (@ (@ (@ tptp.insert528405184_state Y_9) A_76) X_30) (or (= Y_9 X_30) (@ A_76 X_30)))))
% 0.62/0.96 (assert (forall ((B_39 (-> tptp.nat Bool)) (X_29 tptp.nat) (A_75 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_29))) (let ((_let_2 (@ tptp.member_nat X_29))) (=> (not (@ _let_2 A_75)) (=> (not (@ _let_2 B_39)) (= (= (@ _let_1 A_75) (@ _let_1 B_39)) (= A_75 B_39))))))))
% 0.62/0.96 (assert (forall ((B_39 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (X_29 (-> tptp.hoare_2091234717iple_a Bool)) (A_75 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.insert102003750le_a_o X_29))) (let ((_let_2 (@ tptp.member99268621le_a_o X_29))) (=> (not (@ _let_2 A_75)) (=> (not (@ _let_2 B_39)) (= (= (@ _let_1 A_75) (@ _let_1 B_39)) (= A_75 B_39))))))))
% 0.62/0.96 (assert (forall ((B_39 (-> tptp.hoare_2091234717iple_a Bool)) (X_29 tptp.hoare_2091234717iple_a) (A_75 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.insert1597628439iple_a X_29))) (let ((_let_2 (@ tptp.member290856304iple_a X_29))) (=> (not (@ _let_2 A_75)) (=> (not (@ _let_2 B_39)) (= (= (@ _let_1 A_75) (@ _let_1 B_39)) (= A_75 B_39))))))))
% 0.62/0.96 (assert (forall ((B_39 (-> tptp.hoare_1708887482_state Bool)) (X_29 tptp.hoare_1708887482_state) (A_75 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.insert528405184_state X_29))) (let ((_let_2 (@ tptp.member451959335_state X_29))) (=> (not (@ _let_2 A_75)) (=> (not (@ _let_2 B_39)) (= (= (@ _let_1 A_75) (@ _let_1 B_39)) (= A_75 B_39))))))))
% 0.62/0.96 (assert (forall ((B_39 (-> tptp.pname Bool)) (X_29 tptp.pname) (A_75 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_29))) (let ((_let_2 (@ tptp.member_pname X_29))) (=> (not (@ _let_2 A_75)) (=> (not (@ _let_2 B_39)) (= (= (@ _let_1 A_75) (@ _let_1 B_39)) (= A_75 B_39))))))))
% 0.62/0.96 (assert (forall ((A_74 tptp.nat) (A_73 (-> tptp.nat Bool))) (=> (= A_73 tptp.bot_bot_nat_o) (not (@ (@ tptp.member_nat A_74) A_73)))))
% 0.62/0.96 (assert (forall ((A_74 (-> tptp.hoare_2091234717iple_a Bool)) (A_73 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (= A_73 tptp.bot_bo1957696069_a_o_o) (not (@ (@ tptp.member99268621le_a_o A_74) A_73)))))
% 0.62/0.96 (assert (forall ((A_74 tptp.hoare_2091234717iple_a) (A_73 (-> tptp.hoare_2091234717iple_a Bool))) (=> (= A_73 tptp.bot_bo1791335050le_a_o) (not (@ (@ tptp.member290856304iple_a A_74) A_73)))))
% 0.62/0.96 (assert (forall ((A_74 tptp.hoare_1708887482_state) (A_73 (-> tptp.hoare_1708887482_state Bool))) (=> (= A_73 tptp.bot_bo19817387tate_o) (not (@ (@ tptp.member451959335_state A_74) A_73)))))
% 0.62/0.96 (assert (forall ((A_74 tptp.pname) (A_73 (-> tptp.pname Bool))) (=> (= A_73 tptp.bot_bot_pname_o) (not (@ (@ tptp.member_pname A_74) A_73)))))
% 0.62/0.96 (assert (forall ((B_38 tptp.nat) (A_72 tptp.nat) (B_37 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_72))) (=> (@ _let_1 B_37) (@ _let_1 (@ (@ tptp.insert_nat B_38) B_37))))))
% 0.62/0.96 (assert (forall ((B_38 (-> tptp.hoare_2091234717iple_a Bool)) (A_72 (-> tptp.hoare_2091234717iple_a Bool)) (B_37 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.member99268621le_a_o A_72))) (=> (@ _let_1 B_37) (@ _let_1 (@ (@ tptp.insert102003750le_a_o B_38) B_37))))))
% 0.62/0.96 (assert (forall ((B_38 tptp.hoare_2091234717iple_a) (A_72 tptp.hoare_2091234717iple_a) (B_37 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.member290856304iple_a A_72))) (=> (@ _let_1 B_37) (@ _let_1 (@ (@ tptp.insert1597628439iple_a B_38) B_37))))))
% 0.62/0.96 (assert (forall ((B_38 tptp.hoare_1708887482_state) (A_72 tptp.hoare_1708887482_state) (B_37 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.member451959335_state A_72))) (=> (@ _let_1 B_37) (@ _let_1 (@ (@ tptp.insert528405184_state B_38) B_37))))))
% 0.62/0.96 (assert (forall ((B_38 tptp.pname) (A_72 tptp.pname) (B_37 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_72))) (=> (@ _let_1 B_37) (@ _let_1 (@ (@ tptp.insert_pname B_38) B_37))))))
% 0.62/0.96 (assert (forall ((A_71 tptp.nat) (A_70 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat A_71) A_70) (= (@ (@ tptp.insert_nat A_71) A_70) A_70))))
% 0.62/0.96 (assert (forall ((A_71 (-> tptp.hoare_2091234717iple_a Bool)) (A_70 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (@ (@ tptp.member99268621le_a_o A_71) A_70) (= (@ (@ tptp.insert102003750le_a_o A_71) A_70) A_70))))
% 0.62/0.96 (assert (forall ((A_71 tptp.hoare_2091234717iple_a) (A_70 (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ (@ tptp.member290856304iple_a A_71) A_70) (= (@ (@ tptp.insert1597628439iple_a A_71) A_70) A_70))))
% 0.62/0.96 (assert (forall ((A_71 tptp.hoare_1708887482_state) (A_70 (-> tptp.hoare_1708887482_state Bool))) (=> (@ (@ tptp.member451959335_state A_71) A_70) (= (@ (@ tptp.insert528405184_state A_71) A_70) A_70))))
% 0.62/0.96 (assert (forall ((A_71 tptp.pname) (A_70 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname A_71) A_70) (= (@ (@ tptp.insert_pname A_71) A_70) A_70))))
% 0.62/0.96 (assert (forall ((B_36 tptp.nat) (A_69 tptp.nat)) (=> (@ (@ tptp.member_nat B_36) (@ (@ tptp.insert_nat A_69) tptp.bot_bot_nat_o)) (= B_36 A_69))))
% 0.62/0.96 (assert (forall ((B_36 (-> tptp.hoare_2091234717iple_a Bool)) (A_69 (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ (@ tptp.member99268621le_a_o B_36) (@ (@ tptp.insert102003750le_a_o A_69) tptp.bot_bo1957696069_a_o_o)) (= B_36 A_69))))
% 0.62/0.96 (assert (forall ((B_36 tptp.hoare_2091234717iple_a) (A_69 tptp.hoare_2091234717iple_a)) (=> (@ (@ tptp.member290856304iple_a B_36) (@ (@ tptp.insert1597628439iple_a A_69) tptp.bot_bo1791335050le_a_o)) (= B_36 A_69))))
% 0.62/0.96 (assert (forall ((B_36 tptp.hoare_1708887482_state) (A_69 tptp.hoare_1708887482_state)) (=> (@ (@ tptp.member451959335_state B_36) (@ (@ tptp.insert528405184_state A_69) tptp.bot_bo19817387tate_o)) (= B_36 A_69))))
% 0.62/0.96 (assert (forall ((B_36 tptp.pname) (A_69 tptp.pname)) (=> (@ (@ tptp.member_pname B_36) (@ (@ tptp.insert_pname A_69) tptp.bot_bot_pname_o)) (= B_36 A_69))))
% 0.62/0.96 (assert (forall ((A_68 tptp.nat) (B_35 tptp.nat)) (=> (= (@ (@ tptp.insert_nat A_68) tptp.bot_bot_nat_o) (@ (@ tptp.insert_nat B_35) tptp.bot_bot_nat_o)) (= A_68 B_35))))
% 0.62/0.96 (assert (forall ((A_68 (-> tptp.hoare_2091234717iple_a Bool)) (B_35 (-> tptp.hoare_2091234717iple_a Bool))) (=> (= (@ (@ tptp.insert102003750le_a_o A_68) tptp.bot_bo1957696069_a_o_o) (@ (@ tptp.insert102003750le_a_o B_35) tptp.bot_bo1957696069_a_o_o)) (= A_68 B_35))))
% 0.62/0.96 (assert (forall ((A_68 tptp.pname) (B_35 tptp.pname)) (=> (= (@ (@ tptp.insert_pname A_68) tptp.bot_bot_pname_o) (@ (@ tptp.insert_pname B_35) tptp.bot_bot_pname_o)) (= A_68 B_35))))
% 0.62/0.96 (assert (forall ((A_68 tptp.hoare_2091234717iple_a) (B_35 tptp.hoare_2091234717iple_a)) (=> (= (@ (@ tptp.insert1597628439iple_a A_68) tptp.bot_bo1791335050le_a_o) (@ (@ tptp.insert1597628439iple_a B_35) tptp.bot_bo1791335050le_a_o)) (= A_68 B_35))))
% 0.62/0.96 (assert (forall ((A_68 tptp.hoare_1708887482_state) (B_35 tptp.hoare_1708887482_state)) (=> (= (@ (@ tptp.insert528405184_state A_68) tptp.bot_bo19817387tate_o) (@ (@ tptp.insert528405184_state B_35) tptp.bot_bo19817387tate_o)) (= A_68 B_35))))
% 0.62/0.96 (assert (forall ((U tptp.state) (C tptp.com) (S tptp.state) (T tptp.state)) (let ((_let_1 (@ (@ tptp.evalc C) S))) (=> (@ _let_1 T) (=> (@ _let_1 U) (= U T))))))
% 0.62/0.96 (assert (forall ((A_67 tptp.nat) (A_66 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat A_67))) (= (@ _let_1 A_66) (@ (@ tptp.semila848761471_nat_o (@ _let_1 tptp.bot_bot_nat_o)) A_66)))))
% 0.62/0.96 (assert (forall ((A_67 (-> tptp.hoare_2091234717iple_a Bool)) (A_66 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.insert102003750le_a_o A_67))) (= (@ _let_1 A_66) (@ (@ tptp.semila2050116131_a_o_o (@ _let_1 tptp.bot_bo1957696069_a_o_o)) A_66)))))
% 0.62/0.96 (assert (forall ((A_67 tptp.pname) (A_66 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname A_67))) (= (@ _let_1 A_66) (@ (@ tptp.semila1780557381name_o (@ _let_1 tptp.bot_bot_pname_o)) A_66)))))
% 0.62/0.96 (assert (forall ((A_67 tptp.hoare_1708887482_state) (A_66 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.insert528405184_state A_67))) (= (@ _let_1 A_66) (@ (@ tptp.semila1122118281tate_o (@ _let_1 tptp.bot_bo19817387tate_o)) A_66)))))
% 0.62/0.96 (assert (forall ((A_67 tptp.hoare_2091234717iple_a) (A_66 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.insert1597628439iple_a A_67))) (= (@ _let_1 A_66) (@ (@ tptp.semila1052848428le_a_o (@ _let_1 tptp.bot_bo1791335050le_a_o)) A_66)))))
% 0.62/0.96 (assert (forall ((X (-> tptp.hoare_2091234717iple_a Bool)) (Xa (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.insert102003750le_a_o X) Xa) (@ tptp.collec1008234059le_a_o (lambda ((Y_7 (-> tptp.hoare_2091234717iple_a Bool))) (or (= Y_7 X) (@ (@ tptp.member99268621le_a_o Y_7) Xa)))))))
% 0.62/0.96 (assert (forall ((X tptp.hoare_2091234717iple_a) (Xa (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.insert1597628439iple_a X) Xa) (@ tptp.collec992574898iple_a (lambda ((Y_7 tptp.hoare_2091234717iple_a)) (or (= Y_7 X) (@ (@ tptp.member290856304iple_a Y_7) Xa)))))))
% 0.62/0.96 (assert (forall ((X tptp.hoare_1708887482_state) (Xa (-> tptp.hoare_1708887482_state Bool))) (= (@ (@ tptp.insert528405184_state X) Xa) (@ tptp.collec1568722789_state (lambda ((Y_7 tptp.hoare_1708887482_state)) (or (= Y_7 X) (@ (@ tptp.member451959335_state Y_7) Xa)))))))
% 0.62/0.96 (assert (forall ((X tptp.nat) (Xa (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat X) Xa) (@ tptp.collect_nat (lambda ((Y_7 tptp.nat)) (or (= Y_7 X) (@ (@ tptp.member_nat Y_7) Xa)))))))
% 0.62/0.96 (assert (forall ((X tptp.pname) (Xa (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname X) Xa) (@ tptp.collect_pname (lambda ((Y_7 tptp.pname)) (or (= Y_7 X) (@ (@ tptp.member_pname Y_7) Xa)))))))
% 0.62/0.96 (assert (forall ((G_19 (-> tptp.hoare_2091234717iple_a Bool)) (T_3 tptp.hoare_2091234717iple_a) (Ts_1 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.hoare_1467856363rivs_a G_19))) (let ((_let_2 (@ tptp.insert1597628439iple_a T_3))) (=> (@ _let_1 (@ _let_2 Ts_1)) (and (@ _let_1 (@ _let_2 tptp.bot_bo1791335050le_a_o)) (@ _let_1 Ts_1)))))))
% 0.62/0.96 (assert (forall ((G_19 (-> tptp.hoare_1708887482_state Bool)) (T_3 tptp.hoare_1708887482_state) (Ts_1 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.hoare_90032982_state G_19))) (let ((_let_2 (@ tptp.insert528405184_state T_3))) (=> (@ _let_1 (@ _let_2 Ts_1)) (and (@ _let_1 (@ _let_2 tptp.bot_bo19817387tate_o)) (@ _let_1 Ts_1)))))))
% 0.62/0.96 (assert (forall ((Ts (-> tptp.hoare_2091234717iple_a Bool)) (G_18 (-> tptp.hoare_2091234717iple_a Bool)) (T_2 tptp.hoare_2091234717iple_a)) (let ((_let_1 (@ tptp.insert1597628439iple_a T_2))) (let ((_let_2 (@ tptp.hoare_1467856363rivs_a G_18))) (=> (@ _let_2 (@ _let_1 tptp.bot_bo1791335050le_a_o)) (=> (@ _let_2 Ts) (@ _let_2 (@ _let_1 Ts))))))))
% 0.62/0.96 (assert (forall ((Ts (-> tptp.hoare_1708887482_state Bool)) (G_18 (-> tptp.hoare_1708887482_state Bool)) (T_2 tptp.hoare_1708887482_state)) (let ((_let_1 (@ tptp.insert528405184_state T_2))) (let ((_let_2 (@ tptp.hoare_90032982_state G_18))) (=> (@ _let_2 (@ _let_1 tptp.bot_bo19817387tate_o)) (=> (@ _let_2 Ts) (@ _let_2 (@ _let_1 Ts))))))))
% 0.62/0.96 (assert (forall ((C_23 tptp.nat) (A_65 (-> tptp.nat Bool))) (let ((_let_1 (= A_65 tptp.bot_bot_nat_o))) (and (=> _let_1 (= (@ (@ tptp.image_nat_nat (lambda ((X tptp.nat)) C_23)) A_65) tptp.bot_bot_nat_o)) (=> (not _let_1) (= (@ (@ tptp.image_nat_nat (lambda ((X tptp.nat)) C_23)) A_65) (@ (@ tptp.insert_nat C_23) tptp.bot_bot_nat_o)))))))
% 0.62/0.96 (assert (forall ((C_23 tptp.hoare_1708887482_state) (A_65 (-> tptp.pname Bool))) (let ((_let_1 (= A_65 tptp.bot_bot_pname_o))) (and (=> _let_1 (= (@ (@ tptp.image_1116629049_state (lambda ((X tptp.pname)) C_23)) A_65) tptp.bot_bo19817387tate_o)) (=> (not _let_1) (= (@ (@ tptp.image_1116629049_state (lambda ((X tptp.pname)) C_23)) A_65) (@ (@ tptp.insert528405184_state C_23) tptp.bot_bo19817387tate_o)))))))
% 0.62/0.96 (assert (forall ((C_23 tptp.hoare_2091234717iple_a) (A_65 (-> tptp.pname Bool))) (let ((_let_1 (= A_65 tptp.bot_bot_pname_o))) (and (=> _let_1 (= (@ (@ tptp.image_231808478iple_a (lambda ((X tptp.pname)) C_23)) A_65) tptp.bot_bo1791335050le_a_o)) (=> (not _let_1) (= (@ (@ tptp.image_231808478iple_a (lambda ((X tptp.pname)) C_23)) A_65) (@ (@ tptp.insert1597628439iple_a C_23) tptp.bot_bo1791335050le_a_o)))))))
% 0.62/0.96 (assert (forall ((C_22 tptp.nat) (X_28 tptp.nat) (A_64 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_28) A_64) (= (@ (@ tptp.image_nat_nat (lambda ((X tptp.nat)) C_22)) A_64) (@ (@ tptp.insert_nat C_22) tptp.bot_bot_nat_o)))))
% 0.62/0.96 (assert (forall ((C_22 tptp.hoare_1708887482_state) (X_28 tptp.pname) (A_64 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_28) A_64) (= (@ (@ tptp.image_1116629049_state (lambda ((X tptp.pname)) C_22)) A_64) (@ (@ tptp.insert528405184_state C_22) tptp.bot_bo19817387tate_o)))))
% 0.62/0.96 (assert (forall ((C_22 tptp.nat) (X_28 tptp.pname) (A_64 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_28) A_64) (= (@ (@ tptp.image_pname_nat (lambda ((X tptp.pname)) C_22)) A_64) (@ (@ tptp.insert_nat C_22) tptp.bot_bot_nat_o)))))
% 0.62/0.96 (assert (forall ((C_22 (-> tptp.hoare_2091234717iple_a Bool)) (X_28 tptp.pname) (A_64 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_28) A_64) (= (@ (@ tptp.image_742317343le_a_o (lambda ((X tptp.pname) (__flatten_var_0 tptp.hoare_2091234717iple_a)) (@ C_22 __flatten_var_0))) A_64) (@ (@ tptp.insert102003750le_a_o C_22) tptp.bot_bo1957696069_a_o_o)))))
% 0.62/0.96 (assert (forall ((C_22 tptp.pname) (X_28 tptp.pname) (A_64 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_28) A_64) (= (@ (@ tptp.image_pname_pname (lambda ((X tptp.pname)) C_22)) A_64) (@ (@ tptp.insert_pname C_22) tptp.bot_bot_pname_o)))))
% 0.62/0.96 (assert (forall ((C_22 tptp.hoare_2091234717iple_a) (X_28 tptp.pname) (A_64 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_28) A_64) (= (@ (@ tptp.image_231808478iple_a (lambda ((X tptp.pname)) C_22)) A_64) (@ (@ tptp.insert1597628439iple_a C_22) tptp.bot_bo1791335050le_a_o)))))
% 0.62/0.96 (assert (forall ((F_40 (-> tptp.nat tptp.nat)) (A_63 tptp.nat) (B_34 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.image_nat_nat F_40))) (= (@ _let_1 (@ (@ tptp.insert_nat A_63) B_34)) (@ (@ tptp.insert_nat (@ F_40 A_63)) (@ _let_1 B_34))))))
% 0.62/0.96 (assert (forall ((F_40 (-> tptp.pname tptp.hoare_1708887482_state)) (A_63 tptp.pname) (B_34 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_1116629049_state F_40))) (= (@ _let_1 (@ (@ tptp.insert_pname A_63) B_34)) (@ (@ tptp.insert528405184_state (@ F_40 A_63)) (@ _let_1 B_34))))))
% 0.62/0.96 (assert (forall ((F_40 (-> tptp.pname tptp.hoare_2091234717iple_a)) (A_63 tptp.pname) (B_34 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_231808478iple_a F_40))) (= (@ _let_1 (@ (@ tptp.insert_pname A_63) B_34)) (@ (@ tptp.insert1597628439iple_a (@ F_40 A_63)) (@ _let_1 B_34))))))
% 0.62/0.96 (assert (forall ((F_39 (-> tptp.nat tptp.nat)) (X_27 tptp.nat) (A_62 (-> tptp.nat Bool))) (let ((_let_1 (@ (@ tptp.image_nat_nat F_39) A_62))) (=> (@ (@ tptp.member_nat X_27) A_62) (= (@ (@ tptp.insert_nat (@ F_39 X_27)) _let_1) _let_1)))))
% 0.62/0.96 (assert (forall ((F_39 (-> tptp.pname tptp.hoare_1708887482_state)) (X_27 tptp.pname) (A_62 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_1116629049_state F_39) A_62))) (=> (@ (@ tptp.member_pname X_27) A_62) (= (@ (@ tptp.insert528405184_state (@ F_39 X_27)) _let_1) _let_1)))))
% 0.62/0.96 (assert (forall ((F_39 (-> tptp.pname tptp.nat)) (X_27 tptp.pname) (A_62 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_pname_nat F_39) A_62))) (=> (@ (@ tptp.member_pname X_27) A_62) (= (@ (@ tptp.insert_nat (@ F_39 X_27)) _let_1) _let_1)))))
% 0.62/0.96 (assert (forall ((F_39 (-> tptp.pname tptp.hoare_2091234717iple_a Bool)) (X_27 tptp.pname) (A_62 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_742317343le_a_o F_39) A_62))) (=> (@ (@ tptp.member_pname X_27) A_62) (= (@ (@ tptp.insert102003750le_a_o (@ F_39 X_27)) _let_1) _let_1)))))
% 0.62/0.96 (assert (forall ((F_39 (-> tptp.pname tptp.pname)) (X_27 tptp.pname) (A_62 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_pname_pname F_39) A_62))) (=> (@ (@ tptp.member_pname X_27) A_62) (= (@ (@ tptp.insert_pname (@ F_39 X_27)) _let_1) _let_1)))))
% 0.62/0.96 (assert (forall ((F_39 (-> tptp.pname tptp.hoare_2091234717iple_a)) (X_27 tptp.pname) (A_62 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_231808478iple_a F_39) A_62))) (=> (@ (@ tptp.member_pname X_27) A_62) (= (@ (@ tptp.insert1597628439iple_a (@ F_39 X_27)) _let_1) _let_1)))))
% 0.62/0.96 (assert (forall ((A_61 (-> tptp.nat Bool)) (A_60 tptp.nat) (B_33 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila848761471_nat_o A_61))) (let ((_let_2 (@ tptp.insert_nat A_60))) (= (@ _let_1 (@ _let_2 B_33)) (@ _let_2 (@ _let_1 B_33)))))))
% 0.62/0.96 (assert (forall ((A_61 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (A_60 (-> tptp.hoare_2091234717iple_a Bool)) (B_33 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.semila2050116131_a_o_o A_61))) (let ((_let_2 (@ tptp.insert102003750le_a_o A_60))) (= (@ _let_1 (@ _let_2 B_33)) (@ _let_2 (@ _let_1 B_33)))))))
% 0.62/0.96 (assert (forall ((A_61 (-> tptp.pname Bool)) (A_60 tptp.pname) (B_33 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1780557381name_o A_61))) (let ((_let_2 (@ tptp.insert_pname A_60))) (= (@ _let_1 (@ _let_2 B_33)) (@ _let_2 (@ _let_1 B_33)))))))
% 0.62/0.96 (assert (forall ((A_61 (-> tptp.hoare_1708887482_state Bool)) (A_60 tptp.hoare_1708887482_state) (B_33 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.semila1122118281tate_o A_61))) (let ((_let_2 (@ tptp.insert528405184_state A_60))) (= (@ _let_1 (@ _let_2 B_33)) (@ _let_2 (@ _let_1 B_33)))))))
% 0.62/0.96 (assert (forall ((A_61 (-> tptp.hoare_2091234717iple_a Bool)) (A_60 tptp.hoare_2091234717iple_a) (B_33 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila1052848428le_a_o A_61))) (let ((_let_2 (@ tptp.insert1597628439iple_a A_60))) (= (@ _let_1 (@ _let_2 B_33)) (@ _let_2 (@ _let_1 B_33)))))))
% 0.62/0.96 (assert (forall ((A_59 tptp.nat) (B_32 (-> tptp.nat Bool)) (C_21 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat A_59))) (= (@ (@ tptp.semila848761471_nat_o (@ _let_1 B_32)) C_21) (@ _let_1 (@ (@ tptp.semila848761471_nat_o B_32) C_21))))))
% 0.62/0.96 (assert (forall ((A_59 (-> tptp.hoare_2091234717iple_a Bool)) (B_32 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (C_21 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.insert102003750le_a_o A_59))) (= (@ (@ tptp.semila2050116131_a_o_o (@ _let_1 B_32)) C_21) (@ _let_1 (@ (@ tptp.semila2050116131_a_o_o B_32) C_21))))))
% 0.62/0.96 (assert (forall ((A_59 tptp.pname) (B_32 (-> tptp.pname Bool)) (C_21 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname A_59))) (= (@ (@ tptp.semila1780557381name_o (@ _let_1 B_32)) C_21) (@ _let_1 (@ (@ tptp.semila1780557381name_o B_32) C_21))))))
% 0.62/0.96 (assert (forall ((A_59 tptp.hoare_1708887482_state) (B_32 (-> tptp.hoare_1708887482_state Bool)) (C_21 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.insert528405184_state A_59))) (= (@ (@ tptp.semila1122118281tate_o (@ _let_1 B_32)) C_21) (@ _let_1 (@ (@ tptp.semila1122118281tate_o B_32) C_21))))))
% 0.62/0.96 (assert (forall ((A_59 tptp.hoare_2091234717iple_a) (B_32 (-> tptp.hoare_2091234717iple_a Bool)) (C_21 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.insert1597628439iple_a A_59))) (= (@ (@ tptp.semila1052848428le_a_o (@ _let_1 B_32)) C_21) (@ _let_1 (@ (@ tptp.semila1052848428le_a_o B_32) C_21))))))
% 0.62/0.96 (assert (forall ((F_38 (-> tptp.nat tptp.nat)) (A_58 (-> tptp.nat Bool))) (= (= tptp.bot_bot_nat_o (@ (@ tptp.image_nat_nat F_38) A_58)) (= A_58 tptp.bot_bot_nat_o))))
% 0.62/0.96 (assert (forall ((F_38 (-> tptp.pname tptp.hoare_1708887482_state)) (A_58 (-> tptp.pname Bool))) (= (= tptp.bot_bo19817387tate_o (@ (@ tptp.image_1116629049_state F_38) A_58)) (= A_58 tptp.bot_bot_pname_o))))
% 0.62/0.96 (assert (forall ((F_38 (-> tptp.pname tptp.hoare_2091234717iple_a)) (A_58 (-> tptp.pname Bool))) (= (= tptp.bot_bo1791335050le_a_o (@ (@ tptp.image_231808478iple_a F_38) A_58)) (= A_58 tptp.bot_bot_pname_o))))
% 0.62/0.96 (assert (forall ((F_37 (-> tptp.nat tptp.nat))) (= (@ (@ tptp.image_nat_nat F_37) tptp.bot_bot_nat_o) tptp.bot_bot_nat_o)))
% 0.62/0.96 (assert (forall ((F_37 (-> tptp.pname tptp.hoare_1708887482_state))) (= (@ (@ tptp.image_1116629049_state F_37) tptp.bot_bot_pname_o) tptp.bot_bo19817387tate_o)))
% 0.62/0.96 (assert (forall ((F_37 (-> tptp.pname tptp.hoare_2091234717iple_a))) (= (@ (@ tptp.image_231808478iple_a F_37) tptp.bot_bot_pname_o) tptp.bot_bo1791335050le_a_o)))
% 0.62/0.96 (assert (forall ((F_36 (-> tptp.nat tptp.nat)) (A_57 (-> tptp.nat Bool))) (= (= (@ (@ tptp.image_nat_nat F_36) A_57) tptp.bot_bot_nat_o) (= A_57 tptp.bot_bot_nat_o))))
% 0.62/0.96 (assert (forall ((F_36 (-> tptp.pname tptp.hoare_1708887482_state)) (A_57 (-> tptp.pname Bool))) (= (= (@ (@ tptp.image_1116629049_state F_36) A_57) tptp.bot_bo19817387tate_o) (= A_57 tptp.bot_bot_pname_o))))
% 0.62/0.96 (assert (forall ((F_36 (-> tptp.pname tptp.hoare_2091234717iple_a)) (A_57 (-> tptp.pname Bool))) (= (= (@ (@ tptp.image_231808478iple_a F_36) A_57) tptp.bot_bo1791335050le_a_o) (= A_57 tptp.bot_bot_pname_o))))
% 0.62/0.96 (assert (forall ((P_23 (-> tptp.nat Bool)) (X tptp.nat)) (=> (@ (@ tptp.member_nat X) tptp.bot_bot_nat_o) (@ P_23 X))))
% 0.62/0.96 (assert (forall ((P_23 (-> tptp.hoare_2091234717iple_a Bool)) (X tptp.hoare_2091234717iple_a)) (=> (@ (@ tptp.member290856304iple_a X) tptp.bot_bo1791335050le_a_o) (@ P_23 X))))
% 0.62/0.96 (assert (forall ((P_23 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (X (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ (@ tptp.member99268621le_a_o X) tptp.bot_bo1957696069_a_o_o) (@ P_23 X))))
% 0.62/0.96 (assert (forall ((P_23 (-> tptp.pname Bool)) (X tptp.pname)) (=> (@ (@ tptp.member_pname X) tptp.bot_bot_pname_o) (@ P_23 X))))
% 0.62/0.96 (assert (forall ((P_23 (-> tptp.hoare_1708887482_state Bool)) (X tptp.hoare_1708887482_state)) (=> (@ (@ tptp.member451959335_state X) tptp.bot_bo19817387tate_o) (@ P_23 X))))
% 0.62/0.96 (assert (forall ((B_31 (-> tptp.nat Bool))) (= (@ (@ tptp.semila848761471_nat_o tptp.bot_bot_nat_o) B_31) B_31)))
% 0.62/0.96 (assert (forall ((B_31 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.semila2050116131_a_o_o tptp.bot_bo1957696069_a_o_o) B_31) B_31)))
% 0.62/0.96 (assert (forall ((B_31 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o tptp.bot_bot_pname_o) B_31) B_31)))
% 0.62/0.96 (assert (forall ((B_31 (-> tptp.hoare_1708887482_state Bool))) (= (@ (@ tptp.semila1122118281tate_o tptp.bot_bo19817387tate_o) B_31) B_31)))
% 0.62/0.96 (assert (forall ((B_31 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila1052848428le_a_o tptp.bot_bo1791335050le_a_o) B_31) B_31)))
% 0.62/0.96 (assert (forall ((A_56 (-> tptp.nat Bool))) (= (@ (@ tptp.semila848761471_nat_o A_56) tptp.bot_bot_nat_o) A_56)))
% 0.62/0.96 (assert (forall ((A_56 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.semila2050116131_a_o_o A_56) tptp.bot_bo1957696069_a_o_o) A_56)))
% 0.62/0.96 (assert (forall ((A_56 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o A_56) tptp.bot_bot_pname_o) A_56)))
% 0.62/0.96 (assert (forall ((A_56 (-> tptp.hoare_1708887482_state Bool))) (= (@ (@ tptp.semila1122118281tate_o A_56) tptp.bot_bo19817387tate_o) A_56)))
% 0.62/0.96 (assert (forall ((A_56 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila1052848428le_a_o A_56) tptp.bot_bo1791335050le_a_o) A_56)))
% 0.62/0.96 (assert (forall ((A_55 (-> tptp.nat Bool)) (B_30 (-> tptp.nat Bool))) (= (= (@ (@ tptp.semila848761471_nat_o A_55) B_30) tptp.bot_bot_nat_o) (and (= A_55 tptp.bot_bot_nat_o) (= B_30 tptp.bot_bot_nat_o)))))
% 0.62/0.96 (assert (forall ((A_55 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_30 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (= (@ (@ tptp.semila2050116131_a_o_o A_55) B_30) tptp.bot_bo1957696069_a_o_o) (and (= A_55 tptp.bot_bo1957696069_a_o_o) (= B_30 tptp.bot_bo1957696069_a_o_o)))))
% 0.62/0.96 (assert (forall ((A_55 (-> tptp.pname Bool)) (B_30 (-> tptp.pname Bool))) (= (= (@ (@ tptp.semila1780557381name_o A_55) B_30) tptp.bot_bot_pname_o) (and (= A_55 tptp.bot_bot_pname_o) (= B_30 tptp.bot_bot_pname_o)))))
% 0.62/0.96 (assert (forall ((A_55 (-> tptp.hoare_1708887482_state Bool)) (B_30 (-> tptp.hoare_1708887482_state Bool))) (= (= (@ (@ tptp.semila1122118281tate_o A_55) B_30) tptp.bot_bo19817387tate_o) (and (= A_55 tptp.bot_bo19817387tate_o) (= B_30 tptp.bot_bo19817387tate_o)))))
% 0.62/0.96 (assert (forall ((A_55 (-> tptp.hoare_2091234717iple_a Bool)) (B_30 (-> tptp.hoare_2091234717iple_a Bool))) (= (= (@ (@ tptp.semila1052848428le_a_o A_55) B_30) tptp.bot_bo1791335050le_a_o) (and (= A_55 tptp.bot_bo1791335050le_a_o) (= B_30 tptp.bot_bo1791335050le_a_o)))))
% 0.62/0.96 (assert (forall ((G_17 (-> tptp.hoare_2091234717iple_a Bool)) (P_22 (-> tptp.x_a tptp.state Bool)) (C_20 tptp.com) (Q_15 (-> tptp.x_a tptp.state Bool)) (C_19 Bool)) (let ((_let_1 (@ tptp.hoare_1467856363rivs_a G_17))) (=> (=> C_19 (@ _let_1 (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a P_22) C_20) Q_15)) tptp.bot_bo1791335050le_a_o))) (@ _let_1 (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a (lambda ((Z_5 tptp.x_a) (S_2 tptp.state)) (and (@ (@ P_22 Z_5) S_2) C_19))) C_20) Q_15)) tptp.bot_bo1791335050le_a_o))))))
% 0.62/0.96 (assert (forall ((G_17 (-> tptp.hoare_1708887482_state Bool)) (P_22 (-> tptp.state tptp.state Bool)) (C_20 tptp.com) (Q_15 (-> tptp.state tptp.state Bool)) (C_19 Bool)) (let ((_let_1 (@ tptp.hoare_90032982_state G_17))) (=> (=> C_19 (@ _let_1 (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state P_22) C_20) Q_15)) tptp.bot_bo19817387tate_o))) (@ _let_1 (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state (lambda ((Z_5 tptp.state) (S_2 tptp.state)) (and (@ (@ P_22 Z_5) S_2) C_19))) C_20) Q_15)) tptp.bot_bo19817387tate_o))))))
% 0.62/0.96 (assert (forall ((G_16 (-> tptp.hoare_2091234717iple_a Bool))) (@ (@ tptp.hoare_1467856363rivs_a G_16) tptp.bot_bo1791335050le_a_o)))
% 0.62/0.96 (assert (forall ((G_16 (-> tptp.hoare_1708887482_state Bool))) (@ (@ tptp.hoare_90032982_state G_16) tptp.bot_bo19817387tate_o)))
% 0.62/0.96 (assert (forall ((X_26 (-> tptp.nat Bool))) (= (@ (@ tptp.semila848761471_nat_o tptp.bot_bot_nat_o) X_26) X_26)))
% 0.62/0.96 (assert (forall ((X_26 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.semila2050116131_a_o_o tptp.bot_bo1957696069_a_o_o) X_26) X_26)))
% 0.62/0.96 (assert (forall ((X_26 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o tptp.bot_bot_pname_o) X_26) X_26)))
% 0.62/0.96 (assert (forall ((X_26 (-> tptp.hoare_1708887482_state Bool))) (= (@ (@ tptp.semila1122118281tate_o tptp.bot_bo19817387tate_o) X_26) X_26)))
% 0.62/0.96 (assert (forall ((X_26 Bool)) (= (@ (@ tptp.semila10642723_sup_o tptp.bot_bot_o) X_26) X_26)))
% 0.62/0.96 (assert (forall ((X_26 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila1052848428le_a_o tptp.bot_bo1791335050le_a_o) X_26) X_26)))
% 0.62/0.96 (assert (forall ((X_25 (-> tptp.nat Bool))) (= (@ (@ tptp.semila848761471_nat_o X_25) tptp.bot_bot_nat_o) X_25)))
% 0.62/0.96 (assert (forall ((X_25 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.semila2050116131_a_o_o X_25) tptp.bot_bo1957696069_a_o_o) X_25)))
% 0.62/0.96 (assert (forall ((X_25 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o X_25) tptp.bot_bot_pname_o) X_25)))
% 0.62/0.96 (assert (forall ((X_25 (-> tptp.hoare_1708887482_state Bool))) (= (@ (@ tptp.semila1122118281tate_o X_25) tptp.bot_bo19817387tate_o) X_25)))
% 0.62/0.96 (assert (forall ((X_25 Bool)) (= (@ (@ tptp.semila10642723_sup_o X_25) tptp.bot_bot_o) X_25)))
% 0.62/0.96 (assert (forall ((X_25 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila1052848428le_a_o X_25) tptp.bot_bo1791335050le_a_o) X_25)))
% 0.62/0.96 (assert (forall ((X_24 (-> tptp.nat Bool)) (Y_8 (-> tptp.nat Bool))) (= (= (@ (@ tptp.semila848761471_nat_o X_24) Y_8) tptp.bot_bot_nat_o) (and (= X_24 tptp.bot_bot_nat_o) (= Y_8 tptp.bot_bot_nat_o)))))
% 0.62/0.96 (assert (forall ((X_24 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (Y_8 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (= (@ (@ tptp.semila2050116131_a_o_o X_24) Y_8) tptp.bot_bo1957696069_a_o_o) (and (= X_24 tptp.bot_bo1957696069_a_o_o) (= Y_8 tptp.bot_bo1957696069_a_o_o)))))
% 0.62/0.96 (assert (forall ((X_24 (-> tptp.pname Bool)) (Y_8 (-> tptp.pname Bool))) (= (= (@ (@ tptp.semila1780557381name_o X_24) Y_8) tptp.bot_bot_pname_o) (and (= X_24 tptp.bot_bot_pname_o) (= Y_8 tptp.bot_bot_pname_o)))))
% 0.62/0.96 (assert (forall ((X_24 (-> tptp.hoare_1708887482_state Bool)) (Y_8 (-> tptp.hoare_1708887482_state Bool))) (= (= (@ (@ tptp.semila1122118281tate_o X_24) Y_8) tptp.bot_bo19817387tate_o) (and (= X_24 tptp.bot_bo19817387tate_o) (= Y_8 tptp.bot_bo19817387tate_o)))))
% 0.62/0.96 (assert (forall ((X_24 Bool) (Y_8 Bool)) (= (= (@ (@ tptp.semila10642723_sup_o X_24) Y_8) tptp.bot_bot_o) (and (= X_24 tptp.bot_bot_o) (= Y_8 tptp.bot_bot_o)))))
% 0.62/0.96 (assert (forall ((X_24 (-> tptp.hoare_2091234717iple_a Bool)) (Y_8 (-> tptp.hoare_2091234717iple_a Bool))) (= (= (@ (@ tptp.semila1052848428le_a_o X_24) Y_8) tptp.bot_bo1791335050le_a_o) (and (= X_24 tptp.bot_bo1791335050le_a_o) (= Y_8 tptp.bot_bo1791335050le_a_o)))))
% 0.62/0.96 (assert (forall ((N_5 tptp.nat) (T_1 tptp.hoare_1708887482_state)) (=> (@ (@ tptp.hoare_23738522_state (@ tptp.suc N_5)) T_1) (@ (@ tptp.hoare_23738522_state N_5) T_1))))
% 0.62/0.96 (assert (forall ((N_5 tptp.nat) (T_1 tptp.hoare_2091234717iple_a)) (=> (@ (@ tptp.hoare_1421888935alid_a (@ tptp.suc N_5)) T_1) (@ (@ tptp.hoare_1421888935alid_a N_5) T_1))))
% 0.62/0.96 (assert (forall ((A_54 (-> tptp.hoare_2091234717iple_a Bool)) (B_29 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.insert102003750le_a_o A_54) B_29) (@ (@ tptp.semila2050116131_a_o_o (@ tptp.collec1008234059le_a_o (lambda ((X (-> tptp.hoare_2091234717iple_a Bool))) (= X A_54)))) B_29))))
% 0.62/0.96 (assert (forall ((A_54 tptp.pname) (B_29 (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname A_54) B_29) (@ (@ tptp.semila1780557381name_o (@ tptp.collect_pname (lambda ((X tptp.pname)) (= X A_54)))) B_29))))
% 0.62/0.96 (assert (forall ((A_54 tptp.hoare_1708887482_state) (B_29 (-> tptp.hoare_1708887482_state Bool))) (= (@ (@ tptp.insert528405184_state A_54) B_29) (@ (@ tptp.semila1122118281tate_o (@ tptp.collec1568722789_state (lambda ((X tptp.hoare_1708887482_state)) (= X A_54)))) B_29))))
% 0.62/0.96 (assert (forall ((A_54 tptp.hoare_2091234717iple_a) (B_29 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.insert1597628439iple_a A_54) B_29) (@ (@ tptp.semila1052848428le_a_o (@ tptp.collec992574898iple_a (lambda ((X tptp.hoare_2091234717iple_a)) (= X A_54)))) B_29))))
% 0.62/0.96 (assert (forall ((A_54 tptp.nat) (B_29 (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat A_54) B_29) (@ (@ tptp.semila848761471_nat_o (@ tptp.collect_nat (lambda ((X tptp.nat)) (= X A_54)))) B_29))))
% 0.62/0.96 (assert (forall ((G_15 (-> tptp.hoare_2091234717iple_a Bool)) (P_21 (-> tptp.x_a tptp.state Bool)) (Pn_3 tptp.pname) (Q_14 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_657976383iple_a P_21))) (let ((_let_2 (@ tptp.hoare_1467856363rivs_a G_15))) (=> (@ _let_2 (@ (@ tptp.insert1597628439iple_a (@ (@ _let_1 (@ tptp.the_com (@ tptp.body_1 Pn_3))) Q_14)) tptp.bot_bo1791335050le_a_o)) (@ _let_2 (@ (@ tptp.insert1597628439iple_a (@ (@ _let_1 (@ tptp.body Pn_3)) Q_14)) tptp.bot_bo1791335050le_a_o)))))))
% 0.62/0.96 (assert (forall ((G_15 (-> tptp.hoare_1708887482_state Bool)) (P_21 (-> tptp.state tptp.state Bool)) (Pn_3 tptp.pname) (Q_14 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_858012674_state P_21))) (let ((_let_2 (@ tptp.hoare_90032982_state G_15))) (=> (@ _let_2 (@ (@ tptp.insert528405184_state (@ (@ _let_1 (@ tptp.the_com (@ tptp.body_1 Pn_3))) Q_14)) tptp.bot_bo19817387tate_o)) (@ _let_2 (@ (@ tptp.insert528405184_state (@ (@ _let_1 (@ tptp.body Pn_3)) Q_14)) tptp.bot_bo19817387tate_o)))))))
% 0.62/0.96 (assert (forall ((P_20 (-> tptp.x_a tptp.state Bool)) (Pn_2 tptp.pname) (Q_13 (-> tptp.x_a tptp.state Bool)) (G_14 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.hoare_657976383iple_a P_20))) (let ((_let_2 (@ tptp.insert1597628439iple_a (@ (@ _let_1 (@ tptp.body Pn_2)) Q_13)))) (=> (@ (@ tptp.hoare_1467856363rivs_a (@ _let_2 G_14)) (@ (@ tptp.insert1597628439iple_a (@ (@ _let_1 (@ tptp.the_com (@ tptp.body_1 Pn_2))) Q_13)) tptp.bot_bo1791335050le_a_o)) (@ (@ tptp.hoare_1467856363rivs_a G_14) (@ _let_2 tptp.bot_bo1791335050le_a_o)))))))
% 0.62/0.96 (assert (forall ((P_20 (-> tptp.state tptp.state Bool)) (Pn_2 tptp.pname) (Q_13 (-> tptp.state tptp.state Bool)) (G_14 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.hoare_858012674_state P_20))) (let ((_let_2 (@ tptp.insert528405184_state (@ (@ _let_1 (@ tptp.body Pn_2)) Q_13)))) (=> (@ (@ tptp.hoare_90032982_state (@ _let_2 G_14)) (@ (@ tptp.insert528405184_state (@ (@ _let_1 (@ tptp.the_com (@ tptp.body_1 Pn_2))) Q_13)) tptp.bot_bo19817387tate_o)) (@ (@ tptp.hoare_90032982_state G_14) (@ _let_2 tptp.bot_bo19817387tate_o)))))))
% 0.62/0.96 (assert (forall ((G_13 (-> tptp.hoare_2091234717iple_a Bool)) (C_18 tptp.com) (Q_12 (-> tptp.x_a tptp.state Bool)) (P_19 (-> tptp.x_a tptp.state Bool))) (=> (forall ((Z_5 tptp.x_a) (S_2 tptp.state)) (=> (@ (@ P_19 Z_5) S_2) (@ (@ tptp.hoare_1467856363rivs_a G_13) (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a (lambda ((Za tptp.x_a) (S_3 tptp.state)) (= S_3 S_2))) C_18) (lambda ((Z_6 tptp.x_a) (__flatten_var_0 tptp.state)) (@ (@ Q_12 Z_5) __flatten_var_0)))) tptp.bot_bo1791335050le_a_o)))) (@ (@ tptp.hoare_1467856363rivs_a G_13) (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a P_19) C_18) Q_12)) tptp.bot_bo1791335050le_a_o)))))
% 0.62/0.96 (assert (forall ((G_13 (-> tptp.hoare_1708887482_state Bool)) (C_18 tptp.com) (Q_12 (-> tptp.state tptp.state Bool)) (P_19 (-> tptp.state tptp.state Bool))) (=> (forall ((Z_5 tptp.state) (S_2 tptp.state)) (=> (@ (@ P_19 Z_5) S_2) (@ (@ tptp.hoare_90032982_state G_13) (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state (lambda ((Za tptp.state) (S_3 tptp.state)) (= S_3 S_2))) C_18) (lambda ((Z_6 tptp.state) (__flatten_var_0 tptp.state)) (@ (@ Q_12 Z_5) __flatten_var_0)))) tptp.bot_bo19817387tate_o)))) (@ (@ tptp.hoare_90032982_state G_13) (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state P_19) C_18) Q_12)) tptp.bot_bo19817387tate_o)))))
% 0.62/0.96 (assert (forall ((P_18 (-> tptp.x_a tptp.state Bool)) (G_12 (-> tptp.hoare_2091234717iple_a Bool)) (P_17 (-> tptp.x_a tptp.state Bool)) (C_17 tptp.com) (Q_11 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_1467856363rivs_a G_12))) (=> (@ _let_1 (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a P_17) C_17) Q_11)) tptp.bot_bo1791335050le_a_o)) (=> (forall ((Z_5 tptp.x_a) (S_2 tptp.state)) (=> (@ (@ P_18 Z_5) S_2) (@ (@ P_17 Z_5) S_2))) (@ _let_1 (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a P_18) C_17) Q_11)) tptp.bot_bo1791335050le_a_o)))))))
% 0.62/0.96 (assert (forall ((P_18 (-> tptp.state tptp.state Bool)) (G_12 (-> tptp.hoare_1708887482_state Bool)) (P_17 (-> tptp.state tptp.state Bool)) (C_17 tptp.com) (Q_11 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_90032982_state G_12))) (=> (@ _let_1 (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state P_17) C_17) Q_11)) tptp.bot_bo19817387tate_o)) (=> (forall ((Z_5 tptp.state) (S_2 tptp.state)) (=> (@ (@ P_18 Z_5) S_2) (@ (@ P_17 Z_5) S_2))) (@ _let_1 (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state P_18) C_17) Q_11)) tptp.bot_bo19817387tate_o)))))))
% 0.62/0.96 (assert (forall ((Q_10 (-> tptp.x_a tptp.state Bool)) (G_11 (-> tptp.hoare_2091234717iple_a Bool)) (P_16 (-> tptp.x_a tptp.state Bool)) (C_16 tptp.com) (Q_9 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ (@ tptp.hoare_657976383iple_a P_16) C_16))) (let ((_let_2 (@ tptp.hoare_1467856363rivs_a G_11))) (=> (@ _let_2 (@ (@ tptp.insert1597628439iple_a (@ _let_1 Q_9)) tptp.bot_bo1791335050le_a_o)) (=> (forall ((Z_5 tptp.x_a) (S_2 tptp.state)) (=> (@ (@ Q_9 Z_5) S_2) (@ (@ Q_10 Z_5) S_2))) (@ _let_2 (@ (@ tptp.insert1597628439iple_a (@ _let_1 Q_10)) tptp.bot_bo1791335050le_a_o))))))))
% 0.62/0.96 (assert (forall ((Q_10 (-> tptp.state tptp.state Bool)) (G_11 (-> tptp.hoare_1708887482_state Bool)) (P_16 (-> tptp.state tptp.state Bool)) (C_16 tptp.com) (Q_9 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ (@ tptp.hoare_858012674_state P_16) C_16))) (let ((_let_2 (@ tptp.hoare_90032982_state G_11))) (=> (@ _let_2 (@ (@ tptp.insert528405184_state (@ _let_1 Q_9)) tptp.bot_bo19817387tate_o)) (=> (forall ((Z_5 tptp.state) (S_2 tptp.state)) (=> (@ (@ Q_9 Z_5) S_2) (@ (@ Q_10 Z_5) S_2))) (@ _let_2 (@ (@ tptp.insert528405184_state (@ _let_1 Q_10)) tptp.bot_bo19817387tate_o))))))))
% 0.62/0.96 (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_1169027232size_a Fa) (@ (@ (@ tptp.hoare_657976383iple_a Fun1_1) Com_3) Fun2_1)) tptp.zero_zero_nat)))
% 0.62/0.96 (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_518771297_state Fa) (@ (@ (@ tptp.hoare_858012674_state Fun1_1) Com_3) Fun2_1)) tptp.zero_zero_nat)))
% 0.62/0.96 (assert (forall ((C tptp.com)) (= (@ tptp.hoare_Mirabelle_MGT C) (@ (@ (@ tptp.hoare_858012674_state tptp.fequal_state) C) (@ tptp.evalc C)))))
% 0.62/0.96 (assert (forall ((Fun1 (-> tptp.x_a tptp.state Bool)) (Com_2 tptp.com) (Fun2 (-> tptp.x_a tptp.state Bool))) (= (@ tptp.size_s1040486067iple_a (@ (@ (@ tptp.hoare_657976383iple_a Fun1) Com_2) Fun2)) tptp.zero_zero_nat)))
% 0.62/0.96 (assert (forall ((Fun1 (-> tptp.state tptp.state Bool)) (Com_2 tptp.com) (Fun2 (-> tptp.state tptp.state Bool))) (= (@ tptp.size_s1186992420_state (@ (@ (@ tptp.hoare_858012674_state Fun1) Com_2) Fun2)) tptp.zero_zero_nat)))
% 0.62/0.96 (assert (forall ((Q_8 (-> tptp.x_a tptp.state Bool)) (P_15 (-> tptp.x_a tptp.state Bool)) (G_10 (-> tptp.hoare_2091234717iple_a Bool)) (P_14 (-> tptp.x_a tptp.state Bool)) (C_15 tptp.com) (Q_7 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_1467856363rivs_a G_10))) (=> (@ _let_1 (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a P_14) C_15) Q_7)) tptp.bot_bo1791335050le_a_o)) (=> (forall ((Z_5 tptp.x_a) (S_2 tptp.state)) (=> (@ (@ P_15 Z_5) S_2) (forall ((S_3 tptp.state)) (=> (forall ((Z_6 tptp.x_a)) (=> (@ (@ P_14 Z_6) S_2) (@ (@ Q_7 Z_6) S_3))) (@ (@ Q_8 Z_5) S_3))))) (@ _let_1 (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a P_15) C_15) Q_8)) tptp.bot_bo1791335050le_a_o)))))))
% 0.62/0.96 (assert (forall ((Q_8 (-> tptp.state tptp.state Bool)) (P_15 (-> tptp.state tptp.state Bool)) (G_10 (-> tptp.hoare_1708887482_state Bool)) (P_14 (-> tptp.state tptp.state Bool)) (C_15 tptp.com) (Q_7 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_90032982_state G_10))) (=> (@ _let_1 (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state P_14) C_15) Q_7)) tptp.bot_bo19817387tate_o)) (=> (forall ((Z_5 tptp.state) (S_2 tptp.state)) (=> (@ (@ P_15 Z_5) S_2) (forall ((S_3 tptp.state)) (=> (forall ((Z_6 tptp.state)) (=> (@ (@ P_14 Z_6) S_2) (@ (@ Q_7 Z_6) S_3))) (@ (@ Q_8 Z_5) S_3))))) (@ _let_1 (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state P_15) C_15) Q_8)) tptp.bot_bo19817387tate_o)))))))
% 0.62/0.96 (assert (forall ((X_23 tptp.nat)) (= (@ tptp.the_elem_nat (@ (@ tptp.insert_nat X_23) tptp.bot_bot_nat_o)) X_23)))
% 0.62/0.96 (assert (forall ((X_23 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ tptp.the_el1618277441le_a_o (@ (@ tptp.insert102003750le_a_o X_23) tptp.bot_bo1957696069_a_o_o)) X_23)))
% 0.62/0.96 (assert (forall ((X_23 tptp.pname)) (= (@ tptp.the_elem_pname (@ (@ tptp.insert_pname X_23) tptp.bot_bot_pname_o)) X_23)))
% 0.62/0.96 (assert (forall ((X_23 tptp.hoare_2091234717iple_a)) (= (@ tptp.the_el13400124iple_a (@ (@ tptp.insert1597628439iple_a X_23) tptp.bot_bo1791335050le_a_o)) X_23)))
% 0.62/0.96 (assert (forall ((X_23 tptp.hoare_1708887482_state)) (= (@ tptp.the_el864710747_state (@ (@ tptp.insert528405184_state X_23) tptp.bot_bo19817387tate_o)) X_23)))
% 0.62/0.96 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 0.62/0.96 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (not (= N_1 (@ tptp.suc N_1)))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (not (= (@ tptp.suc N_1) N_1))))
% 0.62/0.96 (assert (forall ((Nat_3 tptp.nat) (Nat_2 tptp.nat)) (= (= (@ tptp.suc Nat_3) (@ tptp.suc Nat_2)) (= Nat_3 Nat_2))))
% 0.62/0.96 (assert (forall ((X_1 tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X_1) (@ tptp.suc Y)) (= X_1 Y))))
% 0.62/0.96 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.62/0.96 (assert (forall ((Nat_2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat_2)))))
% 0.62/0.96 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 0.62/0.96 (assert (forall ((Nat_1 tptp.nat)) (not (= (@ tptp.suc Nat_1) tptp.zero_zero_nat))))
% 0.62/0.96 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (=> (not (= N_1 tptp.zero_zero_nat)) (exists ((M_1 tptp.nat)) (= N_1 (@ tptp.suc M_1))))))
% 0.62/0.96 (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)))))
% 0.62/0.96 (assert (forall ((P (-> tptp.nat Bool)) (K_1 tptp.nat)) (=> (@ P K_1) (=> (forall ((N tptp.nat)) (=> (@ P (@ tptp.suc N)) (@ P N))) (@ P tptp.zero_zero_nat)))))
% 0.62/0.96 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat tptp.nat)) (not (= Y (@ tptp.suc Nat))))))))
% 0.62/0.96 (assert (forall ((X tptp.nat)) (= (@ tptp.bot_bot_nat_o X) tptp.bot_bot_o)))
% 0.62/0.96 (assert (forall ((X tptp.hoare_2091234717iple_a)) (= (@ tptp.bot_bo1791335050le_a_o X) tptp.bot_bot_o)))
% 0.62/0.96 (assert (forall ((X (-> tptp.hoare_2091234717iple_a Bool))) (= (@ tptp.bot_bo1957696069_a_o_o X) tptp.bot_bot_o)))
% 0.62/0.96 (assert (forall ((X tptp.pname)) (= (@ tptp.bot_bot_pname_o X) tptp.bot_bot_o)))
% 0.62/0.96 (assert (forall ((X tptp.hoare_1708887482_state)) (= (@ tptp.bot_bo19817387tate_o X) tptp.bot_bot_o)))
% 0.62/0.96 (assert (forall ((X_22 tptp.nat)) (= (@ tptp.bot_bot_nat_o X_22) tptp.bot_bot_o)))
% 0.62/0.96 (assert (forall ((X_22 tptp.hoare_2091234717iple_a)) (= (@ tptp.bot_bo1791335050le_a_o X_22) tptp.bot_bot_o)))
% 0.62/0.96 (assert (forall ((X_22 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ tptp.bot_bo1957696069_a_o_o X_22) tptp.bot_bot_o)))
% 0.62/0.96 (assert (forall ((X_22 tptp.pname)) (= (@ tptp.bot_bot_pname_o X_22) tptp.bot_bot_o)))
% 0.62/0.96 (assert (forall ((X_22 tptp.hoare_1708887482_state)) (= (@ tptp.bot_bo19817387tate_o X_22) tptp.bot_bot_o)))
% 0.62/0.96 (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))))
% 0.62/0.96 (assert (forall ((G_9 (-> tptp.hoare_2091234717iple_a Bool)) (P_13 (-> tptp.x_a tptp.state Bool))) (@ (@ tptp.hoare_1467856363rivs_a G_9) (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a P_13) tptp.skip) P_13)) tptp.bot_bo1791335050le_a_o))))
% 0.62/0.96 (assert (forall ((G_9 (-> tptp.hoare_1708887482_state Bool)) (P_13 (-> tptp.state tptp.state Bool))) (@ (@ tptp.hoare_90032982_state G_9) (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state P_13) tptp.skip) P_13)) tptp.bot_bo19817387tate_o))))
% 0.62/0.96 (assert (forall ((G_8 (-> tptp.hoare_2091234717iple_a Bool)) (P_12 (-> tptp.x_a tptp.state Bool)) (B_28 (-> tptp.state Bool)) (C_14 tptp.com)) (@ (@ tptp.hoare_1467856363rivs_a G_8) (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a (lambda ((Z_5 tptp.x_a) (S_2 tptp.state)) (and (@ (@ P_12 Z_5) S_2) (not (@ B_28 S_2))))) (@ (@ tptp.while B_28) C_14)) P_12)) tptp.bot_bo1791335050le_a_o))))
% 0.62/0.96 (assert (forall ((G_8 (-> tptp.hoare_1708887482_state Bool)) (P_12 (-> tptp.state tptp.state Bool)) (B_28 (-> tptp.state Bool)) (C_14 tptp.com)) (@ (@ tptp.hoare_90032982_state G_8) (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state (lambda ((Z_5 tptp.state) (S_2 tptp.state)) (and (@ (@ P_12 Z_5) S_2) (not (@ B_28 S_2))))) (@ (@ tptp.while B_28) C_14)) P_12)) tptp.bot_bo19817387tate_o))))
% 0.62/0.96 (assert (forall ((C tptp.com) (N_1 tptp.nat) (B (-> tptp.state Bool)) (S tptp.state)) (=> (not (@ B S)) (@ (@ (@ (@ tptp.evaln (@ (@ tptp.while B) C)) S) N_1) S))))
% 0.62/0.96 (assert (forall ((S2 tptp.state) (C 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)))) (=> (@ B S0) (=> (@ (@ (@ (@ tptp.evaln C) S0) N_1) S1) (=> (@ (@ (@ _let_1 S1) N_1) S2) (@ (@ (@ _let_1 S0) N_1) S2)))))))
% 0.62/0.96 (assert (forall ((S2 tptp.state) (C tptp.com) (S1 tptp.state) (B (-> tptp.state Bool)) (S0 tptp.state)) (let ((_let_1 (@ tptp.evalc (@ (@ tptp.while B) C)))) (=> (@ B S0) (=> (@ (@ (@ tptp.evalc C) S0) S1) (=> (@ (@ _let_1 S1) S2) (@ (@ _let_1 S0) S2)))))))
% 0.62/0.96 (assert (forall ((C tptp.com) (B (-> tptp.state Bool)) (S tptp.state)) (=> (not (@ B S)) (@ (@ (@ tptp.evalc (@ (@ tptp.while B) C)) S) S))))
% 0.62/0.96 (assert (forall ((S tptp.state) (N_1 tptp.nat)) (@ (@ (@ (@ tptp.evaln tptp.skip) S) N_1) S)))
% 0.62/0.96 (assert (forall ((S tptp.state) (N_1 tptp.nat) (T tptp.state)) (=> (@ (@ (@ (@ tptp.evaln tptp.skip) S) N_1) T) (= T S))))
% 0.62/0.96 (assert (forall ((S tptp.state) (T tptp.state)) (=> (@ (@ (@ tptp.evalc tptp.skip) S) T) (= T S))))
% 0.62/0.96 (assert (forall ((S tptp.state)) (@ (@ (@ tptp.evalc tptp.skip) S) S)))
% 0.62/0.96 (assert (forall ((Fun (-> tptp.state Bool)) (Com tptp.com)) (not (= tptp.skip (@ (@ tptp.while Fun) Com)))))
% 0.62/0.96 (assert (forall ((Fun (-> tptp.state Bool)) (Com tptp.com)) (not (= (@ (@ tptp.while Fun) Com) tptp.skip))))
% 0.62/0.96 (assert (forall ((Fun_1 (-> tptp.state Bool)) (Com_1 tptp.com) (Fun (-> tptp.state Bool)) (Com tptp.com)) (= (= (@ (@ tptp.while Fun_1) Com_1) (@ (@ tptp.while Fun) Com)) (and (= Fun_1 Fun) (= Com_1 Com)))))
% 0.62/0.96 (assert (forall ((C tptp.com) (S tptp.state) (N_1 tptp.nat) (S_4 tptp.state)) (let ((_let_1 (@ (@ tptp.evaln C) S))) (=> (@ (@ _let_1 N_1) S_4) (@ (@ _let_1 (@ tptp.suc N_1)) S_4)))))
% 0.62/0.96 (assert (forall ((C tptp.com) (S tptp.state) (N_1 tptp.nat) (T tptp.state)) (=> (@ (@ (@ (@ tptp.evaln C) S) N_1) T) (@ (@ (@ tptp.evalc C) S) T))))
% 0.62/0.96 (assert (forall ((C tptp.com) (S tptp.state) (T tptp.state)) (= (@ (@ (@ tptp.evalc C) S) T) (exists ((N tptp.nat)) (@ (@ (@ (@ tptp.evaln C) S) N) T)))))
% 0.62/0.96 (assert (forall ((Pname tptp.pname) (Fun_1 (-> tptp.state Bool)) (Com_1 tptp.com)) (not (= (@ tptp.body Pname) (@ (@ tptp.while Fun_1) Com_1)))))
% 0.62/0.96 (assert (forall ((Fun_1 (-> tptp.state Bool)) (Com_1 tptp.com) (Pname tptp.pname)) (not (= (@ (@ tptp.while Fun_1) Com_1) (@ tptp.body Pname)))))
% 0.62/0.96 (assert (forall ((Pname tptp.pname)) (not (= tptp.skip (@ tptp.body Pname)))))
% 0.62/0.96 (assert (forall ((Pname tptp.pname)) (not (= (@ tptp.body Pname) tptp.skip))))
% 0.62/0.96 (assert (forall ((N_4 tptp.nat) (P_11 (-> tptp.state tptp.state Bool)) (C_13 tptp.com) (Q_6 (-> tptp.state tptp.state Bool))) (= (@ (@ tptp.hoare_23738522_state N_4) (@ (@ (@ tptp.hoare_858012674_state P_11) C_13) Q_6)) (forall ((Z_5 tptp.state) (S_2 tptp.state)) (=> (@ (@ P_11 Z_5) S_2) (forall ((S_3 tptp.state)) (=> (@ (@ (@ (@ tptp.evaln C_13) S_2) N_4) S_3) (@ (@ Q_6 Z_5) S_3))))))))
% 0.62/0.96 (assert (forall ((N_4 tptp.nat) (P_11 (-> tptp.x_a tptp.state Bool)) (C_13 tptp.com) (Q_6 (-> tptp.x_a tptp.state Bool))) (= (@ (@ tptp.hoare_1421888935alid_a N_4) (@ (@ (@ tptp.hoare_657976383iple_a P_11) C_13) Q_6)) (forall ((Z_5 tptp.x_a) (S_2 tptp.state)) (=> (@ (@ P_11 Z_5) S_2) (forall ((S_3 tptp.state)) (=> (@ (@ (@ (@ tptp.evaln C_13) S_2) N_4) S_3) (@ (@ Q_6 Z_5) S_3))))))))
% 0.62/0.96 (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))))))))
% 0.62/0.96 (assert (forall ((B (-> tptp.state Bool)) (C tptp.com) (S tptp.state) (T tptp.state)) (let ((_let_1 (@ B S))) (=> (@ (@ (@ tptp.evalc (@ (@ tptp.while B) C)) S) T) (=> (=> (= T S) _let_1) (not (=> _let_1 (forall ((S1_1 tptp.state)) (=> (@ (@ (@ tptp.evalc C) S) S1_1) (not (@ (@ (@ tptp.evalc (@ (@ tptp.while B) C)) S1_1) T)))))))))))
% 0.62/0.96 (assert (forall ((B (-> tptp.state Bool)) (C tptp.com) (S tptp.state) (N_1 tptp.nat) (T tptp.state)) (let ((_let_1 (@ B S))) (=> (@ (@ (@ (@ tptp.evaln (@ (@ tptp.while B) C)) S) N_1) T) (=> (=> (= T S) _let_1) (not (=> _let_1 (forall ((S1_1 tptp.state)) (=> (@ (@ (@ (@ tptp.evaln C) S) N_1) S1_1) (not (@ (@ (@ (@ tptp.evaln (@ (@ tptp.while B) C)) S1_1) N_1) T)))))))))))
% 0.62/0.96 (assert (forall ((C tptp.com) (S tptp.state) (T tptp.state)) (=> (@ (@ (@ tptp.evalc C) S) T) (exists ((N tptp.nat)) (@ (@ (@ (@ tptp.evaln C) S) N) T)))))
% 0.62/0.96 (assert (forall ((D tptp.com) (R_1 (-> tptp.x_a tptp.state Bool)) (G_7 (-> tptp.hoare_2091234717iple_a Bool)) (P_10 (-> tptp.x_a tptp.state Bool)) (C_12 tptp.com) (Q_5 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_657976383iple_a P_10))) (let ((_let_2 (@ tptp.hoare_1467856363rivs_a G_7))) (=> (@ _let_2 (@ (@ tptp.insert1597628439iple_a (@ (@ _let_1 C_12) Q_5)) tptp.bot_bo1791335050le_a_o)) (=> (@ _let_2 (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a Q_5) D) R_1)) tptp.bot_bo1791335050le_a_o)) (@ _let_2 (@ (@ tptp.insert1597628439iple_a (@ (@ _let_1 (@ (@ tptp.semi C_12) D)) R_1)) tptp.bot_bo1791335050le_a_o))))))))
% 0.62/0.96 (assert (forall ((D tptp.com) (R_1 (-> tptp.state tptp.state Bool)) (G_7 (-> tptp.hoare_1708887482_state Bool)) (P_10 (-> tptp.state tptp.state Bool)) (C_12 tptp.com) (Q_5 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_858012674_state P_10))) (let ((_let_2 (@ tptp.hoare_90032982_state G_7))) (=> (@ _let_2 (@ (@ tptp.insert528405184_state (@ (@ _let_1 C_12) Q_5)) tptp.bot_bo19817387tate_o)) (=> (@ _let_2 (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state Q_5) D) R_1)) tptp.bot_bo19817387tate_o)) (@ _let_2 (@ (@ tptp.insert528405184_state (@ (@ _let_1 (@ (@ tptp.semi C_12) D)) R_1)) tptp.bot_bo19817387tate_o))))))))
% 0.62/0.96 (assert (forall ((X_21 (-> tptp.nat Bool))) (= (@ tptp.the_elem_nat X_21) (@ tptp.the_nat (lambda ((X tptp.nat)) (= X_21 (@ (@ tptp.insert_nat X) tptp.bot_bot_nat_o)))))))
% 0.62/0.96 (assert (forall ((X_21 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ tptp.the_el1618277441le_a_o X_21) (@ tptp.the_Ho2077879471le_a_o (lambda ((X (-> tptp.hoare_2091234717iple_a Bool))) (= X_21 (@ (@ tptp.insert102003750le_a_o X) tptp.bot_bo1957696069_a_o_o)))))))
% 0.62/0.96 (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)))))))
% 0.62/0.96 (assert (forall ((X_21 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ tptp.the_el13400124iple_a X_21) (@ tptp.the_Ho1471183438iple_a (lambda ((X tptp.hoare_2091234717iple_a)) (= X_21 (@ (@ tptp.insert1597628439iple_a X) tptp.bot_bo1791335050le_a_o)))))))
% 0.62/0.96 (assert (forall ((X_21 (-> tptp.hoare_1708887482_state Bool))) (= (@ tptp.the_el864710747_state X_21) (@ tptp.the_Ho851197897_state (lambda ((X tptp.hoare_1708887482_state)) (= X_21 (@ (@ tptp.insert528405184_state X) tptp.bot_bo19817387tate_o)))))))
% 0.62/0.96 (assert (forall ((P_8 (-> tptp.hoare_2091234717iple_a tptp.x_a tptp.state Bool)) (Q_4 (-> tptp.hoare_2091234717iple_a tptp.x_a tptp.state Bool)) (G_6 (-> tptp.hoare_2091234717iple_a Bool)) (P_7 (-> tptp.hoare_2091234717iple_a tptp.x_a tptp.state Bool)) (C0_1 (-> tptp.hoare_2091234717iple_a tptp.com)) (Q_3 (-> tptp.hoare_2091234717iple_a tptp.x_a tptp.state Bool)) (U_1 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.hoare_1467856363rivs_a G_6))) (=> (@ tptp.finite232261744iple_a U_1) (=> (forall ((P_9 tptp.hoare_2091234717iple_a)) (let ((_let_1 (@ C0_1 P_9))) (let ((_let_2 (@ tptp.hoare_1467856363rivs_a G_6))) (=> (@ _let_2 (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a (@ P_7 P_9)) _let_1) (@ Q_3 P_9))) tptp.bot_bo1791335050le_a_o)) (@ _let_2 (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a (@ P_8 P_9)) _let_1) (@ Q_4 P_9))) tptp.bot_bo1791335050le_a_o)))))) (=> (@ _let_1 (@ (@ tptp.image_1661191109iple_a (lambda ((P_9 tptp.hoare_2091234717iple_a)) (@ (@ (@ tptp.hoare_657976383iple_a (@ P_7 P_9)) (@ C0_1 P_9)) (@ Q_3 P_9)))) U_1)) (@ _let_1 (@ (@ tptp.image_1661191109iple_a (lambda ((P_9 tptp.hoare_2091234717iple_a)) (@ (@ (@ tptp.hoare_657976383iple_a (@ P_8 P_9)) (@ C0_1 P_9)) (@ Q_4 P_9)))) U_1))))))))
% 0.62/0.96 (assert (forall ((P_8 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.x_a tptp.state Bool)) (Q_4 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.x_a tptp.state Bool)) (G_6 (-> tptp.hoare_2091234717iple_a Bool)) (P_7 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.x_a tptp.state Bool)) (C0_1 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.com)) (Q_3 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.x_a tptp.state Bool)) (U_1 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.hoare_1467856363rivs_a G_6))) (=> (@ tptp.finite1829014797le_a_o U_1) (=> (forall ((P_9 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ C0_1 P_9))) (let ((_let_2 (@ tptp.hoare_1467856363rivs_a G_6))) (=> (@ _let_2 (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a (@ P_7 P_9)) _let_1) (@ Q_3 P_9))) tptp.bot_bo1791335050le_a_o)) (@ _let_2 (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a (@ P_8 P_9)) _let_1) (@ Q_4 P_9))) tptp.bot_bo1791335050le_a_o)))))) (=> (@ _let_1 (@ (@ tptp.image_136408202iple_a (lambda ((P_9 (-> tptp.hoare_2091234717iple_a Bool))) (@ (@ (@ tptp.hoare_657976383iple_a (@ P_7 P_9)) (@ C0_1 P_9)) (@ Q_3 P_9)))) U_1)) (@ _let_1 (@ (@ tptp.image_136408202iple_a (lambda ((P_9 (-> tptp.hoare_2091234717iple_a Bool))) (@ (@ (@ tptp.hoare_657976383iple_a (@ P_8 P_9)) (@ C0_1 P_9)) (@ Q_4 P_9)))) U_1))))))))
% 0.62/0.96 (assert (forall ((P_8 (-> tptp.pname tptp.state tptp.state Bool)) (Q_4 (-> tptp.pname tptp.state tptp.state Bool)) (G_6 (-> tptp.hoare_1708887482_state Bool)) (P_7 (-> tptp.pname tptp.state tptp.state Bool)) (C0_1 (-> tptp.pname tptp.com)) (Q_3 (-> tptp.pname tptp.state tptp.state Bool)) (U_1 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.hoare_90032982_state G_6))) (=> (@ tptp.finite_finite_pname U_1) (=> (forall ((P_9 tptp.pname)) (let ((_let_1 (@ C0_1 P_9))) (let ((_let_2 (@ tptp.hoare_90032982_state G_6))) (=> (@ _let_2 (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state (@ P_7 P_9)) _let_1) (@ Q_3 P_9))) tptp.bot_bo19817387tate_o)) (@ _let_2 (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state (@ P_8 P_9)) _let_1) (@ Q_4 P_9))) tptp.bot_bo19817387tate_o)))))) (=> (@ _let_1 (@ (@ tptp.image_1116629049_state (lambda ((P_9 tptp.pname)) (@ (@ (@ tptp.hoare_858012674_state (@ P_7 P_9)) (@ C0_1 P_9)) (@ Q_3 P_9)))) U_1)) (@ _let_1 (@ (@ tptp.image_1116629049_state (lambda ((P_9 tptp.pname)) (@ (@ (@ tptp.hoare_858012674_state (@ P_8 P_9)) (@ C0_1 P_9)) (@ Q_4 P_9)))) U_1))))))))
% 0.62/0.96 (assert (forall ((P_8 (-> tptp.hoare_2091234717iple_a tptp.state tptp.state Bool)) (Q_4 (-> tptp.hoare_2091234717iple_a tptp.state tptp.state Bool)) (G_6 (-> tptp.hoare_1708887482_state Bool)) (P_7 (-> tptp.hoare_2091234717iple_a tptp.state tptp.state Bool)) (C0_1 (-> tptp.hoare_2091234717iple_a tptp.com)) (Q_3 (-> tptp.hoare_2091234717iple_a tptp.state tptp.state Bool)) (U_1 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.hoare_90032982_state G_6))) (=> (@ tptp.finite232261744iple_a U_1) (=> (forall ((P_9 tptp.hoare_2091234717iple_a)) (let ((_let_1 (@ C0_1 P_9))) (let ((_let_2 (@ tptp.hoare_90032982_state G_6))) (=> (@ _let_2 (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state (@ P_7 P_9)) _let_1) (@ Q_3 P_9))) tptp.bot_bo19817387tate_o)) (@ _let_2 (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state (@ P_8 P_9)) _let_1) (@ Q_4 P_9))) tptp.bot_bo19817387tate_o)))))) (=> (@ _let_1 (@ (@ tptp.image_1884482962_state (lambda ((P_9 tptp.hoare_2091234717iple_a)) (@ (@ (@ tptp.hoare_858012674_state (@ P_7 P_9)) (@ C0_1 P_9)) (@ Q_3 P_9)))) U_1)) (@ _let_1 (@ (@ tptp.image_1884482962_state (lambda ((P_9 tptp.hoare_2091234717iple_a)) (@ (@ (@ tptp.hoare_858012674_state (@ P_8 P_9)) (@ C0_1 P_9)) (@ Q_4 P_9)))) U_1))))))))
% 0.62/0.96 (assert (forall ((P_8 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.state tptp.state Bool)) (Q_4 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.state tptp.state Bool)) (G_6 (-> tptp.hoare_1708887482_state Bool)) (P_7 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.state tptp.state Bool)) (C0_1 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.com)) (Q_3 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.state tptp.state Bool)) (U_1 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.hoare_90032982_state G_6))) (=> (@ tptp.finite1829014797le_a_o U_1) (=> (forall ((P_9 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ C0_1 P_9))) (let ((_let_2 (@ tptp.hoare_90032982_state G_6))) (=> (@ _let_2 (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state (@ P_7 P_9)) _let_1) (@ Q_3 P_9))) tptp.bot_bo19817387tate_o)) (@ _let_2 (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state (@ P_8 P_9)) _let_1) (@ Q_4 P_9))) tptp.bot_bo19817387tate_o)))))) (=> (@ _let_1 (@ (@ tptp.image_1501246093_state (lambda ((P_9 (-> tptp.hoare_2091234717iple_a Bool))) (@ (@ (@ tptp.hoare_858012674_state (@ P_7 P_9)) (@ C0_1 P_9)) (@ Q_3 P_9)))) U_1)) (@ _let_1 (@ (@ tptp.image_1501246093_state (lambda ((P_9 (-> tptp.hoare_2091234717iple_a Bool))) (@ (@ (@ tptp.hoare_858012674_state (@ P_8 P_9)) (@ C0_1 P_9)) (@ Q_4 P_9)))) U_1))))))))
% 0.62/0.96 (assert (forall ((P_8 (-> tptp.nat tptp.x_a tptp.state Bool)) (Q_4 (-> tptp.nat tptp.x_a tptp.state Bool)) (G_6 (-> tptp.hoare_2091234717iple_a Bool)) (P_7 (-> tptp.nat tptp.x_a tptp.state Bool)) (C0_1 (-> tptp.nat tptp.com)) (Q_3 (-> tptp.nat tptp.x_a tptp.state Bool)) (U_1 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.hoare_1467856363rivs_a G_6))) (=> (@ tptp.finite_finite_nat U_1) (=> (forall ((P_9 tptp.nat)) (let ((_let_1 (@ C0_1 P_9))) (let ((_let_2 (@ tptp.hoare_1467856363rivs_a G_6))) (=> (@ _let_2 (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a (@ P_7 P_9)) _let_1) (@ Q_3 P_9))) tptp.bot_bo1791335050le_a_o)) (@ _let_2 (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a (@ P_8 P_9)) _let_1) (@ Q_4 P_9))) tptp.bot_bo1791335050le_a_o)))))) (=> (@ _let_1 (@ (@ tptp.image_359186840iple_a (lambda ((P_9 tptp.nat)) (@ (@ (@ tptp.hoare_657976383iple_a (@ P_7 P_9)) (@ C0_1 P_9)) (@ Q_3 P_9)))) U_1)) (@ _let_1 (@ (@ tptp.image_359186840iple_a (lambda ((P_9 tptp.nat)) (@ (@ (@ tptp.hoare_657976383iple_a (@ P_8 P_9)) (@ C0_1 P_9)) (@ Q_4 P_9)))) U_1))))))))
% 0.62/0.96 (assert (forall ((P_8 (-> tptp.nat tptp.state tptp.state Bool)) (Q_4 (-> tptp.nat tptp.state tptp.state Bool)) (G_6 (-> tptp.hoare_1708887482_state Bool)) (P_7 (-> tptp.nat tptp.state tptp.state Bool)) (C0_1 (-> tptp.nat tptp.com)) (Q_3 (-> tptp.nat tptp.state tptp.state Bool)) (U_1 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.hoare_90032982_state G_6))) (=> (@ tptp.finite_finite_nat U_1) (=> (forall ((P_9 tptp.nat)) (let ((_let_1 (@ C0_1 P_9))) (let ((_let_2 (@ tptp.hoare_90032982_state G_6))) (=> (@ _let_2 (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state (@ P_7 P_9)) _let_1) (@ Q_3 P_9))) tptp.bot_bo19817387tate_o)) (@ _let_2 (@ (@ tptp.insert528405184_state (@ (@ (@ tptp.hoare_858012674_state (@ P_8 P_9)) _let_1) (@ Q_4 P_9))) tptp.bot_bo19817387tate_o)))))) (=> (@ _let_1 (@ (@ tptp.image_514827263_state (lambda ((P_9 tptp.nat)) (@ (@ (@ tptp.hoare_858012674_state (@ P_7 P_9)) (@ C0_1 P_9)) (@ Q_3 P_9)))) U_1)) (@ _let_1 (@ (@ tptp.image_514827263_state (lambda ((P_9 tptp.nat)) (@ (@ (@ tptp.hoare_858012674_state (@ P_8 P_9)) (@ C0_1 P_9)) (@ Q_4 P_9)))) U_1))))))))
% 0.62/0.96 (assert (forall ((P_8 (-> tptp.pname tptp.x_a tptp.state Bool)) (Q_4 (-> tptp.pname tptp.x_a tptp.state Bool)) (G_6 (-> tptp.hoare_2091234717iple_a Bool)) (P_7 (-> 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_1 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.hoare_1467856363rivs_a G_6))) (=> (@ tptp.finite_finite_pname U_1) (=> (forall ((P_9 tptp.pname)) (let ((_let_1 (@ C0_1 P_9))) (let ((_let_2 (@ tptp.hoare_1467856363rivs_a G_6))) (=> (@ _let_2 (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a (@ P_7 P_9)) _let_1) (@ Q_3 P_9))) tptp.bot_bo1791335050le_a_o)) (@ _let_2 (@ (@ tptp.insert1597628439iple_a (@ (@ (@ tptp.hoare_657976383iple_a (@ P_8 P_9)) _let_1) (@ Q_4 P_9))) tptp.bot_bo1791335050le_a_o)))))) (=> (@ _let_1 (@ (@ tptp.image_231808478iple_a (lambda ((P_9 tptp.pname)) (@ (@ (@ tptp.hoare_657976383iple_a (@ P_7 P_9)) (@ C0_1 P_9)) (@ Q_3 P_9)))) U_1)) (@ _let_1 (@ (@ tptp.image_231808478iple_a (lambda ((P_9 tptp.pname)) (@ (@ (@ tptp.hoare_657976383iple_a (@ P_8 P_9)) (@ C0_1 P_9)) (@ Q_4 P_9)))) U_1))))))))
% 0.62/0.96 (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)))))))
% 0.62/0.96 (assert (forall ((A_53 tptp.nat) (A_52 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat A_53) A_52) (exists ((B_26 (-> tptp.nat Bool))) (and (= A_52 (@ (@ tptp.insert_nat A_53) B_26)) (not (@ (@ tptp.member_nat A_53) B_26)))))))
% 0.62/0.96 (assert (forall ((A_53 (-> tptp.hoare_2091234717iple_a Bool)) (A_52 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (@ (@ tptp.member99268621le_a_o A_53) A_52) (exists ((B_26 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (and (= A_52 (@ (@ tptp.insert102003750le_a_o A_53) B_26)) (not (@ (@ tptp.member99268621le_a_o A_53) B_26)))))))
% 0.62/0.96 (assert (forall ((A_53 tptp.hoare_2091234717iple_a) (A_52 (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ (@ tptp.member290856304iple_a A_53) A_52) (exists ((B_26 (-> tptp.hoare_2091234717iple_a Bool))) (and (= A_52 (@ (@ tptp.insert1597628439iple_a A_53) B_26)) (not (@ (@ tptp.member290856304iple_a A_53) B_26)))))))
% 0.62/0.96 (assert (forall ((A_53 tptp.hoare_1708887482_state) (A_52 (-> tptp.hoare_1708887482_state Bool))) (=> (@ (@ tptp.member451959335_state A_53) A_52) (exists ((B_26 (-> tptp.hoare_1708887482_state Bool))) (and (= A_52 (@ (@ tptp.insert528405184_state A_53) B_26)) (not (@ (@ tptp.member451959335_state A_53) B_26)))))))
% 0.62/0.96 (assert (forall ((A_53 tptp.pname) (A_52 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname A_53) A_52) (exists ((B_26 (-> tptp.pname Bool))) (and (= A_52 (@ (@ tptp.insert_pname A_53) B_26)) (not (@ (@ tptp.member_pname A_53) B_26)))))))
% 0.62/0.96 (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)))))
% 0.62/0.96 (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)))))
% 0.62/0.96 (assert (forall ((Com1_1 tptp.com) (Com2_1 tptp.com) (Com1 tptp.com) (Com2 tptp.com)) (= (= (@ (@ tptp.semi Com1_1) Com2_1) (@ (@ tptp.semi Com1) Com2)) (and (= Com1_1 Com1) (= Com2_1 Com2)))))
% 0.62/0.96 (assert (forall ((Com1_1 tptp.com) (Com2_1 tptp.com) (Pname tptp.pname)) (not (= (@ (@ tptp.semi Com1_1) Com2_1) (@ tptp.body Pname)))))
% 0.62/0.96 (assert (forall ((Pname tptp.pname) (Com1_1 tptp.com) (Com2_1 tptp.com)) (not (= (@ tptp.body Pname) (@ (@ tptp.semi Com1_1) Com2_1)))))
% 0.62/0.96 (assert (forall ((Fun (-> tptp.state Bool)) (Com tptp.com) (Com1_1 tptp.com) (Com2_1 tptp.com)) (not (= (@ (@ tptp.while Fun) Com) (@ (@ tptp.semi Com1_1) Com2_1)))))
% 0.62/0.96 (assert (forall ((Com1_1 tptp.com) (Com2_1 tptp.com) (Fun (-> tptp.state Bool)) (Com tptp.com)) (not (= (@ (@ tptp.semi Com1_1) Com2_1) (@ (@ tptp.while Fun) Com)))))
% 0.62/0.96 (assert (forall ((Com1 tptp.com) (Com2 tptp.com)) (not (= (@ (@ tptp.semi Com1) Com2) tptp.skip))))
% 0.62/0.96 (assert (forall ((Com1 tptp.com) (Com2 tptp.com)) (not (= tptp.skip (@ (@ tptp.semi Com1) Com2)))))
% 0.62/0.96 (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))))))))
% 0.62/0.96 (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))))))))
% 0.62/0.96 (assert (forall ((H_1 (-> tptp.pname tptp.hoare_1708887482_state)) (F_35 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_35) (@ tptp.finite1625599783_state (@ (@ tptp.image_1116629049_state H_1) F_35)))))
% 0.62/0.96 (assert (forall ((H_1 (-> tptp.nat tptp.hoare_2091234717iple_a)) (F_35 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_35) (@ tptp.finite232261744iple_a (@ (@ tptp.image_359186840iple_a H_1) F_35)))))
% 0.62/0.96 (assert (forall ((H_1 (-> tptp.nat tptp.hoare_2091234717iple_a Bool)) (F_35 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_35) (@ tptp.finite1829014797le_a_o (@ (@ tptp.image_1995609573le_a_o H_1) F_35)))))
% 0.62/0.96 (assert (forall ((H_1 (-> tptp.nat tptp.pname)) (F_35 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_35) (@ tptp.finite_finite_pname (@ (@ tptp.image_nat_pname H_1) F_35)))))
% 0.62/0.96 (assert (forall ((H_1 (-> tptp.nat tptp.nat)) (F_35 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_35) (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_nat H_1) F_35)))))
% 0.62/0.96 (assert (forall ((H_1 (-> tptp.hoare_2091234717iple_a tptp.nat)) (F_35 (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ tptp.finite232261744iple_a F_35) (@ tptp.finite_finite_nat (@ (@ tptp.image_1773322034_a_nat H_1) F_35)))))
% 0.62/0.96 (assert (forall ((H_1 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.nat)) (F_35 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (@ tptp.finite1829014797le_a_o F_35) (@ tptp.finite_finite_nat (@ (@ tptp.image_75520503_o_nat H_1) F_35)))))
% 0.62/0.96 (assert (forall ((H_1 (-> tptp.pname tptp.nat)) (F_35 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_35) (@ tptp.finite_finite_nat (@ (@ tptp.image_pname_nat H_1) F_35)))))
% 0.62/0.96 (assert (forall ((H_1 (-> tptp.pname tptp.hoare_2091234717iple_a)) (F_35 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_35) (@ tptp.finite232261744iple_a (@ (@ tptp.image_231808478iple_a H_1) F_35)))))
% 0.62/0.96 (assert (forall ((A_51 (-> tptp.hoare_2091234717iple_a Bool)) (A_50 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (@ tptp.finite1829014797le_a_o A_50) (@ tptp.finite1829014797le_a_o (@ (@ tptp.insert102003750le_a_o A_51) A_50)))))
% 0.62/0.96 (assert (forall ((A_51 tptp.pname) (A_50 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_50) (@ tptp.finite_finite_pname (@ (@ tptp.insert_pname A_51) A_50)))))
% 0.62/0.96 (assert (forall ((A_51 tptp.hoare_2091234717iple_a) (A_50 (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ tptp.finite232261744iple_a A_50) (@ tptp.finite232261744iple_a (@ (@ tptp.insert1597628439iple_a A_51) A_50)))))
% 0.62/0.96 (assert (forall ((A_51 tptp.hoare_1708887482_state) (A_50 (-> tptp.hoare_1708887482_state Bool))) (=> (@ tptp.finite1625599783_state A_50) (@ tptp.finite1625599783_state (@ (@ tptp.insert528405184_state A_51) A_50)))))
% 0.62/0.96 (assert (forall ((A_51 tptp.nat) (A_50 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_50) (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A_51) A_50)))))
% 0.62/0.96 (assert (@ tptp.finite232261744iple_a tptp.bot_bo1791335050le_a_o))
% 0.62/0.96 (assert (@ tptp.finite1829014797le_a_o tptp.bot_bo1957696069_a_o_o))
% 0.62/0.96 (assert (@ tptp.finite_finite_pname tptp.bot_bot_pname_o))
% 0.62/0.96 (assert (@ tptp.finite1625599783_state tptp.bot_bo19817387tate_o))
% 0.62/0.96 (assert (@ tptp.finite_finite_nat tptp.bot_bot_nat_o))
% 0.62/0.96 (assert (forall ((Q_2 (-> tptp.pname Bool)) (P_6 (-> tptp.pname Bool))) (=> (or (@ tptp.finite_finite_pname (@ tptp.collect_pname P_6)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q_2))) (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X tptp.pname)) (and (@ P_6 X) (@ Q_2 X))))))))
% 0.62/0.96 (assert (forall ((Q_2 (-> tptp.hoare_2091234717iple_a Bool)) (P_6 (-> tptp.hoare_2091234717iple_a Bool))) (=> (or (@ tptp.finite232261744iple_a (@ tptp.collec992574898iple_a P_6)) (@ tptp.finite232261744iple_a (@ tptp.collec992574898iple_a Q_2))) (@ tptp.finite232261744iple_a (@ tptp.collec992574898iple_a (lambda ((X tptp.hoare_2091234717iple_a)) (and (@ P_6 X) (@ Q_2 X))))))))
% 0.62/0.96 (assert (forall ((Q_2 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (P_6 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (or (@ tptp.finite1829014797le_a_o (@ tptp.collec1008234059le_a_o P_6)) (@ tptp.finite1829014797le_a_o (@ tptp.collec1008234059le_a_o Q_2))) (@ tptp.finite1829014797le_a_o (@ tptp.collec1008234059le_a_o (lambda ((X (-> tptp.hoare_2091234717iple_a Bool))) (and (@ P_6 X) (@ Q_2 X))))))))
% 0.62/0.96 (assert (forall ((Q_2 (-> tptp.nat Bool)) (P_6 (-> tptp.nat Bool))) (=> (or (@ tptp.finite_finite_nat (@ tptp.collect_nat P_6)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q_2))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ P_6 X) (@ Q_2 X))))))))
% 0.62/0.96 (assert (forall ((F_34 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (G_5 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ tptp.finite1829014797le_a_o (@ (@ tptp.semila2050116131_a_o_o F_34) G_5)) (and (@ tptp.finite1829014797le_a_o F_34) (@ tptp.finite1829014797le_a_o G_5)))))
% 0.62/0.96 (assert (forall ((F_34 (-> tptp.pname Bool)) (G_5 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ (@ tptp.semila1780557381name_o F_34) G_5)) (and (@ tptp.finite_finite_pname F_34) (@ tptp.finite_finite_pname G_5)))))
% 0.62/0.96 (assert (forall ((F_34 (-> tptp.hoare_1708887482_state Bool)) (G_5 (-> tptp.hoare_1708887482_state Bool))) (= (@ tptp.finite1625599783_state (@ (@ tptp.semila1122118281tate_o F_34) G_5)) (and (@ tptp.finite1625599783_state F_34) (@ tptp.finite1625599783_state G_5)))))
% 0.62/0.96 (assert (forall ((F_34 (-> tptp.hoare_2091234717iple_a Bool)) (G_5 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ tptp.finite232261744iple_a (@ (@ tptp.semila1052848428le_a_o F_34) G_5)) (and (@ tptp.finite232261744iple_a F_34) (@ tptp.finite232261744iple_a G_5)))))
% 0.62/0.96 (assert (forall ((F_34 (-> tptp.nat Bool)) (G_5 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ (@ tptp.semila848761471_nat_o F_34) G_5)) (and (@ tptp.finite_finite_nat F_34) (@ tptp.finite_finite_nat G_5)))))
% 0.62/0.96 (assert (forall ((G_4 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (F_33 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (@ tptp.finite1829014797le_a_o F_33) (=> (@ tptp.finite1829014797le_a_o G_4) (@ tptp.finite1829014797le_a_o (@ (@ tptp.semila2050116131_a_o_o F_33) G_4))))))
% 0.62/0.96 (assert (forall ((G_4 (-> tptp.pname Bool)) (F_33 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_33) (=> (@ tptp.finite_finite_pname G_4) (@ tptp.finite_finite_pname (@ (@ tptp.semila1780557381name_o F_33) G_4))))))
% 0.62/0.96 (assert (forall ((G_4 (-> tptp.hoare_1708887482_state Bool)) (F_33 (-> tptp.hoare_1708887482_state Bool))) (=> (@ tptp.finite1625599783_state F_33) (=> (@ tptp.finite1625599783_state G_4) (@ tptp.finite1625599783_state (@ (@ tptp.semila1122118281tate_o F_33) G_4))))))
% 0.62/0.96 (assert (forall ((G_4 (-> tptp.hoare_2091234717iple_a Bool)) (F_33 (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ tptp.finite232261744iple_a F_33) (=> (@ tptp.finite232261744iple_a G_4) (@ tptp.finite232261744iple_a (@ (@ tptp.semila1052848428le_a_o F_33) G_4))))))
% 0.62/0.96 (assert (forall ((G_4 (-> tptp.nat Bool)) (F_33 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_33) (=> (@ tptp.finite_finite_nat G_4) (@ tptp.finite_finite_nat (@ (@ tptp.semila848761471_nat_o F_33) G_4))))))
% 0.62/0.96 (assert (forall ((P_5 (-> tptp.pname Bool)) (Q_1 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X tptp.pname)) (or (@ P_5 X) (@ Q_1 X))))) (and (@ tptp.finite_finite_pname (@ tptp.collect_pname P_5)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q_1))))))
% 0.62/0.96 (assert (forall ((P_5 (-> tptp.hoare_2091234717iple_a Bool)) (Q_1 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ tptp.finite232261744iple_a (@ tptp.collec992574898iple_a (lambda ((X tptp.hoare_2091234717iple_a)) (or (@ P_5 X) (@ Q_1 X))))) (and (@ tptp.finite232261744iple_a (@ tptp.collec992574898iple_a P_5)) (@ tptp.finite232261744iple_a (@ tptp.collec992574898iple_a Q_1))))))
% 0.62/0.96 (assert (forall ((P_5 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (Q_1 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ tptp.finite1829014797le_a_o (@ tptp.collec1008234059le_a_o (lambda ((X (-> tptp.hoare_2091234717iple_a Bool))) (or (@ P_5 X) (@ Q_1 X))))) (and (@ tptp.finite1829014797le_a_o (@ tptp.collec1008234059le_a_o P_5)) (@ tptp.finite1829014797le_a_o (@ tptp.collec1008234059le_a_o Q_1))))))
% 0.62/0.96 (assert (forall ((P_5 (-> tptp.nat Bool)) (Q_1 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (or (@ P_5 X) (@ Q_1 X))))) (and (@ tptp.finite_finite_nat (@ tptp.collect_nat P_5)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q_1))))))
% 0.62/0.96 (assert (forall ((A_49 (-> tptp.hoare_2091234717iple_a Bool)) (A_48 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ tptp.finite1829014797le_a_o (@ (@ tptp.insert102003750le_a_o A_49) A_48)) (@ tptp.finite1829014797le_a_o A_48))))
% 0.62/0.96 (assert (forall ((A_49 tptp.pname) (A_48 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ (@ tptp.insert_pname A_49) A_48)) (@ tptp.finite_finite_pname A_48))))
% 0.62/0.96 (assert (forall ((A_49 tptp.hoare_2091234717iple_a) (A_48 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ tptp.finite232261744iple_a (@ (@ tptp.insert1597628439iple_a A_49) A_48)) (@ tptp.finite232261744iple_a A_48))))
% 0.62/0.96 (assert (forall ((A_49 tptp.hoare_1708887482_state) (A_48 (-> tptp.hoare_1708887482_state Bool))) (= (@ tptp.finite1625599783_state (@ (@ tptp.insert528405184_state A_49) A_48)) (@ tptp.finite1625599783_state A_48))))
% 0.62/0.96 (assert (forall ((A_49 tptp.nat) (A_48 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A_49) A_48)) (@ tptp.finite_finite_nat A_48))))
% 0.62/0.96 (assert (forall ((P_4 (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) Bool)) (F_32 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (@ tptp.finite1829014797le_a_o F_32) (=> (@ P_4 tptp.bot_bo1957696069_a_o_o) (=> (forall ((X (-> tptp.hoare_2091234717iple_a Bool)) (F_25 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (@ tptp.finite1829014797le_a_o F_25) (=> (not (@ (@ tptp.member99268621le_a_o X) F_25)) (=> (@ P_4 F_25) (@ P_4 (@ (@ tptp.insert102003750le_a_o X) F_25)))))) (@ P_4 F_32))))))
% 0.62/0.96 (assert (forall ((P_4 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (F_32 (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ tptp.finite232261744iple_a F_32) (=> (@ P_4 tptp.bot_bo1791335050le_a_o) (=> (forall ((X tptp.hoare_2091234717iple_a) (F_25 (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ tptp.finite232261744iple_a F_25) (=> (not (@ (@ tptp.member290856304iple_a X) F_25)) (=> (@ P_4 F_25) (@ P_4 (@ (@ tptp.insert1597628439iple_a X) F_25)))))) (@ P_4 F_32))))))
% 0.62/0.96 (assert (forall ((P_4 (-> (-> tptp.hoare_1708887482_state Bool) Bool)) (F_32 (-> tptp.hoare_1708887482_state Bool))) (=> (@ tptp.finite1625599783_state F_32) (=> (@ P_4 tptp.bot_bo19817387tate_o) (=> (forall ((X tptp.hoare_1708887482_state) (F_25 (-> tptp.hoare_1708887482_state Bool))) (=> (@ tptp.finite1625599783_state F_25) (=> (not (@ (@ tptp.member451959335_state X) F_25)) (=> (@ P_4 F_25) (@ P_4 (@ (@ tptp.insert528405184_state X) F_25)))))) (@ P_4 F_32))))))
% 0.62/0.96 (assert (forall ((P_4 (-> (-> tptp.nat Bool) Bool)) (F_32 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_32) (=> (@ P_4 tptp.bot_bot_nat_o) (=> (forall ((X tptp.nat) (F_25 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_25) (=> (not (@ (@ tptp.member_nat X) F_25)) (=> (@ P_4 F_25) (@ P_4 (@ (@ tptp.insert_nat X) F_25)))))) (@ P_4 F_32))))))
% 0.62/0.96 (assert (forall ((P_4 (-> (-> tptp.pname Bool) Bool)) (F_32 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_32) (=> (@ P_4 tptp.bot_bot_pname_o) (=> (forall ((X tptp.pname) (F_25 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_25) (=> (not (@ (@ tptp.member_pname X) F_25)) (=> (@ P_4 F_25) (@ P_4 (@ (@ tptp.insert_pname X) F_25)))))) (@ P_4 F_32))))))
% 0.62/0.96 (assert (forall ((A_46 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ tptp.finite1829014797le_a_o A_46) (or (= A_46 tptp.bot_bo1957696069_a_o_o) (exists ((A_47 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (A_45 (-> tptp.hoare_2091234717iple_a Bool))) (and (= A_46 (@ (@ tptp.insert102003750le_a_o A_45) A_47)) (@ tptp.finite1829014797le_a_o A_47)))))))
% 0.62/0.96 (assert (forall ((A_46 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname A_46) (or (= A_46 tptp.bot_bot_pname_o) (exists ((A_47 (-> tptp.pname Bool)) (A_45 tptp.pname)) (and (= A_46 (@ (@ tptp.insert_pname A_45) A_47)) (@ tptp.finite_finite_pname A_47)))))))
% 0.62/0.96 (assert (forall ((A_46 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ tptp.finite232261744iple_a A_46) (or (= A_46 tptp.bot_bo1791335050le_a_o) (exists ((A_47 (-> tptp.hoare_2091234717iple_a Bool)) (A_45 tptp.hoare_2091234717iple_a)) (and (= A_46 (@ (@ tptp.insert1597628439iple_a A_45) A_47)) (@ tptp.finite232261744iple_a A_47)))))))
% 0.62/0.96 (assert (forall ((A_46 (-> tptp.hoare_1708887482_state Bool))) (= (@ tptp.finite1625599783_state A_46) (or (= A_46 tptp.bot_bo19817387tate_o) (exists ((A_47 (-> tptp.hoare_1708887482_state Bool)) (A_45 tptp.hoare_1708887482_state)) (and (= A_46 (@ (@ tptp.insert528405184_state A_45) A_47)) (@ tptp.finite1625599783_state A_47)))))))
% 0.62/0.96 (assert (forall ((A_46 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat A_46) (or (= A_46 tptp.bot_bot_nat_o) (exists ((A_47 (-> tptp.nat Bool)) (A_45 tptp.nat)) (and (= A_46 (@ (@ tptp.insert_nat A_45) A_47)) (@ tptp.finite_finite_nat A_47)))))))
% 0.62/0.96 (assert (forall ((F_31 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.nat)) (A_44 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (not (@ tptp.finite1829014797le_a_o A_44)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_75520503_o_nat F_31) A_44)) (exists ((X (-> tptp.hoare_2091234717iple_a Bool))) (and (@ (@ tptp.member99268621le_a_o X) A_44) (not (@ tptp.finite1829014797le_a_o (@ tptp.collec1008234059le_a_o (lambda ((A_45 (-> tptp.hoare_2091234717iple_a Bool))) (and (@ (@ tptp.member99268621le_a_o A_45) A_44) (= (@ F_31 A_45) (@ F_31 X)))))))))))))
% 0.62/0.96 (assert (forall ((F_31 (-> tptp.hoare_2091234717iple_a tptp.nat)) (A_44 (-> tptp.hoare_2091234717iple_a Bool))) (=> (not (@ tptp.finite232261744iple_a A_44)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_1773322034_a_nat F_31) A_44)) (exists ((X tptp.hoare_2091234717iple_a)) (and (@ (@ tptp.member290856304iple_a X) A_44) (not (@ tptp.finite232261744iple_a (@ tptp.collec992574898iple_a (lambda ((A_45 tptp.hoare_2091234717iple_a)) (and (@ (@ tptp.member290856304iple_a A_45) A_44) (= (@ F_31 A_45) (@ F_31 X)))))))))))))
% 0.62/0.96 (assert (forall ((F_31 (-> tptp.pname tptp.nat)) (A_44 (-> tptp.pname Bool))) (=> (not (@ tptp.finite_finite_pname A_44)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_pname_nat F_31) A_44)) (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) A_44) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_45 tptp.pname)) (and (@ (@ tptp.member_pname A_45) A_44) (= (@ F_31 A_45) (@ F_31 X)))))))))))))
% 0.62/0.96 (assert (forall ((F_31 (-> tptp.nat tptp.nat)) (A_44 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A_44)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_nat F_31) A_44)) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A_44) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A_45 tptp.nat)) (and (@ (@ tptp.member_nat A_45) A_44) (= (@ F_31 A_45) (@ F_31 X)))))))))))))
% 0.62/0.96 (assert (forall ((F_31 (-> tptp.nat tptp.hoare_2091234717iple_a)) (A_44 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A_44)) (=> (@ tptp.finite232261744iple_a (@ (@ tptp.image_359186840iple_a F_31) A_44)) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A_44) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A_45 tptp.nat)) (and (@ (@ tptp.member_nat A_45) A_44) (= (@ F_31 A_45) (@ F_31 X)))))))))))))
% 0.62/0.96 (assert (forall ((F_31 (-> tptp.nat tptp.hoare_2091234717iple_a Bool)) (A_44 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A_44)) (=> (@ tptp.finite1829014797le_a_o (@ (@ tptp.image_1995609573le_a_o F_31) A_44)) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A_44) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A_45 tptp.nat)) (and (@ (@ tptp.member_nat A_45) A_44) (= (@ F_31 A_45) (@ F_31 X)))))))))))))
% 0.62/0.96 (assert (forall ((F_31 (-> tptp.nat tptp.pname)) (A_44 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A_44)) (=> (@ tptp.finite_finite_pname (@ (@ tptp.image_nat_pname F_31) A_44)) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A_44) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A_45 tptp.nat)) (and (@ (@ tptp.member_nat A_45) A_44) (= (@ F_31 A_45) (@ F_31 X)))))))))))))
% 0.62/0.96 (assert (forall ((F_31 (-> tptp.pname tptp.hoare_1708887482_state)) (A_44 (-> tptp.pname Bool))) (=> (not (@ tptp.finite_finite_pname A_44)) (=> (@ tptp.finite1625599783_state (@ (@ tptp.image_1116629049_state F_31) A_44)) (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) A_44) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_45 tptp.pname)) (and (@ (@ tptp.member_pname A_45) A_44) (= (@ F_31 A_45) (@ F_31 X)))))))))))))
% 0.62/0.96 (assert (forall ((F_31 (-> tptp.pname tptp.hoare_2091234717iple_a Bool)) (A_44 (-> tptp.pname Bool))) (=> (not (@ tptp.finite_finite_pname A_44)) (=> (@ tptp.finite1829014797le_a_o (@ (@ tptp.image_742317343le_a_o F_31) A_44)) (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) A_44) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_45 tptp.pname)) (and (@ (@ tptp.member_pname A_45) A_44) (= (@ F_31 A_45) (@ F_31 X)))))))))))))
% 0.62/0.96 (assert (forall ((F_31 (-> tptp.pname tptp.pname)) (A_44 (-> tptp.pname Bool))) (=> (not (@ tptp.finite_finite_pname A_44)) (=> (@ tptp.finite_finite_pname (@ (@ tptp.image_pname_pname F_31) A_44)) (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) A_44) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_45 tptp.pname)) (and (@ (@ tptp.member_pname A_45) A_44) (= (@ F_31 A_45) (@ F_31 X)))))))))))))
% 0.62/0.96 (assert (forall ((F_31 (-> tptp.pname tptp.hoare_2091234717iple_a)) (A_44 (-> tptp.pname Bool))) (=> (not (@ tptp.finite_finite_pname A_44)) (=> (@ tptp.finite232261744iple_a (@ (@ tptp.image_231808478iple_a F_31) A_44)) (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) A_44) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_45 tptp.pname)) (and (@ (@ tptp.member_pname A_45) A_44) (= (@ F_31 A_45) (@ F_31 X)))))))))))))
% 0.62/0.96 (assert (forall ((A_43 (-> tptp.nat Bool))) (= (not (= A_43 tptp.bot_bot_nat_o)) (exists ((X tptp.nat) (B_26 (-> tptp.nat Bool))) (and (= A_43 (@ (@ tptp.insert_nat X) B_26)) (not (@ (@ tptp.member_nat X) B_26)))))))
% 0.62/0.96 (assert (forall ((A_43 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (not (= A_43 tptp.bot_bo1957696069_a_o_o)) (exists ((X (-> tptp.hoare_2091234717iple_a Bool)) (B_26 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (and (= A_43 (@ (@ tptp.insert102003750le_a_o X) B_26)) (not (@ (@ tptp.member99268621le_a_o X) B_26)))))))
% 0.62/0.96 (assert (forall ((A_43 (-> tptp.hoare_2091234717iple_a Bool))) (= (not (= A_43 tptp.bot_bo1791335050le_a_o)) (exists ((X tptp.hoare_2091234717iple_a) (B_26 (-> tptp.hoare_2091234717iple_a Bool))) (and (= A_43 (@ (@ tptp.insert1597628439iple_a X) B_26)) (not (@ (@ tptp.member290856304iple_a X) B_26)))))))
% 0.62/0.96 (assert (forall ((A_43 (-> tptp.hoare_1708887482_state Bool))) (= (not (= A_43 tptp.bot_bo19817387tate_o)) (exists ((X tptp.hoare_1708887482_state) (B_26 (-> tptp.hoare_1708887482_state Bool))) (and (= A_43 (@ (@ tptp.insert528405184_state X) B_26)) (not (@ (@ tptp.member451959335_state X) B_26)))))))
% 0.62/0.96 (assert (forall ((A_43 (-> tptp.pname Bool))) (= (not (= A_43 tptp.bot_bot_pname_o)) (exists ((X tptp.pname) (B_26 (-> tptp.pname Bool))) (and (= A_43 (@ (@ tptp.insert_pname X) B_26)) (not (@ (@ tptp.member_pname X) B_26)))))))
% 0.62/0.96 (assert (forall ((B_27 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (A_42 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (F_30 (-> (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool)) (F_29 (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.hoare_2091234717iple_a Bool))) (=> (@ (@ tptp.finite574580006le_a_o F_30) F_29) (=> (@ tptp.finite1829014797le_a_o A_42) (=> (not (= A_42 tptp.bot_bo1957696069_a_o_o)) (=> (@ tptp.finite1829014797le_a_o B_27) (=> (not (= B_27 tptp.bot_bo1957696069_a_o_o)) (= (@ F_29 (@ (@ tptp.semila2050116131_a_o_o A_42) B_27)) (@ (@ F_30 (@ F_29 A_42)) (@ F_29 B_27))))))))))
% 0.62/0.96 (assert (forall ((B_27 (-> tptp.pname Bool)) (A_42 (-> tptp.pname Bool)) (F_30 (-> tptp.pname tptp.pname tptp.pname)) (F_29 (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite89670078_pname F_30) F_29) (=> (@ tptp.finite_finite_pname A_42) (=> (not (= A_42 tptp.bot_bot_pname_o)) (=> (@ tptp.finite_finite_pname B_27) (=> (not (= B_27 tptp.bot_bot_pname_o)) (= (@ F_29 (@ (@ tptp.semila1780557381name_o A_42) B_27)) (@ (@ F_30 (@ F_29 A_42)) (@ F_29 B_27))))))))))
% 0.62/0.96 (assert (forall ((B_27 (-> tptp.hoare_1708887482_state Bool)) (A_42 (-> tptp.hoare_1708887482_state Bool)) (F_30 (-> tptp.hoare_1708887482_state tptp.hoare_1708887482_state tptp.hoare_1708887482_state)) (F_29 (-> (-> tptp.hoare_1708887482_state Bool) tptp.hoare_1708887482_state))) (=> (@ (@ tptp.finite1347568576_state F_30) F_29) (=> (@ tptp.finite1625599783_state A_42) (=> (not (= A_42 tptp.bot_bo19817387tate_o)) (=> (@ tptp.finite1625599783_state B_27) (=> (not (= B_27 tptp.bot_bo19817387tate_o)) (= (@ F_29 (@ (@ tptp.semila1122118281tate_o A_42) B_27)) (@ (@ F_30 (@ F_29 A_42)) (@ F_29 B_27))))))))))
% 0.62/0.96 (assert (forall ((B_27 (-> tptp.hoare_2091234717iple_a Bool)) (A_42 (-> tptp.hoare_2091234717iple_a Bool)) (F_30 (-> tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a)) (F_29 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a))) (=> (@ (@ tptp.finite1674555159iple_a F_30) F_29) (=> (@ tptp.finite232261744iple_a A_42) (=> (not (= A_42 tptp.bot_bo1791335050le_a_o)) (=> (@ tptp.finite232261744iple_a B_27) (=> (not (= B_27 tptp.bot_bo1791335050le_a_o)) (= (@ F_29 (@ (@ tptp.semila1052848428le_a_o A_42) B_27)) (@ (@ F_30 (@ F_29 A_42)) (@ F_29 B_27))))))))))
% 0.62/0.96 (assert (forall ((B_27 (-> tptp.nat Bool)) (A_42 (-> tptp.nat Bool)) (F_30 (-> tptp.nat tptp.nat tptp.nat)) (F_29 (-> (-> tptp.nat Bool) tptp.nat))) (=> (@ (@ tptp.finite795500164em_nat F_30) F_29) (=> (@ tptp.finite_finite_nat A_42) (=> (not (= A_42 tptp.bot_bot_nat_o)) (=> (@ tptp.finite_finite_nat B_27) (=> (not (= B_27 tptp.bot_bot_nat_o)) (= (@ F_29 (@ (@ tptp.semila848761471_nat_o A_42) B_27)) (@ (@ F_30 (@ F_29 A_42)) (@ F_29 B_27))))))))))
% 0.62/0.96 (assert (forall ((X_20 (-> tptp.hoare_2091234717iple_a Bool)) (A_41 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (F_28 (-> (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool)) (F_27 (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.hoare_2091234717iple_a Bool))) (=> (@ (@ tptp.finite574580006le_a_o F_28) F_27) (=> (@ tptp.finite1829014797le_a_o A_41) (=> (not (= A_41 tptp.bot_bo1957696069_a_o_o)) (= (@ F_27 (@ (@ tptp.insert102003750le_a_o X_20) A_41)) (@ (@ F_28 X_20) (@ F_27 A_41))))))))
% 0.62/0.96 (assert (forall ((X_20 tptp.pname) (A_41 (-> tptp.pname Bool)) (F_28 (-> tptp.pname tptp.pname tptp.pname)) (F_27 (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite89670078_pname F_28) F_27) (=> (@ tptp.finite_finite_pname A_41) (=> (not (= A_41 tptp.bot_bot_pname_o)) (= (@ F_27 (@ (@ tptp.insert_pname X_20) A_41)) (@ (@ F_28 X_20) (@ F_27 A_41))))))))
% 0.62/0.96 (assert (forall ((X_20 tptp.hoare_2091234717iple_a) (A_41 (-> tptp.hoare_2091234717iple_a Bool)) (F_28 (-> tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a)) (F_27 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a))) (=> (@ (@ tptp.finite1674555159iple_a F_28) F_27) (=> (@ tptp.finite232261744iple_a A_41) (=> (not (= A_41 tptp.bot_bo1791335050le_a_o)) (= (@ F_27 (@ (@ tptp.insert1597628439iple_a X_20) A_41)) (@ (@ F_28 X_20) (@ F_27 A_41))))))))
% 0.62/0.96 (assert (forall ((X_20 tptp.hoare_1708887482_state) (A_41 (-> tptp.hoare_1708887482_state Bool)) (F_28 (-> tptp.hoare_1708887482_state tptp.hoare_1708887482_state tptp.hoare_1708887482_state)) (F_27 (-> (-> tptp.hoare_1708887482_state Bool) tptp.hoare_1708887482_state))) (=> (@ (@ tptp.finite1347568576_state F_28) F_27) (=> (@ tptp.finite1625599783_state A_41) (=> (not (= A_41 tptp.bot_bo19817387tate_o)) (= (@ F_27 (@ (@ tptp.insert528405184_state X_20) A_41)) (@ (@ F_28 X_20) (@ F_27 A_41))))))))
% 0.62/0.96 (assert (forall ((X_20 tptp.nat) (A_41 (-> tptp.nat Bool)) (F_28 (-> tptp.nat tptp.nat tptp.nat)) (F_27 (-> (-> tptp.nat Bool) tptp.nat))) (=> (@ (@ tptp.finite795500164em_nat F_28) F_27) (=> (@ tptp.finite_finite_nat A_41) (=> (not (= A_41 tptp.bot_bot_nat_o)) (= (@ F_27 (@ (@ tptp.insert_nat X_20) A_41)) (@ (@ F_28 X_20) (@ F_27 A_41))))))))
% 0.62/0.96 (assert (forall ((F_26 (-> tptp.pname tptp.hoare_1708887482_state)) (A_40 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_40) (= (@ (@ tptp.image_1116629049_state F_26) A_40) (@ (@ (@ (@ tptp.finite2139561282_pname tptp.semila1122118281tate_o) (lambda ((X tptp.pname) (__flatten_var_0 tptp.hoare_1708887482_state)) (@ (@ (@ tptp.insert528405184_state (@ F_26 X)) tptp.bot_bo19817387tate_o) __flatten_var_0))) tptp.bot_bo19817387tate_o) A_40)))))
% 0.62/0.96 (assert (forall ((F_26 (-> tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a)) (A_40 (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ tptp.finite232261744iple_a A_40) (= (@ (@ tptp.image_1661191109iple_a F_26) A_40) (@ (@ (@ (@ tptp.finite1481787452iple_a tptp.semila1052848428le_a_o) (lambda ((X tptp.hoare_2091234717iple_a) (__flatten_var_0 tptp.hoare_2091234717iple_a)) (@ (@ (@ tptp.insert1597628439iple_a (@ F_26 X)) tptp.bot_bo1791335050le_a_o) __flatten_var_0))) tptp.bot_bo1791335050le_a_o) A_40)))))
% 0.62/0.96 (assert (forall ((F_26 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a)) (A_40 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (@ tptp.finite1829014797le_a_o A_40) (= (@ (@ tptp.image_136408202iple_a F_26) A_40) (@ (@ (@ (@ tptp.finite903029825le_a_o tptp.semila1052848428le_a_o) (lambda ((X (-> tptp.hoare_2091234717iple_a Bool)) (__flatten_var_0 tptp.hoare_2091234717iple_a)) (@ (@ (@ tptp.insert1597628439iple_a (@ F_26 X)) tptp.bot_bo1791335050le_a_o) __flatten_var_0))) tptp.bot_bo1791335050le_a_o) A_40)))))
% 0.62/0.96 (assert (forall ((F_26 (-> tptp.nat tptp.nat)) (A_40 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_40) (= (@ (@ tptp.image_nat_nat F_26) A_40) (@ (@ (@ (@ tptp.finite141655318_o_nat tptp.semila848761471_nat_o) (lambda ((X tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ (@ tptp.insert_nat (@ F_26 X)) tptp.bot_bot_nat_o) __flatten_var_0))) tptp.bot_bot_nat_o) A_40)))))
% 0.62/0.96 (assert (forall ((F_26 (-> tptp.nat tptp.hoare_2091234717iple_a Bool)) (A_40 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_40) (= (@ (@ tptp.image_1995609573le_a_o F_26) A_40) (@ (@ (@ (@ tptp.finite2009943022_o_nat tptp.semila2050116131_a_o_o) (lambda ((X tptp.nat) (__flatten_var_0 (-> tptp.hoare_2091234717iple_a Bool))) (@ (@ (@ tptp.insert102003750le_a_o (@ F_26 X)) tptp.bot_bo1957696069_a_o_o) __flatten_var_0))) tptp.bot_bo1957696069_a_o_o) A_40)))))
% 0.62/0.96 (assert (forall ((F_26 (-> tptp.nat tptp.pname)) (A_40 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_40) (= (@ (@ tptp.image_nat_pname F_26) A_40) (@ (@ (@ (@ tptp.finite1427591632_o_nat tptp.semila1780557381name_o) (lambda ((X tptp.nat) (__flatten_var_0 tptp.pname)) (@ (@ (@ tptp.insert_pname (@ F_26 X)) tptp.bot_bot_pname_o) __flatten_var_0))) tptp.bot_bot_pname_o) A_40)))))
% 0.62/0.96 (assert (forall ((F_26 (-> tptp.nat tptp.hoare_2091234717iple_a)) (A_40 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_40) (= (@ (@ tptp.image_359186840iple_a F_26) A_40) (@ (@ (@ (@ tptp.finite2100865449_o_nat tptp.semila1052848428le_a_o) (lambda ((X tptp.nat) (__flatten_var_0 tptp.hoare_2091234717iple_a)) (@ (@ (@ tptp.insert1597628439iple_a (@ F_26 X)) tptp.bot_bo1791335050le_a_o) __flatten_var_0))) tptp.bot_bo1791335050le_a_o) A_40)))))
% 0.62/0.96 (assert (forall ((F_26 (-> tptp.nat tptp.hoare_1708887482_state)) (A_40 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_40) (= (@ (@ tptp.image_514827263_state F_26) A_40) (@ (@ (@ (@ tptp.finite1400355848_o_nat tptp.semila1122118281tate_o) (lambda ((X tptp.nat) (__flatten_var_0 tptp.hoare_1708887482_state)) (@ (@ (@ tptp.insert528405184_state (@ F_26 X)) tptp.bot_bo19817387tate_o) __flatten_var_0))) tptp.bot_bo19817387tate_o) A_40)))))
% 0.62/0.96 (assert (forall ((F_26 (-> tptp.pname tptp.hoare_2091234717iple_a)) (A_40 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_40) (= (@ (@ tptp.image_231808478iple_a F_26) A_40) (@ (@ (@ (@ tptp.finite1290357347_pname tptp.semila1052848428le_a_o) (lambda ((X tptp.pname) (__flatten_var_0 tptp.hoare_2091234717iple_a)) (@ (@ (@ tptp.insert1597628439iple_a (@ F_26 X)) tptp.bot_bo1791335050le_a_o) __flatten_var_0))) tptp.bot_bo1791335050le_a_o) A_40)))))
% 0.62/0.96 (assert (forall ((P_3 (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) Bool)) (F_24 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (@ tptp.finite1829014797le_a_o F_24) (=> (not (= F_24 tptp.bot_bo1957696069_a_o_o)) (=> (forall ((X (-> tptp.hoare_2091234717iple_a Bool))) (@ P_3 (@ (@ tptp.insert102003750le_a_o X) tptp.bot_bo1957696069_a_o_o))) (=> (forall ((X (-> tptp.hoare_2091234717iple_a Bool)) (F_25 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (@ tptp.finite1829014797le_a_o F_25) (=> (not (= F_25 tptp.bot_bo1957696069_a_o_o)) (=> (not (@ (@ tptp.member99268621le_a_o X) F_25)) (=> (@ P_3 F_25) (@ P_3 (@ (@ tptp.insert102003750le_a_o X) F_25))))))) (@ P_3 F_24)))))))
% 0.62/0.96 (assert (forall ((P_3 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (F_24 (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ tptp.finite232261744iple_a F_24) (=> (not (= F_24 tptp.bot_bo1791335050le_a_o)) (=> (forall ((X tptp.hoare_2091234717iple_a)) (@ P_3 (@ (@ tptp.insert1597628439iple_a X) tptp.bot_bo1791335050le_a_o))) (=> (forall ((X tptp.hoare_2091234717iple_a) (F_25 (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ tptp.finite232261744iple_a F_25) (=> (not (= F_25 tptp.bot_bo1791335050le_a_o)) (=> (not (@ (@ tptp.member290856304iple_a X) F_25)) (=> (@ P_3 F_25) (@ P_3 (@ (@ tptp.insert1597628439iple_a X) F_25))))))) (@ P_3 F_24)))))))
% 0.62/0.96 (assert (forall ((P_3 (-> (-> tptp.hoare_1708887482_state Bool) Bool)) (F_24 (-> tptp.hoare_1708887482_state Bool))) (=> (@ tptp.finite1625599783_state F_24) (=> (not (= F_24 tptp.bot_bo19817387tate_o)) (=> (forall ((X tptp.hoare_1708887482_state)) (@ P_3 (@ (@ tptp.insert528405184_state X) tptp.bot_bo19817387tate_o))) (=> (forall ((X tptp.hoare_1708887482_state) (F_25 (-> tptp.hoare_1708887482_state Bool))) (=> (@ tptp.finite1625599783_state F_25) (=> (not (= F_25 tptp.bot_bo19817387tate_o)) (=> (not (@ (@ tptp.member451959335_state X) F_25)) (=> (@ P_3 F_25) (@ P_3 (@ (@ tptp.insert528405184_state X) F_25))))))) (@ P_3 F_24)))))))
% 0.62/0.96 (assert (forall ((P_3 (-> (-> tptp.nat Bool) Bool)) (F_24 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_24) (=> (not (= F_24 tptp.bot_bot_nat_o)) (=> (forall ((X tptp.nat)) (@ P_3 (@ (@ tptp.insert_nat X) tptp.bot_bot_nat_o))) (=> (forall ((X tptp.nat) (F_25 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_25) (=> (not (= F_25 tptp.bot_bot_nat_o)) (=> (not (@ (@ tptp.member_nat X) F_25)) (=> (@ P_3 F_25) (@ P_3 (@ (@ tptp.insert_nat X) F_25))))))) (@ P_3 F_24)))))))
% 0.62/0.96 (assert (forall ((P_3 (-> (-> tptp.pname Bool) Bool)) (F_24 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_24) (=> (not (= F_24 tptp.bot_bot_pname_o)) (=> (forall ((X tptp.pname)) (@ P_3 (@ (@ tptp.insert_pname X) tptp.bot_bot_pname_o))) (=> (forall ((X tptp.pname) (F_25 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_25) (=> (not (= F_25 tptp.bot_bot_pname_o)) (=> (not (@ (@ tptp.member_pname X) F_25)) (=> (@ P_3 F_25) (@ P_3 (@ (@ tptp.insert_pname X) F_25))))))) (@ P_3 F_24)))))))
% 0.62/0.96 (assert (forall ((X_19 tptp.nat) (F_23 (-> tptp.nat tptp.nat tptp.nat)) (F_22 (-> (-> tptp.nat Bool) tptp.nat))) (=> (@ (@ tptp.finite795500164em_nat F_23) F_22) (= (@ (@ F_23 X_19) X_19) X_19))))
% 0.62/0.96 (assert (forall ((X_19 tptp.pname) (F_23 (-> tptp.pname tptp.pname tptp.pname)) (F_22 (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite89670078_pname F_23) F_22) (= (@ (@ F_23 X_19) X_19) X_19))))
% 0.62/0.96 (assert (forall ((X_19 tptp.hoare_2091234717iple_a) (F_23 (-> tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a)) (F_22 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a))) (=> (@ (@ tptp.finite1674555159iple_a F_23) F_22) (= (@ (@ F_23 X_19) X_19) X_19))))
% 0.62/0.96 (assert (forall ((F_21 (-> (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool)) (G_3 (-> tptp.pname tptp.hoare_2091234717iple_a Bool)) (Z_4 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ (@ (@ tptp.finite1290357347_pname F_21) G_3) Z_4) tptp.bot_bot_pname_o) Z_4)))
% 0.62/0.96 (assert (forall ((X_18 (-> tptp.hoare_2091234717iple_a Bool)) (A_39 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (F_20 (-> (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool)) (F_19 (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ F_19 A_39))) (=> (@ (@ tptp.finite574580006le_a_o F_20) F_19) (=> (@ tptp.finite1829014797le_a_o A_39) (=> (@ (@ tptp.member99268621le_a_o X_18) A_39) (= (@ (@ F_20 X_18) _let_1) _let_1)))))))
% 0.62/0.96 (assert (forall ((X_18 tptp.hoare_2091234717iple_a) (A_39 (-> tptp.hoare_2091234717iple_a Bool)) (F_20 (-> tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a)) (F_19 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a))) (let ((_let_1 (@ F_19 A_39))) (=> (@ (@ tptp.finite1674555159iple_a F_20) F_19) (=> (@ tptp.finite232261744iple_a A_39) (=> (@ (@ tptp.member290856304iple_a X_18) A_39) (= (@ (@ F_20 X_18) _let_1) _let_1)))))))
% 0.62/0.96 (assert (forall ((X_18 tptp.nat) (A_39 (-> tptp.nat Bool)) (F_20 (-> tptp.nat tptp.nat tptp.nat)) (F_19 (-> (-> tptp.nat Bool) tptp.nat))) (let ((_let_1 (@ F_19 A_39))) (=> (@ (@ tptp.finite795500164em_nat F_20) F_19) (=> (@ tptp.finite_finite_nat A_39) (=> (@ (@ tptp.member_nat X_18) A_39) (= (@ (@ F_20 X_18) _let_1) _let_1)))))))
% 0.62/0.96 (assert (forall ((X_18 tptp.pname) (A_39 (-> tptp.pname Bool)) (F_20 (-> tptp.pname tptp.pname tptp.pname)) (F_19 (-> (-> tptp.pname Bool) tptp.pname))) (let ((_let_1 (@ F_19 A_39))) (=> (@ (@ tptp.finite89670078_pname F_20) F_19) (=> (@ tptp.finite_finite_pname A_39) (=> (@ (@ tptp.member_pname X_18) A_39) (= (@ (@ F_20 X_18) _let_1) _let_1)))))))
% 0.62/0.96 (assert (forall ((N_3 (-> tptp.hoare_2091234717iple_a Bool)) (H (-> tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a)) (F_18 (-> tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a)) (F_17 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a))) (=> (@ (@ tptp.finite1674555159iple_a F_18) F_17) (=> (forall ((X tptp.hoare_2091234717iple_a) (Y_7 tptp.hoare_2091234717iple_a)) (= (@ H (@ (@ F_18 X) Y_7)) (@ (@ F_18 (@ H X)) (@ H Y_7)))) (=> (@ tptp.finite232261744iple_a N_3) (=> (not (= N_3 tptp.bot_bo1791335050le_a_o)) (= (@ H (@ F_17 N_3)) (@ F_17 (@ (@ tptp.image_1661191109iple_a H) N_3)))))))))
% 0.62/0.96 (assert (forall ((N_3 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (H (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool)) (F_18 (-> (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool)) (F_17 (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.hoare_2091234717iple_a Bool))) (=> (@ (@ tptp.finite574580006le_a_o F_18) F_17) (=> (forall ((X (-> tptp.hoare_2091234717iple_a Bool)) (Y_7 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ H (@ (@ F_18 X) Y_7)) (@ (@ F_18 (@ H X)) (@ H Y_7)))) (=> (@ tptp.finite1829014797le_a_o N_3) (=> (not (= N_3 tptp.bot_bo1957696069_a_o_o)) (= (@ H (@ F_17 N_3)) (@ F_17 (@ (@ tptp.image_784579955le_a_o H) N_3)))))))))
% 0.62/0.96 (assert (forall ((N_3 (-> tptp.pname Bool)) (H (-> tptp.pname tptp.pname)) (F_18 (-> tptp.pname tptp.pname tptp.pname)) (F_17 (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite89670078_pname F_18) F_17) (=> (forall ((X tptp.pname) (Y_7 tptp.pname)) (= (@ H (@ (@ F_18 X) Y_7)) (@ (@ F_18 (@ H X)) (@ H Y_7)))) (=> (@ tptp.finite_finite_pname N_3) (=> (not (= N_3 tptp.bot_bot_pname_o)) (= (@ H (@ F_17 N_3)) (@ F_17 (@ (@ tptp.image_pname_pname H) N_3)))))))))
% 0.62/0.96 (assert (forall ((N_3 (-> tptp.hoare_1708887482_state Bool)) (H (-> tptp.hoare_1708887482_state tptp.hoare_1708887482_state)) (F_18 (-> tptp.hoare_1708887482_state tptp.hoare_1708887482_state tptp.hoare_1708887482_state)) (F_17 (-> (-> tptp.hoare_1708887482_state Bool) tptp.hoare_1708887482_state))) (=> (@ (@ tptp.finite1347568576_state F_18) F_17) (=> (forall ((X tptp.hoare_1708887482_state) (Y_7 tptp.hoare_1708887482_state)) (= (@ H (@ (@ F_18 X) Y_7)) (@ (@ F_18 (@ H X)) (@ H Y_7)))) (=> (@ tptp.finite1625599783_state N_3) (=> (not (= N_3 tptp.bot_bo19817387tate_o)) (= (@ H (@ F_17 N_3)) (@ F_17 (@ (@ tptp.image_757158439_state H) N_3)))))))))
% 0.62/0.96 (assert (forall ((N_3 (-> tptp.nat Bool)) (H (-> tptp.nat tptp.nat)) (F_18 (-> tptp.nat tptp.nat tptp.nat)) (F_17 (-> (-> tptp.nat Bool) tptp.nat))) (=> (@ (@ tptp.finite795500164em_nat F_18) F_17) (=> (forall ((X tptp.nat) (Y_7 tptp.nat)) (= (@ H (@ (@ F_18 X) Y_7)) (@ (@ F_18 (@ H X)) (@ H Y_7)))) (=> (@ tptp.finite_finite_nat N_3) (=> (not (= N_3 tptp.bot_bot_nat_o)) (= (@ H (@ F_17 N_3)) (@ F_17 (@ (@ tptp.image_nat_nat H) N_3)))))))))
% 0.62/0.96 (assert (forall ((G_2 (-> tptp.pname tptp.hoare_2091234717iple_a Bool)) (A_38 (-> tptp.pname Bool)) (F_16 (-> (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool)) (Z_3 (-> tptp.hoare_2091234717iple_a Bool)) (F_15 (-> (-> tptp.pname tptp.hoare_2091234717iple_a Bool) (-> tptp.pname Bool) tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ (@ F_15 G_2) A_38))) (let ((_let_2 (@ tptp.finite_finite_pname A_38))) (=> (@ (@ (@ tptp.big_co1924420859_pname F_16) Z_3) F_15) (and (=> _let_2 (= _let_1 (@ (@ (@ (@ tptp.finite1290357347_pname F_16) G_2) Z_3) A_38))) (=> (not _let_2) (= _let_1 Z_3))))))))
% 0.62/0.96 (assert (forall ((X_17 (-> tptp.hoare_2091234717iple_a Bool)) (A_37 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (F_14 (-> (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool)) (F_13 (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.hoare_2091234717iple_a Bool))) (=> (@ (@ tptp.finite14499299le_a_o F_14) F_13) (=> (@ tptp.finite1829014797le_a_o A_37) (=> (not (@ (@ tptp.member99268621le_a_o X_17) A_37)) (=> (not (= A_37 tptp.bot_bo1957696069_a_o_o)) (= (@ F_13 (@ (@ tptp.insert102003750le_a_o X_17) A_37)) (@ (@ F_14 X_17) (@ F_13 A_37)))))))))
% 0.62/0.96 (assert (forall ((X_17 tptp.hoare_2091234717iple_a) (A_37 (-> tptp.hoare_2091234717iple_a Bool)) (F_14 (-> tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a)) (F_13 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a))) (=> (@ (@ tptp.finite247037978iple_a F_14) F_13) (=> (@ tptp.finite232261744iple_a A_37) (=> (not (@ (@ tptp.member290856304iple_a X_17) A_37)) (=> (not (= A_37 tptp.bot_bo1791335050le_a_o)) (= (@ F_13 (@ (@ tptp.insert1597628439iple_a X_17) A_37)) (@ (@ F_14 X_17) (@ F_13 A_37)))))))))
% 0.62/0.96 (assert (forall ((X_17 tptp.hoare_1708887482_state) (A_37 (-> tptp.hoare_1708887482_state Bool)) (F_14 (-> tptp.hoare_1708887482_state tptp.hoare_1708887482_state tptp.hoare_1708887482_state)) (F_13 (-> (-> tptp.hoare_1708887482_state Bool) tptp.hoare_1708887482_state))) (=> (@ (@ tptp.finite1615457021_state F_14) F_13) (=> (@ tptp.finite1625599783_state A_37) (=> (not (@ (@ tptp.member451959335_state X_17) A_37)) (=> (not (= A_37 tptp.bot_bo19817387tate_o)) (= (@ F_13 (@ (@ tptp.insert528405184_state X_17) A_37)) (@ (@ F_14 X_17) (@ F_13 A_37)))))))))
% 0.62/0.96 (assert (forall ((X_17 tptp.nat) (A_37 (-> tptp.nat Bool)) (F_14 (-> tptp.nat tptp.nat tptp.nat)) (F_13 (-> (-> tptp.nat Bool) tptp.nat))) (=> (@ (@ tptp.finite988810631ne_nat F_14) F_13) (=> (@ tptp.finite_finite_nat A_37) (=> (not (@ (@ tptp.member_nat X_17) A_37)) (=> (not (= A_37 tptp.bot_bot_nat_o)) (= (@ F_13 (@ (@ tptp.insert_nat X_17) A_37)) (@ (@ F_14 X_17) (@ F_13 A_37)))))))))
% 0.62/0.96 (assert (forall ((X_17 tptp.pname) (A_37 (-> tptp.pname Bool)) (F_14 (-> tptp.pname tptp.pname tptp.pname)) (F_13 (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite1282449217_pname F_14) F_13) (=> (@ tptp.finite_finite_pname A_37) (=> (not (@ (@ tptp.member_pname X_17) A_37)) (=> (not (= A_37 tptp.bot_bot_pname_o)) (= (@ F_13 (@ (@ tptp.insert_pname X_17) A_37)) (@ (@ F_14 X_17) (@ F_13 A_37)))))))))
% 0.62/0.96 (assert (forall ((X_16 tptp.nat) (F_12 (-> tptp.nat tptp.nat tptp.nat)) (F_11 (-> (-> tptp.nat Bool) tptp.nat))) (=> (@ (@ tptp.finite988810631ne_nat F_12) F_11) (= (@ F_11 (@ (@ tptp.insert_nat X_16) tptp.bot_bot_nat_o)) X_16))))
% 0.62/0.96 (assert (forall ((X_16 (-> tptp.hoare_2091234717iple_a Bool)) (F_12 (-> (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool)) (F_11 (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.hoare_2091234717iple_a Bool))) (=> (@ (@ tptp.finite14499299le_a_o F_12) F_11) (= (@ F_11 (@ (@ tptp.insert102003750le_a_o X_16) tptp.bot_bo1957696069_a_o_o)) X_16))))
% 0.62/0.96 (assert (forall ((X_16 tptp.pname) (F_12 (-> tptp.pname tptp.pname tptp.pname)) (F_11 (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite1282449217_pname F_12) F_11) (= (@ F_11 (@ (@ tptp.insert_pname X_16) tptp.bot_bot_pname_o)) X_16))))
% 0.62/0.96 (assert (forall ((X_16 tptp.hoare_2091234717iple_a) (F_12 (-> tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a)) (F_11 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a))) (=> (@ (@ tptp.finite247037978iple_a F_12) F_11) (= (@ F_11 (@ (@ tptp.insert1597628439iple_a X_16) tptp.bot_bo1791335050le_a_o)) X_16))))
% 0.62/0.96 (assert (forall ((X_16 tptp.hoare_1708887482_state) (F_12 (-> tptp.hoare_1708887482_state tptp.hoare_1708887482_state tptp.hoare_1708887482_state)) (F_11 (-> (-> tptp.hoare_1708887482_state Bool) tptp.hoare_1708887482_state))) (=> (@ (@ tptp.finite1615457021_state F_12) F_11) (= (@ F_11 (@ (@ tptp.insert528405184_state X_16) tptp.bot_bo19817387tate_o)) X_16))))
% 0.62/0.96 (assert (forall ((A_36 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (F_10 (-> (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool)) (F_9 (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.hoare_2091234717iple_a Bool))) (=> (@ (@ tptp.finite14499299le_a_o F_10) F_9) (=> (@ tptp.finite1829014797le_a_o A_36) (=> (not (= A_36 tptp.bot_bo1957696069_a_o_o)) (=> (forall ((X (-> tptp.hoare_2091234717iple_a Bool)) (Y_7 (-> tptp.hoare_2091234717iple_a Bool))) (@ (@ tptp.member99268621le_a_o (@ (@ F_10 X) Y_7)) (@ (@ tptp.insert102003750le_a_o X) (@ (@ tptp.insert102003750le_a_o Y_7) tptp.bot_bo1957696069_a_o_o)))) (@ (@ tptp.member99268621le_a_o (@ F_9 A_36)) A_36)))))))
% 0.62/0.96 (assert (forall ((A_36 (-> tptp.hoare_2091234717iple_a Bool)) (F_10 (-> tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a)) (F_9 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a))) (=> (@ (@ tptp.finite247037978iple_a F_10) F_9) (=> (@ tptp.finite232261744iple_a A_36) (=> (not (= A_36 tptp.bot_bo1791335050le_a_o)) (=> (forall ((X tptp.hoare_2091234717iple_a) (Y_7 tptp.hoare_2091234717iple_a)) (@ (@ tptp.member290856304iple_a (@ (@ F_10 X) Y_7)) (@ (@ tptp.insert1597628439iple_a X) (@ (@ tptp.insert1597628439iple_a Y_7) tptp.bot_bo1791335050le_a_o)))) (@ (@ tptp.member290856304iple_a (@ F_9 A_36)) A_36)))))))
% 0.62/0.96 (assert (forall ((A_36 (-> tptp.hoare_1708887482_state Bool)) (F_10 (-> tptp.hoare_1708887482_state tptp.hoare_1708887482_state tptp.hoare_1708887482_state)) (F_9 (-> (-> tptp.hoare_1708887482_state Bool) tptp.hoare_1708887482_state))) (=> (@ (@ tptp.finite1615457021_state F_10) F_9) (=> (@ tptp.finite1625599783_state A_36) (=> (not (= A_36 tptp.bot_bo19817387tate_o)) (=> (forall ((X tptp.hoare_1708887482_state) (Y_7 tptp.hoare_1708887482_state)) (@ (@ tptp.member451959335_state (@ (@ F_10 X) Y_7)) (@ (@ tptp.insert528405184_state X) (@ (@ tptp.insert528405184_state Y_7) tptp.bot_bo19817387tate_o)))) (@ (@ tptp.member451959335_state (@ F_9 A_36)) A_36)))))))
% 0.62/0.96 (assert (forall ((A_36 (-> tptp.nat Bool)) (F_10 (-> tptp.nat tptp.nat tptp.nat)) (F_9 (-> (-> tptp.nat Bool) tptp.nat))) (=> (@ (@ tptp.finite988810631ne_nat F_10) F_9) (=> (@ tptp.finite_finite_nat A_36) (=> (not (= A_36 tptp.bot_bot_nat_o)) (=> (forall ((X tptp.nat) (Y_7 tptp.nat)) (@ (@ tptp.member_nat (@ (@ F_10 X) Y_7)) (@ (@ tptp.insert_nat X) (@ (@ tptp.insert_nat Y_7) tptp.bot_bot_nat_o)))) (@ (@ tptp.member_nat (@ F_9 A_36)) A_36)))))))
% 0.62/0.96 (assert (forall ((A_36 (-> 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_36) (=> (not (= A_36 tptp.bot_bot_pname_o)) (=> (forall ((X tptp.pname) (Y_7 tptp.pname)) (@ (@ tptp.member_pname (@ (@ F_10 X) Y_7)) (@ (@ tptp.insert_pname X) (@ (@ tptp.insert_pname Y_7) tptp.bot_bot_pname_o)))) (@ (@ tptp.member_pname (@ F_9 A_36)) A_36)))))))
% 0.62/0.96 (assert (forall ((X_15 tptp.nat) (A_35 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_15) A_35) (not (forall ((B_26 (-> tptp.nat Bool))) (=> (= A_35 (@ (@ tptp.insert_nat X_15) B_26)) (@ (@ tptp.member_nat X_15) B_26)))))))
% 0.62/0.96 (assert (forall ((X_15 (-> tptp.hoare_2091234717iple_a Bool)) (A_35 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (@ (@ tptp.member99268621le_a_o X_15) A_35) (not (forall ((B_26 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (= A_35 (@ (@ tptp.insert102003750le_a_o X_15) B_26)) (@ (@ tptp.member99268621le_a_o X_15) B_26)))))))
% 0.62/0.96 (assert (forall ((X_15 tptp.hoare_2091234717iple_a) (A_35 (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ (@ tptp.member290856304iple_a X_15) A_35) (not (forall ((B_26 (-> tptp.hoare_2091234717iple_a Bool))) (=> (= A_35 (@ (@ tptp.insert1597628439iple_a X_15) B_26)) (@ (@ tptp.member290856304iple_a X_15) B_26)))))))
% 0.62/0.96 (assert (forall ((X_15 tptp.hoare_1708887482_state) (A_35 (-> tptp.hoare_1708887482_state Bool))) (=> (@ (@ tptp.member451959335_state X_15) A_35) (not (forall ((B_26 (-> tptp.hoare_1708887482_state Bool))) (=> (= A_35 (@ (@ tptp.insert528405184_state X_15) B_26)) (@ (@ tptp.member451959335_state X_15) B_26)))))))
% 0.62/0.96 (assert (forall ((X_15 tptp.pname) (A_35 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_15) A_35) (not (forall ((B_26 (-> tptp.pname Bool))) (=> (= A_35 (@ (@ tptp.insert_pname X_15) B_26)) (@ (@ tptp.member_pname X_15) B_26)))))))
% 0.62/0.96 (assert (forall ((A_34 (-> tptp.nat Bool))) (=> (forall ((Y_7 tptp.nat)) (not (@ (@ tptp.member_nat Y_7) A_34))) (= A_34 tptp.bot_bot_nat_o))))
% 0.62/0.96 (assert (forall ((A_34 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (forall ((Y_7 (-> tptp.hoare_2091234717iple_a Bool))) (not (@ (@ tptp.member99268621le_a_o Y_7) A_34))) (= A_34 tptp.bot_bo1957696069_a_o_o))))
% 0.62/0.96 (assert (forall ((A_34 (-> tptp.hoare_2091234717iple_a Bool))) (=> (forall ((Y_7 tptp.hoare_2091234717iple_a)) (not (@ (@ tptp.member290856304iple_a Y_7) A_34))) (= A_34 tptp.bot_bo1791335050le_a_o))))
% 0.62/0.96 (assert (forall ((A_34 (-> tptp.hoare_1708887482_state Bool))) (=> (forall ((Y_7 tptp.hoare_1708887482_state)) (not (@ (@ tptp.member451959335_state Y_7) A_34))) (= A_34 tptp.bot_bo19817387tate_o))))
% 0.62/0.96 (assert (forall ((A_34 (-> tptp.pname Bool))) (=> (forall ((Y_7 tptp.pname)) (not (@ (@ tptp.member_pname Y_7) A_34))) (= A_34 tptp.bot_bot_pname_o))))
% 0.62/0.96 (assert (forall ((B_25 (-> (-> tptp.nat Bool) Bool)) (A_33 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_33) (=> (not (= A_33 tptp.bot_bot_nat_o_o)) (=> (@ tptp.finite_finite_nat_o B_25) (=> (not (= B_25 tptp.bot_bot_nat_o_o)) (= (@ tptp.big_la1658356148_nat_o (@ (@ tptp.semila72246288at_o_o A_33) B_25)) (@ (@ tptp.semila848761471_nat_o (@ tptp.big_la1658356148_nat_o A_33)) (@ tptp.big_la1658356148_nat_o B_25)))))))))
% 0.62/0.96 (assert (forall ((B_25 (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) Bool)) (A_33 (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) Bool))) (=> (@ tptp.finite886417794_a_o_o A_33) (=> (not (= A_33 tptp.bot_bo690906872_o_o_o)) (=> (@ tptp.finite886417794_a_o_o B_25) (=> (not (= B_25 tptp.bot_bo690906872_o_o_o)) (= (@ tptp.big_la1994307886_a_o_o (@ (@ tptp.semila484278426_o_o_o A_33) B_25)) (@ (@ tptp.semila2050116131_a_o_o (@ tptp.big_la1994307886_a_o_o A_33)) (@ tptp.big_la1994307886_a_o_o B_25)))))))))
% 0.62/0.96 (assert (forall ((B_25 (-> (-> tptp.hoare_1708887482_state Bool) Bool)) (A_33 (-> (-> tptp.hoare_1708887482_state Bool) Bool))) (=> (@ tptp.finite1329924456tate_o A_33) (=> (not (= A_33 tptp.bot_bo1678742418te_o_o)) (=> (@ tptp.finite1329924456tate_o B_25) (=> (not (= B_25 tptp.bot_bo1678742418te_o_o)) (= (@ tptp.big_la1088302868tate_o (@ (@ tptp.semila1853742644te_o_o A_33) B_25)) (@ (@ tptp.semila1122118281tate_o (@ tptp.big_la1088302868tate_o A_33)) (@ tptp.big_la1088302868tate_o B_25)))))))))
% 0.62/0.96 (assert (forall ((B_25 (-> (-> tptp.pname Bool) Bool)) (A_33 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_33) (=> (not (= A_33 tptp.bot_bot_pname_o_o)) (=> (@ tptp.finite297249702name_o B_25) (=> (not (= B_25 tptp.bot_bot_pname_o_o)) (= (@ tptp.big_la1286884090name_o (@ (@ tptp.semila181081674me_o_o A_33) B_25)) (@ (@ tptp.semila1780557381name_o (@ tptp.big_la1286884090name_o A_33)) (@ tptp.big_la1286884090name_o B_25)))))))))
% 0.62/0.96 (assert (forall ((B_25 (-> Bool Bool)) (A_33 (-> Bool Bool))) (=> (@ tptp.finite_finite_o A_33) (=> (not (= A_33 tptp.bot_bot_o_o)) (=> (@ tptp.finite_finite_o B_25) (=> (not (= B_25 tptp.bot_bot_o_o)) (= (@ tptp.big_la727467310_fin_o (@ (@ tptp.semila2062604954up_o_o A_33) B_25)) (@ (@ tptp.semila10642723_sup_o (@ tptp.big_la727467310_fin_o A_33)) (@ tptp.big_la727467310_fin_o B_25)))))))))
% 0.62/0.96 (assert (forall ((B_25 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (A_33 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (@ tptp.finite1829014797le_a_o A_33) (=> (not (= A_33 tptp.bot_bo1957696069_a_o_o)) (=> (@ tptp.finite1829014797le_a_o B_25) (=> (not (= B_25 tptp.bot_bo1957696069_a_o_o)) (= (@ tptp.big_la735727201le_a_o (@ (@ tptp.semila2050116131_a_o_o A_33) B_25)) (@ (@ tptp.semila1052848428le_a_o (@ tptp.big_la735727201le_a_o A_33)) (@ tptp.big_la735727201le_a_o B_25)))))))))
% 0.62/0.96 (assert (forall ((B_25 (-> tptp.nat Bool)) (A_33 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_33) (=> (not (= A_33 tptp.bot_bot_nat_o)) (=> (@ tptp.finite_finite_nat B_25) (=> (not (= B_25 tptp.bot_bot_nat_o)) (= (@ tptp.big_la43341705in_nat (@ (@ tptp.semila848761471_nat_o A_33) B_25)) (@ (@ tptp.semila972727038up_nat (@ tptp.big_la43341705in_nat A_33)) (@ tptp.big_la43341705in_nat B_25)))))))))
% 0.62/0.96 (assert (forall ((X_14 (-> tptp.nat Bool)) (A_32 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_32) (=> (not (@ (@ tptp.member_nat_o X_14) A_32)) (=> (not (= A_32 tptp.bot_bot_nat_o_o)) (= (@ tptp.big_la1658356148_nat_o (@ (@ tptp.insert_nat_o X_14) A_32)) (@ (@ tptp.semila848761471_nat_o X_14) (@ tptp.big_la1658356148_nat_o A_32))))))))
% 0.62/0.96 (assert (forall ((X_14 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (A_32 (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) Bool))) (=> (@ tptp.finite886417794_a_o_o A_32) (=> (not (@ (@ tptp.member1297825410_a_o_o X_14) A_32)) (=> (not (= A_32 tptp.bot_bo690906872_o_o_o)) (= (@ tptp.big_la1994307886_a_o_o (@ (@ tptp.insert987231145_a_o_o X_14) A_32)) (@ (@ tptp.semila2050116131_a_o_o X_14) (@ tptp.big_la1994307886_a_o_o A_32))))))))
% 0.62/0.96 (assert (forall ((X_14 (-> tptp.hoare_1708887482_state Bool)) (A_32 (-> (-> tptp.hoare_1708887482_state Bool) Bool))) (=> (@ tptp.finite1329924456tate_o A_32) (=> (not (@ (@ tptp.member814030440tate_o X_14) A_32)) (=> (not (= A_32 tptp.bot_bo1678742418te_o_o)) (= (@ tptp.big_la1088302868tate_o (@ (@ tptp.insert949073679tate_o X_14) A_32)) (@ (@ tptp.semila1122118281tate_o X_14) (@ tptp.big_la1088302868tate_o A_32))))))))
% 0.62/0.96 (assert (forall ((X_14 (-> tptp.pname Bool)) (A_32 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_32) (=> (not (@ (@ tptp.member_pname_o X_14) A_32)) (=> (not (= A_32 tptp.bot_bot_pname_o_o)) (= (@ tptp.big_la1286884090name_o (@ (@ tptp.insert_pname_o X_14) A_32)) (@ (@ tptp.semila1780557381name_o X_14) (@ tptp.big_la1286884090name_o A_32))))))))
% 0.62/0.96 (assert (forall ((X_14 Bool) (A_32 (-> Bool Bool))) (=> (@ tptp.finite_finite_o A_32) (=> (not (@ (@ tptp.member_o X_14) A_32)) (=> (not (= A_32 tptp.bot_bot_o_o)) (= (@ tptp.big_la727467310_fin_o (@ (@ tptp.insert_o X_14) A_32)) (@ (@ tptp.semila10642723_sup_o X_14) (@ tptp.big_la727467310_fin_o A_32))))))))
% 0.62/0.96 (assert (forall ((X_14 (-> tptp.hoare_2091234717iple_a Bool)) (A_32 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (@ tptp.finite1829014797le_a_o A_32) (=> (not (@ (@ tptp.member99268621le_a_o X_14) A_32)) (=> (not (= A_32 tptp.bot_bo1957696069_a_o_o)) (= (@ tptp.big_la735727201le_a_o (@ (@ tptp.insert102003750le_a_o X_14) A_32)) (@ (@ tptp.semila1052848428le_a_o X_14) (@ tptp.big_la735727201le_a_o A_32))))))))
% 0.62/0.96 (assert (forall ((X_14 tptp.nat) (A_32 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_32) (=> (not (@ (@ tptp.member_nat X_14) A_32)) (=> (not (= A_32 tptp.bot_bot_nat_o)) (= (@ tptp.big_la43341705in_nat (@ (@ tptp.insert_nat X_14) A_32)) (@ (@ tptp.semila972727038up_nat X_14) (@ tptp.big_la43341705in_nat A_32))))))))
% 0.62/0.96 (assert (forall ((X_13 (-> tptp.nat Bool)) (A_31 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_31) (=> (not (= A_31 tptp.bot_bot_nat_o_o)) (= (@ tptp.big_la1658356148_nat_o (@ (@ tptp.insert_nat_o X_13) A_31)) (@ (@ tptp.semila848761471_nat_o X_13) (@ tptp.big_la1658356148_nat_o A_31)))))))
% 0.62/0.96 (assert (forall ((X_13 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (A_31 (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) Bool))) (=> (@ tptp.finite886417794_a_o_o A_31) (=> (not (= A_31 tptp.bot_bo690906872_o_o_o)) (= (@ tptp.big_la1994307886_a_o_o (@ (@ tptp.insert987231145_a_o_o X_13) A_31)) (@ (@ tptp.semila2050116131_a_o_o X_13) (@ tptp.big_la1994307886_a_o_o A_31)))))))
% 0.62/0.96 (assert (forall ((X_13 (-> tptp.hoare_1708887482_state Bool)) (A_31 (-> (-> tptp.hoare_1708887482_state Bool) Bool))) (=> (@ tptp.finite1329924456tate_o A_31) (=> (not (= A_31 tptp.bot_bo1678742418te_o_o)) (= (@ tptp.big_la1088302868tate_o (@ (@ tptp.insert949073679tate_o X_13) A_31)) (@ (@ tptp.semila1122118281tate_o X_13) (@ tptp.big_la1088302868tate_o A_31)))))))
% 0.62/0.96 (assert (forall ((X_13 (-> tptp.pname Bool)) (A_31 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_31) (=> (not (= A_31 tptp.bot_bot_pname_o_o)) (= (@ tptp.big_la1286884090name_o (@ (@ tptp.insert_pname_o X_13) A_31)) (@ (@ tptp.semila1780557381name_o X_13) (@ tptp.big_la1286884090name_o A_31)))))))
% 0.62/0.96 (assert (forall ((X_13 Bool) (A_31 (-> Bool Bool))) (=> (@ tptp.finite_finite_o A_31) (=> (not (= A_31 tptp.bot_bot_o_o)) (= (@ tptp.big_la727467310_fin_o (@ (@ tptp.insert_o X_13) A_31)) (@ (@ tptp.semila10642723_sup_o X_13) (@ tptp.big_la727467310_fin_o A_31)))))))
% 0.62/0.96 (assert (forall ((X_13 (-> tptp.hoare_2091234717iple_a Bool)) (A_31 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (@ tptp.finite1829014797le_a_o A_31) (=> (not (= A_31 tptp.bot_bo1957696069_a_o_o)) (= (@ tptp.big_la735727201le_a_o (@ (@ tptp.insert102003750le_a_o X_13) A_31)) (@ (@ tptp.semila1052848428le_a_o X_13) (@ tptp.big_la735727201le_a_o A_31)))))))
% 0.62/0.96 (assert (forall ((X_13 tptp.nat) (A_31 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_31) (=> (not (= A_31 tptp.bot_bot_nat_o)) (= (@ tptp.big_la43341705in_nat (@ (@ tptp.insert_nat X_13) A_31)) (@ (@ tptp.semila972727038up_nat X_13) (@ tptp.big_la43341705in_nat A_31)))))))
% 0.62/0.96 (assert (forall ((B_24 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (A_30 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (F_8 (-> (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool)) (F_7 (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.hoare_2091234717iple_a Bool))) (=> (@ (@ tptp.finite14499299le_a_o F_8) F_7) (=> (@ tptp.finite1829014797le_a_o A_30) (=> (not (= A_30 tptp.bot_bo1957696069_a_o_o)) (=> (@ tptp.finite1829014797le_a_o B_24) (=> (not (= B_24 tptp.bot_bo1957696069_a_o_o)) (=> (= (@ (@ tptp.semila1672913213_a_o_o A_30) B_24) tptp.bot_bo1957696069_a_o_o) (= (@ F_7 (@ (@ tptp.semila2050116131_a_o_o A_30) B_24)) (@ (@ F_8 (@ F_7 A_30)) (@ F_7 B_24)))))))))))
% 0.62/0.96 (assert (forall ((B_24 (-> tptp.pname Bool)) (A_30 (-> tptp.pname Bool)) (F_8 (-> tptp.pname tptp.pname tptp.pname)) (F_7 (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite1282449217_pname F_8) F_7) (=> (@ tptp.finite_finite_pname A_30) (=> (not (= A_30 tptp.bot_bot_pname_o)) (=> (@ tptp.finite_finite_pname B_24) (=> (not (= B_24 tptp.bot_bot_pname_o)) (=> (= (@ (@ tptp.semila1673364395name_o A_30) B_24) tptp.bot_bot_pname_o) (= (@ F_7 (@ (@ tptp.semila1780557381name_o A_30) B_24)) (@ (@ F_8 (@ F_7 A_30)) (@ F_7 B_24)))))))))))
% 0.62/0.96 (assert (forall ((B_24 (-> tptp.hoare_1708887482_state Bool)) (A_30 (-> tptp.hoare_1708887482_state Bool)) (F_8 (-> tptp.hoare_1708887482_state tptp.hoare_1708887482_state tptp.hoare_1708887482_state)) (F_7 (-> (-> tptp.hoare_1708887482_state Bool) tptp.hoare_1708887482_state))) (=> (@ (@ tptp.finite1615457021_state F_8) F_7) (=> (@ tptp.finite1625599783_state A_30) (=> (not (= A_30 tptp.bot_bo19817387tate_o)) (=> (@ tptp.finite1625599783_state B_24) (=> (not (= B_24 tptp.bot_bo19817387tate_o)) (=> (= (@ (@ tptp.semila129691299tate_o A_30) B_24) tptp.bot_bo19817387tate_o) (= (@ F_7 (@ (@ tptp.semila1122118281tate_o A_30) B_24)) (@ (@ F_8 (@ F_7 A_30)) (@ F_7 B_24)))))))))))
% 0.62/0.96 (assert (forall ((B_24 (-> tptp.hoare_2091234717iple_a Bool)) (A_30 (-> tptp.hoare_2091234717iple_a Bool)) (F_8 (-> tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a)) (F_7 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a))) (=> (@ (@ tptp.finite247037978iple_a F_8) F_7) (=> (@ tptp.finite232261744iple_a A_30) (=> (not (= A_30 tptp.bot_bo1791335050le_a_o)) (=> (@ tptp.finite232261744iple_a B_24) (=> (not (= B_24 tptp.bot_bo1791335050le_a_o)) (=> (= (@ (@ tptp.semila2006181266le_a_o A_30) B_24) tptp.bot_bo1791335050le_a_o) (= (@ F_7 (@ (@ tptp.semila1052848428le_a_o A_30) B_24)) (@ (@ F_8 (@ F_7 A_30)) (@ F_7 B_24)))))))))))
% 0.62/0.96 (assert (forall ((B_24 (-> tptp.nat Bool)) (A_30 (-> tptp.nat Bool)) (F_8 (-> tptp.nat tptp.nat tptp.nat)) (F_7 (-> (-> tptp.nat Bool) tptp.nat))) (=> (@ (@ tptp.finite988810631ne_nat F_8) F_7) (=> (@ tptp.finite_finite_nat A_30) (=> (not (= A_30 tptp.bot_bot_nat_o)) (=> (@ tptp.finite_finite_nat B_24) (=> (not (= B_24 tptp.bot_bot_nat_o)) (=> (= (@ (@ tptp.semila1947288293_nat_o A_30) B_24) tptp.bot_bot_nat_o) (= (@ F_7 (@ (@ tptp.semila848761471_nat_o A_30) B_24)) (@ (@ F_8 (@ F_7 A_30)) (@ F_7 B_24)))))))))))
% 0.62/0.96 (assert (forall ((B_23 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (A_29 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (F_6 (-> (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool)) (F_5 (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ (@ tptp.semila1672913213_a_o_o A_29) B_23))) (=> (@ (@ tptp.finite14499299le_a_o F_6) F_5) (=> (@ tptp.finite1829014797le_a_o A_29) (=> (@ tptp.finite1829014797le_a_o B_23) (=> (not (= _let_1 tptp.bot_bo1957696069_a_o_o)) (= (@ (@ F_6 (@ F_5 (@ (@ tptp.semila2050116131_a_o_o A_29) B_23))) (@ F_5 _let_1)) (@ (@ F_6 (@ F_5 A_29)) (@ F_5 B_23))))))))))
% 0.62/0.96 (assert (forall ((B_23 (-> tptp.pname Bool)) (A_29 (-> tptp.pname Bool)) (F_6 (-> tptp.pname tptp.pname tptp.pname)) (F_5 (-> (-> tptp.pname Bool) tptp.pname))) (let ((_let_1 (@ (@ tptp.semila1673364395name_o A_29) B_23))) (=> (@ (@ tptp.finite1282449217_pname F_6) F_5) (=> (@ tptp.finite_finite_pname A_29) (=> (@ tptp.finite_finite_pname B_23) (=> (not (= _let_1 tptp.bot_bot_pname_o)) (= (@ (@ F_6 (@ F_5 (@ (@ tptp.semila1780557381name_o A_29) B_23))) (@ F_5 _let_1)) (@ (@ F_6 (@ F_5 A_29)) (@ F_5 B_23))))))))))
% 0.62/0.96 (assert (forall ((B_23 (-> tptp.hoare_1708887482_state Bool)) (A_29 (-> tptp.hoare_1708887482_state Bool)) (F_6 (-> tptp.hoare_1708887482_state tptp.hoare_1708887482_state tptp.hoare_1708887482_state)) (F_5 (-> (-> tptp.hoare_1708887482_state Bool) tptp.hoare_1708887482_state))) (let ((_let_1 (@ (@ tptp.semila129691299tate_o A_29) B_23))) (=> (@ (@ tptp.finite1615457021_state F_6) F_5) (=> (@ tptp.finite1625599783_state A_29) (=> (@ tptp.finite1625599783_state B_23) (=> (not (= _let_1 tptp.bot_bo19817387tate_o)) (= (@ (@ F_6 (@ F_5 (@ (@ tptp.semila1122118281tate_o A_29) B_23))) (@ F_5 _let_1)) (@ (@ F_6 (@ F_5 A_29)) (@ F_5 B_23))))))))))
% 0.62/0.96 (assert (forall ((B_23 (-> tptp.hoare_2091234717iple_a Bool)) (A_29 (-> tptp.hoare_2091234717iple_a Bool)) (F_6 (-> tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a)) (F_5 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a))) (let ((_let_1 (@ (@ tptp.semila2006181266le_a_o A_29) B_23))) (=> (@ (@ tptp.finite247037978iple_a F_6) F_5) (=> (@ tptp.finite232261744iple_a A_29) (=> (@ tptp.finite232261744iple_a B_23) (=> (not (= _let_1 tptp.bot_bo1791335050le_a_o)) (= (@ (@ F_6 (@ F_5 (@ (@ tptp.semila1052848428le_a_o A_29) B_23))) (@ F_5 _let_1)) (@ (@ F_6 (@ F_5 A_29)) (@ F_5 B_23))))))))))
% 0.62/0.96 (assert (forall ((B_23 (-> tptp.nat Bool)) (A_29 (-> tptp.nat Bool)) (F_6 (-> tptp.nat tptp.nat tptp.nat)) (F_5 (-> (-> tptp.nat Bool) tptp.nat))) (let ((_let_1 (@ (@ tptp.semila1947288293_nat_o A_29) B_23))) (=> (@ (@ tptp.finite988810631ne_nat F_6) F_5) (=> (@ tptp.finite_finite_nat A_29) (=> (@ tptp.finite_finite_nat B_23) (=> (not (= _let_1 tptp.bot_bot_nat_o)) (= (@ (@ F_6 (@ F_5 (@ (@ tptp.semila848761471_nat_o A_29) B_23))) (@ F_5 _let_1)) (@ (@ F_6 (@ F_5 A_29)) (@ F_5 B_23))))))))))
% 0.62/0.96 (assert (forall ((X_12 (-> tptp.hoare_2091234717iple_a Bool)) (A_28 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (F_4 (-> (-> tptp.hoare_2091234717iple_a Bool) (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a Bool)) (F_3 (-> (-> (-> tptp.hoare_2091234717iple_a Bool) Bool) tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.insert102003750le_a_o X_12))) (let ((_let_2 (@ (@ tptp.minus_1746272704_a_o_o A_28) (@ _let_1 tptp.bot_bo1957696069_a_o_o)))) (let ((_let_3 (@ F_3 (@ _let_1 A_28)))) (let ((_let_4 (= _let_2 tptp.bot_bo1957696069_a_o_o))) (=> (@ (@ tptp.finite14499299le_a_o F_4) F_3) (=> (@ tptp.finite1829014797le_a_o A_28) (and (=> _let_4 (= _let_3 X_12)) (=> (not _let_4) (= _let_3 (@ (@ F_4 X_12) (@ F_3 _let_2)))))))))))))
% 0.62/0.96 (assert (forall ((X_12 tptp.pname) (A_28 (-> tptp.pname Bool)) (F_4 (-> tptp.pname tptp.pname tptp.pname)) (F_3 (-> (-> tptp.pname Bool) tptp.pname))) (let ((_let_1 (@ tptp.insert_pname X_12))) (let ((_let_2 (@ (@ tptp.minus_minus_pname_o A_28) (@ _let_1 tptp.bot_bot_pname_o)))) (let ((_let_3 (@ F_3 (@ _let_1 A_28)))) (let ((_let_4 (= _let_2 tptp.bot_bot_pname_o))) (=> (@ (@ tptp.finite1282449217_pname F_4) F_3) (=> (@ tptp.finite_finite_pname A_28) (and (=> _let_4 (= _let_3 X_12)) (=> (not _let_4) (= _let_3 (@ (@ F_4 X_12) (@ F_3 _let_2)))))))))))))
% 0.62/0.96 (assert (forall ((X_12 tptp.hoare_2091234717iple_a) (A_28 (-> tptp.hoare_2091234717iple_a Bool)) (F_4 (-> tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a tptp.hoare_2091234717iple_a)) (F_3 (-> (-> tptp.hoare_2091234717iple_a Bool) tptp.hoare_2091234717iple_a))) (let ((_let_1 (@ tptp.insert1597628439iple_a X_12))) (let ((_let_2 (@ (@ tptp.minus_836160335le_a_o A_28) (@ _let_1 tptp.bot_bo1791335050le_a_o)))) (let ((_let_3 (@ F_3 (@ _let_1 A_28)))) (let ((_let_4 (= _let_2 tptp.bot_bo1791335050le_a_o))) (=> (@ (@ tptp.finite247037978iple_a F_4) F_3) (=> (@ tptp.finite232261744iple_a A_28) (and (=> _let_4 (= _let_3 X_12)) (=> (not _let_4) (= _let_3 (@ (@ F_4 X_12) (@ F_3 _let_2)))))))))))))
% 0.62/0.96 (assert (forall ((X_12 tptp.hoare_1708887482_state) (A_28 (-> tptp.hoare_1708887482_state Bool)) (F_4 (-> tptp.hoare_1708887482_state tptp.hoare_1708887482_state tptp.hoare_1708887482_state)) (F_3 (-> (-> tptp.hoare_1708887482_state Bool) tptp.hoare_1708887482_state))) (let ((_let_1 (@ tptp.insert528405184_state X_12))) (let ((_let_2 (@ (@ tptp.minus_2056855718tate_o A_28) (@ _let_1 tptp.bot_bo19817387tate_o)))) (let ((_let_3 (@ F_3 (@ _let_1 A_28)))) (let ((_let_4 (= _let_2 tptp.bot_bo19817387tate_o))) (=> (@ (@ tptp.finite1615457021_state F_4) F_3) (=> (@ tptp.finite1625599783_state A_28) (and (=> _let_4 (= _let_3 X_12)) (=> (not _let_4) (= _let_3 (@ (@ F_4 X_12) (@ F_3 _let_2)))))))))))))
% 0.62/0.96 (assert (forall ((X_12 tptp.nat) (A_28 (-> tptp.nat Bool)) (F_4 (-> tptp.nat tptp.nat tptp.nat)) (F_3 (-> (-> tptp.nat Bool) tptp.nat))) (let ((_let_1 (@ tptp.insert_nat X_12))) (let ((_let_2 (@ (@ tptp.minus_minus_nat_o A_28) (@ _let_1 tptp.bot_bot_nat_o)))) (let ((_let_3 (@ F_3 (@ _let_1 A_28)))) (let ((_let_4 (= _let_2 tptp.bot_bot_nat_o))) (=> (@ (@ tptp.finite988810631ne_nat F_4) F_3) (=> (@ tptp.finite_finite_nat A_28) (and (=> _let_4 (= _let_3 X_12)) (=> (not _let_4) (= _let_3 (@ (@ F_4 X_12) (@ F_3 _let_2)))))))))))))
% 0.62/0.96 (assert (forall ((B_22 (-> tptp.nat Bool)) (A_27 (-> tptp.nat Bool)) (X_11 tptp.nat)) (=> (@ A_27 X_11) (=> (@ B_22 X_11) (@ (@ (@ tptp.semila1947288293_nat_o A_27) B_22) X_11)))))
% 0.62/0.96 (assert (forall ((B_22 (-> tptp.hoare_2091234717iple_a Bool)) (A_27 (-> tptp.hoare_2091234717iple_a Bool)) (X_11 tptp.hoare_2091234717iple_a)) (=> (@ A_27 X_11) (=> (@ B_22 X_11) (@ (@ (@ tptp.semila2006181266le_a_o A_27) B_22) X_11)))))
% 0.62/0.96 (assert (forall ((B_22 (-> tptp.pname Bool)) (A_27 (-> tptp.pname Bool)) (X_11 tptp.pname)) (=> (@ A_27 X_11) (=> (@ B_22 X_11) (@ (@ (@ tptp.semila1673364395name_o A_27) B_22) X_11)))))
% 0.62/0.96 (assert (forall ((B_21 (-> tptp.nat Bool)) (C_11 tptp.nat) (A_26 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_11))) (=> (@ _let_1 A_26) (=> (@ _let_1 B_21) (@ _let_1 (@ (@ tptp.semila1947288293_nat_o A_26) B_21)))))))
% 0.62/0.96 (assert (forall ((B_21 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (C_11 (-> tptp.hoare_2091234717iple_a Bool)) (A_26 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.member99268621le_a_o C_11))) (=> (@ _let_1 A_26) (=> (@ _let_1 B_21) (@ _let_1 (@ (@ tptp.semila1672913213_a_o_o A_26) B_21)))))))
% 0.62/0.96 (assert (forall ((B_21 (-> tptp.hoare_2091234717iple_a Bool)) (C_11 tptp.hoare_2091234717iple_a) (A_26 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.member290856304iple_a C_11))) (=> (@ _let_1 A_26) (=> (@ _let_1 B_21) (@ _let_1 (@ (@ tptp.semila2006181266le_a_o A_26) B_21)))))))
% 0.62/0.96 (assert (forall ((B_21 (-> tptp.pname Bool)) (C_11 tptp.pname) (A_26 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_11))) (=> (@ _let_1 A_26) (=> (@ _let_1 B_21) (@ _let_1 (@ (@ tptp.semila1673364395name_o A_26) B_21)))))))
% 0.62/0.96 (assert (forall ((C_10 tptp.nat) (A_25 (-> tptp.nat Bool)) (B_20 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_10))) (=> (@ _let_1 (@ (@ tptp.semila1947288293_nat_o A_25) B_20)) (not (=> (@ _let_1 A_25) (not (@ _let_1 B_20))))))))
% 0.62/0.96 (assert (forall ((C_10 (-> tptp.hoare_2091234717iple_a Bool)) (A_25 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_20 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.member99268621le_a_o C_10))) (=> (@ _let_1 (@ (@ tptp.semila1672913213_a_o_o A_25) B_20)) (not (=> (@ _let_1 A_25) (not (@ _let_1 B_20))))))))
% 0.62/0.96 (assert (forall ((C_10 tptp.hoare_2091234717iple_a) (A_25 (-> tptp.hoare_2091234717iple_a Bool)) (B_20 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.member290856304iple_a C_10))) (=> (@ _let_1 (@ (@ tptp.semila2006181266le_a_o A_25) B_20)) (not (=> (@ _let_1 A_25) (not (@ _let_1 B_20))))))))
% 0.62/0.96 (assert (forall ((C_10 tptp.pname) (A_25 (-> tptp.pname Bool)) (B_20 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_10))) (=> (@ _let_1 (@ (@ tptp.semila1673364395name_o A_25) B_20)) (not (=> (@ _let_1 A_25) (not (@ _let_1 B_20))))))))
% 0.62/0.96 (assert (forall ((A_24 (-> tptp.nat Bool)) (B_19 (-> tptp.nat Bool)) (X_10 tptp.nat)) (=> (@ (@ (@ tptp.semila1947288293_nat_o A_24) B_19) X_10) (not (=> (@ A_24 X_10) (not (@ B_19 X_10)))))))
% 0.62/0.96 (assert (forall ((A_24 (-> tptp.hoare_2091234717iple_a Bool)) (B_19 (-> tptp.hoare_2091234717iple_a Bool)) (X_10 tptp.hoare_2091234717iple_a)) (=> (@ (@ (@ tptp.semila2006181266le_a_o A_24) B_19) X_10) (not (=> (@ A_24 X_10) (not (@ B_19 X_10)))))))
% 0.62/0.96 (assert (forall ((A_24 (-> tptp.pname Bool)) (B_19 (-> tptp.pname Bool)) (X_10 tptp.pname)) (=> (@ (@ (@ tptp.semila1673364395name_o A_24) B_19) X_10) (not (=> (@ A_24 X_10) (not (@ B_19 X_10)))))))
% 0.62/0.96 (assert (forall ((B_18 (-> tptp.nat Bool)) (C_9 tptp.nat) (A_23 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_9))) (=> (@ _let_1 A_23) (=> (not (@ _let_1 B_18)) (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_23) B_18)))))))
% 0.62/0.96 (assert (forall ((B_18 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (C_9 (-> tptp.hoare_2091234717iple_a Bool)) (A_23 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.member99268621le_a_o C_9))) (=> (@ _let_1 A_23) (=> (not (@ _let_1 B_18)) (@ _let_1 (@ (@ tptp.minus_1746272704_a_o_o A_23) B_18)))))))
% 0.62/0.96 (assert (forall ((B_18 (-> tptp.hoare_2091234717iple_a Bool)) (C_9 tptp.hoare_2091234717iple_a) (A_23 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.member290856304iple_a C_9))) (=> (@ _let_1 A_23) (=> (not (@ _let_1 B_18)) (@ _let_1 (@ (@ tptp.minus_836160335le_a_o A_23) B_18)))))))
% 0.62/0.96 (assert (forall ((B_18 (-> tptp.pname Bool)) (C_9 tptp.pname) (A_23 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_9))) (=> (@ _let_1 A_23) (=> (not (@ _let_1 B_18)) (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_23) B_18)))))))
% 0.62/0.96 (assert (forall ((C_8 tptp.nat) (A_22 (-> tptp.nat Bool)) (B_17 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_8))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_22) B_17)) (not (=> (@ _let_1 A_22) (@ _let_1 B_17)))))))
% 0.62/0.96 (assert (forall ((C_8 (-> tptp.hoare_2091234717iple_a Bool)) (A_22 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_17 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.member99268621le_a_o C_8))) (=> (@ _let_1 (@ (@ tptp.minus_1746272704_a_o_o A_22) B_17)) (not (=> (@ _let_1 A_22) (@ _let_1 B_17)))))))
% 0.62/0.96 (assert (forall ((C_8 tptp.hoare_2091234717iple_a) (A_22 (-> tptp.hoare_2091234717iple_a Bool)) (B_17 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.member290856304iple_a C_8))) (=> (@ _let_1 (@ (@ tptp.minus_836160335le_a_o A_22) B_17)) (not (=> (@ _let_1 A_22) (@ _let_1 B_17)))))))
% 0.62/0.96 (assert (forall ((C_8 tptp.pname) (A_22 (-> tptp.pname Bool)) (B_17 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_8))) (=> (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_22) B_17)) (not (=> (@ _let_1 A_22) (@ _let_1 B_17)))))))
% 0.62/0.96 (assert (forall ((G_1 (-> tptp.hoare_2091234717iple_a Bool)) (F_2 (-> tptp.hoare_2091234717iple_a Bool))) (=> (or (@ tptp.finite232261744iple_a F_2) (@ tptp.finite232261744iple_a G_1)) (@ tptp.finite232261744iple_a (@ (@ tptp.semila2006181266le_a_o F_2) G_1)))))
% 0.62/0.96 (assert (forall ((G_1 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (F_2 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (or (@ tptp.finite1829014797le_a_o F_2) (@ tptp.finite1829014797le_a_o G_1)) (@ tptp.finite1829014797le_a_o (@ (@ tptp.semila1672913213_a_o_o F_2) G_1)))))
% 0.62/0.96 (assert (forall ((G_1 (-> tptp.pname Bool)) (F_2 (-> tptp.pname Bool))) (=> (or (@ tptp.finite_finite_pname F_2) (@ tptp.finite_finite_pname G_1)) (@ tptp.finite_finite_pname (@ (@ tptp.semila1673364395name_o F_2) G_1)))))
% 0.62/0.96 (assert (forall ((G_1 (-> tptp.nat Bool)) (F_2 (-> tptp.nat Bool))) (=> (or (@ tptp.finite_finite_nat F_2) (@ tptp.finite_finite_nat G_1)) (@ tptp.finite_finite_nat (@ (@ tptp.semila1947288293_nat_o F_2) G_1)))))
% 0.62/0.96 (assert (forall ((B_16 (-> tptp.hoare_2091234717iple_a Bool)) (A_21 (-> tptp.hoare_2091234717iple_a Bool))) (=> (@ tptp.finite232261744iple_a A_21) (@ tptp.finite232261744iple_a (@ (@ tptp.minus_836160335le_a_o A_21) B_16)))))
% 0.62/0.96 (assert (forall ((B_16 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (A_21 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (@ tptp.finite1829014797le_a_o A_21) (@ tptp.finite1829014797le_a_o (@ (@ tptp.minus_1746272704_a_o_o A_21) B_16)))))
% 0.62/0.96 (assert (forall ((B_16 (-> tptp.pname Bool)) (A_21 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_21) (@ tptp.finite_finite_pname (@ (@ tptp.minus_minus_pname_o A_21) B_16)))))
% 0.62/0.96 (assert (forall ((B_16 (-> tptp.nat Bool)) (A_21 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_21) (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_nat_o A_21) B_16)))))
% 0.62/0.96 (assert (forall ((A_20 (-> tptp.hoare_2091234717iple_a Bool)) (A_19 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (=> (@ tptp.finite1829014797le_a_o A_19) (=> (@ (@ tptp.member99268621le_a_o A_20) A_19) (= (@ (@ tptp.semila2006181266le_a_o A_20) (@ tptp.big_la735727201le_a_o A_19)) A_20)))))
% 0.62/0.96 (assert (forall ((A_20 (-> tptp.nat Bool)) (A_19 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_19) (=> (@ (@ tptp.member_nat_o A_20) A_19) (= (@ (@ tptp.semila1947288293_nat_o A_20) (@ tptp.big_la1658356148_nat_o A_19)) A_20)))))
% 0.62/0.96 (assert (forall ((A_20 (-> tptp.pname Bool)) (A_19 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_19) (=> (@ (@ tptp.member_pname_o A_20) A_19) (= (@ (@ tptp.semila1673364395name_o A_20) (@ tptp.big_la1286884090name_o A_19)) A_20)))))
% 0.62/0.96 (assert (forall ((A_20 tptp.nat) (A_19 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_19) (=> (@ (@ tptp.member_nat A_20) A_19) (= (@ (@ tptp.semila80283416nf_nat A_20) (@ tptp.big_la43341705in_nat A_19)) A_20)))))
% 0.62/0.96 (assert (forall ((A_18 (-> tptp.nat Bool)) (B_15 (-> tptp.nat Bool)) (C_7 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.minus_minus_nat_o A_18))) (= (@ _let_1 (@ (@ tptp.semila1947288293_nat_o B_15) C_7)) (@ (@ tptp.semila848761471_nat_o (@ _let_1 B_15)) (@ _let_1 C_7))))))
% 0.62/0.96 (assert (forall ((A_18 (-> tptp.pname Bool)) (B_15 (-> tptp.pname Bool)) (C_7 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.minus_minus_pname_o A_18))) (= (@ _let_1 (@ (@ tptp.semila1673364395name_o B_15) C_7)) (@ (@ tptp.semila1780557381name_o (@ _let_1 B_15)) (@ _let_1 C_7))))))
% 0.62/0.96 (assert (forall ((A_18 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_15 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (C_7 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.minus_1746272704_a_o_o A_18))) (= (@ _let_1 (@ (@ tptp.semila1672913213_a_o_o B_15) C_7)) (@ (@ tptp.semila2050116131_a_o_o (@ _let_1 B_15)) (@ _let_1 C_7))))))
% 0.62/0.96 (assert (forall ((A_18 (-> tptp.hoare_1708887482_state Bool)) (B_15 (-> tptp.hoare_1708887482_state Bool)) (C_7 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.minus_2056855718tate_o A_18))) (= (@ _let_1 (@ (@ tptp.semila129691299tate_o B_15) C_7)) (@ (@ tptp.semila1122118281tate_o (@ _let_1 B_15)) (@ _let_1 C_7))))))
% 0.62/0.96 (assert (forall ((A_18 (-> tptp.hoare_2091234717iple_a Bool)) (B_15 (-> tptp.hoare_2091234717iple_a Bool)) (C_7 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.minus_836160335le_a_o A_18))) (= (@ _let_1 (@ (@ tptp.semila2006181266le_a_o B_15) C_7)) (@ (@ tptp.semila1052848428le_a_o (@ _let_1 B_15)) (@ _let_1 C_7))))))
% 0.62/0.96 (assert (forall ((A_17 (-> tptp.nat Bool)) (B_14 (-> tptp.nat Bool)) (C_6 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.minus_minus_nat_o A_17))) (= (@ _let_1 (@ (@ tptp.semila848761471_nat_o B_14) C_6)) (@ (@ tptp.semila1947288293_nat_o (@ _let_1 B_14)) (@ _let_1 C_6))))))
% 0.62/0.96 (assert (forall ((A_17 (-> tptp.pname Bool)) (B_14 (-> tptp.pname Bool)) (C_6 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.minus_minus_pname_o A_17))) (= (@ _let_1 (@ (@ tptp.semila1780557381name_o B_14) C_6)) (@ (@ tptp.semila1673364395name_o (@ _let_1 B_14)) (@ _let_1 C_6))))))
% 0.62/0.96 (assert (forall ((A_17 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_14 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (C_6 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.minus_1746272704_a_o_o A_17))) (= (@ _let_1 (@ (@ tptp.semila2050116131_a_o_o B_14) C_6)) (@ (@ tptp.semila1672913213_a_o_o (@ _let_1 B_14)) (@ _let_1 C_6))))))
% 0.62/0.96 (assert (forall ((A_17 (-> tptp.hoare_1708887482_state Bool)) (B_14 (-> tptp.hoare_1708887482_state Bool)) (C_6 (-> tptp.hoare_1708887482_state Bool))) (let ((_let_1 (@ tptp.minus_2056855718tate_o A_17))) (= (@ _let_1 (@ (@ tptp.semila1122118281tate_o B_14) C_6)) (@ (@ tptp.semila129691299tate_o (@ _let_1 B_14)) (@ _let_1 C_6))))))
% 0.62/0.96 (assert (forall ((A_17 (-> tptp.hoare_2091234717iple_a Bool)) (B_14 (-> tptp.hoare_2091234717iple_a Bool)) (C_6 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.minus_836160335le_a_o A_17))) (= (@ _let_1 (@ (@ tptp.semila1052848428le_a_o B_14) C_6)) (@ (@ tptp.semila2006181266le_a_o (@ _let_1 B_14)) (@ _let_1 C_6))))))
% 0.62/0.96 (assert (forall ((A_16 (-> tptp.nat Bool)) (B_13 (-> tptp.nat Bool))) (= (@ (@ tptp.semila848761471_nat_o (@ (@ tptp.minus_minus_nat_o A_16) B_13)) (@ (@ tptp.semila1947288293_nat_o A_16) B_13)) A_16)))
% 0.62/0.96 (assert (forall ((A_16 (-> tptp.pname Bool)) (B_13 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1780557381name_o (@ (@ tptp.minus_minus_pname_o A_16) B_13)) (@ (@ tptp.semila1673364395name_o A_16) B_13)) A_16)))
% 0.62/0.96 (assert (forall ((A_16 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_13 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.semila2050116131_a_o_o (@ (@ tptp.minus_1746272704_a_o_o A_16) B_13)) (@ (@ tptp.semila1672913213_a_o_o A_16) B_13)) A_16)))
% 0.62/0.96 (assert (forall ((A_16 (-> tptp.hoare_1708887482_state Bool)) (B_13 (-> tptp.hoare_1708887482_state Bool))) (= (@ (@ tptp.semila1122118281tate_o (@ (@ tptp.minus_2056855718tate_o A_16) B_13)) (@ (@ tptp.semila129691299tate_o A_16) B_13)) A_16)))
% 0.62/0.96 (assert (forall ((A_16 (-> tptp.hoare_2091234717iple_a Bool)) (B_13 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila1052848428le_a_o (@ (@ tptp.minus_836160335le_a_o A_16) B_13)) (@ (@ tptp.semila2006181266le_a_o A_16) B_13)) A_16)))
% 0.62/0.96 (assert (forall ((P_2 (-> tptp.pname Bool)) (Q (-> tptp.pname Bool))) (= (@ tptp.collect_pname (lambda ((X tptp.pname)) (and (@ P_2 X) (@ Q X)))) (@ (@ tptp.semila1673364395name_o (@ tptp.collect_pname P_2)) (@ tptp.collect_pname Q)))))
% 0.62/0.96 (assert (forall ((P_2 (-> tptp.hoare_2091234717iple_a Bool)) (Q (-> tptp.hoare_2091234717iple_a Bool))) (= (@ tptp.collec992574898iple_a (lambda ((X tptp.hoare_2091234717iple_a)) (and (@ P_2 X) (@ Q X)))) (@ (@ tptp.semila2006181266le_a_o (@ tptp.collec992574898iple_a P_2)) (@ tptp.collec992574898iple_a Q)))))
% 0.62/0.96 (assert (forall ((P_2 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ P_2 X) (@ Q X)))) (@ (@ tptp.semila1947288293_nat_o (@ tptp.collect_nat P_2)) (@ tptp.collect_nat Q)))))
% 0.62/0.96 (assert (forall ((X_9 (-> tptp.hoare_2091234717iple_a Bool)) (A_15 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (P_1 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.member99268621le_a_o X_9))) (= (@ _let_1 (@ (@ tptp.semila1672913213_a_o_o A_15) (@ tptp.collec1008234059le_a_o P_1))) (and (@ _let_1 A_15) (@ P_1 X_9))))))
% 0.62/0.96 (assert (forall ((X_9 tptp.nat) (A_15 (-> tptp.nat Bool)) (P_1 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X_9))) (= (@ _let_1 (@ (@ tptp.semila1947288293_nat_o A_15) (@ tptp.collect_nat P_1))) (and (@ _let_1 A_15) (@ P_1 X_9))))))
% 0.62/0.96 (assert (forall ((X_9 tptp.hoare_2091234717iple_a) (A_15 (-> tptp.hoare_2091234717iple_a Bool)) (P_1 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.member290856304iple_a X_9))) (= (@ _let_1 (@ (@ tptp.semila2006181266le_a_o A_15) (@ tptp.collec992574898iple_a P_1))) (and (@ _let_1 A_15) (@ P_1 X_9))))))
% 0.62/0.96 (assert (forall ((X_9 tptp.pname) (A_15 (-> tptp.pname Bool)) (P_1 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_9))) (= (@ _let_1 (@ (@ tptp.semila1673364395name_o A_15) (@ tptp.collect_pname P_1))) (and (@ _let_1 A_15) (@ P_1 X_9))))))
% 0.62/0.96 (assert (forall ((R (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (S_1 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (X (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ (@ tptp.semila1672913213_a_o_o (lambda ((Y_7 (-> tptp.hoare_2091234717iple_a Bool))) (@ (@ tptp.member99268621le_a_o Y_7) R))) (lambda ((Y_7 (-> tptp.hoare_2091234717iple_a Bool))) (@ (@ tptp.member99268621le_a_o Y_7) S_1))) X) (@ (@ tptp.member99268621le_a_o X) (@ (@ tptp.semila1672913213_a_o_o R) S_1)))))
% 0.62/0.96 (assert (forall ((R (-> tptp.nat Bool)) (S_1 (-> tptp.nat Bool)) (X tptp.nat)) (= (@ (@ (@ tptp.semila1947288293_nat_o (lambda ((Y_7 tptp.nat)) (@ (@ tptp.member_nat Y_7) R))) (lambda ((Y_7 tptp.nat)) (@ (@ tptp.member_nat Y_7) S_1))) X) (@ (@ tptp.member_nat X) (@ (@ tptp.semila1947288293_nat_o R) S_1)))))
% 0.62/0.96 (assert (forall ((R (-> tptp.hoare_2091234717iple_a Bool)) (S_1 (-> tptp.hoare_2091234717iple_a Bool)) (X tptp.hoare_2091234717iple_a)) (= (@ (@ (@ tptp.semila2006181266le_a_o (lambda ((Y_7 tptp.hoare_2091234717iple_a)) (@ (@ tptp.member290856304iple_a Y_7) R))) (lambda ((Y_7 tptp.hoare_2091234717iple_a)) (@ (@ tptp.member290856304iple_a Y_7) S_1))) X) (@ (@ tptp.member290856304iple_a X) (@ (@ tptp.semila2006181266le_a_o R) S_1)))))
% 0.62/0.96 (assert (forall ((R (-> tptp.pname Bool)) (S_1 (-> tptp.pname Bool)) (X tptp.pname)) (= (@ (@ (@ tptp.semila1673364395name_o (lambda ((Y_7 tptp.pname)) (@ (@ tptp.member_pname Y_7) R))) (lambda ((Y_7 tptp.pname)) (@ (@ tptp.member_pname Y_7) S_1))) X) (@ (@ tptp.member_pname X) (@ (@ tptp.semila1673364395name_o R) S_1)))))
% 0.62/0.96 (assert (forall ((A_14 (-> tptp.nat Bool))) (= (@ (@ tptp.semila1947288293_nat_o A_14) A_14) A_14)))
% 0.62/0.96 (assert (forall ((A_14 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila2006181266le_a_o A_14) A_14) A_14)))
% 0.62/0.96 (assert (forall ((A_14 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1673364395name_o A_14) A_14) A_14)))
% 0.62/0.96 (assert (forall ((A_13 (-> tptp.nat Bool))) (= (@ (@ tptp.semila1947288293_nat_o A_13) A_13) A_13)))
% 0.62/0.96 (assert (forall ((A_13 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila2006181266le_a_o A_13) A_13) A_13)))
% 0.62/0.96 (assert (forall ((A_13 tptp.nat)) (= (@ (@ tptp.semila80283416nf_nat A_13) A_13) A_13)))
% 0.62/0.96 (assert (forall ((A_13 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1673364395name_o A_13) A_13) A_13)))
% 0.62/0.96 (assert (forall ((X_8 (-> tptp.nat Bool))) (= (@ (@ tptp.semila1947288293_nat_o X_8) X_8) X_8)))
% 0.62/0.96 (assert (forall ((X_8 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila2006181266le_a_o X_8) X_8) X_8)))
% 0.62/0.96 (assert (forall ((X_8 tptp.nat)) (= (@ (@ tptp.semila80283416nf_nat X_8) X_8) X_8)))
% 0.62/0.96 (assert (forall ((X_8 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1673364395name_o X_8) X_8) X_8)))
% 0.62/0.96 (assert (forall ((A_12 (-> tptp.hoare_2091234717iple_a Bool)) (B_12 (-> tptp.hoare_2091234717iple_a Bool)) (X tptp.hoare_2091234717iple_a)) (= (@ (@ (@ tptp.minus_836160335le_a_o A_12) B_12) X) (@ (@ tptp.minus_minus_o (@ A_12 X)) (@ B_12 X)))))
% 0.62/0.96 (assert (forall ((A_12 (-> tptp.pname Bool)) (B_12 (-> tptp.pname Bool)) (X tptp.pname)) (= (@ (@ (@ tptp.minus_minus_pname_o A_12) B_12) X) (@ (@ tptp.minus_minus_o (@ A_12 X)) (@ B_12 X)))))
% 0.62/0.96 (assert (forall ((A_12 (-> tptp.nat Bool)) (B_12 (-> tptp.nat Bool)) (X tptp.nat)) (= (@ (@ (@ tptp.minus_minus_nat_o A_12) B_12) X) (@ (@ tptp.minus_minus_o (@ A_12 X)) (@ B_12 X)))))
% 0.62/0.96 (assert (forall ((F_1 (-> tptp.nat Bool)) (G (-> tptp.nat Bool)) (X tptp.nat)) (= (@ (@ (@ tptp.semila1947288293_nat_o F_1) G) X) (@ (@ tptp.semila854092349_inf_o (@ F_1 X)) (@ G X)))))
% 0.62/0.96 (assert (forall ((F_1 (-> tptp.hoare_2091234717iple_a Bool)) (G (-> tptp.hoare_2091234717iple_a Bool)) (X tptp.hoare_2091234717iple_a)) (= (@ (@ (@ tptp.semila2006181266le_a_o F_1) G) X) (@ (@ tptp.semila854092349_inf_o (@ F_1 X)) (@ G X)))))
% 0.62/0.96 (assert (forall ((F_1 (-> tptp.pname Bool)) (G (-> tptp.pname Bool)) (X tptp.pname)) (= (@ (@ (@ tptp.semila1673364395name_o F_1) G) X) (@ (@ tptp.semila854092349_inf_o (@ F_1 X)) (@ G X)))))
% 0.62/0.96 (assert (forall ((A_11 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_11 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.minus_1746272704_a_o_o A_11) B_11) (@ tptp.collec1008234059le_a_o (lambda ((X (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.member99268621le_a_o X))) (and (@ _let_1 A_11) (not (@ _let_1 B_11)))))))))
% 0.62/0.96 (assert (forall ((A_11 (-> tptp.nat Bool)) (B_11 (-> tptp.nat Bool))) (= (@ (@ tptp.minus_minus_nat_o A_11) B_11) (@ tptp.collect_nat (lambda ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (and (@ _let_1 A_11) (not (@ _let_1 B_11)))))))))
% 0.62/0.96 (assert (forall ((A_11 (-> tptp.hoare_2091234717iple_a Bool)) (B_11 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.minus_836160335le_a_o A_11) B_11) (@ tptp.collec992574898iple_a (lambda ((X tptp.hoare_2091234717iple_a)) (let ((_let_1 (@ tptp.member290856304iple_a X))) (and (@ _let_1 A_11) (not (@ _let_1 B_11)))))))))
% 0.62/0.96 (assert (forall ((A_11 (-> tptp.pname Bool)) (B_11 (-> tptp.pname Bool))) (= (@ (@ tptp.minus_minus_pname_o A_11) B_11) (@ tptp.collect_pname (lambda ((X tptp.pname)) (let ((_let_1 (@ tptp.member_pname X))) (and (@ _let_1 A_11) (not (@ _let_1 B_11)))))))))
% 0.62/0.96 (assert (forall ((A_10 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_10 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (= (@ (@ tptp.semila1672913213_a_o_o A_10) B_10) (@ tptp.collec1008234059le_a_o (lambda ((X (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.member99268621le_a_o X))) (and (@ _let_1 A_10) (@ _let_1 B_10))))))))
% 0.62/0.96 (assert (forall ((A_10 (-> tptp.nat Bool)) (B_10 (-> tptp.nat Bool))) (= (@ (@ tptp.semila1947288293_nat_o A_10) B_10) (@ tptp.collect_nat (lambda ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (and (@ _let_1 A_10) (@ _let_1 B_10))))))))
% 0.62/0.96 (assert (forall ((A_10 (-> tptp.hoare_2091234717iple_a Bool)) (B_10 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila2006181266le_a_o A_10) B_10) (@ tptp.collec992574898iple_a (lambda ((X tptp.hoare_2091234717iple_a)) (let ((_let_1 (@ tptp.member290856304iple_a X))) (and (@ _let_1 A_10) (@ _let_1 B_10))))))))
% 0.62/0.96 (assert (forall ((A_10 (-> tptp.pname Bool)) (B_10 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1673364395name_o A_10) B_10) (@ tptp.collect_pname (lambda ((X tptp.pname)) (let ((_let_1 (@ tptp.member_pname X))) (and (@ _let_1 A_10) (@ _let_1 B_10))))))))
% 0.62/0.96 (assert (forall ((A_9 (-> tptp.nat Bool)) (B_9 (-> tptp.nat Bool))) (= (@ (@ tptp.semila1947288293_nat_o A_9) B_9) (@ (@ tptp.semila1947288293_nat_o B_9) A_9))))
% 0.62/0.96 (assert (forall ((A_9 (-> tptp.hoare_2091234717iple_a Bool)) (B_9 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila2006181266le_a_o A_9) B_9) (@ (@ tptp.semila2006181266le_a_o B_9) A_9))))
% 0.62/0.96 (assert (forall ((A_9 (-> tptp.pname Bool)) (B_9 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1673364395name_o A_9) B_9) (@ (@ tptp.semila1673364395name_o B_9) A_9))))
% 0.62/0.96 (assert (forall ((A_8 (-> tptp.nat Bool)) (B_8 (-> tptp.nat Bool))) (= (@ (@ tptp.semila1947288293_nat_o A_8) B_8) (@ (@ tptp.semila1947288293_nat_o B_8) A_8))))
% 0.62/0.96 (assert (forall ((A_8 (-> tptp.hoare_2091234717iple_a Bool)) (B_8 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila2006181266le_a_o A_8) B_8) (@ (@ tptp.semila2006181266le_a_o B_8) A_8))))
% 0.62/0.96 (assert (forall ((A_8 tptp.nat) (B_8 tptp.nat)) (= (@ (@ tptp.semila80283416nf_nat A_8) B_8) (@ (@ tptp.semila80283416nf_nat B_8) A_8))))
% 0.62/0.96 (assert (forall ((A_8 (-> tptp.pname Bool)) (B_8 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1673364395name_o A_8) B_8) (@ (@ tptp.semila1673364395name_o B_8) A_8))))
% 0.62/0.96 (assert (forall ((X_7 (-> tptp.nat Bool)) (Y_6 (-> tptp.nat Bool))) (= (@ (@ tptp.semila1947288293_nat_o X_7) Y_6) (@ (@ tptp.semila1947288293_nat_o Y_6) X_7))))
% 0.62/0.96 (assert (forall ((X_7 (-> tptp.hoare_2091234717iple_a Bool)) (Y_6 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila2006181266le_a_o X_7) Y_6) (@ (@ tptp.semila2006181266le_a_o Y_6) X_7))))
% 0.62/0.96 (assert (forall ((X_7 tptp.nat) (Y_6 tptp.nat)) (= (@ (@ tptp.semila80283416nf_nat X_7) Y_6) (@ (@ tptp.semila80283416nf_nat Y_6) X_7))))
% 0.62/0.96 (assert (forall ((X_7 (-> tptp.pname Bool)) (Y_6 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1673364395name_o X_7) Y_6) (@ (@ tptp.semila1673364395name_o Y_6) X_7))))
% 0.62/0.96 (assert (forall ((X_6 (-> tptp.nat Bool)) (Y_5 (-> tptp.nat Bool))) (= (@ (@ tptp.semila1947288293_nat_o X_6) Y_5) (@ (@ tptp.semila1947288293_nat_o Y_5) X_6))))
% 0.62/0.96 (assert (forall ((X_6 (-> tptp.hoare_2091234717iple_a Bool)) (Y_5 (-> tptp.hoare_2091234717iple_a Bool))) (= (@ (@ tptp.semila2006181266le_a_o X_6) Y_5) (@ (@ tptp.semila2006181266le_a_o Y_5) X_6))))
% 0.62/0.96 (assert (forall ((X_6 tptp.nat) (Y_5 tptp.nat)) (= (@ (@ tptp.semila80283416nf_nat X_6) Y_5) (@ (@ tptp.semila80283416nf_nat Y_5) X_6))))
% 0.62/0.96 (assert (forall ((X_6 (-> tptp.pname Bool)) (Y_5 (-> tptp.pname Bool))) (= (@ (@ tptp.semila1673364395name_o X_6) Y_5) (@ (@ tptp.semila1673364395name_o Y_5) X_6))))
% 0.62/0.96 (assert (forall ((A_7 (-> tptp.nat Bool)) (B_7 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila1947288293_nat_o A_7))) (let ((_let_2 (@ _let_1 B_7))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((A_7 (-> tptp.hoare_2091234717iple_a Bool)) (B_7 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila2006181266le_a_o A_7))) (let ((_let_2 (@ _let_1 B_7))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((A_7 (-> tptp.pname Bool)) (B_7 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1673364395name_o A_7))) (let ((_let_2 (@ _let_1 B_7))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((A_6 (-> tptp.nat Bool)) (B_6 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila1947288293_nat_o A_6))) (let ((_let_2 (@ _let_1 B_6))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((A_6 (-> tptp.hoare_2091234717iple_a Bool)) (B_6 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila2006181266le_a_o A_6))) (let ((_let_2 (@ _let_1 B_6))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((A_6 tptp.nat) (B_6 tptp.nat)) (let ((_let_1 (@ tptp.semila80283416nf_nat A_6))) (let ((_let_2 (@ _let_1 B_6))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((A_6 (-> tptp.pname Bool)) (B_6 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1673364395name_o A_6))) (let ((_let_2 (@ _let_1 B_6))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_5 (-> tptp.nat Bool)) (Y_4 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila1947288293_nat_o X_5))) (let ((_let_2 (@ _let_1 Y_4))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_5 (-> tptp.hoare_2091234717iple_a Bool)) (Y_4 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila2006181266le_a_o X_5))) (let ((_let_2 (@ _let_1 Y_4))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_5 tptp.nat) (Y_4 tptp.nat)) (let ((_let_1 (@ tptp.semila80283416nf_nat X_5))) (let ((_let_2 (@ _let_1 Y_4))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_5 (-> tptp.pname Bool)) (Y_4 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1673364395name_o X_5))) (let ((_let_2 (@ _let_1 Y_4))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_4 (-> tptp.nat Bool)) (Y_3 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila1947288293_nat_o X_4))) (let ((_let_2 (@ _let_1 Y_3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_4 (-> tptp.hoare_2091234717iple_a Bool)) (Y_3 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila2006181266le_a_o X_4))) (let ((_let_2 (@ _let_1 Y_3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_4 tptp.nat) (Y_3 tptp.nat)) (let ((_let_1 (@ tptp.semila80283416nf_nat X_4))) (let ((_let_2 (@ _let_1 Y_3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((X_4 (-> tptp.pname Bool)) (Y_3 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1673364395name_o X_4))) (let ((_let_2 (@ _let_1 Y_3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/0.96 (assert (forall ((A_5 (-> tptp.nat Bool)) (B_5 (-> tptp.nat Bool)) (C_5 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila1947288293_nat_o A_5))) (let ((_let_2 (@ tptp.semila1947288293_nat_o B_5))) (= (@ _let_1 (@ _let_2 C_5)) (@ _let_2 (@ _let_1 C_5)))))))
% 0.62/0.96 (assert (forall ((A_5 (-> tptp.hoare_2091234717iple_a Bool)) (B_5 (-> tptp.hoare_2091234717iple_a Bool)) (C_5 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila2006181266le_a_o A_5))) (let ((_let_2 (@ tptp.semila2006181266le_a_o B_5))) (= (@ _let_1 (@ _let_2 C_5)) (@ _let_2 (@ _let_1 C_5)))))))
% 0.62/0.96 (assert (forall ((A_5 (-> tptp.pname Bool)) (B_5 (-> tptp.pname Bool)) (C_5 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1673364395name_o A_5))) (let ((_let_2 (@ tptp.semila1673364395name_o B_5))) (= (@ _let_1 (@ _let_2 C_5)) (@ _let_2 (@ _let_1 C_5)))))))
% 0.62/0.96 (assert (forall ((B_4 (-> tptp.nat Bool)) (A_4 (-> tptp.nat Bool)) (C_4 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila1947288293_nat_o B_4))) (let ((_let_2 (@ tptp.semila1947288293_nat_o A_4))) (= (@ _let_1 (@ _let_2 C_4)) (@ _let_2 (@ _let_1 C_4)))))))
% 0.62/0.96 (assert (forall ((B_4 (-> tptp.hoare_2091234717iple_a Bool)) (A_4 (-> tptp.hoare_2091234717iple_a Bool)) (C_4 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila2006181266le_a_o B_4))) (let ((_let_2 (@ tptp.semila2006181266le_a_o A_4))) (= (@ _let_1 (@ _let_2 C_4)) (@ _let_2 (@ _let_1 C_4)))))))
% 0.62/0.96 (assert (forall ((B_4 tptp.nat) (A_4 tptp.nat) (C_4 tptp.nat)) (let ((_let_1 (@ tptp.semila80283416nf_nat B_4))) (let ((_let_2 (@ tptp.semila80283416nf_nat A_4))) (= (@ _let_1 (@ _let_2 C_4)) (@ _let_2 (@ _let_1 C_4)))))))
% 0.62/0.96 (assert (forall ((B_4 (-> tptp.pname Bool)) (A_4 (-> tptp.pname Bool)) (C_4 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1673364395name_o B_4))) (let ((_let_2 (@ tptp.semila1673364395name_o A_4))) (= (@ _let_1 (@ _let_2 C_4)) (@ _let_2 (@ _let_1 C_4)))))))
% 0.62/0.96 (assert (forall ((X_3 (-> tptp.nat Bool)) (Y_2 (-> tptp.nat Bool)) (Z_2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila1947288293_nat_o X_3))) (let ((_let_2 (@ tptp.semila1947288293_nat_o Y_2))) (= (@ _let_1 (@ _let_2 Z_2)) (@ _let_2 (@ _let_1 Z_2)))))))
% 0.62/0.96 (assert (forall ((X_3 (-> tptp.hoare_2091234717iple_a Bool)) (Y_2 (-> tptp.hoare_2091234717iple_a Bool)) (Z_2 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila2006181266le_a_o X_3))) (let ((_let_2 (@ tptp.semila2006181266le_a_o Y_2))) (= (@ _let_1 (@ _let_2 Z_2)) (@ _let_2 (@ _let_1 Z_2)))))))
% 0.62/0.96 (assert (forall ((X_3 tptp.nat) (Y_2 tptp.nat) (Z_2 tptp.nat)) (let ((_let_1 (@ tptp.semila80283416nf_nat X_3))) (let ((_let_2 (@ tptp.semila80283416nf_nat Y_2))) (= (@ _let_1 (@ _let_2 Z_2)) (@ _let_2 (@ _let_1 Z_2)))))))
% 0.62/0.96 (assert (forall ((X_3 (-> tptp.pname Bool)) (Y_2 (-> tptp.pname Bool)) (Z_2 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1673364395name_o X_3))) (let ((_let_2 (@ tptp.semila1673364395name_o Y_2))) (= (@ _let_1 (@ _let_2 Z_2)) (@ _let_2 (@ _let_1 Z_2)))))))
% 0.62/0.96 (assert (forall ((X_2 (-> tptp.nat Bool)) (Y_1 (-> tptp.nat Bool)) (Z_1 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila1947288293_nat_o X_2))) (let ((_let_2 (@ tptp.semila1947288293_nat_o Y_1))) (= (@ _let_1 (@ _let_2 Z_1)) (@ _let_2 (@ _let_1 Z_1)))))))
% 0.62/0.96 (assert (forall ((X_2 (-> tptp.hoare_2091234717iple_a Bool)) (Y_1 (-> tptp.hoare_2091234717iple_a Bool)) (Z_1 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila2006181266le_a_o X_2))) (let ((_let_2 (@ tptp.semila2006181266le_a_o Y_1))) (= (@ _let_1 (@ _let_2 Z_1)) (@ _let_2 (@ _let_1 Z_1)))))))
% 0.62/0.96 (assert (forall ((X_2 tptp.nat) (Y_1 tptp.nat) (Z_1 tptp.nat)) (let ((_let_1 (@ tptp.semila80283416nf_nat X_2))) (let ((_let_2 (@ tptp.semila80283416nf_nat Y_1))) (= (@ _let_1 (@ _let_2 Z_1)) (@ _let_2 (@ _let_1 Z_1)))))))
% 0.62/0.96 (assert (forall ((X_2 (-> tptp.pname Bool)) (Y_1 (-> tptp.pname Bool)) (Z_1 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1673364395name_o X_2))) (let ((_let_2 (@ tptp.semila1673364395name_o Y_1))) (= (@ _let_1 (@ _let_2 Z_1)) (@ _let_2 (@ _let_1 Z_1)))))))
% 0.62/0.96 (assert (forall ((C_3 (-> tptp.hoare_2091234717iple_a Bool)) (A_3 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_3 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.member99268621le_a_o C_3))) (= (@ _let_1 (@ (@ tptp.minus_1746272704_a_o_o A_3) B_3)) (and (@ _let_1 A_3) (not (@ _let_1 B_3)))))))
% 0.62/0.96 (assert (forall ((C_3 tptp.nat) (A_3 (-> tptp.nat Bool)) (B_3 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_3))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_3) B_3)) (and (@ _let_1 A_3) (not (@ _let_1 B_3)))))))
% 0.62/0.96 (assert (forall ((C_3 tptp.hoare_2091234717iple_a) (A_3 (-> tptp.hoare_2091234717iple_a Bool)) (B_3 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.member290856304iple_a C_3))) (= (@ _let_1 (@ (@ tptp.minus_836160335le_a_o A_3) B_3)) (and (@ _let_1 A_3) (not (@ _let_1 B_3)))))))
% 0.62/0.96 (assert (forall ((C_3 tptp.pname) (A_3 (-> tptp.pname Bool)) (B_3 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_3))) (= (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_3) B_3)) (and (@ _let_1 A_3) (not (@ _let_1 B_3)))))))
% 0.62/0.96 (assert (forall ((C_2 (-> tptp.hoare_2091234717iple_a Bool)) (A_2 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool)) (B_2 (-> (-> tptp.hoare_2091234717iple_a Bool) Bool))) (let ((_let_1 (@ tptp.member99268621le_a_o C_2))) (= (@ _let_1 (@ (@ tptp.semila1672913213_a_o_o A_2) B_2)) (and (@ _let_1 A_2) (@ _let_1 B_2))))))
% 0.62/0.96 (assert (forall ((C_2 tptp.nat) (A_2 (-> tptp.nat Bool)) (B_2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_2))) (= (@ _let_1 (@ (@ tptp.semila1947288293_nat_o A_2) B_2)) (and (@ _let_1 A_2) (@ _let_1 B_2))))))
% 0.62/0.96 (assert (forall ((C_2 tptp.hoare_2091234717iple_a) (A_2 (-> tptp.hoare_2091234717iple_a Bool)) (B_2 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.member290856304iple_a C_2))) (= (@ _let_1 (@ (@ tptp.semila2006181266le_a_o A_2) B_2)) (and (@ _let_1 A_2) (@ _let_1 B_2))))))
% 0.62/0.96 (assert (forall ((C_2 tptp.pname) (A_2 (-> tptp.pname Bool)) (B_2 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_2))) (= (@ _let_1 (@ (@ tptp.semila1673364395name_o A_2) B_2)) (and (@ _let_1 A_2) (@ _let_1 B_2))))))
% 0.62/0.96 (assert (forall ((C_1 (-> tptp.hoare_2091234717iple_a Bool)) (A_1 (-> tptp.hoare_2091234717iple_a Bool)) (B_1 (-> tptp.hoare_2091234717iple_a Bool))) (let ((_let_1 (@ tptp.semila2006181266le_a_o C_1))) (= (@ _let_1 (@ (@ tptp.minus_836160335le_a_o A_1) B_1)) (@ (@ tptp.minus_836160335le_a_o (@ _let_1 A_1)) (@ _let_1 B_1))))))
% 0.62/0.96 (assert (forall ((C_1 (-> tptp.pname Bool)) (A_1 (-> tptp.pname Bool)) (B_1 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.semila1673364395name_o C_1))) (= (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_1) B_1)) (@ (@ tptp.minus_minus_pname_o (@ _let_1 A_1)) (@ _let_1 B_1))))))
% 0.62/0.96 (assert (forall ((C_1 (-> tptp.nat Bool)) (A_1 (-> tptp.nat Bool)) (B_1 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.semila1947288293_nat_o C_1))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_1) B_1)) (@ (@ tptp.minus_minus_nat_o (@ _let_1 A_1)) (@ _let_1 B_1))))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N_1) tptp.zero_zero_nat)))
% 0.62/0.96 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 0.62/0.96 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 0.62/0.96 (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)))))
% 0.62/0.96 (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))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N_1)) (@ tptp.suc K_1)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N_1)) K_1))))
% 0.62/0.96 (assert (forall ((I_1 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I_1))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K_1) (@ (@ tptp.minus_minus_nat (@ _let_1 K_1)) J_1)))))
% 0.62/0.96 (assert (forall ((I_1 tptp.nat) (P (-> tptp.nat Bool)) (K_1 tptp.nat)) (=> (@ P K_1) (=> (forall ((N tptp.nat)) (=> (@ P (@ tptp.suc N)) (@ P N))) (@ P (@ (@ tptp.minus_minus_nat K_1) I_1))))))
% 0.62/0.96 (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 tptp.nat)) K)) (@ _let_1 N_1))))))
% 0.62/0.96 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N_1)) tptp.one_one_nat) N_1)))
% 0.62/0.96 (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)))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N_1) N_1)))
% 0.62/0.96 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 0.62/0.96 (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)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N_1) M) (= N_1 tptp.zero_zero_nat))))
% 0.62/0.96 (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))))))
% 0.62/0.96 (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)))))
% 0.62/0.96 (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)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) N_1) (@ (@ tptp.plus_plus_nat N_1) M))))
% 0.62/0.96 (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)))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 N_1)) K_1) (@ _let_1 (@ (@ tptp.plus_plus_nat N_1) K_1))))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K_1))) (= (= (@ _let_1 M) (@ _let_1 N_1)) (= M N_1)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) K_1) (@ (@ tptp.plus_plus_nat N_1) K_1)) (= M N_1))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N_1)) N_1) M)))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N_1) M)) N_1) M)))
% 0.62/0.96 (assert (forall ((I_1 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I_1))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K_1) (@ _let_1 (@ (@ tptp.plus_plus_nat J_1) K_1))))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K_1))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N_1)) (@ (@ tptp.minus_minus_nat M) N_1)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K_1)) (@ (@ tptp.plus_plus_nat N_1) K_1)) (@ (@ tptp.minus_minus_nat M) N_1))))
% 0.62/0.96 (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)))))))
% 0.62/0.96 (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)))))))
% 0.62/0.96 (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)))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (= (@ tptp.suc N_1) (@ (@ tptp.plus_plus_nat N_1) tptp.one_one_nat))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (= (@ tptp.suc N_1) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) N_1))))
% 0.62/0.96 (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)))))))))
% 0.62/0.96 (assert (forall ((Com1_1 tptp.com) (Com2_1 tptp.com)) (= (@ tptp.com_size (@ (@ tptp.semi Com1_1) Com2_1)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.com_size Com1_1)) (@ tptp.com_size Com2_1))) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.62/0.96 (assert (forall ((Fun_1 (-> tptp.state Bool)) (Com_1 tptp.com)) (= (@ tptp.com_size (@ (@ tptp.while Fun_1) Com_1)) (@ (@ tptp.plus_plus_nat (@ tptp.com_size Com_1)) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.62/0.96 (assert (forall ((Pname_1 tptp.pname)) (= (@ tptp.com_size (@ tptp.body Pname_1)) tptp.zero_zero_nat)))
% 0.62/0.96 (assert (= (@ tptp.com_size tptp.skip) tptp.zero_zero_nat))
% 0.62/0.96 (assert (forall ((Com1_1 tptp.com) (Com2_1 tptp.com)) (= (@ tptp.size_size_com (@ (@ tptp.semi Com1_1) Com2_1)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.size_size_com Com1_1)) (@ tptp.size_size_com Com2_1))) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.62/0.96 (assert (forall ((Fun_1 (-> tptp.state Bool)) (Com_1 tptp.com)) (= (@ tptp.size_size_com (@ (@ tptp.while Fun_1) Com_1)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_com Com_1)) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K_1))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N_1)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N_1))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M) N_1)) K_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M) K_1)) (@ (@ tptp.times_times_nat N_1) K_1)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N_1) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N_1 tptp.one_one_nat)))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (= (@ (@ tptp.times_times_nat N_1) tptp.one_one_nat) N_1)))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N_1)) (and (= M tptp.one_one_nat) (= N_1 tptp.one_one_nat)))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N_1) N_1)))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N_1) tptp.zero_zero_nat)))
% 0.62/0.96 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N_1) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N_1 tptp.zero_zero_nat)))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K_1))) (= (= (@ _let_1 M) (@ _let_1 N_1)) (or (= M N_1) (= K_1 tptp.zero_zero_nat))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K_1) (@ (@ tptp.times_times_nat N_1) K_1)) (or (= M N_1) (= K_1 tptp.zero_zero_nat)))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K_1)))) (= (= (@ _let_1 M) (@ _let_1 N_1)) (= M N_1)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N_1)) K_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K_1)) (@ (@ tptp.times_times_nat N_1) K_1)))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K_1))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N_1)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N_1))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M) N_1) _let_1) (and (= M _let_1) (= N_1 _let_1))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M)) N_1) (@ (@ tptp.plus_plus_nat N_1) (@ (@ tptp.times_times_nat M) N_1)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ tptp.suc N_1)) (@ (@ tptp.plus_plus_nat M) (@ _let_1 N_1))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N_1)) (or (= N_1 tptp.one_one_nat) (= M tptp.zero_zero_nat)))))
% 0.62/0.96 (assert (forall ((Pname_1 tptp.pname)) (= (@ tptp.size_size_com (@ tptp.body Pname_1)) tptp.zero_zero_nat)))
% 0.62/0.96 (assert (= (@ tptp.size_size_com tptp.skip) tptp.zero_zero_nat))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat M) N_1))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.plus_plus_nat N_1) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) N_1)))))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.times_times_nat M) N_1) (@ (@ tptp.times_times_nat N_1) M))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ (@ tptp.times_times_nat (@ _let_1 N_1)) K_1) (@ _let_1 (@ (@ tptp.times_times_nat N_1) K_1))))))
% 0.62/0.96 (assert (forall ((I_1 tptp.nat) (U tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J_1) U)) K_1)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I_1) J_1)) U)) K_1))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K_1))) (= (= (@ _let_1 M) (@ _let_1 N_1)) (or (= K_1 tptp.zero_zero_nat) (= M N_1))))))
% 0.62/0.96 (assert (forall ((Fun_1 (-> tptp.state Bool)) (Com1_1 tptp.com) (Com2_1 tptp.com)) (= (@ tptp.size_size_com (@ (@ (@ tptp.cond Fun_1) Com1_1) Com2_1)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.size_size_com Com1_1)) (@ tptp.size_size_com Com2_1))) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.62/0.96 (assert (forall ((Fun_1 (-> tptp.state Bool)) (Com1_1 tptp.com) (Com2_1 tptp.com)) (= (@ tptp.com_size (@ (@ (@ tptp.cond Fun_1) Com1_1) Com2_1)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.com_size Com1_1)) (@ tptp.com_size Com2_1))) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) K_1))))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N_1)))
% 0.62/0.96 (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)))))))))
% 0.62/0.96 (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)))))
% 0.62/0.96 (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)))))
% 0.62/0.96 (assert (forall ((C0 tptp.com) (C1 tptp.com) (S1 tptp.state) (B (-> tptp.state Bool)) (S tptp.state)) (=> (not (@ B S)) (=> (@ (@ (@ tptp.evalc C1) S) S1) (@ (@ (@ tptp.evalc (@ (@ (@ tptp.cond B) C0) C1)) S) S1)))))
% 0.62/0.96 (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)))))
% 0.62/0.96 (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)))))))))
% 0.62/0.96 (assert (forall ((Pname tptp.pname) (Fun_1 (-> tptp.state Bool)) (Com1_1 tptp.com) (Com2_1 tptp.com)) (not (= (@ tptp.body Pname) (@ (@ (@ tptp.cond Fun_1) Com1_1) Com2_1)))))
% 0.62/0.96 (assert (forall ((Fun_1 (-> tptp.state Bool)) (Com1_1 tptp.com) (Com2_1 tptp.com) (Pname tptp.pname)) (not (= (@ (@ (@ tptp.cond Fun_1) Com1_1) Com2_1) (@ tptp.body Pname)))))
% 0.62/0.96 (assert (forall ((Fun_1 (-> tptp.state Bool)) (Com1_1 tptp.com) (Com2_1 tptp.com) (Fun (-> tptp.state Bool)) (Com1 tptp.com) (Com2 tptp.com)) (= (= (@ (@ (@ tptp.cond Fun_1) Com1_1) Com2_1) (@ (@ (@ tptp.cond Fun) Com1) Com2)) (and (= Fun_1 Fun) (= Com1_1 Com1) (= Com2_1 Com2)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N_1) (=> (@ (@ tptp.ord_less_eq_nat N_1) M) (= M N_1)))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J_1) (=> (@ (@ tptp.ord_less_eq_nat J_1) K_1) (@ _let_1 K_1))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (= M N_1) (@ (@ tptp.ord_less_eq_nat M) N_1))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N_1) (@ (@ tptp.ord_less_eq_nat N_1) M))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N_1) N_1)))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N_1) (@ (@ tptp.ord_less_eq_nat M) N_1))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.suc N_1))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N_1)) (= M _let_1)))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N_1) (@ _let_1 (@ tptp.suc N_1))))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N_1)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N_1) M))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.suc N_1))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N_1) (= M _let_1)))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N_1)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N_1)) M))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N_1)) N_1))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N_1) tptp.zero_zero_nat) (= N_1 tptp.zero_zero_nat))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N_1)))
% 0.62/0.96 (assert (forall ((M tptp.nat) (C tptp.com) (S tptp.state) (N_1 tptp.nat) (T tptp.state)) (let ((_let_1 (@ (@ tptp.evaln C) S))) (=> (@ (@ _let_1 N_1) T) (=> (@ (@ tptp.ord_less_eq_nat N_1) M) (@ (@ _let_1 M) T))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N_1)) M)))
% 0.62/0.96 (assert (forall ((L tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M) N_1) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N_1)) (@ _let_1 M))))))
% 0.62/0.96 (assert (forall ((L tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N_1) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L)) (@ (@ tptp.minus_minus_nat N_1) L)))))
% 0.62/0.96 (assert (forall ((I_1 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N_1))) (=> (@ (@ tptp.ord_less_eq_nat I_1) N_1) (= (@ _let_1 (@ _let_1 I_1)) I_1)))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat) (K_1 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K_1))) (=> (@ _let_1 M) (=> (@ _let_1 N_1) (= (= (@ (@ tptp.minus_minus_nat M) K_1) (@ (@ tptp.minus_minus_nat N_1) K_1)) (= M N_1)))))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat) (K_1 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K_1))) (=> (@ _let_2 M) (=> (@ _let_2 N_1) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K_1)) (@ (@ tptp.minus_minus_nat N_1) K_1)) (@ _let_1 N_1))))))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat) (K_1 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K_1))) (=> (@ _let_1 M) (=> (@ _let_1 N_1) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K_1)) (@ (@ tptp.minus_minus_nat N_1) K_1)) (@ (@ tptp.ord_less_eq_nat M) N_1)))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K_1)) N_1) (not (=> (@ (@ tptp.ord_less_eq_nat M) N_1) (not (@ (@ tptp.ord_less_eq_nat K_1) N_1)))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K_1)) N_1) (@ (@ tptp.ord_less_eq_nat M) N_1))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K_1)) N_1) (@ (@ tptp.ord_less_eq_nat K_1) N_1))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (=> (@ (@ tptp.ord_less_eq_nat K_1) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K_1)) (@ (@ tptp.plus_plus_nat J_1) L))))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K_1)) (@ (@ tptp.plus_plus_nat J_1) K_1)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J_1) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J_1))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J_1) (@ _let_1 (@ (@ tptp.plus_plus_nat J_1) M))))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K_1))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N_1)) (@ (@ tptp.ord_less_eq_nat M) N_1)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat M) N_1) (exists ((K tptp.nat)) (= N_1 (@ (@ tptp.plus_plus_nat M) K))))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N_1) (@ (@ tptp.plus_plus_nat N_1) M))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N_1) (@ (@ tptp.plus_plus_nat M) N_1))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (@ (@ tptp.ord_less_eq_nat I) N_1)))) (@ tptp.suc N_1))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N_1) (@ (@ (@ tptp.nat_case_o false) (@ tptp.ord_less_eq_nat M)) N_1))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (=> (@ (@ tptp.ord_less_eq_nat K_1) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I_1) K_1)) (@ (@ tptp.times_times_nat J_1) L))))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K_1))) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I_1)) (@ _let_1 J_1))))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I_1) K_1)) (@ (@ tptp.times_times_nat J_1) K_1)))))
% 0.62/0.96 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 0.62/0.96 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 0.62/0.96 (assert (forall ((Fun_1 (-> tptp.state Bool)) (Com1_1 tptp.com) (Com2_1 tptp.com) (Fun (-> tptp.state Bool)) (Com tptp.com)) (not (= (@ (@ (@ tptp.cond Fun_1) Com1_1) Com2_1) (@ (@ tptp.while Fun) Com)))))
% 0.62/0.96 (assert (forall ((Fun (-> tptp.state Bool)) (Com tptp.com) (Fun_1 (-> tptp.state Bool)) (Com1_1 tptp.com) (Com2_1 tptp.com)) (not (= (@ (@ tptp.while Fun) Com) (@ (@ (@ tptp.cond Fun_1) Com1_1) Com2_1)))))
% 0.62/0.96 (assert (forall ((Fun (-> tptp.state Bool)) (Com1 tptp.com) (Com2 tptp.com) (Com1_1 tptp.com) (Com2_1 tptp.com)) (not (= (@ (@ (@ tptp.cond Fun) Com1) Com2) (@ (@ tptp.semi Com1_1) Com2_1)))))
% 0.62/0.96 (assert (forall ((Com1_1 tptp.com) (Com2_1 tptp.com) (Fun (-> tptp.state Bool)) (Com1 tptp.com) (Com2 tptp.com)) (not (= (@ (@ tptp.semi Com1_1) Com2_1) (@ (@ (@ tptp.cond Fun) Com1) Com2)))))
% 0.62/0.96 (assert (forall ((Fun (-> tptp.state Bool)) (Com1 tptp.com) (Com2 tptp.com)) (not (= (@ (@ (@ tptp.cond Fun) Com1) Com2) tptp.skip))))
% 0.62/0.96 (assert (forall ((Fun (-> tptp.state Bool)) (Com1 tptp.com) (Com2 tptp.com)) (not (= tptp.skip (@ (@ (@ tptp.cond Fun) Com1) Com2)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N_1) (= (@ (@ tptp.minus_minus_nat M) N_1) tptp.zero_zero_nat))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N_1) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N_1))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N_1) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N_1) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N_1))))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K_1)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N_1)) (@ (@ tptp.ord_less_eq_nat M) N_1)))))
% 0.62/0.96 (assert (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K_1) J_1) (= (@ (@ tptp.minus_minus_nat I_1) (@ (@ tptp.minus_minus_nat J_1) K_1)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I_1) K_1)) J_1)))))
% 0.62/0.96 (assert (forall ((J_1 tptp.nat) (K_1 tptp.nat) (I_1 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J_1) K_1)) I_1) (@ (@ tptp.ord_less_eq_nat J_1) (@ (@ tptp.plus_plus_nat I_1) K_1)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K_1) N_1) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N_1) M)) K_1)))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N_1) M) (= (@ (@ tptp.plus_plus_nat N_1) (@ (@ tptp.minus_minus_nat M) N_1)) M))))
% 0.62/0.96 (assert (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I_1))) (=> (@ (@ tptp.ord_less_eq_nat K_1) J_1) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J_1) K_1)) (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K_1))))))
% 0.62/0.96 (assert (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K_1) J_1) (= (@ (@ tptp.ord_less_eq_nat I_1) (@ (@ tptp.minus_minus_nat J_1) K_1)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K_1)) J_1)))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N_1) M) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M) N_1)) N_1) M))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (= (= (@ (@ tptp.minus_minus_nat J_1) I_1) K_1) (= J_1 (@ (@ tptp.plus_plus_nat K_1) I_1))))))
% 0.62/0.96 (assert (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I_1))) (=> (@ (@ tptp.ord_less_eq_nat K_1) J_1) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K_1) (@ _let_1 (@ (@ tptp.minus_minus_nat J_1) K_1)))))))
% 0.62/0.96 (assert (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K_1) J_1) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J_1) K_1)) I_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J_1) I_1)) K_1)))))
% 0.62/0.96 (assert (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K_1) J_1) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J_1) I_1)) K_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J_1) K_1)) I_1)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N_1)) (and (@ _let_1 M) (@ _let_1 N_1))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K_1) J_1) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J_1) K_1))) M) (@ (@ tptp.minus_minus_nat (@ tptp.suc J_1)) (@ (@ tptp.plus_plus_nat K_1) M))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K_1) J_1) (= (@ (@ tptp.minus_minus_nat M) (@ tptp.suc (@ (@ tptp.minus_minus_nat J_1) K_1))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K_1)) (@ tptp.suc J_1))))))
% 0.62/0.96 (assert (forall ((U tptp.nat) (M tptp.nat) (N_1 tptp.nat) (J_1 tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J_1) I_1) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J_1) U)) N_1)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J_1)) U)) M)) N_1)))))
% 0.62/0.96 (assert (forall ((U tptp.nat) (M tptp.nat) (N_1 tptp.nat) (J_1 tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J_1) I_1) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J_1) U)) N_1)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J_1)) U)) M)) N_1)))))
% 0.62/0.96 (assert (forall ((U tptp.nat) (M tptp.nat) (N_1 tptp.nat) (J_1 tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J_1) I_1) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J_1) U)) N_1)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J_1)) U)) M) N_1)))))
% 0.62/0.96 (assert (forall ((U tptp.nat) (M tptp.nat) (N_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J_1) U)) N_1)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J_1) I_1)) U)) N_1))))))
% 0.62/0.96 (assert (forall ((U tptp.nat) (M tptp.nat) (N_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J_1) U)) N_1)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J_1) I_1)) U)) N_1))))))
% 0.62/0.96 (assert (forall ((U tptp.nat) (M tptp.nat) (N_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J_1) U)) N_1)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J_1) I_1)) U)) N_1))))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat) (M_2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N_1)) M_2) (exists ((M_1 tptp.nat)) (= M_2 (@ tptp.suc M_1))))))
% 0.62/0.96 (assert (forall ((P (-> tptp.nat Bool)) (N_1 tptp.nat) (M_2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N_1)) M_2) (=> (forall ((M_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N_1) M_1) (@ P (@ tptp.suc M_1)))) (@ P M_2)))))
% 0.62/0.96 (assert (forall ((N_2 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat N_2) (exists ((M_1 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N_2) (@ (@ tptp.ord_less_eq_nat X) M_1)))))))
% 0.62/0.96 (assert (forall ((U tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ F N))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N)) U)))))))
% 0.62/0.96 (assert (forall ((Z tptp.nat) (X_1 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X_1))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z))))))
% 0.62/0.96 (assert (forall ((Y tptp.nat) (X_1 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X_1))) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z))))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (not (@ (@ tptp.ord_less_nat N_1) tptp.zero_zero_nat))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_nat N_1) (@ tptp.suc N_1))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N_1) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N_1)))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) K_1))))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N_1))))
% 0.62/0.96 (assert (forall ((P (-> tptp.nat Bool)) (I_1 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K tptp.nat)) (and (@ P K) (@ (@ tptp.ord_less_nat K) I_1)))))))
% 0.62/0.96 (assert (forall ((N_2 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat N_2) (exists ((M_1 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N_2) (@ (@ tptp.ord_less_nat X) M_1)))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N_1) (= M N_1)) (@ (@ tptp.ord_less_eq_nat M) N_1))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N_1) (=> (not (= M N_1)) (@ (@ tptp.ord_less_nat M) N_1)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N_1) (@ (@ tptp.ord_less_eq_nat M) N_1))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat M) N_1) (or (@ (@ tptp.ord_less_nat M) N_1) (= M N_1)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) N_1) (and (@ (@ tptp.ord_less_eq_nat M) N_1) (not (= M N_1))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N_1) (@ (@ tptp.ord_less_nat M) N_1))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N_1) (= (@ (@ tptp.ord_less_nat N_1) (@ tptp.suc M)) (= N_1 M)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N_1) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N_1))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N_1) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N_1)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N_1) (@ (@ tptp.ord_less_nat M) N_1))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N_1)) (@ (@ tptp.ord_less_eq_nat M) N_1))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat N_1) M) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N_1)) M))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat) (K_1 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K_1))) (=> (@ _let_1 M) (=> (@ _let_1 N_1) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K_1)) (@ (@ tptp.minus_minus_nat N_1) K_1)) (@ (@ tptp.ord_less_nat M) N_1)))))))
% 0.62/0.96 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C)) (@ (@ tptp.minus_minus_nat B) C))))))
% 0.62/0.96 (assert (forall ((I_1 tptp.nat) (J_1 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) J_1)) I_1))))
% 0.62/0.96 (assert (forall ((J_1 tptp.nat) (I_1 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J_1) I_1)) I_1))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K_1))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N_1)) (@ (@ tptp.ord_less_nat M) N_1)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I_1))) (=> (@ _let_1 J_1) (@ _let_1 (@ (@ tptp.plus_plus_nat J_1) M))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I_1))) (=> (@ _let_1 J_1) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J_1))))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K_1)) (@ (@ tptp.plus_plus_nat J_1) K_1)))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (=> (@ (@ tptp.ord_less_nat K_1) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K_1)) (@ (@ tptp.plus_plus_nat J_1) L))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat K_1) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K_1) N_1)) (@ (@ tptp.ord_less_nat M) N_1)))))
% 0.62/0.96 (assert (forall ((I_1 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) J_1)) K_1) (@ (@ tptp.ord_less_nat I_1) K_1))))
% 0.62/0.96 (assert (forall ((L tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N_1) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N_1)) (@ _let_1 M))))))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J_1) K_1) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J_1) N_1)) K_1))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (not (@ (@ tptp.ord_less_nat N_1) tptp.zero_zero_nat))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (= (not (= N_1 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_1))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (not (@ (@ tptp.ord_less_nat N_1) tptp.zero_zero_nat))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N_1) (not (= N_1 tptp.zero_zero_nat)))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (=> (not (= N_1 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_1))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N_1)) (@ (@ tptp.ord_less_nat N_1) (@ tptp.suc M)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N_1)) (or (@ _let_1 N_1) (= M N_1))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N_1)) (@ (@ tptp.ord_less_nat M) N_1))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N_1))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N_1 M))))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N_1))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N_1))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N_1) (@ _let_1 (@ tptp.suc N_1))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N_1) (=> (not (= _let_1 N_1)) (@ (@ tptp.ord_less_nat _let_1) N_1))))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (=> (@ (@ tptp.ord_less_nat J_1) K_1) (@ (@ tptp.ord_less_nat (@ tptp.suc I_1)) K_1)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N_1)) (=> (not (@ _let_1 N_1)) (= M N_1))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N_1) (@ (@ tptp.ord_less_nat M) N_1))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N_1)) (@ (@ tptp.ord_less_nat M) N_1))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (not (@ (@ tptp.ord_less_nat N_1) N_1))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (not (= M N_1)) (or (@ (@ tptp.ord_less_nat M) N_1) (@ (@ tptp.ord_less_nat N_1) M)))))
% 0.62/0.96 (assert (forall ((X_1 tptp.nat) (Y tptp.nat)) (=> (not (= X_1 Y)) (=> (not (@ (@ tptp.ord_less_nat X_1) Y)) (@ (@ tptp.ord_less_nat Y) X_1)))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (not (@ (@ tptp.ord_less_nat N_1) N_1))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N_1) M) (not (= M N_1)))))
% 0.62/0.96 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 0.62/0.96 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ (@ P N_1) M))) (=> (=> (@ (@ tptp.ord_less_nat M) N_1) _let_1) (=> (=> (= M N_1) _let_1) (=> (=> (@ (@ tptp.ord_less_nat N_1) M) _let_1) _let_1))))))
% 0.62/0.96 (assert (forall ((I_1 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (= (@ (@ tptp.ord_less_nat I_1) (@ (@ tptp.minus_minus_nat J_1) K_1)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K_1)) J_1))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N_1)) (= (@ (@ tptp.plus_plus_nat N_1) (@ (@ tptp.minus_minus_nat M) N_1)) M))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K_1)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N_1)) (@ (@ tptp.ord_less_nat M) N_1)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N_1)) (@ tptp.suc M))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N_1)) (and (@ _let_1 M) (@ _let_1 N_1))))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K_1))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N_1)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K_1) (@ (@ tptp.ord_less_nat M) N_1))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K_1)) (@ (@ tptp.times_times_nat N_1) K_1)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K_1) (@ (@ tptp.ord_less_nat M) N_1)))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K_1) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I_1) K_1)) (@ (@ tptp.times_times_nat J_1) K_1))))))
% 0.62/0.96 (assert (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K_1))) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K_1) (@ (@ tptp.ord_less_nat (@ _let_1 I_1)) (@ _let_1 J_1)))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K_1) (= (= (@ _let_1 M) (@ _let_1 N_1)) (= M N_1))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K_1) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N_1)) (@ (@ tptp.ord_less_nat M) N_1))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N_1) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N_1)) M))))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N_1) M)) (@ (@ tptp.ord_less_nat M) N_1))))
% 0.62/0.96 (assert (forall ((I_1 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I_1) (@ tptp.suc (@ (@ tptp.plus_plus_nat I_1) M)))))
% 0.62/0.96 (assert (forall ((I_1 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I_1) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I_1)))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) N_1) (exists ((K tptp.nat)) (= N_1 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K)))))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N_1)) (or (@ _let_1 M) (@ _let_1 N_1))))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_1) (exists ((M_1 tptp.nat)) (= N_1 (@ tptp.suc M_1))))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (= (@ (@ tptp.ord_less_nat N_1) (@ tptp.suc tptp.zero_zero_nat)) (= N_1 tptp.zero_zero_nat))))
% 0.62/0.96 (assert (forall ((M tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N_1)) (or (= M tptp.zero_zero_nat) (exists ((J tptp.nat)) (and (= M (@ tptp.suc J)) (@ (@ tptp.ord_less_nat J) N_1)))))))
% 0.62/0.96 (assert (forall ((N_1 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (@ (@ tptp.ord_less_nat I) N_1)))) N_1)))
% 0.62/0.96 (assert (forall ((X tptp.nat)) (= (@ tptp.ord_less_nat X) (@ tptp.ord_less_eq_nat (@ tptp.suc X)))))
% 0.62/0.96 (assert (forall ((Z tptp.nat) (X_1 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X_1))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z))))))
% 0.62/0.96 (assert (forall ((Y tptp.nat) (X_1 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X_1))) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z))))))
% 0.62/0.96 (assert (forall ((X_1 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_1) Y) (@ (@ tptp.ord_less_eq_nat X_1) Y))))
% 0.62/0.96 (assert (forall ((X_1 tptp.nat) (Y tptp.nat)) (or (not (@ (@ tptp.fequal_nat X_1) Y)) (= X_1 Y))))
% 0.62/0.96 (assert (forall ((X_1 tptp.nat) (Y tptp.nat)) (or (not (= X_1 Y)) (@ (@ tptp.fequal_nat X_1) Y))))
% 0.62/0.96 (assert (forall ((X_1 tptp.pname) (Y tptp.pname)) (or (not (@ (@ tptp.fequal_pname X_1) Y)) (= X_1 Y))))
% 0.62/0.96 (assert (forall ((X_1 tptp.pname) (Y tptp.pname)) (or (not (= X_1 Y)) (@ (@ tptp.fequal_pname X_1) Y))))
% 0.62/0.96 (assert (forall ((X_1 tptp.state) (Y tptp.state)) (or (not (@ (@ tptp.fequal_state X_1) Y)) (= X_1 Y))))
% 0.62/0.96 (assert (forall ((X_1 tptp.state) (Y tptp.state)) (or (not (= X_1 Y)) (@ (@ tptp.fequal_state X_1) Y))))
% 0.62/0.96 (assert (forall ((X_1 tptp.hoare_2091234717iple_a) (Y tptp.hoare_2091234717iple_a)) (or (not (@ (@ tptp.fequal1604381340iple_a X_1) Y)) (= X_1 Y))))
% 0.62/0.96 (assert (forall ((X_1 tptp/export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 25483 Alarm clock ( read result; case "$result" in
% 299.87/300.30 unsat)
% 299.87/300.30 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.87/300.30 ;;
% 299.87/300.30 sat)
% 299.87/300.30 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.87/300.30 ;;
% 299.87/300.30 esac; exit 1 )
% 299.87/300.30 .hoare_2091234717iple_a) (Y tptp.hoare_2091234717iple_a)) (or (not (= X_1 Y)) (@ (@ tptp.fequal1604381340iple_a X_1) Y))))
% 299.87/300.30 (assert (forall ((X_1 tptp.hoare_1708887482_state) (Y tptp.hoare_1708887482_state)) (or (not (@ (@ tptp.fequal224822779_state X_1) Y)) (= X_1 Y))))
% 299.87/300.30 (assert (forall ((X_1 tptp.hoare_1708887482_state) (Y tptp.hoare_1708887482_state)) (or (not (= X_1 Y)) (@ (@ tptp.fequal224822779_state X_1) Y))))
% 299.87/300.30 (assert (forall ((X_1 (-> tptp.hoare_2091234717iple_a Bool)) (Y (-> tptp.hoare_2091234717iple_a Bool))) (or (not (@ (@ tptp.fequal845167073le_a_o X_1) Y)) (= X_1 Y))))
% 299.87/300.30 (assert (forall ((X_1 (-> tptp.hoare_2091234717iple_a Bool)) (Y (-> tptp.hoare_2091234717iple_a Bool))) (or (not (= X_1 Y)) (@ (@ tptp.fequal845167073le_a_o X_1) Y))))
% 299.87/300.30 (assert (forall ((N tptp.nat)) (=> (forall ((X tptp.hoare_2091234717iple_a)) (=> (@ (@ tptp.member290856304iple_a X) (@ (@ tptp.semila1052848428le_a_o tptp.g) (@ (@ tptp.image_231808478iple_a (lambda ((Pn tptp.pname)) (@ (@ (@ tptp.hoare_657976383iple_a (@ tptp.p Pn)) (@ tptp.body Pn)) (@ tptp.q Pn)))) tptp.procs))) (@ (@ tptp.hoare_1421888935alid_a N) X))) (forall ((X tptp.hoare_2091234717iple_a)) (=> (@ (@ tptp.member290856304iple_a X) (@ (@ tptp.image_231808478iple_a (lambda ((Pn tptp.pname)) (@ (@ (@ tptp.hoare_657976383iple_a (@ tptp.p Pn)) (@ tptp.the_com (@ tptp.body_1 Pn))) (@ tptp.q Pn)))) tptp.procs)) (@ (@ tptp.hoare_1421888935alid_a N) X))))))
% 299.87/300.30 (assert (not (=> (forall ((X tptp.hoare_2091234717iple_a)) (=> (@ (@ tptp.member290856304iple_a X) tptp.g) (@ (@ tptp.hoare_1421888935alid_a tptp.n) X))) (forall ((X tptp.hoare_2091234717iple_a)) (=> (@ (@ tptp.member290856304iple_a X) (@ (@ tptp.image_231808478iple_a (lambda ((Pn tptp.pname)) (@ (@ (@ tptp.hoare_657976383iple_a (@ tptp.p Pn)) (@ tptp.body Pn)) (@ tptp.q Pn)))) tptp.procs)) (@ (@ tptp.hoare_1421888935alid_a tptp.n) X))))))
% 299.87/300.30 (set-info :filename cvc5---1.0.5_25055)
% 299.87/300.30 (check-sat-assuming ( true ))
% 299.87/300.30 ------- get file name : TPTP file name is SWW471^3
% 299.87/300.30 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_25055.smt2...
% 299.87/300.30 --- Run --ho-elim --full-saturate-quant at 10...
% 299.87/300.30 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 299.87/300.30 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 299.87/300.30 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 299.87/300.30 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 299.87/300.30 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 299.87/300.30 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 299.87/300.30 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 299.87/300.30 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
% 299.87/300.30 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
% 299.87/300.30 % cvc5---1.0.5 exiting
% 299.87/300.30 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------