TSTP Solution File: ITP166^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP166^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:18:48 EDT 2023
% Result : Theorem 0.71s 0.90s
% Output : Proof 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.16 % Problem : ITP166^1 : TPTP v8.1.2. Released v7.5.0.
% 0.11/0.18 % Command : do_cvc5 %s %d
% 0.17/0.39 % Computer : n024.cluster.edu
% 0.17/0.39 % Model : x86_64 x86_64
% 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39 % Memory : 8042.1875MB
% 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39 % CPULimit : 300
% 0.17/0.39 % WCLimit : 300
% 0.17/0.39 % DateTime : Sun Aug 27 16:37:54 EDT 2023
% 0.17/0.39 % CPUTime :
% 0.24/0.56 %----Proving TH0
% 0.24/0.56 %------------------------------------------------------------------------------
% 0.24/0.56 % File : ITP166^1 : TPTP v8.1.2. Released v7.5.0.
% 0.24/0.56 % Domain : Interactive Theorem Proving
% 0.24/0.56 % Problem : Sledgehammer RelationalIncorrectness problem prob_274__5902014_1
% 0.24/0.56 % Version : Especial.
% 0.24/0.56 % English :
% 0.24/0.56
% 0.24/0.56 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.24/0.56 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.24/0.56 % Source : [Des21]
% 0.24/0.56 % Names : RelationalIncorrectness/prob_274__5902014_1 [Des21]
% 0.24/0.56
% 0.24/0.56 % Status : Theorem
% 0.24/0.56 % Rating : 0.23 v8.1.0, 0.27 v7.5.0
% 0.24/0.56 % Syntax : Number of formulae : 330 ( 125 unt; 108 typ; 0 def)
% 0.24/0.56 % Number of atoms : 601 ( 284 equ; 0 cnn)
% 0.24/0.56 % Maximal formula atoms : 16 ( 2 avg)
% 0.24/0.56 % Number of connectives : 2463 ( 74 ~; 17 |; 97 &;2079 @)
% 0.24/0.56 % ( 0 <=>; 196 =>; 0 <=; 0 <~>)
% 0.24/0.56 % Maximal formula depth : 24 ( 8 avg)
% 0.24/0.56 % Number of types : 28 ( 27 usr)
% 0.24/0.56 % Number of type conns : 742 ( 742 >; 0 *; 0 +; 0 <<)
% 0.24/0.56 % Number of symbols : 82 ( 81 usr; 7 con; 0-6 aty)
% 0.24/0.56 % Number of variables : 897 ( 98 ^; 747 !; 52 ?; 897 :)
% 0.24/0.56 % SPC : TH0_THM_EQU_NAR
% 0.24/0.56
% 0.24/0.56 % Comments : This file was generated by Sledgehammer 2021-02-23 15:33:22.688
% 0.24/0.56 %------------------------------------------------------------------------------
% 0.24/0.56 % Could-be-implicit typings (27)
% 0.24/0.56 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_Mt__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_J_J,type,
% 0.24/0.56 set_Pr1333062727ar_int: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_Mt__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_J,type,
% 0.24/0.56 produc1346207591ar_int: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_J_J,type,
% 0.24/0.56 set_li1762364675ar_int: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Typerep__Otyperep_J_Mt__List__Olist_It__Typerep__Otyperep_J_J_J,type,
% 0.24/0.56 set_Pr446800905yperep: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_J,type,
% 0.24/0.56 list_P1741976099ar_int: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_J,type,
% 0.24/0.56 set_Pr1148378109ar_int: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J_J,type,
% 0.24/0.56 set_Pr1560408065st_nat: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Typerep__Otyperep_J_Mt__List__Olist_It__Typerep__Otyperep_J_J,type,
% 0.24/0.56 produc490010537yperep: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J,type,
% 0.24/0.56 produc1260470173ar_int: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
% 0.24/0.56 produc1699244961st_nat: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Typerep__Otyperep_Mt__Typerep__Otyperep_J_J,type,
% 0.24/0.56 set_Pr1097818217yperep: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.24/0.56 set_Pr1986765409at_nat: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Product____Type__Oprod_It__Typerep__Otyperep_Mt__Typerep__Otyperep_J,type,
% 0.24/0.56 produc1788831497yperep: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.24/0.56 product_prod_nat_nat: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Set__Oset_It__List__Olist_It__Typerep__Otyperep_J_J,type,
% 0.24/0.56 set_list_typerep: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__List__Olist_It__Typerep__Otyperep_J,type,
% 0.24/0.56 list_typerep: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Set__Oset_It__Typerep__Otyperep_J,type,
% 0.24/0.56 set_typerep: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__List__Olist_It__String__Ochar_J,type,
% 0.24/0.56 list_char: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 0.24/0.56 list_nat: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.24/0.56 set_nat: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Typerep__Otyperep,type,
% 0.24/0.56 typerep: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__String__Oliteral,type,
% 0.24/0.56 literal: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__BExp__Obexp,type,
% 0.24/0.56 bexp: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__AExp__Oaexp,type,
% 0.24/0.56 aexp: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Nat__Onat,type,
% 0.24/0.56 nat: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Int__Oint,type,
% 0.24/0.56 int: $tType ).
% 0.24/0.56
% 0.24/0.56 thf(ty_n_t__Com__Ocom,type,
% 0.24/0.56 com: $tType ).
% 0.24/0.56
% 0.24/0.56 % Explicit typings (81)
% 0.24/0.56 thf(sy_c_BExp_Obval,type,
% 0.24/0.56 bval: bexp > ( list_char > int ) > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Typerep__Otyperep,type,
% 0.24/0.56 bNF_Gr457912949yperep: set_list_typerep > typerep > set_list_typerep ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Typerep__Otyperep,type,
% 0.24/0.56 bNF_Gr1303086585yperep: set_list_typerep > list_typerep > set_typerep ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_001t__Com__Ocom_001_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J,type,
% 0.24/0.56 bNF_Gr202451329ar_int: set_Pr1148378109ar_int > ( produc1260470173ar_int > com ) > ( produc1260470173ar_int > list_char > int ) > set_Pr1148378109ar_int ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.24/0.56 bNF_Gr749752805at_nat: set_Pr1148378109ar_int > ( produc1260470173ar_int > nat ) > ( produc1260470173ar_int > nat ) > set_Pr1986765409at_nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_BNF__Greatest__Fixpoint_OrelImage_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.24/0.56 bNF_Gr1247133574at_nat: set_Pr1986765409at_nat > ( nat > nat ) > set_Pr1986765409at_nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_BNF__Greatest__Fixpoint_OrelInvImage_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.24/0.56 bNF_Gr808751971at_nat: set_nat > set_Pr1986765409at_nat > ( nat > nat ) > set_Pr1986765409at_nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_BNF__Greatest__Fixpoint_OrelInvImage_001t__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_001t__Nat__Onat,type,
% 0.24/0.56 bNF_Gr1143394412nt_nat: set_Pr1148378109ar_int > set_Pr1986765409at_nat > ( produc1260470173ar_int > nat ) > set_Pr1333062727ar_int ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Big__Step_Obig__step,type,
% 0.24/0.56 big_big_step: produc1260470173ar_int > ( list_char > int ) > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Com_Ocom_OAssign,type,
% 0.24/0.56 assign: list_char > aexp > com ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Com_Ocom_OIf,type,
% 0.24/0.56 if: bexp > com > com > com ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Com_Ocom_OSKIP,type,
% 0.24/0.56 skip: com ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Com_Ocom_OSeq,type,
% 0.24/0.56 seq: com > com > com ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Com_Ocom_OWhile,type,
% 0.24/0.56 while: bexp > com > com ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Com_Ocom_Osize__com,type,
% 0.24/0.56 size_com: com > nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Nat__Onat,type,
% 0.24/0.56 unique1592618082ux_nat: product_prod_nat_nat > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 0.24/0.56 plus_plus_nat: nat > nat > nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.24/0.56 zero_zero_nat: nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 0.24/0.56 append_nat: list_nat > list_nat > list_nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_List_Oappend_001t__Typerep__Otyperep,type,
% 0.24/0.56 append_typerep: list_typerep > list_typerep > list_typerep ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_List_Ogen__length_001t__Typerep__Otyperep,type,
% 0.24/0.56 gen_length_typerep: nat > list_typerep > nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_List_Olex_001t__Nat__Onat,type,
% 0.24/0.56 lex_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_List_Olex_001t__Typerep__Otyperep,type,
% 0.24/0.56 lex_typerep: set_Pr1097818217yperep > set_Pr446800905yperep ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_List_Olexord_001t__Nat__Onat,type,
% 0.24/0.56 lexord_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_List_Olexord_001t__Typerep__Otyperep,type,
% 0.24/0.56 lexord_typerep: set_Pr1097818217yperep > set_Pr446800905yperep ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 0.24/0.56 cons_nat: nat > list_nat > list_nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J,type,
% 0.24/0.56 cons_P1254790739ar_int: produc1260470173ar_int > list_P1741976099ar_int > list_P1741976099ar_int ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_List_Olist_OCons_001t__Typerep__Otyperep,type,
% 0.24/0.56 cons_typerep: typerep > list_typerep > list_typerep ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_List_Olist_Osize__list_001t__Typerep__Otyperep,type,
% 0.24/0.56 size_list_typerep: ( typerep > nat ) > list_typerep > nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_List_Olistrel1_001t__Nat__Onat,type,
% 0.24/0.56 listrel1_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_List_Olistrel1_001t__Typerep__Otyperep,type,
% 0.24/0.56 listrel1_typerep: set_Pr1097818217yperep > set_Pr446800905yperep ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_List_Oset__Cons_001t__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J,type,
% 0.24/0.56 set_Co1954412371ar_int: set_Pr1148378109ar_int > set_li1762364675ar_int > set_li1762364675ar_int ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_List_Oset__Cons_001t__Typerep__Otyperep,type,
% 0.24/0.56 set_Cons_typerep: set_typerep > set_list_typerep > set_list_typerep ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Nat_OSuc,type,
% 0.24/0.56 suc: nat > nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Nat_Osize__class_Osize_001t__Com__Ocom,type,
% 0.24/0.56 size_size_com: com > nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 0.24/0.56 size_size_list_nat: list_nat > nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Typerep__Otyperep_J,type,
% 0.24/0.56 size_s416147576yperep: list_typerep > nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Nat_Osize__class_Osize_001t__Typerep__Otyperep,type,
% 0.24/0.56 size_size_typerep: typerep > nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Product__Type_OPair_001t__Com__Ocom_001_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J,type,
% 0.24/0.56 produc1193801173ar_int: com > ( list_char > int ) > produc1260470173ar_int ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Nat__Onat_J,type,
% 0.24/0.56 produc1625736153st_nat: list_nat > list_nat > produc1699244961st_nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Typerep__Otyperep_J_001t__List__Olist_It__Typerep__Otyperep_J,type,
% 0.24/0.56 produc1695567329yperep: list_typerep > list_typerep > produc490010537yperep ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.24/0.56 product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_001t__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J,type,
% 0.24/0.56 produc317451735ar_int: produc1260470173ar_int > produc1260470173ar_int > produc1346207591ar_int ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Product__Type_OPair_001t__Typerep__Otyperep_001t__Typerep__Otyperep,type,
% 0.24/0.56 produc2071514689yperep: typerep > typerep > produc1788831497yperep ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_RelationalIncorrectness__Mirabelle__kefqvmgyto_Oflip,type,
% 0.24/0.56 relati186416454e_flip: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( list_char > int ) > ( list_char > int ) > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_RelationalIncorrectness__Mirabelle__kefqvmgyto_Oget__back_001_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J,type,
% 0.24/0.56 relati23543761ar_int: ( ( list_char > int ) > ( list_char > int ) > $o ) > bexp > com > nat > ( list_char > int ) > ( list_char > int ) > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_RelationalIncorrectness__Mirabelle__kefqvmgyto_Oir__hoare,type,
% 0.24/0.56 relati2102071307_hoare: ( ( list_char > int ) > ( list_char > int ) > $o ) > com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_RelationalIncorrectness__Mirabelle__kefqvmgyto_Oir__valid,type,
% 0.24/0.56 relati775585786_valid: ( ( list_char > int ) > ( list_char > int ) > $o ) > com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Set_OCollect_001t__List__Olist_It__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_J,type,
% 0.24/0.56 collec672902542ar_int: ( list_P1741976099ar_int > $o ) > set_li1762364675ar_int ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Set_OCollect_001t__List__Olist_It__Typerep__Otyperep_J,type,
% 0.24/0.56 collect_list_typerep: ( list_typerep > $o ) > set_list_typerep ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J,type,
% 0.24/0.56 collec770796680ar_int: ( produc1260470173ar_int > $o ) > set_Pr1148378109ar_int ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.24/0.56 collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_Mt__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_J,type,
% 0.24/0.56 collec1834387154ar_int: ( produc1346207591ar_int > $o ) > set_Pr1333062727ar_int ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Typerep_Otyperep_OTyperep,type,
% 0.24/0.56 typerep2: literal > list_typerep > typerep ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_Typerep_Otyperep_Osize__typerep,type,
% 0.24/0.56 size_typerep: typerep > nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_member_001t__List__Olist_It__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_J,type,
% 0.24/0.56 member2052091212ar_int: list_P1741976099ar_int > set_li1762364675ar_int > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_member_001t__List__Olist_It__Typerep__Otyperep_J,type,
% 0.24/0.56 member_list_typerep: list_typerep > set_list_typerep > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_member_001t__Nat__Onat,type,
% 0.24/0.56 member_nat: nat > set_nat > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_member_001t__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J,type,
% 0.24/0.56 member92250950ar_int: produc1260470173ar_int > set_Pr1148378109ar_int > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
% 0.24/0.56 member1926390090st_nat: produc1699244961st_nat > set_Pr1560408065st_nat > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Typerep__Otyperep_J_Mt__List__Olist_It__Typerep__Otyperep_J_J,type,
% 0.24/0.56 member1812711762yperep: produc490010537yperep > set_Pr446800905yperep > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.24/0.56 member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_member_001t__Product____Type__Oprod_It__Typerep__Otyperep_Mt__Typerep__Otyperep_J,type,
% 0.24/0.56 member100911538yperep: produc1788831497yperep > set_Pr1097818217yperep > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_c_member_001t__Typerep__Otyperep,type,
% 0.24/0.56 member_typerep: typerep > set_typerep > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_P,type,
% 0.24/0.56 p: ( list_char > int ) > ( list_char > int ) > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_Q,type,
% 0.24/0.56 q: ( list_char > int ) > ( list_char > int ) > $o ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_b,type,
% 0.24/0.56 b: bexp ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_c,type,
% 0.24/0.56 c: com ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_c_H,type,
% 0.24/0.56 c2: com ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_k,type,
% 0.24/0.56 k: nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_ka____,type,
% 0.24/0.56 ka: nat ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_s_H____,type,
% 0.24/0.56 s: list_char > int ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_s_Ha____,type,
% 0.24/0.56 s_a: list_char > int ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_s____,type,
% 0.24/0.56 s2: list_char > int ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_sa____,type,
% 0.24/0.56 sa: list_char > int ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_t_H____,type,
% 0.24/0.56 t: list_char > int ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_t_Ha____,type,
% 0.24/0.56 t_a: list_char > int ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_t____,type,
% 0.24/0.56 t2: list_char > int ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_ta____,type,
% 0.24/0.56 ta: list_char > int ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_u____,type,
% 0.24/0.56 u: list_char > int ).
% 0.24/0.56
% 0.24/0.56 thf(sy_v_ua____,type,
% 0.24/0.56 ua: list_char > int ).
% 0.24/0.56
% 0.24/0.56 % Relevant facts (221)
% 0.24/0.56 thf(fact_0_Suc_Oprems_I6_J,axiom,
% 0.24/0.56 bval @ b @ sa ).
% 0.24/0.56
% 0.24/0.56 % Suc.prems(6)
% 0.24/0.56 thf(fact_1__092_060open_062bval_Ab_As_____092_060close_062,axiom,
% 0.24/0.56 bval @ b @ s2 ).
% 0.24/0.56
% 0.24/0.56 % \<open>bval b s__\<close>
% 0.24/0.56 thf(fact_2_Suc_Oprems_I3_J,axiom,
% 0.24/0.56 big_big_step @ ( produc1193801173ar_int @ c @ sa ) @ ta ).
% 0.24/0.56
% 0.24/0.56 % Suc.prems(3)
% 0.24/0.56 thf(fact_3_Suc_Oprems_I4_J,axiom,
% 0.24/0.56 big_big_step @ ( produc1193801173ar_int @ c2 @ s_a ) @ t_a ).
% 0.24/0.56
% 0.24/0.56 % Suc.prems(4)
% 0.24/0.56 thf(fact_4_Suc_Oprems_I7_J,axiom,
% 0.24/0.56 relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ sa @ s_a ).
% 0.24/0.56
% 0.24/0.56 % Suc.prems(7)
% 0.24/0.56 thf(fact_5__092_060open_062_Ic_H_M_As_H_____J_A_092_060Rightarrow_062_At_H_____092_060close_062,axiom,
% 0.24/0.56 big_big_step @ ( produc1193801173ar_int @ c2 @ s ) @ t ).
% 0.24/0.56
% 0.24/0.56 % \<open>(c', s'__) \<Rightarrow> t'__\<close>
% 0.24/0.56 thf(fact_6__092_060open_062_Ic_M_As_____J_A_092_060Rightarrow_062_At_____092_060close_062,axiom,
% 0.24/0.56 big_big_step @ ( produc1193801173ar_int @ c @ s2 ) @ t2 ).
% 0.24/0.56
% 0.24/0.56 % \<open>(c, s__) \<Rightarrow> t__\<close>
% 0.24/0.56 thf(fact_7_Suc_Oprems_I5_J,axiom,
% 0.24/0.56 q @ ua @ t_a ).
% 0.24/0.56
% 0.24/0.56 % Suc.prems(5)
% 0.24/0.56 thf(fact_8__092_060open_062get__back_AP_Ab_Ac_Ak_As_____As_H_____092_060close_062,axiom,
% 0.24/0.56 relati23543761ar_int @ p @ b @ c @ k @ s2 @ s ).
% 0.24/0.56
% 0.24/0.56 % \<open>get_back P b c k s__ s'__\<close>
% 0.24/0.56 thf(fact_9_Suc_Oprems_I2_J,axiom,
% 0.24/0.56 big_big_step @ ( produc1193801173ar_int @ ( while @ b @ c ) @ ta ) @ ua ).
% 0.24/0.56
% 0.24/0.56 % Suc.prems(2)
% 0.24/0.56 thf(fact_10__092_060open_062_IWHILE_Ab_ADO_Ac_M_At_____J_A_092_060Rightarrow_062_Au_____092_060close_062,axiom,
% 0.24/0.56 big_big_step @ ( produc1193801173ar_int @ ( while @ b @ c ) @ t2 ) @ u ).
% 0.24/0.56
% 0.24/0.56 % \<open>(WHILE b DO c, t__) \<Rightarrow> u__\<close>
% 0.24/0.56 thf(fact_11_Suc_Oprems_I1_J,axiom,
% 0.24/0.56 relati775585786_valid @ ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) ) @ ( while @ b @ c ) @ c2 @ q ).
% 0.24/0.56
% 0.24/0.56 % Suc.prems(1)
% 0.24/0.56 thf(fact_12_nat_Oinject,axiom,
% 0.24/0.56 ! [X2: nat,Y2: nat] :
% 0.24/0.56 ( ( ( suc @ X2 )
% 0.24/0.56 = ( suc @ Y2 ) )
% 0.24/0.56 = ( X2 = Y2 ) ) ).
% 0.24/0.56
% 0.24/0.56 % nat.inject
% 0.24/0.56 thf(fact_13_old_Onat_Oinject,axiom,
% 0.24/0.56 ! [Nat: nat,Nat2: nat] :
% 0.24/0.56 ( ( ( suc @ Nat )
% 0.24/0.56 = ( suc @ Nat2 ) )
% 0.24/0.56 = ( Nat = Nat2 ) ) ).
% 0.24/0.56
% 0.24/0.56 % old.nat.inject
% 0.24/0.56 thf(fact_14_prod_Oinject,axiom,
% 0.24/0.56 ! [X1: nat,X2: nat,Y1: nat,Y2: nat] :
% 0.24/0.56 ( ( ( product_Pair_nat_nat @ X1 @ X2 )
% 0.24/0.56 = ( product_Pair_nat_nat @ Y1 @ Y2 ) )
% 0.24/0.56 = ( ( X1 = Y1 )
% 0.24/0.56 & ( X2 = Y2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % prod.inject
% 0.24/0.56 thf(fact_15_prod_Oinject,axiom,
% 0.24/0.56 ! [X1: com,X2: list_char > int,Y1: com,Y2: list_char > int] :
% 0.24/0.56 ( ( ( produc1193801173ar_int @ X1 @ X2 )
% 0.24/0.56 = ( produc1193801173ar_int @ Y1 @ Y2 ) )
% 0.24/0.56 = ( ( X1 = Y1 )
% 0.24/0.56 & ( X2 = Y2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % prod.inject
% 0.24/0.56 thf(fact_16_old_Oprod_Oinject,axiom,
% 0.24/0.56 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 0.24/0.56 ( ( ( product_Pair_nat_nat @ A @ B )
% 0.24/0.56 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 0.24/0.56 = ( ( A = A2 )
% 0.24/0.56 & ( B = B2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % old.prod.inject
% 0.24/0.56 thf(fact_17_old_Oprod_Oinject,axiom,
% 0.24/0.56 ! [A: com,B: list_char > int,A2: com,B2: list_char > int] :
% 0.24/0.56 ( ( ( produc1193801173ar_int @ A @ B )
% 0.24/0.56 = ( produc1193801173ar_int @ A2 @ B2 ) )
% 0.24/0.56 = ( ( A = A2 )
% 0.24/0.56 & ( B = B2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % old.prod.inject
% 0.24/0.56 thf(fact_18_Suc_OIH,axiom,
% 0.24/0.56 ! [T: list_char > int,U: list_char > int,S: list_char > int,S2: list_char > int,T2: list_char > int] :
% 0.24/0.56 ( ( relati775585786_valid @ ( relati23543761ar_int @ p @ b @ c @ ka ) @ ( while @ b @ c ) @ c2 @ q )
% 0.24/0.56 => ( ( big_big_step @ ( produc1193801173ar_int @ ( while @ b @ c ) @ T ) @ U )
% 0.24/0.56 => ( ( big_big_step @ ( produc1193801173ar_int @ c @ S ) @ T )
% 0.24/0.56 => ( ( big_big_step @ ( produc1193801173ar_int @ c2 @ S2 ) @ T2 )
% 0.24/0.56 => ( ( q @ U @ T2 )
% 0.24/0.56 => ( ( bval @ b @ S )
% 0.24/0.56 => ( ( relati23543761ar_int @ p @ b @ c @ ka @ S @ S2 )
% 0.24/0.56 => ? [S3: list_char > int,S4: list_char > int] :
% 0.24/0.56 ( ( relati23543761ar_int @ p @ b @ c @ ka @ S3 @ S4 )
% 0.24/0.56 & ( bval @ b @ S3 )
% 0.24/0.56 & ( big_big_step @ ( produc1193801173ar_int @ c @ S3 ) @ T )
% 0.24/0.56 & ( big_big_step @ ( produc1193801173ar_int @ c2 @ S4 ) @ T2 ) ) ) ) ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Suc.IH
% 0.24/0.56 thf(fact_19_sim__sym,axiom,
% 0.24/0.56 ! [C: com,C2: com] :
% 0.24/0.56 ( ( ! [S5: list_char > int,T3: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ C @ S5 ) @ T3 )
% 0.24/0.56 = ( big_big_step @ ( produc1193801173ar_int @ C2 @ S5 ) @ T3 ) ) )
% 0.24/0.56 = ( ! [S5: list_char > int,T3: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ C2 @ S5 ) @ T3 )
% 0.24/0.56 = ( big_big_step @ ( produc1193801173ar_int @ C @ S5 ) @ T3 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % sim_sym
% 0.24/0.56 thf(fact_20_sim__refl,axiom,
% 0.24/0.56 ! [C: com,S6: list_char > int,T4: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ C @ S6 ) @ T4 )
% 0.24/0.56 = ( big_big_step @ ( produc1193801173ar_int @ C @ S6 ) @ T4 ) ) ).
% 0.24/0.56
% 0.24/0.56 % sim_refl
% 0.24/0.56 thf(fact_21__092_060open_062Q_Au_____At_H_____092_060close_062,axiom,
% 0.24/0.56 q @ u @ t ).
% 0.24/0.56
% 0.24/0.56 % \<open>Q u__ t'__\<close>
% 0.24/0.56 thf(fact_22_disj__ir__valid,axiom,
% 0.24/0.56 ! [P_1: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q_1: ( list_char > int ) > ( list_char > int ) > $o,P_2: ( list_char > int ) > ( list_char > int ) > $o,Q_2: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.56 ( ( relati775585786_valid @ P_1 @ C @ C2 @ Q_1 )
% 0.24/0.56 => ( ( relati775585786_valid @ P_2 @ C @ C2 @ Q_2 )
% 0.24/0.56 => ( relati775585786_valid
% 0.24/0.56 @ ^ [S5: list_char > int,S7: list_char > int] :
% 0.24/0.56 ( ( P_1 @ S5 @ S7 )
% 0.24/0.56 | ( P_2 @ S5 @ S7 ) )
% 0.24/0.56 @ C
% 0.24/0.56 @ C2
% 0.24/0.56 @ ^ [T3: list_char > int,T5: list_char > int] :
% 0.24/0.56 ( ( Q_1 @ T3 @ T5 )
% 0.24/0.56 | ( Q_2 @ T3 @ T5 ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % disj_ir_valid
% 0.24/0.56 thf(fact_23__092_060open_062ir__valid_A_Iget__back_AP_Ab_Ac_Ak_J_A_IWHILE_Ab_ADO_Ac_J_Ac_H_AQ_092_060close_062,axiom,
% 0.24/0.56 relati775585786_valid @ ( relati23543761ar_int @ p @ b @ c @ k ) @ ( while @ b @ c ) @ c2 @ q ).
% 0.24/0.56
% 0.24/0.56 % \<open>ir_valid (get_back P b c k) (WHILE b DO c) c' Q\<close>
% 0.24/0.56 thf(fact_24_conseq__ir__valid,axiom,
% 0.24/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,P2: ( list_char > int ) > ( list_char > int ) > $o,Q2: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.56 ( ( relati775585786_valid @ P @ C @ C2 @ Q )
% 0.24/0.56 => ( ! [S3: list_char > int,S4: list_char > int] :
% 0.24/0.56 ( ( P @ S3 @ S4 )
% 0.24/0.56 => ( P2 @ S3 @ S4 ) )
% 0.24/0.56 => ( ! [S3: list_char > int,S4: list_char > int] :
% 0.24/0.56 ( ( Q2 @ S3 @ S4 )
% 0.24/0.56 => ( Q @ S3 @ S4 ) )
% 0.24/0.56 => ( relati775585786_valid @ P2 @ C @ C2 @ Q2 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % conseq_ir_valid
% 0.24/0.56 thf(fact_25_ir__valid__get__back,axiom,
% 0.24/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C: com,K: nat,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.56 ( ( relati775585786_valid @ ( relati23543761ar_int @ P @ B @ C @ ( suc @ K ) ) @ ( while @ B @ C ) @ C2 @ Q )
% 0.24/0.56 => ( relati775585786_valid @ ( relati23543761ar_int @ P @ B @ C @ K ) @ ( while @ B @ C ) @ C2 @ Q ) ) ).
% 0.24/0.56
% 0.24/0.56 % ir_valid_get_back
% 0.24/0.56 thf(fact_26_sim__while__cong__aux,axiom,
% 0.24/0.56 ! [B: bexp,C: com,S: list_char > int,T: list_char > int,C2: com] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S ) @ T )
% 0.24/0.56 => ( ! [S3: list_char > int,T6: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ C @ S3 ) @ T6 )
% 0.24/0.56 = ( big_big_step @ ( produc1193801173ar_int @ C2 @ S3 ) @ T6 ) )
% 0.24/0.56 => ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C2 ) @ S ) @ T ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % sim_while_cong_aux
% 0.24/0.56 thf(fact_27_sim__while__cong,axiom,
% 0.24/0.56 ! [C: com,C2: com,B: bexp] :
% 0.24/0.56 ( ! [S3: list_char > int,T6: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ C @ S3 ) @ T6 )
% 0.24/0.56 = ( big_big_step @ ( produc1193801173ar_int @ C2 @ S3 ) @ T6 ) )
% 0.24/0.56 => ! [S6: list_char > int,T4: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S6 ) @ T4 )
% 0.24/0.56 = ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C2 ) @ S6 ) @ T4 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % sim_while_cong
% 0.24/0.56 thf(fact_28_ir__valid__def,axiom,
% 0.24/0.56 ( relati775585786_valid
% 0.24/0.56 = ( ^ [P3: ( list_char > int ) > ( list_char > int ) > $o,C3: com,C4: com,Q3: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.56 ! [T3: list_char > int,T5: list_char > int] :
% 0.24/0.56 ( ( Q3 @ T3 @ T5 )
% 0.24/0.56 => ? [S5: list_char > int,S7: list_char > int] :
% 0.24/0.56 ( ( P3 @ S5 @ S7 )
% 0.24/0.56 & ( big_big_step @ ( produc1193801173ar_int @ C3 @ S5 ) @ T3 )
% 0.24/0.56 & ( big_big_step @ ( produc1193801173ar_int @ C4 @ S7 ) @ T5 ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ir_valid_def
% 0.24/0.56 thf(fact_29_WhileFalse,axiom,
% 0.24/0.56 ! [B: bexp,S: list_char > int,C: com] :
% 0.24/0.56 ( ~ ( bval @ B @ S )
% 0.24/0.56 => ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S ) @ S ) ) ).
% 0.24/0.56
% 0.24/0.56 % WhileFalse
% 0.24/0.56 thf(fact_30_WhileTrue,axiom,
% 0.24/0.56 ! [B: bexp,S_1: list_char > int,C: com,S_2: list_char > int,S_3: list_char > int] :
% 0.24/0.56 ( ( bval @ B @ S_1 )
% 0.24/0.56 => ( ( big_big_step @ ( produc1193801173ar_int @ C @ S_1 ) @ S_2 )
% 0.24/0.56 => ( ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S_2 ) @ S_3 )
% 0.24/0.56 => ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S_1 ) @ S_3 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % WhileTrue
% 0.24/0.56 thf(fact_31_WhileE,axiom,
% 0.24/0.56 ! [B: bexp,C: com,S: list_char > int,T: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S ) @ T )
% 0.24/0.56 => ( ( ( T = S )
% 0.24/0.56 => ( bval @ B @ S ) )
% 0.24/0.56 => ~ ( ( bval @ B @ S )
% 0.24/0.56 => ! [S_22: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ C @ S ) @ S_22 )
% 0.24/0.56 => ~ ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S_22 ) @ T ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % WhileE
% 0.24/0.56 thf(fact_32_old_Oprod_Oinducts,axiom,
% 0.24/0.56 ! [P: product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 0.24/0.56 ( ! [A3: nat,B3: nat] : ( P @ ( product_Pair_nat_nat @ A3 @ B3 ) )
% 0.24/0.56 => ( P @ Prod ) ) ).
% 0.24/0.56
% 0.24/0.56 % old.prod.inducts
% 0.24/0.56 thf(fact_33_old_Oprod_Oinducts,axiom,
% 0.24/0.56 ! [P: produc1260470173ar_int > $o,Prod: produc1260470173ar_int] :
% 0.24/0.56 ( ! [A3: com,B3: list_char > int] : ( P @ ( produc1193801173ar_int @ A3 @ B3 ) )
% 0.24/0.56 => ( P @ Prod ) ) ).
% 0.24/0.56
% 0.24/0.56 % old.prod.inducts
% 0.24/0.56 thf(fact_34_old_Oprod_Oexhaust,axiom,
% 0.24/0.56 ! [Y: product_prod_nat_nat] :
% 0.24/0.56 ~ ! [A3: nat,B3: nat] :
% 0.24/0.56 ( Y
% 0.24/0.56 != ( product_Pair_nat_nat @ A3 @ B3 ) ) ).
% 0.24/0.56
% 0.24/0.56 % old.prod.exhaust
% 0.24/0.56 thf(fact_35_old_Oprod_Oexhaust,axiom,
% 0.24/0.56 ! [Y: produc1260470173ar_int] :
% 0.24/0.56 ~ ! [A3: com,B3: list_char > int] :
% 0.24/0.56 ( Y
% 0.24/0.56 != ( produc1193801173ar_int @ A3 @ B3 ) ) ).
% 0.24/0.56
% 0.24/0.56 % old.prod.exhaust
% 0.24/0.56 thf(fact_36_Pair__inject,axiom,
% 0.24/0.56 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 0.24/0.56 ( ( ( product_Pair_nat_nat @ A @ B )
% 0.24/0.56 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 0.24/0.56 => ~ ( ( A = A2 )
% 0.24/0.56 => ( B != B2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Pair_inject
% 0.24/0.56 thf(fact_37_Pair__inject,axiom,
% 0.24/0.56 ! [A: com,B: list_char > int,A2: com,B2: list_char > int] :
% 0.24/0.56 ( ( ( produc1193801173ar_int @ A @ B )
% 0.24/0.56 = ( produc1193801173ar_int @ A2 @ B2 ) )
% 0.24/0.56 => ~ ( ( A = A2 )
% 0.24/0.56 => ( B != B2 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Pair_inject
% 0.24/0.56 thf(fact_38_prod__cases,axiom,
% 0.24/0.56 ! [P: product_prod_nat_nat > $o,P4: product_prod_nat_nat] :
% 0.24/0.56 ( ! [A3: nat,B3: nat] : ( P @ ( product_Pair_nat_nat @ A3 @ B3 ) )
% 0.24/0.56 => ( P @ P4 ) ) ).
% 0.24/0.56
% 0.24/0.56 % prod_cases
% 0.24/0.56 thf(fact_39_prod__cases,axiom,
% 0.24/0.56 ! [P: produc1260470173ar_int > $o,P4: produc1260470173ar_int] :
% 0.24/0.56 ( ! [A3: com,B3: list_char > int] : ( P @ ( produc1193801173ar_int @ A3 @ B3 ) )
% 0.24/0.56 => ( P @ P4 ) ) ).
% 0.24/0.56
% 0.24/0.56 % prod_cases
% 0.24/0.56 thf(fact_40_mem__Collect__eq,axiom,
% 0.24/0.56 ! [A: produc1260470173ar_int,P: produc1260470173ar_int > $o] :
% 0.24/0.56 ( ( member92250950ar_int @ A @ ( collec770796680ar_int @ P ) )
% 0.24/0.56 = ( P @ A ) ) ).
% 0.24/0.56
% 0.24/0.56 % mem_Collect_eq
% 0.24/0.56 thf(fact_41_Collect__mem__eq,axiom,
% 0.24/0.56 ! [A4: set_Pr1148378109ar_int] :
% 0.24/0.56 ( ( collec770796680ar_int
% 0.24/0.56 @ ^ [X: produc1260470173ar_int] : ( member92250950ar_int @ X @ A4 ) )
% 0.24/0.56 = A4 ) ).
% 0.24/0.56
% 0.24/0.56 % Collect_mem_eq
% 0.24/0.56 thf(fact_42_surj__pair,axiom,
% 0.24/0.56 ! [P4: product_prod_nat_nat] :
% 0.24/0.56 ? [X3: nat,Y3: nat] :
% 0.24/0.56 ( P4
% 0.24/0.56 = ( product_Pair_nat_nat @ X3 @ Y3 ) ) ).
% 0.24/0.56
% 0.24/0.56 % surj_pair
% 0.24/0.56 thf(fact_43_surj__pair,axiom,
% 0.24/0.56 ! [P4: produc1260470173ar_int] :
% 0.24/0.56 ? [X3: com,Y3: list_char > int] :
% 0.24/0.56 ( P4
% 0.24/0.56 = ( produc1193801173ar_int @ X3 @ Y3 ) ) ).
% 0.24/0.56
% 0.24/0.56 % surj_pair
% 0.24/0.56 thf(fact_44_n__not__Suc__n,axiom,
% 0.24/0.56 ! [N: nat] :
% 0.24/0.56 ( N
% 0.24/0.56 != ( suc @ N ) ) ).
% 0.24/0.56
% 0.24/0.56 % n_not_Suc_n
% 0.24/0.56 thf(fact_45_Suc__inject,axiom,
% 0.24/0.56 ! [X4: nat,Y: nat] :
% 0.24/0.56 ( ( ( suc @ X4 )
% 0.24/0.56 = ( suc @ Y ) )
% 0.24/0.56 => ( X4 = Y ) ) ).
% 0.24/0.56
% 0.24/0.56 % Suc_inject
% 0.24/0.56 thf(fact_46_big__step__determ,axiom,
% 0.24/0.56 ! [C: com,S: list_char > int,T: list_char > int,U: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ C @ S ) @ T )
% 0.24/0.56 => ( ( big_big_step @ ( produc1193801173ar_int @ C @ S ) @ U )
% 0.24/0.56 => ( U = T ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % big_step_determ
% 0.24/0.56 thf(fact_47_sim__trans,axiom,
% 0.24/0.56 ! [C: com,C2: com,C5: com] :
% 0.24/0.56 ( ! [S3: list_char > int,T6: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ C @ S3 ) @ T6 )
% 0.24/0.56 = ( big_big_step @ ( produc1193801173ar_int @ C2 @ S3 ) @ T6 ) )
% 0.24/0.56 => ( ! [S3: list_char > int,T6: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ C2 @ S3 ) @ T6 )
% 0.24/0.56 = ( big_big_step @ ( produc1193801173ar_int @ C5 @ S3 ) @ T6 ) )
% 0.24/0.56 => ! [S6: list_char > int,T4: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ C @ S6 ) @ T4 )
% 0.24/0.56 = ( big_big_step @ ( produc1193801173ar_int @ C5 @ S6 ) @ T4 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % sim_trans
% 0.24/0.56 thf(fact_48_com_Oinject_I4_J,axiom,
% 0.24/0.56 ! [X51: bexp,X52: com,Y51: bexp,Y52: com] :
% 0.24/0.56 ( ( ( while @ X51 @ X52 )
% 0.24/0.56 = ( while @ Y51 @ Y52 ) )
% 0.24/0.56 = ( ( X51 = Y51 )
% 0.24/0.56 & ( X52 = Y52 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % com.inject(4)
% 0.24/0.56 thf(fact_49_While__False__ir__valid,axiom,
% 0.24/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,C: com] :
% 0.24/0.56 ( ( relati775585786_valid
% 0.24/0.56 @ ^ [S5: list_char > int,S7: list_char > int] :
% 0.24/0.56 ( ( P @ S5 @ S7 )
% 0.24/0.56 & ~ ( bval @ B @ S5 ) )
% 0.24/0.56 @ skip
% 0.24/0.56 @ C2
% 0.24/0.56 @ Q )
% 0.24/0.56 => ( relati775585786_valid @ P @ ( while @ B @ C ) @ C2 @ Q ) ) ).
% 0.24/0.56
% 0.24/0.56 % While_False_ir_valid
% 0.24/0.56 thf(fact_50_While__True__ir__valid,axiom,
% 0.24/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.56 ( ( relati775585786_valid
% 0.24/0.56 @ ^ [S5: list_char > int,S7: list_char > int] :
% 0.24/0.56 ( ( P @ S5 @ S7 )
% 0.24/0.56 & ( bval @ B @ S5 ) )
% 0.24/0.56 @ ( seq @ C @ ( while @ B @ C ) )
% 0.24/0.56 @ C2
% 0.24/0.56 @ Q )
% 0.24/0.56 => ( relati775585786_valid @ P @ ( while @ B @ C ) @ C2 @ Q ) ) ).
% 0.24/0.56
% 0.24/0.56 % While_True_ir_valid
% 0.24/0.56 thf(fact_51_get__back_Osimps_I2_J,axiom,
% 0.24/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C: com,N: nat] :
% 0.24/0.56 ( ( relati23543761ar_int @ P @ B @ C @ ( suc @ N ) )
% 0.24/0.56 = ( ^ [T3: list_char > int,T5: list_char > int] :
% 0.24/0.56 ? [S5: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ C @ S5 ) @ T3 )
% 0.24/0.56 & ( bval @ B @ S5 )
% 0.24/0.56 & ( relati23543761ar_int @ P @ B @ C @ N @ S5 @ T5 ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % get_back.simps(2)
% 0.24/0.56 thf(fact_52_Skip__ir__valid,axiom,
% 0.24/0.56 ! [Q: ( list_char > int ) > ( list_char > int ) > $o,P: ( list_char > int ) > ( list_char > int ) > $o,C2: com] :
% 0.24/0.56 ( ! [T6: list_char > int,T7: list_char > int] :
% 0.24/0.56 ( ( Q @ T6 @ T7 )
% 0.24/0.56 => ? [S8: list_char > int] :
% 0.24/0.56 ( ( P @ T6 @ S8 )
% 0.24/0.56 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ S8 ) @ T7 ) ) )
% 0.24/0.56 => ( relati775585786_valid @ P @ skip @ C2 @ Q ) ) ).
% 0.24/0.56
% 0.24/0.56 % Skip_ir_valid
% 0.24/0.56 thf(fact_53_While__backwards__frontier__ir__valid_H,axiom,
% 0.24/0.56 ! [P: nat > ( list_char > int ) > ( list_char > int ) > $o,K: nat,B: bexp,C: com,Q: ( list_char > int ) > ( list_char > int ) > $o,C2: com,T: list_char > int,T2: list_char > int] :
% 0.24/0.56 ( ! [N2: nat,T6: list_char > int,T7: list_char > int] :
% 0.24/0.56 ( ( P @ ( plus_plus_nat @ K @ ( suc @ N2 ) ) @ T6 @ T7 )
% 0.24/0.56 => ? [S6: list_char > int] :
% 0.24/0.56 ( ( P @ ( plus_plus_nat @ K @ N2 ) @ S6 @ T7 )
% 0.24/0.56 & ( bval @ B @ S6 )
% 0.24/0.56 & ( big_big_step @ ( produc1193801173ar_int @ C @ S6 ) @ T6 ) ) )
% 0.24/0.56 => ( ! [T6: list_char > int,T7: list_char > int] :
% 0.24/0.56 ( ( Q @ T6 @ T7 )
% 0.24/0.56 => ? [S6: list_char > int,S8: list_char > int] :
% 0.24/0.56 ( ? [N3: nat] : ( P @ ( plus_plus_nat @ K @ N3 ) @ S6 @ S8 )
% 0.24/0.56 & ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S6 ) @ T6 )
% 0.24/0.56 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ S8 ) @ T7 ) ) )
% 0.24/0.56 => ( ( Q @ T @ T2 )
% 0.24/0.56 => ? [S3: list_char > int,S4: list_char > int] :
% 0.24/0.56 ( ( P @ K @ S3 @ S4 )
% 0.24/0.56 & ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S3 ) @ T )
% 0.24/0.56 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ S4 ) @ T2 ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % While_backwards_frontier_ir_valid'
% 0.24/0.56 thf(fact_54_sym__ir__valid,axiom,
% 0.24/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C2: com,C: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.56 ( ( relati775585786_valid @ ( relati186416454e_flip @ P ) @ C2 @ C @ ( relati186416454e_flip @ Q ) )
% 0.24/0.56 => ( relati775585786_valid @ P @ C @ C2 @ Q ) ) ).
% 0.24/0.56
% 0.24/0.56 % sym_ir_valid
% 0.24/0.56 thf(fact_55_pred__equals__eq2,axiom,
% 0.24/0.56 ! [R: set_Pr1986765409at_nat,S9: set_Pr1986765409at_nat] :
% 0.24/0.56 ( ( ( ^ [X: nat,Y4: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y4 ) @ R ) )
% 0.24/0.56 = ( ^ [X: nat,Y4: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y4 ) @ S9 ) ) )
% 0.24/0.56 = ( R = S9 ) ) ).
% 0.24/0.56
% 0.24/0.56 % pred_equals_eq2
% 0.24/0.56 thf(fact_56_pred__equals__eq2,axiom,
% 0.24/0.56 ! [R: set_Pr1148378109ar_int,S9: set_Pr1148378109ar_int] :
% 0.24/0.56 ( ( ( ^ [X: com,Y4: list_char > int] : ( member92250950ar_int @ ( produc1193801173ar_int @ X @ Y4 ) @ R ) )
% 0.24/0.56 = ( ^ [X: com,Y4: list_char > int] : ( member92250950ar_int @ ( produc1193801173ar_int @ X @ Y4 ) @ S9 ) ) )
% 0.24/0.56 = ( R = S9 ) ) ).
% 0.24/0.56
% 0.24/0.56 % pred_equals_eq2
% 0.24/0.56 thf(fact_57_com_Oinject_I2_J,axiom,
% 0.24/0.56 ! [X31: com,X32: com,Y31: com,Y32: com] :
% 0.24/0.56 ( ( ( seq @ X31 @ X32 )
% 0.24/0.56 = ( seq @ Y31 @ Y32 ) )
% 0.24/0.56 = ( ( X31 = Y31 )
% 0.24/0.56 & ( X32 = Y32 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % com.inject(2)
% 0.24/0.56 thf(fact_58_add__Suc__right,axiom,
% 0.24/0.56 ! [M: nat,N: nat] :
% 0.24/0.56 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 0.24/0.56 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % add_Suc_right
% 0.24/0.56 thf(fact_59_Seq__ir__valid,axiom,
% 0.24/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,D: com,D2: com,R: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.56 ( ( relati775585786_valid @ P @ C @ C2 @ Q )
% 0.24/0.56 => ( ( relati775585786_valid @ Q @ D @ D2 @ R )
% 0.24/0.56 => ( relati775585786_valid @ P @ ( seq @ C @ D ) @ ( seq @ C2 @ D2 ) @ R ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Seq_ir_valid
% 0.24/0.56 thf(fact_60_meh__simp,axiom,
% 0.24/0.56 ! [S2: list_char > int,T2: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ skip @ S2 ) @ T2 )
% 0.24/0.56 = ( S2 = T2 ) ) ).
% 0.24/0.56
% 0.24/0.56 % meh_simp
% 0.24/0.56 thf(fact_61_Seq2__ir__valid,axiom,
% 0.24/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,Q: ( list_char > int ) > ( list_char > int ) > $o,D: com,C2: com,R: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.56 ( ( relati775585786_valid @ P @ C @ skip @ Q )
% 0.24/0.56 => ( ( relati775585786_valid @ Q @ D @ C2 @ R )
% 0.24/0.56 => ( relati775585786_valid @ P @ ( seq @ C @ D ) @ C2 @ R ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Seq2_ir_valid
% 0.24/0.56 thf(fact_62_Seq1__ir__valid,axiom,
% 0.24/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,D: com,R: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.56 ( ( relati775585786_valid @ P @ C @ C2 @ Q )
% 0.24/0.56 => ( ( relati775585786_valid @ Q @ D @ skip @ R )
% 0.24/0.56 => ( relati775585786_valid @ P @ ( seq @ C @ D ) @ C2 @ R ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Seq1_ir_valid
% 0.24/0.56 thf(fact_63_com_Odistinct_I3_J,axiom,
% 0.24/0.56 ! [X31: com,X32: com] :
% 0.24/0.56 ( skip
% 0.24/0.56 != ( seq @ X31 @ X32 ) ) ).
% 0.24/0.56
% 0.24/0.56 % com.distinct(3)
% 0.24/0.56 thf(fact_64_com_Odistinct_I17_J,axiom,
% 0.24/0.56 ! [X31: com,X32: com,X51: bexp,X52: com] :
% 0.24/0.56 ( ( seq @ X31 @ X32 )
% 0.24/0.56 != ( while @ X51 @ X52 ) ) ).
% 0.24/0.56
% 0.24/0.56 % com.distinct(17)
% 0.24/0.56 thf(fact_65_com_Odistinct_I7_J,axiom,
% 0.24/0.56 ! [X51: bexp,X52: com] :
% 0.24/0.56 ( skip
% 0.24/0.56 != ( while @ X51 @ X52 ) ) ).
% 0.24/0.56
% 0.24/0.56 % com.distinct(7)
% 0.24/0.56 thf(fact_66_add__Suc__shift,axiom,
% 0.24/0.56 ! [M: nat,N: nat] :
% 0.24/0.56 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.24/0.56 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % add_Suc_shift
% 0.24/0.56 thf(fact_67_nat__arith_Osuc1,axiom,
% 0.24/0.56 ! [A4: nat,K: nat,A: nat] :
% 0.24/0.56 ( ( A4
% 0.24/0.56 = ( plus_plus_nat @ K @ A ) )
% 0.24/0.56 => ( ( suc @ A4 )
% 0.24/0.56 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % nat_arith.suc1
% 0.24/0.56 thf(fact_68_add__Suc,axiom,
% 0.24/0.56 ! [M: nat,N: nat] :
% 0.24/0.56 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.24/0.56 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % add_Suc
% 0.24/0.56 thf(fact_69_ir__valid__Seq1_H,axiom,
% 0.24/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C1: com,C22: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.56 ( ( relati775585786_valid @ P @ ( seq @ C1 @ C22 ) @ C2 @ Q )
% 0.24/0.56 => ( relati775585786_valid
% 0.24/0.56 @ ^ [T3: list_char > int,T5: list_char > int] :
% 0.24/0.56 ? [S5: list_char > int,S7: list_char > int] :
% 0.24/0.56 ( ( P @ S5 @ S7 )
% 0.24/0.56 & ( big_big_step @ ( produc1193801173ar_int @ C1 @ S5 ) @ T3 )
% 0.24/0.56 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ S7 ) @ T5 )
% 0.24/0.56 & ? [U2: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ C22 @ T3 ) @ U2 )
% 0.24/0.56 & ( Q @ U2 @ T5 ) ) )
% 0.24/0.56 @ C22
% 0.24/0.56 @ skip
% 0.24/0.56 @ Q ) ) ).
% 0.24/0.56
% 0.24/0.56 % ir_valid_Seq1'
% 0.24/0.56 thf(fact_70_flip__def,axiom,
% 0.24/0.56 ( relati186416454e_flip
% 0.24/0.56 = ( ^ [P3: ( list_char > int ) > ( list_char > int ) > $o,S5: list_char > int,S7: list_char > int] : ( P3 @ S7 @ S5 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % flip_def
% 0.24/0.56 thf(fact_71_ir__valid__Seq1,axiom,
% 0.24/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C1: com,C22: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.56 ( ( relati775585786_valid @ P @ ( seq @ C1 @ C22 ) @ C2 @ Q )
% 0.24/0.56 => ( relati775585786_valid @ P @ C1 @ C2
% 0.24/0.56 @ ^ [T3: list_char > int,T5: list_char > int] :
% 0.24/0.56 ? [S5: list_char > int,S7: list_char > int] :
% 0.24/0.56 ( ( P @ S5 @ S7 )
% 0.24/0.56 & ( big_big_step @ ( produc1193801173ar_int @ C1 @ S5 ) @ T3 )
% 0.24/0.56 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ S7 ) @ T5 )
% 0.24/0.56 & ? [U2: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ C22 @ T3 ) @ U2 )
% 0.24/0.56 & ( Q @ U2 @ T5 ) ) ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % ir_valid_Seq1
% 0.24/0.56 thf(fact_72_SeqE,axiom,
% 0.24/0.56 ! [C1: com,C22: com,S1: list_char > int,S32: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ ( seq @ C1 @ C22 ) @ S1 ) @ S32 )
% 0.24/0.56 => ~ ! [S_22: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ C1 @ S1 ) @ S_22 )
% 0.24/0.56 => ~ ( big_big_step @ ( produc1193801173ar_int @ C22 @ S_22 ) @ S32 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % SeqE
% 0.24/0.56 thf(fact_73_Seq__assoc,axiom,
% 0.24/0.56 ! [C1: com,C22: com,C32: com,S: list_char > int,S2: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ ( seq @ ( seq @ C1 @ C22 ) @ C32 ) @ S ) @ S2 )
% 0.24/0.56 = ( big_big_step @ ( produc1193801173ar_int @ ( seq @ C1 @ ( seq @ C22 @ C32 ) ) @ S ) @ S2 ) ) ).
% 0.24/0.56
% 0.24/0.56 % Seq_assoc
% 0.24/0.56 thf(fact_74_Seq,axiom,
% 0.24/0.56 ! [C_1: com,S_1: list_char > int,S_2: list_char > int,C_2: com,S_3: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ C_1 @ S_1 ) @ S_2 )
% 0.24/0.56 => ( ( big_big_step @ ( produc1193801173ar_int @ C_2 @ S_2 ) @ S_3 )
% 0.24/0.56 => ( big_big_step @ ( produc1193801173ar_int @ ( seq @ C_1 @ C_2 ) @ S_1 ) @ S_3 ) ) ) ).
% 0.24/0.56
% 0.24/0.56 % Seq
% 0.24/0.56 thf(fact_75_SkipE,axiom,
% 0.24/0.56 ! [S: list_char > int,T: list_char > int] :
% 0.24/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ skip @ S ) @ T )
% 0.24/0.56 => ( T = S ) ) ).
% 0.24/0.56
% 0.24/0.56 % SkipE
% 0.24/0.56 thf(fact_76_Skip,axiom,
% 0.24/0.56 ! [S: list_char > int] : ( big_big_step @ ( produc1193801173ar_int @ skip @ S ) @ S ) ).
% 0.24/0.56
% 0.24/0.56 % Skip
% 0.24/0.56 thf(fact_77_ir__valid__track__history,axiom,
% 0.24/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,S: list_char > int,S2: list_char > int] :
% 0.24/0.56 ( ( relati775585786_valid @ P @ C @ C2 @ Q )
% 0.24/0.56 => ( relati775585786_valid @ P @ C @ C2
% 0.24/0.56 @ ^ [T3: list_char > int,T5: list_char > int] :
% 0.24/0.56 ( ( Q @ S @ S2 )
% 0.24/0.56 & ? [S5: list_char > int,S7: list_char > int] :
% 0.24/0.56 ( ( P @ S5 @ S7 )
% 0.24/0.56 & ( big_big_step @ ( produc1193801173ar_int @ C @ S5 ) @ T3 )
% 0.24/0.57 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ S7 ) @ T5 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % ir_valid_track_history
% 0.24/0.57 thf(fact_78_ir__valid__While1,axiom,
% 0.24/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C: com,K: nat,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.57 ( ( relati775585786_valid @ ( relati23543761ar_int @ P @ B @ C @ K ) @ ( while @ B @ C ) @ C2 @ Q )
% 0.24/0.57 => ( relati775585786_valid
% 0.24/0.57 @ ^ [S5: list_char > int,S7: list_char > int] :
% 0.24/0.57 ( ( relati23543761ar_int @ P @ B @ C @ K @ S5 @ S7 )
% 0.24/0.57 & ( bval @ B @ S5 ) )
% 0.24/0.57 @ C
% 0.24/0.57 @ skip
% 0.24/0.57 @ ^ [T3: list_char > int,T5: list_char > int] :
% 0.24/0.57 ( ( relati23543761ar_int @ P @ B @ C @ ( suc @ K ) @ T3 @ T5 )
% 0.24/0.57 & ? [U2: list_char > int,U3: list_char > int] :
% 0.24/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ T3 ) @ U2 )
% 0.24/0.57 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ T5 ) @ U3 )
% 0.24/0.57 & ( Q @ U2 @ U3 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % ir_valid_While1
% 0.24/0.57 thf(fact_79_add__right__cancel,axiom,
% 0.24/0.57 ! [B: nat,A: nat,C: nat] :
% 0.24/0.57 ( ( ( plus_plus_nat @ B @ A )
% 0.24/0.57 = ( plus_plus_nat @ C @ A ) )
% 0.24/0.57 = ( B = C ) ) ).
% 0.24/0.57
% 0.24/0.57 % add_right_cancel
% 0.24/0.57 thf(fact_80_add__left__cancel,axiom,
% 0.24/0.57 ! [A: nat,B: nat,C: nat] :
% 0.24/0.57 ( ( ( plus_plus_nat @ A @ B )
% 0.24/0.57 = ( plus_plus_nat @ A @ C ) )
% 0.24/0.57 = ( B = C ) ) ).
% 0.24/0.57
% 0.24/0.57 % add_left_cancel
% 0.24/0.57 thf(fact_81_ir__valid__If,axiom,
% 0.24/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C1: com,C22: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.57 ( ( relati775585786_valid @ P @ ( if @ B @ C1 @ C22 ) @ C2 @ Q )
% 0.24/0.57 => ( ( relati775585786_valid
% 0.24/0.57 @ ^ [S5: list_char > int,S7: list_char > int] :
% 0.24/0.57 ( ( P @ S5 @ S7 )
% 0.24/0.57 & ( bval @ B @ S5 ) )
% 0.24/0.57 @ C1
% 0.24/0.57 @ C2
% 0.24/0.57 @ ^ [T3: list_char > int,T5: list_char > int] :
% 0.24/0.57 ( ( Q @ T3 @ T5 )
% 0.24/0.57 & ? [S5: list_char > int,S7: list_char > int] :
% 0.24/0.57 ( ( P @ S5 @ S7 )
% 0.24/0.57 & ( big_big_step @ ( produc1193801173ar_int @ C1 @ S5 ) @ T3 )
% 0.24/0.57 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ S7 ) @ T5 )
% 0.24/0.57 & ( bval @ B @ S5 ) ) ) )
% 0.24/0.57 & ( relati775585786_valid
% 0.24/0.57 @ ^ [S5: list_char > int,S7: list_char > int] :
% 0.24/0.57 ( ( P @ S5 @ S7 )
% 0.24/0.57 & ~ ( bval @ B @ S5 ) )
% 0.24/0.57 @ C22
% 0.24/0.57 @ C2
% 0.24/0.57 @ ^ [T3: list_char > int,T5: list_char > int] :
% 0.24/0.57 ( ( Q @ T3 @ T5 )
% 0.24/0.57 & ? [S5: list_char > int,S7: list_char > int] :
% 0.24/0.57 ( ( P @ S5 @ S7 )
% 0.24/0.57 & ( big_big_step @ ( produc1193801173ar_int @ C22 @ S5 ) @ T3 )
% 0.24/0.57 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ S7 ) @ T5 )
% 0.24/0.57 & ~ ( bval @ B @ S5 ) ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % ir_valid_If
% 0.24/0.57 thf(fact_82_while__unfold,axiom,
% 0.24/0.57 ! [B: bexp,C: com,S6: list_char > int,T4: list_char > int] :
% 0.24/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S6 ) @ T4 )
% 0.24/0.57 = ( big_big_step @ ( produc1193801173ar_int @ ( if @ B @ ( seq @ C @ ( while @ B @ C ) ) @ skip ) @ S6 ) @ T4 ) ) ).
% 0.24/0.57
% 0.24/0.57 % while_unfold
% 0.24/0.57 thf(fact_83_If__True__ir__valid,axiom,
% 0.24/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C_1: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,C_2: com] :
% 0.24/0.57 ( ( relati775585786_valid
% 0.24/0.57 @ ^ [A5: list_char > int,C3: list_char > int] :
% 0.24/0.57 ( ( P @ A5 @ C3 )
% 0.24/0.57 & ( bval @ B @ A5 ) )
% 0.24/0.57 @ C_1
% 0.24/0.57 @ C2
% 0.24/0.57 @ Q )
% 0.24/0.57 => ( relati775585786_valid @ P @ ( if @ B @ C_1 @ C_2 ) @ C2 @ Q ) ) ).
% 0.24/0.57
% 0.24/0.57 % If_True_ir_valid
% 0.24/0.57 thf(fact_84_If__False__ir__valid,axiom,
% 0.24/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C_2: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,C_1: com] :
% 0.24/0.57 ( ( relati775585786_valid
% 0.24/0.57 @ ^ [A5: list_char > int,C3: list_char > int] :
% 0.24/0.57 ( ( P @ A5 @ C3 )
% 0.24/0.57 & ~ ( bval @ B @ A5 ) )
% 0.24/0.57 @ C_2
% 0.24/0.57 @ C2
% 0.24/0.57 @ Q )
% 0.24/0.57 => ( relati775585786_valid @ P @ ( if @ B @ C_1 @ C_2 ) @ C2 @ Q ) ) ).
% 0.24/0.57
% 0.24/0.57 % If_False_ir_valid
% 0.24/0.57 thf(fact_85_ir__While__True,axiom,
% 0.24/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.57 ( ( relati2102071307_hoare
% 0.24/0.57 @ ^ [S5: list_char > int,S7: list_char > int] :
% 0.24/0.57 ( ( P @ S5 @ S7 )
% 0.24/0.57 & ( bval @ B @ S5 ) )
% 0.24/0.57 @ ( seq @ C @ ( while @ B @ C ) )
% 0.24/0.57 @ C2
% 0.24/0.57 @ Q )
% 0.24/0.57 => ( relati2102071307_hoare @ P @ ( while @ B @ C ) @ C2 @ Q ) ) ).
% 0.24/0.57
% 0.24/0.57 % ir_While_True
% 0.24/0.57 thf(fact_86_com_Oinject_I3_J,axiom,
% 0.24/0.57 ! [X41: bexp,X42: com,X43: com,Y41: bexp,Y42: com,Y43: com] :
% 0.24/0.57 ( ( ( if @ X41 @ X42 @ X43 )
% 0.24/0.57 = ( if @ Y41 @ Y42 @ Y43 ) )
% 0.24/0.57 = ( ( X41 = Y41 )
% 0.24/0.57 & ( X42 = Y42 )
% 0.24/0.57 & ( X43 = Y43 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % com.inject(3)
% 0.24/0.57 thf(fact_87_ir__Skip__Skip,axiom,
% 0.24/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o] : ( relati2102071307_hoare @ P @ skip @ skip @ P ) ).
% 0.24/0.57
% 0.24/0.57 % ir_Skip_Skip
% 0.24/0.57 thf(fact_88_ir__hoare__Skip__Skip,axiom,
% 0.24/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,Q: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.57 ( ( relati2102071307_hoare @ P @ skip @ skip @ Q )
% 0.24/0.57 = ( ! [S5: list_char > int,S7: list_char > int] :
% 0.24/0.57 ( ( Q @ S5 @ S7 )
% 0.24/0.57 => ( P @ S5 @ S7 ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % ir_hoare_Skip_Skip
% 0.24/0.57 thf(fact_89_ir__disj,axiom,
% 0.24/0.57 ! [P_1: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q_1: ( list_char > int ) > ( list_char > int ) > $o,P_2: ( list_char > int ) > ( list_char > int ) > $o,Q_2: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.57 ( ( relati2102071307_hoare @ P_1 @ C @ C2 @ Q_1 )
% 0.24/0.57 => ( ( relati2102071307_hoare @ P_2 @ C @ C2 @ Q_2 )
% 0.24/0.57 => ( relati2102071307_hoare
% 0.24/0.57 @ ^ [S5: list_char > int,S7: list_char > int] :
% 0.24/0.57 ( ( P_1 @ S5 @ S7 )
% 0.24/0.57 | ( P_2 @ S5 @ S7 ) )
% 0.24/0.57 @ C
% 0.24/0.57 @ C2
% 0.24/0.57 @ ^ [T3: list_char > int,T5: list_char > int] :
% 0.24/0.57 ( ( Q_1 @ T3 @ T5 )
% 0.24/0.57 | ( Q_2 @ T3 @ T5 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % ir_disj
% 0.24/0.57 thf(fact_90_ir__pre,axiom,
% 0.24/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,P2: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.57 ( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
% 0.24/0.57 => ( ! [S3: list_char > int,S4: list_char > int] :
% 0.24/0.57 ( ( P @ S3 @ S4 )
% 0.24/0.57 => ( P2 @ S3 @ S4 ) )
% 0.24/0.57 => ( relati2102071307_hoare @ P2 @ C @ C2 @ Q ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % ir_pre
% 0.24/0.57 thf(fact_91_ir__post,axiom,
% 0.24/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,Q2: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.57 ( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
% 0.24/0.57 => ( ! [S3: list_char > int,S4: list_char > int] :
% 0.24/0.57 ( ( Q2 @ S3 @ S4 )
% 0.24/0.57 => ( Q @ S3 @ S4 ) )
% 0.24/0.57 => ( relati2102071307_hoare @ P @ C @ C2 @ Q2 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % ir_post
% 0.24/0.57 thf(fact_92_ir__conseq,axiom,
% 0.24/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,P2: ( list_char > int ) > ( list_char > int ) > $o,Q2: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.57 ( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
% 0.24/0.57 => ( ! [S3: list_char > int,S4: list_char > int] :
% 0.24/0.57 ( ( P @ S3 @ S4 )
% 0.24/0.57 => ( P2 @ S3 @ S4 ) )
% 0.24/0.57 => ( ! [S3: list_char > int,S4: list_char > int] :
% 0.24/0.57 ( ( Q2 @ S3 @ S4 )
% 0.24/0.57 => ( Q @ S3 @ S4 ) )
% 0.24/0.57 => ( relati2102071307_hoare @ P2 @ C @ C2 @ Q2 ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % ir_conseq
% 0.24/0.57 thf(fact_93_ir__If__False,axiom,
% 0.24/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C_2: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,C_1: com] :
% 0.24/0.57 ( ( relati2102071307_hoare
% 0.24/0.57 @ ^ [S5: list_char > int,S7: list_char > int] :
% 0.24/0.57 ( ( P @ S5 @ S7 )
% 0.24/0.57 & ~ ( bval @ B @ S5 ) )
% 0.24/0.57 @ C_2
% 0.24/0.57 @ C2
% 0.24/0.57 @ Q )
% 0.24/0.57 => ( relati2102071307_hoare @ P @ ( if @ B @ C_1 @ C_2 ) @ C2 @ Q ) ) ).
% 0.24/0.57
% 0.24/0.57 % ir_If_False
% 0.24/0.57 thf(fact_94_ir__If__True,axiom,
% 0.24/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C_1: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,C_2: com] :
% 0.24/0.57 ( ( relati2102071307_hoare
% 0.24/0.57 @ ^ [S5: list_char > int,S7: list_char > int] :
% 0.24/0.57 ( ( P @ S5 @ S7 )
% 0.24/0.57 & ( bval @ B @ S5 ) )
% 0.24/0.57 @ C_1
% 0.24/0.57 @ C2
% 0.24/0.57 @ Q )
% 0.24/0.57 => ( relati2102071307_hoare @ P @ ( if @ B @ C_1 @ C_2 ) @ C2 @ Q ) ) ).
% 0.24/0.57
% 0.24/0.57 % ir_If_True
% 0.24/0.57 thf(fact_95_soundness,axiom,
% 0.24/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.57 ( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
% 0.24/0.57 => ( relati775585786_valid @ P @ C @ C2 @ Q ) ) ).
% 0.24/0.57
% 0.24/0.57 % soundness
% 0.24/0.57 thf(fact_96_com_Odistinct_I19_J,axiom,
% 0.24/0.57 ! [X41: bexp,X42: com,X43: com,X51: bexp,X52: com] :
% 0.24/0.57 ( ( if @ X41 @ X42 @ X43 )
% 0.24/0.57 != ( while @ X51 @ X52 ) ) ).
% 0.24/0.57
% 0.24/0.57 % com.distinct(19)
% 0.24/0.57 thf(fact_97_com_Odistinct_I5_J,axiom,
% 0.24/0.57 ! [X41: bexp,X42: com,X43: com] :
% 0.24/0.57 ( skip
% 0.24/0.57 != ( if @ X41 @ X42 @ X43 ) ) ).
% 0.24/0.57
% 0.24/0.57 % com.distinct(5)
% 0.24/0.57 thf(fact_98_com_Odistinct_I15_J,axiom,
% 0.24/0.57 ! [X31: com,X32: com,X41: bexp,X42: com,X43: com] :
% 0.24/0.57 ( ( seq @ X31 @ X32 )
% 0.24/0.57 != ( if @ X41 @ X42 @ X43 ) ) ).
% 0.24/0.57
% 0.24/0.57 % com.distinct(15)
% 0.24/0.57 thf(fact_99_ir__sym,axiom,
% 0.24/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.57 ( ( relati2102071307_hoare @ ( relati186416454e_flip @ P ) @ C @ C2 @ ( relati186416454e_flip @ Q ) )
% 0.24/0.57 => ( relati2102071307_hoare @ P @ C2 @ C @ Q ) ) ).
% 0.24/0.57
% 0.24/0.57 % ir_sym
% 0.24/0.57 thf(fact_100_ir__Seq1,axiom,
% 0.24/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,D: com,R: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.57 ( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
% 0.24/0.57 => ( ( relati2102071307_hoare @ Q @ D @ skip @ R )
% 0.24/0.57 => ( relati2102071307_hoare @ P @ ( seq @ C @ D ) @ C2 @ R ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % ir_Seq1
% 0.24/0.57 thf(fact_101_commute__if,axiom,
% 0.24/0.57 ! [B1: bexp,B22: bexp,C11: com,C12: com,C22: com,S6: list_char > int,T4: list_char > int] :
% 0.24/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ ( if @ B1 @ ( if @ B22 @ C11 @ C12 ) @ C22 ) @ S6 ) @ T4 )
% 0.24/0.57 = ( big_big_step @ ( produc1193801173ar_int @ ( if @ B22 @ ( if @ B1 @ C11 @ C22 ) @ ( if @ B1 @ C12 @ C22 ) ) @ S6 ) @ T4 ) ) ).
% 0.24/0.57
% 0.24/0.57 % commute_if
% 0.24/0.57 thf(fact_102_triv__if,axiom,
% 0.24/0.57 ! [B: bexp,C: com,S6: list_char > int,T4: list_char > int] :
% 0.24/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ ( if @ B @ C @ C ) @ S6 ) @ T4 )
% 0.24/0.57 = ( big_big_step @ ( produc1193801173ar_int @ C @ S6 ) @ T4 ) ) ).
% 0.24/0.57
% 0.24/0.57 % triv_if
% 0.24/0.57 thf(fact_103_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.24/0.57 ! [A: nat,B: nat,C: nat] :
% 0.24/0.57 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.24/0.57 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % ab_semigroup_add_class.add_ac(1)
% 0.24/0.57 thf(fact_104_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.24/0.57 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.24/0.57 ( ( ( I = J )
% 0.24/0.57 & ( K = L ) )
% 0.24/0.57 => ( ( plus_plus_nat @ I @ K )
% 0.24/0.57 = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % add_mono_thms_linordered_semiring(4)
% 0.24/0.57 thf(fact_105_group__cancel_Oadd1,axiom,
% 0.24/0.57 ! [A4: nat,K: nat,A: nat,B: nat] :
% 0.24/0.57 ( ( A4
% 0.24/0.57 = ( plus_plus_nat @ K @ A ) )
% 0.24/0.57 => ( ( plus_plus_nat @ A4 @ B )
% 0.24/0.57 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % group_cancel.add1
% 0.24/0.57 thf(fact_106_group__cancel_Oadd2,axiom,
% 0.24/0.57 ! [B4: nat,K: nat,B: nat,A: nat] :
% 0.24/0.57 ( ( B4
% 0.24/0.57 = ( plus_plus_nat @ K @ B ) )
% 0.24/0.57 => ( ( plus_plus_nat @ A @ B4 )
% 0.24/0.57 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % group_cancel.add2
% 0.24/0.57 thf(fact_107_add_Oassoc,axiom,
% 0.24/0.57 ! [A: nat,B: nat,C: nat] :
% 0.24/0.57 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.24/0.57 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % add.assoc
% 0.24/0.57 thf(fact_108_add_Ocommute,axiom,
% 0.24/0.57 ( plus_plus_nat
% 0.24/0.57 = ( ^ [A5: nat,B5: nat] : ( plus_plus_nat @ B5 @ A5 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % add.commute
% 0.24/0.57 thf(fact_109_add_Oleft__commute,axiom,
% 0.24/0.57 ! [B: nat,A: nat,C: nat] :
% 0.24/0.57 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 0.24/0.57 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % add.left_commute
% 0.24/0.57 thf(fact_110_add__left__imp__eq,axiom,
% 0.24/0.57 ! [A: nat,B: nat,C: nat] :
% 0.24/0.57 ( ( ( plus_plus_nat @ A @ B )
% 0.24/0.57 = ( plus_plus_nat @ A @ C ) )
% 0.24/0.57 => ( B = C ) ) ).
% 0.24/0.57
% 0.24/0.57 % add_left_imp_eq
% 0.24/0.57 thf(fact_111_add__right__imp__eq,axiom,
% 0.24/0.57 ! [B: nat,A: nat,C: nat] :
% 0.24/0.57 ( ( ( plus_plus_nat @ B @ A )
% 0.24/0.57 = ( plus_plus_nat @ C @ A ) )
% 0.24/0.57 => ( B = C ) ) ).
% 0.24/0.57
% 0.24/0.57 % add_right_imp_eq
% 0.24/0.57 thf(fact_112_ir__Skip,axiom,
% 0.24/0.57 ! [Q: ( list_char > int ) > ( list_char > int ) > $o,P: ( list_char > int ) > ( list_char > int ) > $o,C2: com] :
% 0.24/0.57 ( ! [T6: list_char > int,T7: list_char > int] :
% 0.24/0.57 ( ( Q @ T6 @ T7 )
% 0.24/0.57 => ? [S8: list_char > int] :
% 0.24/0.57 ( ( P @ T6 @ S8 )
% 0.24/0.57 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ S8 ) @ T7 ) ) )
% 0.24/0.57 => ( relati2102071307_hoare @ P @ skip @ C2 @ Q ) ) ).
% 0.24/0.57
% 0.24/0.57 % ir_Skip
% 0.24/0.57 thf(fact_113_IfFalse,axiom,
% 0.24/0.57 ! [B: bexp,S: list_char > int,C_2: com,T: list_char > int,C_1: com] :
% 0.24/0.57 ( ~ ( bval @ B @ S )
% 0.24/0.57 => ( ( big_big_step @ ( produc1193801173ar_int @ C_2 @ S ) @ T )
% 0.24/0.57 => ( big_big_step @ ( produc1193801173ar_int @ ( if @ B @ C_1 @ C_2 ) @ S ) @ T ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % IfFalse
% 0.24/0.57 thf(fact_114_IfTrue,axiom,
% 0.24/0.57 ! [B: bexp,S: list_char > int,C_1: com,T: list_char > int,C_2: com] :
% 0.24/0.57 ( ( bval @ B @ S )
% 0.24/0.57 => ( ( big_big_step @ ( produc1193801173ar_int @ C_1 @ S ) @ T )
% 0.24/0.57 => ( big_big_step @ ( produc1193801173ar_int @ ( if @ B @ C_1 @ C_2 ) @ S ) @ T ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % IfTrue
% 0.24/0.57 thf(fact_115_IfE,axiom,
% 0.24/0.57 ! [B: bexp,C1: com,C22: com,S: list_char > int,T: list_char > int] :
% 0.24/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ ( if @ B @ C1 @ C22 ) @ S ) @ T )
% 0.24/0.57 => ( ( ( bval @ B @ S )
% 0.24/0.57 => ~ ( big_big_step @ ( produc1193801173ar_int @ C1 @ S ) @ T ) )
% 0.24/0.57 => ~ ( ~ ( bval @ B @ S )
% 0.24/0.57 => ~ ( big_big_step @ ( produc1193801173ar_int @ C22 @ S ) @ T ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % IfE
% 0.24/0.57 thf(fact_116_ir__While__False,axiom,
% 0.24/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,C: com] :
% 0.24/0.57 ( ( relati2102071307_hoare
% 0.24/0.57 @ ^ [S5: list_char > int,S7: list_char > int] :
% 0.24/0.57 ( ( P @ S5 @ S7 )
% 0.24/0.57 & ~ ( bval @ B @ S5 ) )
% 0.24/0.57 @ skip
% 0.24/0.57 @ C2
% 0.24/0.57 @ Q )
% 0.24/0.57 => ( relati2102071307_hoare @ P @ ( while @ B @ C ) @ C2 @ Q ) ) ).
% 0.24/0.57
% 0.24/0.57 % ir_While_False
% 0.24/0.57 thf(fact_117_com_Oexhaust,axiom,
% 0.24/0.57 ! [Y: com] :
% 0.24/0.57 ( ( Y != skip )
% 0.24/0.57 => ( ! [X21: list_char,X22: aexp] :
% 0.24/0.57 ( Y
% 0.24/0.57 != ( assign @ X21 @ X22 ) )
% 0.24/0.57 => ( ! [X312: com,X322: com] :
% 0.24/0.57 ( Y
% 0.24/0.57 != ( seq @ X312 @ X322 ) )
% 0.24/0.57 => ( ! [X412: bexp,X422: com,X432: com] :
% 0.24/0.57 ( Y
% 0.24/0.57 != ( if @ X412 @ X422 @ X432 ) )
% 0.24/0.57 => ~ ! [X512: bexp,X522: com] :
% 0.24/0.57 ( Y
% 0.24/0.57 != ( while @ X512 @ X522 ) ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % com.exhaust
% 0.24/0.57 thf(fact_118_com_Oinduct,axiom,
% 0.24/0.57 ! [P: com > $o,Com: com] :
% 0.24/0.57 ( ( P @ skip )
% 0.24/0.57 => ( ! [X12: list_char,X23: aexp] : ( P @ ( assign @ X12 @ X23 ) )
% 0.24/0.57 => ( ! [X12: com,X23: com] :
% 0.24/0.57 ( ( P @ X12 )
% 0.24/0.57 => ( ( P @ X23 )
% 0.24/0.57 => ( P @ ( seq @ X12 @ X23 ) ) ) )
% 0.24/0.57 => ( ! [X12: bexp,X23: com,X33: com] :
% 0.24/0.57 ( ( P @ X23 )
% 0.24/0.57 => ( ( P @ X33 )
% 0.24/0.57 => ( P @ ( if @ X12 @ X23 @ X33 ) ) ) )
% 0.24/0.57 => ( ! [X12: bexp,X23: com] :
% 0.24/0.57 ( ( P @ X23 )
% 0.24/0.57 => ( P @ ( while @ X12 @ X23 ) ) )
% 0.24/0.57 => ( P @ Com ) ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % com.induct
% 0.24/0.57 thf(fact_119_image2__def,axiom,
% 0.24/0.57 ( bNF_Gr202451329ar_int
% 0.24/0.57 = ( ^ [A6: set_Pr1148378109ar_int,F: produc1260470173ar_int > com,G: produc1260470173ar_int > list_char > int] :
% 0.24/0.57 ( collec770796680ar_int
% 0.24/0.57 @ ^ [Uu: produc1260470173ar_int] :
% 0.24/0.57 ? [A5: produc1260470173ar_int] :
% 0.24/0.57 ( ( Uu
% 0.24/0.57 = ( produc1193801173ar_int @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 0.24/0.57 & ( member92250950ar_int @ A5 @ A6 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % image2_def
% 0.24/0.57 thf(fact_120_image2__def,axiom,
% 0.24/0.57 ( bNF_Gr749752805at_nat
% 0.24/0.57 = ( ^ [A6: set_Pr1148378109ar_int,F: produc1260470173ar_int > nat,G: produc1260470173ar_int > nat] :
% 0.24/0.57 ( collec7649004at_nat
% 0.24/0.57 @ ^ [Uu: product_prod_nat_nat] :
% 0.24/0.57 ? [A5: produc1260470173ar_int] :
% 0.24/0.57 ( ( Uu
% 0.24/0.57 = ( product_Pair_nat_nat @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 0.24/0.57 & ( member92250950ar_int @ A5 @ A6 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % image2_def
% 0.24/0.57 thf(fact_121_While__backwards__frontier__ir__valid,axiom,
% 0.24/0.57 ! [P: nat > ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.57 ( ! [N2: nat] :
% 0.24/0.57 ( relati775585786_valid
% 0.24/0.57 @ ^ [S5: list_char > int,S7: list_char > int] :
% 0.24/0.57 ( ( P @ N2 @ S5 @ S7 )
% 0.24/0.57 & ( bval @ B @ S5 ) )
% 0.24/0.57 @ C
% 0.24/0.57 @ skip
% 0.24/0.57 @ ( P @ ( suc @ N2 ) ) )
% 0.24/0.57 => ( ( relati775585786_valid
% 0.24/0.57 @ ^ [S5: list_char > int,S7: list_char > int] :
% 0.24/0.57 ? [N4: nat] : ( P @ N4 @ S5 @ S7 )
% 0.24/0.57 @ ( while @ B @ C )
% 0.24/0.57 @ C2
% 0.24/0.57 @ Q )
% 0.24/0.57 => ( relati775585786_valid @ ( P @ zero_zero_nat ) @ ( while @ B @ C ) @ C2 @ Q ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % While_backwards_frontier_ir_valid
% 0.24/0.57 thf(fact_122_com_Oinject_I1_J,axiom,
% 0.24/0.57 ! [X212: list_char,X222: aexp,Y21: list_char,Y22: aexp] :
% 0.24/0.57 ( ( ( assign @ X212 @ X222 )
% 0.24/0.57 = ( assign @ Y21 @ Y22 ) )
% 0.24/0.57 = ( ( X212 = Y21 )
% 0.24/0.57 & ( X222 = Y22 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % com.inject(1)
% 0.24/0.57 thf(fact_123_add_Oleft__neutral,axiom,
% 0.24/0.57 ! [A: nat] :
% 0.24/0.57 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.24/0.57 = A ) ).
% 0.24/0.57
% 0.24/0.57 % add.left_neutral
% 0.24/0.57 thf(fact_124_add_Oright__neutral,axiom,
% 0.24/0.57 ! [A: nat] :
% 0.24/0.57 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.24/0.57 = A ) ).
% 0.24/0.57
% 0.24/0.57 % add.right_neutral
% 0.24/0.57 thf(fact_125_add__cancel__left__left,axiom,
% 0.24/0.57 ! [B: nat,A: nat] :
% 0.24/0.57 ( ( ( plus_plus_nat @ B @ A )
% 0.24/0.57 = A )
% 0.24/0.57 = ( B = zero_zero_nat ) ) ).
% 0.24/0.57
% 0.24/0.57 % add_cancel_left_left
% 0.24/0.57 thf(fact_126_add__cancel__left__right,axiom,
% 0.24/0.57 ! [A: nat,B: nat] :
% 0.24/0.57 ( ( ( plus_plus_nat @ A @ B )
% 0.24/0.57 = A )
% 0.24/0.57 = ( B = zero_zero_nat ) ) ).
% 0.24/0.57
% 0.24/0.57 % add_cancel_left_right
% 0.24/0.57 thf(fact_127_add__cancel__right__left,axiom,
% 0.24/0.57 ! [A: nat,B: nat] :
% 0.24/0.57 ( ( A
% 0.24/0.57 = ( plus_plus_nat @ B @ A ) )
% 0.24/0.57 = ( B = zero_zero_nat ) ) ).
% 0.24/0.57
% 0.24/0.57 % add_cancel_right_left
% 0.24/0.57 thf(fact_128_add__cancel__right__right,axiom,
% 0.24/0.57 ! [A: nat,B: nat] :
% 0.24/0.57 ( ( A
% 0.24/0.57 = ( plus_plus_nat @ A @ B ) )
% 0.24/0.57 = ( B = zero_zero_nat ) ) ).
% 0.24/0.57
% 0.24/0.57 % add_cancel_right_right
% 0.24/0.57 thf(fact_129_add__eq__0__iff__both__eq__0,axiom,
% 0.24/0.57 ! [X4: nat,Y: nat] :
% 0.24/0.57 ( ( ( plus_plus_nat @ X4 @ Y )
% 0.24/0.57 = zero_zero_nat )
% 0.24/0.57 = ( ( X4 = zero_zero_nat )
% 0.24/0.57 & ( Y = zero_zero_nat ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % add_eq_0_iff_both_eq_0
% 0.24/0.57 thf(fact_130_zero__eq__add__iff__both__eq__0,axiom,
% 0.24/0.57 ! [X4: nat,Y: nat] :
% 0.24/0.57 ( ( zero_zero_nat
% 0.24/0.57 = ( plus_plus_nat @ X4 @ Y ) )
% 0.24/0.57 = ( ( X4 = zero_zero_nat )
% 0.24/0.57 & ( Y = zero_zero_nat ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % zero_eq_add_iff_both_eq_0
% 0.24/0.57 thf(fact_131_add__is__0,axiom,
% 0.24/0.57 ! [M: nat,N: nat] :
% 0.24/0.57 ( ( ( plus_plus_nat @ M @ N )
% 0.24/0.57 = zero_zero_nat )
% 0.24/0.57 = ( ( M = zero_zero_nat )
% 0.24/0.57 & ( N = zero_zero_nat ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % add_is_0
% 0.24/0.57 thf(fact_132_Nat_Oadd__0__right,axiom,
% 0.24/0.57 ! [M: nat] :
% 0.24/0.57 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 0.24/0.57 = M ) ).
% 0.24/0.57
% 0.24/0.57 % Nat.add_0_right
% 0.24/0.57 thf(fact_133_zero__reorient,axiom,
% 0.24/0.57 ! [X4: nat] :
% 0.24/0.57 ( ( zero_zero_nat = X4 )
% 0.24/0.57 = ( X4 = zero_zero_nat ) ) ).
% 0.24/0.57
% 0.24/0.57 % zero_reorient
% 0.24/0.57 thf(fact_134_comm__monoid__add__class_Oadd__0,axiom,
% 0.24/0.57 ! [A: nat] :
% 0.24/0.57 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.24/0.57 = A ) ).
% 0.24/0.57
% 0.24/0.57 % comm_monoid_add_class.add_0
% 0.24/0.57 thf(fact_135_add_Ocomm__neutral,axiom,
% 0.24/0.57 ! [A: nat] :
% 0.24/0.57 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.24/0.57 = A ) ).
% 0.24/0.57
% 0.24/0.57 % add.comm_neutral
% 0.24/0.57 thf(fact_136_nat_Odistinct_I1_J,axiom,
% 0.24/0.57 ! [X2: nat] :
% 0.24/0.57 ( zero_zero_nat
% 0.24/0.57 != ( suc @ X2 ) ) ).
% 0.24/0.57
% 0.24/0.57 % nat.distinct(1)
% 0.24/0.57 thf(fact_137_old_Onat_Odistinct_I2_J,axiom,
% 0.24/0.57 ! [Nat2: nat] :
% 0.24/0.57 ( ( suc @ Nat2 )
% 0.24/0.57 != zero_zero_nat ) ).
% 0.24/0.57
% 0.24/0.57 % old.nat.distinct(2)
% 0.24/0.57 thf(fact_138_old_Onat_Odistinct_I1_J,axiom,
% 0.24/0.57 ! [Nat2: nat] :
% 0.24/0.57 ( zero_zero_nat
% 0.24/0.57 != ( suc @ Nat2 ) ) ).
% 0.24/0.57
% 0.24/0.57 % old.nat.distinct(1)
% 0.24/0.57 thf(fact_139_nat_OdiscI,axiom,
% 0.24/0.57 ! [Nat: nat,X2: nat] :
% 0.24/0.57 ( ( Nat
% 0.24/0.57 = ( suc @ X2 ) )
% 0.24/0.57 => ( Nat != zero_zero_nat ) ) ).
% 0.24/0.57
% 0.24/0.57 % nat.discI
% 0.24/0.57 thf(fact_140_nat__induct,axiom,
% 0.24/0.57 ! [P: nat > $o,N: nat] :
% 0.24/0.57 ( ( P @ zero_zero_nat )
% 0.24/0.57 => ( ! [N2: nat] :
% 0.24/0.57 ( ( P @ N2 )
% 0.24/0.57 => ( P @ ( suc @ N2 ) ) )
% 0.24/0.57 => ( P @ N ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % nat_induct
% 0.24/0.57 thf(fact_141_diff__induct,axiom,
% 0.24/0.57 ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.24/0.57 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 0.24/0.57 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 0.24/0.57 => ( ! [X3: nat,Y3: nat] :
% 0.24/0.57 ( ( P @ X3 @ Y3 )
% 0.24/0.57 => ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 0.24/0.57 => ( P @ M @ N ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % diff_induct
% 0.24/0.57 thf(fact_142_zero__induct,axiom,
% 0.24/0.57 ! [P: nat > $o,K: nat] :
% 0.24/0.57 ( ( P @ K )
% 0.24/0.57 => ( ! [N2: nat] :
% 0.24/0.57 ( ( P @ ( suc @ N2 ) )
% 0.24/0.57 => ( P @ N2 ) )
% 0.24/0.57 => ( P @ zero_zero_nat ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % zero_induct
% 0.24/0.57 thf(fact_143_Suc__neq__Zero,axiom,
% 0.24/0.57 ! [M: nat] :
% 0.24/0.57 ( ( suc @ M )
% 0.24/0.57 != zero_zero_nat ) ).
% 0.24/0.57
% 0.24/0.57 % Suc_neq_Zero
% 0.24/0.57 thf(fact_144_Zero__neq__Suc,axiom,
% 0.24/0.57 ! [M: nat] :
% 0.24/0.57 ( zero_zero_nat
% 0.24/0.57 != ( suc @ M ) ) ).
% 0.24/0.57
% 0.24/0.57 % Zero_neq_Suc
% 0.24/0.57 thf(fact_145_Zero__not__Suc,axiom,
% 0.24/0.57 ! [M: nat] :
% 0.24/0.57 ( zero_zero_nat
% 0.24/0.57 != ( suc @ M ) ) ).
% 0.24/0.57
% 0.24/0.57 % Zero_not_Suc
% 0.24/0.57 thf(fact_146_old_Onat_Oexhaust,axiom,
% 0.24/0.57 ! [Y: nat] :
% 0.24/0.57 ( ( Y != zero_zero_nat )
% 0.24/0.57 => ~ ! [Nat3: nat] :
% 0.24/0.57 ( Y
% 0.24/0.57 != ( suc @ Nat3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % old.nat.exhaust
% 0.24/0.57 thf(fact_147_old_Onat_Oinducts,axiom,
% 0.24/0.57 ! [P: nat > $o,Nat: nat] :
% 0.24/0.57 ( ( P @ zero_zero_nat )
% 0.24/0.57 => ( ! [Nat3: nat] :
% 0.24/0.57 ( ( P @ Nat3 )
% 0.24/0.57 => ( P @ ( suc @ Nat3 ) ) )
% 0.24/0.57 => ( P @ Nat ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % old.nat.inducts
% 0.24/0.57 thf(fact_148_not0__implies__Suc,axiom,
% 0.24/0.57 ! [N: nat] :
% 0.24/0.57 ( ( N != zero_zero_nat )
% 0.24/0.57 => ? [M2: nat] :
% 0.24/0.57 ( N
% 0.24/0.57 = ( suc @ M2 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % not0_implies_Suc
% 0.24/0.57 thf(fact_149_plus__nat_Oadd__0,axiom,
% 0.24/0.57 ! [N: nat] :
% 0.24/0.57 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 0.24/0.57 = N ) ).
% 0.24/0.57
% 0.24/0.57 % plus_nat.add_0
% 0.24/0.57 thf(fact_150_add__eq__self__zero,axiom,
% 0.24/0.57 ! [M: nat,N: nat] :
% 0.24/0.57 ( ( ( plus_plus_nat @ M @ N )
% 0.24/0.57 = M )
% 0.24/0.57 => ( N = zero_zero_nat ) ) ).
% 0.24/0.57
% 0.24/0.57 % add_eq_self_zero
% 0.24/0.57 thf(fact_151_image2__eqI,axiom,
% 0.24/0.57 ! [B: com,F2: produc1260470173ar_int > com,X4: produc1260470173ar_int,C: list_char > int,G2: produc1260470173ar_int > list_char > int,A4: set_Pr1148378109ar_int] :
% 0.24/0.57 ( ( B
% 0.24/0.57 = ( F2 @ X4 ) )
% 0.24/0.57 => ( ( C
% 0.24/0.57 = ( G2 @ X4 ) )
% 0.24/0.57 => ( ( member92250950ar_int @ X4 @ A4 )
% 0.24/0.57 => ( member92250950ar_int @ ( produc1193801173ar_int @ B @ C ) @ ( bNF_Gr202451329ar_int @ A4 @ F2 @ G2 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % image2_eqI
% 0.24/0.57 thf(fact_152_image2__eqI,axiom,
% 0.24/0.57 ! [B: nat,F2: produc1260470173ar_int > nat,X4: produc1260470173ar_int,C: nat,G2: produc1260470173ar_int > nat,A4: set_Pr1148378109ar_int] :
% 0.24/0.57 ( ( B
% 0.24/0.57 = ( F2 @ X4 ) )
% 0.24/0.57 => ( ( C
% 0.24/0.57 = ( G2 @ X4 ) )
% 0.24/0.57 => ( ( member92250950ar_int @ X4 @ A4 )
% 0.24/0.57 => ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ C ) @ ( bNF_Gr749752805at_nat @ A4 @ F2 @ G2 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % image2_eqI
% 0.24/0.57 thf(fact_153_com_Odistinct_I13_J,axiom,
% 0.24/0.57 ! [X212: list_char,X222: aexp,X51: bexp,X52: com] :
% 0.24/0.57 ( ( assign @ X212 @ X222 )
% 0.24/0.57 != ( while @ X51 @ X52 ) ) ).
% 0.24/0.57
% 0.24/0.57 % com.distinct(13)
% 0.24/0.57 thf(fact_154_com_Odistinct_I1_J,axiom,
% 0.24/0.57 ! [X212: list_char,X222: aexp] :
% 0.24/0.57 ( skip
% 0.24/0.57 != ( assign @ X212 @ X222 ) ) ).
% 0.24/0.57
% 0.24/0.57 % com.distinct(1)
% 0.24/0.57 thf(fact_155_com_Odistinct_I9_J,axiom,
% 0.24/0.57 ! [X212: list_char,X222: aexp,X31: com,X32: com] :
% 0.24/0.57 ( ( assign @ X212 @ X222 )
% 0.24/0.57 != ( seq @ X31 @ X32 ) ) ).
% 0.24/0.57
% 0.24/0.57 % com.distinct(9)
% 0.24/0.57 thf(fact_156_com_Odistinct_I11_J,axiom,
% 0.24/0.57 ! [X212: list_char,X222: aexp,X41: bexp,X42: com,X43: com] :
% 0.24/0.57 ( ( assign @ X212 @ X222 )
% 0.24/0.57 != ( if @ X41 @ X42 @ X43 ) ) ).
% 0.24/0.57
% 0.24/0.57 % com.distinct(11)
% 0.24/0.57 thf(fact_157_get__back_Osimps_I1_J,axiom,
% 0.24/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C: com] :
% 0.24/0.57 ( ( relati23543761ar_int @ P @ B @ C @ zero_zero_nat )
% 0.24/0.57 = P ) ).
% 0.24/0.57
% 0.24/0.57 % get_back.simps(1)
% 0.24/0.57 thf(fact_158_one__is__add,axiom,
% 0.24/0.57 ! [M: nat,N: nat] :
% 0.24/0.57 ( ( ( suc @ zero_zero_nat )
% 0.24/0.57 = ( plus_plus_nat @ M @ N ) )
% 0.24/0.57 = ( ( ( M
% 0.24/0.57 = ( suc @ zero_zero_nat ) )
% 0.24/0.57 & ( N = zero_zero_nat ) )
% 0.24/0.57 | ( ( M = zero_zero_nat )
% 0.24/0.57 & ( N
% 0.24/0.57 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % one_is_add
% 0.24/0.57 thf(fact_159_add__is__1,axiom,
% 0.24/0.57 ! [M: nat,N: nat] :
% 0.24/0.57 ( ( ( plus_plus_nat @ M @ N )
% 0.24/0.57 = ( suc @ zero_zero_nat ) )
% 0.24/0.57 = ( ( ( M
% 0.24/0.57 = ( suc @ zero_zero_nat ) )
% 0.24/0.57 & ( N = zero_zero_nat ) )
% 0.24/0.57 | ( ( M = zero_zero_nat )
% 0.24/0.57 & ( N
% 0.24/0.57 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % add_is_1
% 0.24/0.57 thf(fact_160_ir__While__backwards__frontier,axiom,
% 0.24/0.57 ! [P: nat > ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
% 0.24/0.57 ( ! [N2: nat] :
% 0.24/0.57 ( relati2102071307_hoare
% 0.24/0.57 @ ^ [S5: list_char > int,S7: list_char > int] :
% 0.24/0.57 ( ( P @ N2 @ S5 @ S7 )
% 0.24/0.57 & ( bval @ B @ S5 ) )
% 0.24/0.57 @ C
% 0.24/0.57 @ skip
% 0.24/0.57 @ ( P @ ( suc @ N2 ) ) )
% 0.24/0.57 => ( ( relati2102071307_hoare
% 0.24/0.57 @ ^ [S5: list_char > int,S7: list_char > int] :
% 0.24/0.57 ? [N4: nat] : ( P @ N4 @ S5 @ S7 )
% 0.24/0.57 @ ( while @ B @ C )
% 0.24/0.57 @ C2
% 0.24/0.57 @ Q )
% 0.24/0.57 => ( relati2102071307_hoare @ ( P @ zero_zero_nat ) @ ( while @ B @ C ) @ C2 @ Q ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % ir_While_backwards_frontier
% 0.24/0.57 thf(fact_161_com_Osize__gen_I4_J,axiom,
% 0.24/0.57 ! [X41: bexp,X42: com,X43: com] :
% 0.24/0.57 ( ( size_com @ ( if @ X41 @ X42 @ X43 ) )
% 0.24/0.57 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_com @ X42 ) @ ( size_com @ X43 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % com.size_gen(4)
% 0.24/0.57 thf(fact_162_com_Osize__gen_I3_J,axiom,
% 0.24/0.57 ! [X31: com,X32: com] :
% 0.24/0.57 ( ( size_com @ ( seq @ X31 @ X32 ) )
% 0.24/0.57 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_com @ X31 ) @ ( size_com @ X32 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % com.size_gen(3)
% 0.24/0.57 thf(fact_163_com_Osize__gen_I5_J,axiom,
% 0.24/0.57 ! [X51: bexp,X52: com] :
% 0.24/0.57 ( ( size_com @ ( while @ X51 @ X52 ) )
% 0.24/0.57 = ( plus_plus_nat @ ( size_com @ X52 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % com.size_gen(5)
% 0.24/0.57 thf(fact_164_com_Osize_I9_J,axiom,
% 0.24/0.57 ! [X41: bexp,X42: com,X43: com] :
% 0.24/0.57 ( ( size_size_com @ ( if @ X41 @ X42 @ X43 ) )
% 0.24/0.57 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_size_com @ X42 ) @ ( size_size_com @ X43 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % com.size(9)
% 0.24/0.57 thf(fact_165_size__neq__size__imp__neq,axiom,
% 0.24/0.57 ! [X4: com,Y: com] :
% 0.24/0.57 ( ( ( size_size_com @ X4 )
% 0.24/0.57 != ( size_size_com @ Y ) )
% 0.24/0.57 => ( X4 != Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % size_neq_size_imp_neq
% 0.24/0.57 thf(fact_166_size__neq__size__imp__neq,axiom,
% 0.24/0.57 ! [X4: typerep,Y: typerep] :
% 0.24/0.57 ( ( ( size_size_typerep @ X4 )
% 0.24/0.57 != ( size_size_typerep @ Y ) )
% 0.24/0.57 => ( X4 != Y ) ) ).
% 0.24/0.57
% 0.24/0.57 % size_neq_size_imp_neq
% 0.24/0.57 thf(fact_167_com_Osize_I6_J,axiom,
% 0.24/0.57 ( ( size_size_com @ skip )
% 0.24/0.57 = zero_zero_nat ) ).
% 0.24/0.57
% 0.24/0.57 % com.size(6)
% 0.24/0.57 thf(fact_168_com_Osize_I7_J,axiom,
% 0.24/0.57 ! [X212: list_char,X222: aexp] :
% 0.24/0.57 ( ( size_size_com @ ( assign @ X212 @ X222 ) )
% 0.24/0.57 = zero_zero_nat ) ).
% 0.24/0.57
% 0.24/0.57 % com.size(7)
% 0.24/0.57 thf(fact_169_com_Osize__gen_I1_J,axiom,
% 0.24/0.57 ( ( size_com @ skip )
% 0.24/0.57 = zero_zero_nat ) ).
% 0.24/0.57
% 0.24/0.57 % com.size_gen(1)
% 0.24/0.57 thf(fact_170_com_Osize__gen_I2_J,axiom,
% 0.24/0.57 ! [X212: list_char,X222: aexp] :
% 0.24/0.57 ( ( size_com @ ( assign @ X212 @ X222 ) )
% 0.24/0.57 = zero_zero_nat ) ).
% 0.24/0.57
% 0.24/0.57 % com.size_gen(2)
% 0.24/0.57 thf(fact_171_com_Osize_I10_J,axiom,
% 0.24/0.57 ! [X51: bexp,X52: com] :
% 0.24/0.57 ( ( size_size_com @ ( while @ X51 @ X52 ) )
% 0.24/0.57 = ( plus_plus_nat @ ( size_size_com @ X52 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % com.size(10)
% 0.24/0.57 thf(fact_172_com_Osize_I8_J,axiom,
% 0.24/0.57 ! [X31: com,X32: com] :
% 0.24/0.57 ( ( size_size_com @ ( seq @ X31 @ X32 ) )
% 0.24/0.57 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_size_com @ X31 ) @ ( size_size_com @ X32 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % com.size(8)
% 0.24/0.57 thf(fact_173_Euclid__induct,axiom,
% 0.24/0.57 ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.24/0.57 ( ! [A3: nat,B3: nat] :
% 0.24/0.57 ( ( P @ A3 @ B3 )
% 0.24/0.57 = ( P @ B3 @ A3 ) )
% 0.24/0.57 => ( ! [A3: nat] : ( P @ A3 @ zero_zero_nat )
% 0.24/0.57 => ( ! [A3: nat,B3: nat] :
% 0.24/0.57 ( ( P @ A3 @ B3 )
% 0.24/0.57 => ( P @ A3 @ ( plus_plus_nat @ A3 @ B3 ) ) )
% 0.24/0.57 => ( P @ A @ B ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % Euclid_induct
% 0.24/0.57 thf(fact_174_verit__sum__simplify,axiom,
% 0.24/0.57 ! [A: nat] :
% 0.24/0.57 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.24/0.57 = A ) ).
% 0.24/0.57
% 0.24/0.57 % verit_sum_simplify
% 0.24/0.57 thf(fact_175_add__0__iff,axiom,
% 0.24/0.57 ! [B: nat,A: nat] :
% 0.24/0.57 ( ( B
% 0.24/0.57 = ( plus_plus_nat @ B @ A ) )
% 0.24/0.57 = ( A = zero_zero_nat ) ) ).
% 0.24/0.57
% 0.24/0.57 % add_0_iff
% 0.24/0.57 thf(fact_176_relImage__def,axiom,
% 0.24/0.57 ( bNF_Gr1247133574at_nat
% 0.24/0.57 = ( ^ [R2: set_Pr1986765409at_nat,F: nat > nat] :
% 0.24/0.57 ( collec7649004at_nat
% 0.24/0.57 @ ^ [Uu: product_prod_nat_nat] :
% 0.24/0.57 ? [A1: nat,A22: nat] :
% 0.24/0.57 ( ( Uu
% 0.24/0.57 = ( product_Pair_nat_nat @ ( F @ A1 ) @ ( F @ A22 ) ) )
% 0.24/0.57 & ( member701585322at_nat @ ( product_Pair_nat_nat @ A1 @ A22 ) @ R2 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % relImage_def
% 0.24/0.57 thf(fact_177_relInvImage__def,axiom,
% 0.24/0.57 ( bNF_Gr1143394412nt_nat
% 0.24/0.57 = ( ^ [A6: set_Pr1148378109ar_int,R2: set_Pr1986765409at_nat,F: produc1260470173ar_int > nat] :
% 0.24/0.57 ( collec1834387154ar_int
% 0.24/0.57 @ ^ [Uu: produc1346207591ar_int] :
% 0.24/0.57 ? [A1: produc1260470173ar_int,A22: produc1260470173ar_int] :
% 0.24/0.57 ( ( Uu
% 0.24/0.57 = ( produc317451735ar_int @ A1 @ A22 ) )
% 0.24/0.57 & ( member92250950ar_int @ A1 @ A6 )
% 0.24/0.57 & ( member92250950ar_int @ A22 @ A6 )
% 0.24/0.57 & ( member701585322at_nat @ ( product_Pair_nat_nat @ ( F @ A1 ) @ ( F @ A22 ) ) @ R2 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % relInvImage_def
% 0.24/0.57 thf(fact_178_relInvImage__def,axiom,
% 0.24/0.57 ( bNF_Gr808751971at_nat
% 0.24/0.57 = ( ^ [A6: set_nat,R2: set_Pr1986765409at_nat,F: nat > nat] :
% 0.24/0.57 ( collec7649004at_nat
% 0.24/0.57 @ ^ [Uu: product_prod_nat_nat] :
% 0.24/0.57 ? [A1: nat,A22: nat] :
% 0.24/0.57 ( ( Uu
% 0.24/0.57 = ( product_Pair_nat_nat @ A1 @ A22 ) )
% 0.24/0.57 & ( member_nat @ A1 @ A6 )
% 0.24/0.57 & ( member_nat @ A22 @ A6 )
% 0.24/0.57 & ( member701585322at_nat @ ( product_Pair_nat_nat @ ( F @ A1 ) @ ( F @ A22 ) ) @ R2 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % relInvImage_def
% 0.24/0.57 thf(fact_179_divides__aux__eq,axiom,
% 0.24/0.57 ! [Q4: nat,R3: nat] :
% 0.24/0.57 ( ( unique1592618082ux_nat @ ( product_Pair_nat_nat @ Q4 @ R3 ) )
% 0.24/0.57 = ( R3 = zero_zero_nat ) ) ).
% 0.24/0.57
% 0.24/0.57 % divides_aux_eq
% 0.24/0.57 thf(fact_180_zero__natural_Orsp,axiom,
% 0.24/0.57 zero_zero_nat = zero_zero_nat ).
% 0.24/0.57
% 0.24/0.57 % zero_natural.rsp
% 0.24/0.57 thf(fact_181_typerep_Osize__neq,axiom,
% 0.24/0.57 ! [X4: typerep] :
% 0.24/0.57 ( ( size_size_typerep @ X4 )
% 0.24/0.57 != zero_zero_nat ) ).
% 0.24/0.57
% 0.24/0.57 % typerep.size_neq
% 0.24/0.57 thf(fact_182_ssubst__Pair__rhs,axiom,
% 0.24/0.57 ! [R3: nat,S: nat,R: set_Pr1986765409at_nat,S2: nat] :
% 0.24/0.57 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ R3 @ S ) @ R )
% 0.24/0.57 => ( ( S2 = S )
% 0.24/0.57 => ( member701585322at_nat @ ( product_Pair_nat_nat @ R3 @ S2 ) @ R ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % ssubst_Pair_rhs
% 0.24/0.57 thf(fact_183_ssubst__Pair__rhs,axiom,
% 0.24/0.57 ! [R3: com,S: list_char > int,R: set_Pr1148378109ar_int,S2: list_char > int] :
% 0.24/0.57 ( ( member92250950ar_int @ ( produc1193801173ar_int @ R3 @ S ) @ R )
% 0.24/0.57 => ( ( S2 = S )
% 0.24/0.57 => ( member92250950ar_int @ ( produc1193801173ar_int @ R3 @ S2 ) @ R ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % ssubst_Pair_rhs
% 0.24/0.57 thf(fact_184_typerep_Osize_I2_J,axiom,
% 0.24/0.57 ! [X1: literal,X2: list_typerep] :
% 0.24/0.57 ( ( size_size_typerep @ ( typerep2 @ X1 @ X2 ) )
% 0.24/0.57 = ( plus_plus_nat @ ( size_list_typerep @ size_size_typerep @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % typerep.size(2)
% 0.24/0.57 thf(fact_185_typerep_Osize__gen,axiom,
% 0.24/0.57 ! [X1: literal,X2: list_typerep] :
% 0.24/0.57 ( ( size_typerep @ ( typerep2 @ X1 @ X2 ) )
% 0.24/0.57 = ( plus_plus_nat @ ( size_list_typerep @ size_typerep @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % typerep.size_gen
% 0.24/0.57 thf(fact_186_list_Osize__gen_I2_J,axiom,
% 0.24/0.57 ! [X4: typerep > nat,X212: typerep,X222: list_typerep] :
% 0.24/0.57 ( ( size_list_typerep @ X4 @ ( cons_typerep @ X212 @ X222 ) )
% 0.24/0.57 = ( plus_plus_nat @ ( plus_plus_nat @ ( X4 @ X212 ) @ ( size_list_typerep @ X4 @ X222 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % list.size_gen(2)
% 0.24/0.57 thf(fact_187_length__Suc__conv,axiom,
% 0.24/0.57 ! [Xs: list_typerep,N: nat] :
% 0.24/0.57 ( ( ( size_s416147576yperep @ Xs )
% 0.24/0.57 = ( suc @ N ) )
% 0.24/0.57 = ( ? [Y4: typerep,Ys: list_typerep] :
% 0.24/0.57 ( ( Xs
% 0.24/0.57 = ( cons_typerep @ Y4 @ Ys ) )
% 0.24/0.57 & ( ( size_s416147576yperep @ Ys )
% 0.24/0.57 = N ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % length_Suc_conv
% 0.24/0.57 thf(fact_188_Suc__length__conv,axiom,
% 0.24/0.57 ! [N: nat,Xs: list_typerep] :
% 0.24/0.57 ( ( ( suc @ N )
% 0.24/0.57 = ( size_s416147576yperep @ Xs ) )
% 0.24/0.57 = ( ? [Y4: typerep,Ys: list_typerep] :
% 0.24/0.57 ( ( Xs
% 0.24/0.57 = ( cons_typerep @ Y4 @ Ys ) )
% 0.24/0.57 & ( ( size_s416147576yperep @ Ys )
% 0.24/0.57 = N ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % Suc_length_conv
% 0.24/0.57 thf(fact_189_length__Cons,axiom,
% 0.24/0.57 ! [X4: typerep,Xs: list_typerep] :
% 0.24/0.57 ( ( size_s416147576yperep @ ( cons_typerep @ X4 @ Xs ) )
% 0.24/0.57 = ( suc @ ( size_s416147576yperep @ Xs ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % length_Cons
% 0.24/0.57 thf(fact_190_list_Osize_I4_J,axiom,
% 0.24/0.57 ! [X212: typerep,X222: list_typerep] :
% 0.24/0.57 ( ( size_s416147576yperep @ ( cons_typerep @ X212 @ X222 ) )
% 0.24/0.57 = ( plus_plus_nat @ ( size_s416147576yperep @ X222 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % list.size(4)
% 0.24/0.57 thf(fact_191_set__Cons__def,axiom,
% 0.24/0.57 ( set_Co1954412371ar_int
% 0.24/0.57 = ( ^ [A6: set_Pr1148378109ar_int,XS: set_li1762364675ar_int] :
% 0.24/0.57 ( collec672902542ar_int
% 0.24/0.57 @ ^ [Z: list_P1741976099ar_int] :
% 0.24/0.57 ? [X: produc1260470173ar_int,Xs2: list_P1741976099ar_int] :
% 0.24/0.57 ( ( Z
% 0.24/0.57 = ( cons_P1254790739ar_int @ X @ Xs2 ) )
% 0.24/0.57 & ( member92250950ar_int @ X @ A6 )
% 0.24/0.57 & ( member2052091212ar_int @ Xs2 @ XS ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % set_Cons_def
% 0.24/0.57 thf(fact_192_set__Cons__def,axiom,
% 0.24/0.57 ( set_Cons_typerep
% 0.24/0.57 = ( ^ [A6: set_typerep,XS: set_list_typerep] :
% 0.24/0.57 ( collect_list_typerep
% 0.24/0.57 @ ^ [Z: list_typerep] :
% 0.24/0.57 ? [X: typerep,Xs2: list_typerep] :
% 0.24/0.57 ( ( Z
% 0.24/0.57 = ( cons_typerep @ X @ Xs2 ) )
% 0.24/0.57 & ( member_typerep @ X @ A6 )
% 0.24/0.57 & ( member_list_typerep @ Xs2 @ XS ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % set_Cons_def
% 0.24/0.57 thf(fact_193_Cons__in__lex,axiom,
% 0.24/0.57 ! [X4: typerep,Xs: list_typerep,Y: typerep,Ys2: list_typerep,R3: set_Pr1097818217yperep] :
% 0.24/0.57 ( ( member1812711762yperep @ ( produc1695567329yperep @ ( cons_typerep @ X4 @ Xs ) @ ( cons_typerep @ Y @ Ys2 ) ) @ ( lex_typerep @ R3 ) )
% 0.24/0.57 = ( ( ( member100911538yperep @ ( produc2071514689yperep @ X4 @ Y ) @ R3 )
% 0.24/0.57 & ( ( size_s416147576yperep @ Xs )
% 0.24/0.57 = ( size_s416147576yperep @ Ys2 ) ) )
% 0.24/0.57 | ( ( X4 = Y )
% 0.24/0.57 & ( member1812711762yperep @ ( produc1695567329yperep @ Xs @ Ys2 ) @ ( lex_typerep @ R3 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % Cons_in_lex
% 0.24/0.57 thf(fact_194_Cons__in__lex,axiom,
% 0.24/0.57 ! [X4: nat,Xs: list_nat,Y: nat,Ys2: list_nat,R3: set_Pr1986765409at_nat] :
% 0.24/0.57 ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( cons_nat @ X4 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) ) @ ( lex_nat @ R3 ) )
% 0.24/0.57 = ( ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ Y ) @ R3 )
% 0.24/0.57 & ( ( size_size_list_nat @ Xs )
% 0.24/0.57 = ( size_size_list_nat @ Ys2 ) ) )
% 0.24/0.57 | ( ( X4 = Y )
% 0.24/0.57 & ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys2 ) @ ( lex_nat @ R3 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % Cons_in_lex
% 0.24/0.57 thf(fact_195_gen__length__code_I2_J,axiom,
% 0.24/0.57 ! [N: nat,X4: typerep,Xs: list_typerep] :
% 0.24/0.57 ( ( gen_length_typerep @ N @ ( cons_typerep @ X4 @ Xs ) )
% 0.24/0.57 = ( gen_length_typerep @ ( suc @ N ) @ Xs ) ) ).
% 0.24/0.57
% 0.24/0.57 % gen_length_code(2)
% 0.24/0.57 thf(fact_196_lexord__cons__cons,axiom,
% 0.24/0.57 ! [A: typerep,X4: list_typerep,B: typerep,Y: list_typerep,R3: set_Pr1097818217yperep] :
% 0.24/0.57 ( ( member1812711762yperep @ ( produc1695567329yperep @ ( cons_typerep @ A @ X4 ) @ ( cons_typerep @ B @ Y ) ) @ ( lexord_typerep @ R3 ) )
% 0.24/0.57 = ( ( member100911538yperep @ ( produc2071514689yperep @ A @ B ) @ R3 )
% 0.24/0.57 | ( ( A = B )
% 0.24/0.57 & ( member1812711762yperep @ ( produc1695567329yperep @ X4 @ Y ) @ ( lexord_typerep @ R3 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % lexord_cons_cons
% 0.24/0.57 thf(fact_197_lexord__cons__cons,axiom,
% 0.24/0.57 ! [A: nat,X4: list_nat,B: nat,Y: list_nat,R3: set_Pr1986765409at_nat] :
% 0.24/0.57 ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( cons_nat @ A @ X4 ) @ ( cons_nat @ B @ Y ) ) @ ( lexord_nat @ R3 ) )
% 0.24/0.57 = ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R3 )
% 0.24/0.57 | ( ( A = B )
% 0.24/0.57 & ( member1926390090st_nat @ ( produc1625736153st_nat @ X4 @ Y ) @ ( lexord_nat @ R3 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % lexord_cons_cons
% 0.24/0.57 thf(fact_198_lexord__irreflexive,axiom,
% 0.24/0.57 ! [R3: set_Pr1986765409at_nat,Xs: list_nat] :
% 0.24/0.57 ( ! [X3: nat] :
% 0.24/0.57 ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) @ R3 )
% 0.24/0.57 => ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Xs ) @ ( lexord_nat @ R3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % lexord_irreflexive
% 0.24/0.57 thf(fact_199_lexord__linear,axiom,
% 0.24/0.57 ! [R3: set_Pr1986765409at_nat,X4: list_nat,Y: list_nat] :
% 0.24/0.57 ( ! [A3: nat,B3: nat] :
% 0.24/0.57 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A3 @ B3 ) @ R3 )
% 0.24/0.57 | ( A3 = B3 )
% 0.24/0.57 | ( member701585322at_nat @ ( product_Pair_nat_nat @ B3 @ A3 ) @ R3 ) )
% 0.24/0.57 => ( ( member1926390090st_nat @ ( produc1625736153st_nat @ X4 @ Y ) @ ( lexord_nat @ R3 ) )
% 0.24/0.57 | ( X4 = Y )
% 0.24/0.57 | ( member1926390090st_nat @ ( produc1625736153st_nat @ Y @ X4 ) @ ( lexord_nat @ R3 ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % lexord_linear
% 0.24/0.57 thf(fact_200_Shift__def,axiom,
% 0.24/0.57 ( bNF_Gr457912949yperep
% 0.24/0.57 = ( ^ [Kl: set_list_typerep,K2: typerep] :
% 0.24/0.57 ( collect_list_typerep
% 0.24/0.57 @ ^ [Kl2: list_typerep] : ( member_list_typerep @ ( cons_typerep @ K2 @ Kl2 ) @ Kl ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % Shift_def
% 0.24/0.57 thf(fact_201_ShiftD,axiom,
% 0.24/0.57 ! [Kl3: list_typerep,Kl4: set_list_typerep,K: typerep] :
% 0.24/0.57 ( ( member_list_typerep @ Kl3 @ ( bNF_Gr457912949yperep @ Kl4 @ K ) )
% 0.24/0.57 => ( member_list_typerep @ ( cons_typerep @ K @ Kl3 ) @ Kl4 ) ) ).
% 0.24/0.57
% 0.24/0.57 % ShiftD
% 0.24/0.57 thf(fact_202_Succ__Shift,axiom,
% 0.24/0.57 ! [Kl4: set_list_typerep,K: typerep,Kl3: list_typerep] :
% 0.24/0.57 ( ( bNF_Gr1303086585yperep @ ( bNF_Gr457912949yperep @ Kl4 @ K ) @ Kl3 )
% 0.24/0.57 = ( bNF_Gr1303086585yperep @ Kl4 @ ( cons_typerep @ K @ Kl3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % Succ_Shift
% 0.24/0.57 thf(fact_203_Cons__listrel1__Cons,axiom,
% 0.24/0.57 ! [X4: typerep,Xs: list_typerep,Y: typerep,Ys2: list_typerep,R3: set_Pr1097818217yperep] :
% 0.24/0.57 ( ( member1812711762yperep @ ( produc1695567329yperep @ ( cons_typerep @ X4 @ Xs ) @ ( cons_typerep @ Y @ Ys2 ) ) @ ( listrel1_typerep @ R3 ) )
% 0.24/0.57 = ( ( ( member100911538yperep @ ( produc2071514689yperep @ X4 @ Y ) @ R3 )
% 0.24/0.57 & ( Xs = Ys2 ) )
% 0.24/0.57 | ( ( X4 = Y )
% 0.24/0.57 & ( member1812711762yperep @ ( produc1695567329yperep @ Xs @ Ys2 ) @ ( listrel1_typerep @ R3 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % Cons_listrel1_Cons
% 0.24/0.57 thf(fact_204_Cons__listrel1__Cons,axiom,
% 0.24/0.57 ! [X4: nat,Xs: list_nat,Y: nat,Ys2: list_nat,R3: set_Pr1986765409at_nat] :
% 0.24/0.57 ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( cons_nat @ X4 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) ) @ ( listrel1_nat @ R3 ) )
% 0.24/0.57 = ( ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ Y ) @ R3 )
% 0.24/0.57 & ( Xs = Ys2 ) )
% 0.24/0.57 | ( ( X4 = Y )
% 0.24/0.57 & ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys2 ) @ ( listrel1_nat @ R3 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % Cons_listrel1_Cons
% 0.24/0.57 thf(fact_205_listrel1I1,axiom,
% 0.24/0.57 ! [X4: typerep,Y: typerep,R3: set_Pr1097818217yperep,Xs: list_typerep] :
% 0.24/0.57 ( ( member100911538yperep @ ( produc2071514689yperep @ X4 @ Y ) @ R3 )
% 0.24/0.57 => ( member1812711762yperep @ ( produc1695567329yperep @ ( cons_typerep @ X4 @ Xs ) @ ( cons_typerep @ Y @ Xs ) ) @ ( listrel1_typerep @ R3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % listrel1I1
% 0.24/0.57 thf(fact_206_listrel1I1,axiom,
% 0.24/0.57 ! [X4: nat,Y: nat,R3: set_Pr1986765409at_nat,Xs: list_nat] :
% 0.24/0.57 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ Y ) @ R3 )
% 0.24/0.57 => ( member1926390090st_nat @ ( produc1625736153st_nat @ ( cons_nat @ X4 @ Xs ) @ ( cons_nat @ Y @ Xs ) ) @ ( listrel1_nat @ R3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % listrel1I1
% 0.24/0.57 thf(fact_207_Cons__listrel1E1,axiom,
% 0.24/0.57 ! [X4: typerep,Xs: list_typerep,Ys2: list_typerep,R3: set_Pr1097818217yperep] :
% 0.24/0.57 ( ( member1812711762yperep @ ( produc1695567329yperep @ ( cons_typerep @ X4 @ Xs ) @ Ys2 ) @ ( listrel1_typerep @ R3 ) )
% 0.24/0.57 => ( ! [Y3: typerep] :
% 0.24/0.57 ( ( Ys2
% 0.24/0.57 = ( cons_typerep @ Y3 @ Xs ) )
% 0.24/0.57 => ~ ( member100911538yperep @ ( produc2071514689yperep @ X4 @ Y3 ) @ R3 ) )
% 0.24/0.57 => ~ ! [Zs: list_typerep] :
% 0.24/0.57 ( ( Ys2
% 0.24/0.57 = ( cons_typerep @ X4 @ Zs ) )
% 0.24/0.57 => ~ ( member1812711762yperep @ ( produc1695567329yperep @ Xs @ Zs ) @ ( listrel1_typerep @ R3 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % Cons_listrel1E1
% 0.24/0.57 thf(fact_208_Cons__listrel1E1,axiom,
% 0.24/0.57 ! [X4: nat,Xs: list_nat,Ys2: list_nat,R3: set_Pr1986765409at_nat] :
% 0.24/0.57 ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( cons_nat @ X4 @ Xs ) @ Ys2 ) @ ( listrel1_nat @ R3 ) )
% 0.24/0.57 => ( ! [Y3: nat] :
% 0.24/0.57 ( ( Ys2
% 0.24/0.57 = ( cons_nat @ Y3 @ Xs ) )
% 0.24/0.57 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ Y3 ) @ R3 ) )
% 0.24/0.57 => ~ ! [Zs: list_nat] :
% 0.24/0.57 ( ( Ys2
% 0.24/0.57 = ( cons_nat @ X4 @ Zs ) )
% 0.24/0.57 => ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Zs ) @ ( listrel1_nat @ R3 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % Cons_listrel1E1
% 0.24/0.57 thf(fact_209_Cons__listrel1E2,axiom,
% 0.24/0.57 ! [Xs: list_typerep,Y: typerep,Ys2: list_typerep,R3: set_Pr1097818217yperep] :
% 0.24/0.57 ( ( member1812711762yperep @ ( produc1695567329yperep @ Xs @ ( cons_typerep @ Y @ Ys2 ) ) @ ( listrel1_typerep @ R3 ) )
% 0.24/0.57 => ( ! [X3: typerep] :
% 0.24/0.57 ( ( Xs
% 0.24/0.57 = ( cons_typerep @ X3 @ Ys2 ) )
% 0.24/0.57 => ~ ( member100911538yperep @ ( produc2071514689yperep @ X3 @ Y ) @ R3 ) )
% 0.24/0.57 => ~ ! [Zs: list_typerep] :
% 0.24/0.57 ( ( Xs
% 0.24/0.57 = ( cons_typerep @ Y @ Zs ) )
% 0.24/0.57 => ~ ( member1812711762yperep @ ( produc1695567329yperep @ Zs @ Ys2 ) @ ( listrel1_typerep @ R3 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % Cons_listrel1E2
% 0.24/0.57 thf(fact_210_Cons__listrel1E2,axiom,
% 0.24/0.57 ! [Xs: list_nat,Y: nat,Ys2: list_nat,R3: set_Pr1986765409at_nat] :
% 0.24/0.57 ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ ( cons_nat @ Y @ Ys2 ) ) @ ( listrel1_nat @ R3 ) )
% 0.24/0.57 => ( ! [X3: nat] :
% 0.24/0.57 ( ( Xs
% 0.24/0.57 = ( cons_nat @ X3 @ Ys2 ) )
% 0.24/0.57 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X3 @ Y ) @ R3 ) )
% 0.24/0.57 => ~ ! [Zs: list_nat] :
% 0.24/0.57 ( ( Xs
% 0.24/0.57 = ( cons_nat @ Y @ Zs ) )
% 0.24/0.57 => ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ Zs @ Ys2 ) @ ( listrel1_nat @ R3 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % Cons_listrel1E2
% 0.24/0.57 thf(fact_211_lexord__append__left__rightI,axiom,
% 0.24/0.57 ! [A: typerep,B: typerep,R3: set_Pr1097818217yperep,U: list_typerep,X4: list_typerep,Y: list_typerep] :
% 0.24/0.57 ( ( member100911538yperep @ ( produc2071514689yperep @ A @ B ) @ R3 )
% 0.24/0.57 => ( member1812711762yperep @ ( produc1695567329yperep @ ( append_typerep @ U @ ( cons_typerep @ A @ X4 ) ) @ ( append_typerep @ U @ ( cons_typerep @ B @ Y ) ) ) @ ( lexord_typerep @ R3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % lexord_append_left_rightI
% 0.24/0.57 thf(fact_212_lexord__append__left__rightI,axiom,
% 0.24/0.57 ! [A: nat,B: nat,R3: set_Pr1986765409at_nat,U: list_nat,X4: list_nat,Y: list_nat] :
% 0.24/0.57 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R3 )
% 0.24/0.57 => ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ U @ ( cons_nat @ A @ X4 ) ) @ ( append_nat @ U @ ( cons_nat @ B @ Y ) ) ) @ ( lexord_nat @ R3 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % lexord_append_left_rightI
% 0.24/0.57 thf(fact_213_listrel1I,axiom,
% 0.24/0.57 ! [X4: typerep,Y: typerep,R3: set_Pr1097818217yperep,Xs: list_typerep,Us: list_typerep,Vs: list_typerep,Ys2: list_typerep] :
% 0.24/0.57 ( ( member100911538yperep @ ( produc2071514689yperep @ X4 @ Y ) @ R3 )
% 0.24/0.57 => ( ( Xs
% 0.24/0.57 = ( append_typerep @ Us @ ( cons_typerep @ X4 @ Vs ) ) )
% 0.24/0.57 => ( ( Ys2
% 0.24/0.57 = ( append_typerep @ Us @ ( cons_typerep @ Y @ Vs ) ) )
% 0.24/0.57 => ( member1812711762yperep @ ( produc1695567329yperep @ Xs @ Ys2 ) @ ( listrel1_typerep @ R3 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % listrel1I
% 0.24/0.57 thf(fact_214_listrel1I,axiom,
% 0.24/0.57 ! [X4: nat,Y: nat,R3: set_Pr1986765409at_nat,Xs: list_nat,Us: list_nat,Vs: list_nat,Ys2: list_nat] :
% 0.24/0.57 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ Y ) @ R3 )
% 0.24/0.57 => ( ( Xs
% 0.24/0.57 = ( append_nat @ Us @ ( cons_nat @ X4 @ Vs ) ) )
% 0.24/0.57 => ( ( Ys2
% 0.24/0.57 = ( append_nat @ Us @ ( cons_nat @ Y @ Vs ) ) )
% 0.24/0.57 => ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys2 ) @ ( listrel1_nat @ R3 ) ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % listrel1I
% 0.24/0.57 thf(fact_215_append__eq__append__conv,axiom,
% 0.24/0.57 ! [Xs: list_typerep,Ys2: list_typerep,Us: list_typerep,Vs: list_typerep] :
% 0.24/0.57 ( ( ( ( size_s416147576yperep @ Xs )
% 0.24/0.57 = ( size_s416147576yperep @ Ys2 ) )
% 0.24/0.57 | ( ( size_s416147576yperep @ Us )
% 0.24/0.57 = ( size_s416147576yperep @ Vs ) ) )
% 0.24/0.57 => ( ( ( append_typerep @ Xs @ Us )
% 0.24/0.57 = ( append_typerep @ Ys2 @ Vs ) )
% 0.24/0.57 = ( ( Xs = Ys2 )
% 0.24/0.57 & ( Us = Vs ) ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % append_eq_append_conv
% 0.24/0.57 thf(fact_216_length__append,axiom,
% 0.24/0.57 ! [Xs: list_typerep,Ys2: list_typerep] :
% 0.24/0.57 ( ( size_s416147576yperep @ ( append_typerep @ Xs @ Ys2 ) )
% 0.24/0.57 = ( plus_plus_nat @ ( size_s416147576yperep @ Xs ) @ ( size_s416147576yperep @ Ys2 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % length_append
% 0.24/0.57 thf(fact_217_size__list__append,axiom,
% 0.24/0.57 ! [F2: typerep > nat,Xs: list_typerep,Ys2: list_typerep] :
% 0.24/0.57 ( ( size_list_typerep @ F2 @ ( append_typerep @ Xs @ Ys2 ) )
% 0.24/0.57 = ( plus_plus_nat @ ( size_list_typerep @ F2 @ Xs ) @ ( size_list_typerep @ F2 @ Ys2 ) ) ) ).
% 0.24/0.57
% 0.24/0.57 % size_list_append
% 0.24/0.57 thf(fact_218_lexord__sufE,axiom,
% 0.24/0.57 ! [Xs: list_typerep,Zs2: list_typerep,Ys2: list_typerep,Qs: list_typerep,R3: set_Pr1097818217yperep] :
% 0.24/0.57 ( ( member1812711762yperep @ ( produc1695567329yperep @ ( append_typerep @ Xs @ Zs2 ) @ ( append_typerep @ Ys2 @ Qs ) ) @ ( lexord_typerep @ R3 ) )
% 0.24/0.57 => ( ( Xs != Ys2 )
% 0.24/0.57 => ( ( ( size_s416147576yperep @ Xs )
% 0.24/0.63 = ( size_s416147576yperep @ Ys2 ) )
% 0.24/0.63 => ( ( ( size_s416147576yperep @ Zs2 )
% 0.24/0.63 = ( size_s416147576yperep @ Qs ) )
% 0.24/0.63 => ( member1812711762yperep @ ( produc1695567329yperep @ Xs @ Ys2 ) @ ( lexord_typerep @ R3 ) ) ) ) ) ) ).
% 0.24/0.63
% 0.24/0.63 % lexord_sufE
% 0.24/0.63 thf(fact_219_lex__append__leftD,axiom,
% 0.24/0.63 ! [R3: set_Pr1097818217yperep,Xs: list_typerep,Ys2: list_typerep,Zs2: list_typerep] :
% 0.24/0.63 ( ! [X3: typerep] :
% 0.24/0.63 ~ ( member100911538yperep @ ( produc2071514689yperep @ X3 @ X3 ) @ R3 )
% 0.24/0.63 => ( ( member1812711762yperep @ ( produc1695567329yperep @ ( append_typerep @ Xs @ Ys2 ) @ ( append_typerep @ Xs @ Zs2 ) ) @ ( lex_typerep @ R3 ) )
% 0.24/0.63 => ( member1812711762yperep @ ( produc1695567329yperep @ Ys2 @ Zs2 ) @ ( lex_typerep @ R3 ) ) ) ) ).
% 0.24/0.63
% 0.24/0.63 % lex_append_leftD
% 0.24/0.63 thf(fact_220_lex__append__leftD,axiom,
% 0.24/0.63 ! [R3: set_Pr1986765409at_nat,Xs: list_nat,Ys2: list_nat,Zs2: list_nat] :
% 0.24/0.63 ( ! [X3: nat] :
% 0.24/0.63 ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) @ R3 )
% 0.24/0.63 => ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ Xs @ Ys2 ) @ ( append_nat @ Xs @ Zs2 ) ) @ ( lex_nat @ R3 ) )
% 0.24/0.63 => ( member1926390090st_nat @ ( produc1625736153st_nat @ Ys2 @ Zs2 ) @ ( lex_nat @ R3 ) ) ) ) ).
% 0.24/0.63
% 0.24/0.63 % lex_append_leftD
% 0.24/0.63
% 0.24/0.63 % Conjectures (1)
% 0.24/0.63 thf(conj_0,conjecture,
% 0.24/0.63 ? [S6: list_char > int,S8: list_char > int] :
% 0.24/0.63 ( ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ S6 @ S8 )
% 0.24/0.63 & ( bval @ b @ S6 )
% 0.24/0.63 & ( big_big_step @ ( produc1193801173ar_int @ c @ S6 ) @ ta )
% 0.24/0.63 & ( big_big_step @ ( produc1193801173ar_int @ c2 @ S8 ) @ t_a ) ) ).
% 0.24/0.63
% 0.24/0.63 %------------------------------------------------------------------------------
% 0.24/0.63 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.QShBI1zVHu/cvc5---1.0.5_10267.p...
% 0.24/0.63 (declare-sort $$unsorted 0)
% 0.24/0.63 (declare-sort tptp.set_Pr1333062727ar_int 0)
% 0.24/0.63 (declare-sort tptp.produc1346207591ar_int 0)
% 0.24/0.63 (declare-sort tptp.set_li1762364675ar_int 0)
% 0.24/0.63 (declare-sort tptp.set_Pr446800905yperep 0)
% 0.24/0.63 (declare-sort tptp.list_P1741976099ar_int 0)
% 0.24/0.63 (declare-sort tptp.set_Pr1148378109ar_int 0)
% 0.24/0.63 (declare-sort tptp.set_Pr1560408065st_nat 0)
% 0.24/0.63 (declare-sort tptp.produc490010537yperep 0)
% 0.24/0.63 (declare-sort tptp.produc1260470173ar_int 0)
% 0.24/0.63 (declare-sort tptp.produc1699244961st_nat 0)
% 0.24/0.63 (declare-sort tptp.set_Pr1097818217yperep 0)
% 0.24/0.63 (declare-sort tptp.set_Pr1986765409at_nat 0)
% 0.24/0.63 (declare-sort tptp.produc1788831497yperep 0)
% 0.24/0.63 (declare-sort tptp.product_prod_nat_nat 0)
% 0.24/0.63 (declare-sort tptp.set_list_typerep 0)
% 0.24/0.63 (declare-sort tptp.list_typerep 0)
% 0.24/0.63 (declare-sort tptp.set_typerep 0)
% 0.24/0.63 (declare-sort tptp.list_char 0)
% 0.24/0.63 (declare-sort tptp.list_nat 0)
% 0.24/0.63 (declare-sort tptp.set_nat 0)
% 0.24/0.63 (declare-sort tptp.typerep 0)
% 0.24/0.63 (declare-sort tptp.literal 0)
% 0.24/0.63 (declare-sort tptp.bexp 0)
% 0.24/0.63 (declare-sort tptp.aexp 0)
% 0.24/0.63 (declare-sort tptp.nat 0)
% 0.24/0.63 (declare-sort tptp.int 0)
% 0.24/0.63 (declare-sort tptp.com 0)
% 0.24/0.63 (declare-fun tptp.bval (tptp.bexp (-> tptp.list_char tptp.int)) Bool)
% 0.24/0.63 (declare-fun tptp.bNF_Gr457912949yperep (tptp.set_list_typerep tptp.typerep) tptp.set_list_typerep)
% 0.24/0.63 (declare-fun tptp.bNF_Gr1303086585yperep (tptp.set_list_typerep tptp.list_typerep) tptp.set_typerep)
% 0.24/0.63 (declare-fun tptp.bNF_Gr202451329ar_int (tptp.set_Pr1148378109ar_int (-> tptp.produc1260470173ar_int tptp.com) (-> tptp.produc1260470173ar_int tptp.list_char tptp.int)) tptp.set_Pr1148378109ar_int)
% 0.24/0.63 (declare-fun tptp.bNF_Gr749752805at_nat (tptp.set_Pr1148378109ar_int (-> tptp.produc1260470173ar_int tptp.nat) (-> tptp.produc1260470173ar_int tptp.nat)) tptp.set_Pr1986765409at_nat)
% 0.24/0.63 (declare-fun tptp.bNF_Gr1247133574at_nat (tptp.set_Pr1986765409at_nat (-> tptp.nat tptp.nat)) tptp.set_Pr1986765409at_nat)
% 0.24/0.63 (declare-fun tptp.bNF_Gr808751971at_nat (tptp.set_nat tptp.set_Pr1986765409at_nat (-> tptp.nat tptp.nat)) tptp.set_Pr1986765409at_nat)
% 0.24/0.63 (declare-fun tptp.bNF_Gr1143394412nt_nat (tptp.set_Pr1148378109ar_int tptp.set_Pr1986765409at_nat (-> tptp.produc1260470173ar_int tptp.nat)) tptp.set_Pr1333062727ar_int)
% 0.24/0.63 (declare-fun tptp.big_big_step (tptp.produc1260470173ar_int (-> tptp.list_char tptp.int)) Bool)
% 0.24/0.63 (declare-fun tptp.assign (tptp.list_char tptp.aexp) tptp.com)
% 0.24/0.63 (declare-fun tptp.if (tptp.bexp tptp.com tptp.com) tptp.com)
% 0.24/0.63 (declare-fun tptp.skip () tptp.com)
% 0.24/0.63 (declare-fun tptp.seq (tptp.com tptp.com) tptp.com)
% 0.24/0.63 (declare-fun tptp.while (tptp.bexp tptp.com) tptp.com)
% 0.24/0.63 (declare-fun tptp.size_com (tptp.com) tptp.nat)
% 0.24/0.63 (declare-fun tptp.unique1592618082ux_nat (tptp.product_prod_nat_nat) Bool)
% 0.24/0.63 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.24/0.63 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 0.24/0.63 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 0.24/0.63 (declare-fun tptp.append_typerep (tptp.list_typerep tptp.list_typerep) tptp.list_typerep)
% 0.24/0.63 (declare-fun tptp.gen_length_typerep (tptp.nat tptp.list_typerep) tptp.nat)
% 0.24/0.63 (declare-fun tptp.lex_nat (tptp.set_Pr1986765409at_nat) tptp.set_Pr1560408065st_nat)
% 0.24/0.63 (declare-fun tptp.lex_typerep (tptp.set_Pr1097818217yperep) tptp.set_Pr446800905yperep)
% 0.24/0.63 (declare-fun tptp.lexord_nat (tptp.set_Pr1986765409at_nat) tptp.set_Pr1560408065st_nat)
% 0.24/0.63 (declare-fun tptp.lexord_typerep (tptp.set_Pr1097818217yperep) tptp.set_Pr446800905yperep)
% 0.24/0.63 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 0.24/0.63 (declare-fun tptp.cons_P1254790739ar_int (tptp.produc1260470173ar_int tptp.list_P1741976099ar_int) tptp.list_P1741976099ar_int)
% 0.24/0.63 (declare-fun tptp.cons_typerep (tptp.typerep tptp.list_typerep) tptp.list_typerep)
% 0.24/0.63 (declare-fun tptp.size_list_typerep ((-> tptp.typerep tptp.nat) tptp.list_typerep) tptp.nat)
% 0.24/0.63 (declare-fun tptp.listrel1_nat (tptp.set_Pr1986765409at_nat) tptp.set_Pr1560408065st_nat)
% 0.24/0.63 (declare-fun tptp.listrel1_typerep (tptp.set_Pr1097818217yperep) tptp.set_Pr446800905yperep)
% 0.24/0.63 (declare-fun tptp.set_Co1954412371ar_int (tptp.set_Pr1148378109ar_int tptp.set_li1762364675ar_int) tptp.set_li1762364675ar_int)
% 0.24/0.63 (declare-fun tptp.set_Cons_typerep (tptp.set_typerep tptp.set_list_typerep) tptp.set_list_typerep)
% 0.24/0.63 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 0.24/0.63 (declare-fun tptp.size_size_com (tptp.com) tptp.nat)
% 0.24/0.63 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 0.24/0.63 (declare-fun tptp.size_s416147576yperep (tptp.list_typerep) tptp.nat)
% 0.24/0.63 (declare-fun tptp.size_size_typerep (tptp.typerep) tptp.nat)
% 0.24/0.63 (declare-fun tptp.produc1193801173ar_int (tptp.com (-> tptp.list_char tptp.int)) tptp.produc1260470173ar_int)
% 0.24/0.63 (declare-fun tptp.produc1625736153st_nat (tptp.list_nat tptp.list_nat) tptp.produc1699244961st_nat)
% 0.24/0.63 (declare-fun tptp.produc1695567329yperep (tptp.list_typerep tptp.list_typerep) tptp.produc490010537yperep)
% 0.24/0.63 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 0.24/0.63 (declare-fun tptp.produc317451735ar_int (tptp.produc1260470173ar_int tptp.produc1260470173ar_int) tptp.produc1346207591ar_int)
% 0.24/0.63 (declare-fun tptp.produc2071514689yperep (tptp.typerep tptp.typerep) tptp.produc1788831497yperep)
% 0.24/0.63 (declare-fun tptp.relati186416454e_flip ((-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool) (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int)) Bool)
% 0.24/0.63 (declare-fun tptp.relati23543761ar_int ((-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool) tptp.bexp tptp.com tptp.nat (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int)) Bool)
% 0.24/0.63 (declare-fun tptp.relati2102071307_hoare ((-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool) tptp.com tptp.com (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) Bool)
% 0.24/0.63 (declare-fun tptp.relati775585786_valid ((-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool) tptp.com tptp.com (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) Bool)
% 0.24/0.63 (declare-fun tptp.collec672902542ar_int ((-> tptp.list_P1741976099ar_int Bool)) tptp.set_li1762364675ar_int)
% 0.24/0.63 (declare-fun tptp.collect_list_typerep ((-> tptp.list_typerep Bool)) tptp.set_list_typerep)
% 0.24/0.63 (declare-fun tptp.collec770796680ar_int ((-> tptp.produc1260470173ar_int Bool)) tptp.set_Pr1148378109ar_int)
% 0.24/0.63 (declare-fun tptp.collec7649004at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1986765409at_nat)
% 0.24/0.63 (declare-fun tptp.collec1834387154ar_int ((-> tptp.produc1346207591ar_int Bool)) tptp.set_Pr1333062727ar_int)
% 0.24/0.63 (declare-fun tptp.typerep2 (tptp.literal tptp.list_typerep) tptp.typerep)
% 0.24/0.63 (declare-fun tptp.size_typerep (tptp.typerep) tptp.nat)
% 0.24/0.63 (declare-fun tptp.member2052091212ar_int (tptp.list_P1741976099ar_int tptp.set_li1762364675ar_int) Bool)
% 0.24/0.63 (declare-fun tptp.member_list_typerep (tptp.list_typerep tptp.set_list_typerep) Bool)
% 0.24/0.63 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 0.24/0.63 (declare-fun tptp.member92250950ar_int (tptp.produc1260470173ar_int tptp.set_Pr1148378109ar_int) Bool)
% 0.24/0.63 (declare-fun tptp.member1926390090st_nat (tptp.produc1699244961st_nat tptp.set_Pr1560408065st_nat) Bool)
% 0.24/0.63 (declare-fun tptp.member1812711762yperep (tptp.produc490010537yperep tptp.set_Pr446800905yperep) Bool)
% 0.24/0.63 (declare-fun tptp.member701585322at_nat (tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat) Bool)
% 0.24/0.63 (declare-fun tptp.member100911538yperep (tptp.produc1788831497yperep tptp.set_Pr1097818217yperep) Bool)
% 0.24/0.63 (declare-fun tptp.member_typerep (tptp.typerep tptp.set_typerep) Bool)
% 0.24/0.63 (declare-fun tptp.p ((-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int)) Bool)
% 0.24/0.63 (declare-fun tptp.q ((-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int)) Bool)
% 0.24/0.63 (declare-fun tptp.b () tptp.bexp)
% 0.24/0.63 (declare-fun tptp.c () tptp.com)
% 0.24/0.63 (declare-fun tptp.c2 () tptp.com)
% 0.24/0.63 (declare-fun tptp.k () tptp.nat)
% 0.24/0.63 (declare-fun tptp.ka () tptp.nat)
% 0.24/0.63 (declare-fun tptp.s (tptp.list_char) tptp.int)
% 0.24/0.63 (declare-fun tptp.s_a (tptp.list_char) tptp.int)
% 0.24/0.63 (declare-fun tptp.s2 (tptp.list_char) tptp.int)
% 0.24/0.63 (declare-fun tptp.sa (tptp.list_char) tptp.int)
% 0.24/0.63 (declare-fun tptp.t (tptp.list_char) tptp.int)
% 0.24/0.63 (declare-fun tptp.t_a (tptp.list_char) tptp.int)
% 0.24/0.63 (declare-fun tptp.t2 (tptp.list_char) tptp.int)
% 0.24/0.63 (declare-fun tptp.ta (tptp.list_char) tptp.int)
% 0.24/0.63 (declare-fun tptp.u (tptp.list_char) tptp.int)
% 0.24/0.63 (declare-fun tptp.ua (tptp.list_char) tptp.int)
% 0.24/0.63 (assert (@ (@ tptp.bval tptp.b) tptp.sa))
% 0.24/0.63 (assert (@ (@ tptp.bval tptp.b) tptp.s2))
% 0.24/0.63 (assert (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.c) tptp.sa)) tptp.ta))
% 0.24/0.63 (assert (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.c2) tptp.s_a)) tptp.t_a))
% 0.24/0.63 (assert (@ (@ (@ (@ (@ (@ tptp.relati23543761ar_int tptp.p) tptp.b) tptp.c) (@ tptp.suc tptp.ka)) tptp.sa) tptp.s_a))
% 0.24/0.63 (assert (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.c2) tptp.s)) tptp.t))
% 0.24/0.63 (assert (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.c) tptp.s2)) tptp.t2))
% 0.24/0.63 (assert (@ (@ tptp.q tptp.ua) tptp.t_a))
% 0.24/0.63 (assert (@ (@ (@ (@ (@ (@ tptp.relati23543761ar_int tptp.p) tptp.b) tptp.c) tptp.k) tptp.s2) tptp.s))
% 0.24/0.63 (assert (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while tptp.b) tptp.c)) tptp.ta)) tptp.ua))
% 0.24/0.63 (assert (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while tptp.b) tptp.c)) tptp.t2)) tptp.u))
% 0.24/0.63 (assert (@ (@ (@ (@ tptp.relati775585786_valid (@ (@ (@ (@ tptp.relati23543761ar_int tptp.p) tptp.b) tptp.c) (@ tptp.suc tptp.ka))) (@ (@ tptp.while tptp.b) tptp.c)) tptp.c2) tptp.q))
% 0.24/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X2) (@ tptp.suc Y2)) (= X2 Y2))))
% 0.24/0.63 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 0.24/0.63 (assert (forall ((X1 tptp.nat) (X2 tptp.nat) (Y1 tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat X1) X2) (@ (@ tptp.product_Pair_nat_nat Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.24/0.63 (assert (forall ((X1 tptp.com) (X2 (-> tptp.list_char tptp.int)) (Y1 tptp.com) (Y2 (-> tptp.list_char tptp.int))) (= (= (@ (@ tptp.produc1193801173ar_int X1) X2) (@ (@ tptp.produc1193801173ar_int Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A2) B2)) (and (= A A2) (= B B2)))))
% 0.24/0.63 (assert (forall ((A tptp.com) (B (-> tptp.list_char tptp.int)) (A2 tptp.com) (B2 (-> tptp.list_char tptp.int))) (= (= (@ (@ tptp.produc1193801173ar_int A) B) (@ (@ tptp.produc1193801173ar_int A2) B2)) (and (= A A2) (= B B2)))))
% 0.24/0.63 (assert (forall ((T (-> tptp.list_char tptp.int)) (U (-> tptp.list_char tptp.int)) (S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int)) (T2 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ (@ (@ (@ tptp.relati23543761ar_int tptp.p) tptp.b) tptp.c) tptp.ka))) (let ((_let_2 (@ (@ tptp.while tptp.b) tptp.c))) (=> (@ (@ (@ (@ tptp.relati775585786_valid _let_1) _let_2) tptp.c2) tptp.q) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int _let_2) T)) U) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.c) S)) T) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.c2) S2)) T2) (=> (@ (@ tptp.q U) T2) (=> (@ (@ tptp.bval tptp.b) S) (=> (@ (@ _let_1 S) S2) (exists ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (and (@ (@ (@ (@ (@ (@ tptp.relati23543761ar_int tptp.p) tptp.b) tptp.c) tptp.ka) S3) S4) (@ (@ tptp.bval tptp.b) S3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.c) S3)) T) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.c2) S4)) T2))))))))))))))
% 0.24/0.63 (assert (forall ((C tptp.com) (C2 tptp.com)) (= (forall ((S5 (-> tptp.list_char tptp.int)) (T3 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S5)) T3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S5)) T3))) (forall ((S5 (-> tptp.list_char tptp.int)) (T3 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S5)) T3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S5)) T3))))))
% 0.24/0.63 (assert (forall ((C tptp.com) (S6 (-> tptp.list_char tptp.int)) (T4 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S6)) T4))) (= _let_1 _let_1))))
% 0.24/0.63 (assert (@ (@ tptp.q tptp.u) tptp.t))
% 0.24/0.63 (assert (forall ((P_1 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q_1 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P_2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (Q_2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid P_1) C) C2) Q_1) (=> (@ (@ (@ (@ tptp.relati775585786_valid P_2) C) C2) Q_2) (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (or (@ (@ P_1 S5) S7) (@ (@ P_2 S5) S7)))) C) C2) (lambda ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (or (@ (@ Q_1 T3) T5) (@ (@ Q_2 T3) T5))))))))
% 0.24/0.63 (assert (@ (@ (@ (@ tptp.relati775585786_valid (@ (@ (@ (@ tptp.relati23543761ar_int tptp.p) tptp.b) tptp.c) tptp.k)) (@ (@ tptp.while tptp.b) tptp.c)) tptp.c2) tptp.q))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (Q2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid P) C) C2) Q) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (=> (@ (@ P S3) S4) (@ (@ P2 S3) S4))) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (=> (@ (@ Q2 S3) S4) (@ (@ Q S3) S4))) (@ (@ (@ (@ tptp.relati775585786_valid P2) C) C2) Q2))))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (K tptp.nat) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ tptp.while B) C))) (let ((_let_2 (@ (@ (@ tptp.relati23543761ar_int P) B) C))) (=> (@ (@ (@ (@ tptp.relati775585786_valid (@ _let_2 (@ tptp.suc K))) _let_1) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid (@ _let_2 K)) _let_1) C2) Q))))))
% 0.24/0.63 (assert (forall ((B tptp.bexp) (C tptp.com) (S (-> tptp.list_char tptp.int)) (T (-> tptp.list_char tptp.int)) (C2 tptp.com)) (let ((_let_1 (@ tptp.while B))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ _let_1 C)) S)) T) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (T6 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S3)) T6) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S3)) T6))) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ _let_1 C2)) S)) T))))))
% 0.24/0.63 (assert (forall ((C tptp.com) (C2 tptp.com) (B tptp.bexp)) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (T6 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S3)) T6) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S3)) T6))) (forall ((S6 (-> tptp.list_char tptp.int)) (T4 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.while B))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ _let_1 C)) S6)) T4) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ _let_1 C2)) S6)) T4)))))))
% 0.24/0.63 (assert (= tptp.relati775585786_valid (lambda ((P3 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C3 tptp.com) (C4 tptp.com) (Q3 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (forall ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (=> (@ (@ Q3 T3) T5) (exists ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P3 S5) S7) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C3) S5)) T3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C4) S7)) T5))))))))
% 0.24/0.63 (assert (forall ((B tptp.bexp) (S (-> tptp.list_char tptp.int)) (C tptp.com)) (=> (not (@ (@ tptp.bval B) S)) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)) S)) S))))
% 0.24/0.63 (assert (forall ((B tptp.bexp) (S_1 (-> tptp.list_char tptp.int)) (C tptp.com) (S_2 (-> tptp.list_char tptp.int)) (S_3 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)))) (=> (@ (@ tptp.bval B) S_1) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S_1)) S_2) (=> (@ (@ tptp.big_big_step (@ _let_1 S_2)) S_3) (@ (@ tptp.big_big_step (@ _let_1 S_1)) S_3)))))))
% 0.24/0.63 (assert (forall ((B tptp.bexp) (C tptp.com) (S (-> tptp.list_char tptp.int)) (T (-> tptp.list_char tptp.int))) (let ((_let_1 (@ (@ tptp.bval B) S))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)) S)) T) (=> (=> (= T S) _let_1) (not (=> _let_1 (forall ((S_22 (-> tptp.list_char tptp.int))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S)) S_22) (not (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)) S_22)) T)))))))))))
% 0.24/0.63 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Prod tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A3) B3))) (@ P Prod))))
% 0.24/0.63 (assert (forall ((P (-> tptp.produc1260470173ar_int Bool)) (Prod tptp.produc1260470173ar_int)) (=> (forall ((A3 tptp.com) (B3 (-> tptp.list_char tptp.int))) (@ P (@ (@ tptp.produc1193801173ar_int A3) B3))) (@ P Prod))))
% 0.24/0.63 (assert (forall ((Y tptp.product_prod_nat_nat)) (not (forall ((A3 tptp.nat) (B3 tptp.nat)) (not (= Y (@ (@ tptp.product_Pair_nat_nat A3) B3)))))))
% 0.24/0.63 (assert (forall ((Y tptp.produc1260470173ar_int)) (not (forall ((A3 tptp.com) (B3 (-> tptp.list_char tptp.int))) (not (= Y (@ (@ tptp.produc1193801173ar_int A3) B3)))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.24/0.63 (assert (forall ((A tptp.com) (B (-> tptp.list_char tptp.int)) (A2 tptp.com) (B2 (-> tptp.list_char tptp.int))) (=> (= (@ (@ tptp.produc1193801173ar_int A) B) (@ (@ tptp.produc1193801173ar_int A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.24/0.63 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (P4 tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A3) B3))) (@ P P4))))
% 0.24/0.63 (assert (forall ((P (-> tptp.produc1260470173ar_int Bool)) (P4 tptp.produc1260470173ar_int)) (=> (forall ((A3 tptp.com) (B3 (-> tptp.list_char tptp.int))) (@ P (@ (@ tptp.produc1193801173ar_int A3) B3))) (@ P P4))))
% 0.24/0.63 (assert (forall ((A tptp.produc1260470173ar_int) (P (-> tptp.produc1260470173ar_int Bool))) (= (@ (@ tptp.member92250950ar_int A) (@ tptp.collec770796680ar_int P)) (@ P A))))
% 0.24/0.63 (assert (forall ((A4 tptp.set_Pr1148378109ar_int)) (= (@ tptp.collec770796680ar_int (lambda ((X tptp.produc1260470173ar_int)) (@ (@ tptp.member92250950ar_int X) A4))) A4)))
% 0.24/0.63 (assert (forall ((P4 tptp.product_prod_nat_nat)) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (= P4 (@ (@ tptp.product_Pair_nat_nat X3) Y3)))))
% 0.24/0.63 (assert (forall ((P4 tptp.produc1260470173ar_int)) (exists ((X3 tptp.com) (Y3 (-> tptp.list_char tptp.int))) (= P4 (@ (@ tptp.produc1193801173ar_int X3) Y3)))))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 0.24/0.63 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X4) (@ tptp.suc Y)) (= X4 Y))))
% 0.24/0.63 (assert (forall ((C tptp.com) (S (-> tptp.list_char tptp.int)) (T (-> tptp.list_char tptp.int)) (U (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S)))) (=> (@ _let_1 T) (=> (@ _let_1 U) (= U T))))))
% 0.24/0.63 (assert (forall ((C tptp.com) (C2 tptp.com) (C5 tptp.com)) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (T6 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S3)) T6) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S3)) T6))) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (T6 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S3)) T6) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C5) S3)) T6))) (forall ((S6 (-> tptp.list_char tptp.int)) (T4 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S6)) T4) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C5) S6)) T4)))))))
% 0.24/0.63 (assert (forall ((X51 tptp.bexp) (X52 tptp.com) (Y51 tptp.bexp) (Y52 tptp.com)) (= (= (@ (@ tptp.while X51) X52) (@ (@ tptp.while Y51) Y52)) (and (= X51 Y51) (= X52 Y52)))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com)) (=> (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (not (@ (@ tptp.bval B) S5))))) tptp.skip) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid P) (@ (@ tptp.while B) C)) C2) Q))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ tptp.while B) C))) (=> (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (@ (@ tptp.bval B) S5)))) (@ (@ tptp.seq C) _let_1)) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid P) _let_1) C2) Q)))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (N tptp.nat)) (= (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) (@ tptp.suc N)) (lambda ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (exists ((S5 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S5)) T3) (@ (@ tptp.bval B) S5) (@ (@ (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) N) S5) T5)))))))
% 0.24/0.63 (assert (forall ((Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C2 tptp.com)) (=> (forall ((T6 (-> tptp.list_char tptp.int)) (T7 (-> tptp.list_char tptp.int))) (=> (@ (@ Q T6) T7) (exists ((S8 (-> tptp.list_char tptp.int))) (and (@ (@ P T6) S8) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S8)) T7))))) (@ (@ (@ (@ tptp.relati775585786_valid P) tptp.skip) C2) Q))))
% 0.24/0.63 (assert (forall ((P (-> tptp.nat (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (K tptp.nat) (B tptp.bexp) (C tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C2 tptp.com) (T (-> tptp.list_char tptp.int)) (T2 (-> tptp.list_char tptp.int))) (=> (forall ((N2 tptp.nat) (T6 (-> tptp.list_char tptp.int)) (T7 (-> tptp.list_char tptp.int))) (=> (@ (@ (@ P (@ (@ tptp.plus_plus_nat K) (@ tptp.suc N2))) T6) T7) (exists ((S6 (-> tptp.list_char tptp.int))) (and (@ (@ (@ P (@ (@ tptp.plus_plus_nat K) N2)) S6) T7) (@ (@ tptp.bval B) S6) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S6)) T6))))) (=> (forall ((T6 (-> tptp.list_char tptp.int)) (T7 (-> tptp.list_char tptp.int))) (=> (@ (@ Q T6) T7) (exists ((S6 (-> tptp.list_char tptp.int)) (S8 (-> tptp.list_char tptp.int))) (and (exists ((N3 tptp.nat)) (@ (@ (@ P (@ (@ tptp.plus_plus_nat K) N3)) S6) S8)) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)) S6)) T6) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S8)) T7))))) (=> (@ (@ Q T) T2) (exists ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (and (@ (@ (@ P K) S3) S4) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)) S3)) T) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S4)) T2))))))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C2 tptp.com) (C tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid (@ tptp.relati186416454e_flip P)) C2) C) (@ tptp.relati186416454e_flip Q)) (@ (@ (@ (@ tptp.relati775585786_valid P) C) C2) Q))))
% 0.24/0.63 (assert (forall ((R tptp.set_Pr1986765409at_nat) (S9 tptp.set_Pr1986765409at_nat)) (= (= (lambda ((X tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X) Y4)) R)) (lambda ((X tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X) Y4)) S9))) (= R S9))))
% 0.24/0.63 (assert (forall ((R tptp.set_Pr1148378109ar_int) (S9 tptp.set_Pr1148378109ar_int)) (= (= (lambda ((X tptp.com) (Y4 (-> tptp.list_char tptp.int))) (@ (@ tptp.member92250950ar_int (@ (@ tptp.produc1193801173ar_int X) Y4)) R)) (lambda ((X tptp.com) (Y4 (-> tptp.list_char tptp.int))) (@ (@ tptp.member92250950ar_int (@ (@ tptp.produc1193801173ar_int X) Y4)) S9))) (= R S9))))
% 0.24/0.63 (assert (forall ((X31 tptp.com) (X32 tptp.com) (Y31 tptp.com) (Y32 tptp.com)) (= (= (@ (@ tptp.seq X31) X32) (@ (@ tptp.seq Y31) Y32)) (and (= X31 Y31) (= X32 Y32)))))
% 0.24/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ tptp.suc (@ _let_1 N))))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (D tptp.com) (D2 tptp.com) (R (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ tptp.relati775585786_valid P))) (=> (@ (@ (@ _let_1 C) C2) Q) (=> (@ (@ (@ (@ tptp.relati775585786_valid Q) D) D2) R) (@ (@ (@ _let_1 (@ (@ tptp.seq C) D)) (@ (@ tptp.seq C2) D2)) R))))))
% 0.24/0.63 (assert (forall ((S2 (-> tptp.list_char tptp.int)) (T2 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.skip) S2)) T2) (= S2 T2))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (D tptp.com) (C2 tptp.com) (R (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ tptp.relati775585786_valid P))) (=> (@ (@ (@ _let_1 C) tptp.skip) Q) (=> (@ (@ (@ (@ tptp.relati775585786_valid Q) D) C2) R) (@ (@ (@ _let_1 (@ (@ tptp.seq C) D)) C2) R))))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (D tptp.com) (R (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ tptp.relati775585786_valid P))) (=> (@ (@ (@ _let_1 C) C2) Q) (=> (@ (@ (@ (@ tptp.relati775585786_valid Q) D) tptp.skip) R) (@ (@ (@ _let_1 (@ (@ tptp.seq C) D)) C2) R))))))
% 0.24/0.63 (assert (forall ((X31 tptp.com) (X32 tptp.com)) (not (= tptp.skip (@ (@ tptp.seq X31) X32)))))
% 0.24/0.63 (assert (forall ((X31 tptp.com) (X32 tptp.com) (X51 tptp.bexp) (X52 tptp.com)) (not (= (@ (@ tptp.seq X31) X32) (@ (@ tptp.while X51) X52)))))
% 0.24/0.63 (assert (forall ((X51 tptp.bexp) (X52 tptp.com)) (not (= tptp.skip (@ (@ tptp.while X51) X52)))))
% 0.24/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))))
% 0.24/0.63 (assert (forall ((A4 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A4 (@ _let_1 A)) (= (@ tptp.suc A4) (@ _let_1 (@ tptp.suc A)))))))
% 0.24/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C1 tptp.com) (C22 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid P) (@ (@ tptp.seq C1) C22)) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (exists ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C1) S5)) T3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S7)) T5) (exists ((U2 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C22) T3)) U2) (@ (@ Q U2) T5))))))) C22) tptp.skip) Q))))
% 0.24/0.63 (assert (= tptp.relati186416454e_flip (lambda ((P3 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (@ (@ P3 S7) S5))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C1 tptp.com) (C22 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ tptp.relati775585786_valid P))) (=> (@ (@ (@ _let_1 (@ (@ tptp.seq C1) C22)) C2) Q) (@ (@ (@ _let_1 C1) C2) (lambda ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (exists ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C1) S5)) T3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S7)) T5) (exists ((U2 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C22) T3)) U2) (@ (@ Q U2) T5)))))))))))
% 0.24/0.63 (assert (forall ((C1 tptp.com) (C22 tptp.com) (S1 (-> tptp.list_char tptp.int)) (S32 (-> tptp.list_char tptp.int))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.seq C1) C22)) S1)) S32) (not (forall ((S_22 (-> tptp.list_char tptp.int))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C1) S1)) S_22) (not (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C22) S_22)) S32))))))))
% 0.24/0.63 (assert (forall ((C1 tptp.com) (C22 tptp.com) (C32 tptp.com) (S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.seq C1))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.seq (@ _let_1 C22)) C32)) S)) S2) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ _let_1 (@ (@ tptp.seq C22) C32))) S)) S2)))))
% 0.24/0.63 (assert (forall ((C_1 tptp.com) (S_1 (-> tptp.list_char tptp.int)) (S_2 (-> tptp.list_char tptp.int)) (C_2 tptp.com) (S_3 (-> tptp.list_char tptp.int))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C_1) S_1)) S_2) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C_2) S_2)) S_3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.seq C_1) C_2)) S_1)) S_3)))))
% 0.24/0.63 (assert (forall ((S (-> tptp.list_char tptp.int)) (T (-> tptp.list_char tptp.int))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.skip) S)) T) (= T S))))
% 0.24/0.63 (assert (forall ((S (-> tptp.list_char tptp.int))) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.skip) S)) S)))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ (@ (@ tptp.relati775585786_valid P) C) C2))) (=> (@ _let_1 Q) (@ _let_1 (lambda ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (and (@ (@ Q S) S2) (exists ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S5)) T3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S7)) T5))))))))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (K tptp.nat) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) K)) (@ (@ tptp.while B) C)) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) K) S5) S7) (@ (@ tptp.bval B) S5)))) C) tptp.skip) (lambda ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (and (@ (@ (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) (@ tptp.suc K)) T3) T5) (exists ((U2 (-> tptp.list_char tptp.int)) (U3 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)) T3)) U2) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) T5)) U3) (@ (@ Q U2) U3)))))))))
% 0.24/0.63 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C1 tptp.com) (C22 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid P) (@ (@ (@ tptp.if B) C1) C22)) C2) Q) (and (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (@ (@ tptp.bval B) S5)))) C1) C2) (lambda ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (and (@ (@ Q T3) T5) (exists ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C1) S5)) T3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S7)) T5) (@ (@ tptp.bval B) S5)))))) (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (not (@ (@ tptp.bval B) S5))))) C22) C2) (lambda ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (and (@ (@ Q T3) T5) (exists ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C22) S5)) T3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S7)) T5) (not (@ (@ tptp.bval B) S5)))))))))))
% 0.24/0.63 (assert (forall ((B tptp.bexp) (C tptp.com) (S6 (-> tptp.list_char tptp.int)) (T4 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ (@ tptp.while B) C))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int _let_1) S6)) T4) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ (@ tptp.if B) (@ (@ tptp.seq C) _let_1)) tptp.skip)) S6)) T4)))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C_1 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C_2 tptp.com)) (=> (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((A5 (-> tptp.list_char tptp.int)) (C3 (-> tptp.list_char tptp.int))) (and (@ (@ P A5) C3) (@ (@ tptp.bval B) A5)))) C_1) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid P) (@ (@ (@ tptp.if B) C_1) C_2)) C2) Q))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C_2 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C_1 tptp.com)) (=> (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((A5 (-> tptp.list_char tptp.int)) (C3 (-> tptp.list_char tptp.int))) (and (@ (@ P A5) C3) (not (@ (@ tptp.bval B) A5))))) C_2) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid P) (@ (@ (@ tptp.if B) C_1) C_2)) C2) Q))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ tptp.while B) C))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (@ (@ tptp.bval B) S5)))) (@ (@ tptp.seq C) _let_1)) C2) Q) (@ (@ (@ (@ tptp.relati2102071307_hoare P) _let_1) C2) Q)))))
% 0.24/0.63 (assert (forall ((X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com) (Y41 tptp.bexp) (Y42 tptp.com) (Y43 tptp.com)) (= (= (@ (@ (@ tptp.if X41) X42) X43) (@ (@ (@ tptp.if Y41) Y42) Y43)) (and (= X41 Y41) (= X42 Y42) (= X43 Y43)))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (@ (@ (@ (@ tptp.relati2102071307_hoare P) tptp.skip) tptp.skip) P)))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (= (@ (@ (@ (@ tptp.relati2102071307_hoare P) tptp.skip) tptp.skip) Q) (forall ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (=> (@ (@ Q S5) S7) (@ (@ P S5) S7))))))
% 0.24/0.63 (assert (forall ((P_1 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q_1 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P_2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (Q_2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare P_1) C) C2) Q_1) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare P_2) C) C2) Q_2) (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (or (@ (@ P_1 S5) S7) (@ (@ P_2 S5) S7)))) C) C2) (lambda ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (or (@ (@ Q_1 T3) T5) (@ (@ Q_2 T3) T5))))))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare P) C) C2) Q) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (=> (@ (@ P S3) S4) (@ (@ P2 S3) S4))) (@ (@ (@ (@ tptp.relati2102071307_hoare P2) C) C2) Q)))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (Q2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ (@ tptp.relati2102071307_hoare P) C) C2))) (=> (@ _let_1 Q) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (=> (@ (@ Q2 S3) S4) (@ (@ Q S3) S4))) (@ _let_1 Q2))))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (Q2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare P) C) C2) Q) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (=> (@ (@ P S3) S4) (@ (@ P2 S3) S4))) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (=> (@ (@ Q2 S3) S4) (@ (@ Q S3) S4))) (@ (@ (@ (@ tptp.relati2102071307_hoare P2) C) C2) Q2))))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C_2 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C_1 tptp.com)) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (not (@ (@ tptp.bval B) S5))))) C_2) C2) Q) (@ (@ (@ (@ tptp.relati2102071307_hoare P) (@ (@ (@ tptp.if B) C_1) C_2)) C2) Q))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C_1 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C_2 tptp.com)) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (@ (@ tptp.bval B) S5)))) C_1) C2) Q) (@ (@ (@ (@ tptp.relati2102071307_hoare P) (@ (@ (@ tptp.if B) C_1) C_2)) C2) Q))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare P) C) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid P) C) C2) Q))))
% 0.24/0.63 (assert (forall ((X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com) (X51 tptp.bexp) (X52 tptp.com)) (not (= (@ (@ (@ tptp.if X41) X42) X43) (@ (@ tptp.while X51) X52)))))
% 0.24/0.63 (assert (forall ((X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com)) (not (= tptp.skip (@ (@ (@ tptp.if X41) X42) X43)))))
% 0.24/0.63 (assert (forall ((X31 tptp.com) (X32 tptp.com) (X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com)) (not (= (@ (@ tptp.seq X31) X32) (@ (@ (@ tptp.if X41) X42) X43)))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare (@ tptp.relati186416454e_flip P)) C) C2) (@ tptp.relati186416454e_flip Q)) (@ (@ (@ (@ tptp.relati2102071307_hoare P) C2) C) Q))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (D tptp.com) (R (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ tptp.relati2102071307_hoare P))) (=> (@ (@ (@ _let_1 C) C2) Q) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare Q) D) tptp.skip) R) (@ (@ (@ _let_1 (@ (@ tptp.seq C) D)) C2) R))))))
% 0.24/0.63 (assert (forall ((B1 tptp.bexp) (B22 tptp.bexp) (C11 tptp.com) (C12 tptp.com) (C22 tptp.com) (S6 (-> tptp.list_char tptp.int)) (T4 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.if B1))) (let ((_let_2 (@ tptp.if B22))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ _let_1 (@ (@ _let_2 C11) C12)) C22)) S6)) T4) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ _let_2 (@ (@ _let_1 C11) C22)) (@ (@ _let_1 C12) C22))) S6)) T4))))))
% 0.24/0.63 (assert (forall ((B tptp.bexp) (C tptp.com) (S6 (-> tptp.list_char tptp.int)) (T4 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ (@ tptp.if B) C) C)) S6)) T4) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S6)) T4))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 0.24/0.63 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.24/0.63 (assert (forall ((A4 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A4) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 0.24/0.63 (assert (forall ((B4 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 0.24/0.63 (assert (= tptp.plus_plus_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ tptp.plus_plus_nat B5) A5))))
% 0.24/0.63 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 0.24/0.63 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 0.24/0.63 (assert (forall ((Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C2 tptp.com)) (=> (forall ((T6 (-> tptp.list_char tptp.int)) (T7 (-> tptp.list_char tptp.int))) (=> (@ (@ Q T6) T7) (exists ((S8 (-> tptp.list_char tptp.int))) (and (@ (@ P T6) S8) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S8)) T7))))) (@ (@ (@ (@ tptp.relati2102071307_hoare P) tptp.skip) C2) Q))))
% 0.24/0.63 (assert (forall ((B tptp.bexp) (S (-> tptp.list_char tptp.int)) (C_2 tptp.com) (T (-> tptp.list_char tptp.int)) (C_1 tptp.com)) (=> (not (@ (@ tptp.bval B) S)) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C_2) S)) T) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ (@ tptp.if B) C_1) C_2)) S)) T)))))
% 0.24/0.63 (assert (forall ((B tptp.bexp) (S (-> tptp.list_char tptp.int)) (C_1 tptp.com) (T (-> tptp.list_char tptp.int)) (C_2 tptp.com)) (=> (@ (@ tptp.bval B) S) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C_1) S)) T) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ (@ tptp.if B) C_1) C_2)) S)) T)))))
% 0.24/0.63 (assert (forall ((B tptp.bexp) (C1 tptp.com) (C22 tptp.com) (S (-> tptp.list_char tptp.int)) (T (-> tptp.list_char tptp.int))) (let ((_let_1 (@ (@ tptp.bval B) S))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ (@ tptp.if B) C1) C22)) S)) T) (=> (=> _let_1 (not (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C1) S)) T))) (not (=> (not _let_1) (not (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C22) S)) T)))))))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com)) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (not (@ (@ tptp.bval B) S5))))) tptp.skip) C2) Q) (@ (@ (@ (@ tptp.relati2102071307_hoare P) (@ (@ tptp.while B) C)) C2) Q))))
% 0.24/0.63 (assert (forall ((Y tptp.com)) (=> (not (= Y tptp.skip)) (=> (forall ((X21 tptp.list_char) (X22 tptp.aexp)) (not (= Y (@ (@ tptp.assign X21) X22)))) (=> (forall ((X312 tptp.com) (X322 tptp.com)) (not (= Y (@ (@ tptp.seq X312) X322)))) (=> (forall ((X412 tptp.bexp) (X422 tptp.com) (X432 tptp.com)) (not (= Y (@ (@ (@ tptp.if X412) X422) X432)))) (not (forall ((X512 tptp.bexp) (X522 tptp.com)) (not (= Y (@ (@ tptp.while X512) X522)))))))))))
% 0.24/0.63 (assert (forall ((P (-> tptp.com Bool)) (Com tptp.com)) (=> (@ P tptp.skip) (=> (forall ((X12 tptp.list_char) (X23 tptp.aexp)) (@ P (@ (@ tptp.assign X12) X23))) (=> (forall ((X12 tptp.com) (X23 tptp.com)) (=> (@ P X12) (=> (@ P X23) (@ P (@ (@ tptp.seq X12) X23))))) (=> (forall ((X12 tptp.bexp) (X23 tptp.com) (X33 tptp.com)) (=> (@ P X23) (=> (@ P X33) (@ P (@ (@ (@ tptp.if X12) X23) X33))))) (=> (forall ((X12 tptp.bexp) (X23 tptp.com)) (=> (@ P X23) (@ P (@ (@ tptp.while X12) X23)))) (@ P Com))))))))
% 0.24/0.63 (assert (= tptp.bNF_Gr202451329ar_int (lambda ((A6 tptp.set_Pr1148378109ar_int) (F (-> tptp.produc1260470173ar_int tptp.com)) (G (-> tptp.produc1260470173ar_int tptp.list_char tptp.int))) (@ tptp.collec770796680ar_int (lambda ((Uu tptp.produc1260470173ar_int)) (exists ((A5 tptp.produc1260470173ar_int)) (and (= Uu (@ (@ tptp.produc1193801173ar_int (@ F A5)) (@ G A5))) (@ (@ tptp.member92250950ar_int A5) A6))))))))
% 0.24/0.63 (assert (= tptp.bNF_Gr749752805at_nat (lambda ((A6 tptp.set_Pr1148378109ar_int) (F (-> tptp.produc1260470173ar_int tptp.nat)) (G (-> tptp.produc1260470173ar_int tptp.nat))) (@ tptp.collec7649004at_nat (lambda ((Uu tptp.product_prod_nat_nat)) (exists ((A5 tptp.produc1260470173ar_int)) (and (= Uu (@ (@ tptp.product_Pair_nat_nat (@ F A5)) (@ G A5))) (@ (@ tptp.member92250950ar_int A5) A6))))))))
% 0.24/0.63 (assert (forall ((P (-> tptp.nat (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ tptp.while B) C))) (=> (forall ((N2 tptp.nat)) (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ (@ P N2) S5) S7) (@ (@ tptp.bval B) S5)))) C) tptp.skip) (@ P (@ tptp.suc N2)))) (=> (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (exists ((N4 tptp.nat)) (@ (@ (@ P N4) S5) S7)))) _let_1) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid (@ P tptp.zero_zero_nat)) _let_1) C2) Q))))))
% 0.24/0.63 (assert (forall ((X212 tptp.list_char) (X222 tptp.aexp) (Y21 tptp.list_char) (Y22 tptp.aexp)) (= (= (@ (@ tptp.assign X212) X222) (@ (@ tptp.assign Y21) Y22)) (and (= X212 Y21) (= X222 Y22)))))
% 0.24/0.63 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 0.24/0.63 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 0.24/0.63 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X4) Y) tptp.zero_zero_nat) (and (= X4 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 0.24/0.63 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X4) Y)) (and (= X4 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 0.24/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 0.24/0.63 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 0.24/0.63 (assert (forall ((X4 tptp.nat)) (= (= tptp.zero_zero_nat X4) (= X4 tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 0.24/0.63 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 0.24/0.63 (assert (forall ((X2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X2)))))
% 0.24/0.63 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 0.24/0.63 (assert (forall ((Nat tptp.nat) (X2 tptp.nat)) (=> (= Nat (@ tptp.suc X2)) (not (= Nat tptp.zero_zero_nat)))))
% 0.24/0.63 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (@ P (@ tptp.suc N2)))) (@ P N)))))
% 0.24/0.63 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (@ (@ P X3) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P X3) Y3) (@ (@ P (@ tptp.suc X3)) (@ tptp.suc Y3)))) (@ (@ P M) N))))))
% 0.24/0.63 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N2 tptp.nat)) (=> (@ P (@ tptp.suc N2)) (@ P N2))) (@ P tptp.zero_zero_nat)))))
% 0.24/0.63 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.24/0.63 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.24/0.63 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))))
% 0.24/0.63 (assert (forall ((P (-> tptp.nat Bool)) (Nat tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((Nat3 tptp.nat)) (=> (@ P Nat3) (@ P (@ tptp.suc Nat3)))) (@ P Nat)))))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M2 tptp.nat)) (= N (@ tptp.suc M2))))))
% 0.24/0.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 0.24/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((B tptp.com) (F2 (-> tptp.produc1260470173ar_int tptp.com)) (X4 tptp.produc1260470173ar_int) (C (-> tptp.list_char tptp.int)) (G2 (-> tptp.produc1260470173ar_int tptp.list_char tptp.int)) (A4 tptp.set_Pr1148378109ar_int)) (=> (= B (@ F2 X4)) (=> (= C (@ G2 X4)) (=> (@ (@ tptp.member92250950ar_int X4) A4) (@ (@ tptp.member92250950ar_int (@ (@ tptp.produc1193801173ar_int B) C)) (@ (@ (@ tptp.bNF_Gr202451329ar_int A4) F2) G2)))))))
% 0.24/0.63 (assert (forall ((B tptp.nat) (F2 (-> tptp.produc1260470173ar_int tptp.nat)) (X4 tptp.produc1260470173ar_int) (C tptp.nat) (G2 (-> tptp.produc1260470173ar_int tptp.nat)) (A4 tptp.set_Pr1148378109ar_int)) (=> (= B (@ F2 X4)) (=> (= C (@ G2 X4)) (=> (@ (@ tptp.member92250950ar_int X4) A4) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat B) C)) (@ (@ (@ tptp.bNF_Gr749752805at_nat A4) F2) G2)))))))
% 0.24/0.63 (assert (forall ((X212 tptp.list_char) (X222 tptp.aexp) (X51 tptp.bexp) (X52 tptp.com)) (not (= (@ (@ tptp.assign X212) X222) (@ (@ tptp.while X51) X52)))))
% 0.24/0.63 (assert (forall ((X212 tptp.list_char) (X222 tptp.aexp)) (not (= tptp.skip (@ (@ tptp.assign X212) X222)))))
% 0.24/0.63 (assert (forall ((X212 tptp.list_char) (X222 tptp.aexp) (X31 tptp.com) (X32 tptp.com)) (not (= (@ (@ tptp.assign X212) X222) (@ (@ tptp.seq X31) X32)))))
% 0.24/0.63 (assert (forall ((X212 tptp.list_char) (X222 tptp.aexp) (X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com)) (not (= (@ (@ tptp.assign X212) X222) (@ (@ (@ tptp.if X41) X42) X43)))))
% 0.24/0.63 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com)) (= (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) tptp.zero_zero_nat) P)))
% 0.24/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 0.24/0.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N) _let_1) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 0.24/0.63 (assert (forall ((P (-> tptp.nat (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ tptp.while B) C))) (=> (forall ((N2 tptp.nat)) (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ (@ P N2) S5) S7) (@ (@ tptp.bval B) S5)))) C) tptp.skip) (@ P (@ tptp.suc N2)))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (exists ((N4 tptp.nat)) (@ (@ (@ P N4) S5) S7)))) _let_1) C2) Q) (@ (@ (@ (@ tptp.relati2102071307_hoare (@ P tptp.zero_zero_nat)) _let_1) C2) Q))))))
% 0.24/0.63 (assert (forall ((X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com)) (= (@ tptp.size_com (@ (@ (@ tptp.if X41) X42) X43)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.size_com X42)) (@ tptp.size_com X43))) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.24/0.63 (assert (forall ((X31 tptp.com) (X32 tptp.com)) (= (@ tptp.size_com (@ (@ tptp.seq X31) X32)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.size_com X31)) (@ tptp.size_com X32))) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.24/0.63 (assert (forall ((X51 tptp.bexp) (X52 tptp.com)) (= (@ tptp.size_com (@ (@ tptp.while X51) X52)) (@ (@ tptp.plus_plus_nat (@ tptp.size_com X52)) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.24/0.63 (assert (forall ((X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com)) (= (@ tptp.size_size_com (@ (@ (@ tptp.if X41) X42) X43)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.size_size_com X42)) (@ tptp.size_size_com X43))) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.24/0.63 (assert (forall ((X4 tptp.com) (Y tptp.com)) (=> (not (= (@ tptp.size_size_com X4) (@ tptp.size_size_com Y))) (not (= X4 Y)))))
% 0.24/0.63 (assert (forall ((X4 tptp.typerep) (Y tptp.typerep)) (=> (not (= (@ tptp.size_size_typerep X4) (@ tptp.size_size_typerep Y))) (not (= X4 Y)))))
% 0.24/0.63 (assert (= (@ tptp.size_size_com tptp.skip) tptp.zero_zero_nat))
% 0.24/0.63 (assert (forall ((X212 tptp.list_char) (X222 tptp.aexp)) (= (@ tptp.size_size_com (@ (@ tptp.assign X212) X222)) tptp.zero_zero_nat)))
% 0.24/0.63 (assert (= (@ tptp.size_com tptp.skip) tptp.zero_zero_nat))
% 0.24/0.63 (assert (forall ((X212 tptp.list_char) (X222 tptp.aexp)) (= (@ tptp.size_com (@ (@ tptp.assign X212) X222)) tptp.zero_zero_nat)))
% 0.24/0.63 (assert (forall ((X51 tptp.bexp) (X52 tptp.com)) (= (@ tptp.size_size_com (@ (@ tptp.while X51) X52)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_com X52)) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.24/0.63 (assert (forall ((X31 tptp.com) (X32 tptp.com)) (= (@ tptp.size_size_com (@ (@ tptp.seq X31) X32)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.size_size_com X31)) (@ tptp.size_size_com X32))) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.24/0.63 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ P A3) B3) (@ (@ P B3) A3))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) tptp.zero_zero_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ P A3))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.plus_plus_nat A3) B3))))) (@ (@ P A) B))))))
% 0.24/0.63 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 0.24/0.63 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 0.24/0.63 (assert (= tptp.bNF_Gr1247133574at_nat (lambda ((R2 tptp.set_Pr1986765409at_nat) (F (-> tptp.nat tptp.nat))) (@ tptp.collec7649004at_nat (lambda ((Uu tptp.product_prod_nat_nat)) (exists ((A1 tptp.nat) (A22 tptp.nat)) (and (= Uu (@ (@ tptp.product_Pair_nat_nat (@ F A1)) (@ F A22))) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A1) A22)) R2))))))))
% 0.24/0.63 (assert (= tptp.bNF_Gr1143394412nt_nat (lambda ((A6 tptp.set_Pr1148378109ar_int) (R2 tptp.set_Pr1986765409at_nat) (F (-> tptp.produc1260470173ar_int tptp.nat))) (@ tptp.collec1834387154ar_int (lambda ((Uu tptp.produc1346207591ar_int)) (exists ((A1 tptp.produc1260470173ar_int) (A22 tptp.produc1260470173ar_int)) (and (= Uu (@ (@ tptp.produc317451735ar_int A1) A22)) (@ (@ tptp.member92250950ar_int A1) A6) (@ (@ tptp.member92250950ar_int A22) A6) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat (@ F A1)) (@ F A22))) R2))))))))
% 0.24/0.63 (assert (= tptp.bNF_Gr808751971at_nat (lambda ((A6 tptp.set_nat) (R2 tptp.set_Pr1986765409at_nat) (F (-> tptp.nat tptp.nat))) (@ tptp.collec7649004at_nat (lambda ((Uu tptp.product_prod_nat_nat)) (exists ((A1 tptp.nat) (A22 tptp.nat)) (and (= Uu (@ (@ tptp.product_Pair_nat_nat A1) A22)) (@ (@ tptp.member_nat A1) A6) (@ (@ tptp.member_nat A22) A6) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat (@ F A1)) (@ F A22))) R2))))))))
% 0.24/0.63 (assert (forall ((Q4 tptp.nat) (R3 tptp.nat)) (= (@ tptp.unique1592618082ux_nat (@ (@ tptp.product_Pair_nat_nat Q4) R3)) (= R3 tptp.zero_zero_nat))))
% 0.24/0.63 (assert (= tptp.zero_zero_nat tptp.zero_zero_nat))
% 0.24/0.63 (assert (forall ((X4 tptp.typerep)) (not (= (@ tptp.size_size_typerep X4) tptp.zero_zero_nat))))
% 0.24/0.63 (assert (forall ((R3 tptp.nat) (S tptp.nat) (R tptp.set_Pr1986765409at_nat) (S2 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat R3))) (=> (@ (@ tptp.member701585322at_nat (@ _let_1 S)) R) (=> (= S2 S) (@ (@ tptp.member701585322at_nat (@ _let_1 S2)) R))))))
% 0.24/0.63 (assert (forall ((R3 tptp.com) (S (-> tptp.list_char tptp.int)) (R tptp.set_Pr1148378109ar_int) (S2 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.produc1193801173ar_int R3))) (=> (@ (@ tptp.member92250950ar_int (@ _let_1 S)) R) (=> (= S2 S) (@ (@ tptp.member92250950ar_int (@ _let_1 S2)) R))))))
% 0.24/0.63 (assert (forall ((X1 tptp.literal) (X2 tptp.list_typerep)) (= (@ tptp.size_size_typerep (@ (@ tptp.typerep2 X1) X2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_typerep tptp.size_size_typerep) X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.24/0.63 (assert (forall ((X1 tptp.literal) (X2 tptp.list_typerep)) (= (@ tptp.size_typerep (@ (@ tptp.typerep2 X1) X2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_typerep tptp.size_typerep) X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.24/0.63 (assert (forall ((X4 (-> tptp.typerep tptp.nat)) (X212 tptp.typerep) (X222 tptp.list_typerep)) (let ((_let_1 (@ tptp.size_list_typerep X4))) (= (@ _let_1 (@ (@ tptp.cons_typerep X212) X222)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ X4 X212)) (@ _let_1 X222))) (@ tptp.suc tptp.zero_zero_nat))))))
% 0.24/0.63 (assert (forall ((Xs tptp.list_typerep) (N tptp.nat)) (= (= (@ tptp.size_s416147576yperep Xs) (@ tptp.suc N)) (exists ((Y4 tptp.typerep) (Ys tptp.list_typerep)) (and (= Xs (@ (@ tptp.cons_typerep Y4) Ys)) (= (@ tptp.size_s416147576yperep Ys) N))))))
% 0.24/0.63 (assert (forall ((N tptp.nat) (Xs tptp.list_typerep)) (= (= (@ tptp.suc N) (@ tptp.size_s416147576yperep Xs)) (exists ((Y4 tptp.typerep) (Ys tptp.list_typerep)) (and (= Xs (@ (@ tptp.cons_typerep Y4) Ys)) (= (@ tptp.size_s416147576yperep Ys) N))))))
% 0.24/0.63 (assert (forall ((X4 tptp.typerep) (Xs tptp.list_typerep)) (= (@ tptp.size_s416147576yperep (@ (@ tptp.cons_typerep X4) Xs)) (@ tptp.suc (@ tptp.size_s416147576yperep Xs)))))
% 0.24/0.63 (assert (forall ((X212 tptp.typerep) (X222 tptp.list_typerep)) (= (@ tptp.size_s416147576yperep (@ (@ tptp.cons_typerep X212) X222)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s416147576yperep X222)) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.24/0.63 (assert (= tptp.set_Co1954412371ar_int (lambda ((A6 tptp.set_Pr1148378109ar_int) (XS tptp.set_li1762364675ar_int)) (@ tptp.collec672902542ar_int (lambda ((Z tptp.list_P1741976099ar_int)) (exists ((X tptp.produc1260470173ar_int) (Xs2 tptp.list_P1741976099ar_int)) (and (= Z (@ (@ tptp.cons_P1254790739ar_int X) Xs2)) (@ (@ tptp.member92250950ar_int X) A6) (@ (@ tptp.member2052091212ar_int Xs2) XS))))))))
% 0.24/0.63 (assert (= tptp.set_Cons_typerep (lambda ((A6 tptp.set_typerep) (XS tptp.set_list_typerep)) (@ tptp.collect_list_typerep (lambda ((Z tptp.list_typerep)) (exists ((X tptp.typerep) (Xs2 tptp.list_typerep)) (and (= Z (@ (@ tptp.cons_typerep X) Xs2)) (@ (@ tptp.member_typerep X) A6) (@ (@ tptp.member_list_typerep Xs2) XS))))))))
% 0.24/0.63 (assert (forall ((X4 tptp.typerep) (Xs tptp.list_typerep) (Y tptp.typerep) (Ys2 tptp.list_typerep) (R3 tptp.set_Pr1097818217yperep)) (let ((_let_1 (@ tptp.lex_typerep R3))) (= (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep (@ (@ tptp.cons_typerep X4) Xs)) (@ (@ tptp.cons_typerep Y) Ys2))) _let_1) (or (and (@ (@ tptp.member100911538yperep (@ (@ tptp.produc2071514689yperep X4) Y)) R3) (= (@ tptp.size_s416147576yperep Xs) (@ tptp.size_s416147576yperep Ys2))) (and (= X4 Y) (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep Xs) Ys2)) _let_1)))))))
% 0.24/0.63 (assert (forall ((X4 tptp.nat) (Xs tptp.list_nat) (Y tptp.nat) (Ys2 tptp.list_nat) (R3 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.lex_nat R3))) (= (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat (@ (@ tptp.cons_nat X4) Xs)) (@ (@ tptp.cons_nat Y) Ys2))) _let_1) (or (and (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y)) R3) (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys2))) (and (= X4 Y) (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat Xs) Ys2)) _let_1)))))))
% 0.24/0.63 (assert (forall ((N tptp.nat) (X4 tptp.typerep) (Xs tptp.list_typerep)) (= (@ (@ tptp.gen_length_typerep N) (@ (@ tptp.cons_typerep X4) Xs)) (@ (@ tptp.gen_length_typerep (@ tptp.suc N)) Xs))))
% 0.24/0.63 (assert (forall ((A tptp.typerep) (X4 tptp.list_typerep) (B tptp.typerep) (Y tptp.list_typerep) (R3 tptp.set_Pr1097818217yperep)) (let ((_let_1 (@ tptp.lexord_typerep R3))) (= (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep (@ (@ tptp.cons_typerep A) X4)) (@ (@ tptp.cons_typerep B) Y))) _let_1) (or (@ (@ tptp.member100911538yperep (@ (@ tptp.produc2071514689yperep A) B)) R3) (and (= A B) (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep X4) Y)) _let_1)))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (X4 tptp.list_nat) (B tptp.nat) (Y tptp.list_nat) (R3 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.lexord_nat R3))) (= (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat (@ (@ tptp.cons_nat A) X4)) (@ (@ tptp.cons_nat B) Y))) _let_1) (or (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) R3) (and (= A B) (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat X4) Y)) _let_1)))))))
% 0.24/0.63 (assert (forall ((R3 tptp.set_Pr1986765409at_nat) (Xs tptp.list_nat)) (=> (forall ((X3 tptp.nat)) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X3) X3)) R3))) (not (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat Xs) Xs)) (@ tptp.lexord_nat R3))))))
% 0.24/0.63 (assert (forall ((R3 tptp.set_Pr1986765409at_nat) (X4 tptp.list_nat) (Y tptp.list_nat)) (let ((_let_1 (@ tptp.lexord_nat R3))) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (or (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A3) B3)) R3) (= A3 B3) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat B3) A3)) R3))) (or (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat X4) Y)) _let_1) (= X4 Y) (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat Y) X4)) _let_1))))))
% 0.24/0.63 (assert (= tptp.bNF_Gr457912949yperep (lambda ((Kl tptp.set_list_typerep) (K2 tptp.typerep)) (@ tptp.collect_list_typerep (lambda ((Kl2 tptp.list_typerep)) (@ (@ tptp.member_list_typerep (@ (@ tptp.cons_typerep K2) Kl2)) Kl))))))
% 0.24/0.63 (assert (forall ((Kl3 tptp.list_typerep) (Kl4 tptp.set_list_typerep) (K tptp.typerep)) (=> (@ (@ tptp.member_list_typerep Kl3) (@ (@ tptp.bNF_Gr457912949yperep Kl4) K)) (@ (@ tptp.member_list_typerep (@ (@ tptp.cons_typerep K) Kl3)) Kl4))))
% 0.24/0.63 (assert (forall ((Kl4 tptp.set_list_typerep) (K tptp.typerep) (Kl3 tptp.list_typerep)) (= (@ (@ tptp.bNF_Gr1303086585yperep (@ (@ tptp.bNF_Gr457912949yperep Kl4) K)) Kl3) (@ (@ tptp.bNF_Gr1303086585yperep Kl4) (@ (@ tptp.cons_typerep K) Kl3)))))
% 0.24/0.63 (assert (forall ((X4 tptp.typerep) (Xs tptp.list_typerep) (Y tptp.typerep) (Ys2 tptp.list_typerep) (R3 tptp.set_Pr1097818217yperep)) (let ((_let_1 (@ tptp.listrel1_typerep R3))) (= (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep (@ (@ tptp.cons_typerep X4) Xs)) (@ (@ tptp.cons_typerep Y) Ys2))) _let_1) (or (and (@ (@ tptp.member100911538yperep (@ (@ tptp.produc2071514689yperep X4) Y)) R3) (= Xs Ys2)) (and (= X4 Y) (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep Xs) Ys2)) _let_1)))))))
% 0.24/0.63 (assert (forall ((X4 tptp.nat) (Xs tptp.list_nat) (Y tptp.nat) (Ys2 tptp.list_nat) (R3 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.listrel1_nat R3))) (= (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat (@ (@ tptp.cons_nat X4) Xs)) (@ (@ tptp.cons_nat Y) Ys2))) _let_1) (or (and (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y)) R3) (= Xs Ys2)) (and (= X4 Y) (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat Xs) Ys2)) _let_1)))))))
% 0.24/0.63 (assert (forall ((X4 tptp.typerep) (Y tptp.typerep) (R3 tptp.set_Pr1097818217yperep) (Xs tptp.list_typerep)) (=> (@ (@ tptp.member100911538yperep (@ (@ tptp.produc2071514689yperep X4) Y)) R3) (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep (@ (@ tptp.cons_typerep X4) Xs)) (@ (@ tptp.cons_typerep Y) Xs))) (@ tptp.listrel1_typerep R3)))))
% 0.24/0.63 (assert (forall ((X4 tptp.nat) (Y tptp.nat) (R3 tptp.set_Pr1986765409at_nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y)) R3) (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat (@ (@ tptp.cons_nat X4) Xs)) (@ (@ tptp.cons_nat Y) Xs))) (@ tptp.listrel1_nat R3)))))
% 0.24/0.63 (assert (forall ((X4 tptp.typerep) (Xs tptp.list_typerep) (Ys2 tptp.list_typerep) (R3 tptp.set_Pr1097818217yperep)) (=> (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep (@ (@ tptp.cons_typerep X4) Xs)) Ys2)) (@ tptp.listrel1_typerep R3)) (=> (forall ((Y3 tptp.typerep)) (=> (= Ys2 (@ (@ tptp.cons_typerep Y3) Xs)) (not (@ (@ tptp.member100911538yperep (@ (@ tptp.produc2071514689yperep X4) Y3)) R3)))) (not (forall ((Zs tptp.list_typerep)) (=> (= Ys2 (@ (@ tptp.cons_typerep X4) Zs)) (not (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep Xs) Zs)) (@ tptp.listrel1_typerep R3))))))))))
% 0.24/0.63 (assert (forall ((X4 tptp.nat) (Xs tptp.list_nat) (Ys2 tptp.list_nat) (R3 tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat (@ (@ tptp.cons_nat X4) Xs)) Ys2)) (@ tptp.listrel1_nat R3)) (=> (forall ((Y3 tptp.nat)) (=> (= Ys2 (@ (@ tptp.cons_nat Y3) Xs)) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y3)) R3)))) (not (forall ((Zs tptp.list_nat)) (=> (= Ys2 (@ (@ tptp.cons_nat X4) Zs)) (not (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat Xs) Zs)) (@ tptp.listrel1_nat R3))))))))))
% 0.24/0.63 (assert (forall ((Xs tptp.list_typerep) (Y tptp.typerep) (Ys2 tptp.list_typerep) (R3 tptp.set_Pr1097818217yperep)) (=> (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep Xs) (@ (@ tptp.cons_typerep Y) Ys2))) (@ tptp.listrel1_typerep R3)) (=> (forall ((X3 tptp.typerep)) (=> (= Xs (@ (@ tptp.cons_typerep X3) Ys2)) (not (@ (@ tptp.member100911538yperep (@ (@ tptp.produc2071514689yperep X3) Y)) R3)))) (not (forall ((Zs tptp.list_typerep)) (=> (= Xs (@ (@ tptp.cons_typerep Y) Zs)) (not (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep Zs) Ys2)) (@ tptp.listrel1_typerep R3))))))))))
% 0.24/0.63 (assert (forall ((Xs tptp.list_nat) (Y tptp.nat) (Ys2 tptp.list_nat) (R3 tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat Xs) (@ (@ tptp.cons_nat Y) Ys2))) (@ tptp.listrel1_nat R3)) (=> (forall ((X3 tptp.nat)) (=> (= Xs (@ (@ tptp.cons_nat X3) Ys2)) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y)) R3)))) (not (forall ((Zs tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat Y) Zs)) (not (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat Zs) Ys2)) (@ tptp.listrel1_nat R3))))))))))
% 0.24/0.63 (assert (forall ((A tptp.typerep) (B tptp.typerep) (R3 tptp.set_Pr1097818217yperep) (U tptp.list_typerep) (X4 tptp.list_typerep) (Y tptp.list_typerep)) (let ((_let_1 (@ tptp.append_typerep U))) (=> (@ (@ tptp.member100911538yperep (@ (@ tptp.produc2071514689yperep A) B)) R3) (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep (@ _let_1 (@ (@ tptp.cons_typerep A) X4))) (@ _let_1 (@ (@ tptp.cons_typerep B) Y)))) (@ tptp.lexord_typerep R3))))))
% 0.24/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (R3 tptp.set_Pr1986765409at_nat) (U tptp.list_nat) (X4 tptp.list_nat) (Y tptp.list_nat)) (let ((_let_1 (@ tptp.append_nat U))) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) R3) (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat (@ _let_1 (@ (@ tptp.cons_nat A) X4))) (@ _let_1 (@ (@ tptp.cons_nat B) Y)))) (@ tptp.lexord_nat R3))))))
% 0.24/0.63 (assert (forall ((X4 tptp.typerep) (Y tptp.typerep) (R3 tptp.set_Pr1097818217yperep) (Xs tptp.list_typerep) (Us tptp.list_typerep) (Vs tptp.list_typerep) (Ys2 tptp.list_typerep)) (let ((_let_1 (@ tptp.append_typerep Us))) (=> (@ (@ tptp.member100911538yperep (@ (@ tptp.produc2071514689yperep X4) Y)) R3) (=> (= Xs (@ _let_1 (@ (@ tptp.cons_typerep X4) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_typerep Y) Vs))) (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep Xs) Ys2)) (@ tptp.listrel1_typerep R3))))))))
% 0.24/0.63 (assert (forall ((X4 tptp.nat) (Y tptp.nat) (R3 tptp.set_Pr1986765409at_nat) (Xs tptp.list_nat) (Us tptp.list_nat) (Vs tptp.list_nat) (Ys2 tptp.list_nat)) (let ((_let_1 (@ tptp.append_nat Us))) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y)) R3) (=> (= Xs (@ _let_1 (@ (@ tptp.cons_nat X4) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_nat Y) Vs))) (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat Xs) Ys2)) (@ tptp.listrel1_nat R3))))))))
% 0.71/0.90 (assert (forall ((Xs tptp.list_typerep) (Ys2 tptp.list_typerep) (Us tptp.list_typerep) (Vs tptp.list_typerep)) (=> (or (= (@ tptp.size_s416147576yperep Xs) (@ tptp.size_s416147576yperep Ys2)) (= (@ tptp.size_s416147576yperep Us) (@ tptp.size_s416147576yperep Vs))) (= (= (@ (@ tptp.append_typerep Xs) Us) (@ (@ tptp.append_typerep Ys2) Vs)) (and (= Xs Ys2) (= Us Vs))))))
% 0.71/0.90 (assert (forall ((Xs tptp.list_typerep) (Ys2 tptp.list_typerep)) (= (@ tptp.size_s416147576yperep (@ (@ tptp.append_typerep Xs) Ys2)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s416147576yperep Xs)) (@ tptp.size_s416147576yperep Ys2)))))
% 0.71/0.90 (assert (forall ((F2 (-> tptp.typerep tptp.nat)) (Xs tptp.list_typerep) (Ys2 tptp.list_typerep)) (let ((_let_1 (@ tptp.size_list_typerep F2))) (= (@ _let_1 (@ (@ tptp.append_typerep Xs) Ys2)) (@ (@ tptp.plus_plus_nat (@ _let_1 Xs)) (@ _let_1 Ys2))))))
% 0.71/0.90 (assert (forall ((Xs tptp.list_typerep) (Zs2 tptp.list_typerep) (Ys2 tptp.list_typerep) (Qs tptp.list_typerep) (R3 tptp.set_Pr1097818217yperep)) (let ((_let_1 (@ tptp.lexord_typerep R3))) (=> (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep (@ (@ tptp.append_typerep Xs) Zs2)) (@ (@ tptp.append_typerep Ys2) Qs))) _let_1) (=> (not (= Xs Ys2)) (=> (= (@ tptp.size_s416147576yperep Xs) (@ tptp.size_s416147576yperep Ys2)) (=> (= (@ tptp.size_s416147576yperep Zs2) (@ tptp.size_s416147576yperep Qs)) (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep Xs) Ys2)) _let_1))))))))
% 0.71/0.90 (assert (forall ((R3 tptp.set_Pr1097818217yperep) (Xs tptp.list_typerep) (Ys2 tptp.list_typerep) (Zs2 tptp.list_typerep)) (let ((_let_1 (@ tptp.lex_typerep R3))) (let ((_let_2 (@ tptp.append_typerep Xs))) (=> (forall ((X3 tptp.typerep)) (not (@ (@ tptp.member100911538yperep (@ (@ tptp.produc2071514689yperep X3) X3)) R3))) (=> (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep (@ _let_2 Ys2)) (@ _let_2 Zs2))) _let_1) (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep Ys2) Zs2)) _let_1)))))))
% 0.71/0.90 (assert (forall ((R3 tptp.set_Pr1986765409at_nat) (Xs tptp.list_nat) (Ys2 tptp.list_nat) (Zs2 tptp.list_nat)) (let ((_let_1 (@ tptp.lex_nat R3))) (let ((_let_2 (@ tptp.append_nat Xs))) (=> (forall ((X3 tptp.nat)) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X3) X3)) R3))) (=> (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat (@ _let_2 Ys2)) (@ _let_2 Zs2))) _let_1) (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat Ys2) Zs2)) _let_1)))))))
% 0.71/0.90 (assert (not (exists ((S6 (-> tptp.list_char tptp.int)) (S8 (-> tptp.list_char tptp.int))) (and (@ (@ (@ (@ (@ (@ tptp.relati23543761ar_int tptp.p) tptp.b) tptp.c) (@ tptp.suc tptp.ka)) S6) S8) (@ (@ tptp.bval tptp.b) S6) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.c) S6)) tptp.ta) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.c2) S8)) tptp.t_a)))))
% 0.71/0.90 (set-info :filename cvc5---1.0.5_10267)
% 0.71/0.90 (check-sat-assuming ( true ))
% 0.71/0.90 ------- get file name : TPTP file name is ITP166^1
% 0.71/0.90 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10267.smt2...
% 0.71/0.90 --- Run --ho-elim --full-saturate-quant at 10...
% 0.71/0.90 % SZS status Theorem for ITP166^1
% 0.71/0.90 % SZS output start Proof for ITP166^1
% 0.71/0.90 (
% 0.71/0.90 (let ((_let_1 (not (exists ((S6 (-> tptp.list_char tptp.int)) (S8 (-> tptp.list_char tptp.int))) (and (@ (@ (@ (@ (@ (@ tptp.relati23543761ar_int tptp.p) tptp.b) tptp.c) (@ tptp.suc tptp.ka)) S6) S8) (@ (@ tptp.bval tptp.b) S6) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.c) S6)) tptp.ta) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.c2) S8)) tptp.t_a)))))) (let ((_let_2 (@ (@ tptp.while tptp.b) tptp.c))) (let ((_let_3 (@ (@ (@ tptp.relati23543761ar_int tptp.p) tptp.b) tptp.c))) (let ((_let_4 (@ _let_3 tptp.k))) (let ((_let_5 (@ _let_3 (@ tptp.suc tptp.ka)))) (let ((_let_6 (@ tptp.produc1193801173ar_int _let_2))) (let ((_let_7 (@ tptp.produc1193801173ar_int tptp.c))) (let ((_let_8 (@ tptp.produc1193801173ar_int tptp.c2))) (let ((_let_9 (@ (@ _let_5 tptp.sa) tptp.s_a))) (let ((_let_10 (@ (@ tptp.big_big_step (@ _let_8 tptp.s_a)) tptp.t_a))) (let ((_let_11 (@ (@ tptp.big_big_step (@ _let_7 tptp.sa)) tptp.ta))) (let ((_let_12 (@ tptp.bval tptp.b))) (let ((_let_13 (@ _let_12 tptp.sa))) (let ((_let_14 (forall ((BOUND_VARIABLE_15448 |u_(-> tptp.list_char tptp.int)|) (BOUND_VARIABLE_15443 |u_(-> tptp.list_char tptp.int)|)) (or (not (ho_41 (ho_40 (ho_35 (ho_98 (ho_97 (ho_96 k_99 k_109) tptp.b) tptp.c) (ho_72 k_108 tptp.ka)) BOUND_VARIABLE_15448) BOUND_VARIABLE_15443)) (not (ho_41 (ho_43 k_42 tptp.b) BOUND_VARIABLE_15448)) (not (ho_41 (ho_101 k_100 (ho_67 (ho_66 k_65 tptp.c) BOUND_VARIABLE_15448)) k_105)) (not (ho_41 (ho_101 k_100 (ho_67 (ho_66 k_65 tptp.c2) BOUND_VARIABLE_15443)) k_106)))))) (let ((_let_15 (ho_41 (ho_101 k_100 (ho_67 (ho_66 k_65 tptp.c2) k_107)) k_106))) (let ((_let_16 (not _let_15))) (let ((_let_17 (ho_41 (ho_101 k_100 (ho_67 (ho_66 k_65 tptp.c) k_103)) k_105))) (let ((_let_18 (not _let_17))) (let ((_let_19 (ho_41 (ho_43 k_42 tptp.b) k_103))) (let ((_let_20 (not _let_19))) (let ((_let_21 (ho_41 (ho_40 (ho_35 (ho_98 (ho_97 (ho_96 k_99 k_109) tptp.b) tptp.c) (ho_72 k_108 tptp.ka)) k_103) k_107))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_22 _let_20 _let_18 _let_16))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((S6 (-> tptp.list_char tptp.int)) (S8 (-> tptp.list_char tptp.int))) (or (not (@ (@ (@ (@ (@ (@ tptp.relati23543761ar_int tptp.p) tptp.b) tptp.c) (@ tptp.suc tptp.ka)) S6) S8)) (not (@ (@ tptp.bval tptp.b) S6)) (not (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.c) S6)) tptp.ta)) (not (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.c2) S8)) tptp.t_a)))) _let_14))))))) (let ((_let_25 (not _let_23))) (let ((_let_26 (forall ((u |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ tptp.com tptp.com _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ Bool)|) (e |u_(-> tptp.com tptp.com _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ Bool)|) (i |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ tptp.com tptp.com _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (= (ho_126 v ii) (ite (= i ii) e (ho_126 u ii)))))))))) (let ((_let_27 (forall ((x |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ tptp.com tptp.com _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ tptp.com tptp.com _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (= (ho_126 x z) (ho_126 y z)))) (= x y))))) (let ((_let_28 (forall ((u |u_(-> tptp.set_Pr1986765409at_nat tptp.nat tptp.nat Bool)|) (e |u_(-> tptp.nat tptp.nat Bool)|) (i tptp.set_Pr1986765409at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1986765409at_nat tptp.nat tptp.nat Bool)|)) (not (forall ((ii tptp.set_Pr1986765409at_nat)) (= (ho_88 v ii) (ite (= i ii) e (ho_88 u ii)))))))))) (let ((_let_29 (forall ((x |u_(-> tptp.set_Pr1986765409at_nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.set_Pr1986765409at_nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_Pr1986765409at_nat)) (= (ho_88 x z) (ho_88 y z)))) (= x y))))) (let ((_let_30 (forall ((u |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ Bool)|) (e Bool) (i |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (= (ho_129 v ii) (ite (= i ii) e (ho_129 u ii)))))))))) (let ((_let_31 (forall ((x |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (= (ho_129 x z) (ho_129 y z)))) (= x y))))) (let ((_let_32 (forall ((u |u_(-> tptp.bexp tptp.com tptp.com)|) (e |u_(-> tptp.com tptp.com)|) (i tptp.bexp)) (not (forall ((v |u_(-> tptp.bexp tptp.com tptp.com)|)) (not (forall ((ii tptp.bexp)) (= (ho_116 v ii) (ite (= i ii) e (ho_116 u ii)))))))))) (let ((_let_33 (forall ((x |u_(-> tptp.bexp tptp.com tptp.com)|) (y |u_(-> tptp.bexp tptp.com tptp.com)|)) (or (not (forall ((z tptp.bexp)) (= (ho_116 x z) (ho_116 y z)))) (= x y))))) (let ((_let_34 (forall ((u |u_(-> tptp.produc1260470173ar_int _u_(-> tptp.list_char tptp.int)_ Bool)|) (e |u_(-> _u_(-> tptp.list_char tptp.int)_ Bool)|) (i tptp.produc1260470173ar_int)) (not (forall ((v |u_(-> tptp.produc1260470173ar_int _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((ii tptp.produc1260470173ar_int)) (= (ho_101 v ii) (ite (= i ii) e (ho_101 u ii)))))))))) (let ((_let_35 (forall ((x |u_(-> tptp.produc1260470173ar_int _u_(-> tptp.list_char tptp.int)_ Bool)|) (y |u_(-> tptp.produc1260470173ar_int _u_(-> tptp.list_char tptp.int)_ Bool)|)) (or (not (forall ((z tptp.produc1260470173ar_int)) (= (ho_101 x z) (ho_101 y z)))) (= x y))))) (let ((_let_36 (forall ((u |u_(-> tptp.bexp _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (e |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (i tptp.bexp)) (not (forall ((v |u_(-> tptp.bexp _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((ii tptp.bexp)) (= (ho_39 v ii) (ite (= i ii) e (ho_39 u ii)))))))))) (let ((_let_37 (forall ((x |u_(-> tptp.bexp _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (y |u_(-> tptp.bexp _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (or (not (forall ((z tptp.bexp)) (= (ho_39 x z) (ho_39 y z)))) (= x y))))) (let ((_let_38 (forall ((u |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ tptp.bexp tptp.com tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (e |u_(-> tptp.bexp tptp.com tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (i |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ tptp.bexp tptp.com tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (= (ho_96 v ii) (ite (= i ii) e (ho_96 u ii)))))))))) (let ((_let_39 (forall ((x |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ tptp.bexp tptp.com tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ tptp.bexp tptp.com tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (= (ho_96 x z) (ho_96 y z)))) (= x y))))) (let ((_let_40 (forall ((u |u_(-> tptp.bexp tptp.com tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (e |u_(-> tptp.com tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (i tptp.bexp)) (not (forall ((v |u_(-> tptp.bexp tptp.com tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((ii tptp.bexp)) (= (ho_97 v ii) (ite (= i ii) e (ho_97 u ii)))))))))) (let ((_let_41 (forall ((x |u_(-> tptp.bexp tptp.com tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (y |u_(-> tptp.bexp tptp.com tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (or (not (forall ((z tptp.bexp)) (= (ho_97 x z) (ho_97 y z)))) (= x y))))) (let ((_let_42 (forall ((u |u_(-> tptp.com tptp.com)|) (e tptp.com) (i tptp.com)) (not (forall ((v |u_(-> tptp.com tptp.com)|)) (not (forall ((ii tptp.com)) (= (ho_117 v ii) (ite (= i ii) e (ho_117 u ii)))))))))) (let ((_let_43 (forall ((x |u_(-> tptp.com tptp.com)|) (y |u_(-> tptp.com tptp.com)|)) (or (not (forall ((z tptp.com)) (= (ho_117 x z) (ho_117 y z)))) (= x y))))) (let ((_let_44 (forall ((u |u_(-> tptp.nat tptp.nat tptp.nat)|) (e |u_(-> tptp.nat tptp.nat)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_71 v ii) (ite (= i ii) e (ho_71 u ii)))))))))) (let ((_let_45 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_71 x z) (ho_71 y z)))) (= x y))))) (let ((_let_46 (forall ((u |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat Bool)|) (e |u_(-> tptp.set_Pr1986765409at_nat Bool)|) (i tptp.product_prod_nat_nat)) (not (forall ((v |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat Bool)|)) (not (forall ((ii tptp.product_prod_nat_nat)) (= (ho_92 v ii) (ite (= i ii) e (ho_92 u ii)))))))))) (let ((_let_47 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat Bool)|) (y |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat Bool)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_92 x z) (ho_92 y z)))) (= x y))))) (let ((_let_48 (forall ((u |u_(-> tptp.set_Pr1986765409at_nat Bool)|) (e Bool) (i tptp.set_Pr1986765409at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1986765409at_nat Bool)|)) (not (forall ((ii tptp.set_Pr1986765409at_nat)) (= (ho_93 v ii) (ite (= i ii) e (ho_93 u ii)))))))))) (let ((_let_49 (forall ((x |u_(-> tptp.set_Pr1986765409at_nat Bool)|) (y |u_(-> tptp.set_Pr1986765409at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1986765409at_nat)) (= (ho_93 x z) (ho_93 y z)))) (= x y))))) (let ((_let_50 (forall ((u |u_(-> _u_(-> tptp.produc1260470173ar_int Bool)_ tptp.set_Pr1148378109ar_int)|) (e tptp.set_Pr1148378109ar_int) (i |u_(-> tptp.produc1260470173ar_int Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1260470173ar_int Bool)_ tptp.set_Pr1148378109ar_int)|)) (not (forall ((ii |u_(-> tptp.produc1260470173ar_int Bool)|)) (= (ho_120 v ii) (ite (= i ii) e (ho_120 u ii)))))))))) (let ((_let_51 (forall ((x |u_(-> _u_(-> tptp.produc1260470173ar_int Bool)_ tptp.set_Pr1148378109ar_int)|) (y |u_(-> _u_(-> tptp.produc1260470173ar_int Bool)_ tptp.set_Pr1148378109ar_int)|)) (or (not (forall ((z |u_(-> tptp.produc1260470173ar_int Bool)|)) (= (ho_120 x z) (ho_120 y z)))) (= x y))))) (let ((_let_52 (forall ((u |u_(-> tptp.nat tptp.nat Bool)|) (e |u_(-> tptp.nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_89 v ii) (ite (= i ii) e (ho_89 u ii)))))))))) (let ((_let_53 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_89 x z) (ho_89 y z)))) (= x y))))) (let ((_let_54 (forall ((u |u_(-> tptp.nat Bool)|) (e Bool) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_90 v ii) (ite (= i ii) e (ho_90 u ii)))))))))) (let ((_let_55 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_90 x z) (ho_90 y z)))) (= x y))))) (let ((_let_56 (forall ((u |u_(-> _u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (e |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (i |u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((ii |u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (= (ho_45 v ii) (ite (= i ii) e (ho_45 u ii)))))))))) (let ((_let_57 (forall ((x |u_(-> _u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (= (ho_45 x z) (ho_45 y z)))) (= x y))))) (let ((_let_58 (forall ((u |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat)|) (e |u_(-> tptp.nat tptp.product_prod_nat_nat)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat)|)) (not (forall ((ii tptp.nat)) (= (ho_56 v ii) (ite (= i ii) e (ho_56 u ii)))))))))) (let ((_let_59 (forall ((x |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_56 x z) (ho_56 y z)))) (= x y))))) (let ((_let_60 (forall ((u |u_(-> tptp.aexp tptp.com)|) (e tptp.com) (i tptp.aexp)) (not (forall ((v |u_(-> tptp.aexp tptp.com)|)) (not (forall ((ii tptp.aexp)) (= (ho_132 v ii) (ite (= i ii) e (ho_132 u ii)))))))))) (let ((_let_61 (forall ((x |u_(-> tptp.aexp tptp.com)|) (y |u_(-> tptp.aexp tptp.com)|)) (or (not (forall ((z tptp.aexp)) (= (ho_132 x z) (ho_132 y z)))) (= x y))))) (let ((_let_62 (forall ((u |u_(-> tptp.produc1260470173ar_int tptp.com)|) (e tptp.com) (i tptp.produc1260470173ar_int)) (not (forall ((v |u_(-> tptp.produc1260470173ar_int tptp.com)|)) (not (forall ((ii tptp.produc1260470173ar_int)) (= (ho_59 v ii) (ite (= i ii) e (ho_59 u ii)))))))))) (let ((_let_63 (forall ((x |u_(-> tptp.produc1260470173ar_int tptp.com)|) (y |u_(-> tptp.produc1260470173ar_int tptp.com)|)) (or (not (forall ((z tptp.produc1260470173ar_int)) (= (ho_59 x z) (ho_59 y z)))) (= x y))))) (let ((_let_64 (forall ((u |u_(-> tptp.set_Pr1148378109ar_int tptp.com _u_(-> tptp.list_char tptp.int)_ Bool)|) (e |u_(-> tptp.com _u_(-> tptp.list_char tptp.int)_ Bool)|) (i tptp.set_Pr1148378109ar_int)) (not (forall ((v |u_(-> tptp.set_Pr1148378109ar_int tptp.com _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((ii tptp.set_Pr1148378109ar_int)) (= (ho_84 v ii) (ite (= i ii) e (ho_84 u ii)))))))))) (let ((_let_65 (forall ((x |u_(-> tptp.set_Pr1148378109ar_int tptp.com _u_(-> tptp.list_char tptp.int)_ Bool)|) (y |u_(-> tptp.set_Pr1148378109ar_int tptp.com _u_(-> tptp.list_char tptp.int)_ Bool)|)) (or (not (forall ((z tptp.set_Pr1148378109ar_int)) (= (ho_84 x z) (ho_84 y z)))) (= x y))))) (let ((_let_66 (forall ((u |u_(-> tptp.nat tptp.bexp _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (e |u_(-> tptp.bexp _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.bexp _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_38 v ii) (ite (= i ii) e (ho_38 u ii)))))))))) (let ((_let_67 (forall ((x |u_(-> tptp.nat tptp.bexp _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (y |u_(-> tptp.nat tptp.bexp _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_38 x z) (ho_38 y z)))) (= x y))))) (let ((_let_68 (forall ((u |u_(-> tptp.com _u_(-> tptp.list_char tptp.int)_ Bool)|) (e |u_(-> _u_(-> tptp.list_char tptp.int)_ Bool)|) (i tptp.com)) (not (forall ((v |u_(-> tptp.com _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((ii tptp.com)) (= (ho_85 v ii) (ite (= i ii) e (ho_85 u ii)))))))))) (let ((_let_69 (forall ((x |u_(-> tptp.com _u_(-> tptp.list_char tptp.int)_ Bool)|) (y |u_(-> tptp.com _u_(-> tptp.list_char tptp.int)_ Bool)|)) (or (not (forall ((z tptp.com)) (= (ho_85 x z) (ho_85 y z)))) (= x y))))) (let ((_let_70 (forall ((u |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (e |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (i |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (= (ho_75 v ii) (ite (= i ii) e (ho_75 u ii)))))))))) (let ((_let_71 (forall ((x |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (= (ho_75 x z) (ho_75 y z)))) (= x y))))) (let ((_let_72 (forall ((u |u_(-> _u_(-> tptp.list_char tptp.int)_ tptp.produc1260470173ar_int)|) (e tptp.produc1260470173ar_int) (i |u_(-> tptp.list_char tptp.int)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_char tptp.int)_ tptp.produc1260470173ar_int)|)) (not (forall ((ii |u_(-> tptp.list_char tptp.int)|)) (= (ho_67 v ii) (ite (= i ii) e (ho_67 u ii)))))))))) (let ((_let_73 (forall ((x |u_(-> _u_(-> tptp.list_char tptp.int)_ tptp.produc1260470173ar_int)|) (y |u_(-> _u_(-> tptp.list_char tptp.int)_ tptp.produc1260470173ar_int)|)) (or (not (forall ((z |u_(-> tptp.list_char tptp.int)|)) (= (ho_67 x z) (ho_67 y z)))) (= x y))))) (let ((_let_74 (forall ((u |u_(-> tptp.list_nat tptp.produc1699244961st_nat)|) (e tptp.produc1699244961st_nat) (i tptp.list_nat)) (not (forall ((v |u_(-> tptp.list_nat tptp.produc1699244961st_nat)|)) (not (forall ((ii tptp.list_nat)) (= (ho_168 v ii) (ite (= i ii) e (ho_168 u ii)))))))))) (let ((_let_75 (forall ((x |u_(-> tptp.list_nat tptp.produc1699244961st_nat)|) (y |u_(-> tptp.list_nat tptp.produc1699244961st_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_168 x z) (ho_168 y z)))) (= x y))))) (let ((_let_76 (forall ((u |u_(-> tptp.com _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ Bool)|) (i tptp.com)) (not (forall ((v |u_(-> tptp.com _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ Bool)|)) (not (forall ((ii tptp.com)) (= (ho_128 v ii) (ite (= i ii) e (ho_128 u ii)))))))))) (let ((_let_77 (forall ((x |u_(-> tptp.com _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ Bool)|) (y |u_(-> tptp.com _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ Bool)|)) (or (not (forall ((z tptp.com)) (= (ho_128 x z) (ho_128 y z)))) (= x y))))) (let ((_let_78 (forall ((u |u_(-> _u_(-> tptp.produc1260470173ar_int tptp.com)_ _u_(-> tptp.produc1260470173ar_int tptp.list_char tptp.int)_ tptp.set_Pr1148378109ar_int tptp.produc1260470173ar_int Bool)|) (e |u_(-> _u_(-> tptp.produc1260470173ar_int tptp.list_char tptp.int)_ tptp.set_Pr1148378109ar_int tptp.produc1260470173ar_int Bool)|) (i |u_(-> tptp.produc1260470173ar_int tptp.com)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1260470173ar_int tptp.com)_ _u_(-> tptp.produc1260470173ar_int tptp.list_char tptp.int)_ tptp.set_Pr1148378109ar_int tptp.produc1260470173ar_int Bool)|)) (not (forall ((ii |u_(-> tptp.produc1260470173ar_int tptp.com)|)) (= (ho_61 v ii) (ite (= i ii) e (ho_61 u ii)))))))))) (let ((_let_79 (forall ((x |u_(-> _u_(-> tptp.produc1260470173ar_int tptp.com)_ _u_(-> tptp.produc1260470173ar_int tptp.list_char tptp.int)_ tptp.set_Pr1148378109ar_int tptp.produc1260470173ar_int Bool)|) (y |u_(-> _u_(-> tptp.produc1260470173ar_int tptp.com)_ _u_(-> tptp.produc1260470173ar_int tptp.list_char tptp.int)_ tptp.set_Pr1148378109ar_int tptp.produc1260470173ar_int Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1260470173ar_int tptp.com)|)) (= (ho_61 x z) (ho_61 y z)))) (= x y))))) (let ((_let_80 (forall ((u |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ tptp.bexp _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (e |u_(-> tptp.bexp _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (i |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ tptp.bexp _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (= (ho_69 v ii) (ite (= i ii) e (ho_69 u ii)))))))))) (let ((_let_81 (forall ((x |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ tptp.bexp _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ tptp.bexp _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (= (ho_69 x z) (ho_69 y z)))) (= x y))))) (let ((_let_82 (forall ((u |u_(-> tptp.nat tptp.product_prod_nat_nat)|) (e tptp.product_prod_nat_nat) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.product_prod_nat_nat)|)) (not (forall ((ii tptp.nat)) (= (ho_57 v ii) (ite (= i ii) e (ho_57 u ii)))))))))) (let ((_let_83 (forall ((x |u_(-> tptp.nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_57 x z) (ho_57 y z)))) (= x y))))) (let ((_let_84 (forall ((u |u_(-> tptp.list_typerep tptp.list_typerep tptp.produc490010537yperep)|) (e |u_(-> tptp.list_typerep tptp.produc490010537yperep)|) (i tptp.list_typerep)) (not (forall ((v |u_(-> tptp.list_typerep tptp.list_typerep tptp.produc490010537yperep)|)) (not (forall ((ii tptp.list_typerep)) (= (ho_153 v ii) (ite (= i ii) e (ho_153 u ii)))))))))) (let ((_let_85 (forall ((x |u_(-> tptp.list_typerep tptp.list_typerep tptp.produc490010537yperep)|) (y |u_(-> tptp.list_typerep tptp.list_typerep tptp.produc490010537yperep)|)) (or (not (forall ((z tptp.list_typerep)) (= (ho_153 x z) (ho_153 y z)))) (= x y))))) (let ((_let_86 (forall ((u |u_(-> tptp.com tptp.com tptp.com)|) (e |u_(-> tptp.com tptp.com)|) (i tptp.com)) (not (forall ((v |u_(-> tptp.com tptp.com tptp.com)|)) (not (forall ((ii tptp.com)) (= (ho_122 v ii) (ite (= i ii) e (ho_122 u ii)))))))))) (let ((_let_87 (forall ((x |u_(-> tptp.com tptp.com tptp.com)|) (y |u_(-> tptp.com tptp.com tptp.com)|)) (or (not (forall ((z tptp.com)) (= (ho_122 x z) (ho_122 y z)))) (= x y))))) (let ((_let_88 (forall ((u |u_(-> _u_(-> tptp.list_char tptp.int)_ Bool)|) (e Bool) (i |u_(-> tptp.list_char tptp.int)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((ii |u_(-> tptp.list_char tptp.int)|)) (= (ho_41 v ii) (ite (= i ii) e (ho_41 u ii)))))))))) (let ((_let_89 (forall ((x |u_(-> _u_(-> tptp.list_char tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.list_char tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.list_char tptp.int)|)) (= (ho_41 x z) (ho_41 y z)))) (= x y))))) (let ((_let_90 (forall ((u |u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (e |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_35 v ii) (ite (= i ii) e (ho_35 u ii)))))))))) (let ((_let_91 (forall ((x |u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_35 x z) (ho_35 y z)))) (= x y))))) (let ((_let_92 (forall ((u |u_(-> tptp.bexp _u_(-> tptp.list_char tptp.int)_ Bool)|) (e |u_(-> _u_(-> tptp.list_char tptp.int)_ Bool)|) (i tptp.bexp)) (not (forall ((v |u_(-> tptp.bexp _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((ii tptp.bexp)) (= (ho_43 v ii) (ite (= i ii) e (ho_43 u ii)))))))))) (let ((_let_93 (forall ((x |u_(-> tptp.bexp _u_(-> tptp.list_char tptp.int)_ Bool)|) (y |u_(-> tptp.bexp _u_(-> tptp.list_char tptp.int)_ Bool)|)) (or (not (forall ((z tptp.bexp)) (= (ho_43 x z) (ho_43 y z)))) (= x y))))) (let ((_let_94 (forall ((u |u_(-> tptp.list_char tptp.int)|) (e tptp.int) (i tptp.list_char)) (not (forall ((v |u_(-> tptp.list_char tptp.int)|)) (not (forall ((ii tptp.list_char)) (= (ho_34 v ii) (ite (= i ii) e (ho_34 u ii)))))))))) (let ((_let_95 (forall ((x |u_(-> tptp.list_char tptp.int)|) (y |u_(-> tptp.list_char tptp.int)|)) (or (not (forall ((z tptp.list_char)) (= (ho_34 x z) (ho_34 y z)))) (= x y))))) (let ((_let_96 (forall ((u |u_(-> tptp.produc1260470173ar_int tptp.set_Pr1148378109ar_int Bool)|) (e |u_(-> tptp.set_Pr1148378109ar_int Bool)|) (i tptp.produc1260470173ar_int)) (not (forall ((v |u_(-> tptp.produc1260470173ar_int tptp.set_Pr1148378109ar_int Bool)|)) (not (forall ((ii tptp.produc1260470173ar_int)) (= (ho_53 v ii) (ite (= i ii) e (ho_53 u ii)))))))))) (let ((_let_97 (forall ((x |u_(-> tptp.produc1260470173ar_int tptp.set_Pr1148378109ar_int Bool)|) (y |u_(-> tptp.produc1260470173ar_int tptp.set_Pr1148378109ar_int Bool)|)) (or (not (forall ((z tptp.produc1260470173ar_int)) (= (ho_53 x z) (ho_53 y z)))) (= x y))))) (let ((_let_98 (forall ((u |u_(-> tptp.set_Pr1148378109ar_int tptp.product_prod_nat_nat Bool)|) (e |u_(-> tptp.product_prod_nat_nat Bool)|) (i tptp.set_Pr1148378109ar_int)) (not (forall ((v |u_(-> tptp.set_Pr1148378109ar_int tptp.product_prod_nat_nat Bool)|)) (not (forall ((ii tptp.set_Pr1148378109ar_int)) (= (ho_50 v ii) (ite (= i ii) e (ho_50 u ii)))))))))) (let ((_let_99 (forall ((x |u_(-> tptp.set_Pr1148378109ar_int tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.set_Pr1148378109ar_int tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1148378109ar_int)) (= (ho_50 x z) (ho_50 y z)))) (= x y))))) (let ((_let_100 (forall ((u |u_(-> tptp.list_nat tptp.nat)|) (e tptp.nat) (i tptp.list_nat)) (not (forall ((v |u_(-> tptp.list_nat tptp.nat)|)) (not (forall ((ii tptp.list_nat)) (= (ho_173 v ii) (ite (= i ii) e (ho_173 u ii)))))))))) (let ((_let_101 (forall ((x |u_(-> tptp.list_nat tptp.nat)|) (y |u_(-> tptp.list_nat tptp.nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_173 x z) (ho_173 y z)))) (= x y))))) (let ((_let_102 (forall ((u |u_(-> tptp.list_typerep tptp.set_list_typerep Bool)|) (e |u_(-> tptp.set_list_typerep Bool)|) (i tptp.list_typerep)) (not (forall ((v |u_(-> tptp.list_typerep tptp.set_list_typerep Bool)|)) (not (forall ((ii tptp.list_typerep)) (= (ho_31 v ii) (ite (= i ii) e (ho_31 u ii)))))))))) (let ((_let_103 (forall ((x |u_(-> tptp.list_typerep tptp.set_list_typerep Bool)|) (y |u_(-> tptp.list_typerep tptp.set_list_typerep Bool)|)) (or (not (forall ((z tptp.list_typerep)) (= (ho_31 x z) (ho_31 y z)))) (= x y))))) (let ((_let_104 (forall ((u |u_(-> tptp.com tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (e |u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (i tptp.com)) (not (forall ((v |u_(-> tptp.com tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((ii tptp.com)) (= (ho_98 v ii) (ite (= i ii) e (ho_98 u ii)))))))))) (let ((_let_105 (forall ((x |u_(-> tptp.com tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (y |u_(-> tptp.com tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (or (not (forall ((z tptp.com)) (= (ho_98 x z) (ho_98 y z)))) (= x y))))) (let ((_let_106 (forall ((u |u_(-> tptp.set_list_typerep Bool)|) (e Bool) (i tptp.set_list_typerep)) (not (forall ((v |u_(-> tptp.set_list_typerep Bool)|)) (not (forall ((ii tptp.set_list_typerep)) (= (ho_32 v ii) (ite (= i ii) e (ho_32 u ii)))))))))) (let ((_let_107 (forall ((x |u_(-> tptp.set_list_typerep Bool)|) (y |u_(-> tptp.set_list_typerep Bool)|)) (or (not (forall ((z tptp.set_list_typerep)) (= (ho_32 x z) (ho_32 y z)))) (= x y))))) (let ((_let_108 (forall ((u |u_(-> tptp.list_typerep tptp.list_typerep)|) (e tptp.list_typerep) (i tptp.list_typerep)) (not (forall ((v |u_(-> tptp.list_typerep tptp.list_typerep)|)) (not (forall ((ii tptp.list_typerep)) (= (ho_29 v ii) (ite (= i ii) e (ho_29 u ii)))))))))) (let ((_let_109 (forall ((x |u_(-> tptp.list_typerep tptp.list_typerep)|) (y |u_(-> tptp.list_typerep tptp.list_typerep)|)) (or (not (forall ((z tptp.list_typerep)) (= (ho_29 x z) (ho_29 y z)))) (= x y))))) (let ((_let_110 (forall ((u |u_(-> tptp.produc1260470173ar_int Bool)|) (e Bool) (i tptp.produc1260470173ar_int)) (not (forall ((v |u_(-> tptp.produc1260470173ar_int Bool)|)) (not (forall ((ii tptp.produc1260470173ar_int)) (= (ho_64 v ii) (ite (= i ii) e (ho_64 u ii)))))))))) (let ((_let_111 (forall ((x |u_(-> tptp.produc1260470173ar_int Bool)|) (y |u_(-> tptp.produc1260470173ar_int Bool)|)) (or (not (forall ((z tptp.produc1260470173ar_int)) (= (ho_64 x z) (ho_64 y z)))) (= x y))))) (let ((_let_112 (forall ((u |u_(-> tptp.set_list_typerep tptp.list_typerep Bool)|) (e |u_(-> tptp.list_typerep Bool)|) (i tptp.set_list_typerep)) (not (forall ((v |u_(-> tptp.set_list_typerep tptp.list_typerep Bool)|)) (not (forall ((ii tptp.set_list_typerep)) (= (ho_25 v ii) (ite (= i ii) e (ho_25 u ii)))))))))) (let ((_let_113 (forall ((x |u_(-> tptp.set_list_typerep tptp.list_typerep Bool)|) (y |u_(-> tptp.set_list_typerep tptp.list_typerep Bool)|)) (or (not (forall ((z tptp.set_list_typerep)) (= (ho_25 x z) (ho_25 y z)))) (= x y))))) (let ((_let_114 (forall ((u |u_(-> tptp.list_nat tptp.list_nat)|) (e tptp.list_nat) (i tptp.list_nat)) (not (forall ((v |u_(-> tptp.list_nat tptp.list_nat)|)) (not (forall ((ii tptp.list_nat)) (= (ho_176 v ii) (ite (= i ii) e (ho_176 u ii)))))))))) (let ((_let_115 (forall ((x |u_(-> tptp.list_nat tptp.list_nat)|) (y |u_(-> tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_176 x z) (ho_176 y z)))) (= x y))))) (let ((_let_116 (forall ((u |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (e |u_(-> _u_(-> tptp.list_char tptp.int)_ Bool)|) (i |u_(-> tptp.list_char tptp.int)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((ii |u_(-> tptp.list_char tptp.int)|)) (= (ho_40 v ii) (ite (= i ii) e (ho_40 u ii)))))))))) (let ((_let_117 (forall ((x |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.list_char tptp.int)|)) (= (ho_40 x z) (ho_40 y z)))) (= x y))))) (let ((_let_118 (forall ((u |u_(-> tptp.typerep tptp.set_list_typerep tptp.list_typerep Bool)|) (e |u_(-> tptp.set_list_typerep tptp.list_typerep Bool)|) (i tptp.typerep)) (not (forall ((v |u_(-> tptp.typerep tptp.set_list_typerep tptp.list_typerep Bool)|)) (not (forall ((ii tptp.typerep)) (= (ho_24 v ii) (ite (= i ii) e (ho_24 u ii)))))))))) (let ((_let_119 (forall ((x |u_(-> tptp.typerep tptp.set_list_typerep tptp.list_typerep Bool)|) (y |u_(-> tptp.typerep tptp.set_list_typerep tptp.list_typerep Bool)|)) (or (not (forall ((z tptp.typerep)) (= (ho_24 x z) (ho_24 y z)))) (= x y))))) (let ((_let_120 (forall ((u |u_(-> tptp.produc1260470173ar_int tptp.nat)|) (e tptp.nat) (i tptp.produc1260470173ar_int)) (not (forall ((v |u_(-> tptp.produc1260470173ar_int tptp.nat)|)) (not (forall ((ii tptp.produc1260470173ar_int)) (= (ho_46 v ii) (ite (= i ii) e (ho_46 u ii)))))))))) (let ((_let_121 (forall ((x |u_(-> tptp.produc1260470173ar_int tptp.nat)|) (y |u_(-> tptp.produc1260470173ar_int tptp.nat)|)) (or (not (forall ((z tptp.produc1260470173ar_int)) (= (ho_46 x z) (ho_46 y z)))) (= x y))))) (let ((_let_122 (forall ((u |u_(-> tptp.set_Pr1560408065st_nat Bool)|) (e Bool) (i tptp.set_Pr1560408065st_nat)) (not (forall ((v |u_(-> tptp.set_Pr1560408065st_nat Bool)|)) (not (forall ((ii tptp.set_Pr1560408065st_nat)) (= (ho_171 v ii) (ite (= i ii) e (ho_171 u ii)))))))))) (let ((_let_123 (forall ((x |u_(-> tptp.set_Pr1560408065st_nat Bool)|) (y |u_(-> tptp.set_Pr1560408065st_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1560408065st_nat)) (= (ho_171 x z) (ho_171 y z)))) (= x y))))) (let ((_let_124 (forall ((u |u_(-> tptp.typerep tptp.list_typerep tptp.list_typerep)|) (e |u_(-> tptp.list_typerep tptp.list_typerep)|) (i tptp.typerep)) (not (forall ((v |u_(-> tptp.typerep tptp.list_typerep tptp.list_typerep)|)) (not (forall ((ii tptp.typerep)) (= (ho_28 v ii) (ite (= i ii) e (ho_28 u ii)))))))))) (let ((_let_125 (forall ((x |u_(-> tptp.typerep tptp.list_typerep tptp.list_typerep)|) (y |u_(-> tptp.typerep tptp.list_typerep tptp.list_typerep)|)) (or (not (forall ((z tptp.typerep)) (= (ho_28 x z) (ho_28 y z)))) (= x y))))) (let ((_let_126 (forall ((u |u_(-> tptp.list_typerep Bool)|) (e Bool) (i tptp.list_typerep)) (not (forall ((v |u_(-> tptp.list_typerep Bool)|)) (not (forall ((ii tptp.list_typerep)) (= (ho_26 v ii) (ite (= i ii) e (ho_26 u ii)))))))))) (let ((_let_127 (forall ((x |u_(-> tptp.list_typerep Bool)|) (y |u_(-> tptp.list_typerep Bool)|)) (or (not (forall ((z tptp.list_typerep)) (= (ho_26 x z) (ho_26 y z)))) (= x y))))) (let ((_let_128 (forall ((u |u_(-> tptp.list_typerep tptp.produc490010537yperep)|) (e tptp.produc490010537yperep) (i tptp.list_typerep)) (not (forall ((v |u_(-> tptp.list_typerep tptp.produc490010537yperep)|)) (not (forall ((ii tptp.list_typerep)) (= (ho_154 v ii) (ite (= i ii) e (ho_154 u ii)))))))))) (let ((_let_129 (forall ((x |u_(-> tptp.list_typerep tptp.produc490010537yperep)|) (y |u_(-> tptp.list_typerep tptp.produc490010537yperep)|)) (or (not (forall ((z tptp.list_typerep)) (= (ho_154 x z) (ho_154 y z)))) (= x y))))) (let ((_let_130 (forall ((u |u_(-> _u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ tptp.nat tptp.bexp _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (e |u_(-> tptp.nat tptp.bexp _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (i |u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ tptp.nat tptp.bexp _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((ii |u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (= (ho_37 v ii) (ite (= i ii) e (ho_37 u ii)))))))))) (let ((_let_131 (forall ((x |u_(-> _u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ tptp.nat tptp.bexp _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ tptp.nat tptp.bexp _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (= (ho_37 x z) (ho_37 y z)))) (= x y))))) (let ((_let_132 (forall ((u |u_(-> tptp.bexp tptp.com tptp.com tptp.com)|) (e |u_(-> tptp.com tptp.com tptp.com)|) (i tptp.bexp)) (not (forall ((v |u_(-> tptp.bexp tptp.com tptp.com tptp.com)|)) (not (forall ((ii tptp.bexp)) (= (ho_124 v ii) (ite (= i ii) e (ho_124 u ii)))))))))) (let ((_let_133 (forall ((x |u_(-> tptp.bexp tptp.com tptp.com tptp.com)|) (y |u_(-> tptp.bexp tptp.com tptp.com tptp.com)|)) (or (not (forall ((z tptp.bexp)) (= (ho_124 x z) (ho_124 y z)))) (= x y))))) (let ((_let_134 (forall ((u |u_(-> _u_(-> tptp.produc1260470173ar_int tptp.list_char tptp.int)_ tptp.set_Pr1148378109ar_int tptp.produc1260470173ar_int Bool)|) (e |u_(-> tptp.set_Pr1148378109ar_int tptp.produc1260470173ar_int Bool)|) (i |u_(-> tptp.produc1260470173ar_int tptp.list_char tptp.int)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1260470173ar_int tptp.list_char tptp.int)_ tptp.set_Pr1148378109ar_int tptp.produc1260470173ar_int Bool)|)) (not (forall ((ii |u_(-> tptp.produc1260470173ar_int tptp.list_char tptp.int)|)) (= (ho_62 v ii) (ite (= i ii) e (ho_62 u ii)))))))))) (let ((_let_135 (forall ((x |u_(-> _u_(-> tptp.produc1260470173ar_int tptp.list_char tptp.int)_ tptp.set_Pr1148378109ar_int tptp.produc1260470173ar_int Bool)|) (y |u_(-> _u_(-> tptp.produc1260470173ar_int tptp.list_char tptp.int)_ tptp.set_Pr1148378109ar_int tptp.produc1260470173ar_int Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1260470173ar_int tptp.list_char tptp.int)|)) (= (ho_62 x z) (ho_62 y z)))) (= x y))))) (let ((_let_136 (forall ((u |u_(-> tptp.product_prod_nat_nat Bool)|) (e Bool) (i tptp.product_prod_nat_nat)) (not (forall ((v |u_(-> tptp.product_prod_nat_nat Bool)|)) (not (forall ((ii tptp.product_prod_nat_nat)) (= (ho_51 v ii) (ite (= i ii) e (ho_51 u ii)))))))))) (let ((_let_137 (forall ((x |u_(-> tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_51 x z) (ho_51 y z)))) (= x y))))) (let ((_let_138 (forall ((u |u_(-> _u_(-> tptp.produc1260470173ar_int tptp.nat)_ tptp.set_Pr1148378109ar_int tptp.product_prod_nat_nat Bool)|) (e |u_(-> tptp.set_Pr1148378109ar_int tptp.product_prod_nat_nat Bool)|) (i |u_(-> tptp.produc1260470173ar_int tptp.nat)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1260470173ar_int tptp.nat)_ tptp.set_Pr1148378109ar_int tptp.product_prod_nat_nat Bool)|)) (not (forall ((ii |u_(-> tptp.produc1260470173ar_int tptp.nat)|)) (= (ho_49 v ii) (ite (= i ii) e (ho_49 u ii)))))))))) (let ((_let_139 (forall ((x |u_(-> _u_(-> tptp.produc1260470173ar_int tptp.nat)_ tptp.set_Pr1148378109ar_int tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.produc1260470173ar_int tptp.nat)_ tptp.set_Pr1148378109ar_int tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1260470173ar_int tptp.nat)|)) (= (ho_49 x z) (ho_49 y z)))) (= x y))))) (let ((_let_140 (forall ((u |u_(-> _u_(-> tptp.produc1260470173ar_int tptp.nat)_ _u_(-> tptp.produc1260470173ar_int tptp.nat)_ tptp.set_Pr1148378109ar_int tptp.product_prod_nat_nat Bool)|) (e |u_(-> _u_(-> tptp.produc1260470173ar_int tptp.nat)_ tptp.set_Pr1148378109ar_int tptp.product_prod_nat_nat Bool)|) (i |u_(-> tptp.produc1260470173ar_int tptp.nat)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1260470173ar_int tptp.nat)_ _u_(-> tptp.produc1260470173ar_int tptp.nat)_ tptp.set_Pr1148378109ar_int tptp.product_prod_nat_nat Bool)|)) (not (forall ((ii |u_(-> tptp.produc1260470173ar_int tptp.nat)|)) (= (ho_48 v ii) (ite (= i ii) e (ho_48 u ii)))))))))) (let ((_let_141 (forall ((x |u_(-> _u_(-> tptp.produc1260470173ar_int tptp.nat)_ _u_(-> tptp.produc1260470173ar_int tptp.nat)_ tptp.set_Pr1148378109ar_int tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.produc1260470173ar_int tptp.nat)_ _u_(-> tptp.produc1260470173ar_int tptp.nat)_ tptp.set_Pr1148378109ar_int tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1260470173ar_int tptp.nat)|)) (= (ho_48 x z) (ho_48 y z)))) (= x y))))) (let ((_let_142 (forall ((u |u_(-> _u_(-> tptp.typerep tptp.nat)_ tptp.list_typerep tptp.nat)|) (e |u_(-> tptp.list_typerep tptp.nat)|) (i |u_(-> tptp.typerep tptp.nat)|)) (not (forall ((v |u_(-> _u_(-> tptp.typerep tptp.nat)_ tptp.list_typerep tptp.nat)|)) (not (forall ((ii |u_(-> tptp.typerep tptp.nat)|)) (= (ho_143 v ii) (ite (= i ii) e (ho_143 u ii)))))))))) (let ((_let_143 (forall ((x |u_(-> _u_(-> tptp.typerep tptp.nat)_ tptp.list_typerep tptp.nat)|) (y |u_(-> _u_(-> tptp.typerep tptp.nat)_ tptp.list_typerep tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.typerep tptp.nat)|)) (= (ho_143 x z) (ho_143 y z)))) (= x y))))) (let ((_let_144 (forall ((u |u_(-> tptp.set_Pr1148378109ar_int Bool)|) (e Bool) (i tptp.set_Pr1148378109ar_int)) (not (forall ((v |u_(-> tptp.set_Pr1148378109ar_int Bool)|)) (not (forall ((ii tptp.set_Pr1148378109ar_int)) (= (ho_54 v ii) (ite (= i ii) e (ho_54 u ii)))))))))) (let ((_let_145 (forall ((x |u_(-> tptp.set_Pr1148378109ar_int Bool)|) (y |u_(-> tptp.set_Pr1148378109ar_int Bool)|)) (or (not (forall ((z tptp.set_Pr1148378109ar_int)) (= (ho_54 x z) (ho_54 y z)))) (= x y))))) (let ((_let_146 (forall ((u |u_(-> tptp.set_Pr446800905yperep Bool)|) (e Bool) (i tptp.set_Pr446800905yperep)) (not (forall ((v |u_(-> tptp.set_Pr446800905yperep Bool)|)) (not (forall ((ii tptp.set_Pr446800905yperep)) (= (ho_157 v ii) (ite (= i ii) e (ho_157 u ii)))))))))) (let ((_let_147 (forall ((x |u_(-> tptp.set_Pr446800905yperep Bool)|) (y |u_(-> tptp.set_Pr446800905yperep Bool)|)) (or (not (forall ((z tptp.set_Pr446800905yperep)) (= (ho_157 x z) (ho_157 y z)))) (= x y))))) (let ((_let_148 (forall ((u |u_(-> tptp.com tptp.com _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ Bool)|) (e |u_(-> tptp.com _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ Bool)|) (i tptp.com)) (not (forall ((v |u_(-> tptp.com tptp.com _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ Bool)|)) (not (forall ((ii tptp.com)) (= (ho_127 v ii) (ite (= i ii) e (ho_127 u ii)))))))))) (let ((_let_149 (forall ((x |u_(-> tptp.com tptp.com _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ Bool)|) (y |u_(-> tptp.com tptp.com _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ Bool)|)) (or (not (forall ((z tptp.com)) (= (ho_127 x z) (ho_127 y z)))) (= x y))))) (let ((_let_150 (forall ((u |u_(-> tptp.nat tptp.nat)|) (e tptp.nat) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_72 v ii) (ite (= i ii) e (ho_72 u ii)))))))))) (let ((_let_151 (forall ((x |u_(-> tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_72 x z) (ho_72 y z)))) (= x y))))) (let ((_let_152 (forall ((u |u_(-> tptp.com _u_(-> tptp.list_char tptp.int)_ tptp.produc1260470173ar_int)|) (e |u_(-> _u_(-> tptp.list_char tptp.int)_ tptp.produc1260470173ar_int)|) (i tptp.com)) (not (forall ((v |u_(-> tptp.com _u_(-> tptp.list_char tptp.int)_ tptp.produc1260470173ar_int)|)) (not (forall ((ii tptp.com)) (= (ho_66 v ii) (ite (= i ii) e (ho_66 u ii)))))))))) (let ((_let_153 (forall ((x |u_(-> tptp.com _u_(-> tptp.list_char tptp.int)_ tptp.produc1260470173ar_int)|) (y |u_(-> tptp.com _u_(-> tptp.list_char tptp.int)_ tptp.produc1260470173ar_int)|)) (or (not (forall ((z tptp.com)) (= (ho_66 x z) (ho_66 y z)))) (= x y))))) (let ((_let_154 (forall ((u |u_(-> tptp.set_Pr1148378109ar_int tptp.produc1260470173ar_int Bool)|) (e |u_(-> tptp.produc1260470173ar_int Bool)|) (i tptp.set_Pr1148378109ar_int)) (not (forall ((v |u_(-> tptp.set_Pr1148378109ar_int tptp.produc1260470173ar_int Bool)|)) (not (forall ((ii tptp.set_Pr1148378109ar_int)) (= (ho_63 v ii) (ite (= i ii) e (ho_63 u ii)))))))))) (let ((_let_155 (forall ((x |u_(-> tptp.set_Pr1148378109ar_int tptp.produc1260470173ar_int Bool)|) (y |u_(-> tptp.set_Pr1148378109ar_int tptp.produc1260470173ar_int Bool)|)) (or (not (forall ((z tptp.set_Pr1148378109ar_int)) (= (ho_63 x z) (ho_63 y z)))) (= x y))))) (let ((_let_156 (forall ((u |u_(-> tptp.set_Pr1097818217yperep tptp.set_Pr446800905yperep)|) (e tptp.set_Pr446800905yperep) (i tptp.set_Pr1097818217yperep)) (not (forall ((v |u_(-> tptp.set_Pr1097818217yperep tptp.set_Pr446800905yperep)|)) (not (forall ((ii tptp.set_Pr1097818217yperep)) (= (ho_151 v ii) (ite (= i ii) e (ho_151 u ii)))))))))) (let ((_let_157 (forall ((x |u_(-> tptp.set_Pr1097818217yperep tptp.set_Pr446800905yperep)|) (y |u_(-> tptp.set_Pr1097818217yperep tptp.set_Pr446800905yperep)|)) (or (not (forall ((z tptp.set_Pr1097818217yperep)) (= (ho_151 x z) (ho_151 y z)))) (= x y))))) (let ((_let_158 (forall ((u |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (e |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (i |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (= (ho_80 v ii) (ite (= i ii) e (ho_80 u ii)))))))))) (let ((_let_159 (forall ((x |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ _u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)_ _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|)) (= (ho_80 x z) (ho_80 y z)))) (= x y))))) (let ((_let_160 (forall ((u |u_(-> tptp.com tptp.nat)|) (e tptp.nat) (i tptp.com)) (not (forall ((v |u_(-> tptp.com tptp.nat)|)) (not (forall ((ii tptp.com)) (= (ho_135 v ii) (ite (= i ii) e (ho_135 u ii)))))))))) (let ((_let_161 (forall ((x |u_(-> tptp.com tptp.nat)|) (y |u_(-> tptp.com tptp.nat)|)) (or (not (forall ((z tptp.com)) (= (ho_135 x z) (ho_135 y z)))) (= x y))))) (let ((_let_162 (forall ((u |u_(-> tptp.produc1260470173ar_int tptp.list_char tptp.int)|) (e |u_(-> tptp.list_char tptp.int)|) (i tptp.produc1260470173ar_int)) (not (forall ((v |u_(-> tptp.produc1260470173ar_int tptp.list_char tptp.int)|)) (not (forall ((ii tptp.produc1260470173ar_int)) (= (ho_58 v ii) (ite (= i ii) e (ho_58 u ii)))))))))) (let ((_let_163 (forall ((x |u_(-> tptp.produc1260470173ar_int tptp.list_char tptp.int)|) (y |u_(-> tptp.produc1260470173ar_int tptp.list_char tptp.int)|)) (or (not (forall ((z tptp.produc1260470173ar_int)) (= (ho_58 x z) (ho_58 y z)))) (= x y))))) (let ((_let_164 (forall ((u |u_(-> tptp.list_char tptp.aexp tptp.com)|) (e |u_(-> tptp.aexp tptp.com)|) (i tptp.list_char)) (not (forall ((v |u_(-> tptp.list_char tptp.aexp tptp.com)|)) (not (forall ((ii tptp.list_char)) (= (ho_131 v ii) (ite (= i ii) e (ho_131 u ii)))))))))) (let ((_let_165 (forall ((x |u_(-> tptp.list_char tptp.aexp tptp.com)|) (y |u_(-> tptp.list_char tptp.aexp tptp.com)|)) (or (not (forall ((z tptp.list_char)) (= (ho_131 x z) (ho_131 y z)))) (= x y))))) (let ((_let_166 (forall ((u |u_(-> tptp.com Bool)|) (e Bool) (i tptp.com)) (not (forall ((v |u_(-> tptp.com Bool)|)) (not (forall ((ii tptp.com)) (= (ho_133 v ii) (ite (= i ii) e (ho_133 u ii)))))))))) (let ((_let_167 (forall ((x |u_(-> tptp.com Bool)|) (y |u_(-> tptp.com Bool)|)) (or (not (forall ((z tptp.com)) (= (ho_133 x z) (ho_133 y z)))) (= x y))))) (let ((_let_168 (forall ((u |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.set_Pr1986765409at_nat)|) (e tptp.set_Pr1986765409at_nat) (i |u_(-> tptp.product_prod_nat_nat Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.set_Pr1986765409at_nat)|)) (not (forall ((ii |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_137 v ii) (ite (= i ii) e (ho_137 u ii)))))))))) (let ((_let_169 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.set_Pr1986765409at_nat)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.set_Pr1986765409at_nat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_137 x z) (ho_137 y z)))) (= x y))))) (let ((_let_170 (forall ((u |u_(-> tptp.typerep tptp.nat)|) (e tptp.nat) (i tptp.typerep)) (not (forall ((v |u_(-> tptp.typerep tptp.nat)|)) (not (forall ((ii tptp.typerep)) (= (ho_141 v ii) (ite (= i ii) e (ho_141 u ii)))))))))) (let ((_let_171 (forall ((x |u_(-> tptp.typerep tptp.nat)|) (y |u_(-> tptp.typerep tptp.nat)|)) (or (not (forall ((z tptp.typerep)) (= (ho_141 x z) (ho_141 y z)))) (= x y))))) (let ((_let_172 (forall ((u |u_(-> tptp.list_typerep tptp.set_typerep)|) (e tptp.set_typerep) (i tptp.list_typerep)) (not (forall ((v |u_(-> tptp.list_typerep tptp.set_typerep)|)) (not (forall ((ii tptp.list_typerep)) (= (ho_185 v ii) (ite (= i ii) e (ho_185 u ii)))))))))) (let ((_let_173 (forall ((x |u_(-> tptp.list_typerep tptp.set_typerep)|) (y |u_(-> tptp.list_typerep tptp.set_typerep)|)) (or (not (forall ((z tptp.list_typerep)) (= (ho_185 x z) (ho_185 y z)))) (= x y))))) (let ((_let_174 (forall ((u |u_(-> tptp.list_typerep tptp.nat)|) (e tptp.nat) (i tptp.list_typerep)) (not (forall ((v |u_(-> tptp.list_typerep tptp.nat)|)) (not (forall ((ii tptp.list_typerep)) (= (ho_144 v ii) (ite (= i ii) e (ho_144 u ii)))))))))) (let ((_let_175 (forall ((x |u_(-> tptp.list_typerep tptp.nat)|) (y |u_(-> tptp.list_typerep tptp.nat)|)) (or (not (forall ((z tptp.list_typerep)) (= (ho_144 x z) (ho_144 y z)))) (= x y))))) (let ((_let_176 (forall ((u |u_(-> tptp.list_typerep tptp.typerep)|) (e tptp.typerep) (i tptp.list_typerep)) (not (forall ((v |u_(-> tptp.list_typerep tptp.typerep)|)) (not (forall ((ii tptp.list_typerep)) (= (ho_147 v ii) (ite (= i ii) e (ho_147 u ii)))))))))) (let ((_let_177 (forall ((x |u_(-> tptp.list_typerep tptp.typerep)|) (y |u_(-> tptp.list_typerep tptp.typerep)|)) (or (not (forall ((z tptp.list_typerep)) (= (ho_147 x z) (ho_147 y z)))) (= x y))))) (let ((_let_178 (forall ((u |u_(-> tptp.literal tptp.list_typerep tptp.typerep)|) (e |u_(-> tptp.list_typerep tptp.typerep)|) (i tptp.literal)) (not (forall ((v |u_(-> tptp.literal tptp.list_typerep tptp.typerep)|)) (not (forall ((ii tptp.literal)) (= (ho_146 v ii) (ite (= i ii) e (ho_146 u ii)))))))))) (let ((_let_179 (forall ((x |u_(-> tptp.literal tptp.list_typerep tptp.typerep)|) (y |u_(-> tptp.literal tptp.list_typerep tptp.typerep)|)) (or (not (forall ((z tptp.literal)) (= (ho_146 x z) (ho_146 y z)))) (= x y))))) (let ((_let_180 (forall ((u |u_(-> tptp.set_Pr1097818217yperep Bool)|) (e Bool) (i tptp.set_Pr1097818217yperep)) (not (forall ((v |u_(-> tptp.set_Pr1097818217yperep Bool)|)) (not (forall ((ii tptp.set_Pr1097818217yperep)) (= (ho_163 v ii) (ite (= i ii) e (ho_163 u ii)))))))))) (let ((_let_181 (forall ((x |u_(-> tptp.set_Pr1097818217yperep Bool)|) (y |u_(-> tptp.set_Pr1097818217yperep Bool)|)) (or (not (forall ((z tptp.set_Pr1097818217yperep)) (= (ho_163 x z) (ho_163 y z)))) (= x y))))) (let ((_let_182 (forall ((u |u_(-> tptp.produc490010537yperep tptp.set_Pr446800905yperep Bool)|) (e |u_(-> tptp.set_Pr446800905yperep Bool)|) (i tptp.produc490010537yperep)) (not (forall ((v |u_(-> tptp.produc490010537yperep tptp.set_Pr446800905yperep Bool)|)) (not (forall ((ii tptp.produc490010537yperep)) (= (ho_156 v ii) (ite (= i ii) e (ho_156 u ii)))))))))) (let ((_let_183 (forall ((x |u_(-> tptp.produc490010537yperep tptp.set_Pr446800905yperep Bool)|) (y |u_(-> tptp.produc490010537yperep tptp.set_Pr446800905yperep Bool)|)) (or (not (forall ((z tptp.produc490010537yperep)) (= (ho_156 x z) (ho_156 y z)))) (= x y))))) (let ((_let_184 (forall ((u |u_(-> tptp.typerep tptp.produc1788831497yperep)|) (e tptp.produc1788831497yperep) (i tptp.typerep)) (not (forall ((v |u_(-> tptp.typerep tptp.produc1788831497yperep)|)) (not (forall ((ii tptp.typerep)) (= (ho_160 v ii) (ite (= i ii) e (ho_160 u ii)))))))))) (let ((_let_185 (forall ((x |u_(-> tptp.typerep tptp.produc1788831497yperep)|) (y |u_(-> tptp.typerep tptp.produc1788831497yperep)|)) (or (not (forall ((z tptp.typerep)) (= (ho_160 x z) (ho_160 y z)))) (= x y))))) (let ((_let_186 (forall ((u |u_(-> tptp.typerep tptp.typerep tptp.produc1788831497yperep)|) (e |u_(-> tptp.typerep tptp.produc1788831497yperep)|) (i tptp.typerep)) (not (forall ((v |u_(-> tptp.typerep tptp.typerep tptp.produc1788831497yperep)|)) (not (forall ((ii tptp.typerep)) (= (ho_159 v ii) (ite (= i ii) e (ho_159 u ii)))))))))) (let ((_let_187 (forall ((x |u_(-> tptp.typerep tptp.typerep tptp.produc1788831497yperep)|) (y |u_(-> tptp.typerep tptp.typerep tptp.produc1788831497yperep)|)) (or (not (forall ((z tptp.typerep)) (= (ho_159 x z) (ho_159 y z)))) (= x y))))) (let ((_let_188 (forall ((u |u_(-> tptp.produc1788831497yperep tptp.set_Pr1097818217yperep Bool)|) (e |u_(-> tptp.set_Pr1097818217yperep Bool)|) (i tptp.produc1788831497yperep)) (not (forall ((v |u_(-> tptp.produc1788831497yperep tptp.set_Pr1097818217yperep Bool)|)) (not (forall ((ii tptp.produc1788831497yperep)) (= (ho_162 v ii) (ite (= i ii) e (ho_162 u ii)))))))))) (let ((_let_189 (forall ((x |u_(-> tptp.produc1788831497yperep tptp.set_Pr1097818217yperep Bool)|) (y |u_(-> tptp.produc1788831497yperep tptp.set_Pr1097818217yperep Bool)|)) (or (not (forall ((z tptp.produc1788831497yperep)) (= (ho_162 x z) (ho_162 y z)))) (= x y))))) (let ((_let_190 (forall ((u |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1560408065st_nat)|) (e tptp.set_Pr1560408065st_nat) (i tptp.set_Pr1986765409at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1560408065st_nat)|)) (not (forall ((ii tptp.set_Pr1986765409at_nat)) (= (ho_165 v ii) (ite (= i ii) e (ho_165 u ii)))))))))) (let ((_let_191 (forall ((x |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1560408065st_nat)|) (y |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1560408065st_nat)|)) (or (not (forall ((z tptp.set_Pr1986765409at_nat)) (= (ho_165 x z) (ho_165 y z)))) (= x y))))) (let ((_let_192 (forall ((u |u_(-> tptp.list_nat tptp.list_nat tptp.produc1699244961st_nat)|) (e |u_(-> tptp.list_nat tptp.produc1699244961st_nat)|) (i tptp.list_nat)) (not (forall ((v |u_(-> tptp.list_nat tptp.list_nat tptp.produc1699244961st_nat)|)) (not (forall ((ii tptp.list_nat)) (= (ho_167 v ii) (ite (= i ii) e (ho_167 u ii)))))))))) (let ((_let_193 (forall ((x |u_(-> tptp.list_nat tptp.list_nat tptp.produc1699244961st_nat)|) (y |u_(-> tptp.list_nat tptp.list_nat tptp.produc1699244961st_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_167 x z) (ho_167 y z)))) (= x y))))) (let ((_let_194 (forall ((u |u_(-> tptp.produc1699244961st_nat tptp.set_Pr1560408065st_nat Bool)|) (e |u_(-> tptp.set_Pr1560408065st_nat Bool)|) (i tptp.produc1699244961st_nat)) (not (forall ((v |u_(-> tptp.produc1699244961st_nat tptp.set_Pr1560408065st_nat Bool)|)) (not (forall ((ii tptp.produc1699244961st_nat)) (= (ho_170 v ii) (ite (= i ii) e (ho_170 u ii)))))))))) (let ((_let_195 (forall ((x |u_(-> tptp.produc1699244961st_nat tptp.set_Pr1560408065st_nat Bool)|) (y |u_(-> tptp.produc1699244961st_nat tptp.set_Pr1560408065st_nat Bool)|)) (or (not (forall ((z tptp.produc1699244961st_nat)) (= (ho_170 x z) (ho_170 y z)))) (= x y))))) (let ((_let_196 (forall ((u |u_(-> tptp.nat tptp.list_nat tptp.list_nat)|) (e |u_(-> tptp.list_nat tptp.list_nat)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.list_nat tptp.list_nat)|)) (not (forall ((ii tptp.nat)) (= (ho_175 v ii) (ite (= i ii) e (ho_175 u ii)))))))))) (let ((_let_197 (forall ((x |u_(-> tptp.nat tptp.list_nat tptp.list_nat)|) (y |u_(-> tptp.nat tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_175 x z) (ho_175 y z)))) (= x y))))) (let ((_let_198 (forall ((u |u_(-> tptp.nat tptp.list_typerep tptp.nat)|) (e |u_(-> tptp.list_typerep tptp.nat)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.list_typerep tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_178 v ii) (ite (= i ii) e (ho_178 u ii)))))))))) (let ((_let_199 (forall ((x |u_(-> tptp.nat tptp.list_typerep tptp.nat)|) (y |u_(-> tptp.nat tptp.list_typerep tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_178 x z) (ho_178 y z)))) (= x y))))) (let ((_let_200 (forall ((u |u_(-> _u_(-> tptp.list_typerep Bool)_ tptp.set_list_typerep)|) (e tptp.set_list_typerep) (i |u_(-> tptp.list_typerep Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_typerep Bool)_ tptp.set_list_typerep)|)) (not (forall ((ii |u_(-> tptp.list_typerep Bool)|)) (= (ho_182 v ii) (ite (= i ii) e (ho_182 u ii)))))))))) (let ((_let_201 (forall ((x |u_(-> _u_(-> tptp.list_typerep Bool)_ tptp.set_list_typerep)|) (y |u_(-> _u_(-> tptp.list_typerep Bool)_ tptp.set_list_typerep)|)) (or (not (forall ((z |u_(-> tptp.list_typerep Bool)|)) (= (ho_182 x z) (ho_182 y z)))) (= x y))))) (let ((_let_202 (forall ((u |u_(-> tptp.set_list_typerep tptp.list_typerep tptp.set_typerep)|) (e |u_(-> tptp.list_typerep tptp.set_typerep)|) (i tptp.set_list_typerep)) (not (forall ((v |u_(-> tptp.set_list_typerep tptp.list_typerep tptp.set_typerep)|)) (not (forall ((ii tptp.set_list_typerep)) (= (ho_184 v ii) (ite (= i ii) e (ho_184 u ii)))))))))) (let ((_let_203 (forall ((x |u_(-> tptp.set_list_typerep tptp.list_typerep tptp.set_typerep)|) (y |u_(-> tptp.set_list_typerep tptp.list_typerep tptp.set_typerep)|)) (or (not (forall ((z tptp.set_list_typerep)) (= (ho_184 x z) (ho_184 y z)))) (= x y))))) (let ((_let_204 (forall ((u |u_(-> tptp.list_typerep tptp.list_typerep tptp.list_typerep)|) (e |u_(-> tptp.list_typerep tptp.list_typerep)|) (i tptp.list_typerep)) (not (forall ((v |u_(-> tptp.list_typerep tptp.list_typerep tptp.list_typerep)|)) (not (forall ((ii tptp.list_typerep)) (= (ho_189 v ii) (ite (= i ii) e (ho_189 u ii)))))))))) (let ((_let_205 (forall ((x |u_(-> tptp.list_typerep tptp.list_typerep tptp.list_typerep)|) (y |u_(-> tptp.list_typerep tptp.list_typerep tptp.list_typerep)|)) (or (not (forall ((z tptp.list_typerep)) (= (ho_189 x z) (ho_189 y z)))) (= x y))))) (let ((_let_206 (forall ((u |u_(-> tptp.list_nat tptp.list_nat tptp.list_nat)|) (e |u_(-> tptp.list_nat tptp.list_nat)|) (i tptp.list_nat)) (not (forall ((v |u_(-> tptp.list_nat tptp.list_nat tptp.list_nat)|)) (not (forall ((ii tptp.list_nat)) (= (ho_191 v ii) (ite (= i ii) e (ho_191 u ii)))))))))) (let ((_let_207 (forall ((x |u_(-> tptp.list_nat tptp.list_nat tptp.list_nat)|) (y |u_(-> tptp.list_nat tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_191 x z) (ho_191 y z)))) (= x y))))) (let ((_let_208 (forall ((BOUND_VARIABLE_10551 tptp.typerep) (BOUND_VARIABLE_10552 tptp.set_list_typerep) (BOUND_VARIABLE_10553 tptp.list_typerep)) (= (ho_26 (ho_25 (ho_24 k_23 BOUND_VARIABLE_10551) BOUND_VARIABLE_10552) BOUND_VARIABLE_10553) (ho_32 (ho_31 k_30 (ho_29 (ho_28 k_27 BOUND_VARIABLE_10551) BOUND_VARIABLE_10553)) BOUND_VARIABLE_10552))))) (let ((_let_209 (forall ((BOUND_VARIABLE_10540 tptp.typerep) (BOUND_VARIABLE_10541 tptp.set_list_typerep) (BOUND_VARIABLE_10542 tptp.list_typerep)) (= (ho_26 (ho_25 (ho_24 k_33 BOUND_VARIABLE_10540) BOUND_VARIABLE_10541) BOUND_VARIABLE_10542) (ho_32 (ho_31 k_30 (ho_29 (ho_28 k_27 BOUND_VARIABLE_10540) BOUND_VARIABLE_10542)) BOUND_VARIABLE_10541))))) (let ((_let_210 (forall ((BOUND_VARIABLE_10669 |u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (BOUND_VARIABLE_10526 tptp.nat) (BOUND_VARIABLE_10527 tptp.bexp) (BOUND_VARIABLE_10666 |u_(-> tptp.list_char tptp.int)|) (BOUND_VARIABLE_10663 |u_(-> tptp.list_char tptp.int)|)) (= (ho_41 (ho_40 (ho_39 (ho_38 (ho_37 k_36 BOUND_VARIABLE_10669) BOUND_VARIABLE_10526) BOUND_VARIABLE_10527) BOUND_VARIABLE_10666) BOUND_VARIABLE_10663) (and (ho_41 (ho_40 (ho_35 BOUND_VARIABLE_10669 BOUND_VARIABLE_10526) BOUND_VARIABLE_10666) BOUND_VARIABLE_10663) (ho_41 (ho_43 k_42 BOUND_VARIABLE_10527) BOUND_VARIABLE_10666)))))) (let ((_let_211 (forall ((BOUND_VARIABLE_10717 |u_(-> tptp.nat _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (BOUND_VARIABLE_10716 |u_(-> tptp.list_char tptp.int)|) (BOUND_VARIABLE_10715 |u_(-> tptp.list_char tptp.int)|)) (= (ho_41 (ho_40 (ho_45 k_44 BOUND_VARIABLE_10717) BOUND_VARIABLE_10716) BOUND_VARIABLE_10715) (not (forall ((N4 tptp.nat)) (not (ho_41 (ho_40 (ho_35 BOUND_VARIABLE_10717 N4) BOUND_VARIABLE_10716) BOUND_VARIABLE_10715)))))))) (let ((_let_212 (forall ((BOUND_VARIABLE_10743 |u_(-> tptp.produc1260470173ar_int tptp.nat)|) (BOUND_VARIABLE_10740 |u_(-> tptp.produc1260470173ar_int tptp.nat)|) (BOUND_VARIABLE_10495 tptp.set_Pr1148378109ar_int) (BOUND_VARIABLE_10496 tptp.product_prod_nat_nat)) (= (ho_51 (ho_50 (ho_49 (ho_48 k_47 BOUND_VARIABLE_10743) BOUND_VARIABLE_10740) BOUND_VARIABLE_10495) BOUND_VARIABLE_10496) (not (forall ((A5 tptp.produc1260470173ar_int)) (or (not (= BOUND_VARIABLE_10496 (ho_57 (ho_56 k_55 (ho_46 BOUND_VARIABLE_10743 A5)) (ho_46 BOUND_VARIABLE_10740 A5)))) (not (ho_54 (ho_53 k_52 A5) BOUND_VARIABLE_10495))))))))) (let ((_let_213 (forall ((BOUND_VARIABLE_10801 |u_(-> tptp.produc1260470173ar_int tptp.com)|) (BOUND_VARIABLE_10797 |u_(-> tptp.produc1260470173ar_int tptp.list_char tptp.int)|) (BOUND_VARIABLE_10476 tptp.set_Pr1148378109ar_int) (BOUND_VARIABLE_10477 tptp.produc1260470173ar_int)) (= (ho_64 (ho_63 (ho_62 (ho_61 k_60 BOUND_VARIABLE_10801) BOUND_VARIABLE_10797) BOUND_VARIABLE_10476) BOUND_VARIABLE_10477) (not (forall ((A5 tptp.produc1260470173ar_int)) (or (not (= BOUND_VARIABLE_10477 (ho_67 (ho_66 k_65 (ho_59 BOUND_VARIABLE_10801 A5)) (ho_58 BOUND_VARIABLE_10797 A5)))) (not (ho_54 (ho_53 k_52 A5) BOUND_VARIABLE_10476))))))))) (let ((_let_214 (forall ((BOUND_VARIABLE_10853 |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (BOUND_VARIABLE_10461 tptp.bexp) (BOUND_VARIABLE_10852 |u_(-> tptp.list_char tptp.int)|) (BOUND_VARIABLE_10851 |u_(-> tptp.list_char tptp.int)|)) (= (ho_41 (ho_40 (ho_39 (ho_69 k_68 BOUND_VARIABLE_10853) BOUND_VARIABLE_10461) BOUND_VARIABLE_10852) BOUND_VARIABLE_10851) (and (ho_41 (ho_40 BOUND_VARIABLE_10853 BOUND_VARIABLE_10852) BOUND_VARIABLE_10851) (not (ho_41 (ho_43 k_42 BOUND_VARIABLE_10461) BOUND_VARIABLE_10852))))))) (let ((_let_215 (forall ((BOUND_VARIABLE_10452 tptp.nat) (BOUND_VARIABLE_10453 tptp.nat)) (= (ho_72 (ho_71 k_70 BOUND_VARIABLE_10452) BOUND_VARIABLE_10453) (ho_72 (ho_71 k_73 BOUND_VARIABLE_10453) BOUND_VARIABLE_10452))))) (let ((_let_216 (forall ((BOUND_VARIABLE_10893 |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (BOUND_VARIABLE_10892 |u_(-> tptp.list_char tptp.int)|) (BOUND_VARIABLE_10891 |u_(-> tptp.list_char tptp.int)|)) (= (ho_41 (ho_40 (ho_75 k_74 BOUND_VARIABLE_10893) BOUND_VARIABLE_10892) BOUND_VARIABLE_10891) (ho_41 (ho_40 BOUND_VARIABLE_10893 BOUND_VARIABLE_10891) BOUND_VARIABLE_10892))))) (let ((_let_217 (forall ((BOUND_VARIABLE_10912 |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (BOUND_VARIABLE_10911 |u_(-> tptp.list_char tptp.int)|) (BOUND_VARIABLE_10910 |u_(-> tptp.list_char tptp.int)|)) (= (ho_41 (ho_40 (ho_75 k_76 BOUND_VARIABLE_10912) BOUND_VARIABLE_10911) BOUND_VARIABLE_10910) (ho_41 (ho_40 BOUND_VARIABLE_10912 BOUND_VARIABLE_10910) BOUND_VARIABLE_10911))))) (let ((_let_218 (forall ((BOUND_VARIABLE_10928 |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (BOUND_VARIABLE_10422 tptp.bexp) (BOUND_VARIABLE_10927 |u_(-> tptp.list_char tptp.int)|) (BOUND_VARIABLE_10926 |u_(-> tptp.list_char tptp.int)|)) (= (ho_41 (ho_40 (ho_39 (ho_69 k_77 BOUND_VARIABLE_10928) BOUND_VARIABLE_10422) BOUND_VARIABLE_10927) BOUND_VARIABLE_10926) (and (ho_41 (ho_40 BOUND_VARIABLE_10928 BOUND_VARIABLE_10927) BOUND_VARIABLE_10926) (ho_41 (ho_43 k_42 BOUND_VARIABLE_10422) BOUND_VARIABLE_10927)))))) (let ((_let_219 (forall ((BOUND_VARIABLE_10948 |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (BOUND_VARIABLE_10408 tptp.bexp) (BOUND_VARIABLE_10947 |u_(-> tptp.list_char tptp.int)|) (BOUND_VARIABLE_10946 |u_(-> tptp.list_char tptp.int)|)) (= (ho_41 (ho_40 (ho_39 (ho_69 k_78 BOUND_VARIABLE_10948) BOUND_VARIABLE_10408) BOUND_VARIABLE_10947) BOUND_VARIABLE_10946) (and (ho_41 (ho_40 BOUND_VARIABLE_10948 BOUND_VARIABLE_10947) BOUND_VARIABLE_10946) (not (ho_41 (ho_43 k_42 BOUND_VARIABLE_10408) BOUND_VARIABLE_10947))))))) (let ((_let_220 (forall ((BOUND_VARIABLE_10970 |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (BOUND_VARIABLE_10969 |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (BOUND_VARIABLE_10968 |u_(-> tptp.list_char tptp.int)|) (BOUND_VARIABLE_10967 |u_(-> tptp.list_char tptp.int)|)) (= (ho_41 (ho_40 (ho_75 (ho_80 k_79 BOUND_VARIABLE_10970) BOUND_VARIABLE_10969) BOUND_VARIABLE_10968) BOUND_VARIABLE_10967) (or (ho_41 (ho_40 BOUND_VARIABLE_10970 BOUND_VARIABLE_10968) BOUND_VARIABLE_10967) (ho_41 (ho_40 BOUND_VARIABLE_10969 BOUND_VARIABLE_10968) BOUND_VARIABLE_10967)))))) (let ((_let_221 (forall ((BOUND_VARIABLE_10995 |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (BOUND_VARIABLE_10994 |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (BOUND_VARIABLE_10993 |u_(-> tptp.list_char tptp.int)|) (BOUND_VARIABLE_10992 |u_(-> tptp.list_char tptp.int)|)) (= (ho_41 (ho_40 (ho_75 (ho_80 k_81 BOUND_VARIABLE_10995) BOUND_VARIABLE_10994) BOUND_VARIABLE_10993) BOUND_VARIABLE_10992) (or (ho_41 (ho_40 BOUND_VARIABLE_10995 BOUND_VARIABLE_10993) BOUND_VARIABLE_10992) (ho_41 (ho_40 BOUND_VARIABLE_10994 BOUND_VARIABLE_10993) BOUND_VARIABLE_10992)))))) (let ((_let_222 (forall ((BOUND_VARIABLE_11015 |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (BOUND_VARIABLE_10369 tptp.bexp) (BOUND_VARIABLE_11014 |u_(-> tptp.list_char tptp.int)|) (BOUND_VARIABLE_11013 |u_(-> tptp.list_char tptp.int)|)) (= (ho_41 (ho_40 (ho_39 (ho_69 k_82 BOUND_VARIABLE_11015) BOUND_VARIABLE_10369) BOUND_VARIABLE_11014) BOUND_VARIABLE_11013) (and (ho_41 (ho_40 BOUND_VARIABLE_11015 BOUND_VARIABLE_11014) BOUND_VARIABLE_11013) (ho_41 (ho_43 k_42 BOUND_VARIABLE_10369) BOUND_VARIABLE_11014)))))) (let ((_let_223 (forall ((BOUND_VARIABLE_10357 tptp.set_Pr1148378109ar_int) (BOUND_VARIABLE_10358 tptp.com) (BOUND_VARIABLE_11032 |u_(-> tptp.list_char tptp.int)|)) (= (ho_41 (ho_85 (ho_84 k_83 BOUND_VARIABLE_10357) BOUND_VARIABLE_10358) BOUND_VARIABLE_11032) (ho_54 (ho_53 k_52 (ho_67 (ho_66 k_65 BOUND_VARIABLE_10358) BOUND_VARIABLE_11032)) BOUND_VARIABLE_10357))))) (let ((_let_224 (forall ((BOUND_VARIABLE_10346 tptp.set_Pr1148378109ar_int) (BOUND_VARIABLE_10347 tptp.com) (BOUND_VARIABLE_11055 |u_(-> tptp.list_char tptp.int)|)) (= (ho_41 (ho_85 (ho_84 k_86 BOUND_VARIABLE_10346) BOUND_VARIABLE_10347) BOUND_VARIABLE_11055) (ho_54 (ho_53 k_52 (ho_67 (ho_66 k_65 BOUND_VARIABLE_10347) BOUND_VARIABLE_11055)) BOUND_VARIABLE_10346))))) (let ((_let_225 (forall ((BOUND_VARIABLE_10335 tptp.set_Pr1986765409at_nat) (BOUND_VARIABLE_10336 tptp.nat) (BOUND_VARIABLE_10337 tptp.nat)) (= (ho_90 (ho_89 (ho_88 k_87 BOUND_VARIABLE_10335) BOUND_VARIABLE_10336) BOUND_VARIABLE_10337) (ho_93 (ho_92 k_91 (ho_57 (ho_56 k_55 BOUND_VARIABLE_10336) BOUND_VARIABLE_10337)) BOUND_VARIABLE_10335))))) (let ((_let_226 (forall ((BOUND_VARIABLE_10324 tptp.set_Pr1986765409at_nat) (BOUND_VARIABLE_10325 tptp.nat) (BOUND_VARIABLE_10326 tptp.nat)) (= (ho_90 (ho_89 (ho_88 k_94 BOUND_VARIABLE_10324) BOUND_VARIABLE_10325) BOUND_VARIABLE_10326) (ho_93 (ho_92 k_91 (ho_57 (ho_56 k_55 BOUND_VARIABLE_10325) BOUND_VARIABLE_10326)) BOUND_VARIABLE_10324))))) (let ((_let_227 (forall ((BOUND_VARIABLE_11117 |u_(-> _u_(-> tptp.list_char tptp.int)_ _u_(-> tptp.list_char tptp.int)_ Bool)|) (BOUND_VARIABLE_10297 tptp.bexp) (BOUND_VARIABLE_10298 tptp.com) (BOUND_VARIABLE_10299 tptp.nat) (BOUND_VARIABLE_11116 |u_(-> tptp.list_char tptp.int)|) (BOUND_VARIABLE_11115 |u_(-> tptp.list_char tptp.int)|)) (= (ho_41 (ho_40 (ho_35 (ho_98 (ho_97 (ho_96 k_95 BOUND_VARIABLE_11117) BOUND_VARIABLE_10297) BOUND_VARIABLE_10298) BOUND_VARIABLE_10299) BOUND_VARIABLE_11116) BOUND_VARIABLE_11115) (not (forall ((BOUND_VARIABLE_11137 |u_(-> tptp.list_char tptp.int)|)) (or (not (ho_41 (ho_101 k_100 (ho_67 (ho_66 k_65 BOUND_VARIABLE_10298) BOUND_VARIABLE_11137)) BOUND_VARIABLE_11116)) (not (ho_41 (ho_43 k_42 BOUND_VARIABLE_10297) BOUND_VARIABLE_11137)) (not (ho_41 (ho_40 (ho_35 (ho_98 (ho_97 (ho_96 k_99 BOUND_VARIABLE_11117) BOUND_VARIABLE_10297) BOUND_VARIABLE_10298) BOUND_VARIABLE_10299) BOUND_VARIABLE_11137) BOUND_VARIABLE_11115))))))))) (let ((_let_228 (forall ((BOUND_VARIABLE_10288 tptp.set_Pr1148378109ar_int) (BOUND_VARIABLE_10289 tptp.produc1260470173ar_int)) (= (ho_64 (ho_63 k_102 BOUND_VARIABLE_10288) BOUND_VARIABLE_10289) (ho_54 (ho_53 k_52 BOUND_VARIABLE_10289) BOUND_VARIABLE_10288))))) (let ((_let_229 (forall ((BOUND_VARIABLE_10551 tptp.typerep) (BOUND_VARIABLE_10552 tptp.set_list_typerep) (BOUND_VARIABLE_10553 tptp.list_typerep)) (= (@ (@ tptp.member_list_typerep (@ (@ tptp.cons_typerep BOUND_VARIABLE_10551) BOUND_VARIABLE_10553)) BOUND_VARIABLE_10552) (ll_22 BOUND_VARIABLE_10551 BOUND_VARIABLE_10552 BOUND_VARIABLE_10553))))) (let ((_let_230 (forall ((BOUND_VARIABLE_10540 tptp.typerep) (BOUND_VARIABLE_10541 tptp.set_list_typerep) (BOUND_VARIABLE_10542 tptp.list_typerep)) (= (@ (@ tptp.member_list_typerep (@ (@ tptp.cons_typerep BOUND_VARIABLE_10540) BOUND_VARIABLE_10542)) BOUND_VARIABLE_10541) (ll_21 BOUND_VARIABLE_10540 BOUND_VARIABLE_10541 BOUND_VARIABLE_10542))))) (let ((_let_231 (forall ((BOUND_VARIABLE_10525 (-> tptp.nat (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (BOUND_VARIABLE_10526 tptp.nat) (BOUND_VARIABLE_10527 tptp.bexp) (BOUND_VARIABLE_10528 (-> tptp.list_char tptp.int)) (BOUND_VARIABLE_10529 (-> tptp.list_char tptp.int))) (= (and (@ (@ (@ BOUND_VARIABLE_10525 BOUND_VARIABLE_10526) BOUND_VARIABLE_10528) BOUND_VARIABLE_10529) (@ (@ tptp.bval BOUND_VARIABLE_10527) BOUND_VARIABLE_10528)) (ll_20 BOUND_VARIABLE_10525 BOUND_VARIABLE_10526 BOUND_VARIABLE_10527 BOUND_VARIABLE_10528 BOUND_VARIABLE_10529))))) (let ((_let_232 (forall ((BOUND_VARIABLE_10512 (-> tptp.nat (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (BOUND_VARIABLE_10513 (-> tptp.list_char tptp.int)) (BOUND_VARIABLE_10514 (-> tptp.list_char tptp.int))) (= (not (forall ((N4 tptp.nat)) (not (@ (@ (@ BOUND_VARIABLE_10512 N4) BOUND_VARIABLE_10513) BOUND_VARIABLE_10514)))) (ll_19 BOUND_VARIABLE_10512 BOUND_VARIABLE_10513 BOUND_VARIABLE_10514))))) (let ((_let_233 (forall ((BOUND_VARIABLE_10493 (-> tptp.produc1260470173ar_int tptp.nat)) (BOUND_VARIABLE_10494 (-> tptp.produc1260470173ar_int tptp.nat)) (BOUND_VARIABLE_10495 tptp.set_Pr1148378109ar_int) (BOUND_VARIABLE_10496 tptp.product_prod_nat_nat)) (= (not (forall ((A5 tptp.produc1260470173ar_int)) (or (not (= BOUND_VARIABLE_10496 (@ (@ tptp.product_Pair_nat_nat (@ BOUND_VARIABLE_10493 A5)) (@ BOUND_VARIABLE_10494 A5)))) (not (@ (@ tptp.member92250950ar_int A5) BOUND_VARIABLE_10495))))) (ll_18 BOUND_VARIABLE_10493 BOUND_VARIABLE_10494 BOUND_VARIABLE_10495 BOUND_VARIABLE_10496))))) (let ((_let_234 (forall ((BOUND_VARIABLE_10474 (-> tptp.produc1260470173ar_int tptp.com)) (BOUND_VARIABLE_10475 (-> tptp.produc1260470173ar_int tptp.list_char tptp.int)) (BOUND_VARIABLE_10476 tptp.set_Pr1148378109ar_int) (BOUND_VARIABLE_10477 tptp.produc1260470173ar_int)) (= (not (forall ((A5 tptp.produc1260470173ar_int)) (or (not (= BOUND_VARIABLE_10477 (@ (@ tptp.produc1193801173ar_int (@ BOUND_VARIABLE_10474 A5)) (@ BOUND_VARIABLE_10475 A5)))) (not (@ (@ tptp.member92250950ar_int A5) BOUND_VARIABLE_10476))))) (ll_17 BOUND_VARIABLE_10474 BOUND_VARIABLE_10475 BOUND_VARIABLE_10476 BOUND_VARIABLE_10477))))) (let ((_let_235 (forall ((BOUND_VARIABLE_10460 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (BOUND_VARIABLE_10461 tptp.bexp) (BOUND_VARIABLE_10462 (-> tptp.list_char tptp.int)) (BOUND_VARIABLE_10463 (-> tptp.list_char tptp.int))) (= (and (@ (@ BOUND_VARIABLE_10460 BOUND_VARIABLE_10462) BOUND_VARIABLE_10463) (not (@ (@ tptp.bval BOUND_VARIABLE_10461) BOUND_VARIABLE_10462))) (ll_16 BOUND_VARIABLE_10460 BOUND_VARIABLE_10461 BOUND_VARIABLE_10462 BOUND_VARIABLE_10463))))) (let ((_let_236 (forall ((BOUND_VARIABLE_10452 tptp.nat) (BOUND_VARIABLE_10453 tptp.nat)) (= (@ (@ tptp.plus_plus_nat BOUND_VARIABLE_10453) BOUND_VARIABLE_10452) (ll_15 BOUND_VARIABLE_10452 BOUND_VARIABLE_10453))))) (let ((_let_237 (forall ((BOUND_VARIABLE_10443 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (BOUND_VARIABLE_10444 (-> tptp.list_char tptp.int)) (BOUND_VARIABLE_10445 (-> tptp.list_char tptp.int))) (= (@ (@ BOUND_VARIABLE_10443 BOUND_VARIABLE_10445) BOUND_VARIABLE_10444) (ll_14 BOUND_VARIABLE_10443 BOUND_VARIABLE_10444 BOUND_VARIABLE_10445))))) (let ((_let_238 (forall ((BOUND_VARIABLE_10434 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (BOUND_VARIABLE_10435 (-> tptp.list_char tptp.int)) (BOUND_VARIABLE_10436 (-> tptp.list_char tptp.int))) (= (@ (@ BOUND_VARIABLE_10434 BOUND_VARIABLE_10436) BOUND_VARIABLE_10435) (ll_13 BOUND_VARIABLE_10434 BOUND_VARIABLE_10435 BOUND_VARIABLE_10436))))) (let ((_let_239 (forall ((BOUND_VARIABLE_10421 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (BOUND_VARIABLE_10422 tptp.bexp) (BOUND_VARIABLE_10423 (-> tptp.list_char tptp.int)) (BOUND_VARIABLE_10424 (-> tptp.list_char tptp.int))) (= (and (@ (@ BOUND_VARIABLE_10421 BOUND_VARIABLE_10423) BOUND_VARIABLE_10424) (@ (@ tptp.bval BOUND_VARIABLE_10422) BOUND_VARIABLE_10423)) (ll_12 BOUND_VARIABLE_10421 BOUND_VARIABLE_10422 BOUND_VARIABLE_10423 BOUND_VARIABLE_10424))))) (let ((_let_240 (forall ((BOUND_VARIABLE_10407 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (BOUND_VARIABLE_10408 tptp.bexp) (BOUND_VARIABLE_10409 (-> tptp.list_char tptp.int)) (BOUND_VARIABLE_10410 (-> tptp.list_char tptp.int))) (= (and (@ (@ BOUND_VARIABLE_10407 BOUND_VARIABLE_10409) BOUND_VARIABLE_10410) (not (@ (@ tptp.bval BOUND_VARIABLE_10408) BOUND_VARIABLE_10409))) (ll_11 BOUND_VARIABLE_10407 BOUND_VARIABLE_10408 BOUND_VARIABLE_10409 BOUND_VARIABLE_10410))))) (let ((_let_241 (forall ((BOUND_VARIABLE_10394 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (BOUND_VARIABLE_10395 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (BOUND_VARIABLE_10396 (-> tptp.list_char tptp.int)) (BOUND_VARIABLE_10397 (-> tptp.list_char tptp.int))) (= (or (@ (@ BOUND_VARIABLE_10394 BOUND_VARIABLE_10396) BOUND_VARIABLE_10397) (@ (@ BOUND_VARIABLE_10395 BOUND_VARIABLE_10396) BOUND_VARIABLE_10397)) (ll_10 BOUND_VARIABLE_10394 BOUND_VARIABLE_10395 BOUND_VARIABLE_10396 BOUND_VARIABLE_10397))))) (let ((_let_242 (forall ((BOUND_VARIABLE_10381 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (BOUND_VARIABLE_10382 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (BOUND_VARIABLE_10383 (-> tptp.list_char tptp.int)) (BOUND_VARIABLE_10384 (-> tptp.list_char tptp.int))) (= (or (@ (@ BOUND_VARIABLE_10381 BOUND_VARIABLE_10383) BOUND_VARIABLE_10384) (@ (@ BOUND_VARIABLE_10382 BOUND_VARIABLE_10383) BOUND_VARIABLE_10384)) (ll_9 BOUND_VARIABLE_10381 BOUND_VARIABLE_10382 BOUND_VARIABLE_10383 BOUND_VARIABLE_10384))))) (let ((_let_243 (forall ((BOUND_VARIABLE_10368 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (BOUND_VARIABLE_10369 tptp.bexp) (BOUND_VARIABLE_10370 (-> tptp.list_char tptp.int)) (BOUND_VARIABLE_10371 (-> tptp.list_char tptp.int))) (= (and (@ (@ BOUND_VARIABLE_10368 BOUND_VARIABLE_10370) BOUND_VARIABLE_10371) (@ (@ tptp.bval BOUND_VARIABLE_10369) BOUND_VARIABLE_10370)) (ll_8 BOUND_VARIABLE_10368 BOUND_VARIABLE_10369 BOUND_VARIABLE_10370 BOUND_VARIABLE_10371))))) (let ((_let_244 (forall ((BOUND_VARIABLE_10357 tptp.set_Pr1148378109ar_int) (BOUND_VARIABLE_10358 tptp.com) (BOUND_VARIABLE_10359 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.member92250950ar_int (@ (@ tptp.produc1193801173ar_int BOUND_VARIABLE_10358) BOUND_VARIABLE_10359)) BOUND_VARIABLE_10357) (ll_7 BOUND_VARIABLE_10357 BOUND_VARIABLE_10358 BOUND_VARIABLE_10359))))) (let ((_let_245 (forall ((BOUND_VARIABLE_10346 tptp.set_Pr1148378109ar_int) (BOUND_VARIABLE_10347 tptp.com) (BOUND_VARIABLE_10348 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.member92250950ar_int (@ (@ tptp.produc1193801173ar_int BOUND_VARIABLE_10347) BOUND_VARIABLE_10348)) BOUND_VARIABLE_10346) (ll_6 BOUND_VARIABLE_10346 BOUND_VARIABLE_10347 BOUND_VARIABLE_10348))))) (let ((_let_246 (forall ((BOUND_VARIABLE_10335 tptp.set_Pr1986765409at_nat) (BOUND_VARIABLE_10336 tptp.nat) (BOUND_VARIABLE_10337 tptp.nat)) (= (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat BOUND_VARIABLE_10336) BOUND_VARIABLE_10337)) BOUND_VARIABLE_10335) (ll_5 BOUND_VARIABLE_10335 BOUND_VARIABLE_10336 BOUND_VARIABLE_10337))))) (let ((_let_247 (forall ((BOUND_VARIABLE_10324 tptp.set_Pr1986765409at_nat) (BOUND_VARIABLE_10325 tptp.nat) (BOUND_VARIABLE_10326 tptp.nat)) (= (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat BOUND_VARIABLE_10325) BOUND_VARIABLE_10326)) BOUND_VARIABLE_10324) (ll_4 BOUND_VARIABLE_10324 BOUND_VARIABLE_10325 BOUND_VARIABLE_10326))))) (let ((_let_248 (forall ((BOUND_VARIABLE_10296 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (BOUND_VARIABLE_10297 tptp.bexp) (BOUND_VARIABLE_10298 tptp.com) (BOUND_VARIABLE_10299 tptp.nat) (BOUND_VARIABLE_10300 (-> tptp.list_char tptp.int)) (BOUND_VARIABLE_10301 (-> tptp.list_char tptp.int))) (= (not (forall ((S5 (-> tptp.list_char tptp.int))) (or (not (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int BOUND_VARIABLE_10298) S5)) BOUND_VARIABLE_10300)) (not (@ (@ tptp.bval BOUND_VARIABLE_10297) S5)) (not (@ (@ (@ (@ (@ (@ tptp.relati23543761ar_int BOUND_VARIABLE_10296) BOUND_VARIABLE_10297) BOUND_VARIABLE_10298) BOUND_VARIABLE_10299) S5) BOUND_VARIABLE_10301))))) (ll_3 BOUND_VARIABLE_10296 BOUND_VARIABLE_10297 BOUND_VARIABLE_10298 BOUND_VARIABLE_10299 BOUND_VARIABLE_10300 BOUND_VARIABLE_10301))))) (let ((_let_249 (forall ((BOUND_VARIABLE_10288 tptp.set_Pr1148378109ar_int) (BOUND_VARIABLE_10289 tptp.produc1260470173ar_int)) (= (@ (@ tptp.member92250950ar_int BOUND_VARIABLE_10289) BOUND_VARIABLE_10288) (ll_2 BOUND_VARIABLE_10288 BOUND_VARIABLE_10289))))) (let ((_let_250 (and _let_13 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (k_103 k_107 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_14))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_20 _let_18 _let_16 _let_22 _let_25))) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (ASSUME :args (_let_13)) (PREPROCESS :args ((and _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229)))) :args (_let_250)) (PREPROCESS :args ((= _let_250 (and _let_19 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208))))) (PREPROCESS :args ((and _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26)))) :args ((and _let_19 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26))) :args (0)) (EQ_RESOLVE (ASSUME :args (_let_11)) (PREPROCESS :args ((= _let_11 _let_17)))) (EQ_RESOLVE (ASSUME :args (_let_10)) (PREPROCESS :args ((= _let_10 _let_15)))) (EQ_RESOLVE (ASSUME :args (_let_9)) (PREPROCESS :args ((= _let_9 _let_21)))) :args (_let_25 false _let_19 false _let_17 false _let_15 false _let_21)) _let_24 :args (false true _let_23 false _let_14)) :args (_let_13 (@ _let_12 tptp.s2) _let_11 _let_10 _let_9 (@ (@ tptp.big_big_step (@ _let_8 tptp.s)) tptp.t) (@ (@ tptp.big_big_step (@ _let_7 tptp.s2)) tptp.t2) (@ (@ tptp.q tptp.ua) tptp.t_a) (@ (@ _let_4 tptp.s2) tptp.s) (@ (@ tptp.big_big_step (@ _let_6 tptp.ta)) tptp.ua) (@ (@ tptp.big_big_step (@ _let_6 tptp.t2)) tptp.u) (@ (@ (@ (@ tptp.relati775585786_valid _let_5) _let_2) tptp.c2) tptp.q) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X2) (@ tptp.suc Y2)) (= X2 Y2))) (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))) (forall ((X1 tptp.nat) (X2 tptp.nat) (Y1 tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat X1) X2) (@ (@ tptp.product_Pair_nat_nat Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 tptp.com) (X2 (-> tptp.list_char tptp.int)) (Y1 tptp.com) (Y2 (-> tptp.list_char tptp.int))) (= (= (@ (@ tptp.produc1193801173ar_int X1) X2) (@ (@ tptp.produc1193801173ar_int Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((A tptp.nat) (B tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A2) B2)) (and (= A A2) (= B B2)))) (forall ((A tptp.com) (B (-> tptp.list_char tptp.int)) (A2 tptp.com) (B2 (-> tptp.list_char tptp.int))) (= (= (@ (@ tptp.produc1193801173ar_int A) B) (@ (@ tptp.produc1193801173ar_int A2) B2)) (and (= A A2) (= B B2)))) (forall ((T (-> tptp.list_char tptp.int)) (U (-> tptp.list_char tptp.int)) (S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int)) (T2 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ (@ (@ (@ tptp.relati23543761ar_int tptp.p) tptp.b) tptp.c) tptp.ka))) (let ((_let_2 (@ (@ tptp.while tptp.b) tptp.c))) (=> (@ (@ (@ (@ tptp.relati775585786_valid _let_1) _let_2) tptp.c2) tptp.q) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int _let_2) T)) U) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.c) S)) T) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.c2) S2)) T2) (=> (@ (@ tptp.q U) T2) (=> (@ (@ tptp.bval tptp.b) S) (=> (@ (@ _let_1 S) S2) (exists ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (and (@ (@ (@ (@ (@ (@ tptp.relati23543761ar_int tptp.p) tptp.b) tptp.c) tptp.ka) S3) S4) (@ (@ tptp.bval tptp.b) S3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.c) S3)) T) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.c2) S4)) T2))))))))))))) (forall ((C tptp.com) (C2 tptp.com)) (= (forall ((S5 (-> tptp.list_char tptp.int)) (T3 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S5)) T3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S5)) T3))) (forall ((S5 (-> tptp.list_char tptp.int)) (T3 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S5)) T3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S5)) T3))))) (forall ((C tptp.com) (S6 (-> tptp.list_char tptp.int)) (T4 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S6)) T4))) (= _let_1 _let_1))) (@ (@ tptp.q tptp.u) tptp.t) (forall ((P_1 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q_1 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P_2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (Q_2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid P_1) C) C2) Q_1) (=> (@ (@ (@ (@ tptp.relati775585786_valid P_2) C) C2) Q_2) (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (or (@ (@ P_1 S5) S7) (@ (@ P_2 S5) S7)))) C) C2) (lambda ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (or (@ (@ Q_1 T3) T5) (@ (@ Q_2 T3) T5))))))) (@ (@ (@ (@ tptp.relati775585786_valid _let_4) _let_2) tptp.c2) tptp.q) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (Q2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid P) C) C2) Q) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (=> (@ (@ P S3) S4) (@ (@ P2 S3) S4))) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (=> (@ (@ Q2 S3) S4) (@ (@ Q S3) S4))) (@ (@ (@ (@ tptp.relati775585786_valid P2) C) C2) Q2))))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (K tptp.nat) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ tptp.while B) C))) (let ((_let_2 (@ (@ (@ tptp.relati23543761ar_int P) B) C))) (=> (@ (@ (@ (@ tptp.relati775585786_valid (@ _let_2 (@ tptp.suc K))) _let_1) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid (@ _let_2 K)) _let_1) C2) Q))))) (forall ((B tptp.bexp) (C tptp.com) (S (-> tptp.list_char tptp.int)) (T (-> tptp.list_char tptp.int)) (C2 tptp.com)) (let ((_let_1 (@ tptp.while B))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ _let_1 C)) S)) T) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (T6 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S3)) T6) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S3)) T6))) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ _let_1 C2)) S)) T))))) (forall ((C tptp.com) (C2 tptp.com) (B tptp.bexp)) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (T6 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S3)) T6) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S3)) T6))) (forall ((S6 (-> tptp.list_char tptp.int)) (T4 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.while B))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ _let_1 C)) S6)) T4) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ _let_1 C2)) S6)) T4)))))) (= tptp.relati775585786_valid (lambda ((P3 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C3 tptp.com) (C4 tptp.com) (Q3 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (forall ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (=> (@ (@ Q3 T3) T5) (exists ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P3 S5) S7) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C3) S5)) T3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C4) S7)) T5))))))) (forall ((B tptp.bexp) (S (-> tptp.list_char tptp.int)) (C tptp.com)) (=> (not (@ (@ tptp.bval B) S)) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)) S)) S))) (forall ((B tptp.bexp) (S_1 (-> tptp.list_char tptp.int)) (C tptp.com) (S_2 (-> tptp.list_char tptp.int)) (S_3 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)))) (=> (@ (@ tptp.bval B) S_1) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S_1)) S_2) (=> (@ (@ tptp.big_big_step (@ _let_1 S_2)) S_3) (@ (@ tptp.big_big_step (@ _let_1 S_1)) S_3)))))) (forall ((B tptp.bexp) (C tptp.com) (S (-> tptp.list_char tptp.int)) (T (-> tptp.list_char tptp.int))) (let ((_let_1 (@ (@ tptp.bval B) S))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)) S)) T) (=> (=> (= T S) _let_1) (not (=> _let_1 (forall ((S_22 (-> tptp.list_char tptp.int))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S)) S_22) (not (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)) S_22)) T)))))))))) (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Prod tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A3) B3))) (@ P Prod))) (forall ((P (-> tptp.produc1260470173ar_int Bool)) (Prod tptp.produc1260470173ar_int)) (=> (forall ((A3 tptp.com) (B3 (-> tptp.list_char tptp.int))) (@ P (@ (@ tptp.produc1193801173ar_int A3) B3))) (@ P Prod))) (forall ((Y tptp.product_prod_nat_nat)) (not (forall ((A3 tptp.nat) (B3 tptp.nat)) (not (= Y (@ (@ tptp.product_Pair_nat_nat A3) B3)))))) (forall ((Y tptp.produc1260470173ar_int)) (not (forall ((A3 tptp.com) (B3 (-> tptp.list_char tptp.int))) (not (= Y (@ (@ tptp.produc1193801173ar_int A3) B3)))))) (forall ((A tptp.nat) (B tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))) (forall ((A tptp.com) (B (-> tptp.list_char tptp.int)) (A2 tptp.com) (B2 (-> tptp.list_char tptp.int))) (=> (= (@ (@ tptp.produc1193801173ar_int A) B) (@ (@ tptp.produc1193801173ar_int A2) B2)) (not (=> (= A A2) (not (= B B2)))))) (forall ((P (-> tptp.product_prod_nat_nat Bool)) (P4 tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A3) B3))) (@ P P4))) (forall ((P (-> tptp.produc1260470173ar_int Bool)) (P4 tptp.produc1260470173ar_int)) (=> (forall ((A3 tptp.com) (B3 (-> tptp.list_char tptp.int))) (@ P (@ (@ tptp.produc1193801173ar_int A3) B3))) (@ P P4))) (forall ((A tptp.produc1260470173ar_int) (P (-> tptp.produc1260470173ar_int Bool))) (= (@ (@ tptp.member92250950ar_int A) (@ tptp.collec770796680ar_int P)) (@ P A))) (forall ((A4 tptp.set_Pr1148378109ar_int)) (= (@ tptp.collec770796680ar_int (lambda ((X tptp.produc1260470173ar_int)) (@ (@ tptp.member92250950ar_int X) A4))) A4)) (forall ((P4 tptp.product_prod_nat_nat)) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (= P4 (@ (@ tptp.product_Pair_nat_nat X3) Y3)))) (forall ((P4 tptp.produc1260470173ar_int)) (exists ((X3 tptp.com) (Y3 (-> tptp.list_char tptp.int))) (= P4 (@ (@ tptp.produc1193801173ar_int X3) Y3)))) (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))) (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X4) (@ tptp.suc Y)) (= X4 Y))) (forall ((C tptp.com) (S (-> tptp.list_char tptp.int)) (T (-> tptp.list_char tptp.int)) (U (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S)))) (=> (@ _let_1 T) (=> (@ _let_1 U) (= U T))))) (forall ((C tptp.com) (C2 tptp.com) (C5 tptp.com)) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (T6 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S3)) T6) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S3)) T6))) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (T6 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S3)) T6) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C5) S3)) T6))) (forall ((S6 (-> tptp.list_char tptp.int)) (T4 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S6)) T4) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C5) S6)) T4)))))) (forall ((X51 tptp.bexp) (X52 tptp.com) (Y51 tptp.bexp) (Y52 tptp.com)) (= (= (@ (@ tptp.while X51) X52) (@ (@ tptp.while Y51) Y52)) (and (= X51 Y51) (= X52 Y52)))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com)) (=> (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (not (@ (@ tptp.bval B) S5))))) tptp.skip) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid P) (@ (@ tptp.while B) C)) C2) Q))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ tptp.while B) C))) (=> (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (@ (@ tptp.bval B) S5)))) (@ (@ tptp.seq C) _let_1)) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid P) _let_1) C2) Q)))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (N tptp.nat)) (= (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) (@ tptp.suc N)) (lambda ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (exists ((S5 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S5)) T3) (@ (@ tptp.bval B) S5) (@ (@ (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) N) S5) T5)))))) (forall ((Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C2 tptp.com)) (=> (forall ((T6 (-> tptp.list_char tptp.int)) (T7 (-> tptp.list_char tptp.int))) (=> (@ (@ Q T6) T7) (exists ((S8 (-> tptp.list_char tptp.int))) (and (@ (@ P T6) S8) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S8)) T7))))) (@ (@ (@ (@ tptp.relati775585786_valid P) tptp.skip) C2) Q))) (forall ((P (-> tptp.nat (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (K tptp.nat) (B tptp.bexp) (C tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C2 tptp.com) (T (-> tptp.list_char tptp.int)) (T2 (-> tptp.list_char tptp.int))) (=> (forall ((N2 tptp.nat) (T6 (-> tptp.list_char tptp.int)) (T7 (-> tptp.list_char tptp.int))) (=> (@ (@ (@ P (@ (@ tptp.plus_plus_nat K) (@ tptp.suc N2))) T6) T7) (exists ((S6 (-> tptp.list_char tptp.int))) (and (@ (@ (@ P (@ (@ tptp.plus_plus_nat K) N2)) S6) T7) (@ (@ tptp.bval B) S6) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S6)) T6))))) (=> (forall ((T6 (-> tptp.list_char tptp.int)) (T7 (-> tptp.list_char tptp.int))) (=> (@ (@ Q T6) T7) (exists ((S6 (-> tptp.list_char tptp.int)) (S8 (-> tptp.list_char tptp.int))) (and (exists ((N3 tptp.nat)) (@ (@ (@ P (@ (@ tptp.plus_plus_nat K) N3)) S6) S8)) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)) S6)) T6) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S8)) T7))))) (=> (@ (@ Q T) T2) (exists ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (and (@ (@ (@ P K) S3) S4) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)) S3)) T) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S4)) T2))))))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C2 tptp.com) (C tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid (@ tptp.relati186416454e_flip P)) C2) C) (@ tptp.relati186416454e_flip Q)) (@ (@ (@ (@ tptp.relati775585786_valid P) C) C2) Q))) (forall ((R tptp.set_Pr1986765409at_nat) (S9 tptp.set_Pr1986765409at_nat)) (= (= (lambda ((X tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X) Y4)) R)) (lambda ((X tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X) Y4)) S9))) (= R S9))) (forall ((R tptp.set_Pr1148378109ar_int) (S9 tptp.set_Pr1148378109ar_int)) (= (= (lambda ((X tptp.com) (Y4 (-> tptp.list_char tptp.int))) (@ (@ tptp.member92250950ar_int (@ (@ tptp.produc1193801173ar_int X) Y4)) R)) (lambda ((X tptp.com) (Y4 (-> tptp.list_char tptp.int))) (@ (@ tptp.member92250950ar_int (@ (@ tptp.produc1193801173ar_int X) Y4)) S9))) (= R S9))) (forall ((X31 tptp.com) (X32 tptp.com) (Y31 tptp.com) (Y32 tptp.com)) (= (= (@ (@ tptp.seq X31) X32) (@ (@ tptp.seq Y31) Y32)) (and (= X31 Y31) (= X32 Y32)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ tptp.suc (@ _let_1 N))))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (D tptp.com) (D2 tptp.com) (R (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ tptp.relati775585786_valid P))) (=> (@ (@ (@ _let_1 C) C2) Q) (=> (@ (@ (@ (@ tptp.relati775585786_valid Q) D) D2) R) (@ (@ (@ _let_1 (@ (@ tptp.seq C) D)) (@ (@ tptp.seq C2) D2)) R))))) (forall ((S2 (-> tptp.list_char tptp.int)) (T2 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.skip) S2)) T2) (= S2 T2))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (D tptp.com) (C2 tptp.com) (R (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ tptp.relati775585786_valid P))) (=> (@ (@ (@ _let_1 C) tptp.skip) Q) (=> (@ (@ (@ (@ tptp.relati775585786_valid Q) D) C2) R) (@ (@ (@ _let_1 (@ (@ tptp.seq C) D)) C2) R))))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (D tptp.com) (R (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ tptp.relati775585786_valid P))) (=> (@ (@ (@ _let_1 C) C2) Q) (=> (@ (@ (@ (@ tptp.relati775585786_valid Q) D) tptp.skip) R) (@ (@ (@ _let_1 (@ (@ tptp.seq C) D)) C2) R))))) (forall ((X31 tptp.com) (X32 tptp.com)) (not (= tptp.skip (@ (@ tptp.seq X31) X32)))) (forall ((X31 tptp.com) (X32 tptp.com) (X51 tptp.bexp) (X52 tptp.com)) (not (= (@ (@ tptp.seq X31) X32) (@ (@ tptp.while X51) X52)))) (forall ((X51 tptp.bexp) (X52 tptp.com)) (not (= tptp.skip (@ (@ tptp.while X51) X52)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))) (forall ((A4 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A4 (@ _let_1 A)) (= (@ tptp.suc A4) (@ _let_1 (@ tptp.suc A)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C1 tptp.com) (C22 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid P) (@ (@ tptp.seq C1) C22)) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (exists ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C1) S5)) T3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S7)) T5) (exists ((U2 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C22) T3)) U2) (@ (@ Q U2) T5))))))) C22) tptp.skip) Q))) (= tptp.relati186416454e_flip (lambda ((P3 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (@ (@ P3 S7) S5))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C1 tptp.com) (C22 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ tptp.relati775585786_valid P))) (=> (@ (@ (@ _let_1 (@ (@ tptp.seq C1) C22)) C2) Q) (@ (@ (@ _let_1 C1) C2) (lambda ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (exists ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C1) S5)) T3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S7)) T5) (exists ((U2 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C22) T3)) U2) (@ (@ Q U2) T5)))))))))) (forall ((C1 tptp.com) (C22 tptp.com) (S1 (-> tptp.list_char tptp.int)) (S32 (-> tptp.list_char tptp.int))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.seq C1) C22)) S1)) S32) (not (forall ((S_22 (-> tptp.list_char tptp.int))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C1) S1)) S_22) (not (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C22) S_22)) S32))))))) (forall ((C1 tptp.com) (C22 tptp.com) (C32 tptp.com) (S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.seq C1))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.seq (@ _let_1 C22)) C32)) S)) S2) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ _let_1 (@ (@ tptp.seq C22) C32))) S)) S2)))) (forall ((C_1 tptp.com) (S_1 (-> tptp.list_char tptp.int)) (S_2 (-> tptp.list_char tptp.int)) (C_2 tptp.com) (S_3 (-> tptp.list_char tptp.int))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C_1) S_1)) S_2) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C_2) S_2)) S_3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.seq C_1) C_2)) S_1)) S_3)))) (forall ((S (-> tptp.list_char tptp.int)) (T (-> tptp.list_char tptp.int))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.skip) S)) T) (= T S))) (forall ((S (-> tptp.list_char tptp.int))) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.skip) S)) S)) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ (@ (@ tptp.relati775585786_valid P) C) C2))) (=> (@ _let_1 Q) (@ _let_1 (lambda ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (and (@ (@ Q S) S2) (exists ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S5)) T3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S7)) T5))))))))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (K tptp.nat) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) K)) (@ (@ tptp.while B) C)) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) K) S5) S7) (@ (@ tptp.bval B) S5)))) C) tptp.skip) (lambda ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (and (@ (@ (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) (@ tptp.suc K)) T3) T5) (exists ((U2 (-> tptp.list_char tptp.int)) (U3 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)) T3)) U2) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) T5)) U3) (@ (@ Q U2) U3)))))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C1 tptp.com) (C22 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid P) (@ (@ (@ tptp.if B) C1) C22)) C2) Q) (and (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (@ (@ tptp.bval B) S5)))) C1) C2) (lambda ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (and (@ (@ Q T3) T5) (exists ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C1) S5)) T3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S7)) T5) (@ (@ tptp.bval B) S5)))))) (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (not (@ (@ tptp.bval B) S5))))) C22) C2) (lambda ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (and (@ (@ Q T3) T5) (exists ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C22) S5)) T3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S7)) T5) (not (@ (@ tptp.bval B) S5)))))))))) (forall ((B tptp.bexp) (C tptp.com) (S6 (-> tptp.list_char tptp.int)) (T4 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ (@ tptp.while B) C))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int _let_1) S6)) T4) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ (@ tptp.if B) (@ (@ tptp.seq C) _let_1)) tptp.skip)) S6)) T4)))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C_1 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C_2 tptp.com)) (=> (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((A5 (-> tptp.list_char tptp.int)) (C3 (-> tptp.list_char tptp.int))) (and (@ (@ P A5) C3) (@ (@ tptp.bval B) A5)))) C_1) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid P) (@ (@ (@ tptp.if B) C_1) C_2)) C2) Q))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C_2 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C_1 tptp.com)) (=> (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((A5 (-> tptp.list_char tptp.int)) (C3 (-> tptp.list_char tptp.int))) (and (@ (@ P A5) C3) (not (@ (@ tptp.bval B) A5))))) C_2) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid P) (@ (@ (@ tptp.if B) C_1) C_2)) C2) Q))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ tptp.while B) C))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (@ (@ tptp.bval B) S5)))) (@ (@ tptp.seq C) _let_1)) C2) Q) (@ (@ (@ (@ tptp.relati2102071307_hoare P) _let_1) C2) Q)))) (forall ((X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com) (Y41 tptp.bexp) (Y42 tptp.com) (Y43 tptp.com)) (= (= (@ (@ (@ tptp.if X41) X42) X43) (@ (@ (@ tptp.if Y41) Y42) Y43)) (and (= X41 Y41) (= X42 Y42) (= X43 Y43)))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (@ (@ (@ (@ tptp.relati2102071307_hoare P) tptp.skip) tptp.skip) P)) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (= (@ (@ (@ (@ tptp.relati2102071307_hoare P) tptp.skip) tptp.skip) Q) (forall ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (=> (@ (@ Q S5) S7) (@ (@ P S5) S7))))) (forall ((P_1 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q_1 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P_2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (Q_2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare P_1) C) C2) Q_1) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare P_2) C) C2) Q_2) (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (or (@ (@ P_1 S5) S7) (@ (@ P_2 S5) S7)))) C) C2) (lambda ((T3 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (or (@ (@ Q_1 T3) T5) (@ (@ Q_2 T3) T5))))))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare P) C) C2) Q) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (=> (@ (@ P S3) S4) (@ (@ P2 S3) S4))) (@ (@ (@ (@ tptp.relati2102071307_hoare P2) C) C2) Q)))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (Q2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ (@ tptp.relati2102071307_hoare P) C) C2))) (=> (@ _let_1 Q) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (=> (@ (@ Q2 S3) S4) (@ (@ Q S3) S4))) (@ _let_1 Q2))))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (Q2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare P) C) C2) Q) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (=> (@ (@ P S3) S4) (@ (@ P2 S3) S4))) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (=> (@ (@ Q2 S3) S4) (@ (@ Q S3) S4))) (@ (@ (@ (@ tptp.relati2102071307_hoare P2) C) C2) Q2))))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C_2 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C_1 tptp.com)) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (not (@ (@ tptp.bval B) S5))))) C_2) C2) Q) (@ (@ (@ (@ tptp.relati2102071307_hoare P) (@ (@ (@ tptp.if B) C_1) C_2)) C2) Q))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C_1 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C_2 tptp.com)) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (@ (@ tptp.bval B) S5)))) C_1) C2) Q) (@ (@ (@ (@ tptp.relati2102071307_hoare P) (@ (@ (@ tptp.if B) C_1) C_2)) C2) Q))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare P) C) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid P) C) C2) Q))) (forall ((X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com) (X51 tptp.bexp) (X52 tptp.com)) (not (= (@ (@ (@ tptp.if X41) X42) X43) (@ (@ tptp.while X51) X52)))) (forall ((X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com)) (not (= tptp.skip (@ (@ (@ tptp.if X41) X42) X43)))) (forall ((X31 tptp.com) (X32 tptp.com) (X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com)) (not (= (@ (@ tptp.seq X31) X32) (@ (@ (@ tptp.if X41) X42) X43)))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare (@ tptp.relati186416454e_flip P)) C) C2) (@ tptp.relati186416454e_flip Q)) (@ (@ (@ (@ tptp.relati2102071307_hoare P) C2) C) Q))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (D tptp.com) (R (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ tptp.relati2102071307_hoare P))) (=> (@ (@ (@ _let_1 C) C2) Q) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare Q) D) tptp.skip) R) (@ (@ (@ _let_1 (@ (@ tptp.seq C) D)) C2) R))))) (forall ((B1 tptp.bexp) (B22 tptp.bexp) (C11 tptp.com) (C12 tptp.com) (C22 tptp.com) (S6 (-> tptp.list_char tptp.int)) (T4 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.if B1))) (let ((_let_2 (@ tptp.if B22))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ _let_1 (@ (@ _let_2 C11) C12)) C22)) S6)) T4) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ _let_2 (@ (@ _let_1 C11) C22)) (@ (@ _let_1 C12) C22))) S6)) T4))))) (forall ((B tptp.bexp) (C tptp.com) (S6 (-> tptp.list_char tptp.int)) (T4 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ (@ tptp.if B) C) C)) S6)) T4) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S6)) T4))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((A4 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A4) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))) (forall ((B4 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))) (= tptp.plus_plus_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ tptp.plus_plus_nat B5) A5))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))) (forall ((Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C2 tptp.com)) (=> (forall ((T6 (-> tptp.list_char tptp.int)) (T7 (-> tptp.list_char tptp.int))) (=> (@ (@ Q T6) T7) (exists ((S8 (-> tptp.list_char tptp.int))) (and (@ (@ P T6) S8) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S8)) T7))))) (@ (@ (@ (@ tptp.relati2102071307_hoare P) tptp.skip) C2) Q))) (forall ((B tptp.bexp) (S (-> tptp.list_char tptp.int)) (C_2 tptp.com) (T (-> tptp.list_char tptp.int)) (C_1 tptp.com)) (=> (not (@ (@ tptp.bval B) S)) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C_2) S)) T) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ (@ tptp.if B) C_1) C_2)) S)) T)))) (forall ((B tptp.bexp) (S (-> tptp.list_char tptp.int)) (C_1 tptp.com) (T (-> tptp.list_char tptp.int)) (C_2 tptp.com)) (=> (@ (@ tptp.bval B) S) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C_1) S)) T) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ (@ tptp.if B) C_1) C_2)) S)) T)))) (forall ((B tptp.bexp) (C1 tptp.com) (C22 tptp.com) (S (-> tptp.list_char tptp.int)) (T (-> tptp.list_char tptp.int))) (let ((_let_1 (@ (@ tptp.bval B) S))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ (@ tptp.if B) C1) C22)) S)) T) (=> (=> _let_1 (not (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C1) S)) T))) (not (=> (not _let_1) (not (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C22) S)) T)))))))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com)) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) S7) (not (@ (@ tptp.bval B) S5))))) tptp.skip) C2) Q) (@ (@ (@ (@ tptp.relati2102071307_hoare P) (@ (@ tptp.while B) C)) C2) Q))) (forall ((Y tptp.com)) (=> (not (= Y tptp.skip)) (=> (forall ((X21 tptp.list_char) (X22 tptp.aexp)) (not (= Y (@ (@ tptp.assign X21) X22)))) (=> (forall ((X312 tptp.com) (X322 tptp.com)) (not (= Y (@ (@ tptp.seq X312) X322)))) (=> (forall ((X412 tptp.bexp) (X422 tptp.com) (X432 tptp.com)) (not (= Y (@ (@ (@ tptp.if X412) X422) X432)))) (not (forall ((X512 tptp.bexp) (X522 tptp.com)) (not (= Y (@ (@ tptp.while X512) X522)))))))))) (forall ((P (-> tptp.com Bool)) (Com tptp.com)) (=> (@ P tptp.skip) (=> (forall ((X12 tptp.list_char) (X23 tptp.aexp)) (@ P (@ (@ tptp.assign X12) X23))) (=> (forall ((X12 tptp.com) (X23 tptp.com)) (=> (@ P X12) (=> (@ P X23) (@ P (@ (@ tptp.seq X12) X23))))) (=> (forall ((X12 tptp.bexp) (X23 tptp.com) (X33 tptp.com)) (=> (@ P X23) (=> (@ P X33) (@ P (@ (@ (@ tptp.if X12) X23) X33))))) (=> (forall ((X12 tptp.bexp) (X23 tptp.com)) (=> (@ P X23) (@ P (@ (@ tptp.while X12) X23)))) (@ P Com))))))) (= tptp.bNF_Gr202451329ar_int (lambda ((A6 tptp.set_Pr1148378109ar_int) (F (-> tptp.produc1260470173ar_int tptp.com)) (G (-> tptp.produc1260470173ar_int tptp.list_char tptp.int))) (@ tptp.collec770796680ar_int (lambda ((Uu tptp.produc1260470173ar_int)) (exists ((A5 tptp.produc1260470173ar_int)) (and (= Uu (@ (@ tptp.produc1193801173ar_int (@ F A5)) (@ G A5))) (@ (@ tptp.member92250950ar_int A5) A6))))))) (= tptp.bNF_Gr749752805at_nat (lambda ((A6 tptp.set_Pr1148378109ar_int) (F (-> tptp.produc1260470173ar_int tptp.nat)) (G (-> tptp.produc1260470173ar_int tptp.nat))) (@ tptp.collec7649004at_nat (lambda ((Uu tptp.product_prod_nat_nat)) (exists ((A5 tptp.produc1260470173ar_int)) (and (= Uu (@ (@ tptp.product_Pair_nat_nat (@ F A5)) (@ G A5))) (@ (@ tptp.member92250950ar_int A5) A6))))))) (forall ((P (-> tptp.nat (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ tptp.while B) C))) (=> (forall ((N2 tptp.nat)) (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ (@ P N2) S5) S7) (@ (@ tptp.bval B) S5)))) C) tptp.skip) (@ P (@ tptp.suc N2)))) (=> (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (exists ((N4 tptp.nat)) (@ (@ (@ P N4) S5) S7)))) _let_1) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid (@ P tptp.zero_zero_nat)) _let_1) C2) Q))))) (forall ((X212 tptp.list_char) (X222 tptp.aexp) (Y21 tptp.list_char) (Y22 tptp.aexp)) (= (= (@ (@ tptp.assign X212) X222) (@ (@ tptp.assign Y21) Y22)) (and (= X212 Y21) (= X222 Y22)))) (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)) (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))) (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))) (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))) (forall ((X4 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X4) Y) tptp.zero_zero_nat) (and (= X4 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))) (forall ((X4 tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X4) Y)) (and (= X4 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)) (forall ((X4 tptp.nat)) (= (= tptp.zero_zero_nat X4) (= X4 tptp.zero_zero_nat))) (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)) (forall ((X2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X2)))) (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))) (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))) (forall ((Nat tptp.nat) (X2 tptp.nat)) (=> (= Nat (@ tptp.suc X2)) (not (= Nat tptp.zero_zero_nat)))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (@ P (@ tptp.suc N2)))) (@ P N)))) (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (@ (@ P X3) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P X3) Y3) (@ (@ P (@ tptp.suc X3)) (@ tptp.suc Y3)))) (@ (@ P M) N))))) (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N2 tptp.nat)) (=> (@ P (@ tptp.suc N2)) (@ P N2))) (@ P tptp.zero_zero_nat)))) (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))) (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))) (forall ((P (-> tptp.nat Bool)) (Nat tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((Nat3 tptp.nat)) (=> (@ P Nat3) (@ P (@ tptp.suc Nat3)))) (@ P Nat)))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M2 tptp.nat)) (= N (@ tptp.suc M2))))) (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)) (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))) (forall ((B tptp.com) (F2 (-> tptp.produc1260470173ar_int tptp.com)) (X4 tptp.produc1260470173ar_int) (C (-> tptp.list_char tptp.int)) (G2 (-> tptp.produc1260470173ar_int tptp.list_char tptp.int)) (A4 tptp.set_Pr1148378109ar_int)) (=> (= B (@ F2 X4)) (=> (= C (@ G2 X4)) (=> (@ (@ tptp.member92250950ar_int X4) A4) (@ (@ tptp.member92250950ar_int (@ (@ tptp.produc1193801173ar_int B) C)) (@ (@ (@ tptp.bNF_Gr202451329ar_int A4) F2) G2)))))) (forall ((B tptp.nat) (F2 (-> tptp.produc1260470173ar_int tptp.nat)) (X4 tptp.produc1260470173ar_int) (C tptp.nat) (G2 (-> tptp.produc1260470173ar_int tptp.nat)) (A4 tptp.set_Pr1148378109ar_int)) (=> (= B (@ F2 X4)) (=> (= C (@ G2 X4)) (=> (@ (@ tptp.member92250950ar_int X4) A4) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat B) C)) (@ (@ (@ tptp.bNF_Gr749752805at_nat A4) F2) G2)))))) (forall ((X212 tptp.list_char) (X222 tptp.aexp) (X51 tptp.bexp) (X52 tptp.com)) (not (= (@ (@ tptp.assign X212) X222) (@ (@ tptp.while X51) X52)))) (forall ((X212 tptp.list_char) (X222 tptp.aexp)) (not (= tptp.skip (@ (@ tptp.assign X212) X222)))) (forall ((X212 tptp.list_char) (X222 tptp.aexp) (X31 tptp.com) (X32 tptp.com)) (not (= (@ (@ tptp.assign X212) X222) (@ (@ tptp.seq X31) X32)))) (forall ((X212 tptp.list_char) (X222 tptp.aexp) (X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com)) (not (= (@ (@ tptp.assign X212) X222) (@ (@ (@ tptp.if X41) X42) X43)))) (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com)) (= (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) tptp.zero_zero_nat) P)) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N) _let_1) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))) (forall ((P (-> tptp.nat (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ tptp.while B) C))) (=> (forall ((N2 tptp.nat)) (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (and (@ (@ (@ P N2) S5) S7) (@ (@ tptp.bval B) S5)))) C) tptp.skip) (@ P (@ tptp.suc N2)))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S5 (-> tptp.list_char tptp.int)) (S7 (-> tptp.list_char tptp.int))) (exists ((N4 tptp.nat)) (@ (@ (@ P N4) S5) S7)))) _let_1) C2) Q) (@ (@ (@ (@ tptp.relati2102071307_hoare (@ P tptp.zero_zero_nat)) _let_1) C2) Q))))) (forall ((X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com)) (= (@ tptp.size_com (@ (@ (@ tptp.if X41) X42) X43)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.size_com X42)) (@ tptp.size_com X43))) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X31 tptp.com) (X32 tptp.com)) (= (@ tptp.size_com (@ (@ tptp.seq X31) X32)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.size_com X31)) (@ tptp.size_com X32))) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X51 tptp.bexp) (X52 tptp.com)) (= (@ tptp.size_com (@ (@ tptp.while X51) X52)) (@ (@ tptp.plus_plus_nat (@ tptp.size_com X52)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com)) (= (@ tptp.size_size_com (@ (@ (@ tptp.if X41) X42) X43)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.size_size_com X42)) (@ tptp.size_size_com X43))) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X4 tptp.com) (Y tptp.com)) (=> (not (= (@ tptp.size_size_com X4) (@ tptp.size_size_com Y))) (not (= X4 Y)))) (forall ((X4 tptp.typerep) (Y tptp.typerep)) (=> (not (= (@ tptp.size_size_typerep X4) (@ tptp.size_size_typerep Y))) (not (= X4 Y)))) (= (@ tptp.size_size_com tptp.skip) tptp.zero_zero_nat) (forall ((X212 tptp.list_char) (X222 tptp.aexp)) (= (@ tptp.size_size_com (@ (@ tptp.assign X212) X222)) tptp.zero_zero_nat)) (= (@ tptp.size_com tptp.skip) tptp.zero_zero_nat) (forall ((X212 tptp.list_char) (X222 tptp.aexp)) (= (@ tptp.size_com (@ (@ tptp.assign X212) X222)) tptp.zero_zero_nat)) (forall ((X51 tptp.bexp) (X52 tptp.com)) (= (@ tptp.size_size_com (@ (@ tptp.while X51) X52)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_com X52)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X31 tptp.com) (X32 tptp.com)) (= (@ tptp.size_size_com (@ (@ tptp.seq X31) X32)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.size_size_com X31)) (@ tptp.size_size_com X32))) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ P A3) B3) (@ (@ P B3) A3))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) tptp.zero_zero_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ P A3))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.plus_plus_nat A3) B3))))) (@ (@ P A) B))))) (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)) (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))) (= tptp.bNF_Gr1247133574at_nat (lambda ((R2 tptp.set_Pr1986765409at_nat) (F (-> tptp.nat tptp.nat))) (@ tptp.collec7649004at_nat (lambda ((Uu tptp.product_prod_nat_nat)) (exists ((A1 tptp.nat) (A22 tptp.nat)) (and (= Uu (@ (@ tptp.product_Pair_nat_nat (@ F A1)) (@ F A22))) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A1) A22)) R2))))))) (= tptp.bNF_Gr1143394412nt_nat (lambda ((A6 tptp.set_Pr1148378109ar_int) (R2 tptp.set_Pr1986765409at_nat) (F (-> tptp.produc1260470173ar_int tptp.nat))) (@ tptp.collec1834387154ar_int (lambda ((Uu tptp.produc1346207591ar_int)) (exists ((A1 tptp.produc1260470173ar_int) (A22 tptp.produc1260470173ar_int)) (and (= Uu (@ (@ tptp.produc317451735ar_int A1) A22)) (@ (@ tptp.member92250950ar_int A1) A6) (@ (@ tptp.member92250950ar_int A22) A6) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat (@ F A1)) (@ F A22))) R2))))))) (= tptp.bNF_Gr808751971at_nat (lambda ((A6 tptp.set_nat) (R2 tptp.set_Pr1986765409at_nat) (F (-> tptp.nat tptp.nat))) (@ tptp.collec7649004at_nat (lambda ((Uu tptp.product_prod_nat_nat)) (exists ((A1 tptp.nat) (A22 tptp.nat)) (and (= Uu (@ (@ tptp.product_Pair_nat_nat A1) A22)) (@ (@ tptp.member_nat A1) A6) (@ (@ tptp.member_nat A22) A6) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat (@ F A1)) (@ F A22))) R2))))))) (forall ((Q4 tptp.nat) (R3 tptp.nat)) (= (@ tptp.unique1592618082ux_nat (@ (@ tptp.product_Pair_nat_nat Q4) R3)) (= R3 tptp.zero_zero_nat))) (= tptp.zero_zero_nat tptp.zero_zero_nat) (forall ((X4 tptp.typerep)) (not (= (@ tptp.size_size_typerep X4) tptp.zero_zero_nat))) (forall ((R3 tptp.nat) (S tptp.nat) (R tptp.set_Pr1986765409at_nat) (S2 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat R3))) (=> (@ (@ tptp.member701585322at_nat (@ _let_1 S)) R) (=> (= S2 S) (@ (@ tptp.member701585322at_nat (@ _let_1 S2)) R))))) (forall ((R3 tptp.com) (S (-> tptp.list_char tptp.int)) (R tptp.set_Pr1148378109ar_int) (S2 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.produc1193801173ar_int R3))) (=> (@ (@ tptp.member92250950ar_int (@ _let_1 S)) R) (=> (= S2 S) (@ (@ tptp.member92250950ar_int (@ _let_1 S2)) R))))) (forall ((X1 tptp.literal) (X2 tptp.list_typerep)) (= (@ tptp.size_size_typerep (@ (@ tptp.typerep2 X1) X2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_typerep tptp.size_size_typerep) X2)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X1 tptp.literal) (X2 tptp.list_typerep)) (= (@ tptp.size_typerep (@ (@ tptp.typerep2 X1) X2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_typerep tptp.size_typerep) X2)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X4 (-> tptp.typerep tptp.nat)) (X212 tptp.typerep) (X222 tptp.list_typerep)) (let ((_let_1 (@ tptp.size_list_typerep X4))) (= (@ _let_1 (@ (@ tptp.cons_typerep X212) X222)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ X4 X212)) (@ _let_1 X222))) (@ tptp.suc tptp.zero_zero_nat))))) (forall ((Xs tptp.list_typerep) (N tptp.nat)) (= (= (@ tptp.size_s416147576yperep Xs) (@ tptp.suc N)) (exists ((Y4 tptp.typerep) (Ys tptp.list_typerep)) (and (= Xs (@ (@ tptp.cons_typerep Y4) Ys)) (= (@ tptp.size_s416147576yperep Ys) N))))) (forall ((N tptp.nat) (Xs tptp.list_typerep)) (= (= (@ tptp.suc N) (@ tptp.size_s416147576yperep Xs)) (exists ((Y4 tptp.typerep) (Ys tptp.list_typerep)) (and (= Xs (@ (@ tptp.cons_typerep Y4) Ys)) (= (@ tptp.size_s416147576yperep Ys) N))))) (forall ((X4 tptp.typerep) (Xs tptp.list_typerep)) (= (@ tptp.size_s416147576yperep (@ (@ tptp.cons_typerep X4) Xs)) (@ tptp.suc (@ tptp.size_s416147576yperep Xs)))) (forall ((X212 tptp.typerep) (X222 tptp.list_typerep)) (= (@ tptp.size_s416147576yperep (@ (@ tptp.cons_typerep X212) X222)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s416147576yperep X222)) (@ tptp.suc tptp.zero_zero_nat)))) (= tptp.set_Co1954412371ar_int (lambda ((A6 tptp.set_Pr1148378109ar_int) (XS tptp.set_li1762364675ar_int)) (@ tptp.collec672902542ar_int (lambda ((Z tptp.list_P1741976099ar_int)) (exists ((X tptp.produc1260470173ar_int) (Xs2 tptp.list_P1741976099ar_int)) (and (= Z (@ (@ tptp.cons_P1254790739ar_int X) Xs2)) (@ (@ tptp.member92250950ar_int X) A6) (@ (@ tptp.member2052091212ar_int Xs2) XS))))))) (= tptp.set_Cons_typerep (lambda ((A6 tptp.set_typerep) (XS tptp.set_list_typerep)) (@ tptp.collect_list_typerep (lambda ((Z tptp.list_typerep)) (exists ((X tptp.typerep) (Xs2 tptp.list_typerep)) (and (= Z (@ (@ tptp.cons_typerep X) Xs2)) (@ (@ tptp.member_typerep X) A6) (@ (@ tptp.member_list_typerep Xs2) XS))))))) (forall ((X4 tptp.typerep) (Xs tptp.list_typerep) (Y tptp.typerep) (Ys2 tptp.list_typerep) (R3 tptp.set_Pr1097818217yperep)) (let ((_let_1 (@ tptp.lex_typerep R3))) (= (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep (@ (@ tptp.cons_typerep X4) Xs)) (@ (@ tptp.cons_typerep Y) Ys2))) _let_1) (or (and (@ (@ tptp.member100911538yperep (@ (@ tptp.produc2071514689yperep X4) Y)) R3) (= (@ tptp.size_s416147576yperep Xs) (@ tptp.size_s416147576yperep Ys2))) (and (= X4 Y) (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep Xs) Ys2)) _let_1)))))) (forall ((X4 tptp.nat) (Xs tptp.list_nat) (Y tptp.nat) (Ys2 tptp.list_nat) (R3 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.lex_nat R3))) (= (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat (@ (@ tptp.cons_nat X4) Xs)) (@ (@ tptp.cons_nat Y) Ys2))) _let_1) (or (and (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y)) R3) (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys2))) (and (= X4 Y) (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat Xs) Ys2)) _let_1)))))) (forall ((N tptp.nat) (X4 tptp.typerep) (Xs tptp.list_typerep)) (= (@ (@ tptp.gen_length_typerep N) (@ (@ tptp.cons_typerep X4) Xs)) (@ (@ tptp.gen_length_typerep (@ tptp.suc N)) Xs))) (forall ((A tptp.typerep) (X4 tptp.list_typerep) (B tptp.typerep) (Y tptp.list_typerep) (R3 tptp.set_Pr1097818217yperep)) (let ((_let_1 (@ tptp.lexord_typerep R3))) (= (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep (@ (@ tptp.cons_typerep A) X4)) (@ (@ tptp.cons_typerep B) Y))) _let_1) (or (@ (@ tptp.member100911538yperep (@ (@ tptp.produc2071514689yperep A) B)) R3) (and (= A B) (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep X4) Y)) _let_1)))))) (forall ((A tptp.nat) (X4 tptp.list_nat) (B tptp.nat) (Y tptp.list_nat) (R3 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.lexord_nat R3))) (= (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat (@ (@ tptp.cons_nat A) X4)) (@ (@ tptp.cons_nat B) Y))) _let_1) (or (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) R3) (and (= A B) (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat X4) Y)) _let_1)))))) (forall ((R3 tptp.set_Pr1986765409at_nat) (Xs tptp.list_nat)) (=> (forall ((X3 tptp.nat)) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X3) X3)) R3))) (not (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat Xs) Xs)) (@ tptp.lexord_nat R3))))) (forall ((R3 tptp.set_Pr1986765409at_nat) (X4 tptp.list_nat) (Y tptp.list_nat)) (let ((_let_1 (@ tptp.lexord_nat R3))) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (or (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A3) B3)) R3) (= A3 B3) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat B3) A3)) R3))) (or (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat X4) Y)) _let_1) (= X4 Y) (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat Y) X4)) _let_1))))) (= tptp.bNF_Gr457912949yperep (lambda ((Kl tptp.set_list_typerep) (K2 tptp.typerep)) (@ tptp.collect_list_typerep (lambda ((Kl2 tptp.list_typerep)) (@ (@ tptp.member_list_typerep (@ (@ tptp.cons_typerep K2) Kl2)) Kl))))) (forall ((Kl3 tptp.list_typerep) (Kl4 tptp.set_list_typerep) (K tptp.typerep)) (=> (@ (@ tptp.member_list_typerep Kl3) (@ (@ tptp.bNF_Gr457912949yperep Kl4) K)) (@ (@ tptp.member_list_typerep (@ (@ tptp.cons_typerep K) Kl3)) Kl4))) (forall ((Kl4 tptp.set_list_typerep) (K tptp.typerep) (Kl3 tptp.list_typerep)) (= (@ (@ tptp.bNF_Gr1303086585yperep (@ (@ tptp.bNF_Gr457912949yperep Kl4) K)) Kl3) (@ (@ tptp.bNF_Gr1303086585yperep Kl4) (@ (@ tptp.cons_typerep K) Kl3)))) (forall ((X4 tptp.typerep) (Xs tptp.list_typerep) (Y tptp.typerep) (Ys2 tptp.list_typerep) (R3 tptp.set_Pr1097818217yperep)) (let ((_let_1 (@ tptp.listrel1_typerep R3))) (= (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep (@ (@ tptp.cons_typerep X4) Xs)) (@ (@ tptp.cons_typerep Y) Ys2))) _let_1) (or (and (@ (@ tptp.member100911538yperep (@ (@ tptp.produc2071514689yperep X4) Y)) R3) (= Xs Ys2)) (and (= X4 Y) (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep Xs) Ys2)) _let_1)))))) (forall ((X4 tptp.nat) (Xs tptp.list_nat) (Y tptp.nat) (Ys2 tptp.list_nat) (R3 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.listrel1_nat R3))) (= (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat (@ (@ tptp.cons_nat X4) Xs)) (@ (@ tptp.cons_nat Y) Ys2))) _let_1) (or (and (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y)) R3) (= Xs Ys2)) (and (= X4 Y) (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat Xs) Ys2)) _let_1)))))) (forall ((X4 tptp.typerep) (Y tptp.typerep) (R3 tptp.set_Pr1097818217yperep) (Xs tptp.list_typerep)) (=> (@ (@ tptp.member100911538yperep (@ (@ tptp.produc2071514689yperep X4) Y)) R3) (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep (@ (@ tptp.cons_typerep X4) Xs)) (@ (@ tptp.cons_typerep Y) Xs))) (@ tptp.listrel1_typerep R3)))) (forall ((X4 tptp.nat) (Y tptp.nat) (R3 tptp.set_Pr1986765409at_nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y)) R3) (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat (@ (@ tptp.cons_nat X4) Xs)) (@ (@ tptp.cons_nat Y) Xs))) (@ tptp.listrel1_nat R3)))) (forall ((X4 tptp.typerep) (Xs tptp.list_typerep) (Ys2 tptp.list_typerep) (R3 tptp.set_Pr1097818217yperep)) (=> (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep (@ (@ tptp.cons_typerep X4) Xs)) Ys2)) (@ tptp.listrel1_typerep R3)) (=> (forall ((Y3 tptp.typerep)) (=> (= Ys2 (@ (@ tptp.cons_typerep Y3) Xs)) (not (@ (@ tptp.member100911538yperep (@ (@ tptp.produc2071514689yperep X4) Y3)) R3)))) (not (forall ((Zs tptp.list_typerep)) (=> (= Ys2 (@ (@ tptp.cons_typerep X4) Zs)) (not (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep Xs) Zs)) (@ tptp.listrel1_typerep R3))))))))) (forall ((X4 tptp.nat) (Xs tptp.list_nat) (Ys2 tptp.list_nat) (R3 tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat (@ (@ tptp.cons_nat X4) Xs)) Ys2)) (@ tptp.listrel1_nat R3)) (=> (forall ((Y3 tptp.nat)) (=> (= Ys2 (@ (@ tptp.cons_nat Y3) Xs)) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y3)) R3)))) (not (forall ((Zs tptp.list_nat)) (=> (= Ys2 (@ (@ tptp.cons_nat X4) Zs)) (not (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat Xs) Zs)) (@ tptp.listrel1_nat R3))))))))) (forall ((Xs tptp.list_typerep) (Y tptp.typerep) (Ys2 tptp.list_typerep) (R3 tptp.set_Pr1097818217yperep)) (=> (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep Xs) (@ (@ tptp.cons_typerep Y) Ys2))) (@ tptp.listrel1_typerep R3)) (=> (forall ((X3 tptp.typerep)) (=> (= Xs (@ (@ tptp.cons_typerep X3) Ys2)) (not (@ (@ tptp.member100911538yperep (@ (@ tptp.produc2071514689yperep X3) Y)) R3)))) (not (forall ((Zs tptp.list_typerep)) (=> (= Xs (@ (@ tptp.cons_typerep Y) Zs)) (not (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep Zs) Ys2)) (@ tptp.listrel1_typerep R3))))))))) (forall ((Xs tptp.list_nat) (Y tptp.nat) (Ys2 tptp.list_nat) (R3 tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat Xs) (@ (@ tptp.cons_nat Y) Ys2))) (@ tptp.listrel1_nat R3)) (=> (forall ((X3 tptp.nat)) (=> (= Xs (@ (@ tptp.cons_nat X3) Ys2)) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y)) R3)))) (not (forall ((Zs tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat Y) Zs)) (not (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat Zs) Ys2)) (@ tptp.listrel1_nat R3))))))))) (forall ((A tptp.typerep) (B tptp.typerep) (R3 tptp.set_Pr1097818217yperep) (U tptp.list_typerep) (X4 tptp.list_typerep) (Y tptp.list_typerep)) (let ((_let_1 (@ tptp.append_typerep U))) (=> (@ (@ tptp.member100911538yperep (@ (@ tptp.produc2071514689yperep A) B)) R3) (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep (@ _let_1 (@ (@ tptp.cons_typerep A) X4))) (@ _let_1 (@ (@ tptp.cons_typerep B) Y)))) (@ tptp.lexord_typerep R3))))) (forall ((A tptp.nat) (B tptp.nat) (R3 tptp.set_Pr1986765409at_nat) (U tptp.list_nat) (X4 tptp.list_nat) (Y tptp.list_nat)) (let ((_let_1 (@ tptp.append_nat U))) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) R3) (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat (@ _let_1 (@ (@ tptp.cons_nat A) X4))) (@ _let_1 (@ (@ tptp.cons_nat B) Y)))) (@ tptp.lexord_nat R3))))) (forall ((X4 tptp.typerep) (Y tptp.typerep) (R3 tptp.set_Pr1097818217yperep) (Xs tptp.list_typerep) (Us tptp.list_typerep) (Vs tptp.list_typerep) (Ys2 tptp.list_typerep)) (let ((_let_1 (@ tptp.append_typerep Us))) (=> (@ (@ tptp.member100911538yperep (@ (@ tptp.produc2071514689yperep X4) Y)) R3) (=> (= Xs (@ _let_1 (@ (@ tptp.cons_typerep X4) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_typerep Y) Vs))) (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep Xs) Ys2)) (@ tptp.listrel1_typerep R3))))))) (forall ((X4 tptp.nat) (Y tptp.nat) (R3 tptp.set_Pr1986765409at_nat) (Xs tptp.list_nat) (Us tptp.list_nat) (Vs tptp.list_nat) (Ys2 tptp.list_nat)) (let ((_let_1 (@ tptp.append_nat Us))) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y)) R3) (=> (= Xs (@ _let_1 (@ (@ tptp.cons_nat X4) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_nat Y) Vs))) (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat Xs) Ys2)) (@ tptp.listrel1_nat R3))))))) (forall ((Xs tptp.list_typerep) (Ys2 tptp.list_typerep) (Us tptp.list_typerep) (Vs tptp.list_typerep)) (=> (or (= (@ tptp.size_s416147576yperep Xs) (@ tptp.size_s416147576yperep Ys2)) (= (@ tptp.size_s416147576yperep Us) (@ tptp.size_s416147576yperep Vs))) (= (= (@ (@ tptp.append_typerep Xs) Us) (@ (@ tptp.append_typerep Ys2) Vs)) (and (= Xs Ys2) (= Us Vs))))) (forall ((Xs tptp.list_typerep) (Ys2 tptp.list_typerep)) (= (@ tptp.size_s416147576yperep (@ (@ tptp.append_typerep Xs) Ys2)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s416147576yperep Xs)) (@ tptp.size_s416147576yperep Ys2)))) (forall ((F2 (-> tptp.typerep tptp.nat)) (Xs tptp.list_typerep) (Ys2 tptp.list_typerep)) (let ((_let_1 (@ tptp.size_list_typerep F2))) (= (@ _let_1 (@ (@ tptp.append_typerep Xs) Ys2)) (@ (@ tptp.plus_plus_nat (@ _let_1 Xs)) (@ _let_1 Ys2))))) (forall ((Xs tptp.list_typerep) (Zs2 tptp.list_typerep) (Ys2 tptp.list_typerep) (Qs tptp.list_typerep) (R3 tptp.set_Pr1097818217yperep)) (let ((_let_1 (@ tptp.lexord_typerep R3))) (=> (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep (@ (@ tptp.append_typerep Xs) Zs2)) (@ (@ tptp.append_typerep Ys2) Qs))) _let_1) (=> (not (= Xs Ys2)) (=> (= (@ tptp.size_s416147576yperep Xs) (@ tptp.size_s416147576yperep Ys2)) (=> (= (@ tptp.size_s416147576yperep Zs2) (@ tptp.size_s416147576yperep Qs)) (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep Xs) Ys2)) _let_1))))))) (forall ((R3 tptp.set_Pr1097818217yperep) (Xs tptp.list_typerep) (Ys2 tptp.list_typerep) (Zs2 tptp.list_typerep)) (let ((_let_1 (@ tptp.lex_typerep R3))) (let ((_let_2 (@ tptp.append_typerep Xs))) (=> (forall ((X3 tptp.typerep)) (not (@ (@ tptp.member100911538yperep (@ (@ tptp.produc2071514689yperep X3) X3)) R3))) (=> (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep (@ _let_2 Ys2)) (@ _let_2 Zs2))) _let_1) (@ (@ tptp.member1812711762yperep (@ (@ tptp.produc1695567329yperep Ys2) Zs2)) _let_1)))))) (forall ((R3 tptp.set_Pr1986765409at_nat) (Xs tptp.list_nat) (Ys2 tptp.list_nat) (Zs2 tptp.list_nat)) (let ((_let_1 (@ tptp.lex_nat R3))) (let ((_let_2 (@ tptp.append_nat Xs))) (=> (forall ((X3 tptp.nat)) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X3) X3)) R3))) (=> (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat (@ _let_2 Ys2)) (@ _let_2 Zs2))) _let_1) (@ (@ tptp.member1926390090st_nat (@ (@ tptp.produc1625736153st_nat Ys2) Zs2)) _let_1)))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.71/0.91 )
% 0.71/0.91 % SZS output end Proof for ITP166^1
% 0.71/0.91 % cvc5---1.0.5 exiting
% 0.71/0.91 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------