%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : COM162^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 : Wed Feb 25 08:41:48 AM UTC 2026
% Result : Theorem 10.64s 2.98s
% Output : Refutation 10.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COM162^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n004.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 04:15:26 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : COM162^1 : TPTP v9.2.1. Released v7.0.0.
% 0.29/0.45 % Domain : Computing Theory
% 0.29/0.45 % Problem : Binary decision diagram 38
% 0.29/0.45 % Version : [Bla16] axioms : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [OS08] Ortner & Schirmer (2008), BDD Normalisation
% 0.29/0.45 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.29/0.45 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Bla16]
% 0.29/0.45 % Names : bindag__38.p [Bla16]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.00 v9.0.0, 0.33 v8.1.0, 0.00 v7.1.0
% 0.29/0.45 % Syntax : Number of formulae : 473 ( 238 unt; 103 typ; 0 def)
% 0.29/0.45 % Number of atoms : 642 ( 385 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 6 ( 1 avg)
% 0.29/0.45 % Number of connectives : 2965 ( 61 ~; 8 |; 44 &;2665 @)
% 0.29/0.45 % ( 0 <=>; 187 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 18 ( 4 avg)
% 0.29/0.45 % Number of types : 10 ( 9 usr)
% 0.29/0.45 % Number of type conns : 246 ( 246 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 97 ( 94 usr; 8 con; 0-7 aty)
% 0.29/0.45 % Number of variables : 802 ( 43 ^; 673 !; 11 ?; 802 :)
% 0.29/0.45 % ( 75 !>; 0 ?*; 0 @-; 0 @+)
% 0.29/0.45 % SPC : TH1_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.29/0.45 % 2016-07-13 14:44:49.360
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 %----Could-be-implicit typings (16)
% 0.29/0.45 thf(ty_t_BinDag__Mirabelle__rybootvolr_Odag,type,
% 0.29/0.45 binDag_Mirabelle_dag: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Record_Otuple__isomorphism,type,
% 0.29/0.45 tuple_isomorphism: $tType > $tType > $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Code__Numeral_Onatural,type,
% 0.29/0.45 code_natural: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Code__Evaluation_Oterm,type,
% 0.29/0.45 code_term: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Product__Type_Ounit,type,
% 0.29/0.45 product_unit: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Product__Type_Oprod,type,
% 0.29/0.45 product_prod: $tType > $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Typerep_Otyperep,type,
% 0.29/0.45 typerep: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Simpl__Heap_Oref,type,
% 0.29/0.45 simpl_ref: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_String_Oliteral,type,
% 0.29/0.45 literal: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Sum__Type_Osum,type,
% 0.29/0.45 sum_sum: $tType > $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Option_Ooption,type,
% 0.29/0.45 option: $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_List_Olist,type,
% 0.29/0.45 list: $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Set_Oset,type,
% 0.29/0.45 set: $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Num_Onum,type,
% 0.29/0.45 num: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Nat_Onat,type,
% 0.29/0.45 nat: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_itself,type,
% 0.29/0.45 itself: $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 %----Explicit typings (87)
% 0.29/0.45 thf(sy_cl_Enum_Oenum,type,
% 0.29/0.45 enum:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Typerep_Otyperep,type,
% 0.29/0.45 typerep2:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_HOL_Otype,type,
% 0.29/0.45 type:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_HOL_Oequal,type,
% 0.29/0.45 cl_HOL_Oequal:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Code__Evaluation_Oterm__of,type,
% 0.29/0.45 code_term_of:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Nat_Osize,type,
% 0.29/0.45 size:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Oone,type,
% 0.29/0.45 one:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Ozero,type,
% 0.29/0.45 zero:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Num_Onumeral,type,
% 0.29/0.45 numeral:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Fields_Ofield,type,
% 0.29/0.45 field:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Num_Oneg__numeral,type,
% 0.29/0.45 neg_numeral:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Ogroup__add,type,
% 0.29/0.45 group_add:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Omonoid__add,type,
% 0.29/0.45 monoid_add:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Ozero__neq__one,type,
% 0.29/0.45 zero_neq_one:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Nat_Osemiring__char__0,type,
% 0.29/0.45 semiring_char_0:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Divides_Osemiring__div,type,
% 0.29/0.45 semiring_div:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Fields_Odivision__ring,type,
% 0.29/0.45 division_ring:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.29/0.45 semigroup_add:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Osemidom__divide,type,
% 0.29/0.45 semidom_divide:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Ocomm__semiring__1,type,
% 0.29/0.45 comm_semiring_1:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 0.29/0.45 comm_monoid_add:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Fields_Olinordered__field,type,
% 0.29/0.45 linordered_field:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.29/0.45 ab_semigroup_add:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Quickcheck__Random_Orandom,type,
% 0.29/0.45 quickcheck_random:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Divides_Osemiring__div__parity,type,
% 0.29/0.45 semiring_div_parity:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.29/0.45 cancel_semigroup_add:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.29/0.45 cancel1352612707id_add:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 0.29/0.45 linord219039673up_add:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.29/0.45 ordere779506340up_add:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.29/0.45 canoni770627133id_add:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
% 0.29/0.45 semiri456707255roduct:
% 0.29/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_BNF__Greatest__Fixpoint_OShift,type,
% 0.29/0.45 bNF_Greatest_Shift:
% 0.29/0.45 !>[A: $tType] : ( ( set @ ( list @ A ) ) > A > ( set @ ( list @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Basic__BNF__LFPs_Osum_Osize__sum,type,
% 0.29/0.45 basic_BNF_size_sum:
% 0.29/0.45 !>[A: $tType,B: $tType] : ( ( A > nat ) > ( B > nat ) > ( sum_sum @ A @ B ) > nat ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_ONode,type,
% 0.29/0.45 binDag476092410e_Node: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > binDag_Mirabelle_dag ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_OTip,type,
% 0.29/0.45 binDag_Mirabelle_Tip: binDag_Mirabelle_dag ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_Ocase__dag,type,
% 0.29/0.45 binDag1297733282se_dag:
% 0.29/0.45 !>[A: $tType] : ( A > ( binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A ) > binDag_Mirabelle_dag > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_Orec__dag,type,
% 0.29/0.45 binDag1442713106ec_dag:
% 0.29/0.45 !>[A: $tType] : ( A > ( binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A > A > A ) > binDag_Mirabelle_dag > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_Osize__dag,type,
% 0.29/0.45 binDag1924123185ze_dag: binDag_Mirabelle_dag > nat ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Code__Numeral_OSuc,type,
% 0.29/0.45 code_Suc: code_natural > code_natural ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Code__Numeral_Onatural_Ocase__natural,type,
% 0.29/0.45 code_case_natural:
% 0.29/0.45 !>[T: $tType] : ( T > ( code_natural > T ) > code_natural > T ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Code__Numeral_Onatural_Orec__natural,type,
% 0.29/0.45 code_rec_natural:
% 0.29/0.45 !>[T: $tType] : ( T > ( code_natural > T > T ) > code_natural > T ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Code__Numeral_Onatural_Osize__natural,type,
% 0.29/0.45 code_size_natural: code_natural > nat ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.29/0.45 one_one:
% 0.29/0.45 !>[A: $tType] : A ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.29/0.45 plus_plus:
% 0.29/0.45 !>[A: $tType] : ( A > A > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.29/0.45 zero_zero:
% 0.29/0.45 !>[A: $tType] : A ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_HOL_Obool_Osize__bool,type,
% 0.29/0.45 size_bool: $o > nat ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_HOL_Odefault__class_Odefault,type,
% 0.29/0.45 default_default:
% 0.29/0.45 !>[A: $tType] : A ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_HOL_Oundefined,type,
% 0.29/0.45 undefined:
% 0.29/0.45 !>[A: $tType] : A ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_If,type,
% 0.29/0.45 if:
% 0.29/0.45 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_List_Ogen__length,type,
% 0.29/0.45 gen_length:
% 0.29/0.45 !>[A: $tType] : ( nat > ( list @ A ) > nat ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_List_Olist_OCons,type,
% 0.29/0.45 cons:
% 0.29/0.45 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_List_Olist_Osize__list,type,
% 0.29/0.45 size_list:
% 0.29/0.45 !>[A: $tType] : ( ( A > nat ) > ( list @ A ) > nat ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_List_Osplice,type,
% 0.29/0.45 splice:
% 0.29/0.45 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Nat_OSuc,type,
% 0.29/0.45 suc: nat > nat ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.29/0.45 size_size:
% 0.29/0.45 !>[A: $tType] : ( A > nat ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Num_Oinc,type,
% 0.29/0.45 inc: num > num ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Num_Onat__of__num,type,
% 0.29/0.45 nat_of_num: num > nat ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc,type,
% 0.29/0.45 neg_numeral_dbl_inc:
% 0.29/0.45 !>[A: $tType] : ( A > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Num_Onum_OBit0,type,
% 0.29/0.45 bit0: num > num ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Num_Onum_OBit1,type,
% 0.29/0.45 bit1: num > num ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Num_Onum_OOne,type,
% 0.29/0.45 one2: num ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Num_Onum_Osize__num,type,
% 0.29/0.45 size_num: num > nat ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Num_Onumeral__class_Onumeral,type,
% 0.29/0.45 numeral_numeral:
% 0.29/0.45 !>[A: $tType] : ( num > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Option_Ooption_ONone,type,
% 0.29/0.45 none:
% 0.29/0.45 !>[A: $tType] : ( option @ A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Option_Ooption_OSome,type,
% 0.29/0.45 some:
% 0.29/0.45 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Option_Ooption_Ocase__option,type,
% 0.29/0.45 case_option:
% 0.29/0.45 !>[B: $tType,A: $tType] : ( B > ( A > B ) > ( option @ A ) > B ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Option_Ooption_Osize__option,type,
% 0.29/0.45 size_option:
% 0.29/0.45 !>[A: $tType] : ( ( A > nat ) > ( option @ A ) > nat ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Option_Ooption_Othe,type,
% 0.29/0.45 the:
% 0.29/0.45 !>[A: $tType] : ( ( option @ A ) > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Product__Type_OUnity,type,
% 0.29/0.45 product_Unity: product_unit ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Product__Type_Oold_Obool_Orec__bool,type,
% 0.29/0.45 product_rec_bool:
% 0.29/0.45 !>[T: $tType] : ( T > T > $o > T ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Product__Type_Oold_Ounit_Orec__unit,type,
% 0.29/0.45 product_rec_unit:
% 0.29/0.45 !>[T: $tType] : ( T > product_unit > T ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Product__Type_Ounit_Ocase__unit,type,
% 0.29/0.45 product_case_unit:
% 0.29/0.45 !>[A: $tType] : ( A > product_unit > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Product__Type_Ounit_Osize__unit,type,
% 0.29/0.45 product_size_unit: product_unit > nat ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Pure_Otype,type,
% 0.29/0.45 type2:
% 0.29/0.45 !>[A: $tType] : ( itself @ A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Record_Otuple__isomorphism_OTuple__Isomorphism,type,
% 0.29/0.45 tuple_742722141rphism:
% 0.29/0.45 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( product_prod @ B @ C ) ) > ( ( product_prod @ B @ C ) > A ) > ( tuple_isomorphism @ A @ B @ C ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Record_Otuple__isomorphism_Osize__tuple__isomorphism,type,
% 0.29/0.45 tuple_1907371454rphism:
% 0.29/0.45 !>[A: $tType,B: $tType,C: $tType] : ( ( A > nat ) > ( B > nat ) > ( C > nat ) > ( tuple_isomorphism @ A @ B @ C ) > nat ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Rings_Odivide__class_Odivide,type,
% 0.29/0.45 divide_divide:
% 0.29/0.45 !>[A: $tType] : ( A > A > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Set_OCollect,type,
% 0.29/0.45 collect:
% 0.29/0.45 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Sum__Type_OInl,type,
% 0.29/0.45 sum_Inl:
% 0.29/0.45 !>[A: $tType,B: $tType] : ( A > ( sum_sum @ A @ B ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Sum__Type_OInr,type,
% 0.29/0.45 sum_Inr:
% 0.29/0.45 !>[B: $tType,A: $tType] : ( B > ( sum_sum @ A @ B ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Transitive__Closure_Ontrancl,type,
% 0.29/0.45 transitive_ntrancl:
% 0.29/0.45 !>[A: $tType] : ( nat > ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Typerep_Otyperep_OTyperep,type,
% 0.29/0.45 typerep3: literal > ( list @ typerep ) > typerep ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Typerep_Otyperep_Osize__typerep,type,
% 0.29/0.45 size_typerep: typerep > nat ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_member,type,
% 0.29/0.45 member:
% 0.29/0.45 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_v_a,type,
% 0.29/0.45 a: simpl_ref ).
% 0.29/0.45
% 0.29/0.45 thf(sy_v_lt,type,
% 0.29/0.45 lt: binDag_Mirabelle_dag ).
% 0.29/0.45
% 0.29/0.45 thf(sy_v_rt,type,
% 0.29/0.45 rt: binDag_Mirabelle_dag ).
% 0.29/0.45
% 0.29/0.45 %----Relevant facts (251)
% 0.29/0.45 thf(fact_0_dag_Oinject,axiom,
% 0.29/0.45 ! [X21: binDag_Mirabelle_dag,X22: simpl_ref,X23: binDag_Mirabelle_dag,Y21: binDag_Mirabelle_dag,Y22: simpl_ref,Y23: binDag_Mirabelle_dag] :
% 0.29/0.45 ( ( ( binDag476092410e_Node @ X21 @ X22 @ X23 )
% 0.29/0.45 = ( binDag476092410e_Node @ Y21 @ Y22 @ Y23 ) )
% 0.29/0.45 = ( ( X21 = Y21 )
% 0.29/0.45 & ( X22 = Y22 )
% 0.29/0.45 & ( X23 = Y23 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % dag.inject
% 0.29/0.45 thf(fact_1_dag_Odistinct_I1_J,axiom,
% 0.29/0.45 ! [X21: binDag_Mirabelle_dag,X22: simpl_ref,X23: binDag_Mirabelle_dag] :
% 0.29/0.45 ( binDag_Mirabelle_Tip
% 0.29/0.45 != ( binDag476092410e_Node @ X21 @ X22 @ X23 ) ) ).
% 0.29/0.45
% 0.29/0.45 % dag.distinct(1)
% 0.29/0.45 thf(fact_2_dag_Oinduct,axiom,
% 0.29/0.45 ! [P: binDag_Mirabelle_dag > $o,Dag: binDag_Mirabelle_dag] :
% 0.29/0.45 ( ( P @ binDag_Mirabelle_Tip )
% 0.29/0.45 => ( ! [X1: binDag_Mirabelle_dag,X2: simpl_ref,X3: binDag_Mirabelle_dag] :
% 0.29/0.45 ( ( P @ X1 )
% 0.29/0.45 => ( ( P @ X3 )
% 0.29/0.45 => ( P @ ( binDag476092410e_Node @ X1 @ X2 @ X3 ) ) ) )
% 0.29/0.45 => ( P @ Dag ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % dag.induct
% 0.29/0.45 thf(fact_3_dag_Oexhaust,axiom,
% 0.29/0.45 ! [Y: binDag_Mirabelle_dag] :
% 0.29/0.45 ( ( Y != binDag_Mirabelle_Tip )
% 0.29/0.45 => ~ ! [X212: binDag_Mirabelle_dag,X222: simpl_ref,X232: binDag_Mirabelle_dag] :
% 0.29/0.45 ( Y
% 0.29/0.45 != ( binDag476092410e_Node @ X212 @ X222 @ X232 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % dag.exhaust
% 0.29/0.45 thf(fact_4_dag_Osimps_I7_J,axiom,
% 0.29/0.45 ! [A: $tType,F1: A,F2: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A > A > A,X21: binDag_Mirabelle_dag,X22: simpl_ref,X23: binDag_Mirabelle_dag] :
% 0.29/0.45 ( ( binDag1442713106ec_dag @ A @ F1 @ F2 @ ( binDag476092410e_Node @ X21 @ X22 @ X23 ) )
% 0.29/0.45 = ( F2 @ X21 @ X22 @ X23 @ ( binDag1442713106ec_dag @ A @ F1 @ F2 @ X21 ) @ ( binDag1442713106ec_dag @ A @ F1 @ F2 @ X23 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % dag.simps(7)
% 0.29/0.45 thf(fact_5_dag_Osimps_I5_J,axiom,
% 0.29/0.45 ! [A: $tType,F1: A,F2: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A,X21: binDag_Mirabelle_dag,X22: simpl_ref,X23: binDag_Mirabelle_dag] :
% 0.29/0.45 ( ( binDag1297733282se_dag @ A @ F1 @ F2 @ ( binDag476092410e_Node @ X21 @ X22 @ X23 ) )
% 0.29/0.45 = ( F2 @ X21 @ X22 @ X23 ) ) ).
% 0.29/0.45
% 0.29/0.45 % dag.simps(5)
% 0.29/0.45 thf(fact_6_dag_Osimps_I6_J,axiom,
% 0.29/0.45 ! [A: $tType,F1: A,F2: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A > A > A] :
% 0.29/0.45 ( ( binDag1442713106ec_dag @ A @ F1 @ F2 @ binDag_Mirabelle_Tip )
% 0.29/0.45 = F1 ) ).
% 0.29/0.45
% 0.29/0.45 % dag.simps(6)
% 0.29/0.45 thf(fact_7_dag_Osimps_I4_J,axiom,
% 0.29/0.45 ! [A: $tType,F1: A,F2: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A] :
% 0.29/0.45 ( ( binDag1297733282se_dag @ A @ F1 @ F2 @ binDag_Mirabelle_Tip )
% 0.29/0.45 = F1 ) ).
% 0.29/0.45
% 0.29/0.45 % dag.simps(4)
% 0.29/0.45 thf(fact_8_dag_Osize__gen_I1_J,axiom,
% 0.29/0.45 ( ( binDag1924123185ze_dag @ binDag_Mirabelle_Tip )
% 0.29/0.45 = ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % dag.size_gen(1)
% 0.29/0.45 thf(fact_9_dag_Osize_I3_J,axiom,
% 0.29/0.45 ( ( size_size @ binDag_Mirabelle_dag @ binDag_Mirabelle_Tip )
% 0.29/0.45 = ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % dag.size(3)
% 0.29/0.45 thf(fact_10_dag_Ocase__distrib,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType,H: A > B,F1: A,F2: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A,Dag: binDag_Mirabelle_dag] :
% 0.29/0.45 ( ( H @ ( binDag1297733282se_dag @ A @ F1 @ F2 @ Dag ) )
% 0.29/0.45 = ( binDag1297733282se_dag @ B @ ( H @ F1 )
% 0.29/0.45 @ ^ [X12: binDag_Mirabelle_dag,X24: simpl_ref,X32: binDag_Mirabelle_dag] : ( H @ ( F2 @ X12 @ X24 @ X32 ) )
% 0.29/0.45 @ Dag ) ) ).
% 0.29/0.45
% 0.29/0.45 % dag.case_distrib
% 0.29/0.45 thf(fact_11_fun__cong__unused__0,axiom,
% 0.29/0.45 ! [A: $tType,B: $tType,C: $tType] :
% 0.29/0.45 ( ( zero @ B @ ( type2 @ B ) )
% 0.29/0.45 => ! [F: ( A > B ) > C,G: C] :
% 0.29/0.45 ( ( F
% 0.29/0.45 = ( ^ [X: A > B] : G ) )
% 0.29/0.45 => ( ( F
% 0.29/0.45 @ ^ [X: A] : ( zero_zero @ B ) )
% 0.29/0.45 = G ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % fun_cong_unused_0
% 0.29/0.45 thf(fact_12_size__ne__size__imp__ne,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( size @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [X4: A,Y: A] :
% 0.29/0.45 ( ( ( size_size @ A @ X4 )
% 0.29/0.45 != ( size_size @ A @ Y ) )
% 0.29/0.45 => ( X4 != Y ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % size_ne_size_imp_ne
% 0.29/0.45 thf(fact_13_zero__natural_Orsp,axiom,
% 0.29/0.45 ( ( zero_zero @ nat )
% 0.29/0.45 = ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % zero_natural.rsp
% 0.29/0.45 thf(fact_14_zero__reorient,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( zero @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [X4: A] :
% 0.29/0.45 ( ( ( zero_zero @ A )
% 0.29/0.45 = X4 )
% 0.29/0.45 = ( X4
% 0.29/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % zero_reorient
% 0.29/0.45 thf(fact_15_bool_Osize_I1_J,axiom,
% 0.29/0.45 ( ( size_bool @ $true )
% 0.29/0.45 = ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % bool.size(1)
% 0.29/0.45 thf(fact_16_bool_Osize_I2_J,axiom,
% 0.29/0.45 ( ( size_bool @ $false )
% 0.29/0.45 = ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % bool.size(2)
% 0.29/0.45 thf(fact_17_dag_Osize__gen_I2_J,axiom,
% 0.29/0.45 ! [X21: binDag_Mirabelle_dag,X22: simpl_ref,X23: binDag_Mirabelle_dag] :
% 0.29/0.45 ( ( binDag1924123185ze_dag @ ( binDag476092410e_Node @ X21 @ X22 @ X23 ) )
% 0.29/0.45 = ( plus_plus @ nat @ ( plus_plus @ nat @ ( binDag1924123185ze_dag @ X21 ) @ ( binDag1924123185ze_dag @ X23 ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % dag.size_gen(2)
% 0.29/0.45 thf(fact_18_dag_Osize_I4_J,axiom,
% 0.29/0.45 ! [X21: binDag_Mirabelle_dag,X22: simpl_ref,X23: binDag_Mirabelle_dag] :
% 0.29/0.45 ( ( size_size @ binDag_Mirabelle_dag @ ( binDag476092410e_Node @ X21 @ X22 @ X23 ) )
% 0.29/0.45 = ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ binDag_Mirabelle_dag @ X21 ) @ ( size_size @ binDag_Mirabelle_dag @ X23 ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % dag.size(4)
% 0.29/0.45 thf(fact_19_ntrancl__Zero,axiom,
% 0.29/0.45 ! [A: $tType,R: set @ ( product_prod @ A @ A )] :
% 0.29/0.45 ( ( transitive_ntrancl @ A @ ( zero_zero @ nat ) @ R )
% 0.29/0.45 = R ) ).
% 0.29/0.45
% 0.29/0.45 % ntrancl_Zero
% 0.29/0.45 thf(fact_20_add__left__cancel,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.45 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.29/0.45 = ( plus_plus @ A @ A2 @ C2 ) )
% 0.29/0.45 = ( B2 = C2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_left_cancel
% 0.29/0.45 thf(fact_21_add__right__cancel,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [B2: A,A2: A,C2: A] :
% 0.29/0.45 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.29/0.45 = ( plus_plus @ A @ C2 @ A2 ) )
% 0.29/0.45 = ( B2 = C2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_right_cancel
% 0.29/0.45 thf(fact_22_natural_Osize_I3_J,axiom,
% 0.29/0.45 ( ( size_size @ code_natural @ ( zero_zero @ code_natural ) )
% 0.29/0.45 = ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % natural.size(3)
% 0.29/0.45 thf(fact_23_bool_Osize_I4_J,axiom,
% 0.29/0.45 ( ( size_size @ $o @ $false )
% 0.29/0.45 = ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % bool.size(4)
% 0.29/0.45 thf(fact_24_bool_Osize_I3_J,axiom,
% 0.29/0.45 ( ( size_size @ $o @ $true )
% 0.29/0.45 = ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % bool.size(3)
% 0.29/0.45 thf(fact_25_nat_Oinject,axiom,
% 0.29/0.45 ! [X25: nat,Y2: nat] :
% 0.29/0.45 ( ( ( suc @ X25 )
% 0.29/0.45 = ( suc @ Y2 ) )
% 0.29/0.45 = ( X25 = Y2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % nat.inject
% 0.29/0.45 thf(fact_26_old_Onat_Oinject,axiom,
% 0.29/0.45 ! [Nat: nat,Nat2: nat] :
% 0.29/0.45 ( ( ( suc @ Nat )
% 0.29/0.45 = ( suc @ Nat2 ) )
% 0.29/0.45 = ( Nat = Nat2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % old.nat.inject
% 0.29/0.45 thf(fact_27_add_Oleft__neutral,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( monoid_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.45 = A2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % add.left_neutral
% 0.29/0.45 thf(fact_28_add_Oright__neutral,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( monoid_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.45 = A2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % add.right_neutral
% 0.29/0.45 thf(fact_29_double__zero,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( ( plus_plus @ A @ A2 @ A2 )
% 0.29/0.45 = ( zero_zero @ A ) )
% 0.29/0.45 = ( A2
% 0.29/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % double_zero
% 0.29/0.45 thf(fact_30_double__zero__sym,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( ( zero_zero @ A )
% 0.29/0.45 = ( plus_plus @ A @ A2 @ A2 ) )
% 0.29/0.45 = ( A2
% 0.29/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % double_zero_sym
% 0.29/0.45 thf(fact_31_add__cancel__left__left,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [B2: A,A2: A] :
% 0.29/0.45 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.29/0.45 = A2 )
% 0.29/0.45 = ( B2
% 0.29/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_cancel_left_left
% 0.29/0.45 thf(fact_32_add__cancel__left__right,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A,B2: A] :
% 0.29/0.45 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.29/0.45 = A2 )
% 0.29/0.45 = ( B2
% 0.29/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_cancel_left_right
% 0.29/0.45 thf(fact_33_add__cancel__right__left,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A,B2: A] :
% 0.29/0.45 ( ( A2
% 0.29/0.45 = ( plus_plus @ A @ B2 @ A2 ) )
% 0.29/0.45 = ( B2
% 0.29/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_cancel_right_left
% 0.29/0.45 thf(fact_34_add__cancel__right__right,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A,B2: A] :
% 0.29/0.45 ( ( A2
% 0.29/0.45 = ( plus_plus @ A @ A2 @ B2 ) )
% 0.29/0.45 = ( B2
% 0.29/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_cancel_right_right
% 0.29/0.45 thf(fact_35_add__is__0,axiom,
% 0.29/0.45 ! [M: nat,N: nat] :
% 0.29/0.45 ( ( ( plus_plus @ nat @ M @ N )
% 0.29/0.45 = ( zero_zero @ nat ) )
% 0.29/0.45 = ( ( M
% 0.29/0.45 = ( zero_zero @ nat ) )
% 0.29/0.45 & ( N
% 0.29/0.45 = ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_is_0
% 0.29/0.45 thf(fact_36_Nat_Oadd__0__right,axiom,
% 0.29/0.45 ! [M: nat] :
% 0.29/0.45 ( ( plus_plus @ nat @ M @ ( zero_zero @ nat ) )
% 0.29/0.45 = M ) ).
% 0.29/0.45
% 0.29/0.45 % Nat.add_0_right
% 0.29/0.45 thf(fact_37_add__Suc__right,axiom,
% 0.29/0.45 ! [M: nat,N: nat] :
% 0.29/0.45 ( ( plus_plus @ nat @ M @ ( suc @ N ) )
% 0.29/0.45 = ( suc @ ( plus_plus @ nat @ M @ N ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_Suc_right
% 0.29/0.45 thf(fact_38_one__is__add,axiom,
% 0.29/0.45 ! [M: nat,N: nat] :
% 0.29/0.45 ( ( ( suc @ ( zero_zero @ nat ) )
% 0.29/0.45 = ( plus_plus @ nat @ M @ N ) )
% 0.29/0.45 = ( ( ( M
% 0.29/0.45 = ( suc @ ( zero_zero @ nat ) ) )
% 0.29/0.45 & ( N
% 0.29/0.45 = ( zero_zero @ nat ) ) )
% 0.29/0.45 | ( ( M
% 0.29/0.45 = ( zero_zero @ nat ) )
% 0.29/0.45 & ( N
% 0.29/0.45 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % one_is_add
% 0.29/0.45 thf(fact_39_add__is__1,axiom,
% 0.29/0.45 ! [M: nat,N: nat] :
% 0.29/0.45 ( ( ( plus_plus @ nat @ M @ N )
% 0.29/0.45 = ( suc @ ( zero_zero @ nat ) ) )
% 0.29/0.45 = ( ( ( M
% 0.29/0.45 = ( suc @ ( zero_zero @ nat ) ) )
% 0.29/0.45 & ( N
% 0.29/0.45 = ( zero_zero @ nat ) ) )
% 0.29/0.45 | ( ( M
% 0.29/0.45 = ( zero_zero @ nat ) )
% 0.29/0.45 & ( N
% 0.29/0.45 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_is_1
% 0.29/0.45 thf(fact_40_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.45 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 0.29/0.45 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % ab_semigroup_add_class.add_ac(1)
% 0.29/0.45 thf(fact_41_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [I: A,J: A,K: A,L: A] :
% 0.29/0.45 ( ( ( I = J )
% 0.29/0.45 & ( K = L ) )
% 0.29/0.45 => ( ( plus_plus @ A @ I @ K )
% 0.29/0.45 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_mono_thms_linordered_semiring(4)
% 0.29/0.45 thf(fact_42_mem__Collect__eq,axiom,
% 0.29/0.45 ! [A: $tType,A2: A,P: A > $o] :
% 0.29/0.45 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.29/0.45 = ( P @ A2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % mem_Collect_eq
% 0.29/0.45 thf(fact_43_Collect__mem__eq,axiom,
% 0.29/0.45 ! [A: $tType,A3: set @ A] :
% 0.29/0.45 ( ( collect @ A
% 0.29/0.45 @ ^ [X: A] : ( member @ A @ X @ A3 ) )
% 0.29/0.45 = A3 ) ).
% 0.29/0.45
% 0.29/0.45 % Collect_mem_eq
% 0.29/0.45 thf(fact_44_Collect__cong,axiom,
% 0.29/0.45 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.29/0.45 ( ! [X5: A] :
% 0.29/0.45 ( ( P @ X5 )
% 0.29/0.45 = ( Q @ X5 ) )
% 0.29/0.45 => ( ( collect @ A @ P )
% 0.29/0.45 = ( collect @ A @ Q ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Collect_cong
% 0.29/0.45 thf(fact_45_ext,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.29/0.45 ( ! [X5: A] :
% 0.29/0.45 ( ( F @ X5 )
% 0.29/0.45 = ( G @ X5 ) )
% 0.29/0.45 => ( F = G ) ) ).
% 0.29/0.45
% 0.29/0.45 % ext
% 0.29/0.45 thf(fact_46_Suc__inject,axiom,
% 0.29/0.45 ! [X4: nat,Y: nat] :
% 0.29/0.45 ( ( ( suc @ X4 )
% 0.29/0.45 = ( suc @ Y ) )
% 0.29/0.45 => ( X4 = Y ) ) ).
% 0.29/0.45
% 0.29/0.45 % Suc_inject
% 0.29/0.45 thf(fact_47_n__not__Suc__n,axiom,
% 0.29/0.45 ! [N: nat] :
% 0.29/0.45 ( N
% 0.29/0.45 != ( suc @ N ) ) ).
% 0.29/0.45
% 0.29/0.45 % n_not_Suc_n
% 0.29/0.45 thf(fact_48_add__Suc__shift,axiom,
% 0.29/0.45 ! [M: nat,N: nat] :
% 0.29/0.45 ( ( plus_plus @ nat @ ( suc @ M ) @ N )
% 0.29/0.45 = ( plus_plus @ nat @ M @ ( suc @ N ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_Suc_shift
% 0.29/0.45 thf(fact_49_add__Suc,axiom,
% 0.29/0.45 ! [M: nat,N: nat] :
% 0.29/0.45 ( ( plus_plus @ nat @ ( suc @ M ) @ N )
% 0.29/0.45 = ( suc @ ( plus_plus @ nat @ M @ N ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_Suc
% 0.29/0.45 thf(fact_50_nat__add__left__cancel,axiom,
% 0.29/0.45 ! [K: nat,M: nat,N: nat] :
% 0.29/0.45 ( ( ( plus_plus @ nat @ K @ M )
% 0.29/0.45 = ( plus_plus @ nat @ K @ N ) )
% 0.29/0.45 = ( M = N ) ) ).
% 0.29/0.45
% 0.29/0.45 % nat_add_left_cancel
% 0.29/0.45 thf(fact_51_nat__add__right__cancel,axiom,
% 0.29/0.45 ! [M: nat,K: nat,N: nat] :
% 0.29/0.45 ( ( ( plus_plus @ nat @ M @ K )
% 0.29/0.45 = ( plus_plus @ nat @ N @ K ) )
% 0.29/0.45 = ( M = N ) ) ).
% 0.29/0.45
% 0.29/0.45 % nat_add_right_cancel
% 0.29/0.45 thf(fact_52_add_Oassoc,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semigroup_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.45 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 0.29/0.45 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add.assoc
% 0.29/0.45 thf(fact_53_add_Oleft__cancel,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( group_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.45 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.29/0.45 = ( plus_plus @ A @ A2 @ C2 ) )
% 0.29/0.45 = ( B2 = C2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add.left_cancel
% 0.29/0.45 thf(fact_54_add_Oright__cancel,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( group_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [B2: A,A2: A,C2: A] :
% 0.29/0.45 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.29/0.45 = ( plus_plus @ A @ C2 @ A2 ) )
% 0.29/0.45 = ( B2 = C2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add.right_cancel
% 0.29/0.45 thf(fact_55_add_Ocommute,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ( ( plus_plus @ A )
% 0.29/0.45 = ( ^ [A4: A,B3: A] : ( plus_plus @ A @ B3 @ A4 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add.commute
% 0.29/0.45 thf(fact_56_add_Oleft__commute,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [B2: A,A2: A,C2: A] :
% 0.29/0.45 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) )
% 0.29/0.45 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add.left_commute
% 0.29/0.45 thf(fact_57_add__left__imp__eq,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.45 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.29/0.45 = ( plus_plus @ A @ A2 @ C2 ) )
% 0.29/0.45 => ( B2 = C2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_left_imp_eq
% 0.29/0.45 thf(fact_58_add__right__imp__eq,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [B2: A,A2: A,C2: A] :
% 0.29/0.45 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.29/0.45 = ( plus_plus @ A @ C2 @ A2 ) )
% 0.29/0.45 => ( B2 = C2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_right_imp_eq
% 0.29/0.45 thf(fact_59_comm__monoid__add__class_Oadd__0,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_monoid_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.45 = A2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % comm_monoid_add_class.add_0
% 0.29/0.45 thf(fact_60_add_Ocomm__neutral,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_monoid_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.45 = A2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % add.comm_neutral
% 0.29/0.45 thf(fact_61_add_Ogroup__left__neutral,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( group_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.45 = A2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % add.group_left_neutral
% 0.29/0.45 thf(fact_62_add__eq__0__iff__both__eq__0,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [X4: A,Y: A] :
% 0.29/0.45 ( ( ( plus_plus @ A @ X4 @ Y )
% 0.29/0.45 = ( zero_zero @ A ) )
% 0.29/0.45 = ( ( X4
% 0.29/0.45 = ( zero_zero @ A ) )
% 0.29/0.45 & ( Y
% 0.29/0.45 = ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_eq_0_iff_both_eq_0
% 0.29/0.45 thf(fact_63_nat_Odistinct_I1_J,axiom,
% 0.29/0.45 ! [X25: nat] :
% 0.29/0.45 ( ( zero_zero @ nat )
% 0.29/0.45 != ( suc @ X25 ) ) ).
% 0.29/0.45
% 0.29/0.45 % nat.distinct(1)
% 0.29/0.45 thf(fact_64_old_Onat_Odistinct_I2_J,axiom,
% 0.29/0.45 ! [Nat3: nat] :
% 0.29/0.45 ( ( suc @ Nat3 )
% 0.29/0.45 != ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % old.nat.distinct(2)
% 0.29/0.45 thf(fact_65_old_Onat_Odistinct_I1_J,axiom,
% 0.29/0.45 ! [Nat2: nat] :
% 0.29/0.45 ( ( zero_zero @ nat )
% 0.29/0.45 != ( suc @ Nat2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % old.nat.distinct(1)
% 0.29/0.45 thf(fact_66_nat_OdiscI,axiom,
% 0.29/0.45 ! [Nat: nat,X25: nat] :
% 0.29/0.45 ( ( Nat
% 0.29/0.45 = ( suc @ X25 ) )
% 0.29/0.45 => ( Nat
% 0.29/0.45 != ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % nat.discI
% 0.29/0.45 thf(fact_67_nat__induct,axiom,
% 0.29/0.45 ! [P: nat > $o,N: nat] :
% 0.29/0.45 ( ( P @ ( zero_zero @ nat ) )
% 0.29/0.45 => ( ! [N2: nat] :
% 0.29/0.45 ( ( P @ N2 )
% 0.29/0.45 => ( P @ ( suc @ N2 ) ) )
% 0.29/0.45 => ( P @ N ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % nat_induct
% 0.29/0.45 thf(fact_68_diff__induct,axiom,
% 0.29/0.45 ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.29/0.45 ( ! [X5: nat] : ( P @ X5 @ ( zero_zero @ nat ) )
% 0.29/0.45 => ( ! [Y3: nat] : ( P @ ( zero_zero @ nat ) @ ( suc @ Y3 ) )
% 0.29/0.45 => ( ! [X5: nat,Y3: nat] :
% 0.29/0.45 ( ( P @ X5 @ Y3 )
% 0.29/0.45 => ( P @ ( suc @ X5 ) @ ( suc @ Y3 ) ) )
% 0.29/0.45 => ( P @ M @ N ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % diff_induct
% 0.29/0.45 thf(fact_69_zero__induct,axiom,
% 0.29/0.45 ! [P: nat > $o,K: nat] :
% 0.29/0.45 ( ( P @ K )
% 0.29/0.45 => ( ! [N2: nat] :
% 0.29/0.45 ( ( P @ ( suc @ N2 ) )
% 0.29/0.45 => ( P @ N2 ) )
% 0.29/0.45 => ( P @ ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % zero_induct
% 0.29/0.45 thf(fact_70_Suc__neq__Zero,axiom,
% 0.29/0.45 ! [M: nat] :
% 0.29/0.45 ( ( suc @ M )
% 0.29/0.45 != ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % Suc_neq_Zero
% 0.29/0.45 thf(fact_71_Zero__neq__Suc,axiom,
% 0.29/0.45 ! [M: nat] :
% 0.29/0.45 ( ( zero_zero @ nat )
% 0.29/0.45 != ( suc @ M ) ) ).
% 0.29/0.45
% 0.29/0.45 % Zero_neq_Suc
% 0.29/0.45 thf(fact_72_Zero__not__Suc,axiom,
% 0.29/0.45 ! [M: nat] :
% 0.29/0.45 ( ( zero_zero @ nat )
% 0.29/0.45 != ( suc @ M ) ) ).
% 0.29/0.45
% 0.29/0.45 % Zero_not_Suc
% 0.29/0.45 thf(fact_73_old_Onat_Oexhaust,axiom,
% 0.29/0.45 ! [Y: nat] :
% 0.29/0.45 ( ( Y
% 0.29/0.45 != ( zero_zero @ nat ) )
% 0.29/0.45 => ~ ! [Nat4: nat] :
% 0.29/0.45 ( Y
% 0.29/0.45 != ( suc @ Nat4 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % old.nat.exhaust
% 0.29/0.45 thf(fact_74_old_Onat_Oinducts,axiom,
% 0.29/0.45 ! [P: nat > $o,Nat: nat] :
% 0.29/0.45 ( ( P @ ( zero_zero @ nat ) )
% 0.29/0.45 => ( ! [Nat4: nat] :
% 0.29/0.45 ( ( P @ Nat4 )
% 0.29/0.45 => ( P @ ( suc @ Nat4 ) ) )
% 0.29/0.45 => ( P @ Nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % old.nat.inducts
% 0.29/0.45 thf(fact_75_not0__implies__Suc,axiom,
% 0.29/0.45 ! [N: nat] :
% 0.29/0.45 ( ( N
% 0.29/0.45 != ( zero_zero @ nat ) )
% 0.29/0.45 => ? [M2: nat] :
% 0.29/0.45 ( N
% 0.29/0.45 = ( suc @ M2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % not0_implies_Suc
% 0.29/0.45 thf(fact_76_plus__nat_Oadd__0,axiom,
% 0.29/0.45 ! [N: nat] :
% 0.29/0.45 ( ( plus_plus @ nat @ ( zero_zero @ nat ) @ N )
% 0.29/0.45 = N ) ).
% 0.29/0.45
% 0.29/0.45 % plus_nat.add_0
% 0.29/0.45 thf(fact_77_add__eq__self__zero,axiom,
% 0.29/0.45 ! [M: nat,N: nat] :
% 0.29/0.45 ( ( ( plus_plus @ nat @ M @ N )
% 0.29/0.45 = M )
% 0.29/0.45 => ( N
% 0.29/0.45 = ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_eq_self_zero
% 0.29/0.45 thf(fact_78_size__bool,axiom,
% 0.29/0.45 ( ( size_size @ $o )
% 0.29/0.45 = ( ^ [B3: $o] : ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % size_bool
% 0.29/0.45 thf(fact_79_sum_Osize__neq,axiom,
% 0.29/0.45 ! [A: $tType,B: $tType,X4: sum_sum @ A @ B] :
% 0.29/0.45 ( ( size_size @ ( sum_sum @ A @ B ) @ X4 )
% 0.29/0.45 != ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % sum.size_neq
% 0.29/0.45 thf(fact_80_prod_Osize__neq,axiom,
% 0.29/0.45 ! [A: $tType,B: $tType,X4: product_prod @ A @ B] :
% 0.29/0.45 ( ( size_size @ ( product_prod @ A @ B ) @ X4 )
% 0.29/0.45 != ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % prod.size_neq
% 0.29/0.45 thf(fact_81_size__bool__def,axiom,
% 0.29/0.45 ( size_bool
% 0.29/0.45 = ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % size_bool_def
% 0.29/0.45 thf(fact_82_dependent__nat__choice,axiom,
% 0.29/0.45 ! [A: $tType,P: nat > A > $o,Q: nat > A > A > $o] :
% 0.29/0.45 ( ? [X13: A] : ( P @ ( zero_zero @ nat ) @ X13 )
% 0.29/0.45 => ( ! [X5: A,N2: nat] :
% 0.29/0.45 ( ( P @ N2 @ X5 )
% 0.29/0.45 => ? [Y4: A] :
% 0.29/0.45 ( ( P @ ( suc @ N2 ) @ Y4 )
% 0.29/0.45 & ( Q @ N2 @ X5 @ Y4 ) ) )
% 0.29/0.45 => ? [F3: nat > A] :
% 0.29/0.45 ! [N3: nat] :
% 0.29/0.45 ( ( P @ N3 @ ( F3 @ N3 ) )
% 0.29/0.45 & ( Q @ N3 @ ( F3 @ N3 ) @ ( F3 @ ( suc @ N3 ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % dependent_nat_choice
% 0.29/0.45 thf(fact_83_size__natural__overloaded__def,axiom,
% 0.29/0.45 ( ( size_size @ code_natural )
% 0.29/0.45 = ( code_rec_natural @ nat @ ( zero_zero @ nat )
% 0.29/0.45 @ ^ [X: code_natural,Y5: nat] : ( plus_plus @ nat @ Y5 @ ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % size_natural_overloaded_def
% 0.29/0.45 thf(fact_84_semiring__normalization__rules_I6_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.45 = A2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % semiring_normalization_rules(6)
% 0.29/0.45 thf(fact_85_semiring__normalization__rules_I5_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.45 = A2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % semiring_normalization_rules(5)
% 0.29/0.45 thf(fact_86_add__0__iff,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semiri456707255roduct @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [B2: A,A2: A] :
% 0.29/0.45 ( ( B2
% 0.29/0.45 = ( plus_plus @ A @ B2 @ A2 ) )
% 0.29/0.45 = ( A2
% 0.29/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_0_iff
% 0.29/0.45 thf(fact_87_natural_Osize_I1_J,axiom,
% 0.29/0.45 ( ( code_size_natural @ ( zero_zero @ code_natural ) )
% 0.29/0.45 = ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % natural.size(1)
% 0.29/0.45 thf(fact_88_natural_Osize_I4_J,axiom,
% 0.29/0.45 ! [Natural: code_natural] :
% 0.29/0.45 ( ( size_size @ code_natural @ ( code_Suc @ Natural ) )
% 0.29/0.45 = ( plus_plus @ nat @ ( size_size @ code_natural @ Natural ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % natural.size(4)
% 0.29/0.45 thf(fact_89_size__natural__def,axiom,
% 0.29/0.45 ( code_size_natural
% 0.29/0.45 = ( code_rec_natural @ nat @ ( zero_zero @ nat )
% 0.29/0.45 @ ^ [X: code_natural,Y5: nat] : ( plus_plus @ nat @ Y5 @ ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % size_natural_def
% 0.29/0.45 thf(fact_90_option_Osize__neq,axiom,
% 0.29/0.45 ! [A: $tType,X4: option @ A] :
% 0.29/0.45 ( ( size_size @ ( option @ A ) @ X4 )
% 0.29/0.45 != ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.size_neq
% 0.29/0.45 thf(fact_91_natural_Oinject,axiom,
% 0.29/0.45 ! [Natural: code_natural,Natural2: code_natural] :
% 0.29/0.45 ( ( ( code_Suc @ Natural )
% 0.29/0.45 = ( code_Suc @ Natural2 ) )
% 0.29/0.45 = ( Natural = Natural2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % natural.inject
% 0.29/0.45 thf(fact_92_natural_Osimps_I6_J,axiom,
% 0.29/0.45 ! [T: $tType,F1: T,F2: code_natural > T > T] :
% 0.29/0.45 ( ( code_rec_natural @ T @ F1 @ F2 @ ( zero_zero @ code_natural ) )
% 0.29/0.45 = F1 ) ).
% 0.29/0.45
% 0.29/0.45 % natural.simps(6)
% 0.29/0.45 thf(fact_93_natural_Osimps_I7_J,axiom,
% 0.29/0.45 ! [T: $tType,F1: T,F2: code_natural > T > T,Natural: code_natural] :
% 0.29/0.45 ( ( code_rec_natural @ T @ F1 @ F2 @ ( code_Suc @ Natural ) )
% 0.29/0.45 = ( F2 @ Natural @ ( code_rec_natural @ T @ F1 @ F2 @ Natural ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % natural.simps(7)
% 0.29/0.45 thf(fact_94_natural_Osize_I2_J,axiom,
% 0.29/0.45 ! [Natural: code_natural] :
% 0.29/0.45 ( ( code_size_natural @ ( code_Suc @ Natural ) )
% 0.29/0.45 = ( plus_plus @ nat @ ( code_size_natural @ Natural ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % natural.size(2)
% 0.29/0.45 thf(fact_95_natural_Oinducts,axiom,
% 0.29/0.45 ! [P: code_natural > $o,Natural: code_natural] :
% 0.29/0.45 ( ( P @ ( zero_zero @ code_natural ) )
% 0.29/0.45 => ( ! [Natural3: code_natural] :
% 0.29/0.45 ( ( P @ Natural3 )
% 0.29/0.45 => ( P @ ( code_Suc @ Natural3 ) ) )
% 0.29/0.45 => ( P @ Natural ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % natural.inducts
% 0.29/0.45 thf(fact_96_natural_Oexhaust,axiom,
% 0.29/0.45 ! [Y: code_natural] :
% 0.29/0.45 ( ( Y
% 0.29/0.45 != ( zero_zero @ code_natural ) )
% 0.29/0.45 => ~ ! [Natural3: code_natural] :
% 0.29/0.45 ( Y
% 0.29/0.45 != ( code_Suc @ Natural3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % natural.exhaust
% 0.29/0.45 thf(fact_97_natural_Odistinct_I1_J,axiom,
% 0.29/0.45 ! [Natural2: code_natural] :
% 0.29/0.45 ( ( zero_zero @ code_natural )
% 0.29/0.45 != ( code_Suc @ Natural2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % natural.distinct(1)
% 0.29/0.45 thf(fact_98_natural_Odistinct_I2_J,axiom,
% 0.29/0.45 ! [Natural4: code_natural] :
% 0.29/0.45 ( ( code_Suc @ Natural4 )
% 0.29/0.45 != ( zero_zero @ code_natural ) ) ).
% 0.29/0.45
% 0.29/0.45 % natural.distinct(2)
% 0.29/0.45 thf(fact_99_size__bool__overloaded__def,axiom,
% 0.29/0.45 ( ( size_size @ $o )
% 0.29/0.45 = ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % size_bool_overloaded_def
% 0.29/0.45 thf(fact_100_semiring__normalization__rules_I20_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A,B2: A,C2: A,D: A] :
% 0.29/0.45 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( plus_plus @ A @ C2 @ D ) )
% 0.29/0.45 = ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % semiring_normalization_rules(20)
% 0.29/0.45 thf(fact_101_semiring__normalization__rules_I21_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.45 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 0.29/0.45 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % semiring_normalization_rules(21)
% 0.29/0.45 thf(fact_102_semiring__normalization__rules_I22_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A,C2: A,D: A] :
% 0.29/0.45 ( ( plus_plus @ A @ A2 @ ( plus_plus @ A @ C2 @ D ) )
% 0.29/0.45 = ( plus_plus @ A @ C2 @ ( plus_plus @ A @ A2 @ D ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % semiring_normalization_rules(22)
% 0.29/0.45 thf(fact_103_semiring__normalization__rules_I23_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.45 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 0.29/0.45 = ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C2 ) @ B2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % semiring_normalization_rules(23)
% 0.29/0.45 thf(fact_104_semiring__normalization__rules_I24_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.29/0.45 => ( ( plus_plus @ A )
% 0.29/0.45 = ( ^ [A4: A,C3: A] : ( plus_plus @ A @ C3 @ A4 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % semiring_normalization_rules(24)
% 0.29/0.45 thf(fact_105_semiring__normalization__rules_I25_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A,C2: A,D: A] :
% 0.29/0.45 ( ( plus_plus @ A @ A2 @ ( plus_plus @ A @ C2 @ D ) )
% 0.29/0.45 = ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C2 ) @ D ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % semiring_normalization_rules(25)
% 0.29/0.45 thf(fact_106_old_Obool_Osimps_I5_J,axiom,
% 0.29/0.45 ! [T: $tType,F1: T,F2: T] :
% 0.29/0.45 ( ( product_rec_bool @ T @ F1 @ F2 @ $true )
% 0.29/0.45 = F1 ) ).
% 0.29/0.45
% 0.29/0.45 % old.bool.simps(5)
% 0.29/0.45 thf(fact_107_old_Obool_Osimps_I6_J,axiom,
% 0.29/0.45 ! [T: $tType,F1: T,F2: T] :
% 0.29/0.45 ( ( product_rec_bool @ T @ F1 @ F2 @ $false )
% 0.29/0.45 = F2 ) ).
% 0.29/0.45
% 0.29/0.45 % old.bool.simps(6)
% 0.29/0.45 thf(fact_108_natural_Osimps_I5_J,axiom,
% 0.29/0.45 ! [T: $tType,F1: T,F2: code_natural > T,Natural: code_natural] :
% 0.29/0.45 ( ( code_case_natural @ T @ F1 @ F2 @ ( code_Suc @ Natural ) )
% 0.29/0.45 = ( F2 @ Natural ) ) ).
% 0.29/0.45
% 0.29/0.45 % natural.simps(5)
% 0.29/0.45 thf(fact_109_random__aux__set_Oinduct,axiom,
% 0.29/0.45 ! [B: $tType] :
% 0.29/0.45 ( ( quickcheck_random @ B @ ( type2 @ B ) )
% 0.29/0.45 => ! [P: code_natural > code_natural > $o,A0: code_natural,A1: code_natural] :
% 0.29/0.45 ( ! [X1: code_natural] : ( P @ ( zero_zero @ code_natural ) @ X1 )
% 0.29/0.45 => ( ! [I2: code_natural,J2: code_natural] :
% 0.29/0.45 ( ! [X6: product_prod @ B @ ( product_unit > code_term )] : ( P @ I2 @ J2 )
% 0.29/0.45 => ( P @ ( code_Suc @ I2 ) @ J2 ) )
% 0.29/0.45 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % random_aux_set.induct
% 0.29/0.45 thf(fact_110_random__aux__rec,axiom,
% 0.29/0.45 ! [A: $tType,Random_aux: code_natural > A,Rhs: code_natural > A,K: code_natural] :
% 0.29/0.45 ( ( ( Random_aux @ ( zero_zero @ code_natural ) )
% 0.29/0.45 = ( Rhs @ ( zero_zero @ code_natural ) ) )
% 0.29/0.45 => ( ! [K2: code_natural] :
% 0.29/0.45 ( ( Random_aux @ ( code_Suc @ K2 ) )
% 0.29/0.45 = ( Rhs @ ( code_Suc @ K2 ) ) )
% 0.29/0.45 => ( ( Random_aux @ K )
% 0.29/0.45 = ( Rhs @ K ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % random_aux_rec
% 0.29/0.45 thf(fact_111_natural_Osimps_I4_J,axiom,
% 0.29/0.45 ! [T: $tType,F1: T,F2: code_natural > T] :
% 0.29/0.45 ( ( code_case_natural @ T @ F1 @ F2 @ ( zero_zero @ code_natural ) )
% 0.29/0.45 = F1 ) ).
% 0.29/0.45
% 0.29/0.45 % natural.simps(4)
% 0.29/0.45 thf(fact_112_case__natural__def,axiom,
% 0.29/0.45 ! [T: $tType] :
% 0.29/0.45 ( ( code_case_natural @ T )
% 0.29/0.45 = ( ^ [F12: T,F22: code_natural > T] :
% 0.29/0.45 ( code_rec_natural @ T @ F12
% 0.29/0.45 @ ^ [X12: code_natural,X24: T] : ( F22 @ X12 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % case_natural_def
% 0.29/0.45 thf(fact_113_option_Osize_I3_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( size_size @ ( option @ A ) @ ( none @ A ) )
% 0.29/0.45 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.size(3)
% 0.29/0.45 thf(fact_114_option_Osize_I4_J,axiom,
% 0.29/0.45 ! [A: $tType,X25: A] :
% 0.29/0.45 ( ( size_size @ ( option @ A ) @ ( some @ A @ X25 ) )
% 0.29/0.45 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.size(4)
% 0.29/0.45 thf(fact_115_sum_Osize_I3_J,axiom,
% 0.29/0.45 ! [A: $tType,B: $tType,X14: A] :
% 0.29/0.45 ( ( size_size @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B @ X14 ) )
% 0.29/0.45 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sum.size(3)
% 0.29/0.45 thf(fact_116_sum_Osize_I4_J,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType,X25: B] :
% 0.29/0.45 ( ( size_size @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A @ X25 ) )
% 0.29/0.45 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sum.size(4)
% 0.29/0.45 thf(fact_117_typerep_Osize__neq,axiom,
% 0.29/0.45 ! [X4: typerep] :
% 0.29/0.45 ( ( size_size @ typerep @ X4 )
% 0.29/0.45 != ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % typerep.size_neq
% 0.29/0.45 thf(fact_118_option_Oinject,axiom,
% 0.29/0.45 ! [A: $tType,X25: A,Y2: A] :
% 0.29/0.45 ( ( ( some @ A @ X25 )
% 0.29/0.45 = ( some @ A @ Y2 ) )
% 0.29/0.45 = ( X25 = Y2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.inject
% 0.29/0.45 thf(fact_119_not__None__eq,axiom,
% 0.29/0.45 ! [A: $tType,X4: option @ A] :
% 0.29/0.45 ( ( X4
% 0.29/0.45 != ( none @ A ) )
% 0.29/0.45 = ( ? [Y5: A] :
% 0.29/0.45 ( X4
% 0.29/0.45 = ( some @ A @ Y5 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % not_None_eq
% 0.29/0.45 thf(fact_120_not__Some__eq,axiom,
% 0.29/0.45 ! [A: $tType,X4: option @ A] :
% 0.29/0.45 ( ( ! [Y5: A] :
% 0.29/0.45 ( X4
% 0.29/0.45 != ( some @ A @ Y5 ) ) )
% 0.29/0.45 = ( X4
% 0.29/0.45 = ( none @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % not_Some_eq
% 0.29/0.45 thf(fact_121_Inl__Inr__False,axiom,
% 0.29/0.45 ! [A: $tType,B: $tType,X4: A,Y: B] :
% 0.29/0.45 ( ( sum_Inl @ A @ B @ X4 )
% 0.29/0.45 != ( sum_Inr @ B @ A @ Y ) ) ).
% 0.29/0.45
% 0.29/0.45 % Inl_Inr_False
% 0.29/0.45 thf(fact_122_Inr__Inl__False,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType,X4: B,Y: A] :
% 0.29/0.45 ( ( sum_Inr @ B @ A @ X4 )
% 0.29/0.45 != ( sum_Inl @ A @ B @ Y ) ) ).
% 0.29/0.45
% 0.29/0.45 % Inr_Inl_False
% 0.29/0.45 thf(fact_123_obj__sumE__f,axiom,
% 0.29/0.45 ! [A: $tType,C: $tType,B: $tType,S: B,F: ( sum_sum @ A @ C ) > B,P: $o] :
% 0.29/0.45 ( ! [X5: A] :
% 0.29/0.45 ( ( S
% 0.29/0.45 = ( F @ ( sum_Inl @ A @ C @ X5 ) ) )
% 0.29/0.45 => P )
% 0.29/0.45 => ( ! [X5: C] :
% 0.29/0.45 ( ( S
% 0.29/0.45 = ( F @ ( sum_Inr @ C @ A @ X5 ) ) )
% 0.29/0.45 => P )
% 0.29/0.45 => ! [X6: sum_sum @ A @ C] :
% 0.29/0.45 ( ( S
% 0.29/0.45 = ( F @ X6 ) )
% 0.29/0.45 => P ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % obj_sumE_f
% 0.29/0.45 thf(fact_124_option_Odistinct_I1_J,axiom,
% 0.29/0.45 ! [A: $tType,X25: A] :
% 0.29/0.45 ( ( none @ A )
% 0.29/0.45 != ( some @ A @ X25 ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.distinct(1)
% 0.29/0.45 thf(fact_125_option_OdiscI,axiom,
% 0.29/0.45 ! [A: $tType,Option: option @ A,X25: A] :
% 0.29/0.45 ( ( Option
% 0.29/0.45 = ( some @ A @ X25 ) )
% 0.29/0.45 => ( Option
% 0.29/0.45 != ( none @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.discI
% 0.29/0.45 thf(fact_126_option_Oexhaust,axiom,
% 0.29/0.45 ! [A: $tType,Y: option @ A] :
% 0.29/0.45 ( ( Y
% 0.29/0.45 != ( none @ A ) )
% 0.29/0.45 => ~ ! [X2: A] :
% 0.29/0.45 ( Y
% 0.29/0.45 != ( some @ A @ X2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.exhaust
% 0.29/0.45 thf(fact_127_option_Oinducts,axiom,
% 0.29/0.45 ! [A: $tType,P: ( option @ A ) > $o,Option: option @ A] :
% 0.29/0.45 ( ( P @ ( none @ A ) )
% 0.29/0.45 => ( ! [X5: A] : ( P @ ( some @ A @ X5 ) )
% 0.29/0.45 => ( P @ Option ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.inducts
% 0.29/0.45 thf(fact_128_split__option__ex,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ^ [P2: ( option @ A ) > $o] :
% 0.29/0.45 ? [X7: option @ A] : ( P2 @ X7 ) )
% 0.29/0.45 = ( ^ [P3: ( option @ A ) > $o] :
% 0.29/0.45 ( ( P3 @ ( none @ A ) )
% 0.29/0.45 | ? [X: A] : ( P3 @ ( some @ A @ X ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % split_option_ex
% 0.29/0.45 thf(fact_129_split__option__all,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ^ [P2: ( option @ A ) > $o] :
% 0.29/0.45 ! [X7: option @ A] : ( P2 @ X7 ) )
% 0.29/0.45 = ( ^ [P3: ( option @ A ) > $o] :
% 0.29/0.45 ( ( P3 @ ( none @ A ) )
% 0.29/0.45 & ! [X: A] : ( P3 @ ( some @ A @ X ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % split_option_all
% 0.29/0.45 thf(fact_130_combine__options__cases,axiom,
% 0.29/0.45 ! [A: $tType,B: $tType,X4: option @ A,P: ( option @ A ) > ( option @ B ) > $o,Y: option @ B] :
% 0.29/0.45 ( ( ( X4
% 0.29/0.45 = ( none @ A ) )
% 0.29/0.45 => ( P @ X4 @ Y ) )
% 0.29/0.45 => ( ( ( Y
% 0.29/0.45 = ( none @ B ) )
% 0.29/0.45 => ( P @ X4 @ Y ) )
% 0.29/0.45 => ( ! [A5: A,B4: B] :
% 0.29/0.45 ( ( X4
% 0.29/0.45 = ( some @ A @ A5 ) )
% 0.29/0.45 => ( ( Y
% 0.29/0.45 = ( some @ B @ B4 ) )
% 0.29/0.45 => ( P @ X4 @ Y ) ) )
% 0.29/0.45 => ( P @ X4 @ Y ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % combine_options_cases
% 0.29/0.45 thf(fact_131_sum_Osize__gen_I1_J,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType,Xa: A > nat,X4: B > nat,X14: A] :
% 0.29/0.45 ( ( basic_BNF_size_sum @ A @ B @ Xa @ X4 @ ( sum_Inl @ A @ B @ X14 ) )
% 0.29/0.45 = ( plus_plus @ nat @ ( Xa @ X14 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sum.size_gen(1)
% 0.29/0.45 thf(fact_132_sum_Osize__gen_I2_J,axiom,
% 0.29/0.45 ! [A: $tType,B: $tType,Xa: A > nat,X4: B > nat,X25: B] :
% 0.29/0.45 ( ( basic_BNF_size_sum @ A @ B @ Xa @ X4 @ ( sum_Inr @ B @ A @ X25 ) )
% 0.29/0.45 = ( plus_plus @ nat @ ( X4 @ X25 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sum.size_gen(2)
% 0.29/0.45 thf(fact_133_option_Osize__gen_I2_J,axiom,
% 0.29/0.45 ! [A: $tType,X4: A > nat,X25: A] :
% 0.29/0.45 ( ( size_option @ A @ X4 @ ( some @ A @ X25 ) )
% 0.29/0.45 = ( plus_plus @ nat @ ( X4 @ X25 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.size_gen(2)
% 0.29/0.45 thf(fact_134_option_Osize__gen_I1_J,axiom,
% 0.29/0.45 ! [A: $tType,X4: A > nat] :
% 0.29/0.45 ( ( size_option @ A @ X4 @ ( none @ A ) )
% 0.29/0.45 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.size_gen(1)
% 0.29/0.45 thf(fact_135_typerep_Osize_I2_J,axiom,
% 0.29/0.45 ! [X14: literal,X25: list @ typerep] :
% 0.29/0.45 ( ( size_size @ typerep @ ( typerep3 @ X14 @ X25 ) )
% 0.29/0.45 = ( plus_plus @ nat @ ( size_list @ typerep @ ( size_size @ typerep ) @ X25 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % typerep.size(2)
% 0.29/0.45 thf(fact_136_tuple__isomorphism_Osize__neq,axiom,
% 0.29/0.45 ! [A: $tType,B: $tType,C: $tType,X4: tuple_isomorphism @ A @ B @ C] :
% 0.29/0.45 ( ( size_size @ ( tuple_isomorphism @ A @ B @ C ) @ X4 )
% 0.29/0.45 != ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % tuple_isomorphism.size_neq
% 0.29/0.45 thf(fact_137_size__literal__def,axiom,
% 0.29/0.45 ( ( size_size @ literal )
% 0.29/0.45 = ( ^ [S2: literal] : ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % size_literal_def
% 0.29/0.45 thf(fact_138_size__unit__overloaded__def,axiom,
% 0.29/0.45 ( ( size_size @ product_unit )
% 0.29/0.45 = ( product_rec_unit @ nat @ ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % size_unit_overloaded_def
% 0.29/0.45 thf(fact_139_typerep_Osize__gen,axiom,
% 0.29/0.45 ! [X14: literal,X25: list @ typerep] :
% 0.29/0.45 ( ( size_typerep @ ( typerep3 @ X14 @ X25 ) )
% 0.29/0.45 = ( plus_plus @ nat @ ( size_list @ typerep @ size_typerep @ X25 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % typerep.size_gen
% 0.29/0.45 thf(fact_140_size__unit__def,axiom,
% 0.29/0.45 ( product_size_unit
% 0.29/0.45 = ( product_rec_unit @ nat @ ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % size_unit_def
% 0.29/0.45 thf(fact_141_tuple__isomorphism_Osize_I2_J,axiom,
% 0.29/0.45 ! [B: $tType,C: $tType,A: $tType,X14: A > ( product_prod @ B @ C ),X25: ( product_prod @ B @ C ) > A] :
% 0.29/0.45 ( ( size_size @ ( tuple_isomorphism @ A @ B @ C ) @ ( tuple_742722141rphism @ A @ B @ C @ X14 @ X25 ) )
% 0.29/0.45 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % tuple_isomorphism.size(2)
% 0.29/0.45 thf(fact_142_unit_Osize_I2_J,axiom,
% 0.29/0.45 ( ( size_size @ product_unit @ product_Unity )
% 0.29/0.45 = ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % unit.size(2)
% 0.29/0.45 thf(fact_143_unit__abs__eta__conv,axiom,
% 0.29/0.45 ! [A: $tType,F: product_unit > A] :
% 0.29/0.45 ( ( ^ [U: product_unit] : ( F @ product_Unity ) )
% 0.29/0.45 = F ) ).
% 0.29/0.45
% 0.29/0.45 % unit_abs_eta_conv
% 0.29/0.45 thf(fact_144_old_Ounit_Orec,axiom,
% 0.29/0.45 ! [T: $tType,F1: T] :
% 0.29/0.45 ( ( product_rec_unit @ T @ F1 @ product_Unity )
% 0.29/0.45 = F1 ) ).
% 0.29/0.45
% 0.29/0.45 % old.unit.rec
% 0.29/0.45 thf(fact_145_unit_Osize_I1_J,axiom,
% 0.29/0.45 ( ( product_size_unit @ product_Unity )
% 0.29/0.45 = ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % unit.size(1)
% 0.29/0.45 thf(fact_146_eq__sym__Unity__conv,axiom,
% 0.29/0.45 ! [X4: $o] :
% 0.29/0.45 ( ( X4
% 0.29/0.45 = ( product_Unity = product_Unity ) )
% 0.29/0.45 = X4 ) ).
% 0.29/0.45
% 0.29/0.45 % eq_sym_Unity_conv
% 0.29/0.45 thf(fact_147_unit__all__impI,axiom,
% 0.29/0.45 ! [P: product_unit > $o,Q: product_unit > $o] :
% 0.29/0.45 ( ( ( P @ product_Unity )
% 0.29/0.45 => ( Q @ product_Unity ) )
% 0.29/0.45 => ! [X6: product_unit] :
% 0.29/0.45 ( ( P @ X6 )
% 0.29/0.45 => ( Q @ X6 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % unit_all_impI
% 0.29/0.45 thf(fact_148_old_Ounit_Oinducts,axiom,
% 0.29/0.45 ! [P: product_unit > $o,Unit: product_unit] :
% 0.29/0.45 ( ( P @ product_Unity )
% 0.29/0.45 => ( P @ Unit ) ) ).
% 0.29/0.45
% 0.29/0.45 % old.unit.inducts
% 0.29/0.45 thf(fact_149_old_Ounit_Oexhaust,axiom,
% 0.29/0.45 ! [Y: product_unit] : ( Y = product_Unity ) ).
% 0.29/0.45
% 0.29/0.45 % old.unit.exhaust
% 0.29/0.45 thf(fact_150_tuple__isomorphism_Osize__gen,axiom,
% 0.29/0.45 ! [B: $tType,C: $tType,A: $tType,Xb: A > nat,Xa: B > nat,X4: C > nat,X14: A > ( product_prod @ B @ C ),X25: ( product_prod @ B @ C ) > A] :
% 0.29/0.45 ( ( tuple_1907371454rphism @ A @ B @ C @ Xb @ Xa @ X4 @ ( tuple_742722141rphism @ A @ B @ C @ X14 @ X25 ) )
% 0.29/0.45 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % tuple_isomorphism.size_gen
% 0.29/0.45 thf(fact_151_default__unit__def,axiom,
% 0.29/0.45 ( ( default_default @ product_unit )
% 0.29/0.45 = product_Unity ) ).
% 0.29/0.45
% 0.29/0.45 % default_unit_def
% 0.29/0.45 thf(fact_152_list_Osize__gen_I2_J,axiom,
% 0.29/0.45 ! [A: $tType,X4: A > nat,X21: A,X22: list @ A] :
% 0.29/0.45 ( ( size_list @ A @ X4 @ ( cons @ A @ X21 @ X22 ) )
% 0.29/0.45 = ( plus_plus @ nat @ ( plus_plus @ nat @ ( X4 @ X21 ) @ ( size_list @ A @ X4 @ X22 ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % list.size_gen(2)
% 0.29/0.45 thf(fact_153_length__Suc__conv,axiom,
% 0.29/0.45 ! [A: $tType,Xs: list @ A,N: nat] :
% 0.29/0.45 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.29/0.45 = ( suc @ N ) )
% 0.29/0.45 = ( ? [Y5: A,Ys: list @ A] :
% 0.29/0.45 ( ( Xs
% 0.29/0.45 = ( cons @ A @ Y5 @ Ys ) )
% 0.29/0.45 & ( ( size_size @ ( list @ A ) @ Ys )
% 0.29/0.45 = N ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % length_Suc_conv
% 0.29/0.45 thf(fact_154_Suc__length__conv,axiom,
% 0.29/0.45 ! [A: $tType,N: nat,Xs: list @ A] :
% 0.29/0.45 ( ( ( suc @ N )
% 0.29/0.45 = ( size_size @ ( list @ A ) @ Xs ) )
% 0.29/0.45 = ( ? [Y5: A,Ys: list @ A] :
% 0.29/0.45 ( ( Xs
% 0.29/0.45 = ( cons @ A @ Y5 @ Ys ) )
% 0.29/0.45 & ( ( size_size @ ( list @ A ) @ Ys )
% 0.29/0.45 = N ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Suc_length_conv
% 0.29/0.45 thf(fact_155_list_Osize_I4_J,axiom,
% 0.29/0.45 ! [A: $tType,X21: A,X22: list @ A] :
% 0.29/0.45 ( ( size_size @ ( list @ A ) @ ( cons @ A @ X21 @ X22 ) )
% 0.29/0.45 = ( plus_plus @ nat @ ( size_size @ ( list @ A ) @ X22 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % list.size(4)
% 0.29/0.45 thf(fact_156_length__Cons,axiom,
% 0.29/0.45 ! [A: $tType,X4: A,Xs: list @ A] :
% 0.29/0.45 ( ( size_size @ ( list @ A ) @ ( cons @ A @ X4 @ Xs ) )
% 0.29/0.45 = ( suc @ ( size_size @ ( list @ A ) @ Xs ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % length_Cons
% 0.29/0.45 thf(fact_157_gen__length__code_I2_J,axiom,
% 0.29/0.45 ! [B: $tType,N: nat,X4: B,Xs: list @ B] :
% 0.29/0.45 ( ( gen_length @ B @ N @ ( cons @ B @ X4 @ Xs ) )
% 0.29/0.45 = ( gen_length @ B @ ( suc @ N ) @ Xs ) ) ).
% 0.29/0.45
% 0.29/0.45 % gen_length_code(2)
% 0.29/0.45 thf(fact_158_linordered__field__class_Osign__simps_I26_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.45 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 0.29/0.45 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % linordered_field_class.sign_simps(26)
% 0.29/0.45 thf(fact_159_length__code,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( size_size @ ( list @ A ) )
% 0.29/0.45 = ( gen_length @ A @ ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % length_code
% 0.29/0.45 thf(fact_160_gen__length__def,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( gen_length @ A )
% 0.29/0.45 = ( ^ [N4: nat,Xs2: list @ A] : ( plus_plus @ nat @ N4 @ ( size_size @ ( list @ A ) @ Xs2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % gen_length_def
% 0.29/0.45 thf(fact_161_linordered__field__class_Osign__simps_I28_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [B2: A,A2: A,C2: A] :
% 0.29/0.45 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) )
% 0.29/0.45 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % linordered_field_class.sign_simps(28)
% 0.29/0.45 thf(fact_162_linordered__field__class_Osign__simps_I27_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.29/0.45 => ( ( plus_plus @ A )
% 0.29/0.45 = ( ^ [A4: A,B3: A] : ( plus_plus @ A @ B3 @ A4 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % linordered_field_class.sign_simps(27)
% 0.29/0.45 thf(fact_163_length__splice,axiom,
% 0.29/0.45 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.29/0.45 ( ( size_size @ ( list @ A ) @ ( splice @ A @ Xs @ Ys2 ) )
% 0.29/0.45 = ( plus_plus @ nat @ ( size_size @ ( list @ A ) @ Xs ) @ ( size_size @ ( list @ A ) @ Ys2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % length_splice
% 0.29/0.45 thf(fact_164_Shift__def,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( bNF_Greatest_Shift @ A )
% 0.29/0.45 = ( ^ [Kl: set @ ( list @ A ),K3: A] :
% 0.29/0.45 ( collect @ ( list @ A )
% 0.29/0.45 @ ^ [Kl2: list @ A] : ( member @ ( list @ A ) @ ( cons @ A @ K3 @ Kl2 ) @ Kl ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Shift_def
% 0.29/0.45 thf(fact_165_is__num__normalize_I1_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.45 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 0.29/0.45 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % is_num_normalize(1)
% 0.29/0.45 thf(fact_166_option_Ocollapse,axiom,
% 0.29/0.45 ! [A: $tType,Option: option @ A] :
% 0.29/0.45 ( ( Option
% 0.29/0.45 != ( none @ A ) )
% 0.29/0.45 => ( ( some @ A @ ( the @ A @ Option ) )
% 0.29/0.45 = Option ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.collapse
% 0.29/0.45 thf(fact_167_old_Ounit_Ocase,axiom,
% 0.29/0.45 ! [A: $tType,F: A] :
% 0.29/0.45 ( ( product_case_unit @ A @ F @ product_Unity )
% 0.29/0.45 = F ) ).
% 0.29/0.45
% 0.29/0.45 % old.unit.case
% 0.29/0.45 thf(fact_168_case__optionE,axiom,
% 0.29/0.45 ! [A: $tType,P: $o,Q: A > $o,X4: option @ A] :
% 0.29/0.45 ( ( case_option @ $o @ A @ P @ Q @ X4 )
% 0.29/0.45 => ( ( ( X4
% 0.29/0.45 = ( none @ A ) )
% 0.29/0.45 => ~ P )
% 0.29/0.45 => ~ ! [Y3: A] :
% 0.29/0.45 ( ( X4
% 0.29/0.45 = ( some @ A @ Y3 ) )
% 0.29/0.45 => ~ ( Q @ Y3 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % case_optionE
% 0.29/0.45 thf(fact_169_option_Odisc__eq__case_I1_J,axiom,
% 0.29/0.45 ! [A: $tType,Option: option @ A] :
% 0.29/0.45 ( ( Option
% 0.29/0.45 = ( none @ A ) )
% 0.29/0.45 = ( case_option @ $o @ A @ $true
% 0.29/0.45 @ ^ [Uu: A] : $false
% 0.29/0.45 @ Option ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.disc_eq_case(1)
% 0.29/0.45 thf(fact_170_option_Odisc__eq__case_I2_J,axiom,
% 0.29/0.45 ! [A: $tType,Option: option @ A] :
% 0.29/0.45 ( ( Option
% 0.29/0.45 != ( none @ A ) )
% 0.29/0.45 = ( case_option @ $o @ A @ $false
% 0.29/0.45 @ ^ [Uu: A] : $true
% 0.29/0.45 @ Option ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.disc_eq_case(2)
% 0.29/0.45 thf(fact_171_option_Osimps_I4_J,axiom,
% 0.29/0.45 ! [A: $tType,B: $tType,F1: B,F2: A > B] :
% 0.29/0.45 ( ( case_option @ B @ A @ F1 @ F2 @ ( none @ A ) )
% 0.29/0.45 = F1 ) ).
% 0.29/0.45
% 0.29/0.45 % option.simps(4)
% 0.29/0.45 thf(fact_172_option_Osimps_I5_J,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType,F1: B,F2: A > B,X25: A] :
% 0.29/0.45 ( ( case_option @ B @ A @ F1 @ F2 @ ( some @ A @ X25 ) )
% 0.29/0.45 = ( F2 @ X25 ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.simps(5)
% 0.29/0.45 thf(fact_173_option_Ocase__distrib,axiom,
% 0.29/0.45 ! [C: $tType,B: $tType,A: $tType,H: B > C,F1: B,F2: A > B,Option: option @ A] :
% 0.29/0.45 ( ( H @ ( case_option @ B @ A @ F1 @ F2 @ Option ) )
% 0.29/0.45 = ( case_option @ C @ A @ ( H @ F1 )
% 0.29/0.45 @ ^ [X: A] : ( H @ ( F2 @ X ) )
% 0.29/0.45 @ Option ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.case_distrib
% 0.29/0.45 thf(fact_174_option_Osplit__sel,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > B,Option: option @ A] :
% 0.29/0.45 ( ( P @ ( case_option @ B @ A @ F1 @ F2 @ Option ) )
% 0.29/0.45 = ( ( ( Option
% 0.29/0.45 = ( none @ A ) )
% 0.29/0.45 => ( P @ F1 ) )
% 0.29/0.45 & ( ( Option
% 0.29/0.45 = ( some @ A @ ( the @ A @ Option ) ) )
% 0.29/0.45 => ( P @ ( F2 @ ( the @ A @ Option ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.split_sel
% 0.29/0.45 thf(fact_175_option_Ocase__eq__if,axiom,
% 0.29/0.45 ! [A: $tType,B: $tType] :
% 0.29/0.45 ( ( case_option @ B @ A )
% 0.29/0.45 = ( ^ [F12: B,F22: A > B,Option2: option @ A] :
% 0.29/0.45 ( if @ B
% 0.29/0.45 @ ( Option2
% 0.29/0.45 = ( none @ A ) )
% 0.29/0.45 @ F12
% 0.29/0.45 @ ( F22 @ ( the @ A @ Option2 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.case_eq_if
% 0.29/0.45 thf(fact_176_option_Osplit__sel__asm,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > B,Option: option @ A] :
% 0.29/0.45 ( ( P @ ( case_option @ B @ A @ F1 @ F2 @ Option ) )
% 0.29/0.45 = ( ~ ( ( ( Option
% 0.29/0.45 = ( none @ A ) )
% 0.29/0.45 & ~ ( P @ F1 ) )
% 0.29/0.45 | ( ( Option
% 0.29/0.45 = ( some @ A @ ( the @ A @ Option ) ) )
% 0.29/0.45 & ~ ( P @ ( F2 @ ( the @ A @ Option ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.split_sel_asm
% 0.29/0.45 thf(fact_177_case__unit__Unity,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( product_case_unit @ A )
% 0.29/0.45 = ( ^ [F4: A,U: product_unit] : F4 ) ) ).
% 0.29/0.45
% 0.29/0.45 % case_unit_Unity
% 0.29/0.45 thf(fact_178_unit_Ocase__distrib,axiom,
% 0.29/0.45 ! [A: $tType,B: $tType,H: A > B,F: A,Unit: product_unit] :
% 0.29/0.45 ( ( H @ ( product_case_unit @ A @ F @ Unit ) )
% 0.29/0.45 = ( product_case_unit @ B @ ( H @ F ) @ Unit ) ) ).
% 0.29/0.45
% 0.29/0.45 % unit.case_distrib
% 0.29/0.45 thf(fact_179_option_Osel,axiom,
% 0.29/0.45 ! [A: $tType,X25: A] :
% 0.29/0.45 ( ( the @ A @ ( some @ A @ X25 ) )
% 0.29/0.45 = X25 ) ).
% 0.29/0.45
% 0.29/0.45 % option.sel
% 0.29/0.45 thf(fact_180_option_Oexpand,axiom,
% 0.29/0.45 ! [A: $tType,Option: option @ A,Option3: option @ A] :
% 0.29/0.45 ( ( ( Option
% 0.29/0.45 = ( none @ A ) )
% 0.29/0.45 = ( Option3
% 0.29/0.45 = ( none @ A ) ) )
% 0.29/0.45 => ( ( ( Option
% 0.29/0.45 != ( none @ A ) )
% 0.29/0.45 => ( ( Option3
% 0.29/0.45 != ( none @ A ) )
% 0.29/0.45 => ( ( the @ A @ Option )
% 0.29/0.45 = ( the @ A @ Option3 ) ) ) )
% 0.29/0.45 => ( Option = Option3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.expand
% 0.29/0.45 thf(fact_181_option_Oexhaust__sel,axiom,
% 0.29/0.45 ! [A: $tType,Option: option @ A] :
% 0.29/0.45 ( ( Option
% 0.29/0.45 != ( none @ A ) )
% 0.29/0.45 => ( Option
% 0.29/0.45 = ( some @ A @ ( the @ A @ Option ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.exhaust_sel
% 0.29/0.45 thf(fact_182_disjE__realizer2,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType,P: $o,Q: A > $o,X4: option @ A,R: B > $o,F: B,G: A > B] :
% 0.29/0.45 ( ( case_option @ $o @ A @ P @ Q @ X4 )
% 0.29/0.45 => ( ( P
% 0.29/0.45 => ( R @ F ) )
% 0.29/0.45 => ( ! [Q2: A] :
% 0.29/0.45 ( ( Q @ Q2 )
% 0.29/0.45 => ( R @ ( G @ Q2 ) ) )
% 0.29/0.45 => ( R @ ( case_option @ B @ A @ F @ G @ X4 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % disjE_realizer2
% 0.29/0.45 thf(fact_183_option_Othe__def,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( the @ A )
% 0.29/0.45 = ( case_option @ A @ A @ ( undefined @ A )
% 0.29/0.45 @ ^ [X24: A] : X24 ) ) ).
% 0.29/0.45
% 0.29/0.45 % option.the_def
% 0.29/0.45 thf(fact_184_num_Osize_I5_J,axiom,
% 0.29/0.45 ! [X25: num] :
% 0.29/0.45 ( ( size_size @ num @ ( bit0 @ X25 ) )
% 0.29/0.45 = ( plus_plus @ nat @ ( size_size @ num @ X25 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % num.size(5)
% 0.29/0.45 thf(fact_185_num_Osize__gen_I2_J,axiom,
% 0.29/0.45 ! [X25: num] :
% 0.29/0.45 ( ( size_num @ ( bit0 @ X25 ) )
% 0.29/0.45 = ( plus_plus @ nat @ ( size_num @ X25 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % num.size_gen(2)
% 0.29/0.45 thf(fact_186_num_Osize_I6_J,axiom,
% 0.29/0.45 ! [X33: num] :
% 0.29/0.45 ( ( size_size @ num @ ( bit1 @ X33 ) )
% 0.29/0.45 = ( plus_plus @ nat @ ( size_size @ num @ X33 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % num.size(6)
% 0.29/0.45 thf(fact_187_num_Osize__gen_I3_J,axiom,
% 0.29/0.45 ! [X33: num] :
% 0.29/0.45 ( ( size_num @ ( bit1 @ X33 ) )
% 0.29/0.45 = ( plus_plus @ nat @ ( size_num @ X33 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % num.size_gen(3)
% 0.29/0.45 thf(fact_188_nat__of__num__code_I3_J,axiom,
% 0.29/0.45 ! [N: num] :
% 0.29/0.45 ( ( nat_of_num @ ( bit1 @ N ) )
% 0.29/0.45 = ( suc @ ( plus_plus @ nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % nat_of_num_code(3)
% 0.29/0.45 thf(fact_189_nat__of__num_Osimps_I3_J,axiom,
% 0.29/0.45 ! [X4: num] :
% 0.29/0.45 ( ( nat_of_num @ ( bit1 @ X4 ) )
% 0.29/0.45 = ( suc @ ( plus_plus @ nat @ ( nat_of_num @ X4 ) @ ( nat_of_num @ X4 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % nat_of_num.simps(3)
% 0.29/0.45 thf(fact_190_nat__of__num__add,axiom,
% 0.29/0.45 ! [X4: num,Y: num] :
% 0.29/0.45 ( ( nat_of_num @ ( plus_plus @ num @ X4 @ Y ) )
% 0.29/0.45 = ( plus_plus @ nat @ ( nat_of_num @ X4 ) @ ( nat_of_num @ Y ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % nat_of_num_add
% 0.29/0.45 thf(fact_191_nat__of__num__neq__0,axiom,
% 0.29/0.45 ! [X4: num] :
% 0.29/0.45 ( ( nat_of_num @ X4 )
% 0.29/0.45 != ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % nat_of_num_neq_0
% 0.29/0.45 thf(fact_192_nat__of__num_Osimps_I2_J,axiom,
% 0.29/0.45 ! [X4: num] :
% 0.29/0.45 ( ( nat_of_num @ ( bit0 @ X4 ) )
% 0.29/0.45 = ( plus_plus @ nat @ ( nat_of_num @ X4 ) @ ( nat_of_num @ X4 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % nat_of_num.simps(2)
% 0.29/0.45 thf(fact_193_nat__of__num__code_I2_J,axiom,
% 0.29/0.45 ! [N: num] :
% 0.29/0.45 ( ( nat_of_num @ ( bit0 @ N ) )
% 0.29/0.45 = ( plus_plus @ nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % nat_of_num_code(2)
% 0.29/0.45 thf(fact_194_nat__of__num__inc,axiom,
% 0.29/0.45 ! [X4: num] :
% 0.29/0.45 ( ( nat_of_num @ ( inc @ X4 ) )
% 0.29/0.45 = ( suc @ ( nat_of_num @ X4 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % nat_of_num_inc
% 0.29/0.45 thf(fact_195_nat__of__num_Osimps_I1_J,axiom,
% 0.29/0.45 ( ( nat_of_num @ one2 )
% 0.29/0.45 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % nat_of_num.simps(1)
% 0.29/0.45 thf(fact_196_num_Osize__gen_I1_J,axiom,
% 0.29/0.45 ( ( size_num @ one2 )
% 0.29/0.45 = ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % num.size_gen(1)
% 0.29/0.45 thf(fact_197_num_Osize_I4_J,axiom,
% 0.29/0.45 ( ( size_size @ num @ one2 )
% 0.29/0.45 = ( zero_zero @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 % num.size(4)
% 0.29/0.45 thf(fact_198_add__2__eq__Suc,axiom,
% 0.29/0.45 ! [N: nat] :
% 0.29/0.45 ( ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ N )
% 0.29/0.45 = ( suc @ ( suc @ N ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_2_eq_Suc
% 0.29/0.45 thf(fact_199_add__2__eq__Suc_H,axiom,
% 0.29/0.45 ! [N: nat] :
% 0.29/0.45 ( ( plus_plus @ nat @ N @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) )
% 0.29/0.45 = ( suc @ ( suc @ N ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_2_eq_Suc'
% 0.29/0.45 thf(fact_200_numeral__plus__numeral,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( numeral @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [M: num,N: num] :
% 0.29/0.45 ( ( plus_plus @ A @ ( numeral_numeral @ A @ M ) @ ( numeral_numeral @ A @ N ) )
% 0.29/0.45 = ( numeral_numeral @ A @ ( plus_plus @ num @ M @ N ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % numeral_plus_numeral
% 0.29/0.45 thf(fact_201_add__numeral__left,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( numeral @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [V: num,W: num,Z: A] :
% 0.29/0.45 ( ( plus_plus @ A @ ( numeral_numeral @ A @ V ) @ ( plus_plus @ A @ ( numeral_numeral @ A @ W ) @ Z ) )
% 0.29/0.45 = ( plus_plus @ A @ ( numeral_numeral @ A @ ( plus_plus @ num @ V @ W ) ) @ Z ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add_numeral_left
% 0.29/0.45 thf(fact_202_Suc__numeral,axiom,
% 0.29/0.45 ! [N: num] :
% 0.29/0.45 ( ( suc @ ( numeral_numeral @ nat @ N ) )
% 0.29/0.45 = ( numeral_numeral @ nat @ ( plus_plus @ num @ N @ one2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Suc_numeral
% 0.29/0.45 thf(fact_203_numeral__Bit0,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( numeral @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [N: num] :
% 0.29/0.45 ( ( numeral_numeral @ A @ ( bit0 @ N ) )
% 0.29/0.45 = ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % numeral_Bit0
% 0.29/0.45 thf(fact_204_numeral__code_I2_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( numeral @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [N: num] :
% 0.29/0.45 ( ( numeral_numeral @ A @ ( bit0 @ N ) )
% 0.29/0.45 = ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % numeral_code(2)
% 0.29/0.45 thf(fact_205_zero__neq__numeral,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 0.29/0.45 => ! [N: num] :
% 0.29/0.45 ( ( zero_zero @ A )
% 0.29/0.45 != ( numeral_numeral @ A @ N ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % zero_neq_numeral
% 0.29/0.45 thf(fact_206_eval__nat__numeral_I3_J,axiom,
% 0.29/0.45 ! [N: num] :
% 0.29/0.45 ( ( numeral_numeral @ nat @ ( bit1 @ N ) )
% 0.29/0.45 = ( suc @ ( numeral_numeral @ nat @ ( bit0 @ N ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % eval_nat_numeral(3)
% 0.29/0.45 thf(fact_207_numeral__1__eq__Suc__0,axiom,
% 0.29/0.45 ( ( numeral_numeral @ nat @ one2 )
% 0.29/0.45 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % numeral_1_eq_Suc_0
% 0.29/0.45 thf(fact_208_numeral__2__eq__2,axiom,
% 0.29/0.45 ( ( numeral_numeral @ nat @ ( bit0 @ one2 ) )
% 0.29/0.45 = ( suc @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % numeral_2_eq_2
% 0.29/0.45 thf(fact_209_numeral__3__eq__3,axiom,
% 0.29/0.45 ( ( numeral_numeral @ nat @ ( bit1 @ one2 ) )
% 0.29/0.45 = ( suc @ ( suc @ ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % numeral_3_eq_3
% 0.29/0.45 thf(fact_210_Suc3__eq__add__3,axiom,
% 0.29/0.46 ! [N: nat] :
% 0.29/0.46 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 0.29/0.46 = ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) @ N ) ) ).
% 0.29/0.46
% 0.29/0.46 % Suc3_eq_add_3
% 0.29/0.46 thf(fact_211_Suc__nat__number__of__add,axiom,
% 0.29/0.46 ! [V: num,N: nat] :
% 0.29/0.46 ( ( suc @ ( plus_plus @ nat @ ( numeral_numeral @ nat @ V ) @ N ) )
% 0.29/0.46 = ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( plus_plus @ num @ V @ one2 ) ) @ N ) ) ).
% 0.29/0.46
% 0.29/0.46 % Suc_nat_number_of_add
% 0.29/0.46 thf(fact_212_zero__not__eq__two,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semiring_div_parity @ A @ ( type2 @ A ) )
% 0.29/0.46 => ( ( zero_zero @ A )
% 0.29/0.46 != ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_not_eq_two
% 0.29/0.46 thf(fact_213_one__plus__numeral,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( numeral @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [N: num] :
% 0.29/0.46 ( ( plus_plus @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ N ) )
% 0.29/0.46 = ( numeral_numeral @ A @ ( plus_plus @ num @ one2 @ N ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % one_plus_numeral
% 0.29/0.46 thf(fact_214_Suc__1,axiom,
% 0.29/0.46 ( ( suc @ ( one_one @ nat ) )
% 0.29/0.46 = ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Suc_1
% 0.29/0.46 thf(fact_215_one__add__one,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( numeral @ A @ ( type2 @ A ) )
% 0.29/0.46 => ( ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
% 0.29/0.46 = ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % one_add_one
% 0.29/0.46 thf(fact_216_numeral__plus__one,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( numeral @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [N: num] :
% 0.29/0.46 ( ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( one_one @ A ) )
% 0.29/0.46 = ( numeral_numeral @ A @ ( plus_plus @ num @ N @ one2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % numeral_plus_one
% 0.29/0.46 thf(fact_217_one__plus__numeral__commute,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( numeral @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [X4: num] :
% 0.29/0.46 ( ( plus_plus @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ X4 ) )
% 0.29/0.46 = ( plus_plus @ A @ ( numeral_numeral @ A @ X4 ) @ ( one_one @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % one_plus_numeral_commute
% 0.29/0.46 thf(fact_218_One__nat__def,axiom,
% 0.29/0.46 ( ( one_one @ nat )
% 0.29/0.46 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % One_nat_def
% 0.29/0.46 thf(fact_219_one__reorient,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( one @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [X4: A] :
% 0.29/0.46 ( ( ( one_one @ A )
% 0.29/0.46 = X4 )
% 0.29/0.46 = ( X4
% 0.29/0.46 = ( one_one @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % one_reorient
% 0.29/0.46 thf(fact_220_Suc__eq__plus1,axiom,
% 0.29/0.46 ( suc
% 0.29/0.46 = ( ^ [N4: nat] : ( plus_plus @ nat @ N4 @ ( one_one @ nat ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Suc_eq_plus1
% 0.29/0.46 thf(fact_221_Suc__eq__plus1__left,axiom,
% 0.29/0.46 ( suc
% 0.29/0.46 = ( plus_plus @ nat @ ( one_one @ nat ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Suc_eq_plus1_left
% 0.29/0.46 thf(fact_222_numeral__Bit1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( numeral @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [N: num] :
% 0.29/0.46 ( ( numeral_numeral @ A @ ( bit1 @ N ) )
% 0.29/0.46 = ( plus_plus @ A @ ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( numeral_numeral @ A @ N ) ) @ ( one_one @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % numeral_Bit1
% 0.29/0.46 thf(fact_223_numeral__inc,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( numeral @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [X4: num] :
% 0.29/0.46 ( ( numeral_numeral @ A @ ( inc @ X4 ) )
% 0.29/0.46 = ( plus_plus @ A @ ( numeral_numeral @ A @ X4 ) @ ( one_one @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % numeral_inc
% 0.29/0.46 thf(fact_224_numeral__code_I3_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( numeral @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [N: num] :
% 0.29/0.46 ( ( numeral_numeral @ A @ ( bit1 @ N ) )
% 0.29/0.46 = ( plus_plus @ A @ ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( numeral_numeral @ A @ N ) ) @ ( one_one @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % numeral_code(3)
% 0.29/0.46 thf(fact_225_nat__1__add__1,axiom,
% 0.29/0.46 ( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
% 0.29/0.46 = ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % nat_1_add_1
% 0.29/0.46 thf(fact_226_zero__neq__one,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( zero_neq_one @ A @ ( type2 @ A ) )
% 0.29/0.46 => ( ( zero_zero @ A )
% 0.29/0.46 != ( one_one @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_neq_one
% 0.29/0.46 thf(fact_227_dbl__inc__simps_I2_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.29/0.46 => ( ( neg_numeral_dbl_inc @ A @ ( zero_zero @ A ) )
% 0.29/0.46 = ( one_one @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % dbl_inc_simps(2)
% 0.29/0.46 thf(fact_228_one__natural_Orsp,axiom,
% 0.29/0.46 ( ( one_one @ nat )
% 0.29/0.46 = ( one_one @ nat ) ) ).
% 0.29/0.46
% 0.29/0.46 % one_natural.rsp
% 0.29/0.46 thf(fact_229_dbl__inc__def,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.29/0.46 => ( ( neg_numeral_dbl_inc @ A )
% 0.29/0.46 = ( ^ [X: A] : ( plus_plus @ A @ ( plus_plus @ A @ X @ X ) @ ( one_one @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % dbl_inc_def
% 0.29/0.46 thf(fact_230_Suc__div__eq__add3__div__numeral,axiom,
% 0.29/0.46 ! [M: nat,V: num] :
% 0.29/0.46 ( ( divide_divide @ nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral @ nat @ V ) )
% 0.29/0.46 = ( divide_divide @ nat @ ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) @ M ) @ ( numeral_numeral @ nat @ V ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Suc_div_eq_add3_div_numeral
% 0.29/0.46 thf(fact_231_div__Suc__eq__div__add3,axiom,
% 0.29/0.46 ! [M: nat,N: nat] :
% 0.29/0.46 ( ( divide_divide @ nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 0.29/0.46 = ( divide_divide @ nat @ M @ ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) @ N ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % div_Suc_eq_div_add3
% 0.29/0.46 thf(fact_232_divide__zero,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semidom_divide @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( divide_divide @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.46 = ( zero_zero @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % divide_zero
% 0.29/0.46 thf(fact_233_divide__zero__left,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semidom_divide @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( divide_divide @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 = ( zero_zero @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % divide_zero_left
% 0.29/0.46 thf(fact_234_divide__eq__0__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( field @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ( divide_divide @ A @ A2 @ B2 )
% 0.29/0.46 = ( zero_zero @ A ) )
% 0.29/0.46 = ( ( A2
% 0.29/0.46 = ( zero_zero @ A ) )
% 0.29/0.46 | ( B2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % divide_eq_0_iff
% 0.29/0.46 thf(fact_235_divide__cancel__left,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( field @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [C2: A,A2: A,B2: A] :
% 0.29/0.46 ( ( ( divide_divide @ A @ C2 @ A2 )
% 0.29/0.46 = ( divide_divide @ A @ C2 @ B2 ) )
% 0.29/0.46 = ( ( C2
% 0.29/0.46 = ( zero_zero @ A ) )
% 0.29/0.46 | ( A2 = B2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % divide_cancel_left
% 0.29/0.46 thf(fact_236_divide__cancel__right,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( field @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [A2: A,C2: A,B2: A] :
% 0.29/0.46 ( ( ( divide_divide @ A @ A2 @ C2 )
% 0.29/0.46 = ( divide_divide @ A @ B2 @ C2 ) )
% 0.29/0.46 = ( ( C2
% 0.29/0.46 = ( zero_zero @ A ) )
% 0.29/0.46 | ( A2 = B2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % divide_cancel_right
% 0.29/0.46 thf(fact_237_division__ring__divide__zero,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( division_ring @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( divide_divide @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.46 = ( zero_zero @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % division_ring_divide_zero
% 0.29/0.46 thf(fact_238_div__0,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semiring_div @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( divide_divide @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 = ( zero_zero @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % div_0
% 0.29/0.46 thf(fact_239_div__by__0,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semiring_div @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( divide_divide @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.46 = ( zero_zero @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % div_by_0
% 0.29/0.46 thf(fact_240_div__self,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semidom_divide @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( A2
% 0.29/0.46 != ( zero_zero @ A ) )
% 0.29/0.46 => ( ( divide_divide @ A @ A2 @ A2 )
% 0.29/0.46 = ( one_one @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % div_self
% 0.29/0.46 thf(fact_241_divide__eq__1__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( field @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ( divide_divide @ A @ A2 @ B2 )
% 0.29/0.46 = ( one_one @ A ) )
% 0.29/0.46 = ( ( B2
% 0.29/0.46 != ( zero_zero @ A ) )
% 0.29/0.46 & ( A2 = B2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % divide_eq_1_iff
% 0.29/0.46 thf(fact_242_one__eq__divide__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( field @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ( one_one @ A )
% 0.29/0.46 = ( divide_divide @ A @ A2 @ B2 ) )
% 0.29/0.46 = ( ( B2
% 0.29/0.46 != ( zero_zero @ A ) )
% 0.29/0.46 & ( A2 = B2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % one_eq_divide_iff
% 0.29/0.46 thf(fact_243_divide__self,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( division_ring @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( A2
% 0.29/0.46 != ( zero_zero @ A ) )
% 0.29/0.46 => ( ( divide_divide @ A @ A2 @ A2 )
% 0.29/0.46 = ( one_one @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % divide_self
% 0.29/0.46 thf(fact_244_divide__self__if,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( division_ring @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( ( A2
% 0.29/0.46 = ( zero_zero @ A ) )
% 0.29/0.46 => ( ( divide_divide @ A @ A2 @ A2 )
% 0.29/0.46 = ( zero_zero @ A ) ) )
% 0.29/0.46 & ( ( A2
% 0.29/0.46 != ( zero_zero @ A ) )
% 0.29/0.46 => ( ( divide_divide @ A @ A2 @ A2 )
% 0.29/0.46 = ( one_one @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % divide_self_if
% 0.29/0.46 thf(fact_245_divide__eq__eq__1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [B2: A,A2: A] :
% 0.29/0.46 ( ( ( divide_divide @ A @ B2 @ A2 )
% 0.29/0.46 = ( one_one @ A ) )
% 0.29/0.46 = ( ( A2
% 0.29/0.46 != ( zero_zero @ A ) )
% 0.29/0.46 & ( A2 = B2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % divide_eq_eq_1
% 0.29/0.46 thf(fact_246_eq__divide__eq__1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [B2: A,A2: A] :
% 0.29/0.46 ( ( ( one_one @ A )
% 0.29/0.46 = ( divide_divide @ A @ B2 @ A2 ) )
% 0.29/0.46 = ( ( A2
% 0.29/0.46 != ( zero_zero @ A ) )
% 0.29/0.46 & ( A2 = B2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % eq_divide_eq_1
% 0.29/0.46 thf(fact_247_one__divide__eq__0__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( ( divide_divide @ A @ ( one_one @ A ) @ A2 )
% 0.29/0.46 = ( zero_zero @ A ) )
% 0.29/0.46 = ( A2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % one_divide_eq_0_iff
% 0.29/0.46 thf(fact_248_zero__eq__1__divide__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( ( zero_zero @ A )
% 0.29/0.46 = ( divide_divide @ A @ ( one_one @ A ) @ A2 ) )
% 0.29/0.46 = ( A2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_eq_1_divide_iff
% 0.29/0.46 thf(fact_249_div__1,axiom,
% 0.29/0.46 ! [M: nat] :
% 0.29/0.46 ( ( divide_divide @ nat @ M @ ( suc @ ( zero_zero @ nat ) ) )
% 0.29/0.46 = M ) ).
% 0.29/0.46
% 0.29/0.46 % div_1
% 0.29/0.46 thf(fact_250_div__add__self2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semiring_div @ A @ ( type2 @ A ) )
% 0.29/0.46 => ! [B2: A,A2: A] :
% 0.29/0.46 ( ( B2
% 0.29/0.46 != ( zero_zero @ A ) )
% 0.29/0.46 => ( ( divide_divide @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 0.29/0.46 = ( plus_plus @ A @ ( divide_divide @ A @ A2 @ B2 ) @ ( one_one @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % div_add_self2
% 0.29/0.46
% 0.29/0.46 %----Type constructors (115)
% 0.29/0.46 thf(tcon_BinDag__Mirabelle__rybootvolr_Odag___Code__Evaluation_Oterm__of,axiom,
% 0.29/0.46 code_term_of @ binDag_Mirabelle_dag @ ( type2 @ binDag_Mirabelle_dag ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_BinDag__Mirabelle__rybootvolr_Odag___HOL_Oequal,axiom,
% 0.29/0.46 cl_HOL_Oequal @ binDag_Mirabelle_dag @ ( type2 @ binDag_Mirabelle_dag ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Record_Otuple__isomorphism___Code__Evaluation_Oterm__of_1,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType,A8: $tType] :
% 0.29/0.46 ( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 & ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 0.29/0.46 & ( typerep2 @ A8 @ ( type2 @ A8 ) ) )
% 0.29/0.46 => ( code_term_of @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) @ ( type2 @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Record_Otuple__isomorphism___HOL_Oequal_2,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType,A8: $tType] : ( cl_HOL_Oequal @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) @ ( type2 @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Numeral_Onatural___Code__Evaluation_Oterm__of_3,axiom,
% 0.29/0.46 code_term_of @ code_natural @ ( type2 @ code_natural ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Numeral_Onatural___HOL_Oequal_4,axiom,
% 0.29/0.46 cl_HOL_Oequal @ code_natural @ ( type2 @ code_natural ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Evaluation_Oterm___Code__Evaluation_Oterm__of_5,axiom,
% 0.29/0.46 code_term_of @ code_term @ ( type2 @ code_term ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Evaluation_Oterm___HOL_Oequal_6,axiom,
% 0.29/0.46 cl_HOL_Oequal @ code_term @ ( type2 @ code_term ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Code__Evaluation_Oterm__of_7,axiom,
% 0.29/0.46 code_term_of @ product_unit @ ( type2 @ product_unit ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___HOL_Oequal_8,axiom,
% 0.29/0.46 cl_HOL_Oequal @ product_unit @ ( type2 @ product_unit ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___Code__Evaluation_Oterm__of_9,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] :
% 0.29/0.46 ( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 & ( typerep2 @ A7 @ ( type2 @ A7 ) ) )
% 0.29/0.46 => ( code_term_of @ ( product_prod @ A6 @ A7 ) @ ( type2 @ ( product_prod @ A6 @ A7 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___HOL_Oequal_10,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] : ( cl_HOL_Oequal @ ( product_prod @ A6 @ A7 ) @ ( type2 @ ( product_prod @ A6 @ A7 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Typerep_Otyperep___Code__Evaluation_Oterm__of_11,axiom,
% 0.29/0.46 code_term_of @ typerep @ ( type2 @ typerep ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Typerep_Otyperep___HOL_Oequal_12,axiom,
% 0.29/0.46 cl_HOL_Oequal @ typerep @ ( type2 @ typerep ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_String_Oliteral___Code__Evaluation_Oterm__of_13,axiom,
% 0.29/0.46 code_term_of @ literal @ ( type2 @ literal ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_String_Oliteral___HOL_Oequal_14,axiom,
% 0.29/0.46 cl_HOL_Oequal @ literal @ ( type2 @ literal ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Simpl__Heap_Oref___Code__Evaluation_Oterm__of_15,axiom,
% 0.29/0.46 code_term_of @ simpl_ref @ ( type2 @ simpl_ref ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Option_Ooption___Code__Evaluation_Oterm__of_16,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 => ( code_term_of @ ( option @ A6 ) @ ( type2 @ ( option @ A6 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Option_Ooption___HOL_Oequal_17,axiom,
% 0.29/0.46 ! [A6: $tType] : ( cl_HOL_Oequal @ ( option @ A6 ) @ ( type2 @ ( option @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Sum__Type_Osum___Code__Evaluation_Oterm__of_18,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] :
% 0.29/0.46 ( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 & ( typerep2 @ A7 @ ( type2 @ A7 ) ) )
% 0.29/0.46 => ( code_term_of @ ( sum_sum @ A6 @ A7 ) @ ( type2 @ ( sum_sum @ A6 @ A7 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Sum__Type_Osum___HOL_Oequal_19,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] : ( cl_HOL_Oequal @ ( sum_sum @ A6 @ A7 ) @ ( type2 @ ( sum_sum @ A6 @ A7 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_List_Olist___Code__Evaluation_Oterm__of_20,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 => ( code_term_of @ ( list @ A6 ) @ ( type2 @ ( list @ A6 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_List_Olist___HOL_Oequal_21,axiom,
% 0.29/0.46 ! [A6: $tType] : ( cl_HOL_Oequal @ ( list @ A6 ) @ ( type2 @ ( list @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Code__Evaluation_Oterm__of_22,axiom,
% 0.29/0.46 code_term_of @ $o @ ( type2 @ $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___HOL_Oequal_23,axiom,
% 0.29/0.46 cl_HOL_Oequal @ $o @ ( type2 @ $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Code__Evaluation_Oterm__of_24,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 => ( code_term_of @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___HOL_Oequal_25,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( cl_HOL_Oequal @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 => ( cl_HOL_Oequal @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Num_Onum___Code__Evaluation_Oterm__of_26,axiom,
% 0.29/0.46 code_term_of @ num @ ( type2 @ num ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Num_Onum___HOL_Oequal_27,axiom,
% 0.29/0.46 cl_HOL_Oequal @ num @ ( type2 @ num ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Code__Evaluation_Oterm__of_28,axiom,
% 0.29/0.46 code_term_of @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___HOL_Oequal_29,axiom,
% 0.29/0.46 cl_HOL_Oequal @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Code__Evaluation_Oterm__of_30,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] :
% 0.29/0.46 ( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 & ( typerep2 @ A7 @ ( type2 @ A7 ) ) )
% 0.29/0.46 => ( code_term_of @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___HOL_Oequal_31,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] :
% 0.29/0.46 ( ( ( enum @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 & ( cl_HOL_Oequal @ A7 @ ( type2 @ A7 ) ) )
% 0.29/0.46 => ( cl_HOL_Oequal @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Typerep_Otyperep,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] :
% 0.29/0.46 ( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 & ( typerep2 @ A7 @ ( type2 @ A7 ) ) )
% 0.29/0.46 => ( typerep2 @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Enum_Oenum,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] :
% 0.29/0.46 ( ( ( enum @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 & ( enum @ A7 @ ( type2 @ A7 ) ) )
% 0.29/0.46 => ( enum @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Typerep_Otyperep_32,axiom,
% 0.29/0.46 typerep2 @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Num_Onum___Typerep_Otyperep_33,axiom,
% 0.29/0.46 typerep2 @ num @ ( type2 @ num ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Typerep_Otyperep_34,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 => ( typerep2 @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Enum_Oenum_35,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( enum @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 => ( enum @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Typerep_Otyperep_36,axiom,
% 0.29/0.46 typerep2 @ $o @ ( type2 @ $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Enum_Oenum_37,axiom,
% 0.29/0.46 enum @ $o @ ( type2 @ $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_List_Olist___Typerep_Otyperep_38,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 => ( typerep2 @ ( list @ A6 ) @ ( type2 @ ( list @ A6 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Sum__Type_Osum___Typerep_Otyperep_39,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] :
% 0.29/0.46 ( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 & ( typerep2 @ A7 @ ( type2 @ A7 ) ) )
% 0.29/0.46 => ( typerep2 @ ( sum_sum @ A6 @ A7 ) @ ( type2 @ ( sum_sum @ A6 @ A7 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Sum__Type_Osum___Enum_Oenum_40,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] :
% 0.29/0.46 ( ( ( enum @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 & ( enum @ A7 @ ( type2 @ A7 ) ) )
% 0.29/0.46 => ( enum @ ( sum_sum @ A6 @ A7 ) @ ( type2 @ ( sum_sum @ A6 @ A7 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Option_Ooption___Typerep_Otyperep_41,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 => ( typerep2 @ ( option @ A6 ) @ ( type2 @ ( option @ A6 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Option_Ooption___Enum_Oenum_42,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( enum @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 => ( enum @ ( option @ A6 ) @ ( type2 @ ( option @ A6 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Simpl__Heap_Oref___Typerep_Otyperep_43,axiom,
% 0.29/0.46 typerep2 @ simpl_ref @ ( type2 @ simpl_ref ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_String_Oliteral___Typerep_Otyperep_44,axiom,
% 0.29/0.46 typerep2 @ literal @ ( type2 @ literal ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Typerep_Otyperep___Typerep_Otyperep_45,axiom,
% 0.29/0.46 typerep2 @ typerep @ ( type2 @ typerep ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___Typerep_Otyperep_46,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] :
% 0.29/0.46 ( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 & ( typerep2 @ A7 @ ( type2 @ A7 ) ) )
% 0.29/0.46 => ( typerep2 @ ( product_prod @ A6 @ A7 ) @ ( type2 @ ( product_prod @ A6 @ A7 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___Enum_Oenum_47,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] :
% 0.29/0.46 ( ( ( enum @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 & ( enum @ A7 @ ( type2 @ A7 ) ) )
% 0.29/0.46 => ( enum @ ( product_prod @ A6 @ A7 ) @ ( type2 @ ( product_prod @ A6 @ A7 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Typerep_Otyperep_48,axiom,
% 0.29/0.46 typerep2 @ product_unit @ ( type2 @ product_unit ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Enum_Oenum_49,axiom,
% 0.29/0.46 enum @ product_unit @ ( type2 @ product_unit ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Evaluation_Oterm___Typerep_Otyperep_50,axiom,
% 0.29/0.46 typerep2 @ code_term @ ( type2 @ code_term ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Numeral_Onatural___Typerep_Otyperep_51,axiom,
% 0.29/0.46 typerep2 @ code_natural @ ( type2 @ code_natural ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Record_Otuple__isomorphism___Typerep_Otyperep_52,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType,A8: $tType] :
% 0.29/0.46 ( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 & ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 0.29/0.46 & ( typerep2 @ A8 @ ( type2 @ A8 ) ) )
% 0.29/0.46 => ( typerep2 @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) @ ( type2 @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_BinDag__Mirabelle__rybootvolr_Odag___Typerep_Otyperep_53,axiom,
% 0.29/0.46 typerep2 @ binDag_Mirabelle_dag @ ( type2 @ binDag_Mirabelle_dag ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Quickcheck__Random_Orandom,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] :
% 0.29/0.46 ( ( ( code_term_of @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 & ( cl_HOL_Oequal @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 & ( quickcheck_random @ A7 @ ( type2 @ A7 ) ) )
% 0.29/0.46 => ( quickcheck_random @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 0.29/0.46 semiri456707255roduct @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.29/0.46 canoni770627133id_add @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 0.29/0.46 ordere779506340up_add @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 0.29/0.46 cancel1352612707id_add @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 0.29/0.46 cancel_semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Divides_Osemiring__div__parity,axiom,
% 0.29/0.46 semiring_div_parity @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Quickcheck__Random_Orandom_54,axiom,
% 0.29/0.46 quickcheck_random @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 0.29/0.46 ab_semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 0.29/0.46 comm_monoid_add @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
% 0.29/0.46 comm_semiring_1 @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Rings_Osemidom__divide,axiom,
% 0.29/0.46 semidom_divide @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 0.29/0.46 semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Divides_Osemiring__div,axiom,
% 0.29/0.46 semiring_div @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Nat_Osemiring__char__0,axiom,
% 0.29/0.46 semiring_char_0 @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Rings_Ozero__neq__one,axiom,
% 0.29/0.46 zero_neq_one @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Omonoid__add,axiom,
% 0.29/0.46 monoid_add @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Num_Onumeral,axiom,
% 0.29/0.46 numeral @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 0.29/0.46 zero @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.29/0.46 one @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 0.29/0.46 size @ nat @ ( type2 @ nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Num_Onum___Quickcheck__Random_Orandom_55,axiom,
% 0.29/0.46 quickcheck_random @ num @ ( type2 @ num ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Num_Onum___Nat_Osize_56,axiom,
% 0.29/0.46 size @ num @ ( type2 @ num ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Quickcheck__Random_Orandom_57,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( quickcheck_random @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 => ( quickcheck_random @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Quickcheck__Random_Orandom_58,axiom,
% 0.29/0.46 quickcheck_random @ $o @ ( type2 @ $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Nat_Osize_59,axiom,
% 0.29/0.46 size @ $o @ ( type2 @ $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_List_Olist___Quickcheck__Random_Orandom_60,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( quickcheck_random @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 => ( quickcheck_random @ ( list @ A6 ) @ ( type2 @ ( list @ A6 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_List_Olist___Nat_Osize_61,axiom,
% 0.29/0.46 ! [A6: $tType] : ( size @ ( list @ A6 ) @ ( type2 @ ( list @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Sum__Type_Osum___Quickcheck__Random_Orandom_62,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] :
% 0.29/0.46 ( ( ( quickcheck_random @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 & ( quickcheck_random @ A7 @ ( type2 @ A7 ) ) )
% 0.29/0.46 => ( quickcheck_random @ ( sum_sum @ A6 @ A7 ) @ ( type2 @ ( sum_sum @ A6 @ A7 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Sum__Type_Osum___Nat_Osize_63,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] : ( size @ ( sum_sum @ A6 @ A7 ) @ ( type2 @ ( sum_sum @ A6 @ A7 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Option_Ooption___Quickcheck__Random_Orandom_64,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( quickcheck_random @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 => ( quickcheck_random @ ( option @ A6 ) @ ( type2 @ ( option @ A6 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Option_Ooption___Nat_Osize_65,axiom,
% 0.29/0.46 ! [A6: $tType] : ( size @ ( option @ A6 ) @ ( type2 @ ( option @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_String_Oliteral___Quickcheck__Random_Orandom_66,axiom,
% 0.29/0.46 quickcheck_random @ literal @ ( type2 @ literal ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_String_Oliteral___Nat_Osize_67,axiom,
% 0.29/0.46 size @ literal @ ( type2 @ literal ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Typerep_Otyperep___Nat_Osize_68,axiom,
% 0.29/0.46 size @ typerep @ ( type2 @ typerep ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___Quickcheck__Random_Orandom_69,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] :
% 0.29/0.46 ( ( ( quickcheck_random @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 & ( quickcheck_random @ A7 @ ( type2 @ A7 ) ) )
% 0.29/0.46 => ( quickcheck_random @ ( product_prod @ A6 @ A7 ) @ ( type2 @ ( product_prod @ A6 @ A7 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Oprod___Nat_Osize_70,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] : ( size @ ( product_prod @ A6 @ A7 ) @ ( type2 @ ( product_prod @ A6 @ A7 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Quickcheck__Random_Orandom_71,axiom,
% 0.29/0.46 quickcheck_random @ product_unit @ ( type2 @ product_unit ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Nat_Osize_72,axiom,
% 0.29/0.46 size @ product_unit @ ( type2 @ product_unit ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__add_73,axiom,
% 0.29/0.46 ordere779506340up_add @ code_natural @ ( type2 @ code_natural ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Numeral_Onatural___Groups_Ocancel__comm__monoid__add_74,axiom,
% 0.29/0.46 cancel1352612707id_add @ code_natural @ ( type2 @ code_natural ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Numeral_Onatural___Groups_Ocancel__semigroup__add_75,axiom,
% 0.29/0.46 cancel_semigroup_add @ code_natural @ ( type2 @ code_natural ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Numeral_Onatural___Quickcheck__Random_Orandom_76,axiom,
% 0.29/0.46 quickcheck_random @ code_natural @ ( type2 @ code_natural ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Numeral_Onatural___Groups_Oab__semigroup__add_77,axiom,
% 0.29/0.46 ab_semigroup_add @ code_natural @ ( type2 @ code_natural ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Numeral_Onatural___Groups_Ocomm__monoid__add_78,axiom,
% 0.29/0.46 comm_monoid_add @ code_natural @ ( type2 @ code_natural ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Numeral_Onatural___Rings_Ocomm__semiring__1_79,axiom,
% 0.29/0.46 comm_semiring_1 @ code_natural @ ( type2 @ code_natural ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Numeral_Onatural___Rings_Osemidom__divide_80,axiom,
% 0.29/0.46 semidom_divide @ code_natural @ ( type2 @ code_natural ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Numeral_Onatural___Groups_Osemigroup__add_81,axiom,
% 0.29/0.46 semigroup_add @ code_natural @ ( type2 @ code_natural ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Numeral_Onatural___Divides_Osemiring__div_82,axiom,
% 0.29/0.46 semiring_div @ code_natural @ ( type2 @ code_natural ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Numeral_Onatural___Rings_Ozero__neq__one_83,axiom,
% 0.29/0.46 zero_neq_one @ code_natural @ ( type2 @ code_natural ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Numeral_Onatural___Groups_Omonoid__add_84,axiom,
% 0.29/0.46 monoid_add @ code_natural @ ( type2 @ code_natural ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Numeral_Onatural___Num_Onumeral_85,axiom,
% 0.29/0.46 numeral @ code_natural @ ( type2 @ code_natural ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Numeral_Onatural___Groups_Ozero_86,axiom,
% 0.29/0.46 zero @ code_natural @ ( type2 @ code_natural ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Numeral_Onatural___Groups_Oone_87,axiom,
% 0.29/0.46 one @ code_natural @ ( type2 @ code_natural ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Code__Numeral_Onatural___Nat_Osize_88,axiom,
% 0.29/0.46 size @ code_natural @ ( type2 @ code_natural ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Record_Otuple__isomorphism___Quickcheck__Random_Orandom_89,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType,A8: $tType] :
% 0.29/0.46 ( ( ( code_term_of @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 & ( cl_HOL_Oequal @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 & ( quickcheck_random @ A6 @ ( type2 @ A6 ) )
% 0.29/0.46 & ( quickcheck_random @ A7 @ ( type2 @ A7 ) )
% 0.29/0.46 & ( quickcheck_random @ A8 @ ( type2 @ A8 ) ) )
% 0.29/0.46 => ( quickcheck_random @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) @ ( type2 @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Record_Otuple__isomorphism___Nat_Osize_90,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType,A8: $tType] : ( size @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) @ ( type2 @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_BinDag__Mirabelle__rybootvolr_Odag___Nat_Osize_91,axiom,
% 0.29/0.46 size @ binDag_Mirabelle_dag @ ( type2 @ binDag_Mirabelle_dag ) ).
% 0.29/0.46
% 0.29/0.46 %----Helper facts (3)
% 0.29/0.46 thf(help_If_3_1_T,axiom,
% 0.29/0.46 ! [P: $o] :
% 0.29/0.46 ( ( P = $true )
% 0.29/0.46 | ( P = $false ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(help_If_2_1_T,axiom,
% 0.29/0.46 ! [A: $tType,X4: A,Y: A] :
% 0.29/0.46 ( ( if @ A @ $false @ X4 @ Y )
% 0.29/0.46 = Y ) ).
% 0.29/0.46
% 0.29/0.46 thf(help_If_1_1_T,axiom,
% 0.29/0.46 ! [A: $tType,X4: A,Y: A] :
% 0.29/0.46 ( ( if @ A @ $true @ X4 @ Y )
% 0.29/0.46 = X4 ) ).
% 0.29/0.46
% 0.29/0.46 %----Conjectures (1)
% 0.29/0.46 thf(conj_0,conjecture,
% 0.29/0.46 ( ( binDag476092410e_Node @ lt @ a @ rt )
% 0.29/0.46 != lt ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 2.49/1.44 ---- Embedded in THF ---
% 2.49/1.44 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.49/1.44 %%% Generated on Tue Feb 24 04:15:27 EST 2026
% 2.49/1.44 %%% using '$$dhol' embedding, version 1.3.0.
% 2.49/1.44 %%% Logic specification used:
% 2.49/1.44 %%% thf(spec, logic, $$dhol).
% 2.49/1.44
% 2.49/1.44 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.m3AuIGZJso/DTF2DTF32018.p
% 2.49/1.44 thf(ty_t_BinDag__Mirabelle__rybootvolr_Odag, type, binDag_Mirabelle_dag: $tType).
% 2.49/1.44 thf(ty_t_Record_Otuple__isomorphism, type, tuple_isomorphism: ($tType > ($tType > ($tType > $tType)))).
% 2.49/1.44 thf(ty_t_Code__Numeral_Onatural, type, code_natural: $tType).
% 2.49/1.44 thf(ty_t_Code__Evaluation_Oterm, type, code_term: $tType).
% 2.49/1.44 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 2.49/1.44 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.49/1.44 thf(ty_t_Typerep_Otyperep, type, typerep: $tType).
% 2.49/1.44 thf(ty_t_Simpl__Heap_Oref, type, simpl_ref: $tType).
% 2.49/1.44 thf(ty_t_String_Oliteral, type, literal: $tType).
% 2.49/1.44 thf(ty_t_Sum__Type_Osum, type, sum_sum: ($tType > ($tType > $tType))).
% 2.49/1.44 thf(ty_t_Option_Ooption, type, option: ($tType > $tType)).
% 2.49/1.44 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.49/1.44 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.49/1.44 thf(ty_t_Num_Onum, type, num: $tType).
% 2.49/1.44 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.49/1.44 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.49/1.44 thf(sy_cl_Enum_Oenum, type, enum: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Typerep_Otyperep, type, typerep2: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_HOL_Oequal, type, cl_HOL_Oequal: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Code__Evaluation_Oterm__of, type, code_term_of: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Nat_Osize, type, size: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Num_Onumeral, type, numeral: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Fields_Ofield, type, field: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Num_Oneg__numeral, type, neg_numeral: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Groups_Omonoid__add, type, monoid_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Rings_Ozero__neq__one, type, zero_neq_one: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Nat_Osemiring__char__0, type, semiring_char_0: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Divides_Osemiring__div, type, semiring_div: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Fields_Odivision__ring, type, division_ring: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Groups_Osemigroup__add, type, semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Rings_Osemidom__divide, type, semidom_divide: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Rings_Ocomm__semiring__1, type, comm_semiring_1: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Groups_Ocomm__monoid__add, type, comm_monoid_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Fields_Olinordered__field, type, linordered_field: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Groups_Oab__semigroup__add, type, ab_semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Quickcheck__Random_Orandom, type, quickcheck_random: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Divides_Osemiring__div__parity, type, semiring_div_parity: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Groups_Ocancel__semigroup__add, type, cancel_semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Groups_Ocancel__comm__monoid__add, type, cancel1352612707id_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Groups_Olinordered__ab__group__add, type, linord219039673up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Groups_Oordered__ab__semigroup__add, type, ordere779506340up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, type, semiri456707255roduct: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.49/1.44 thf(sy_c_BNF__Greatest__Fixpoint_OShift, type, bNF_Greatest_Shift: (!> [A:$tType]: (((set @ (list @ A)) > (A > (set @ (list @ A))))))).
% 2.49/1.44 thf(sy_c_Basic__BNF__LFPs_Osum_Osize__sum, type, basic_BNF_size_sum: (!> [A:$tType,B:$tType]: (((A > nat) > ((B > nat) > (((sum_sum @ A) @ B) > nat)))))).
% 2.49/1.44 thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_ONode, type, binDag476092410e_Node: (binDag_Mirabelle_dag > (simpl_ref > (binDag_Mirabelle_dag > binDag_Mirabelle_dag)))).
% 2.49/1.44 thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_OTip, type, binDag_Mirabelle_Tip: binDag_Mirabelle_dag).
% 2.49/1.44 thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_Ocase__dag, type, binDag1297733282se_dag: (!> [A:$tType]: ((A > ((binDag_Mirabelle_dag > (simpl_ref > (binDag_Mirabelle_dag > A))) > (binDag_Mirabelle_dag > A)))))).
% 2.49/1.44 thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_Orec__dag, type, binDag1442713106ec_dag: (!> [A:$tType]: ((A > ((binDag_Mirabelle_dag > (simpl_ref > (binDag_Mirabelle_dag > (A > (A > A))))) > (binDag_Mirabelle_dag > A)))))).
% 2.49/1.44 thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_Osize__dag, type, binDag1924123185ze_dag: (binDag_Mirabelle_dag > nat)).
% 2.49/1.44 thf(sy_c_Code__Numeral_OSuc, type, code_Suc: (code_natural > code_natural)).
% 2.49/1.44 thf(sy_c_Code__Numeral_Onatural_Ocase__natural, type, code_case_natural: (!> [T:$tType]: ((T > ((code_natural > T) > (code_natural > T)))))).
% 2.49/1.44 thf(sy_c_Code__Numeral_Onatural_Orec__natural, type, code_rec_natural: (!> [T:$tType]: ((T > ((code_natural > (T > T)) > (code_natural > T)))))).
% 2.49/1.44 thf(sy_c_Code__Numeral_Onatural_Osize__natural, type, code_size_natural: (code_natural > nat)).
% 2.49/1.44 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 2.49/1.44 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 2.49/1.44 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.49/1.44 thf(sy_c_HOL_Obool_Osize__bool, type, size_bool: ($o > nat)).
% 2.49/1.44 thf(sy_c_HOL_Odefault__class_Odefault, type, default_default: (!> [A:$tType]: (A))).
% 2.49/1.44 thf(sy_c_HOL_Oundefined, type, undefined: (!> [A:$tType]: (A))).
% 2.49/1.44 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.49/1.44 thf(sy_c_List_Ogen__length, type, gen_length: (!> [A:$tType]: ((nat > ((list @ A) > nat))))).
% 2.49/1.44 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.49/1.44 thf(sy_c_List_Olist_Osize__list, type, size_list: (!> [A:$tType]: (((A > nat) > ((list @ A) > nat))))).
% 2.49/1.44 thf(sy_c_List_Osplice, type, splice: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.49/1.44 thf(sy_c_Nat_OSuc, type, suc: (nat > nat)).
% 2.49/1.44 thf(sy_c_Nat_Osize__class_Osize, type, size_size: (!> [A:$tType]: ((A > nat)))).
% 2.49/1.44 thf(sy_c_Num_Oinc, type, inc: (num > num)).
% 2.49/1.44 thf(sy_c_Num_Onat__of__num, type, nat_of_num: (num > nat)).
% 2.49/1.44 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc, type, neg_numeral_dbl_inc: (!> [A:$tType]: ((A > A)))).
% 2.49/1.44 thf(sy_c_Num_Onum_OBit0, type, bit0: (num > num)).
% 2.49/1.44 thf(sy_c_Num_Onum_OBit1, type, bit1: (num > num)).
% 2.49/1.44 thf(sy_c_Num_Onum_OOne, type, one2: num).
% 2.49/1.44 thf(sy_c_Num_Onum_Osize__num, type, size_num: (num > nat)).
% 2.49/1.44 thf(sy_c_Num_Onumeral__class_Onumeral, type, numeral_numeral: (!> [A:$tType]: ((num > A)))).
% 2.49/1.44 thf(sy_c_Option_Ooption_ONone, type, none: (!> [A:$tType]: ((option @ A)))).
% 2.49/1.44 thf(sy_c_Option_Ooption_OSome, type, some: (!> [A:$tType]: ((A > (option @ A))))).
% 2.49/1.44 thf(sy_c_Option_Ooption_Ocase__option, type, case_option: (!> [B:$tType,A:$tType]: ((B > ((A > B) > ((option @ A) > B)))))).
% 2.49/1.44 thf(sy_c_Option_Ooption_Osize__option, type, size_option: (!> [A:$tType]: (((A > nat) > ((option @ A) > nat))))).
% 2.49/1.44 thf(sy_c_Option_Ooption_Othe, type, the: (!> [A:$tType]: (((option @ A) > A)))).
% 2.49/1.44 thf(sy_c_Product__Type_OUnity, type, product_Unity: product_unit).
% 2.49/1.44 thf(sy_c_Product__Type_Oold_Obool_Orec__bool, type, product_rec_bool: (!> [T:$tType]: ((T > (T > ($o > T)))))).
% 2.49/1.44 thf(sy_c_Product__Type_Oold_Ounit_Orec__unit, type, product_rec_unit: (!> [T:$tType]: ((T > (product_unit > T))))).
% 2.49/1.44 thf(sy_c_Product__Type_Ounit_Ocase__unit, type, product_case_unit: (!> [A:$tType]: ((A > (product_unit > A))))).
% 2.49/1.44 thf(sy_c_Product__Type_Ounit_Osize__unit, type, product_size_unit: (product_unit > nat)).
% 2.49/1.44 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.49/1.44 thf(sy_c_Record_Otuple__isomorphism_OTuple__Isomorphism, type, tuple_742722141rphism: (!> [A:$tType,B:$tType,C:$tType]: (((A > ((product_prod @ B) @ C)) > ((((product_prod @ B) @ C) > A) > (((tuple_isomorphism @ A) @ B) @ C)))))).
% 2.49/1.44 thf(sy_c_Record_Otuple__isomorphism_Osize__tuple__isomorphism, type, tuple_1907371454rphism: (!> [A:$tType,B:$tType,C:$tType]: (((A > nat) > ((B > nat) > ((C > nat) > ((((tuple_isomorphism @ A) @ B) @ C) > nat))))))).
% 2.49/1.44 thf(sy_c_Rings_Odivide__class_Odivide, type, divide_divide: (!> [A:$tType]: ((A > (A > A))))).
% 2.49/1.44 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.49/1.44 thf(sy_c_Sum__Type_OInl, type, sum_Inl: (!> [A:$tType,B:$tType]: ((A > ((sum_sum @ A) @ B))))).
% 2.49/1.44 thf(sy_c_Sum__Type_OInr, type, sum_Inr: (!> [B:$tType,A:$tType]: ((B > ((sum_sum @ A) @ B))))).
% 2.49/1.44 thf(sy_c_Transitive__Closure_Ontrancl, type, transitive_ntrancl: (!> [A:$tType]: ((nat > ((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ A) @ A))))))).
% 2.49/1.44 thf(sy_c_Typerep_Otyperep_OTyperep, type, typerep3: (literal > ((list @ typerep) > typerep))).
% 2.49/1.44 thf(sy_c_Typerep_Otyperep_Osize__typerep, type, size_typerep: (typerep > nat)).
% 2.49/1.44 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.49/1.44 thf(sy_v_a, type, a: simpl_ref).
% 2.49/1.44 thf(sy_v_lt, type, lt: binDag_Mirabelle_dag).
% 2.49/1.44 thf(sy_v_rt, type, rt: binDag_Mirabelle_dag).
% 2.49/1.44 thf(fact_0_dag_Oinject, axiom, (! [X21:binDag_Mirabelle_dag,X22:simpl_ref,X23:binDag_Mirabelle_dag,Y21:binDag_Mirabelle_dag,Y22:simpl_ref,Y23:binDag_Mirabelle_dag]: ((((((binDag476092410e_Node @ X21) @ X22) @ X23) = (((binDag476092410e_Node @ Y21) @ Y22) @ Y23)) = ((X21 = Y21) & ((X22 = Y22) & (X23 = Y23))))))).
% 2.49/1.44 thf(fact_1_dag_Odistinct_I1_J, axiom, (! [X21:binDag_Mirabelle_dag,X22:simpl_ref,X23:binDag_Mirabelle_dag]: ((binDag_Mirabelle_Tip != (((binDag476092410e_Node @ X21) @ X22) @ X23))))).
% 2.49/1.44 thf(fact_2_dag_Oinduct, axiom, (! [P:(binDag_Mirabelle_dag > $o),Dag:binDag_Mirabelle_dag]: (((P @ binDag_Mirabelle_Tip) => ((! [X1:binDag_Mirabelle_dag,X2:simpl_ref,X3:binDag_Mirabelle_dag]: (((P @ X1) => ((P @ X3) => (P @ (((binDag476092410e_Node @ X1) @ X2) @ X3)))))) => (P @ Dag)))))).
% 2.49/1.44 thf(fact_3_dag_Oexhaust, axiom, (! [Y:binDag_Mirabelle_dag]: (((Y != binDag_Mirabelle_Tip) => (~ ((! [X212:binDag_Mirabelle_dag,X222:simpl_ref,X232:binDag_Mirabelle_dag]: ((Y != (((binDag476092410e_Node @ X212) @ X222) @ X232)))))))))).
% 2.49/1.44 thf(fact_4_dag_Osimps_I7_J, axiom, (! [A:$tType,F1:A,F2:(binDag_Mirabelle_dag > (simpl_ref > (binDag_Mirabelle_dag > (A > (A > A))))),X21:binDag_Mirabelle_dag,X22:simpl_ref,X23:binDag_Mirabelle_dag]: ((((((binDag1442713106ec_dag @ A) @ F1) @ F2) @ (((binDag476092410e_Node @ X21) @ X22) @ X23)) = (((((F2 @ X21) @ X22) @ X23) @ ((((binDag1442713106ec_dag @ A) @ F1) @ F2) @ X21)) @ ((((binDag1442713106ec_dag @ A) @ F1) @ F2) @ X23)))))).
% 2.49/1.44 thf(fact_5_dag_Osimps_I5_J, axiom, (! [A:$tType,F1:A,F2:(binDag_Mirabelle_dag > (simpl_ref > (binDag_Mirabelle_dag > A))),X21:binDag_Mirabelle_dag,X22:simpl_ref,X23:binDag_Mirabelle_dag]: ((((((binDag1297733282se_dag @ A) @ F1) @ F2) @ (((binDag476092410e_Node @ X21) @ X22) @ X23)) = (((F2 @ X21) @ X22) @ X23))))).
% 2.49/1.44 thf(fact_6_dag_Osimps_I6_J, axiom, (! [A:$tType,F1:A,F2:(binDag_Mirabelle_dag > (simpl_ref > (binDag_Mirabelle_dag > (A > (A > A)))))]: ((((((binDag1442713106ec_dag @ A) @ F1) @ F2) @ binDag_Mirabelle_Tip) = F1)))).
% 2.49/1.44 thf(fact_7_dag_Osimps_I4_J, axiom, (! [A:$tType,F1:A,F2:(binDag_Mirabelle_dag > (simpl_ref > (binDag_Mirabelle_dag > A)))]: ((((((binDag1297733282se_dag @ A) @ F1) @ F2) @ binDag_Mirabelle_Tip) = F1)))).
% 2.49/1.44 thf(fact_8_dag_Osize__gen_I1_J, axiom, ((binDag1924123185ze_dag @ binDag_Mirabelle_Tip) = (zero_zero @ nat))).
% 2.49/1.44 thf(fact_9_dag_Osize_I3_J, axiom, (((size_size @ binDag_Mirabelle_dag) @ binDag_Mirabelle_Tip) = (zero_zero @ nat))).
% 2.49/1.44 thf(fact_10_dag_Ocase__distrib, axiom, (! [B:$tType,A:$tType,H:(A > B),F1:A,F2:(binDag_Mirabelle_dag > (simpl_ref > (binDag_Mirabelle_dag > A))),Dag:binDag_Mirabelle_dag]: (((H @ ((((binDag1297733282se_dag @ A) @ F1) @ F2) @ Dag)) = ((((binDag1297733282se_dag @ B) @ (H @ F1)) @ (^ [X12:binDag_Mirabelle_dag,X24:simpl_ref,X32:binDag_Mirabelle_dag]: ((H @ (((F2 @ X12) @ X24) @ X32))))) @ Dag))))).
% 2.49/1.44 thf(fact_11_fun__cong__unused__0, axiom, (! [A:$tType,B:$tType,C:$tType]: ((((zero @ B) @ (type2 @ B)) => (! [F:((A > B) > C),G:C]: (((F = (^ [X:(A > B)]: (G))) => ((F @ (^ [X:A]: ((zero_zero @ B)))) = G)))))))).
% 2.49/1.44 thf(fact_12_size__ne__size__imp__ne, axiom, (! [A:$tType]: ((((size @ A) @ (type2 @ A)) => (! [X4:A,Y:A]: (((((size_size @ A) @ X4) != ((size_size @ A) @ Y)) => (X4 != Y)))))))).
% 2.49/1.44 thf(fact_13_zero__natural_Orsp, axiom, ((zero_zero @ nat) = (zero_zero @ nat))).
% 2.49/1.44 thf(fact_14_zero__reorient, axiom, (! [A:$tType]: ((((zero @ A) @ (type2 @ A)) => (! [X4:A]: ((((zero_zero @ A) = X4) = (X4 = (zero_zero @ A))))))))).
% 2.49/1.44 thf(fact_15_bool_Osize_I1_J, axiom, ((size_bool @ $true) = (zero_zero @ nat))).
% 2.49/1.44 thf(fact_16_bool_Osize_I2_J, axiom, ((size_bool @ $false) = (zero_zero @ nat))).
% 2.49/1.44 thf(fact_17_dag_Osize__gen_I2_J, axiom, (! [X21:binDag_Mirabelle_dag,X22:simpl_ref,X23:binDag_Mirabelle_dag]: (((binDag1924123185ze_dag @ (((binDag476092410e_Node @ X21) @ X22) @ X23)) = (((plus_plus @ nat) @ (((plus_plus @ nat) @ (binDag1924123185ze_dag @ X21)) @ (binDag1924123185ze_dag @ X23))) @ (suc @ (zero_zero @ nat))))))).
% 2.49/1.44 thf(fact_18_dag_Osize_I4_J, axiom, (! [X21:binDag_Mirabelle_dag,X22:simpl_ref,X23:binDag_Mirabelle_dag]: ((((size_size @ binDag_Mirabelle_dag) @ (((binDag476092410e_Node @ X21) @ X22) @ X23)) = (((plus_plus @ nat) @ (((plus_plus @ nat) @ ((size_size @ binDag_Mirabelle_dag) @ X21)) @ ((size_size @ binDag_Mirabelle_dag) @ X23))) @ (suc @ (zero_zero @ nat))))))).
% 2.49/1.44 thf(fact_19_ntrancl__Zero, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A))]: (((((transitive_ntrancl @ A) @ (zero_zero @ nat)) @ R) = R)))).
% 2.49/1.44 thf(fact_20_add__left__cancel, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C2:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C2)) = (B2 = C2)))))))).
% 2.49/1.44 thf(fact_21_add__right__cancel, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C2:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C2) @ A2)) = (B2 = C2)))))))).
% 2.49/1.44 thf(fact_22_natural_Osize_I3_J, axiom, (((size_size @ code_natural) @ (zero_zero @ code_natural)) = (zero_zero @ nat))).
% 2.49/1.44 thf(fact_23_bool_Osize_I4_J, axiom, (((size_size @ $o) @ $false) = (zero_zero @ nat))).
% 2.49/1.44 thf(fact_24_bool_Osize_I3_J, axiom, (((size_size @ $o) @ $true) = (zero_zero @ nat))).
% 2.49/1.44 thf(fact_25_nat_Oinject, axiom, (! [X25:nat,Y2:nat]: ((((suc @ X25) = (suc @ Y2)) = (X25 = Y2))))).
% 2.49/1.44 thf(fact_26_old_Onat_Oinject, axiom, (! [Nat:nat,Nat2:nat]: ((((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))).
% 2.49/1.44 thf(fact_27_add_Oleft__neutral, axiom, (! [A:$tType]: ((((monoid_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.49/1.44 thf(fact_28_add_Oright__neutral, axiom, (! [A:$tType]: ((((monoid_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.49/1.44 thf(fact_29_double__zero, axiom, (! [A:$tType]: ((((linord219039673up_add @ A) @ (type2 @ A)) => (! [A2:A]: ((((((plus_plus @ A) @ A2) @ A2) = (zero_zero @ A)) = (A2 = (zero_zero @ A))))))))).
% 2.49/1.44 thf(fact_30_double__zero__sym, axiom, (! [A:$tType]: ((((linord219039673up_add @ A) @ (type2 @ A)) => (! [A2:A]: ((((zero_zero @ A) = (((plus_plus @ A) @ A2) @ A2)) = (A2 = (zero_zero @ A))))))))).
% 2.49/1.44 thf(fact_31_add__cancel__left__left, axiom, (! [A:$tType]: ((((cancel1352612707id_add @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: ((((((plus_plus @ A) @ B2) @ A2) = A2) = (B2 = (zero_zero @ A))))))))).
% 2.49/1.44 thf(fact_32_add__cancel__left__right, axiom, (! [A:$tType]: ((((cancel1352612707id_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: ((((((plus_plus @ A) @ A2) @ B2) = A2) = (B2 = (zero_zero @ A))))))))).
% 2.49/1.44 thf(fact_33_add__cancel__right__left, axiom, (! [A:$tType]: ((((cancel1352612707id_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((A2 = (((plus_plus @ A) @ B2) @ A2)) = (B2 = (zero_zero @ A))))))))).
% 2.49/1.44 thf(fact_34_add__cancel__right__right, axiom, (! [A:$tType]: ((((cancel1352612707id_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((A2 = (((plus_plus @ A) @ A2) @ B2)) = (B2 = (zero_zero @ A))))))))).
% 2.49/1.44 thf(fact_35_add__is__0, axiom, (! [M:nat,N:nat]: ((((((plus_plus @ nat) @ M) @ N) = (zero_zero @ nat)) = ((M = (zero_zero @ nat)) & (N = (zero_zero @ nat))))))).
% 2.49/1.44 thf(fact_36_Nat_Oadd__0__right, axiom, (! [M:nat]: (((((plus_plus @ nat) @ M) @ (zero_zero @ nat)) = M)))).
% 2.49/1.44 thf(fact_37_add__Suc__right, axiom, (! [M:nat,N:nat]: (((((plus_plus @ nat) @ M) @ (suc @ N)) = (suc @ (((plus_plus @ nat) @ M) @ N)))))).
% 2.49/1.44 thf(fact_38_one__is__add, axiom, (! [M:nat,N:nat]: ((((suc @ (zero_zero @ nat)) = (((plus_plus @ nat) @ M) @ N)) = (((M = (suc @ (zero_zero @ nat))) & (N = (zero_zero @ nat))) | ((M = (zero_zero @ nat)) & (N = (suc @ (zero_zero @ nat))))))))).
% 2.49/1.44 thf(fact_39_add__is__1, axiom, (! [M:nat,N:nat]: ((((((plus_plus @ nat) @ M) @ N) = (suc @ (zero_zero @ nat))) = (((M = (suc @ (zero_zero @ nat))) & (N = (zero_zero @ nat))) | ((M = (zero_zero @ nat)) & (N = (suc @ (zero_zero @ nat))))))))).
% 2.49/1.44 thf(fact_40_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C2) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.49/1.44 thf(fact_41_add__mono__thms__linordered__semiring_I4_J, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (K = L)) => ((((plus_plus @ A) @ I) @ K) = (((plus_plus @ A) @ J) @ L))))))))).
% 2.49/1.44 thf(fact_42_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.49/1.44 thf(fact_43_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A3)))) = A3)))).
% 2.49/1.44 thf(fact_44_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P @ X5) = (Q @ X5)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.49/1.44 thf(fact_45_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X5:A]: (((F @ X5) = (G @ X5)))) => (F = G))))).
% 2.49/1.44 thf(fact_46_Suc__inject, axiom, (! [X4:nat,Y:nat]: ((((suc @ X4) = (suc @ Y)) => (X4 = Y))))).
% 2.49/1.44 thf(fact_47_n__not__Suc__n, axiom, (! [N:nat]: ((N != (suc @ N))))).
% 2.49/1.44 thf(fact_48_add__Suc__shift, axiom, (! [M:nat,N:nat]: (((((plus_plus @ nat) @ (suc @ M)) @ N) = (((plus_plus @ nat) @ M) @ (suc @ N)))))).
% 2.49/1.44 thf(fact_49_add__Suc, axiom, (! [M:nat,N:nat]: (((((plus_plus @ nat) @ (suc @ M)) @ N) = (suc @ (((plus_plus @ nat) @ M) @ N)))))).
% 2.49/1.44 thf(fact_50_nat__add__left__cancel, axiom, (! [K:nat,M:nat,N:nat]: ((((((plus_plus @ nat) @ K) @ M) = (((plus_plus @ nat) @ K) @ N)) = (M = N))))).
% 2.49/1.44 thf(fact_51_nat__add__right__cancel, axiom, (! [M:nat,K:nat,N:nat]: ((((((plus_plus @ nat) @ M) @ K) = (((plus_plus @ nat) @ N) @ K)) = (M = N))))).
% 2.49/1.44 thf(fact_52_add_Oassoc, axiom, (! [A:$tType]: ((((semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C2) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.49/1.44 thf(fact_53_add_Oleft__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C2:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C2)) = (B2 = C2)))))))).
% 2.49/1.44 thf(fact_54_add_Oright__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C2:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C2) @ A2)) = (B2 = C2)))))))).
% 2.49/1.44 thf(fact_55_add_Ocommute, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => ((plus_plus @ A) = (^ [A4:A,B3:A]: ((((plus_plus @ A) @ B3) @ A4)))))))).
% 2.49/1.44 thf(fact_56_add_Oleft__commute, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C2:A]: (((((plus_plus @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C2)) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.49/1.44 thf(fact_57_add__left__imp__eq, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C2:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C2)) => (B2 = C2)))))))).
% 2.49/1.44 thf(fact_58_add__right__imp__eq, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C2:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C2) @ A2)) => (B2 = C2)))))))).
% 2.49/1.44 thf(fact_59_comm__monoid__add__class_Oadd__0, axiom, (! [A:$tType]: ((((comm_monoid_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.49/1.44 thf(fact_60_add_Ocomm__neutral, axiom, (! [A:$tType]: ((((comm_monoid_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.49/1.44 thf(fact_61_add_Ogroup__left__neutral, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.49/1.44 thf(fact_62_add__eq__0__iff__both__eq__0, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => (! [X4:A,Y:A]: ((((((plus_plus @ A) @ X4) @ Y) = (zero_zero @ A)) = ((X4 = (zero_zero @ A)) & (Y = (zero_zero @ A)))))))))).
% 2.49/1.44 thf(fact_63_nat_Odistinct_I1_J, axiom, (! [X25:nat]: (((zero_zero @ nat) != (suc @ X25))))).
% 2.49/1.44 thf(fact_64_old_Onat_Odistinct_I2_J, axiom, (! [Nat3:nat]: (((suc @ Nat3) != (zero_zero @ nat))))).
% 2.49/1.44 thf(fact_65_old_Onat_Odistinct_I1_J, axiom, (! [Nat2:nat]: (((zero_zero @ nat) != (suc @ Nat2))))).
% 2.49/1.44 thf(fact_66_nat_OdiscI, axiom, (! [Nat:nat,X25:nat]: (((Nat = (suc @ X25)) => (Nat != (zero_zero @ nat)))))).
% 2.49/1.44 thf(fact_67_nat__induct, axiom, (! [P:(nat > $o),N:nat]: (((P @ (zero_zero @ nat)) => ((! [N2:nat]: (((P @ N2) => (P @ (suc @ N2))))) => (P @ N)))))).
% 2.49/1.44 thf(fact_68_diff__induct, axiom, (! [P:(nat > (nat > $o)),M:nat,N:nat]: (((! [X5:nat]: (((P @ X5) @ (zero_zero @ nat)))) => ((! [Y3:nat]: (((P @ (zero_zero @ nat)) @ (suc @ Y3)))) => ((! [X5:nat,Y3:nat]: ((((P @ X5) @ Y3) => ((P @ (suc @ X5)) @ (suc @ Y3))))) => ((P @ M) @ N))))))).
% 2.49/1.44 thf(fact_69_zero__induct, axiom, (! [P:(nat > $o),K:nat]: (((P @ K) => ((! [N2:nat]: (((P @ (suc @ N2)) => (P @ N2)))) => (P @ (zero_zero @ nat))))))).
% 2.49/1.44 thf(fact_70_Suc__neq__Zero, axiom, (! [M:nat]: (((suc @ M) != (zero_zero @ nat))))).
% 2.49/1.44 thf(fact_71_Zero__neq__Suc, axiom, (! [M:nat]: (((zero_zero @ nat) != (suc @ M))))).
% 2.49/1.44 thf(fact_72_Zero__not__Suc, axiom, (! [M:nat]: (((zero_zero @ nat) != (suc @ M))))).
% 2.49/1.44 thf(fact_73_old_Onat_Oexhaust, axiom, (! [Y:nat]: (((Y != (zero_zero @ nat)) => (~ ((! [Nat4:nat]: ((Y != (suc @ Nat4)))))))))).
% 2.49/1.44 thf(fact_74_old_Onat_Oinducts, axiom, (! [P:(nat > $o),Nat:nat]: (((P @ (zero_zero @ nat)) => ((! [Nat4:nat]: (((P @ Nat4) => (P @ (suc @ Nat4))))) => (P @ Nat)))))).
% 2.49/1.44 thf(fact_75_not0__implies__Suc, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) => (? [M2:nat]: ((N = (suc @ M2)))))))).
% 2.49/1.44 thf(fact_76_plus__nat_Oadd__0, axiom, (! [N:nat]: (((((plus_plus @ nat) @ (zero_zero @ nat)) @ N) = N)))).
% 2.49/1.44 thf(fact_77_add__eq__self__zero, axiom, (! [M:nat,N:nat]: ((((((plus_plus @ nat) @ M) @ N) = M) => (N = (zero_zero @ nat)))))).
% 2.49/1.44 thf(fact_78_size__bool, axiom, ((size_size @ $o) = (^ [B3:$o]: ((zero_zero @ nat))))).
% 2.49/1.44 thf(fact_79_sum_Osize__neq, axiom, (! [A:$tType,B:$tType,X4:((sum_sum @ A) @ B)]: ((((size_size @ ((sum_sum @ A) @ B)) @ X4) != (zero_zero @ nat))))).
% 2.49/1.44 thf(fact_80_prod_Osize__neq, axiom, (! [A:$tType,B:$tType,X4:((product_prod @ A) @ B)]: ((((size_size @ ((product_prod @ A) @ B)) @ X4) != (zero_zero @ nat))))).
% 2.49/1.44 thf(fact_81_size__bool__def, axiom, (size_bool = (((product_rec_bool @ nat) @ (zero_zero @ nat)) @ (zero_zero @ nat)))).
% 2.49/1.44 thf(fact_82_dependent__nat__choice, axiom, (! [A:$tType,P:(nat > (A > $o)),Q:(nat > (A > (A > $o)))]: (((? [X13:A]: (((P @ (zero_zero @ nat)) @ X13))) => ((! [X5:A,N2:nat]: ((((P @ N2) @ X5) => (? [Y4:A]: ((((P @ (suc @ N2)) @ Y4) & (((Q @ N2) @ X5) @ Y4))))))) => (? [F3:(nat > A)]: ((! [N3:nat]: ((((P @ N3) @ (F3 @ N3)) & (((Q @ N3) @ (F3 @ N3)) @ (F3 @ (suc @ N3))))))))))))).
% 2.49/1.44 thf(fact_83_size__natural__overloaded__def, axiom, ((size_size @ code_natural) = (((code_rec_natural @ nat) @ (zero_zero @ nat)) @ (^ [X:code_natural,Y5:nat]: ((((plus_plus @ nat) @ Y5) @ (suc @ (zero_zero @ nat)))))))).
% 2.49/1.44 thf(fact_84_semiring__normalization__rules_I6_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.49/1.44 thf(fact_85_semiring__normalization__rules_I5_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.49/1.44 thf(fact_86_add__0__iff, axiom, (! [A:$tType]: ((((semiri456707255roduct @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: (((B2 = (((plus_plus @ A) @ B2) @ A2)) = (A2 = (zero_zero @ A))))))))).
% 2.49/1.44 thf(fact_87_natural_Osize_I1_J, axiom, ((code_size_natural @ (zero_zero @ code_natural)) = (zero_zero @ nat))).
% 2.49/1.44 thf(fact_88_natural_Osize_I4_J, axiom, (! [Natural:code_natural]: ((((size_size @ code_natural) @ (code_Suc @ Natural)) = (((plus_plus @ nat) @ ((size_size @ code_natural) @ Natural)) @ (suc @ (zero_zero @ nat))))))).
% 2.49/1.44 thf(fact_89_size__natural__def, axiom, (code_size_natural = (((code_rec_natural @ nat) @ (zero_zero @ nat)) @ (^ [X:code_natural,Y5:nat]: ((((plus_plus @ nat) @ Y5) @ (suc @ (zero_zero @ nat)))))))).
% 2.49/1.44 thf(fact_90_option_Osize__neq, axiom, (! [A:$tType,X4:(option @ A)]: ((((size_size @ (option @ A)) @ X4) != (zero_zero @ nat))))).
% 2.49/1.44 thf(fact_91_natural_Oinject, axiom, (! [Natural:code_natural,Natural2:code_natural]: ((((code_Suc @ Natural) = (code_Suc @ Natural2)) = (Natural = Natural2))))).
% 2.49/1.44 thf(fact_92_natural_Osimps_I6_J, axiom, (! [T:$tType,F1:T,F2:(code_natural > (T > T))]: ((((((code_rec_natural @ T) @ F1) @ F2) @ (zero_zero @ code_natural)) = F1)))).
% 2.49/1.44 thf(fact_93_natural_Osimps_I7_J, axiom, (! [T:$tType,F1:T,F2:(code_natural > (T > T)),Natural:code_natural]: ((((((code_rec_natural @ T) @ F1) @ F2) @ (code_Suc @ Natural)) = ((F2 @ Natural) @ ((((code_rec_natural @ T) @ F1) @ F2) @ Natural)))))).
% 2.49/1.44 thf(fact_94_natural_Osize_I2_J, axiom, (! [Natural:code_natural]: (((code_size_natural @ (code_Suc @ Natural)) = (((plus_plus @ nat) @ (code_size_natural @ Natural)) @ (suc @ (zero_zero @ nat))))))).
% 2.49/1.44 thf(fact_95_natural_Oinducts, axiom, (! [P:(code_natural > $o),Natural:code_natural]: (((P @ (zero_zero @ code_natural)) => ((! [Natural3:code_natural]: (((P @ Natural3) => (P @ (code_Suc @ Natural3))))) => (P @ Natural)))))).
% 2.49/1.44 thf(fact_96_natural_Oexhaust, axiom, (! [Y:code_natural]: (((Y != (zero_zero @ code_natural)) => (~ ((! [Natural3:code_natural]: ((Y != (code_Suc @ Natural3)))))))))).
% 2.49/1.44 thf(fact_97_natural_Odistinct_I1_J, axiom, (! [Natural2:code_natural]: (((zero_zero @ code_natural) != (code_Suc @ Natural2))))).
% 2.49/1.44 thf(fact_98_natural_Odistinct_I2_J, axiom, (! [Natural4:code_natural]: (((code_Suc @ Natural4) != (zero_zero @ code_natural))))).
% 2.49/1.44 thf(fact_99_size__bool__overloaded__def, axiom, ((size_size @ $o) = (((product_rec_bool @ nat) @ (zero_zero @ nat)) @ (zero_zero @ nat)))).
% 2.49/1.44 thf(fact_100_semiring__normalization__rules_I20_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C2:A,D:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ (((plus_plus @ A) @ C2) @ D)) = (((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B2) @ D))))))))).
% 2.49/1.44 thf(fact_101_semiring__normalization__rules_I21_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C2) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.49/1.44 thf(fact_102_semiring__normalization__rules_I22_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A,C2:A,D:A]: (((((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ C2) @ D)) = (((plus_plus @ A) @ C2) @ (((plus_plus @ A) @ A2) @ D))))))))).
% 2.49/1.44 thf(fact_103_semiring__normalization__rules_I23_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C2) = (((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ B2)))))))).
% 2.49/1.44 thf(fact_104_semiring__normalization__rules_I24_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => ((plus_plus @ A) = (^ [A4:A,C3:A]: ((((plus_plus @ A) @ C3) @ A4)))))))).
% 2.49/1.44 thf(fact_105_semiring__normalization__rules_I25_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A,C2:A,D:A]: (((((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ C2) @ D)) = (((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ D)))))))).
% 2.49/1.44 thf(fact_106_old_Obool_Osimps_I5_J, axiom, (! [T:$tType,F1:T,F2:T]: ((((((product_rec_bool @ T) @ F1) @ F2) @ $true) = F1)))).
% 2.49/1.44 thf(fact_107_old_Obool_Osimps_I6_J, axiom, (! [T:$tType,F1:T,F2:T]: ((((((product_rec_bool @ T) @ F1) @ F2) @ $false) = F2)))).
% 2.49/1.44 thf(fact_108_natural_Osimps_I5_J, axiom, (! [T:$tType,F1:T,F2:(code_natural > T),Natural:code_natural]: ((((((code_case_natural @ T) @ F1) @ F2) @ (code_Suc @ Natural)) = (F2 @ Natural))))).
% 2.49/1.44 thf(fact_109_random__aux__set_Oinduct, axiom, (! [B:$tType]: ((((quickcheck_random @ B) @ (type2 @ B)) => (! [P:(code_natural > (code_natural > $o)),A0:code_natural,A1:code_natural]: (((! [X1:code_natural]: (((P @ (zero_zero @ code_natural)) @ X1))) => ((! [I2:code_natural,J2:code_natural]: (((! [X6:((product_prod @ B) @ (product_unit > code_term))]: (((P @ I2) @ J2))) => ((P @ (code_Suc @ I2)) @ J2)))) => ((P @ A0) @ A1))))))))).
% 2.49/1.44 thf(fact_110_random__aux__rec, axiom, (! [A:$tType,Random_aux:(code_natural > A),Rhs:(code_natural > A),K:code_natural]: ((((Random_aux @ (zero_zero @ code_natural)) = (Rhs @ (zero_zero @ code_natural))) => ((! [K2:code_natural]: (((Random_aux @ (code_Suc @ K2)) = (Rhs @ (code_Suc @ K2))))) => ((Random_aux @ K) = (Rhs @ K))))))).
% 2.49/1.44 thf(fact_111_natural_Osimps_I4_J, axiom, (! [T:$tType,F1:T,F2:(code_natural > T)]: ((((((code_case_natural @ T) @ F1) @ F2) @ (zero_zero @ code_natural)) = F1)))).
% 2.49/1.44 thf(fact_112_case__natural__def, axiom, (! [T:$tType]: (((code_case_natural @ T) = (^ [F12:T,F22:(code_natural > T)]: ((((code_rec_natural @ T) @ F12) @ (^ [X12:code_natural,X24:T]: ((F22 @ X12)))))))))).
% 2.49/1.44 thf(fact_113_option_Osize_I3_J, axiom, (! [A:$tType]: ((((size_size @ (option @ A)) @ (none @ A)) = (suc @ (zero_zero @ nat)))))).
% 2.49/1.44 thf(fact_114_option_Osize_I4_J, axiom, (! [A:$tType,X25:A]: ((((size_size @ (option @ A)) @ ((some @ A) @ X25)) = (suc @ (zero_zero @ nat)))))).
% 2.49/1.44 thf(fact_115_sum_Osize_I3_J, axiom, (! [A:$tType,B:$tType,X14:A]: ((((size_size @ ((sum_sum @ A) @ B)) @ (((sum_Inl @ A) @ B) @ X14)) = (suc @ (zero_zero @ nat)))))).
% 2.49/1.44 thf(fact_116_sum_Osize_I4_J, axiom, (! [B:$tType,A:$tType,X25:B]: ((((size_size @ ((sum_sum @ A) @ B)) @ (((sum_Inr @ B) @ A) @ X25)) = (suc @ (zero_zero @ nat)))))).
% 2.49/1.44 thf(fact_117_typerep_Osize__neq, axiom, (! [X4:typerep]: ((((size_size @ typerep) @ X4) != (zero_zero @ nat))))).
% 2.49/1.44 thf(fact_118_option_Oinject, axiom, (! [A:$tType,X25:A,Y2:A]: (((((some @ A) @ X25) = ((some @ A) @ Y2)) = (X25 = Y2))))).
% 2.49/1.44 thf(fact_119_not__None__eq, axiom, (! [A:$tType,X4:(option @ A)]: (((X4 != (none @ A)) = (? [Y5:A]: ((X4 = ((some @ A) @ Y5)))))))).
% 2.49/1.44 thf(fact_120_not__Some__eq, axiom, (! [A:$tType,X4:(option @ A)]: (((! [Y5:A]: ((X4 != ((some @ A) @ Y5)))) = (X4 = (none @ A)))))).
% 2.49/1.44 thf(fact_121_Inl__Inr__False, axiom, (! [A:$tType,B:$tType,X4:A,Y:B]: (((((sum_Inl @ A) @ B) @ X4) != (((sum_Inr @ B) @ A) @ Y))))).
% 2.49/1.44 thf(fact_122_Inr__Inl__False, axiom, (! [B:$tType,A:$tType,X4:B,Y:A]: (((((sum_Inr @ B) @ A) @ X4) != (((sum_Inl @ A) @ B) @ Y))))).
% 2.49/1.44 thf(fact_123_obj__sumE__f, axiom, (! [A:$tType,C:$tType,B:$tType,S:B,F:(((sum_sum @ A) @ C) > B),P:$o]: (((! [X5:A]: (((S = (F @ (((sum_Inl @ A) @ C) @ X5))) => P))) => ((! [X5:C]: (((S = (F @ (((sum_Inr @ C) @ A) @ X5))) => P))) => (! [X6:((sum_sum @ A) @ C)]: (((S = (F @ X6)) => P)))))))).
% 2.49/1.44 thf(fact_124_option_Odistinct_I1_J, axiom, (! [A:$tType,X25:A]: (((none @ A) != ((some @ A) @ X25))))).
% 2.49/1.44 thf(fact_125_option_OdiscI, axiom, (! [A:$tType,Option:(option @ A),X25:A]: (((Option = ((some @ A) @ X25)) => (Option != (none @ A)))))).
% 2.49/1.44 thf(fact_126_option_Oexhaust, axiom, (! [A:$tType,Y:(option @ A)]: (((Y != (none @ A)) => (~ ((! [X2:A]: ((Y != ((some @ A) @ X2)))))))))).
% 2.49/1.44 thf(fact_127_option_Oinducts, axiom, (! [A:$tType,P:((option @ A) > $o),Option:(option @ A)]: (((P @ (none @ A)) => ((! [X5:A]: ((P @ ((some @ A) @ X5)))) => (P @ Option)))))).
% 2.49/1.44 thf(fact_128_split__option__ex, axiom, (! [A:$tType]: (((^ [P2:((option @ A) > $o)]: ((? [X7:(option @ A)]: ((P2 @ X7))))) = (^ [P3:((option @ A) > $o)]: (((P3 @ (none @ A)) | (? [X:A]: ((P3 @ ((some @ A) @ X))))))))))).
% 2.49/1.44 thf(fact_129_split__option__all, axiom, (! [A:$tType]: (((^ [P2:((option @ A) > $o)]: ((! [X7:(option @ A)]: ((P2 @ X7))))) = (^ [P3:((option @ A) > $o)]: (((P3 @ (none @ A)) & (! [X:A]: ((P3 @ ((some @ A) @ X))))))))))).
% 2.49/1.44 thf(fact_130_combine__options__cases, axiom, (! [A:$tType,B:$tType,X4:(option @ A),P:((option @ A) > ((option @ B) > $o)),Y:(option @ B)]: ((((X4 = (none @ A)) => ((P @ X4) @ Y)) => (((Y = (none @ B)) => ((P @ X4) @ Y)) => ((! [A5:A,B4:B]: (((X4 = ((some @ A) @ A5)) => ((Y = ((some @ B) @ B4)) => ((P @ X4) @ Y))))) => ((P @ X4) @ Y))))))).
% 2.49/1.44 thf(fact_131_sum_Osize__gen_I1_J, axiom, (! [B:$tType,A:$tType,Xa:(A > nat),X4:(B > nat),X14:A]: (((((((basic_BNF_size_sum @ A) @ B) @ Xa) @ X4) @ (((sum_Inl @ A) @ B) @ X14)) = (((plus_plus @ nat) @ (Xa @ X14)) @ (suc @ (zero_zero @ nat))))))).
% 2.49/1.44 thf(fact_132_sum_Osize__gen_I2_J, axiom, (! [A:$tType,B:$tType,Xa:(A > nat),X4:(B > nat),X25:B]: (((((((basic_BNF_size_sum @ A) @ B) @ Xa) @ X4) @ (((sum_Inr @ B) @ A) @ X25)) = (((plus_plus @ nat) @ (X4 @ X25)) @ (suc @ (zero_zero @ nat))))))).
% 2.49/1.44 thf(fact_133_option_Osize__gen_I2_J, axiom, (! [A:$tType,X4:(A > nat),X25:A]: (((((size_option @ A) @ X4) @ ((some @ A) @ X25)) = (((plus_plus @ nat) @ (X4 @ X25)) @ (suc @ (zero_zero @ nat))))))).
% 2.49/1.44 thf(fact_134_option_Osize__gen_I1_J, axiom, (! [A:$tType,X4:(A > nat)]: (((((size_option @ A) @ X4) @ (none @ A)) = (suc @ (zero_zero @ nat)))))).
% 2.49/1.44 thf(fact_135_typerep_Osize_I2_J, axiom, (! [X14:literal,X25:(list @ typerep)]: ((((size_size @ typerep) @ ((typerep3 @ X14) @ X25)) = (((plus_plus @ nat) @ (((size_list @ typerep) @ (size_size @ typerep)) @ X25)) @ (suc @ (zero_zero @ nat))))))).
% 2.49/1.44 thf(fact_136_tuple__isomorphism_Osize__neq, axiom, (! [A:$tType,B:$tType,C:$tType,X4:(((tuple_isomorphism @ A) @ B) @ C)]: ((((size_size @ (((tuple_isomorphism @ A) @ B) @ C)) @ X4) != (zero_zero @ nat))))).
% 2.49/1.44 thf(fact_137_size__literal__def, axiom, ((size_size @ literal) = (^ [S2:literal]: ((zero_zero @ nat))))).
% 2.49/1.44 thf(fact_138_size__unit__overloaded__def, axiom, ((size_size @ product_unit) = ((product_rec_unit @ nat) @ (zero_zero @ nat)))).
% 2.49/1.44 thf(fact_139_typerep_Osize__gen, axiom, (! [X14:literal,X25:(list @ typerep)]: (((size_typerep @ ((typerep3 @ X14) @ X25)) = (((plus_plus @ nat) @ (((size_list @ typerep) @ size_typerep) @ X25)) @ (suc @ (zero_zero @ nat))))))).
% 2.49/1.44 thf(fact_140_size__unit__def, axiom, (product_size_unit = ((product_rec_unit @ nat) @ (zero_zero @ nat)))).
% 2.49/1.44 thf(fact_141_tuple__isomorphism_Osize_I2_J, axiom, (! [B:$tType,C:$tType,A:$tType,X14:(A > ((product_prod @ B) @ C)),X25:(((product_prod @ B) @ C) > A)]: ((((size_size @ (((tuple_isomorphism @ A) @ B) @ C)) @ (((((tuple_742722141rphism @ A) @ B) @ C) @ X14) @ X25)) = (suc @ (zero_zero @ nat)))))).
% 2.49/1.44 thf(fact_142_unit_Osize_I2_J, axiom, (((size_size @ product_unit) @ product_Unity) = (zero_zero @ nat))).
% 2.49/1.44 thf(fact_143_unit__abs__eta__conv, axiom, (! [A:$tType,F:(product_unit > A)]: (((^ [U:product_unit]: ((F @ product_Unity))) = F)))).
% 2.49/1.44 thf(fact_144_old_Ounit_Orec, axiom, (! [T:$tType,F1:T]: (((((product_rec_unit @ T) @ F1) @ product_Unity) = F1)))).
% 2.49/1.44 thf(fact_145_unit_Osize_I1_J, axiom, ((product_size_unit @ product_Unity) = (zero_zero @ nat))).
% 2.49/1.44 thf(fact_146_eq__sym__Unity__conv, axiom, (! [X4:$o]: (((X4 = (product_Unity = product_Unity)) = X4)))).
% 2.49/1.44 thf(fact_147_unit__all__impI, axiom, (! [P:(product_unit > $o),Q:(product_unit > $o)]: ((((P @ product_Unity) => (Q @ product_Unity)) => (! [X6:product_unit]: (((P @ X6) => (Q @ X6)))))))).
% 2.49/1.44 thf(fact_148_old_Ounit_Oinducts, axiom, (! [P:(product_unit > $o),Unit:product_unit]: (((P @ product_Unity) => (P @ Unit))))).
% 2.49/1.44 thf(fact_149_old_Ounit_Oexhaust, axiom, (! [Y:product_unit]: ((Y = product_Unity)))).
% 2.49/1.44 thf(fact_150_tuple__isomorphism_Osize__gen, axiom, (! [B:$tType,C:$tType,A:$tType,Xb:(A > nat),Xa:(B > nat),X4:(C > nat),X14:(A > ((product_prod @ B) @ C)),X25:(((product_prod @ B) @ C) > A)]: (((((((((tuple_1907371454rphism @ A) @ B) @ C) @ Xb) @ Xa) @ X4) @ (((((tuple_742722141rphism @ A) @ B) @ C) @ X14) @ X25)) = (suc @ (zero_zero @ nat)))))).
% 2.49/1.44 thf(fact_151_default__unit__def, axiom, ((default_default @ product_unit) = product_Unity)).
% 2.49/1.44 thf(fact_152_list_Osize__gen_I2_J, axiom, (! [A:$tType,X4:(A > nat),X21:A,X22:(list @ A)]: (((((size_list @ A) @ X4) @ (((cons @ A) @ X21) @ X22)) = (((plus_plus @ nat) @ (((plus_plus @ nat) @ (X4 @ X21)) @ (((size_list @ A) @ X4) @ X22))) @ (suc @ (zero_zero @ nat))))))).
% 2.49/1.44 thf(fact_153_length__Suc__conv, axiom, (! [A:$tType,Xs:(list @ A),N:nat]: (((((size_size @ (list @ A)) @ Xs) = (suc @ N)) = (? [Y5:A,Ys:(list @ A)]: (((Xs = (((cons @ A) @ Y5) @ Ys)) & (((size_size @ (list @ A)) @ Ys) = N)))))))).
% 2.49/1.44 thf(fact_154_Suc__length__conv, axiom, (! [A:$tType,N:nat,Xs:(list @ A)]: ((((suc @ N) = ((size_size @ (list @ A)) @ Xs)) = (? [Y5:A,Ys:(list @ A)]: (((Xs = (((cons @ A) @ Y5) @ Ys)) & (((size_size @ (list @ A)) @ Ys) = N)))))))).
% 2.49/1.44 thf(fact_155_list_Osize_I4_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: ((((size_size @ (list @ A)) @ (((cons @ A) @ X21) @ X22)) = (((plus_plus @ nat) @ ((size_size @ (list @ A)) @ X22)) @ (suc @ (zero_zero @ nat))))))).
% 2.49/1.44 thf(fact_156_length__Cons, axiom, (! [A:$tType,X4:A,Xs:(list @ A)]: ((((size_size @ (list @ A)) @ (((cons @ A) @ X4) @ Xs)) = (suc @ ((size_size @ (list @ A)) @ Xs)))))).
% 2.49/1.44 thf(fact_157_gen__length__code_I2_J, axiom, (! [B:$tType,N:nat,X4:B,Xs:(list @ B)]: (((((gen_length @ B) @ N) @ (((cons @ B) @ X4) @ Xs)) = (((gen_length @ B) @ (suc @ N)) @ Xs))))).
% 2.49/1.44 thf(fact_158_linordered__field__class_Osign__simps_I26_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C2) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.49/1.44 thf(fact_159_length__code, axiom, (! [A:$tType]: (((size_size @ (list @ A)) = ((gen_length @ A) @ (zero_zero @ nat)))))).
% 2.49/1.44 thf(fact_160_gen__length__def, axiom, (! [A:$tType]: (((gen_length @ A) = (^ [N4:nat,Xs2:(list @ A)]: ((((plus_plus @ nat) @ N4) @ ((size_size @ (list @ A)) @ Xs2)))))))).
% 2.49/1.44 thf(fact_161_linordered__field__class_Osign__simps_I28_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C2:A]: (((((plus_plus @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C2)) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.49/1.44 thf(fact_162_linordered__field__class_Osign__simps_I27_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => ((plus_plus @ A) = (^ [A4:A,B3:A]: ((((plus_plus @ A) @ B3) @ A4)))))))).
% 2.49/1.44 thf(fact_163_length__splice, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((size_size @ (list @ A)) @ (((splice @ A) @ Xs) @ Ys2)) = (((plus_plus @ nat) @ ((size_size @ (list @ A)) @ Xs)) @ ((size_size @ (list @ A)) @ Ys2)))))).
% 2.49/1.44 thf(fact_164_Shift__def, axiom, (! [A:$tType]: (((bNF_Greatest_Shift @ A) = (^ [Kl:(set @ (list @ A)),K3:A]: (((collect @ (list @ A)) @ (^ [Kl2:(list @ A)]: ((((member @ (list @ A)) @ (((cons @ A) @ K3) @ Kl2)) @ Kl)))))))))).
% 2.49/1.44 thf(fact_165_is__num__normalize_I1_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C2) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.49/1.44 thf(fact_166_option_Ocollapse, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) => (((some @ A) @ ((the @ A) @ Option)) = Option))))).
% 2.49/1.44 thf(fact_167_old_Ounit_Ocase, axiom, (! [A:$tType,F:A]: (((((product_case_unit @ A) @ F) @ product_Unity) = F)))).
% 2.49/1.44 thf(fact_168_case__optionE, axiom, (! [A:$tType,P:$o,Q:(A > $o),X4:(option @ A)]: (((((((case_option @ $o) @ A) @ P) @ Q) @ X4) => (((X4 = (none @ A)) => (~ (P))) => (~ ((! [Y3:A]: (((X4 = ((some @ A) @ Y3)) => (~ ((Q @ Y3))))))))))))).
% 2.49/1.44 thf(fact_169_option_Odisc__eq__case_I1_J, axiom, (! [A:$tType,Option:(option @ A)]: (((Option = (none @ A)) = (((((case_option @ $o) @ A) @ $true) @ (^ [Uu:A]: ($false))) @ Option))))).
% 2.49/1.44 thf(fact_170_option_Odisc__eq__case_I2_J, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) = (((((case_option @ $o) @ A) @ $false) @ (^ [Uu:A]: ($true))) @ Option))))).
% 2.49/1.44 thf(fact_171_option_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F1:B,F2:(A > B)]: (((((((case_option @ B) @ A) @ F1) @ F2) @ (none @ A)) = F1)))).
% 2.49/1.44 thf(fact_172_option_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:B,F2:(A > B),X25:A]: (((((((case_option @ B) @ A) @ F1) @ F2) @ ((some @ A) @ X25)) = (F2 @ X25))))).
% 2.49/1.44 thf(fact_173_option_Ocase__distrib, axiom, (! [C:$tType,B:$tType,A:$tType,H:(B > C),F1:B,F2:(A > B),Option:(option @ A)]: (((H @ (((((case_option @ B) @ A) @ F1) @ F2) @ Option)) = (((((case_option @ C) @ A) @ (H @ F1)) @ (^ [X:A]: ((H @ (F2 @ X))))) @ Option))))).
% 2.49/1.44 thf(fact_174_option_Osplit__sel, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F2:(A > B),Option:(option @ A)]: (((P @ (((((case_option @ B) @ A) @ F1) @ F2) @ Option)) = (((Option = (none @ A)) => (P @ F1)) & ((Option = ((some @ A) @ ((the @ A) @ Option))) => (P @ (F2 @ ((the @ A) @ Option))))))))).
% 2.49/1.44 thf(fact_175_option_Ocase__eq__if, axiom, (! [A:$tType,B:$tType]: ((((case_option @ B) @ A) = (^ [F12:B,F22:(A > B),Option2:(option @ A)]: (((((if @ B) @ (Option2 = (none @ A))) @ F12) @ (F22 @ ((the @ A) @ Option2))))))))).
% 2.49/1.44 thf(fact_176_option_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F2:(A > B),Option:(option @ A)]: (((P @ (((((case_option @ B) @ A) @ F1) @ F2) @ Option)) = (~ ((((Option = (none @ A)) & (~ ((P @ F1)))) | ((Option = ((some @ A) @ ((the @ A) @ Option))) & (~ ((P @ (F2 @ ((the @ A) @ Option))))))))))))).
% 2.49/1.44 thf(fact_177_case__unit__Unity, axiom, (! [A:$tType]: (((product_case_unit @ A) = (^ [F4:A,U:product_unit]: (F4)))))).
% 2.49/1.44 thf(fact_178_unit_Ocase__distrib, axiom, (! [A:$tType,B:$tType,H:(A > B),F:A,Unit:product_unit]: (((H @ (((product_case_unit @ A) @ F) @ Unit)) = (((product_case_unit @ B) @ (H @ F)) @ Unit))))).
% 2.49/1.44 thf(fact_179_option_Osel, axiom, (! [A:$tType,X25:A]: ((((the @ A) @ ((some @ A) @ X25)) = X25)))).
% 2.49/1.44 thf(fact_180_option_Oexpand, axiom, (! [A:$tType,Option:(option @ A),Option3:(option @ A)]: ((((Option = (none @ A)) = (Option3 = (none @ A))) => (((Option != (none @ A)) => ((Option3 != (none @ A)) => (((the @ A) @ Option) = ((the @ A) @ Option3)))) => (Option = Option3)))))).
% 2.49/1.44 thf(fact_181_option_Oexhaust__sel, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) => (Option = ((some @ A) @ ((the @ A) @ Option))))))).
% 2.49/1.44 thf(fact_182_disjE__realizer2, axiom, (! [B:$tType,A:$tType,P:$o,Q:(A > $o),X4:(option @ A),R:(B > $o),F:B,G:(A > B)]: (((((((case_option @ $o) @ A) @ P) @ Q) @ X4) => ((P => (R @ F)) => ((! [Q2:A]: (((Q @ Q2) => (R @ (G @ Q2))))) => (R @ (((((case_option @ B) @ A) @ F) @ G) @ X4)))))))).
% 2.49/1.44 thf(fact_183_option_Othe__def, axiom, (! [A:$tType]: (((the @ A) = ((((case_option @ A) @ A) @ (undefined @ A)) @ (^ [X24:A]: (X24))))))).
% 2.49/1.44 thf(fact_184_num_Osize_I5_J, axiom, (! [X25:num]: ((((size_size @ num) @ (bit0 @ X25)) = (((plus_plus @ nat) @ ((size_size @ num) @ X25)) @ (suc @ (zero_zero @ nat))))))).
% 2.49/1.44 thf(fact_185_num_Osize__gen_I2_J, axiom, (! [X25:num]: (((size_num @ (bit0 @ X25)) = (((plus_plus @ nat) @ (size_num @ X25)) @ (suc @ (zero_zero @ nat))))))).
% 2.49/1.44 thf(fact_186_num_Osize_I6_J, axiom, (! [X33:num]: ((((size_size @ num) @ (bit1 @ X33)) = (((plus_plus @ nat) @ ((size_size @ num) @ X33)) @ (suc @ (zero_zero @ nat))))))).
% 2.49/1.44 thf(fact_187_num_Osize__gen_I3_J, axiom, (! [X33:num]: (((size_num @ (bit1 @ X33)) = (((plus_plus @ nat) @ (size_num @ X33)) @ (suc @ (zero_zero @ nat))))))).
% 2.49/1.44 thf(fact_188_nat__of__num__code_I3_J, axiom, (! [N:num]: (((nat_of_num @ (bit1 @ N)) = (suc @ (((plus_plus @ nat) @ (nat_of_num @ N)) @ (nat_of_num @ N))))))).
% 2.49/1.44 thf(fact_189_nat__of__num_Osimps_I3_J, axiom, (! [X4:num]: (((nat_of_num @ (bit1 @ X4)) = (suc @ (((plus_plus @ nat) @ (nat_of_num @ X4)) @ (nat_of_num @ X4))))))).
% 2.49/1.44 thf(fact_190_nat__of__num__add, axiom, (! [X4:num,Y:num]: (((nat_of_num @ (((plus_plus @ num) @ X4) @ Y)) = (((plus_plus @ nat) @ (nat_of_num @ X4)) @ (nat_of_num @ Y)))))).
% 2.49/1.44 thf(fact_191_nat__of__num__neq__0, axiom, (! [X4:num]: (((nat_of_num @ X4) != (zero_zero @ nat))))).
% 2.49/1.44 thf(fact_192_nat__of__num_Osimps_I2_J, axiom, (! [X4:num]: (((nat_of_num @ (bit0 @ X4)) = (((plus_plus @ nat) @ (nat_of_num @ X4)) @ (nat_of_num @ X4)))))).
% 2.49/1.44 thf(fact_193_nat__of__num__code_I2_J, axiom, (! [N:num]: (((nat_of_num @ (bit0 @ N)) = (((plus_plus @ nat) @ (nat_of_num @ N)) @ (nat_of_num @ N)))))).
% 2.49/1.44 thf(fact_194_nat__of__num__inc, axiom, (! [X4:num]: (((nat_of_num @ (inc @ X4)) = (suc @ (nat_of_num @ X4)))))).
% 2.49/1.44 thf(fact_195_nat__of__num_Osimps_I1_J, axiom, ((nat_of_num @ one2) = (suc @ (zero_zero @ nat)))).
% 2.49/1.44 thf(fact_196_num_Osize__gen_I1_J, axiom, ((size_num @ one2) = (zero_zero @ nat))).
% 2.49/1.44 thf(fact_197_num_Osize_I4_J, axiom, (((size_size @ num) @ one2) = (zero_zero @ nat))).
% 2.49/1.44 thf(fact_198_add__2__eq__Suc, axiom, (! [N:nat]: (((((plus_plus @ nat) @ ((numeral_numeral @ nat) @ (bit0 @ one2))) @ N) = (suc @ (suc @ N)))))).
% 2.49/1.44 thf(fact_199_add__2__eq__Suc_H, axiom, (! [N:nat]: (((((plus_plus @ nat) @ N) @ ((numeral_numeral @ nat) @ (bit0 @ one2))) = (suc @ (suc @ N)))))).
% 2.49/1.44 thf(fact_200_numeral__plus__numeral, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [M:num,N:num]: (((((plus_plus @ A) @ ((numeral_numeral @ A) @ M)) @ ((numeral_numeral @ A) @ N)) = ((numeral_numeral @ A) @ (((plus_plus @ num) @ M) @ N))))))))).
% 2.49/1.44 thf(fact_201_add__numeral__left, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [V:num,W:num,Z:A]: (((((plus_plus @ A) @ ((numeral_numeral @ A) @ V)) @ (((plus_plus @ A) @ ((numeral_numeral @ A) @ W)) @ Z)) = (((plus_plus @ A) @ ((numeral_numeral @ A) @ (((plus_plus @ num) @ V) @ W))) @ Z)))))))).
% 2.49/1.44 thf(fact_202_Suc__numeral, axiom, (! [N:num]: (((suc @ ((numeral_numeral @ nat) @ N)) = ((numeral_numeral @ nat) @ (((plus_plus @ num) @ N) @ one2)))))).
% 2.49/1.44 thf(fact_203_numeral__Bit0, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [N:num]: ((((numeral_numeral @ A) @ (bit0 @ N)) = (((plus_plus @ A) @ ((numeral_numeral @ A) @ N)) @ ((numeral_numeral @ A) @ N))))))))).
% 2.49/1.44 thf(fact_204_numeral__code_I2_J, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [N:num]: ((((numeral_numeral @ A) @ (bit0 @ N)) = (((plus_plus @ A) @ ((numeral_numeral @ A) @ N)) @ ((numeral_numeral @ A) @ N))))))))).
% 2.49/1.44 thf(fact_205_zero__neq__numeral, axiom, (! [A:$tType]: ((((semiring_char_0 @ A) @ (type2 @ A)) => (! [N:num]: (((zero_zero @ A) != ((numeral_numeral @ A) @ N)))))))).
% 2.49/1.44 thf(fact_206_eval__nat__numeral_I3_J, axiom, (! [N:num]: ((((numeral_numeral @ nat) @ (bit1 @ N)) = (suc @ ((numeral_numeral @ nat) @ (bit0 @ N))))))).
% 2.49/1.44 thf(fact_207_numeral__1__eq__Suc__0, axiom, (((numeral_numeral @ nat) @ one2) = (suc @ (zero_zero @ nat)))).
% 2.49/1.44 thf(fact_208_numeral__2__eq__2, axiom, (((numeral_numeral @ nat) @ (bit0 @ one2)) = (suc @ (suc @ (zero_zero @ nat))))).
% 2.49/1.44 thf(fact_209_numeral__3__eq__3, axiom, (((numeral_numeral @ nat) @ (bit1 @ one2)) = (suc @ (suc @ (suc @ (zero_zero @ nat)))))).
% 2.49/1.44 thf(fact_210_Suc3__eq__add__3, axiom, (! [N:nat]: (((suc @ (suc @ (suc @ N))) = (((plus_plus @ nat) @ ((numeral_numeral @ nat) @ (bit1 @ one2))) @ N))))).
% 2.49/1.44 thf(fact_211_Suc__nat__number__of__add, axiom, (! [V:num,N:nat]: (((suc @ (((plus_plus @ nat) @ ((numeral_numeral @ nat) @ V)) @ N)) = (((plus_plus @ nat) @ ((numeral_numeral @ nat) @ (((plus_plus @ num) @ V) @ one2))) @ N))))).
% 2.49/1.44 thf(fact_212_zero__not__eq__two, axiom, (! [A:$tType]: ((((semiring_div_parity @ A) @ (type2 @ A)) => ((zero_zero @ A) != ((numeral_numeral @ A) @ (bit0 @ one2))))))).
% 2.49/1.44 thf(fact_213_one__plus__numeral, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [N:num]: (((((plus_plus @ A) @ (one_one @ A)) @ ((numeral_numeral @ A) @ N)) = ((numeral_numeral @ A) @ (((plus_plus @ num) @ one2) @ N))))))))).
% 2.49/1.44 thf(fact_214_Suc__1, axiom, ((suc @ (one_one @ nat)) = ((numeral_numeral @ nat) @ (bit0 @ one2)))).
% 2.49/1.44 thf(fact_215_one__add__one, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => ((((plus_plus @ A) @ (one_one @ A)) @ (one_one @ A)) = ((numeral_numeral @ A) @ (bit0 @ one2))))))).
% 2.49/1.44 thf(fact_216_numeral__plus__one, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [N:num]: (((((plus_plus @ A) @ ((numeral_numeral @ A) @ N)) @ (one_one @ A)) = ((numeral_numeral @ A) @ (((plus_plus @ num) @ N) @ one2))))))))).
% 2.49/1.44 thf(fact_217_one__plus__numeral__commute, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [X4:num]: (((((plus_plus @ A) @ (one_one @ A)) @ ((numeral_numeral @ A) @ X4)) = (((plus_plus @ A) @ ((numeral_numeral @ A) @ X4)) @ (one_one @ A))))))))).
% 2.49/1.44 thf(fact_218_One__nat__def, axiom, ((one_one @ nat) = (suc @ (zero_zero @ nat)))).
% 2.49/1.44 thf(fact_219_one__reorient, axiom, (! [A:$tType]: ((((one @ A) @ (type2 @ A)) => (! [X4:A]: ((((one_one @ A) = X4) = (X4 = (one_one @ A))))))))).
% 2.49/1.44 thf(fact_220_Suc__eq__plus1, axiom, (suc = (^ [N4:nat]: ((((plus_plus @ nat) @ N4) @ (one_one @ nat)))))).
% 2.49/1.44 thf(fact_221_Suc__eq__plus1__left, axiom, (suc = ((plus_plus @ nat) @ (one_one @ nat)))).
% 2.49/1.44 thf(fact_222_numeral__Bit1, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [N:num]: ((((numeral_numeral @ A) @ (bit1 @ N)) = (((plus_plus @ A) @ (((plus_plus @ A) @ ((numeral_numeral @ A) @ N)) @ ((numeral_numeral @ A) @ N))) @ (one_one @ A))))))))).
% 2.49/1.44 thf(fact_223_numeral__inc, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [X4:num]: ((((numeral_numeral @ A) @ (inc @ X4)) = (((plus_plus @ A) @ ((numeral_numeral @ A) @ X4)) @ (one_one @ A))))))))).
% 2.49/1.44 thf(fact_224_numeral__code_I3_J, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [N:num]: ((((numeral_numeral @ A) @ (bit1 @ N)) = (((plus_plus @ A) @ (((plus_plus @ A) @ ((numeral_numeral @ A) @ N)) @ ((numeral_numeral @ A) @ N))) @ (one_one @ A))))))))).
% 2.49/1.44 thf(fact_225_nat__1__add__1, axiom, ((((plus_plus @ nat) @ (one_one @ nat)) @ (one_one @ nat)) = ((numeral_numeral @ nat) @ (bit0 @ one2)))).
% 2.49/1.44 thf(fact_226_zero__neq__one, axiom, (! [A:$tType]: ((((zero_neq_one @ A) @ (type2 @ A)) => ((zero_zero @ A) != (one_one @ A)))))).
% 2.49/1.44 thf(fact_227_dbl__inc__simps_I2_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (((neg_numeral_dbl_inc @ A) @ (zero_zero @ A)) = (one_one @ A)))))).
% 2.49/1.44 thf(fact_228_one__natural_Orsp, axiom, ((one_one @ nat) = (one_one @ nat))).
% 2.49/1.44 thf(fact_229_dbl__inc__def, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => ((neg_numeral_dbl_inc @ A) = (^ [X:A]: ((((plus_plus @ A) @ (((plus_plus @ A) @ X) @ X)) @ (one_one @ A))))))))).
% 2.49/1.44 thf(fact_230_Suc__div__eq__add3__div__numeral, axiom, (! [M:nat,V:num]: (((((divide_divide @ nat) @ (suc @ (suc @ (suc @ M)))) @ ((numeral_numeral @ nat) @ V)) = (((divide_divide @ nat) @ (((plus_plus @ nat) @ ((numeral_numeral @ nat) @ (bit1 @ one2))) @ M)) @ ((numeral_numeral @ nat) @ V)))))).
% 2.49/1.44 thf(fact_231_div__Suc__eq__div__add3, axiom, (! [M:nat,N:nat]: (((((divide_divide @ nat) @ M) @ (suc @ (suc @ (suc @ N)))) = (((divide_divide @ nat) @ M) @ (((plus_plus @ nat) @ ((numeral_numeral @ nat) @ (bit1 @ one2))) @ N)))))).
% 2.49/1.44 thf(fact_232_divide__zero, axiom, (! [A:$tType]: ((((semidom_divide @ A) @ (type2 @ A)) => (! [A2:A]: (((((divide_divide @ A) @ A2) @ (zero_zero @ A)) = (zero_zero @ A)))))))).
% 2.49/1.44 thf(fact_233_divide__zero__left, axiom, (! [A:$tType]: ((((semidom_divide @ A) @ (type2 @ A)) => (! [A2:A]: (((((divide_divide @ A) @ (zero_zero @ A)) @ A2) = (zero_zero @ A)))))))).
% 2.49/1.44 thf(fact_234_divide__eq__0__iff, axiom, (! [A:$tType]: ((((field @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: ((((((divide_divide @ A) @ A2) @ B2) = (zero_zero @ A)) = ((A2 = (zero_zero @ A)) | (B2 = (zero_zero @ A)))))))))).
% 2.49/1.44 thf(fact_235_divide__cancel__left, axiom, (! [A:$tType]: ((((field @ A) @ (type2 @ A)) => (! [C2:A,A2:A,B2:A]: ((((((divide_divide @ A) @ C2) @ A2) = (((divide_divide @ A) @ C2) @ B2)) = ((C2 = (zero_zero @ A)) | (A2 = B2))))))))).
% 2.49/1.44 thf(fact_236_divide__cancel__right, axiom, (! [A:$tType]: ((((field @ A) @ (type2 @ A)) => (! [A2:A,C2:A,B2:A]: ((((((divide_divide @ A) @ A2) @ C2) = (((divide_divide @ A) @ B2) @ C2)) = ((C2 = (zero_zero @ A)) | (A2 = B2))))))))).
% 2.49/1.44 thf(fact_237_division__ring__divide__zero, axiom, (! [A:$tType]: ((((division_ring @ A) @ (type2 @ A)) => (! [A2:A]: (((((divide_divide @ A) @ A2) @ (zero_zero @ A)) = (zero_zero @ A)))))))).
% 2.49/1.44 thf(fact_238_div__0, axiom, (! [A:$tType]: ((((semiring_div @ A) @ (type2 @ A)) => (! [A2:A]: (((((divide_divide @ A) @ (zero_zero @ A)) @ A2) = (zero_zero @ A)))))))).
% 2.49/1.44 thf(fact_239_div__by__0, axiom, (! [A:$tType]: ((((semiring_div @ A) @ (type2 @ A)) => (! [A2:A]: (((((divide_divide @ A) @ A2) @ (zero_zero @ A)) = (zero_zero @ A)))))))).
% 2.49/1.44 thf(fact_240_div__self, axiom, (! [A:$tType]: ((((semidom_divide @ A) @ (type2 @ A)) => (! [A2:A]: (((A2 != (zero_zero @ A)) => ((((divide_divide @ A) @ A2) @ A2) = (one_one @ A))))))))).
% 2.49/1.44 thf(fact_241_divide__eq__1__iff, axiom, (! [A:$tType]: ((((field @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: ((((((divide_divide @ A) @ A2) @ B2) = (one_one @ A)) = ((B2 != (zero_zero @ A)) & (A2 = B2))))))))).
% 2.49/1.44 thf(fact_242_one__eq__divide__iff, axiom, (! [A:$tType]: ((((field @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: ((((one_one @ A) = (((divide_divide @ A) @ A2) @ B2)) = ((B2 != (zero_zero @ A)) & (A2 = B2))))))))).
% 2.49/1.44 thf(fact_243_divide__self, axiom, (! [A:$tType]: ((((division_ring @ A) @ (type2 @ A)) => (! [A2:A]: (((A2 != (zero_zero @ A)) => ((((divide_divide @ A) @ A2) @ A2) = (one_one @ A))))))))).
% 2.49/1.44 thf(fact_244_divide__self__if, axiom, (! [A:$tType]: ((((division_ring @ A) @ (type2 @ A)) => (! [A2:A]: ((((A2 = (zero_zero @ A)) => ((((divide_divide @ A) @ A2) @ A2) = (zero_zero @ A))) & ((A2 != (zero_zero @ A)) => ((((divide_divide @ A) @ A2) @ A2) = (one_one @ A)))))))))).
% 2.49/1.44 thf(fact_245_divide__eq__eq__1, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: ((((((divide_divide @ A) @ B2) @ A2) = (one_one @ A)) = ((A2 != (zero_zero @ A)) & (A2 = B2))))))))).
% 2.49/1.44 thf(fact_246_eq__divide__eq__1, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: ((((one_one @ A) = (((divide_divide @ A) @ B2) @ A2)) = ((A2 != (zero_zero @ A)) & (A2 = B2))))))))).
% 2.49/1.44 thf(fact_247_one__divide__eq__0__iff, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [A2:A]: ((((((divide_divide @ A) @ (one_one @ A)) @ A2) = (zero_zero @ A)) = (A2 = (zero_zero @ A))))))))).
% 2.49/1.44 thf(fact_248_zero__eq__1__divide__iff, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [A2:A]: ((((zero_zero @ A) = (((divide_divide @ A) @ (one_one @ A)) @ A2)) = (A2 = (zero_zero @ A))))))))).
% 2.49/1.44 thf(fact_249_div__1, axiom, (! [M:nat]: (((((divide_divide @ nat) @ M) @ (suc @ (zero_zero @ nat))) = M)))).
% 2.49/1.44 thf(fact_250_div__add__self2, axiom, (! [A:$tType]: ((((semiring_div @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: (((B2 != (zero_zero @ A)) => ((((divide_divide @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ B2) = (((plus_plus @ A) @ (((divide_divide @ A) @ A2) @ B2)) @ (one_one @ A)))))))))).
% 2.49/1.44 thf(tcon_BinDag__Mirabelle__rybootvolr_Odag___Code__Evaluation_Oterm__of, axiom, ((code_term_of @ binDag_Mirabelle_dag) @ (type2 @ binDag_Mirabelle_dag))).
% 2.49/1.44 thf(tcon_BinDag__Mirabelle__rybootvolr_Odag___HOL_Oequal, axiom, ((cl_HOL_Oequal @ binDag_Mirabelle_dag) @ (type2 @ binDag_Mirabelle_dag))).
% 2.49/1.44 thf(tcon_Record_Otuple__isomorphism___Code__Evaluation_Oterm__of_1, axiom, (! [A6:$tType,A7:$tType,A8:$tType]: (((((typerep2 @ A6) @ (type2 @ A6)) & (((typerep2 @ A7) @ (type2 @ A7)) & ((typerep2 @ A8) @ (type2 @ A8)))) => ((code_term_of @ (((tuple_isomorphism @ A6) @ A7) @ A8)) @ (type2 @ (((tuple_isomorphism @ A6) @ A7) @ A8))))))).
% 2.49/1.44 thf(tcon_Record_Otuple__isomorphism___HOL_Oequal_2, axiom, (! [A6:$tType,A7:$tType,A8:$tType]: (((cl_HOL_Oequal @ (((tuple_isomorphism @ A6) @ A7) @ A8)) @ (type2 @ (((tuple_isomorphism @ A6) @ A7) @ A8)))))).
% 2.49/1.44 thf(tcon_Code__Numeral_Onatural___Code__Evaluation_Oterm__of_3, axiom, ((code_term_of @ code_natural) @ (type2 @ code_natural))).
% 2.49/1.44 thf(tcon_Code__Numeral_Onatural___HOL_Oequal_4, axiom, ((cl_HOL_Oequal @ code_natural) @ (type2 @ code_natural))).
% 2.49/1.44 thf(tcon_Code__Evaluation_Oterm___Code__Evaluation_Oterm__of_5, axiom, ((code_term_of @ code_term) @ (type2 @ code_term))).
% 2.49/1.44 thf(tcon_Code__Evaluation_Oterm___HOL_Oequal_6, axiom, ((cl_HOL_Oequal @ code_term) @ (type2 @ code_term))).
% 2.49/1.44 thf(tcon_Product__Type_Ounit___Code__Evaluation_Oterm__of_7, axiom, ((code_term_of @ product_unit) @ (type2 @ product_unit))).
% 2.49/1.44 thf(tcon_Product__Type_Ounit___HOL_Oequal_8, axiom, ((cl_HOL_Oequal @ product_unit) @ (type2 @ product_unit))).
% 2.49/1.44 thf(tcon_Product__Type_Oprod___Code__Evaluation_Oterm__of_9, axiom, (! [A6:$tType,A7:$tType]: (((((typerep2 @ A6) @ (type2 @ A6)) & ((typerep2 @ A7) @ (type2 @ A7))) => ((code_term_of @ ((product_prod @ A6) @ A7)) @ (type2 @ ((product_prod @ A6) @ A7))))))).
% 2.49/1.44 thf(tcon_Product__Type_Oprod___HOL_Oequal_10, axiom, (! [A6:$tType,A7:$tType]: (((cl_HOL_Oequal @ ((product_prod @ A6) @ A7)) @ (type2 @ ((product_prod @ A6) @ A7)))))).
% 2.49/1.44 thf(tcon_Typerep_Otyperep___Code__Evaluation_Oterm__of_11, axiom, ((code_term_of @ typerep) @ (type2 @ typerep))).
% 2.49/1.44 thf(tcon_Typerep_Otyperep___HOL_Oequal_12, axiom, ((cl_HOL_Oequal @ typerep) @ (type2 @ typerep))).
% 2.49/1.44 thf(tcon_String_Oliteral___Code__Evaluation_Oterm__of_13, axiom, ((code_term_of @ literal) @ (type2 @ literal))).
% 2.49/1.44 thf(tcon_String_Oliteral___HOL_Oequal_14, axiom, ((cl_HOL_Oequal @ literal) @ (type2 @ literal))).
% 2.49/1.44 thf(tcon_Simpl__Heap_Oref___Code__Evaluation_Oterm__of_15, axiom, ((code_term_of @ simpl_ref) @ (type2 @ simpl_ref))).
% 2.49/1.44 thf(tcon_Option_Ooption___Code__Evaluation_Oterm__of_16, axiom, (! [A6:$tType]: ((((typerep2 @ A6) @ (type2 @ A6)) => ((code_term_of @ (option @ A6)) @ (type2 @ (option @ A6))))))).
% 2.49/1.44 thf(tcon_Option_Ooption___HOL_Oequal_17, axiom, (! [A6:$tType]: (((cl_HOL_Oequal @ (option @ A6)) @ (type2 @ (option @ A6)))))).
% 2.49/1.44 thf(tcon_Sum__Type_Osum___Code__Evaluation_Oterm__of_18, axiom, (! [A6:$tType,A7:$tType]: (((((typerep2 @ A6) @ (type2 @ A6)) & ((typerep2 @ A7) @ (type2 @ A7))) => ((code_term_of @ ((sum_sum @ A6) @ A7)) @ (type2 @ ((sum_sum @ A6) @ A7))))))).
% 2.49/1.44 thf(tcon_Sum__Type_Osum___HOL_Oequal_19, axiom, (! [A6:$tType,A7:$tType]: (((cl_HOL_Oequal @ ((sum_sum @ A6) @ A7)) @ (type2 @ ((sum_sum @ A6) @ A7)))))).
% 2.49/1.44 thf(tcon_List_Olist___Code__Evaluation_Oterm__of_20, axiom, (! [A6:$tType]: ((((typerep2 @ A6) @ (type2 @ A6)) => ((code_term_of @ (list @ A6)) @ (type2 @ (list @ A6))))))).
% 2.49/1.44 thf(tcon_List_Olist___HOL_Oequal_21, axiom, (! [A6:$tType]: (((cl_HOL_Oequal @ (list @ A6)) @ (type2 @ (list @ A6)))))).
% 2.49/1.44 thf(tcon_HOL_Obool___Code__Evaluation_Oterm__of_22, axiom, ((code_term_of @ $o) @ (type2 @ $o))).
% 2.49/1.44 thf(tcon_HOL_Obool___HOL_Oequal_23, axiom, ((cl_HOL_Oequal @ $o) @ (type2 @ $o))).
% 2.49/1.44 thf(tcon_Set_Oset___Code__Evaluation_Oterm__of_24, axiom, (! [A6:$tType]: ((((typerep2 @ A6) @ (type2 @ A6)) => ((code_term_of @ (set @ A6)) @ (type2 @ (set @ A6))))))).
% 2.49/1.44 thf(tcon_Set_Oset___HOL_Oequal_25, axiom, (! [A6:$tType]: ((((cl_HOL_Oequal @ A6) @ (type2 @ A6)) => ((cl_HOL_Oequal @ (set @ A6)) @ (type2 @ (set @ A6))))))).
% 2.49/1.44 thf(tcon_Num_Onum___Code__Evaluation_Oterm__of_26, axiom, ((code_term_of @ num) @ (type2 @ num))).
% 2.49/1.44 thf(tcon_Num_Onum___HOL_Oequal_27, axiom, ((cl_HOL_Oequal @ num) @ (type2 @ num))).
% 2.49/1.44 thf(tcon_Nat_Onat___Code__Evaluation_Oterm__of_28, axiom, ((code_term_of @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___HOL_Oequal_29, axiom, ((cl_HOL_Oequal @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_fun___Code__Evaluation_Oterm__of_30, axiom, (! [A6:$tType,A7:$tType]: (((((typerep2 @ A6) @ (type2 @ A6)) & ((typerep2 @ A7) @ (type2 @ A7))) => ((code_term_of @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.49/1.44 thf(tcon_fun___HOL_Oequal_31, axiom, (! [A6:$tType,A7:$tType]: (((((enum @ A6) @ (type2 @ A6)) & ((cl_HOL_Oequal @ A7) @ (type2 @ A7))) => ((cl_HOL_Oequal @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.49/1.44 thf(tcon_fun___Typerep_Otyperep, axiom, (! [A6:$tType,A7:$tType]: (((((typerep2 @ A6) @ (type2 @ A6)) & ((typerep2 @ A7) @ (type2 @ A7))) => ((typerep2 @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.49/1.44 thf(tcon_fun___Enum_Oenum, axiom, (! [A6:$tType,A7:$tType]: (((((enum @ A6) @ (type2 @ A6)) & ((enum @ A7) @ (type2 @ A7))) => ((enum @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.49/1.44 thf(tcon_Nat_Onat___Typerep_Otyperep_32, axiom, ((typerep2 @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Num_Onum___Typerep_Otyperep_33, axiom, ((typerep2 @ num) @ (type2 @ num))).
% 2.49/1.44 thf(tcon_Set_Oset___Typerep_Otyperep_34, axiom, (! [A6:$tType]: ((((typerep2 @ A6) @ (type2 @ A6)) => ((typerep2 @ (set @ A6)) @ (type2 @ (set @ A6))))))).
% 2.49/1.44 thf(tcon_Set_Oset___Enum_Oenum_35, axiom, (! [A6:$tType]: ((((enum @ A6) @ (type2 @ A6)) => ((enum @ (set @ A6)) @ (type2 @ (set @ A6))))))).
% 2.49/1.44 thf(tcon_HOL_Obool___Typerep_Otyperep_36, axiom, ((typerep2 @ $o) @ (type2 @ $o))).
% 2.49/1.44 thf(tcon_HOL_Obool___Enum_Oenum_37, axiom, ((enum @ $o) @ (type2 @ $o))).
% 2.49/1.44 thf(tcon_List_Olist___Typerep_Otyperep_38, axiom, (! [A6:$tType]: ((((typerep2 @ A6) @ (type2 @ A6)) => ((typerep2 @ (list @ A6)) @ (type2 @ (list @ A6))))))).
% 2.49/1.44 thf(tcon_Sum__Type_Osum___Typerep_Otyperep_39, axiom, (! [A6:$tType,A7:$tType]: (((((typerep2 @ A6) @ (type2 @ A6)) & ((typerep2 @ A7) @ (type2 @ A7))) => ((typerep2 @ ((sum_sum @ A6) @ A7)) @ (type2 @ ((sum_sum @ A6) @ A7))))))).
% 2.49/1.44 thf(tcon_Sum__Type_Osum___Enum_Oenum_40, axiom, (! [A6:$tType,A7:$tType]: (((((enum @ A6) @ (type2 @ A6)) & ((enum @ A7) @ (type2 @ A7))) => ((enum @ ((sum_sum @ A6) @ A7)) @ (type2 @ ((sum_sum @ A6) @ A7))))))).
% 2.49/1.44 thf(tcon_Option_Ooption___Typerep_Otyperep_41, axiom, (! [A6:$tType]: ((((typerep2 @ A6) @ (type2 @ A6)) => ((typerep2 @ (option @ A6)) @ (type2 @ (option @ A6))))))).
% 2.49/1.44 thf(tcon_Option_Ooption___Enum_Oenum_42, axiom, (! [A6:$tType]: ((((enum @ A6) @ (type2 @ A6)) => ((enum @ (option @ A6)) @ (type2 @ (option @ A6))))))).
% 2.49/1.44 thf(tcon_Simpl__Heap_Oref___Typerep_Otyperep_43, axiom, ((typerep2 @ simpl_ref) @ (type2 @ simpl_ref))).
% 2.49/1.44 thf(tcon_String_Oliteral___Typerep_Otyperep_44, axiom, ((typerep2 @ literal) @ (type2 @ literal))).
% 2.49/1.44 thf(tcon_Typerep_Otyperep___Typerep_Otyperep_45, axiom, ((typerep2 @ typerep) @ (type2 @ typerep))).
% 2.49/1.44 thf(tcon_Product__Type_Oprod___Typerep_Otyperep_46, axiom, (! [A6:$tType,A7:$tType]: (((((typerep2 @ A6) @ (type2 @ A6)) & ((typerep2 @ A7) @ (type2 @ A7))) => ((typerep2 @ ((product_prod @ A6) @ A7)) @ (type2 @ ((product_prod @ A6) @ A7))))))).
% 2.49/1.44 thf(tcon_Product__Type_Oprod___Enum_Oenum_47, axiom, (! [A6:$tType,A7:$tType]: (((((enum @ A6) @ (type2 @ A6)) & ((enum @ A7) @ (type2 @ A7))) => ((enum @ ((product_prod @ A6) @ A7)) @ (type2 @ ((product_prod @ A6) @ A7))))))).
% 2.49/1.44 thf(tcon_Product__Type_Ounit___Typerep_Otyperep_48, axiom, ((typerep2 @ product_unit) @ (type2 @ product_unit))).
% 2.49/1.44 thf(tcon_Product__Type_Ounit___Enum_Oenum_49, axiom, ((enum @ product_unit) @ (type2 @ product_unit))).
% 2.49/1.44 thf(tcon_Code__Evaluation_Oterm___Typerep_Otyperep_50, axiom, ((typerep2 @ code_term) @ (type2 @ code_term))).
% 2.49/1.44 thf(tcon_Code__Numeral_Onatural___Typerep_Otyperep_51, axiom, ((typerep2 @ code_natural) @ (type2 @ code_natural))).
% 2.49/1.44 thf(tcon_Record_Otuple__isomorphism___Typerep_Otyperep_52, axiom, (! [A6:$tType,A7:$tType,A8:$tType]: (((((typerep2 @ A6) @ (type2 @ A6)) & (((typerep2 @ A7) @ (type2 @ A7)) & ((typerep2 @ A8) @ (type2 @ A8)))) => ((typerep2 @ (((tuple_isomorphism @ A6) @ A7) @ A8)) @ (type2 @ (((tuple_isomorphism @ A6) @ A7) @ A8))))))).
% 2.49/1.44 thf(tcon_BinDag__Mirabelle__rybootvolr_Odag___Typerep_Otyperep_53, axiom, ((typerep2 @ binDag_Mirabelle_dag) @ (type2 @ binDag_Mirabelle_dag))).
% 2.49/1.44 thf(tcon_fun___Quickcheck__Random_Orandom, axiom, (! [A6:$tType,A7:$tType]: (((((code_term_of @ A6) @ (type2 @ A6)) & (((cl_HOL_Oequal @ A6) @ (type2 @ A6)) & ((quickcheck_random @ A7) @ (type2 @ A7)))) => ((quickcheck_random @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.49/1.44 thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, axiom, ((semiri456707255roduct @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, ((canoni770627133id_add @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add, axiom, ((ordere779506340up_add @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add, axiom, ((cancel1352612707id_add @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add, axiom, ((cancel_semigroup_add @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___Divides_Osemiring__div__parity, axiom, ((semiring_div_parity @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___Quickcheck__Random_Orandom_54, axiom, ((quickcheck_random @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add, axiom, ((ab_semigroup_add @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add, axiom, ((comm_monoid_add @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1, axiom, ((comm_semiring_1 @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___Rings_Osemidom__divide, axiom, ((semidom_divide @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___Groups_Osemigroup__add, axiom, ((semigroup_add @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___Divides_Osemiring__div, axiom, ((semiring_div @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___Nat_Osemiring__char__0, axiom, ((semiring_char_0 @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___Rings_Ozero__neq__one, axiom, ((zero_neq_one @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___Groups_Omonoid__add, axiom, ((monoid_add @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___Num_Onumeral, axiom, ((numeral @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___Groups_Ozero, axiom, ((zero @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___Groups_Oone, axiom, ((one @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Nat_Onat___Nat_Osize, axiom, ((size @ nat) @ (type2 @ nat))).
% 2.49/1.44 thf(tcon_Num_Onum___Quickcheck__Random_Orandom_55, axiom, ((quickcheck_random @ num) @ (type2 @ num))).
% 2.49/1.44 thf(tcon_Num_Onum___Nat_Osize_56, axiom, ((size @ num) @ (type2 @ num))).
% 2.49/1.44 thf(tcon_Set_Oset___Quickcheck__Random_Orandom_57, axiom, (! [A6:$tType]: ((((quickcheck_random @ A6) @ (type2 @ A6)) => ((quickcheck_random @ (set @ A6)) @ (type2 @ (set @ A6))))))).
% 2.49/1.44 thf(tcon_HOL_Obool___Quickcheck__Random_Orandom_58, axiom, ((quickcheck_random @ $o) @ (type2 @ $o))).
% 2.49/1.44 thf(tcon_HOL_Obool___Nat_Osize_59, axiom, ((size @ $o) @ (type2 @ $o))).
% 2.49/1.44 thf(tcon_List_Olist___Quickcheck__Random_Orandom_60, axiom, (! [A6:$tType]: ((((quickcheck_random @ A6) @ (type2 @ A6)) => ((quickcheck_random @ (list @ A6)) @ (type2 @ (list @ A6))))))).
% 2.49/1.44 thf(tcon_List_Olist___Nat_Osize_61, axiom, (! [A6:$tType]: (((size @ (list @ A6)) @ (type2 @ (list @ A6)))))).
% 2.49/1.44 thf(tcon_Sum__Type_Osum___Quickcheck__Random_Orandom_62, axiom, (! [A6:$tType,A7:$tType]: (((((quickcheck_random @ A6) @ (type2 @ A6)) & ((quickcheck_random @ A7) @ (type2 @ A7))) => ((quickcheck_random @ ((sum_sum @ A6) @ A7)) @ (type2 @ ((sum_sum @ A6) @ A7))))))).
% 2.49/1.44 thf(tcon_Sum__Type_Osum___Nat_Osize_63, axiom, (! [A6:$tType,A7:$tType]: (((size @ ((sum_sum @ A6) @ A7)) @ (type2 @ ((sum_sum @ A6) @ A7)))))).
% 2.49/1.44 thf(tcon_Option_Ooption___Quickcheck__Random_Orandom_64, axiom, (! [A6:$tType]: ((((quickcheck_random @ A6) @ (type2 @ A6)) => ((quickcheck_random @ (option @ A6)) @ (type2 @ (option @ A6))))))).
% 2.49/1.44 thf(tcon_Option_Ooption___Nat_Osize_65, axiom, (! [A6:$tType]: (((size @ (option @ A6)) @ (type2 @ (option @ A6)))))).
% 2.49/1.44 thf(tcon_String_Oliteral___Quickcheck__Random_Orandom_66, axiom, ((quickcheck_random @ literal) @ (type2 @ literal))).
% 2.49/1.44 thf(tcon_String_Oliteral___Nat_Osize_67, axiom, ((size @ literal) @ (type2 @ literal))).
% 2.49/1.44 thf(tcon_Typerep_Otyperep___Nat_Osize_68, axiom, ((size @ typerep) @ (type2 @ typerep))).
% 2.49/1.44 thf(tcon_Product__Type_Oprod___Quickcheck__Random_Orandom_69, axiom, (! [A6:$tType,A7:$tType]: (((((quickcheck_random @ A6) @ (type2 @ A6)) & ((quickcheck_random @ A7) @ (type2 @ A7))) => ((quickcheck_random @ ((product_prod @ A6) @ A7)) @ (type2 @ ((product_prod @ A6) @ A7))))))).
% 2.49/1.44 thf(tcon_Product__Type_Oprod___Nat_Osize_70, axiom, (! [A6:$tType,A7:$tType]: (((size @ ((product_prod @ A6) @ A7)) @ (type2 @ ((product_prod @ A6) @ A7)))))).
% 2.49/1.44 thf(tcon_Product__Type_Ounit___Quickcheck__Random_Orandom_71, axiom, ((quickcheck_random @ product_unit) @ (type2 @ product_unit))).
% 2.49/1.44 thf(tcon_Product__Type_Ounit___Nat_Osize_72, axiom, ((size @ product_unit) @ (type2 @ product_unit))).
% 2.49/1.44 thf(tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__add_73, axiom, ((ordere779506340up_add @ code_natural) @ (type2 @ code_natural))).
% 2.49/1.44 thf(tcon_Code__Numeral_Onatural___Groups_Ocancel__comm__monoid__add_74, axiom, ((cancel1352612707id_add @ code_natural) @ (type2 @ code_natural))).
% 2.49/1.44 thf(tcon_Code__Numeral_Onatural___Groups_Ocancel__semigroup__add_75, axiom, ((cancel_semigroup_add @ code_natural) @ (type2 @ code_natural))).
% 2.49/1.44 thf(tcon_Code__Numeral_Onatural___Quickcheck__Random_Orandom_76, axiom, ((quickcheck_random @ code_natural) @ (type2 @ code_natural))).
% 2.49/1.44 thf(tcon_Code__Numeral_Onatural___Groups_Oab__semigroup__add_77, axiom, ((ab_semigroup_add @ code_natural) @ (type2 @ code_natural))).
% 2.49/1.44 thf(tcon_Code__Numeral_Onatural___Groups_Ocomm__monoid__add_78, axiom, ((comm_monoid_add @ code_natural) @ (type2 @ code_natural))).
% 2.49/1.44 thf(tcon_Code__Numeral_Onatural___Rings_Ocomm__semiring__1_79, axiom, ((comm_semiring_1 @ code_natural) @ (type2 @ code_natural))).
% 2.49/1.44 thf(tcon_Code__Numeral_Onatural___Rings_Osemidom__divide_80, axiom, ((semidom_divide @ code_natural) @ (type2 @ code_natural))).
% 2.49/1.44 thf(tcon_Code__Numeral_Onatural___Groups_Osemigroup__add_81, axiom, ((semigroup_add @ code_natural) @ (type2 @ code_natural))).
% 2.49/1.44 thf(tcon_Code__Numeral_Onatural___Divides_Osemiring__div_82, axiom, ((semiring_div @ code_natural) @ (type2 @ code_natural))).
% 2.49/1.44 thf(tcon_Code__Numeral_Onatural___Rings_Ozero__neq__one_83, axiom, ((zero_neq_one @ code_natural) @ (type2 @ code_natural))).
% 2.49/1.44 thf(tcon_Code__Numeral_Onatural___Groups_Omonoid__add_84, axiom, ((monoid_add @ code_natural) @ (type2 @ code_natural))).
% 2.49/1.44 thf(tcon_Code__Numeral_Onatural___Num_Onumeral_85, axiom, ((numeral @ code_natural) @ (type2 @ code_natural))).
% 2.49/1.44 thf(tcon_Code__Numeral_Onatural___Groups_Ozero_86, axiom, ((zero @ code_natural) @ (type2 @ code_natural))).
% 2.49/1.44 thf(tcon_Code__Numeral_Onatural___Groups_Oone_87, axiom, ((one @ code_natural) @ (type2 @ code_natural))).
% 2.49/1.44 thf(tcon_Code__Numeral_Onatural___Nat_Osize_88, axiom, ((size @ code_natural) @ (type2 @ code_natural))).
% 2.49/1.44 thf(tcon_Record_Otuple__isomorphism___Quickcheck__Random_Orandom_89, axiom, (! [A6:$tType,A7:$tType,A8:$tType]: (((((code_term_of @ A6) @ (type2 @ A6)) & (((cl_HOL_Oequal @ A6) @ (type2 @ A6)) & (((quickcheck_random @ A6) @ (type2 @ A6)) & (((quickcheck_random @ A7) @ (type2 @ A7)) & ((quickcheck_random @ A8) @ (type2 @ A8)))))) => ((quickcheck_random @ (((tuple_isomorphism @ A6) @ A7) @ A8)) @ (type2 @ (((tuple_isomorphism @ A6) @ A7) @ A8))))))).
% 2.49/1.44 thf(tcon_Record_Otuple__isomorphism___Nat_Osize_90, axiom, (! [A6:$tType,A7:$tType,A8:$tType]: (((size @ (((tuple_isomorphism @ A6) @ A7) @ A8)) @ (type2 @ (((tuple_isomorphism @ A6) @ A7) @ A8)))))).
% 2.49/1.44 thf(tcon_BinDag__Mirabelle__rybootvolr_Odag___Nat_Osize_91, axiom, ((size @ binDag_Mirabelle_dag) @ (type2 @ binDag_Mirabelle_dag))).
% 2.49/1.44 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.49/1.44 thf(help_If_2_1_T, axiom, (! [A:$tType,X4:A,Y:A]: ((((((if @ A) @ $false) @ X4) @ Y) = Y)))).
% 2.49/1.44 thf(help_If_1_1_T, axiom, (! [A:$tType,X4:A,Y:A]: ((((((if @ A) @ $true) @ X4) @ Y) = X4)))).
% 2.49/1.44 thf(conj_0, conjecture, ((((binDag476092410e_Node @ lt) @ a) @ rt) != lt)).
% 2.49/1.44 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.m3AuIGZJso/DTF2DTF32018.p
% 2.49/1.44 ------------------------
% 2.49/1.46 ---- Cleaned THF ---
% 2.49/1.47 thf(ty_t_BinDag__Mirabelle__rybootvolr_Odag,type,
% 2.49/1.47 binDag_Mirabelle_dag: $tType ).
% 2.49/1.47
% 2.49/1.47 thf(ty_t_Record_Otuple__isomorphism,type,
% 2.49/1.47 tuple_isomorphism: $tType > $tType > $tType > $tType ).
% 2.49/1.47
% 2.49/1.47 thf(ty_t_Code__Numeral_Onatural,type,
% 2.49/1.47 code_natural: $tType ).
% 2.49/1.47
% 2.49/1.47 thf(ty_t_Code__Evaluation_Oterm,type,
% 2.49/1.47 code_term: $tType ).
% 2.49/1.47
% 2.49/1.47 thf(ty_t_Product__Type_Ounit,type,
% 2.49/1.47 product_unit: $tType ).
% 2.49/1.47
% 2.49/1.47 thf(ty_t_Product__Type_Oprod,type,
% 2.49/1.47 product_prod: $tType > $tType > $tType ).
% 2.49/1.47
% 2.49/1.47 thf(ty_t_Typerep_Otyperep,type,
% 2.49/1.47 typerep: $tType ).
% 2.49/1.47
% 2.49/1.47 thf(ty_t_Simpl__Heap_Oref,type,
% 2.49/1.47 simpl_ref: $tType ).
% 2.49/1.47
% 2.49/1.47 thf(ty_t_String_Oliteral,type,
% 2.49/1.47 literal: $tType ).
% 2.49/1.47
% 2.49/1.47 thf(ty_t_Sum__Type_Osum,type,
% 2.49/1.47 sum_sum: $tType > $tType > $tType ).
% 2.49/1.47
% 2.49/1.47 thf(ty_t_Option_Ooption,type,
% 2.49/1.47 option: $tType > $tType ).
% 2.49/1.47
% 2.49/1.47 thf(ty_t_List_Olist,type,
% 2.49/1.47 list: $tType > $tType ).
% 2.49/1.47
% 2.49/1.47 thf(ty_t_Set_Oset,type,
% 2.49/1.47 set: $tType > $tType ).
% 2.49/1.47
% 2.49/1.47 thf(ty_t_Num_Onum,type,
% 2.49/1.47 num: $tType ).
% 2.49/1.47
% 2.49/1.47 thf(ty_t_Nat_Onat,type,
% 2.49/1.47 nat: $tType ).
% 2.49/1.47
% 2.49/1.47 thf(ty_t_itself,type,
% 2.49/1.47 itself: $tType > $tType ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Enum_Oenum,type,
% 2.49/1.47 enum:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Typerep_Otyperep,type,
% 2.49/1.47 typerep2:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_HOL_Otype,type,
% 2.49/1.47 type:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_HOL_Oequal,type,
% 2.49/1.47 cl_HOL_Oequal:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Code__Evaluation_Oterm__of,type,
% 2.49/1.47 code_term_of:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Nat_Osize,type,
% 2.49/1.47 size:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Groups_Oone,type,
% 2.49/1.47 one:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Groups_Ozero,type,
% 2.49/1.47 zero:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Num_Onumeral,type,
% 2.49/1.47 numeral:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Fields_Ofield,type,
% 2.49/1.47 field:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Num_Oneg__numeral,type,
% 2.49/1.47 neg_numeral:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Groups_Ogroup__add,type,
% 2.49/1.47 group_add:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Groups_Omonoid__add,type,
% 2.49/1.47 monoid_add:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Rings_Ozero__neq__one,type,
% 2.49/1.47 zero_neq_one:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Nat_Osemiring__char__0,type,
% 2.49/1.47 semiring_char_0:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Divides_Osemiring__div,type,
% 2.49/1.47 semiring_div:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Fields_Odivision__ring,type,
% 2.49/1.47 division_ring:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Groups_Osemigroup__add,type,
% 2.49/1.47 semigroup_add:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Rings_Osemidom__divide,type,
% 2.49/1.47 semidom_divide:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Rings_Ocomm__semiring__1,type,
% 2.49/1.47 comm_semiring_1:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 2.49/1.47 comm_monoid_add:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Fields_Olinordered__field,type,
% 2.49/1.47 linordered_field:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 2.49/1.47 ab_semigroup_add:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Quickcheck__Random_Orandom,type,
% 2.49/1.47 quickcheck_random:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Divides_Osemiring__div__parity,type,
% 2.49/1.47 semiring_div_parity:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 2.49/1.47 cancel_semigroup_add:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 2.49/1.47 cancel1352612707id_add:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 2.49/1.47 linord219039673up_add:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 2.49/1.47 ordere779506340up_add:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.49/1.47 canoni770627133id_add:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
% 2.49/1.47 semiri456707255roduct:
% 2.49/1.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_BNF__Greatest__Fixpoint_OShift,type,
% 2.49/1.47 bNF_Greatest_Shift:
% 2.49/1.47 !>[A: $tType] : ( ( set @ ( list @ A ) ) > A > ( set @ ( list @ A ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Basic__BNF__LFPs_Osum_Osize__sum,type,
% 2.49/1.47 basic_BNF_size_sum:
% 2.49/1.47 !>[A: $tType,B: $tType] : ( ( A > nat ) > ( B > nat ) > ( sum_sum @ A @ B ) > nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_ONode,type,
% 2.49/1.47 binDag476092410e_Node: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > binDag_Mirabelle_dag ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_OTip,type,
% 2.49/1.47 binDag_Mirabelle_Tip: binDag_Mirabelle_dag ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_Ocase__dag,type,
% 2.49/1.47 binDag1297733282se_dag:
% 2.49/1.47 !>[A: $tType] : ( A > ( binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A ) > binDag_Mirabelle_dag > A ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_Orec__dag,type,
% 2.49/1.47 binDag1442713106ec_dag:
% 2.49/1.47 !>[A: $tType] : ( A > ( binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A > A > A ) > binDag_Mirabelle_dag > A ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_Osize__dag,type,
% 2.49/1.47 binDag1924123185ze_dag: binDag_Mirabelle_dag > nat ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Code__Numeral_OSuc,type,
% 2.49/1.47 code_Suc: code_natural > code_natural ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Code__Numeral_Onatural_Ocase__natural,type,
% 2.49/1.47 code_case_natural:
% 2.49/1.47 !>[T: $tType] : ( T > ( code_natural > T ) > code_natural > T ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Code__Numeral_Onatural_Orec__natural,type,
% 2.49/1.47 code_rec_natural:
% 2.49/1.47 !>[T: $tType] : ( T > ( code_natural > T > T ) > code_natural > T ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Code__Numeral_Onatural_Osize__natural,type,
% 2.49/1.47 code_size_natural: code_natural > nat ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Groups_Oone__class_Oone,type,
% 2.49/1.47 one_one:
% 2.49/1.47 !>[A: $tType] : A ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 2.49/1.47 plus_plus:
% 2.49/1.47 !>[A: $tType] : ( A > A > A ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.49/1.47 zero_zero:
% 2.49/1.47 !>[A: $tType] : A ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_HOL_Obool_Osize__bool,type,
% 2.49/1.47 size_bool: $o > nat ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_HOL_Odefault__class_Odefault,type,
% 2.49/1.47 default_default:
% 2.49/1.47 !>[A: $tType] : A ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_HOL_Oundefined,type,
% 2.49/1.47 undefined:
% 2.49/1.47 !>[A: $tType] : A ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_If,type,
% 2.49/1.47 if:
% 2.49/1.47 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_List_Ogen__length,type,
% 2.49/1.47 gen_length:
% 2.49/1.47 !>[A: $tType] : ( nat > ( list @ A ) > nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_List_Olist_OCons,type,
% 2.49/1.47 cons:
% 2.49/1.47 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_List_Olist_Osize__list,type,
% 2.49/1.47 size_list:
% 2.49/1.47 !>[A: $tType] : ( ( A > nat ) > ( list @ A ) > nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_List_Osplice,type,
% 2.49/1.47 splice:
% 2.49/1.47 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Nat_OSuc,type,
% 2.49/1.47 suc: nat > nat ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Nat_Osize__class_Osize,type,
% 2.49/1.47 size_size:
% 2.49/1.47 !>[A: $tType] : ( A > nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Num_Oinc,type,
% 2.49/1.47 inc: num > num ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Num_Onat__of__num,type,
% 2.49/1.47 nat_of_num: num > nat ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc,type,
% 2.49/1.47 neg_numeral_dbl_inc:
% 2.49/1.47 !>[A: $tType] : ( A > A ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Num_Onum_OBit0,type,
% 2.49/1.47 bit0: num > num ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Num_Onum_OBit1,type,
% 2.49/1.47 bit1: num > num ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Num_Onum_OOne,type,
% 2.49/1.47 one2: num ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Num_Onum_Osize__num,type,
% 2.49/1.47 size_num: num > nat ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Num_Onumeral__class_Onumeral,type,
% 2.49/1.47 numeral_numeral:
% 2.49/1.47 !>[A: $tType] : ( num > A ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Option_Ooption_ONone,type,
% 2.49/1.47 none:
% 2.49/1.47 !>[A: $tType] : ( option @ A ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Option_Ooption_OSome,type,
% 2.49/1.47 some:
% 2.49/1.47 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Option_Ooption_Ocase__option,type,
% 2.49/1.47 case_option:
% 2.49/1.47 !>[B: $tType,A: $tType] : ( B > ( A > B ) > ( option @ A ) > B ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Option_Ooption_Osize__option,type,
% 2.49/1.47 size_option:
% 2.49/1.47 !>[A: $tType] : ( ( A > nat ) > ( option @ A ) > nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Option_Ooption_Othe,type,
% 2.49/1.47 the:
% 2.49/1.47 !>[A: $tType] : ( ( option @ A ) > A ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Product__Type_OUnity,type,
% 2.49/1.47 product_Unity: product_unit ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Product__Type_Oold_Obool_Orec__bool,type,
% 2.49/1.47 product_rec_bool:
% 2.49/1.47 !>[T: $tType] : ( T > T > $o > T ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Product__Type_Oold_Ounit_Orec__unit,type,
% 2.49/1.47 product_rec_unit:
% 2.49/1.47 !>[T: $tType] : ( T > product_unit > T ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Product__Type_Ounit_Ocase__unit,type,
% 2.49/1.47 product_case_unit:
% 2.49/1.47 !>[A: $tType] : ( A > product_unit > A ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Product__Type_Ounit_Osize__unit,type,
% 2.49/1.47 product_size_unit: product_unit > nat ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Pure_Otype,type,
% 2.49/1.47 type2:
% 2.49/1.47 !>[A: $tType] : ( itself @ A ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Record_Otuple__isomorphism_OTuple__Isomorphism,type,
% 2.49/1.47 tuple_742722141rphism:
% 2.49/1.47 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( product_prod @ B @ C ) ) > ( ( product_prod @ B @ C ) > A ) > ( tuple_isomorphism @ A @ B @ C ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Record_Otuple__isomorphism_Osize__tuple__isomorphism,type,
% 2.49/1.47 tuple_1907371454rphism:
% 2.49/1.47 !>[A: $tType,B: $tType,C: $tType] : ( ( A > nat ) > ( B > nat ) > ( C > nat ) > ( tuple_isomorphism @ A @ B @ C ) > nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Rings_Odivide__class_Odivide,type,
% 2.49/1.47 divide_divide:
% 2.49/1.47 !>[A: $tType] : ( A > A > A ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Set_OCollect,type,
% 2.49/1.47 collect:
% 2.49/1.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Sum__Type_OInl,type,
% 2.49/1.47 sum_Inl:
% 2.49/1.47 !>[A: $tType,B: $tType] : ( A > ( sum_sum @ A @ B ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Sum__Type_OInr,type,
% 2.49/1.47 sum_Inr:
% 2.49/1.47 !>[B: $tType,A: $tType] : ( B > ( sum_sum @ A @ B ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Transitive__Closure_Ontrancl,type,
% 2.49/1.47 transitive_ntrancl:
% 2.49/1.47 !>[A: $tType] : ( nat > ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Typerep_Otyperep_OTyperep,type,
% 2.49/1.47 typerep3: literal > ( list @ typerep ) > typerep ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_Typerep_Otyperep_Osize__typerep,type,
% 2.49/1.47 size_typerep: typerep > nat ).
% 2.49/1.47
% 2.49/1.47 thf(sy_c_member,type,
% 2.49/1.47 member:
% 2.49/1.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(sy_v_a,type,
% 2.49/1.47 a: simpl_ref ).
% 2.49/1.47
% 2.49/1.47 thf(sy_v_lt,type,
% 2.49/1.47 lt: binDag_Mirabelle_dag ).
% 2.49/1.47
% 2.49/1.47 thf(sy_v_rt,type,
% 2.49/1.47 rt: binDag_Mirabelle_dag ).
% 2.49/1.47
% 2.49/1.47 thf(fact_0_dag_Oinject,axiom,
% 2.49/1.47 ! [X21: binDag_Mirabelle_dag,X22: simpl_ref,X23: binDag_Mirabelle_dag,Y21: binDag_Mirabelle_dag,Y22: simpl_ref,Y23: binDag_Mirabelle_dag] :
% 2.49/1.47 ( ( ( binDag476092410e_Node @ X21 @ X22 @ X23 )
% 2.49/1.47 = ( binDag476092410e_Node @ Y21 @ Y22 @ Y23 ) )
% 2.49/1.47 = ( ( X21 = Y21 )
% 2.49/1.47 & ( X22 = Y22 )
% 2.49/1.47 & ( X23 = Y23 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_1_dag_Odistinct_I1_J,axiom,
% 2.49/1.47 ! [X21: binDag_Mirabelle_dag,X22: simpl_ref,X23: binDag_Mirabelle_dag] :
% 2.49/1.47 ( binDag_Mirabelle_Tip
% 2.49/1.47 != ( binDag476092410e_Node @ X21 @ X22 @ X23 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_2_dag_Oinduct,axiom,
% 2.49/1.47 ! [P: binDag_Mirabelle_dag > $o,Dag: binDag_Mirabelle_dag] :
% 2.49/1.47 ( ( P @ binDag_Mirabelle_Tip )
% 2.49/1.47 => ( ! [X1: binDag_Mirabelle_dag,X2: simpl_ref,X3: binDag_Mirabelle_dag] :
% 2.49/1.47 ( ( P @ X1 )
% 2.49/1.47 => ( ( P @ X3 )
% 2.49/1.47 => ( P @ ( binDag476092410e_Node @ X1 @ X2 @ X3 ) ) ) )
% 2.49/1.47 => ( P @ Dag ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_3_dag_Oexhaust,axiom,
% 2.49/1.47 ! [Y: binDag_Mirabelle_dag] :
% 2.49/1.47 ( ( Y != binDag_Mirabelle_Tip )
% 2.49/1.47 => ~ ! [X212: binDag_Mirabelle_dag,X222: simpl_ref,X232: binDag_Mirabelle_dag] :
% 2.49/1.47 ( Y
% 2.49/1.47 != ( binDag476092410e_Node @ X212 @ X222 @ X232 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_4_dag_Osimps_I7_J,axiom,
% 2.49/1.47 ! [A: $tType,F1: A,F2: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A > A > A,X21: binDag_Mirabelle_dag,X22: simpl_ref,X23: binDag_Mirabelle_dag] :
% 2.49/1.47 ( ( binDag1442713106ec_dag @ A @ F1 @ F2 @ ( binDag476092410e_Node @ X21 @ X22 @ X23 ) )
% 2.49/1.47 = ( F2 @ X21 @ X22 @ X23 @ ( binDag1442713106ec_dag @ A @ F1 @ F2 @ X21 ) @ ( binDag1442713106ec_dag @ A @ F1 @ F2 @ X23 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_5_dag_Osimps_I5_J,axiom,
% 2.49/1.47 ! [A: $tType,F1: A,F2: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A,X21: binDag_Mirabelle_dag,X22: simpl_ref,X23: binDag_Mirabelle_dag] :
% 2.49/1.47 ( ( binDag1297733282se_dag @ A @ F1 @ F2 @ ( binDag476092410e_Node @ X21 @ X22 @ X23 ) )
% 2.49/1.47 = ( F2 @ X21 @ X22 @ X23 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_6_dag_Osimps_I6_J,axiom,
% 2.49/1.47 ! [A: $tType,F1: A,F2: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A > A > A] :
% 2.49/1.47 ( ( binDag1442713106ec_dag @ A @ F1 @ F2 @ binDag_Mirabelle_Tip )
% 2.49/1.47 = F1 ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_7_dag_Osimps_I4_J,axiom,
% 2.49/1.47 ! [A: $tType,F1: A,F2: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A] :
% 2.49/1.47 ( ( binDag1297733282se_dag @ A @ F1 @ F2 @ binDag_Mirabelle_Tip )
% 2.49/1.47 = F1 ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_8_dag_Osize__gen_I1_J,axiom,
% 2.49/1.47 ( ( binDag1924123185ze_dag @ binDag_Mirabelle_Tip )
% 2.49/1.47 = ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_9_dag_Osize_I3_J,axiom,
% 2.49/1.47 ( ( size_size @ binDag_Mirabelle_dag @ binDag_Mirabelle_Tip )
% 2.49/1.47 = ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_10_dag_Ocase__distrib,axiom,
% 2.49/1.47 ! [B: $tType,A: $tType,H: A > B,F1: A,F2: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A,Dag: binDag_Mirabelle_dag] :
% 2.49/1.47 ( ( H @ ( binDag1297733282se_dag @ A @ F1 @ F2 @ Dag ) )
% 2.49/1.47 = ( binDag1297733282se_dag @ B @ ( H @ F1 )
% 2.49/1.47 @ ^ [X12: binDag_Mirabelle_dag,X24: simpl_ref,X32: binDag_Mirabelle_dag] : ( H @ ( F2 @ X12 @ X24 @ X32 ) )
% 2.49/1.47 @ Dag ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_11_fun__cong__unused__0,axiom,
% 2.49/1.47 ! [A: $tType,B: $tType,C: $tType] :
% 2.49/1.47 ( ( zero @ B @ ( type2 @ B ) )
% 2.49/1.47 => ! [F: ( A > B ) > C,G: C] :
% 2.49/1.47 ( ( F
% 2.49/1.47 = ( ^ [X: A > B] : G ) )
% 2.49/1.47 => ( ( F
% 2.49/1.47 @ ^ [X: A] : ( zero_zero @ B ) )
% 2.49/1.47 = G ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_12_size__ne__size__imp__ne,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( size @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [X4: A,Y: A] :
% 2.49/1.47 ( ( ( size_size @ A @ X4 )
% 2.49/1.47 != ( size_size @ A @ Y ) )
% 2.49/1.47 => ( X4 != Y ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_13_zero__natural_Orsp,axiom,
% 2.49/1.47 ( ( zero_zero @ nat )
% 2.49/1.47 = ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_14_zero__reorient,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( zero @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [X4: A] :
% 2.49/1.47 ( ( ( zero_zero @ A )
% 2.49/1.47 = X4 )
% 2.49/1.47 = ( X4
% 2.49/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_15_bool_Osize_I1_J,axiom,
% 2.49/1.47 ( ( size_bool @ $true )
% 2.49/1.47 = ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_16_bool_Osize_I2_J,axiom,
% 2.49/1.47 ( ( size_bool @ $false )
% 2.49/1.47 = ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_17_dag_Osize__gen_I2_J,axiom,
% 2.49/1.47 ! [X21: binDag_Mirabelle_dag,X22: simpl_ref,X23: binDag_Mirabelle_dag] :
% 2.49/1.47 ( ( binDag1924123185ze_dag @ ( binDag476092410e_Node @ X21 @ X22 @ X23 ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( plus_plus @ nat @ ( binDag1924123185ze_dag @ X21 ) @ ( binDag1924123185ze_dag @ X23 ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_18_dag_Osize_I4_J,axiom,
% 2.49/1.47 ! [X21: binDag_Mirabelle_dag,X22: simpl_ref,X23: binDag_Mirabelle_dag] :
% 2.49/1.47 ( ( size_size @ binDag_Mirabelle_dag @ ( binDag476092410e_Node @ X21 @ X22 @ X23 ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ binDag_Mirabelle_dag @ X21 ) @ ( size_size @ binDag_Mirabelle_dag @ X23 ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_19_ntrancl__Zero,axiom,
% 2.49/1.47 ! [A: $tType,R: set @ ( product_prod @ A @ A )] :
% 2.49/1.47 ( ( transitive_ntrancl @ A @ ( zero_zero @ nat ) @ R )
% 2.49/1.47 = R ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_20_add__left__cancel,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A,B2: A,C2: A] :
% 2.49/1.47 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.49/1.47 = ( plus_plus @ A @ A2 @ C2 ) )
% 2.49/1.47 = ( B2 = C2 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_21_add__right__cancel,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [B2: A,A2: A,C2: A] :
% 2.49/1.47 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.49/1.47 = ( plus_plus @ A @ C2 @ A2 ) )
% 2.49/1.47 = ( B2 = C2 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_22_natural_Osize_I3_J,axiom,
% 2.49/1.47 ( ( size_size @ code_natural @ ( zero_zero @ code_natural ) )
% 2.49/1.47 = ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_23_bool_Osize_I4_J,axiom,
% 2.49/1.47 ( ( size_size @ $o @ $false )
% 2.49/1.47 = ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_24_bool_Osize_I3_J,axiom,
% 2.49/1.47 ( ( size_size @ $o @ $true )
% 2.49/1.47 = ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_25_nat_Oinject,axiom,
% 2.49/1.47 ! [X25: nat,Y2: nat] :
% 2.49/1.47 ( ( ( suc @ X25 )
% 2.49/1.47 = ( suc @ Y2 ) )
% 2.49/1.47 = ( X25 = Y2 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_26_old_Onat_Oinject,axiom,
% 2.49/1.47 ! [Nat: nat,Nat2: nat] :
% 2.49/1.47 ( ( ( suc @ Nat )
% 2.49/1.47 = ( suc @ Nat2 ) )
% 2.49/1.47 = ( Nat = Nat2 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_27_add_Oleft__neutral,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( monoid_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A] :
% 2.49/1.47 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.49/1.47 = A2 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_28_add_Oright__neutral,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( monoid_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A] :
% 2.49/1.47 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 2.49/1.47 = A2 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_29_double__zero,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A] :
% 2.49/1.47 ( ( ( plus_plus @ A @ A2 @ A2 )
% 2.49/1.47 = ( zero_zero @ A ) )
% 2.49/1.47 = ( A2
% 2.49/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_30_double__zero__sym,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A] :
% 2.49/1.47 ( ( ( zero_zero @ A )
% 2.49/1.47 = ( plus_plus @ A @ A2 @ A2 ) )
% 2.49/1.47 = ( A2
% 2.49/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_31_add__cancel__left__left,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [B2: A,A2: A] :
% 2.49/1.47 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.49/1.47 = A2 )
% 2.49/1.47 = ( B2
% 2.49/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_32_add__cancel__left__right,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A,B2: A] :
% 2.49/1.47 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.49/1.47 = A2 )
% 2.49/1.47 = ( B2
% 2.49/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_33_add__cancel__right__left,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A,B2: A] :
% 2.49/1.47 ( ( A2
% 2.49/1.47 = ( plus_plus @ A @ B2 @ A2 ) )
% 2.49/1.47 = ( B2
% 2.49/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_34_add__cancel__right__right,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A,B2: A] :
% 2.49/1.47 ( ( A2
% 2.49/1.47 = ( plus_plus @ A @ A2 @ B2 ) )
% 2.49/1.47 = ( B2
% 2.49/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_35_add__is__0,axiom,
% 2.49/1.47 ! [M: nat,N: nat] :
% 2.49/1.47 ( ( ( plus_plus @ nat @ M @ N )
% 2.49/1.47 = ( zero_zero @ nat ) )
% 2.49/1.47 = ( ( M
% 2.49/1.47 = ( zero_zero @ nat ) )
% 2.49/1.47 & ( N
% 2.49/1.47 = ( zero_zero @ nat ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_36_Nat_Oadd__0__right,axiom,
% 2.49/1.47 ! [M: nat] :
% 2.49/1.47 ( ( plus_plus @ nat @ M @ ( zero_zero @ nat ) )
% 2.49/1.47 = M ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_37_add__Suc__right,axiom,
% 2.49/1.47 ! [M: nat,N: nat] :
% 2.49/1.47 ( ( plus_plus @ nat @ M @ ( suc @ N ) )
% 2.49/1.47 = ( suc @ ( plus_plus @ nat @ M @ N ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_38_one__is__add,axiom,
% 2.49/1.47 ! [M: nat,N: nat] :
% 2.49/1.47 ( ( ( suc @ ( zero_zero @ nat ) )
% 2.49/1.47 = ( plus_plus @ nat @ M @ N ) )
% 2.49/1.47 = ( ( ( M
% 2.49/1.47 = ( suc @ ( zero_zero @ nat ) ) )
% 2.49/1.47 & ( N
% 2.49/1.47 = ( zero_zero @ nat ) ) )
% 2.49/1.47 | ( ( M
% 2.49/1.47 = ( zero_zero @ nat ) )
% 2.49/1.47 & ( N
% 2.49/1.47 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_39_add__is__1,axiom,
% 2.49/1.47 ! [M: nat,N: nat] :
% 2.49/1.47 ( ( ( plus_plus @ nat @ M @ N )
% 2.49/1.47 = ( suc @ ( zero_zero @ nat ) ) )
% 2.49/1.47 = ( ( ( M
% 2.49/1.47 = ( suc @ ( zero_zero @ nat ) ) )
% 2.49/1.47 & ( N
% 2.49/1.47 = ( zero_zero @ nat ) ) )
% 2.49/1.47 | ( ( M
% 2.49/1.47 = ( zero_zero @ nat ) )
% 2.49/1.47 & ( N
% 2.49/1.47 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_40_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A,B2: A,C2: A] :
% 2.49/1.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 2.49/1.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_41_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [I: A,J: A,K: A,L: A] :
% 2.49/1.47 ( ( ( I = J )
% 2.49/1.47 & ( K = L ) )
% 2.49/1.47 => ( ( plus_plus @ A @ I @ K )
% 2.49/1.47 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_42_mem__Collect__eq,axiom,
% 2.49/1.47 ! [A: $tType,A2: A,P: A > $o] :
% 2.49/1.47 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.49/1.47 = ( P @ A2 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_43_Collect__mem__eq,axiom,
% 2.49/1.47 ! [A: $tType,A3: set @ A] :
% 2.49/1.47 ( ( collect @ A
% 2.49/1.47 @ ^ [X: A] : ( member @ A @ X @ A3 ) )
% 2.49/1.47 = A3 ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_44_Collect__cong,axiom,
% 2.49/1.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.49/1.47 ( ! [X5: A] :
% 2.49/1.47 ( ( P @ X5 )
% 2.49/1.47 = ( Q @ X5 ) )
% 2.49/1.47 => ( ( collect @ A @ P )
% 2.49/1.47 = ( collect @ A @ Q ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_45_ext,axiom,
% 2.49/1.47 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.49/1.47 ( ! [X5: A] :
% 2.49/1.47 ( ( F @ X5 )
% 2.49/1.47 = ( G @ X5 ) )
% 2.49/1.47 => ( F = G ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_46_Suc__inject,axiom,
% 2.49/1.47 ! [X4: nat,Y: nat] :
% 2.49/1.47 ( ( ( suc @ X4 )
% 2.49/1.47 = ( suc @ Y ) )
% 2.49/1.47 => ( X4 = Y ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_47_n__not__Suc__n,axiom,
% 2.49/1.47 ! [N: nat] :
% 2.49/1.47 ( N
% 2.49/1.47 != ( suc @ N ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_48_add__Suc__shift,axiom,
% 2.49/1.47 ! [M: nat,N: nat] :
% 2.49/1.47 ( ( plus_plus @ nat @ ( suc @ M ) @ N )
% 2.49/1.47 = ( plus_plus @ nat @ M @ ( suc @ N ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_49_add__Suc,axiom,
% 2.49/1.47 ! [M: nat,N: nat] :
% 2.49/1.47 ( ( plus_plus @ nat @ ( suc @ M ) @ N )
% 2.49/1.47 = ( suc @ ( plus_plus @ nat @ M @ N ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_50_nat__add__left__cancel,axiom,
% 2.49/1.47 ! [K: nat,M: nat,N: nat] :
% 2.49/1.47 ( ( ( plus_plus @ nat @ K @ M )
% 2.49/1.47 = ( plus_plus @ nat @ K @ N ) )
% 2.49/1.47 = ( M = N ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_51_nat__add__right__cancel,axiom,
% 2.49/1.47 ! [M: nat,K: nat,N: nat] :
% 2.49/1.47 ( ( ( plus_plus @ nat @ M @ K )
% 2.49/1.47 = ( plus_plus @ nat @ N @ K ) )
% 2.49/1.47 = ( M = N ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_52_add_Oassoc,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( semigroup_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A,B2: A,C2: A] :
% 2.49/1.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 2.49/1.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_53_add_Oleft__cancel,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( group_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A,B2: A,C2: A] :
% 2.49/1.47 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.49/1.47 = ( plus_plus @ A @ A2 @ C2 ) )
% 2.49/1.47 = ( B2 = C2 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_54_add_Oright__cancel,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( group_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [B2: A,A2: A,C2: A] :
% 2.49/1.47 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.49/1.47 = ( plus_plus @ A @ C2 @ A2 ) )
% 2.49/1.47 = ( B2 = C2 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_55_add_Ocommute,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ( ( plus_plus @ A )
% 2.49/1.47 = ( ^ [A4: A,B3: A] : ( plus_plus @ A @ B3 @ A4 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_56_add_Oleft__commute,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [B2: A,A2: A,C2: A] :
% 2.49/1.47 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) )
% 2.49/1.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_57_add__left__imp__eq,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A,B2: A,C2: A] :
% 2.49/1.47 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.49/1.47 = ( plus_plus @ A @ A2 @ C2 ) )
% 2.49/1.47 => ( B2 = C2 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_58_add__right__imp__eq,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [B2: A,A2: A,C2: A] :
% 2.49/1.47 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.49/1.47 = ( plus_plus @ A @ C2 @ A2 ) )
% 2.49/1.47 => ( B2 = C2 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_59_comm__monoid__add__class_Oadd__0,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( comm_monoid_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A] :
% 2.49/1.47 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.49/1.47 = A2 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_60_add_Ocomm__neutral,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( comm_monoid_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A] :
% 2.49/1.47 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 2.49/1.47 = A2 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_61_add_Ogroup__left__neutral,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( group_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A] :
% 2.49/1.47 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.49/1.47 = A2 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_62_add__eq__0__iff__both__eq__0,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [X4: A,Y: A] :
% 2.49/1.47 ( ( ( plus_plus @ A @ X4 @ Y )
% 2.49/1.47 = ( zero_zero @ A ) )
% 2.49/1.47 = ( ( X4
% 2.49/1.47 = ( zero_zero @ A ) )
% 2.49/1.47 & ( Y
% 2.49/1.47 = ( zero_zero @ A ) ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_63_nat_Odistinct_I1_J,axiom,
% 2.49/1.47 ! [X25: nat] :
% 2.49/1.47 ( ( zero_zero @ nat )
% 2.49/1.47 != ( suc @ X25 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_64_old_Onat_Odistinct_I2_J,axiom,
% 2.49/1.47 ! [Nat3: nat] :
% 2.49/1.47 ( ( suc @ Nat3 )
% 2.49/1.47 != ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_65_old_Onat_Odistinct_I1_J,axiom,
% 2.49/1.47 ! [Nat2: nat] :
% 2.49/1.47 ( ( zero_zero @ nat )
% 2.49/1.47 != ( suc @ Nat2 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_66_nat_OdiscI,axiom,
% 2.49/1.47 ! [Nat: nat,X25: nat] :
% 2.49/1.47 ( ( Nat
% 2.49/1.47 = ( suc @ X25 ) )
% 2.49/1.47 => ( Nat
% 2.49/1.47 != ( zero_zero @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_67_nat__induct,axiom,
% 2.49/1.47 ! [P: nat > $o,N: nat] :
% 2.49/1.47 ( ( P @ ( zero_zero @ nat ) )
% 2.49/1.47 => ( ! [N2: nat] :
% 2.49/1.47 ( ( P @ N2 )
% 2.49/1.47 => ( P @ ( suc @ N2 ) ) )
% 2.49/1.47 => ( P @ N ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_68_diff__induct,axiom,
% 2.49/1.47 ! [P: nat > nat > $o,M: nat,N: nat] :
% 2.49/1.47 ( ! [X5: nat] : ( P @ X5 @ ( zero_zero @ nat ) )
% 2.49/1.47 => ( ! [Y3: nat] : ( P @ ( zero_zero @ nat ) @ ( suc @ Y3 ) )
% 2.49/1.47 => ( ! [X5: nat,Y3: nat] :
% 2.49/1.47 ( ( P @ X5 @ Y3 )
% 2.49/1.47 => ( P @ ( suc @ X5 ) @ ( suc @ Y3 ) ) )
% 2.49/1.47 => ( P @ M @ N ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_69_zero__induct,axiom,
% 2.49/1.47 ! [P: nat > $o,K: nat] :
% 2.49/1.47 ( ( P @ K )
% 2.49/1.47 => ( ! [N2: nat] :
% 2.49/1.47 ( ( P @ ( suc @ N2 ) )
% 2.49/1.47 => ( P @ N2 ) )
% 2.49/1.47 => ( P @ ( zero_zero @ nat ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_70_Suc__neq__Zero,axiom,
% 2.49/1.47 ! [M: nat] :
% 2.49/1.47 ( ( suc @ M )
% 2.49/1.47 != ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_71_Zero__neq__Suc,axiom,
% 2.49/1.47 ! [M: nat] :
% 2.49/1.47 ( ( zero_zero @ nat )
% 2.49/1.47 != ( suc @ M ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_72_Zero__not__Suc,axiom,
% 2.49/1.47 ! [M: nat] :
% 2.49/1.47 ( ( zero_zero @ nat )
% 2.49/1.47 != ( suc @ M ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_73_old_Onat_Oexhaust,axiom,
% 2.49/1.47 ! [Y: nat] :
% 2.49/1.47 ( ( Y
% 2.49/1.47 != ( zero_zero @ nat ) )
% 2.49/1.47 => ~ ! [Nat4: nat] :
% 2.49/1.47 ( Y
% 2.49/1.47 != ( suc @ Nat4 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_74_old_Onat_Oinducts,axiom,
% 2.49/1.47 ! [P: nat > $o,Nat: nat] :
% 2.49/1.47 ( ( P @ ( zero_zero @ nat ) )
% 2.49/1.47 => ( ! [Nat4: nat] :
% 2.49/1.47 ( ( P @ Nat4 )
% 2.49/1.47 => ( P @ ( suc @ Nat4 ) ) )
% 2.49/1.47 => ( P @ Nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_75_not0__implies__Suc,axiom,
% 2.49/1.47 ! [N: nat] :
% 2.49/1.47 ( ( N
% 2.49/1.47 != ( zero_zero @ nat ) )
% 2.49/1.47 => ? [M2: nat] :
% 2.49/1.47 ( N
% 2.49/1.47 = ( suc @ M2 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_76_plus__nat_Oadd__0,axiom,
% 2.49/1.47 ! [N: nat] :
% 2.49/1.47 ( ( plus_plus @ nat @ ( zero_zero @ nat ) @ N )
% 2.49/1.47 = N ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_77_add__eq__self__zero,axiom,
% 2.49/1.47 ! [M: nat,N: nat] :
% 2.49/1.47 ( ( ( plus_plus @ nat @ M @ N )
% 2.49/1.47 = M )
% 2.49/1.47 => ( N
% 2.49/1.47 = ( zero_zero @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_78_size__bool,axiom,
% 2.49/1.47 ( ( size_size @ $o )
% 2.49/1.47 = ( ^ [B3: $o] : ( zero_zero @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_79_sum_Osize__neq,axiom,
% 2.49/1.47 ! [A: $tType,B: $tType,X4: sum_sum @ A @ B] :
% 2.49/1.47 ( ( size_size @ ( sum_sum @ A @ B ) @ X4 )
% 2.49/1.47 != ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_80_prod_Osize__neq,axiom,
% 2.49/1.47 ! [A: $tType,B: $tType,X4: product_prod @ A @ B] :
% 2.49/1.47 ( ( size_size @ ( product_prod @ A @ B ) @ X4 )
% 2.49/1.47 != ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_81_size__bool__def,axiom,
% 2.49/1.47 ( size_bool
% 2.49/1.47 = ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_82_dependent__nat__choice,axiom,
% 2.49/1.47 ! [A: $tType,P: nat > A > $o,Q: nat > A > A > $o] :
% 2.49/1.47 ( ? [X13: A] : ( P @ ( zero_zero @ nat ) @ X13 )
% 2.49/1.47 => ( ! [X5: A,N2: nat] :
% 2.49/1.47 ( ( P @ N2 @ X5 )
% 2.49/1.47 => ? [Y4: A] :
% 2.49/1.47 ( ( P @ ( suc @ N2 ) @ Y4 )
% 2.49/1.47 & ( Q @ N2 @ X5 @ Y4 ) ) )
% 2.49/1.47 => ? [F3: nat > A] :
% 2.49/1.47 ! [N3: nat] :
% 2.49/1.47 ( ( P @ N3 @ ( F3 @ N3 ) )
% 2.49/1.47 & ( Q @ N3 @ ( F3 @ N3 ) @ ( F3 @ ( suc @ N3 ) ) ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_83_size__natural__overloaded__def,axiom,
% 2.49/1.47 ( ( size_size @ code_natural )
% 2.49/1.47 = ( code_rec_natural @ nat @ ( zero_zero @ nat )
% 2.49/1.47 @ ^ [X: code_natural,Y5: nat] : ( plus_plus @ nat @ Y5 @ ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_84_semiring__normalization__rules_I6_J,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A] :
% 2.49/1.47 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 2.49/1.47 = A2 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_85_semiring__normalization__rules_I5_J,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A] :
% 2.49/1.47 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.49/1.47 = A2 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_86_add__0__iff,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( semiri456707255roduct @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [B2: A,A2: A] :
% 2.49/1.47 ( ( B2
% 2.49/1.47 = ( plus_plus @ A @ B2 @ A2 ) )
% 2.49/1.47 = ( A2
% 2.49/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_87_natural_Osize_I1_J,axiom,
% 2.49/1.47 ( ( code_size_natural @ ( zero_zero @ code_natural ) )
% 2.49/1.47 = ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_88_natural_Osize_I4_J,axiom,
% 2.49/1.47 ! [Natural: code_natural] :
% 2.49/1.47 ( ( size_size @ code_natural @ ( code_Suc @ Natural ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( size_size @ code_natural @ Natural ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_89_size__natural__def,axiom,
% 2.49/1.47 ( code_size_natural
% 2.49/1.47 = ( code_rec_natural @ nat @ ( zero_zero @ nat )
% 2.49/1.47 @ ^ [X: code_natural,Y5: nat] : ( plus_plus @ nat @ Y5 @ ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_90_option_Osize__neq,axiom,
% 2.49/1.47 ! [A: $tType,X4: option @ A] :
% 2.49/1.47 ( ( size_size @ ( option @ A ) @ X4 )
% 2.49/1.47 != ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_91_natural_Oinject,axiom,
% 2.49/1.47 ! [Natural: code_natural,Natural2: code_natural] :
% 2.49/1.47 ( ( ( code_Suc @ Natural )
% 2.49/1.47 = ( code_Suc @ Natural2 ) )
% 2.49/1.47 = ( Natural = Natural2 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_92_natural_Osimps_I6_J,axiom,
% 2.49/1.47 ! [T: $tType,F1: T,F2: code_natural > T > T] :
% 2.49/1.47 ( ( code_rec_natural @ T @ F1 @ F2 @ ( zero_zero @ code_natural ) )
% 2.49/1.47 = F1 ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_93_natural_Osimps_I7_J,axiom,
% 2.49/1.47 ! [T: $tType,F1: T,F2: code_natural > T > T,Natural: code_natural] :
% 2.49/1.47 ( ( code_rec_natural @ T @ F1 @ F2 @ ( code_Suc @ Natural ) )
% 2.49/1.47 = ( F2 @ Natural @ ( code_rec_natural @ T @ F1 @ F2 @ Natural ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_94_natural_Osize_I2_J,axiom,
% 2.49/1.47 ! [Natural: code_natural] :
% 2.49/1.47 ( ( code_size_natural @ ( code_Suc @ Natural ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( code_size_natural @ Natural ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_95_natural_Oinducts,axiom,
% 2.49/1.47 ! [P: code_natural > $o,Natural: code_natural] :
% 2.49/1.47 ( ( P @ ( zero_zero @ code_natural ) )
% 2.49/1.47 => ( ! [Natural3: code_natural] :
% 2.49/1.47 ( ( P @ Natural3 )
% 2.49/1.47 => ( P @ ( code_Suc @ Natural3 ) ) )
% 2.49/1.47 => ( P @ Natural ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_96_natural_Oexhaust,axiom,
% 2.49/1.47 ! [Y: code_natural] :
% 2.49/1.47 ( ( Y
% 2.49/1.47 != ( zero_zero @ code_natural ) )
% 2.49/1.47 => ~ ! [Natural3: code_natural] :
% 2.49/1.47 ( Y
% 2.49/1.47 != ( code_Suc @ Natural3 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_97_natural_Odistinct_I1_J,axiom,
% 2.49/1.47 ! [Natural2: code_natural] :
% 2.49/1.47 ( ( zero_zero @ code_natural )
% 2.49/1.47 != ( code_Suc @ Natural2 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_98_natural_Odistinct_I2_J,axiom,
% 2.49/1.47 ! [Natural4: code_natural] :
% 2.49/1.47 ( ( code_Suc @ Natural4 )
% 2.49/1.47 != ( zero_zero @ code_natural ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_99_size__bool__overloaded__def,axiom,
% 2.49/1.47 ( ( size_size @ $o )
% 2.49/1.47 = ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_100_semiring__normalization__rules_I20_J,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A,B2: A,C2: A,D: A] :
% 2.49/1.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( plus_plus @ A @ C2 @ D ) )
% 2.49/1.47 = ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_101_semiring__normalization__rules_I21_J,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A,B2: A,C2: A] :
% 2.49/1.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 2.49/1.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_102_semiring__normalization__rules_I22_J,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A,C2: A,D: A] :
% 2.49/1.47 ( ( plus_plus @ A @ A2 @ ( plus_plus @ A @ C2 @ D ) )
% 2.49/1.47 = ( plus_plus @ A @ C2 @ ( plus_plus @ A @ A2 @ D ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_103_semiring__normalization__rules_I23_J,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A,B2: A,C2: A] :
% 2.49/1.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 2.49/1.47 = ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C2 ) @ B2 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_104_semiring__normalization__rules_I24_J,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.49/1.47 => ( ( plus_plus @ A )
% 2.49/1.47 = ( ^ [A4: A,C3: A] : ( plus_plus @ A @ C3 @ A4 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_105_semiring__normalization__rules_I25_J,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A,C2: A,D: A] :
% 2.49/1.47 ( ( plus_plus @ A @ A2 @ ( plus_plus @ A @ C2 @ D ) )
% 2.49/1.47 = ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C2 ) @ D ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_106_old_Obool_Osimps_I5_J,axiom,
% 2.49/1.47 ! [T: $tType,F1: T,F2: T] :
% 2.49/1.47 ( ( product_rec_bool @ T @ F1 @ F2 @ $true )
% 2.49/1.47 = F1 ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_107_old_Obool_Osimps_I6_J,axiom,
% 2.49/1.47 ! [T: $tType,F1: T,F2: T] :
% 2.49/1.47 ( ( product_rec_bool @ T @ F1 @ F2 @ $false )
% 2.49/1.47 = F2 ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_108_natural_Osimps_I5_J,axiom,
% 2.49/1.47 ! [T: $tType,F1: T,F2: code_natural > T,Natural: code_natural] :
% 2.49/1.47 ( ( code_case_natural @ T @ F1 @ F2 @ ( code_Suc @ Natural ) )
% 2.49/1.47 = ( F2 @ Natural ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_109_random__aux__set_Oinduct,axiom,
% 2.49/1.47 ! [B: $tType] :
% 2.49/1.47 ( ( quickcheck_random @ B @ ( type2 @ B ) )
% 2.49/1.47 => ! [P: code_natural > code_natural > $o,A0: code_natural,A1: code_natural] :
% 2.49/1.47 ( ! [X1: code_natural] : ( P @ ( zero_zero @ code_natural ) @ X1 )
% 2.49/1.47 => ( ! [I2: code_natural,J2: code_natural] :
% 2.49/1.47 ( ! [X6: product_prod @ B @ ( product_unit > code_term )] : ( P @ I2 @ J2 )
% 2.49/1.47 => ( P @ ( code_Suc @ I2 ) @ J2 ) )
% 2.49/1.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_110_random__aux__rec,axiom,
% 2.49/1.47 ! [A: $tType,Random_aux: code_natural > A,Rhs: code_natural > A,K: code_natural] :
% 2.49/1.47 ( ( ( Random_aux @ ( zero_zero @ code_natural ) )
% 2.49/1.47 = ( Rhs @ ( zero_zero @ code_natural ) ) )
% 2.49/1.47 => ( ! [K2: code_natural] :
% 2.49/1.47 ( ( Random_aux @ ( code_Suc @ K2 ) )
% 2.49/1.47 = ( Rhs @ ( code_Suc @ K2 ) ) )
% 2.49/1.47 => ( ( Random_aux @ K )
% 2.49/1.47 = ( Rhs @ K ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_111_natural_Osimps_I4_J,axiom,
% 2.49/1.47 ! [T: $tType,F1: T,F2: code_natural > T] :
% 2.49/1.47 ( ( code_case_natural @ T @ F1 @ F2 @ ( zero_zero @ code_natural ) )
% 2.49/1.47 = F1 ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_112_case__natural__def,axiom,
% 2.49/1.47 ! [T: $tType] :
% 2.49/1.47 ( ( code_case_natural @ T )
% 2.49/1.47 = ( ^ [F12: T,F22: code_natural > T] :
% 2.49/1.47 ( code_rec_natural @ T @ F12
% 2.49/1.47 @ ^ [X12: code_natural,X24: T] : ( F22 @ X12 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_113_option_Osize_I3_J,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( size_size @ ( option @ A ) @ ( none @ A ) )
% 2.49/1.47 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_114_option_Osize_I4_J,axiom,
% 2.49/1.47 ! [A: $tType,X25: A] :
% 2.49/1.47 ( ( size_size @ ( option @ A ) @ ( some @ A @ X25 ) )
% 2.49/1.47 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_115_sum_Osize_I3_J,axiom,
% 2.49/1.47 ! [A: $tType,B: $tType,X14: A] :
% 2.49/1.47 ( ( size_size @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B @ X14 ) )
% 2.49/1.47 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_116_sum_Osize_I4_J,axiom,
% 2.49/1.47 ! [B: $tType,A: $tType,X25: B] :
% 2.49/1.47 ( ( size_size @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A @ X25 ) )
% 2.49/1.47 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_117_typerep_Osize__neq,axiom,
% 2.49/1.47 ! [X4: typerep] :
% 2.49/1.47 ( ( size_size @ typerep @ X4 )
% 2.49/1.47 != ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_118_option_Oinject,axiom,
% 2.49/1.47 ! [A: $tType,X25: A,Y2: A] :
% 2.49/1.47 ( ( ( some @ A @ X25 )
% 2.49/1.47 = ( some @ A @ Y2 ) )
% 2.49/1.47 = ( X25 = Y2 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_119_not__None__eq,axiom,
% 2.49/1.47 ! [A: $tType,X4: option @ A] :
% 2.49/1.47 ( ( X4
% 2.49/1.47 != ( none @ A ) )
% 2.49/1.47 = ( ? [Y5: A] :
% 2.49/1.47 ( X4
% 2.49/1.47 = ( some @ A @ Y5 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_120_not__Some__eq,axiom,
% 2.49/1.47 ! [A: $tType,X4: option @ A] :
% 2.49/1.47 ( ( ! [Y5: A] :
% 2.49/1.47 ( X4
% 2.49/1.47 != ( some @ A @ Y5 ) ) )
% 2.49/1.47 = ( X4
% 2.49/1.47 = ( none @ A ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_121_Inl__Inr__False,axiom,
% 2.49/1.47 ! [A: $tType,B: $tType,X4: A,Y: B] :
% 2.49/1.47 ( ( sum_Inl @ A @ B @ X4 )
% 2.49/1.47 != ( sum_Inr @ B @ A @ Y ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_122_Inr__Inl__False,axiom,
% 2.49/1.47 ! [B: $tType,A: $tType,X4: B,Y: A] :
% 2.49/1.47 ( ( sum_Inr @ B @ A @ X4 )
% 2.49/1.47 != ( sum_Inl @ A @ B @ Y ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_123_obj__sumE__f,axiom,
% 2.49/1.47 ! [A: $tType,C: $tType,B: $tType,S: B,F: ( sum_sum @ A @ C ) > B,P: $o] :
% 2.49/1.47 ( ! [X5: A] :
% 2.49/1.47 ( ( S
% 2.49/1.47 = ( F @ ( sum_Inl @ A @ C @ X5 ) ) )
% 2.49/1.47 => P )
% 2.49/1.47 => ( ! [X5: C] :
% 2.49/1.47 ( ( S
% 2.49/1.47 = ( F @ ( sum_Inr @ C @ A @ X5 ) ) )
% 2.49/1.47 => P )
% 2.49/1.47 => ! [X6: sum_sum @ A @ C] :
% 2.49/1.47 ( ( S
% 2.49/1.47 = ( F @ X6 ) )
% 2.49/1.47 => P ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_124_option_Odistinct_I1_J,axiom,
% 2.49/1.47 ! [A: $tType,X25: A] :
% 2.49/1.47 ( ( none @ A )
% 2.49/1.47 != ( some @ A @ X25 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_125_option_OdiscI,axiom,
% 2.49/1.47 ! [A: $tType,Option: option @ A,X25: A] :
% 2.49/1.47 ( ( Option
% 2.49/1.47 = ( some @ A @ X25 ) )
% 2.49/1.47 => ( Option
% 2.49/1.47 != ( none @ A ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_126_option_Oexhaust,axiom,
% 2.49/1.47 ! [A: $tType,Y: option @ A] :
% 2.49/1.47 ( ( Y
% 2.49/1.47 != ( none @ A ) )
% 2.49/1.47 => ~ ! [X2: A] :
% 2.49/1.47 ( Y
% 2.49/1.47 != ( some @ A @ X2 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_127_option_Oinducts,axiom,
% 2.49/1.47 ! [A: $tType,P: ( option @ A ) > $o,Option: option @ A] :
% 2.49/1.47 ( ( P @ ( none @ A ) )
% 2.49/1.47 => ( ! [X5: A] : ( P @ ( some @ A @ X5 ) )
% 2.49/1.47 => ( P @ Option ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_128_split__option__ex,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( ^ [P2: ( option @ A ) > $o] :
% 2.49/1.47 ? [X7: option @ A] : ( P2 @ X7 ) )
% 2.49/1.47 = ( ^ [P3: ( option @ A ) > $o] :
% 2.49/1.47 ( ( P3 @ ( none @ A ) )
% 2.49/1.47 | ? [X: A] : ( P3 @ ( some @ A @ X ) ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_129_split__option__all,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( ^ [P2: ( option @ A ) > $o] :
% 2.49/1.47 ! [X7: option @ A] : ( P2 @ X7 ) )
% 2.49/1.47 = ( ^ [P3: ( option @ A ) > $o] :
% 2.49/1.47 ( ( P3 @ ( none @ A ) )
% 2.49/1.47 & ! [X: A] : ( P3 @ ( some @ A @ X ) ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_130_combine__options__cases,axiom,
% 2.49/1.47 ! [A: $tType,B: $tType,X4: option @ A,P: ( option @ A ) > ( option @ B ) > $o,Y: option @ B] :
% 2.49/1.47 ( ( ( X4
% 2.49/1.47 = ( none @ A ) )
% 2.49/1.47 => ( P @ X4 @ Y ) )
% 2.49/1.47 => ( ( ( Y
% 2.49/1.47 = ( none @ B ) )
% 2.49/1.47 => ( P @ X4 @ Y ) )
% 2.49/1.47 => ( ! [A5: A,B4: B] :
% 2.49/1.47 ( ( X4
% 2.49/1.47 = ( some @ A @ A5 ) )
% 2.49/1.47 => ( ( Y
% 2.49/1.47 = ( some @ B @ B4 ) )
% 2.49/1.47 => ( P @ X4 @ Y ) ) )
% 2.49/1.47 => ( P @ X4 @ Y ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_131_sum_Osize__gen_I1_J,axiom,
% 2.49/1.47 ! [B: $tType,A: $tType,Xa: A > nat,X4: B > nat,X14: A] :
% 2.49/1.47 ( ( basic_BNF_size_sum @ A @ B @ Xa @ X4 @ ( sum_Inl @ A @ B @ X14 ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( Xa @ X14 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_132_sum_Osize__gen_I2_J,axiom,
% 2.49/1.47 ! [A: $tType,B: $tType,Xa: A > nat,X4: B > nat,X25: B] :
% 2.49/1.47 ( ( basic_BNF_size_sum @ A @ B @ Xa @ X4 @ ( sum_Inr @ B @ A @ X25 ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( X4 @ X25 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_133_option_Osize__gen_I2_J,axiom,
% 2.49/1.47 ! [A: $tType,X4: A > nat,X25: A] :
% 2.49/1.47 ( ( size_option @ A @ X4 @ ( some @ A @ X25 ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( X4 @ X25 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_134_option_Osize__gen_I1_J,axiom,
% 2.49/1.47 ! [A: $tType,X4: A > nat] :
% 2.49/1.47 ( ( size_option @ A @ X4 @ ( none @ A ) )
% 2.49/1.47 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_135_typerep_Osize_I2_J,axiom,
% 2.49/1.47 ! [X14: literal,X25: list @ typerep] :
% 2.49/1.47 ( ( size_size @ typerep @ ( typerep3 @ X14 @ X25 ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( size_list @ typerep @ ( size_size @ typerep ) @ X25 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_136_tuple__isomorphism_Osize__neq,axiom,
% 2.49/1.47 ! [A: $tType,B: $tType,C: $tType,X4: tuple_isomorphism @ A @ B @ C] :
% 2.49/1.47 ( ( size_size @ ( tuple_isomorphism @ A @ B @ C ) @ X4 )
% 2.49/1.47 != ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_137_size__literal__def,axiom,
% 2.49/1.47 ( ( size_size @ literal )
% 2.49/1.47 = ( ^ [S2: literal] : ( zero_zero @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_138_size__unit__overloaded__def,axiom,
% 2.49/1.47 ( ( size_size @ product_unit )
% 2.49/1.47 = ( product_rec_unit @ nat @ ( zero_zero @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_139_typerep_Osize__gen,axiom,
% 2.49/1.47 ! [X14: literal,X25: list @ typerep] :
% 2.49/1.47 ( ( size_typerep @ ( typerep3 @ X14 @ X25 ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( size_list @ typerep @ size_typerep @ X25 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_140_size__unit__def,axiom,
% 2.49/1.47 ( product_size_unit
% 2.49/1.47 = ( product_rec_unit @ nat @ ( zero_zero @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_141_tuple__isomorphism_Osize_I2_J,axiom,
% 2.49/1.47 ! [B: $tType,C: $tType,A: $tType,X14: A > ( product_prod @ B @ C ),X25: ( product_prod @ B @ C ) > A] :
% 2.49/1.47 ( ( size_size @ ( tuple_isomorphism @ A @ B @ C ) @ ( tuple_742722141rphism @ A @ B @ C @ X14 @ X25 ) )
% 2.49/1.47 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_142_unit_Osize_I2_J,axiom,
% 2.49/1.47 ( ( size_size @ product_unit @ product_Unity )
% 2.49/1.47 = ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_143_unit__abs__eta__conv,axiom,
% 2.49/1.47 ! [A: $tType,F: product_unit > A] :
% 2.49/1.47 ( ( ^ [U: product_unit] : ( F @ product_Unity ) )
% 2.49/1.47 = F ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_144_old_Ounit_Orec,axiom,
% 2.49/1.47 ! [T: $tType,F1: T] :
% 2.49/1.47 ( ( product_rec_unit @ T @ F1 @ product_Unity )
% 2.49/1.47 = F1 ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_145_unit_Osize_I1_J,axiom,
% 2.49/1.47 ( ( product_size_unit @ product_Unity )
% 2.49/1.47 = ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_146_eq__sym__Unity__conv,axiom,
% 2.49/1.47 ! [X4: $o] :
% 2.49/1.47 ( ( X4
% 2.49/1.47 = ( product_Unity = product_Unity ) )
% 2.49/1.47 = X4 ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_147_unit__all__impI,axiom,
% 2.49/1.47 ! [P: product_unit > $o,Q: product_unit > $o] :
% 2.49/1.47 ( ( ( P @ product_Unity )
% 2.49/1.47 => ( Q @ product_Unity ) )
% 2.49/1.47 => ! [X6: product_unit] :
% 2.49/1.47 ( ( P @ X6 )
% 2.49/1.47 => ( Q @ X6 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_148_old_Ounit_Oinducts,axiom,
% 2.49/1.47 ! [P: product_unit > $o,Unit: product_unit] :
% 2.49/1.47 ( ( P @ product_Unity )
% 2.49/1.47 => ( P @ Unit ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_149_old_Ounit_Oexhaust,axiom,
% 2.49/1.47 ! [Y: product_unit] : ( Y = product_Unity ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_150_tuple__isomorphism_Osize__gen,axiom,
% 2.49/1.47 ! [B: $tType,C: $tType,A: $tType,Xb: A > nat,Xa: B > nat,X4: C > nat,X14: A > ( product_prod @ B @ C ),X25: ( product_prod @ B @ C ) > A] :
% 2.49/1.47 ( ( tuple_1907371454rphism @ A @ B @ C @ Xb @ Xa @ X4 @ ( tuple_742722141rphism @ A @ B @ C @ X14 @ X25 ) )
% 2.49/1.47 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_151_default__unit__def,axiom,
% 2.49/1.47 ( ( default_default @ product_unit )
% 2.49/1.47 = product_Unity ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_152_list_Osize__gen_I2_J,axiom,
% 2.49/1.47 ! [A: $tType,X4: A > nat,X21: A,X22: list @ A] :
% 2.49/1.47 ( ( size_list @ A @ X4 @ ( cons @ A @ X21 @ X22 ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( plus_plus @ nat @ ( X4 @ X21 ) @ ( size_list @ A @ X4 @ X22 ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_153_length__Suc__conv,axiom,
% 2.49/1.47 ! [A: $tType,Xs: list @ A,N: nat] :
% 2.49/1.47 ( ( ( size_size @ ( list @ A ) @ Xs )
% 2.49/1.47 = ( suc @ N ) )
% 2.49/1.47 = ( ? [Y5: A,Ys: list @ A] :
% 2.49/1.47 ( ( Xs
% 2.49/1.47 = ( cons @ A @ Y5 @ Ys ) )
% 2.49/1.47 & ( ( size_size @ ( list @ A ) @ Ys )
% 2.49/1.47 = N ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_154_Suc__length__conv,axiom,
% 2.49/1.47 ! [A: $tType,N: nat,Xs: list @ A] :
% 2.49/1.47 ( ( ( suc @ N )
% 2.49/1.47 = ( size_size @ ( list @ A ) @ Xs ) )
% 2.49/1.47 = ( ? [Y5: A,Ys: list @ A] :
% 2.49/1.47 ( ( Xs
% 2.49/1.47 = ( cons @ A @ Y5 @ Ys ) )
% 2.49/1.47 & ( ( size_size @ ( list @ A ) @ Ys )
% 2.49/1.47 = N ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_155_list_Osize_I4_J,axiom,
% 2.49/1.47 ! [A: $tType,X21: A,X22: list @ A] :
% 2.49/1.47 ( ( size_size @ ( list @ A ) @ ( cons @ A @ X21 @ X22 ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( size_size @ ( list @ A ) @ X22 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_156_length__Cons,axiom,
% 2.49/1.47 ! [A: $tType,X4: A,Xs: list @ A] :
% 2.49/1.47 ( ( size_size @ ( list @ A ) @ ( cons @ A @ X4 @ Xs ) )
% 2.49/1.47 = ( suc @ ( size_size @ ( list @ A ) @ Xs ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_157_gen__length__code_I2_J,axiom,
% 2.49/1.47 ! [B: $tType,N: nat,X4: B,Xs: list @ B] :
% 2.49/1.47 ( ( gen_length @ B @ N @ ( cons @ B @ X4 @ Xs ) )
% 2.49/1.47 = ( gen_length @ B @ ( suc @ N ) @ Xs ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_158_linordered__field__class_Osign__simps_I26_J,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A,B2: A,C2: A] :
% 2.49/1.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 2.49/1.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_159_length__code,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( size_size @ ( list @ A ) )
% 2.49/1.47 = ( gen_length @ A @ ( zero_zero @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_160_gen__length__def,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( gen_length @ A )
% 2.49/1.47 = ( ^ [N4: nat,Xs2: list @ A] : ( plus_plus @ nat @ N4 @ ( size_size @ ( list @ A ) @ Xs2 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_161_linordered__field__class_Osign__simps_I28_J,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [B2: A,A2: A,C2: A] :
% 2.49/1.47 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) )
% 2.49/1.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_162_linordered__field__class_Osign__simps_I27_J,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.49/1.47 => ( ( plus_plus @ A )
% 2.49/1.47 = ( ^ [A4: A,B3: A] : ( plus_plus @ A @ B3 @ A4 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_163_length__splice,axiom,
% 2.49/1.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.49/1.47 ( ( size_size @ ( list @ A ) @ ( splice @ A @ Xs @ Ys2 ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( size_size @ ( list @ A ) @ Xs ) @ ( size_size @ ( list @ A ) @ Ys2 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_164_Shift__def,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( bNF_Greatest_Shift @ A )
% 2.49/1.47 = ( ^ [Kl: set @ ( list @ A ),K3: A] :
% 2.49/1.47 ( collect @ ( list @ A )
% 2.49/1.47 @ ^ [Kl2: list @ A] : ( member @ ( list @ A ) @ ( cons @ A @ K3 @ Kl2 ) @ Kl ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_165_is__num__normalize_I1_J,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A,B2: A,C2: A] :
% 2.49/1.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 2.49/1.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_166_option_Ocollapse,axiom,
% 2.49/1.47 ! [A: $tType,Option: option @ A] :
% 2.49/1.47 ( ( Option
% 2.49/1.47 != ( none @ A ) )
% 2.49/1.47 => ( ( some @ A @ ( the @ A @ Option ) )
% 2.49/1.47 = Option ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_167_old_Ounit_Ocase,axiom,
% 2.49/1.47 ! [A: $tType,F: A] :
% 2.49/1.47 ( ( product_case_unit @ A @ F @ product_Unity )
% 2.49/1.47 = F ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_168_case__optionE,axiom,
% 2.49/1.47 ! [A: $tType,P: $o,Q: A > $o,X4: option @ A] :
% 2.49/1.47 ( ( case_option @ $o @ A @ P @ Q @ X4 )
% 2.49/1.47 => ( ( ( X4
% 2.49/1.47 = ( none @ A ) )
% 2.49/1.47 => ~ P )
% 2.49/1.47 => ~ ! [Y3: A] :
% 2.49/1.47 ( ( X4
% 2.49/1.47 = ( some @ A @ Y3 ) )
% 2.49/1.47 => ~ ( Q @ Y3 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_169_option_Odisc__eq__case_I1_J,axiom,
% 2.49/1.47 ! [A: $tType,Option: option @ A] :
% 2.49/1.47 ( ( Option
% 2.49/1.47 = ( none @ A ) )
% 2.49/1.47 = ( case_option @ $o @ A @ $true
% 2.49/1.47 @ ^ [Uu: A] : $false
% 2.49/1.47 @ Option ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_170_option_Odisc__eq__case_I2_J,axiom,
% 2.49/1.47 ! [A: $tType,Option: option @ A] :
% 2.49/1.47 ( ( Option
% 2.49/1.47 != ( none @ A ) )
% 2.49/1.47 = ( case_option @ $o @ A @ $false
% 2.49/1.47 @ ^ [Uu: A] : $true
% 2.49/1.47 @ Option ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_171_option_Osimps_I4_J,axiom,
% 2.49/1.47 ! [A: $tType,B: $tType,F1: B,F2: A > B] :
% 2.49/1.47 ( ( case_option @ B @ A @ F1 @ F2 @ ( none @ A ) )
% 2.49/1.47 = F1 ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_172_option_Osimps_I5_J,axiom,
% 2.49/1.47 ! [B: $tType,A: $tType,F1: B,F2: A > B,X25: A] :
% 2.49/1.47 ( ( case_option @ B @ A @ F1 @ F2 @ ( some @ A @ X25 ) )
% 2.49/1.47 = ( F2 @ X25 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_173_option_Ocase__distrib,axiom,
% 2.49/1.47 ! [C: $tType,B: $tType,A: $tType,H: B > C,F1: B,F2: A > B,Option: option @ A] :
% 2.49/1.47 ( ( H @ ( case_option @ B @ A @ F1 @ F2 @ Option ) )
% 2.49/1.47 = ( case_option @ C @ A @ ( H @ F1 )
% 2.49/1.47 @ ^ [X: A] : ( H @ ( F2 @ X ) )
% 2.49/1.47 @ Option ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_174_option_Osplit__sel,axiom,
% 2.49/1.47 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > B,Option: option @ A] :
% 2.49/1.47 ( ( P @ ( case_option @ B @ A @ F1 @ F2 @ Option ) )
% 2.49/1.47 = ( ( ( Option
% 2.49/1.47 = ( none @ A ) )
% 2.49/1.47 => ( P @ F1 ) )
% 2.49/1.47 & ( ( Option
% 2.49/1.47 = ( some @ A @ ( the @ A @ Option ) ) )
% 2.49/1.47 => ( P @ ( F2 @ ( the @ A @ Option ) ) ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_175_option_Ocase__eq__if,axiom,
% 2.49/1.47 ! [A: $tType,B: $tType] :
% 2.49/1.47 ( ( case_option @ B @ A )
% 2.49/1.47 = ( ^ [F12: B,F22: A > B,Option2: option @ A] :
% 2.49/1.47 ( if @ B
% 2.49/1.47 @ ( Option2
% 2.49/1.47 = ( none @ A ) )
% 2.49/1.47 @ F12
% 2.49/1.47 @ ( F22 @ ( the @ A @ Option2 ) ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_176_option_Osplit__sel__asm,axiom,
% 2.49/1.47 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > B,Option: option @ A] :
% 2.49/1.47 ( ( P @ ( case_option @ B @ A @ F1 @ F2 @ Option ) )
% 2.49/1.47 = ( ~ ( ( ( Option
% 2.49/1.47 = ( none @ A ) )
% 2.49/1.47 & ~ ( P @ F1 ) )
% 2.49/1.47 | ( ( Option
% 2.49/1.47 = ( some @ A @ ( the @ A @ Option ) ) )
% 2.49/1.47 & ~ ( P @ ( F2 @ ( the @ A @ Option ) ) ) ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_177_case__unit__Unity,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( product_case_unit @ A )
% 2.49/1.47 = ( ^ [F4: A,U: product_unit] : F4 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_178_unit_Ocase__distrib,axiom,
% 2.49/1.47 ! [A: $tType,B: $tType,H: A > B,F: A,Unit: product_unit] :
% 2.49/1.47 ( ( H @ ( product_case_unit @ A @ F @ Unit ) )
% 2.49/1.47 = ( product_case_unit @ B @ ( H @ F ) @ Unit ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_179_option_Osel,axiom,
% 2.49/1.47 ! [A: $tType,X25: A] :
% 2.49/1.47 ( ( the @ A @ ( some @ A @ X25 ) )
% 2.49/1.47 = X25 ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_180_option_Oexpand,axiom,
% 2.49/1.47 ! [A: $tType,Option: option @ A,Option3: option @ A] :
% 2.49/1.47 ( ( ( Option
% 2.49/1.47 = ( none @ A ) )
% 2.49/1.47 = ( Option3
% 2.49/1.47 = ( none @ A ) ) )
% 2.49/1.47 => ( ( ( Option
% 2.49/1.47 != ( none @ A ) )
% 2.49/1.47 => ( ( Option3
% 2.49/1.47 != ( none @ A ) )
% 2.49/1.47 => ( ( the @ A @ Option )
% 2.49/1.47 = ( the @ A @ Option3 ) ) ) )
% 2.49/1.47 => ( Option = Option3 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_181_option_Oexhaust__sel,axiom,
% 2.49/1.47 ! [A: $tType,Option: option @ A] :
% 2.49/1.47 ( ( Option
% 2.49/1.47 != ( none @ A ) )
% 2.49/1.47 => ( Option
% 2.49/1.47 = ( some @ A @ ( the @ A @ Option ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_182_disjE__realizer2,axiom,
% 2.49/1.47 ! [B: $tType,A: $tType,P: $o,Q: A > $o,X4: option @ A,R: B > $o,F: B,G: A > B] :
% 2.49/1.47 ( ( case_option @ $o @ A @ P @ Q @ X4 )
% 2.49/1.47 => ( ( P
% 2.49/1.47 => ( R @ F ) )
% 2.49/1.47 => ( ! [Q2: A] :
% 2.49/1.47 ( ( Q @ Q2 )
% 2.49/1.47 => ( R @ ( G @ Q2 ) ) )
% 2.49/1.47 => ( R @ ( case_option @ B @ A @ F @ G @ X4 ) ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_183_option_Othe__def,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( the @ A )
% 2.49/1.47 = ( case_option @ A @ A @ ( undefined @ A )
% 2.49/1.47 @ ^ [X24: A] : X24 ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_184_num_Osize_I5_J,axiom,
% 2.49/1.47 ! [X25: num] :
% 2.49/1.47 ( ( size_size @ num @ ( bit0 @ X25 ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( size_size @ num @ X25 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_185_num_Osize__gen_I2_J,axiom,
% 2.49/1.47 ! [X25: num] :
% 2.49/1.47 ( ( size_num @ ( bit0 @ X25 ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( size_num @ X25 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_186_num_Osize_I6_J,axiom,
% 2.49/1.47 ! [X33: num] :
% 2.49/1.47 ( ( size_size @ num @ ( bit1 @ X33 ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( size_size @ num @ X33 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_187_num_Osize__gen_I3_J,axiom,
% 2.49/1.47 ! [X33: num] :
% 2.49/1.47 ( ( size_num @ ( bit1 @ X33 ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( size_num @ X33 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_188_nat__of__num__code_I3_J,axiom,
% 2.49/1.47 ! [N: num] :
% 2.49/1.47 ( ( nat_of_num @ ( bit1 @ N ) )
% 2.49/1.47 = ( suc @ ( plus_plus @ nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_189_nat__of__num_Osimps_I3_J,axiom,
% 2.49/1.47 ! [X4: num] :
% 2.49/1.47 ( ( nat_of_num @ ( bit1 @ X4 ) )
% 2.49/1.47 = ( suc @ ( plus_plus @ nat @ ( nat_of_num @ X4 ) @ ( nat_of_num @ X4 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_190_nat__of__num__add,axiom,
% 2.49/1.47 ! [X4: num,Y: num] :
% 2.49/1.47 ( ( nat_of_num @ ( plus_plus @ num @ X4 @ Y ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( nat_of_num @ X4 ) @ ( nat_of_num @ Y ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_191_nat__of__num__neq__0,axiom,
% 2.49/1.47 ! [X4: num] :
% 2.49/1.47 ( ( nat_of_num @ X4 )
% 2.49/1.47 != ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_192_nat__of__num_Osimps_I2_J,axiom,
% 2.49/1.47 ! [X4: num] :
% 2.49/1.47 ( ( nat_of_num @ ( bit0 @ X4 ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( nat_of_num @ X4 ) @ ( nat_of_num @ X4 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_193_nat__of__num__code_I2_J,axiom,
% 2.49/1.47 ! [N: num] :
% 2.49/1.47 ( ( nat_of_num @ ( bit0 @ N ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_194_nat__of__num__inc,axiom,
% 2.49/1.47 ! [X4: num] :
% 2.49/1.47 ( ( nat_of_num @ ( inc @ X4 ) )
% 2.49/1.47 = ( suc @ ( nat_of_num @ X4 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_195_nat__of__num_Osimps_I1_J,axiom,
% 2.49/1.47 ( ( nat_of_num @ one2 )
% 2.49/1.47 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_196_num_Osize__gen_I1_J,axiom,
% 2.49/1.47 ( ( size_num @ one2 )
% 2.49/1.47 = ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_197_num_Osize_I4_J,axiom,
% 2.49/1.47 ( ( size_size @ num @ one2 )
% 2.49/1.47 = ( zero_zero @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_198_add__2__eq__Suc,axiom,
% 2.49/1.47 ! [N: nat] :
% 2.49/1.47 ( ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ N )
% 2.49/1.47 = ( suc @ ( suc @ N ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_199_add__2__eq__Suc_H,axiom,
% 2.49/1.47 ! [N: nat] :
% 2.49/1.47 ( ( plus_plus @ nat @ N @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) )
% 2.49/1.47 = ( suc @ ( suc @ N ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_200_numeral__plus__numeral,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( numeral @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [M: num,N: num] :
% 2.49/1.47 ( ( plus_plus @ A @ ( numeral_numeral @ A @ M ) @ ( numeral_numeral @ A @ N ) )
% 2.49/1.47 = ( numeral_numeral @ A @ ( plus_plus @ num @ M @ N ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_201_add__numeral__left,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( numeral @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [V: num,W: num,Z: A] :
% 2.49/1.47 ( ( plus_plus @ A @ ( numeral_numeral @ A @ V ) @ ( plus_plus @ A @ ( numeral_numeral @ A @ W ) @ Z ) )
% 2.49/1.47 = ( plus_plus @ A @ ( numeral_numeral @ A @ ( plus_plus @ num @ V @ W ) ) @ Z ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_202_Suc__numeral,axiom,
% 2.49/1.47 ! [N: num] :
% 2.49/1.47 ( ( suc @ ( numeral_numeral @ nat @ N ) )
% 2.49/1.47 = ( numeral_numeral @ nat @ ( plus_plus @ num @ N @ one2 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_203_numeral__Bit0,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( numeral @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [N: num] :
% 2.49/1.47 ( ( numeral_numeral @ A @ ( bit0 @ N ) )
% 2.49/1.47 = ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_204_numeral__code_I2_J,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( numeral @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [N: num] :
% 2.49/1.47 ( ( numeral_numeral @ A @ ( bit0 @ N ) )
% 2.49/1.47 = ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_205_zero__neq__numeral,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [N: num] :
% 2.49/1.47 ( ( zero_zero @ A )
% 2.49/1.47 != ( numeral_numeral @ A @ N ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_206_eval__nat__numeral_I3_J,axiom,
% 2.49/1.47 ! [N: num] :
% 2.49/1.47 ( ( numeral_numeral @ nat @ ( bit1 @ N ) )
% 2.49/1.47 = ( suc @ ( numeral_numeral @ nat @ ( bit0 @ N ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_207_numeral__1__eq__Suc__0,axiom,
% 2.49/1.47 ( ( numeral_numeral @ nat @ one2 )
% 2.49/1.47 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_208_numeral__2__eq__2,axiom,
% 2.49/1.47 ( ( numeral_numeral @ nat @ ( bit0 @ one2 ) )
% 2.49/1.47 = ( suc @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_209_numeral__3__eq__3,axiom,
% 2.49/1.47 ( ( numeral_numeral @ nat @ ( bit1 @ one2 ) )
% 2.49/1.47 = ( suc @ ( suc @ ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_210_Suc3__eq__add__3,axiom,
% 2.49/1.47 ! [N: nat] :
% 2.49/1.47 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) @ N ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_211_Suc__nat__number__of__add,axiom,
% 2.49/1.47 ! [V: num,N: nat] :
% 2.49/1.47 ( ( suc @ ( plus_plus @ nat @ ( numeral_numeral @ nat @ V ) @ N ) )
% 2.49/1.47 = ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( plus_plus @ num @ V @ one2 ) ) @ N ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_212_zero__not__eq__two,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( semiring_div_parity @ A @ ( type2 @ A ) )
% 2.49/1.47 => ( ( zero_zero @ A )
% 2.49/1.47 != ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_213_one__plus__numeral,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( numeral @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [N: num] :
% 2.49/1.47 ( ( plus_plus @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ N ) )
% 2.49/1.47 = ( numeral_numeral @ A @ ( plus_plus @ num @ one2 @ N ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_214_Suc__1,axiom,
% 2.49/1.47 ( ( suc @ ( one_one @ nat ) )
% 2.49/1.47 = ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_215_one__add__one,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( numeral @ A @ ( type2 @ A ) )
% 2.49/1.47 => ( ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
% 2.49/1.47 = ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_216_numeral__plus__one,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( numeral @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [N: num] :
% 2.49/1.47 ( ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( one_one @ A ) )
% 2.49/1.47 = ( numeral_numeral @ A @ ( plus_plus @ num @ N @ one2 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_217_one__plus__numeral__commute,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( numeral @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [X4: num] :
% 2.49/1.47 ( ( plus_plus @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ X4 ) )
% 2.49/1.47 = ( plus_plus @ A @ ( numeral_numeral @ A @ X4 ) @ ( one_one @ A ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_218_One__nat__def,axiom,
% 2.49/1.47 ( ( one_one @ nat )
% 2.49/1.47 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_219_one__reorient,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( one @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [X4: A] :
% 2.49/1.47 ( ( ( one_one @ A )
% 2.49/1.47 = X4 )
% 2.49/1.47 = ( X4
% 2.49/1.47 = ( one_one @ A ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_220_Suc__eq__plus1,axiom,
% 2.49/1.47 ( suc
% 2.49/1.47 = ( ^ [N4: nat] : ( plus_plus @ nat @ N4 @ ( one_one @ nat ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_221_Suc__eq__plus1__left,axiom,
% 2.49/1.47 ( suc
% 2.49/1.47 = ( plus_plus @ nat @ ( one_one @ nat ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_222_numeral__Bit1,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( numeral @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [N: num] :
% 2.49/1.47 ( ( numeral_numeral @ A @ ( bit1 @ N ) )
% 2.49/1.47 = ( plus_plus @ A @ ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( numeral_numeral @ A @ N ) ) @ ( one_one @ A ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_223_numeral__inc,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( numeral @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [X4: num] :
% 2.49/1.47 ( ( numeral_numeral @ A @ ( inc @ X4 ) )
% 2.49/1.47 = ( plus_plus @ A @ ( numeral_numeral @ A @ X4 ) @ ( one_one @ A ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_224_numeral__code_I3_J,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( numeral @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [N: num] :
% 2.49/1.47 ( ( numeral_numeral @ A @ ( bit1 @ N ) )
% 2.49/1.47 = ( plus_plus @ A @ ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( numeral_numeral @ A @ N ) ) @ ( one_one @ A ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_225_nat__1__add__1,axiom,
% 2.49/1.47 ( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
% 2.49/1.47 = ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_226_zero__neq__one,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( zero_neq_one @ A @ ( type2 @ A ) )
% 2.49/1.47 => ( ( zero_zero @ A )
% 2.49/1.47 != ( one_one @ A ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_227_dbl__inc__simps_I2_J,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.49/1.47 => ( ( neg_numeral_dbl_inc @ A @ ( zero_zero @ A ) )
% 2.49/1.47 = ( one_one @ A ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_228_one__natural_Orsp,axiom,
% 2.49/1.47 ( ( one_one @ nat )
% 2.49/1.47 = ( one_one @ nat ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_229_dbl__inc__def,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.49/1.47 => ( ( neg_numeral_dbl_inc @ A )
% 2.49/1.47 = ( ^ [X: A] : ( plus_plus @ A @ ( plus_plus @ A @ X @ X ) @ ( one_one @ A ) ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_230_Suc__div__eq__add3__div__numeral,axiom,
% 2.49/1.47 ! [M: nat,V: num] :
% 2.49/1.47 ( ( divide_divide @ nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral @ nat @ V ) )
% 2.49/1.47 = ( divide_divide @ nat @ ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) @ M ) @ ( numeral_numeral @ nat @ V ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_231_div__Suc__eq__div__add3,axiom,
% 2.49/1.47 ! [M: nat,N: nat] :
% 2.49/1.47 ( ( divide_divide @ nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 2.49/1.47 = ( divide_divide @ nat @ M @ ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) @ N ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_232_divide__zero,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( semidom_divide @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A] :
% 2.49/1.47 ( ( divide_divide @ A @ A2 @ ( zero_zero @ A ) )
% 2.49/1.47 = ( zero_zero @ A ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_233_divide__zero__left,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( semidom_divide @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A] :
% 2.49/1.47 ( ( divide_divide @ A @ ( zero_zero @ A ) @ A2 )
% 2.49/1.47 = ( zero_zero @ A ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_234_divide__eq__0__iff,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( field @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A,B2: A] :
% 2.49/1.47 ( ( ( divide_divide @ A @ A2 @ B2 )
% 2.49/1.47 = ( zero_zero @ A ) )
% 2.49/1.47 = ( ( A2
% 2.49/1.47 = ( zero_zero @ A ) )
% 2.49/1.47 | ( B2
% 2.49/1.47 = ( zero_zero @ A ) ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_235_divide__cancel__left,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( field @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [C2: A,A2: A,B2: A] :
% 2.49/1.47 ( ( ( divide_divide @ A @ C2 @ A2 )
% 2.49/1.47 = ( divide_divide @ A @ C2 @ B2 ) )
% 2.49/1.47 = ( ( C2
% 2.49/1.47 = ( zero_zero @ A ) )
% 2.49/1.47 | ( A2 = B2 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_236_divide__cancel__right,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( field @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A,C2: A,B2: A] :
% 2.49/1.47 ( ( ( divide_divide @ A @ A2 @ C2 )
% 2.49/1.47 = ( divide_divide @ A @ B2 @ C2 ) )
% 2.49/1.47 = ( ( C2
% 2.49/1.47 = ( zero_zero @ A ) )
% 2.49/1.47 | ( A2 = B2 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_237_division__ring__divide__zero,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( division_ring @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A] :
% 2.49/1.47 ( ( divide_divide @ A @ A2 @ ( zero_zero @ A ) )
% 2.49/1.47 = ( zero_zero @ A ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_238_div__0,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( semiring_div @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A] :
% 2.49/1.47 ( ( divide_divide @ A @ ( zero_zero @ A ) @ A2 )
% 2.49/1.47 = ( zero_zero @ A ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_239_div__by__0,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( semiring_div @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A] :
% 2.49/1.47 ( ( divide_divide @ A @ A2 @ ( zero_zero @ A ) )
% 2.49/1.47 = ( zero_zero @ A ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_240_div__self,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( semidom_divide @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A] :
% 2.49/1.47 ( ( A2
% 2.49/1.47 != ( zero_zero @ A ) )
% 2.49/1.47 => ( ( divide_divide @ A @ A2 @ A2 )
% 2.49/1.47 = ( one_one @ A ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_241_divide__eq__1__iff,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( field @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A,B2: A] :
% 2.49/1.47 ( ( ( divide_divide @ A @ A2 @ B2 )
% 2.49/1.47 = ( one_one @ A ) )
% 2.49/1.47 = ( ( B2
% 2.49/1.47 != ( zero_zero @ A ) )
% 2.49/1.47 & ( A2 = B2 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_242_one__eq__divide__iff,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( field @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A,B2: A] :
% 2.49/1.47 ( ( ( one_one @ A )
% 2.49/1.47 = ( divide_divide @ A @ A2 @ B2 ) )
% 2.49/1.47 = ( ( B2
% 2.49/1.47 != ( zero_zero @ A ) )
% 2.49/1.47 & ( A2 = B2 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_243_divide__self,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( division_ring @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A] :
% 2.49/1.47 ( ( A2
% 2.49/1.47 != ( zero_zero @ A ) )
% 2.49/1.47 => ( ( divide_divide @ A @ A2 @ A2 )
% 2.49/1.47 = ( one_one @ A ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_244_divide__self__if,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( division_ring @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A] :
% 2.49/1.47 ( ( ( A2
% 2.49/1.47 = ( zero_zero @ A ) )
% 2.49/1.47 => ( ( divide_divide @ A @ A2 @ A2 )
% 2.49/1.47 = ( zero_zero @ A ) ) )
% 2.49/1.47 & ( ( A2
% 2.49/1.47 != ( zero_zero @ A ) )
% 2.49/1.47 => ( ( divide_divide @ A @ A2 @ A2 )
% 2.49/1.47 = ( one_one @ A ) ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_245_divide__eq__eq__1,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [B2: A,A2: A] :
% 2.49/1.47 ( ( ( divide_divide @ A @ B2 @ A2 )
% 2.49/1.47 = ( one_one @ A ) )
% 2.49/1.47 = ( ( A2
% 2.49/1.47 != ( zero_zero @ A ) )
% 2.49/1.47 & ( A2 = B2 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_246_eq__divide__eq__1,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [B2: A,A2: A] :
% 2.49/1.47 ( ( ( one_one @ A )
% 2.49/1.47 = ( divide_divide @ A @ B2 @ A2 ) )
% 2.49/1.47 = ( ( A2
% 2.49/1.47 != ( zero_zero @ A ) )
% 2.49/1.47 & ( A2 = B2 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_247_one__divide__eq__0__iff,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A] :
% 2.49/1.47 ( ( ( divide_divide @ A @ ( one_one @ A ) @ A2 )
% 2.49/1.47 = ( zero_zero @ A ) )
% 2.49/1.47 = ( A2
% 2.49/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_248_zero__eq__1__divide__iff,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [A2: A] :
% 2.49/1.47 ( ( ( zero_zero @ A )
% 2.49/1.47 = ( divide_divide @ A @ ( one_one @ A ) @ A2 ) )
% 2.49/1.47 = ( A2
% 2.49/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_249_div__1,axiom,
% 2.49/1.47 ! [M: nat] :
% 2.49/1.47 ( ( divide_divide @ nat @ M @ ( suc @ ( zero_zero @ nat ) ) )
% 2.49/1.47 = M ) ).
% 2.49/1.47
% 2.49/1.47 thf(fact_250_div__add__self2,axiom,
% 2.49/1.47 ! [A: $tType] :
% 2.49/1.47 ( ( semiring_div @ A @ ( type2 @ A ) )
% 2.49/1.47 => ! [B2: A,A2: A] :
% 2.49/1.47 ( ( B2
% 2.49/1.47 != ( zero_zero @ A ) )
% 2.49/1.47 => ( ( divide_divide @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 2.49/1.47 = ( plus_plus @ A @ ( divide_divide @ A @ A2 @ B2 ) @ ( one_one @ A ) ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_BinDag__Mirabelle__rybootvolr_Odag___Code__Evaluation_Oterm__of,axiom,
% 2.49/1.47 code_term_of @ binDag_Mirabelle_dag @ ( type2 @ binDag_Mirabelle_dag ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_BinDag__Mirabelle__rybootvolr_Odag___HOL_Oequal,axiom,
% 2.49/1.47 cl_HOL_Oequal @ binDag_Mirabelle_dag @ ( type2 @ binDag_Mirabelle_dag ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Record_Otuple__isomorphism___Code__Evaluation_Oterm__of_1,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType,A8: $tType] :
% 2.49/1.47 ( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 & ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 2.49/1.47 & ( typerep2 @ A8 @ ( type2 @ A8 ) ) )
% 2.49/1.47 => ( code_term_of @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) @ ( type2 @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Record_Otuple__isomorphism___HOL_Oequal_2,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType,A8: $tType] : ( cl_HOL_Oequal @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) @ ( type2 @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Numeral_Onatural___Code__Evaluation_Oterm__of_3,axiom,
% 2.49/1.47 code_term_of @ code_natural @ ( type2 @ code_natural ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Numeral_Onatural___HOL_Oequal_4,axiom,
% 2.49/1.47 cl_HOL_Oequal @ code_natural @ ( type2 @ code_natural ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Evaluation_Oterm___Code__Evaluation_Oterm__of_5,axiom,
% 2.49/1.47 code_term_of @ code_term @ ( type2 @ code_term ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Evaluation_Oterm___HOL_Oequal_6,axiom,
% 2.49/1.47 cl_HOL_Oequal @ code_term @ ( type2 @ code_term ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Product__Type_Ounit___Code__Evaluation_Oterm__of_7,axiom,
% 2.49/1.47 code_term_of @ product_unit @ ( type2 @ product_unit ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Product__Type_Ounit___HOL_Oequal_8,axiom,
% 2.49/1.47 cl_HOL_Oequal @ product_unit @ ( type2 @ product_unit ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Product__Type_Oprod___Code__Evaluation_Oterm__of_9,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType] :
% 2.49/1.47 ( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 & ( typerep2 @ A7 @ ( type2 @ A7 ) ) )
% 2.49/1.47 => ( code_term_of @ ( product_prod @ A6 @ A7 ) @ ( type2 @ ( product_prod @ A6 @ A7 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Product__Type_Oprod___HOL_Oequal_10,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType] : ( cl_HOL_Oequal @ ( product_prod @ A6 @ A7 ) @ ( type2 @ ( product_prod @ A6 @ A7 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Typerep_Otyperep___Code__Evaluation_Oterm__of_11,axiom,
% 2.49/1.47 code_term_of @ typerep @ ( type2 @ typerep ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Typerep_Otyperep___HOL_Oequal_12,axiom,
% 2.49/1.47 cl_HOL_Oequal @ typerep @ ( type2 @ typerep ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_String_Oliteral___Code__Evaluation_Oterm__of_13,axiom,
% 2.49/1.47 code_term_of @ literal @ ( type2 @ literal ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_String_Oliteral___HOL_Oequal_14,axiom,
% 2.49/1.47 cl_HOL_Oequal @ literal @ ( type2 @ literal ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Simpl__Heap_Oref___Code__Evaluation_Oterm__of_15,axiom,
% 2.49/1.47 code_term_of @ simpl_ref @ ( type2 @ simpl_ref ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Option_Ooption___Code__Evaluation_Oterm__of_16,axiom,
% 2.49/1.47 ! [A6: $tType] :
% 2.49/1.47 ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 => ( code_term_of @ ( option @ A6 ) @ ( type2 @ ( option @ A6 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Option_Ooption___HOL_Oequal_17,axiom,
% 2.49/1.47 ! [A6: $tType] : ( cl_HOL_Oequal @ ( option @ A6 ) @ ( type2 @ ( option @ A6 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Sum__Type_Osum___Code__Evaluation_Oterm__of_18,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType] :
% 2.49/1.47 ( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 & ( typerep2 @ A7 @ ( type2 @ A7 ) ) )
% 2.49/1.47 => ( code_term_of @ ( sum_sum @ A6 @ A7 ) @ ( type2 @ ( sum_sum @ A6 @ A7 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Sum__Type_Osum___HOL_Oequal_19,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType] : ( cl_HOL_Oequal @ ( sum_sum @ A6 @ A7 ) @ ( type2 @ ( sum_sum @ A6 @ A7 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_List_Olist___Code__Evaluation_Oterm__of_20,axiom,
% 2.49/1.47 ! [A6: $tType] :
% 2.49/1.47 ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 => ( code_term_of @ ( list @ A6 ) @ ( type2 @ ( list @ A6 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_List_Olist___HOL_Oequal_21,axiom,
% 2.49/1.47 ! [A6: $tType] : ( cl_HOL_Oequal @ ( list @ A6 ) @ ( type2 @ ( list @ A6 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_HOL_Obool___Code__Evaluation_Oterm__of_22,axiom,
% 2.49/1.47 code_term_of @ $o @ ( type2 @ $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_HOL_Obool___HOL_Oequal_23,axiom,
% 2.49/1.47 cl_HOL_Oequal @ $o @ ( type2 @ $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Set_Oset___Code__Evaluation_Oterm__of_24,axiom,
% 2.49/1.47 ! [A6: $tType] :
% 2.49/1.47 ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 => ( code_term_of @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Set_Oset___HOL_Oequal_25,axiom,
% 2.49/1.47 ! [A6: $tType] :
% 2.49/1.47 ( ( cl_HOL_Oequal @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 => ( cl_HOL_Oequal @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Num_Onum___Code__Evaluation_Oterm__of_26,axiom,
% 2.49/1.47 code_term_of @ num @ ( type2 @ num ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Num_Onum___HOL_Oequal_27,axiom,
% 2.49/1.47 cl_HOL_Oequal @ num @ ( type2 @ num ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Code__Evaluation_Oterm__of_28,axiom,
% 2.49/1.47 code_term_of @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___HOL_Oequal_29,axiom,
% 2.49/1.47 cl_HOL_Oequal @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_fun___Code__Evaluation_Oterm__of_30,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType] :
% 2.49/1.47 ( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 & ( typerep2 @ A7 @ ( type2 @ A7 ) ) )
% 2.49/1.47 => ( code_term_of @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_fun___HOL_Oequal_31,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType] :
% 2.49/1.47 ( ( ( enum @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 & ( cl_HOL_Oequal @ A7 @ ( type2 @ A7 ) ) )
% 2.49/1.47 => ( cl_HOL_Oequal @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_fun___Typerep_Otyperep,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType] :
% 2.49/1.47 ( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 & ( typerep2 @ A7 @ ( type2 @ A7 ) ) )
% 2.49/1.47 => ( typerep2 @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_fun___Enum_Oenum,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType] :
% 2.49/1.47 ( ( ( enum @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 & ( enum @ A7 @ ( type2 @ A7 ) ) )
% 2.49/1.47 => ( enum @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Typerep_Otyperep_32,axiom,
% 2.49/1.47 typerep2 @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Num_Onum___Typerep_Otyperep_33,axiom,
% 2.49/1.47 typerep2 @ num @ ( type2 @ num ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Set_Oset___Typerep_Otyperep_34,axiom,
% 2.49/1.47 ! [A6: $tType] :
% 2.49/1.47 ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 => ( typerep2 @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Set_Oset___Enum_Oenum_35,axiom,
% 2.49/1.47 ! [A6: $tType] :
% 2.49/1.47 ( ( enum @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 => ( enum @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_HOL_Obool___Typerep_Otyperep_36,axiom,
% 2.49/1.47 typerep2 @ $o @ ( type2 @ $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_HOL_Obool___Enum_Oenum_37,axiom,
% 2.49/1.47 enum @ $o @ ( type2 @ $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_List_Olist___Typerep_Otyperep_38,axiom,
% 2.49/1.47 ! [A6: $tType] :
% 2.49/1.47 ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 => ( typerep2 @ ( list @ A6 ) @ ( type2 @ ( list @ A6 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Sum__Type_Osum___Typerep_Otyperep_39,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType] :
% 2.49/1.47 ( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 & ( typerep2 @ A7 @ ( type2 @ A7 ) ) )
% 2.49/1.47 => ( typerep2 @ ( sum_sum @ A6 @ A7 ) @ ( type2 @ ( sum_sum @ A6 @ A7 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Sum__Type_Osum___Enum_Oenum_40,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType] :
% 2.49/1.47 ( ( ( enum @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 & ( enum @ A7 @ ( type2 @ A7 ) ) )
% 2.49/1.47 => ( enum @ ( sum_sum @ A6 @ A7 ) @ ( type2 @ ( sum_sum @ A6 @ A7 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Option_Ooption___Typerep_Otyperep_41,axiom,
% 2.49/1.47 ! [A6: $tType] :
% 2.49/1.47 ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 => ( typerep2 @ ( option @ A6 ) @ ( type2 @ ( option @ A6 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Option_Ooption___Enum_Oenum_42,axiom,
% 2.49/1.47 ! [A6: $tType] :
% 2.49/1.47 ( ( enum @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 => ( enum @ ( option @ A6 ) @ ( type2 @ ( option @ A6 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Simpl__Heap_Oref___Typerep_Otyperep_43,axiom,
% 2.49/1.47 typerep2 @ simpl_ref @ ( type2 @ simpl_ref ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_String_Oliteral___Typerep_Otyperep_44,axiom,
% 2.49/1.47 typerep2 @ literal @ ( type2 @ literal ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Typerep_Otyperep___Typerep_Otyperep_45,axiom,
% 2.49/1.47 typerep2 @ typerep @ ( type2 @ typerep ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Product__Type_Oprod___Typerep_Otyperep_46,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType] :
% 2.49/1.47 ( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 & ( typerep2 @ A7 @ ( type2 @ A7 ) ) )
% 2.49/1.47 => ( typerep2 @ ( product_prod @ A6 @ A7 ) @ ( type2 @ ( product_prod @ A6 @ A7 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Product__Type_Oprod___Enum_Oenum_47,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType] :
% 2.49/1.47 ( ( ( enum @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 & ( enum @ A7 @ ( type2 @ A7 ) ) )
% 2.49/1.47 => ( enum @ ( product_prod @ A6 @ A7 ) @ ( type2 @ ( product_prod @ A6 @ A7 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Product__Type_Ounit___Typerep_Otyperep_48,axiom,
% 2.49/1.47 typerep2 @ product_unit @ ( type2 @ product_unit ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Product__Type_Ounit___Enum_Oenum_49,axiom,
% 2.49/1.47 enum @ product_unit @ ( type2 @ product_unit ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Evaluation_Oterm___Typerep_Otyperep_50,axiom,
% 2.49/1.47 typerep2 @ code_term @ ( type2 @ code_term ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Numeral_Onatural___Typerep_Otyperep_51,axiom,
% 2.49/1.47 typerep2 @ code_natural @ ( type2 @ code_natural ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Record_Otuple__isomorphism___Typerep_Otyperep_52,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType,A8: $tType] :
% 2.49/1.47 ( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 & ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 2.49/1.47 & ( typerep2 @ A8 @ ( type2 @ A8 ) ) )
% 2.49/1.47 => ( typerep2 @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) @ ( type2 @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_BinDag__Mirabelle__rybootvolr_Odag___Typerep_Otyperep_53,axiom,
% 2.49/1.47 typerep2 @ binDag_Mirabelle_dag @ ( type2 @ binDag_Mirabelle_dag ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_fun___Quickcheck__Random_Orandom,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType] :
% 2.49/1.47 ( ( ( code_term_of @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 & ( cl_HOL_Oequal @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 & ( quickcheck_random @ A7 @ ( type2 @ A7 ) ) )
% 2.49/1.47 => ( quickcheck_random @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 2.49/1.47 semiri456707255roduct @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 2.49/1.47 canoni770627133id_add @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 2.49/1.47 ordere779506340up_add @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 2.49/1.47 cancel1352612707id_add @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 2.49/1.47 cancel_semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Divides_Osemiring__div__parity,axiom,
% 2.49/1.47 semiring_div_parity @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Quickcheck__Random_Orandom_54,axiom,
% 2.49/1.47 quickcheck_random @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 2.49/1.47 ab_semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 2.49/1.47 comm_monoid_add @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
% 2.49/1.47 comm_semiring_1 @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Rings_Osemidom__divide,axiom,
% 2.49/1.47 semidom_divide @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 2.49/1.47 semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Divides_Osemiring__div,axiom,
% 2.49/1.47 semiring_div @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Nat_Osemiring__char__0,axiom,
% 2.49/1.47 semiring_char_0 @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Rings_Ozero__neq__one,axiom,
% 2.49/1.47 zero_neq_one @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Groups_Omonoid__add,axiom,
% 2.49/1.47 monoid_add @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Num_Onumeral,axiom,
% 2.49/1.47 numeral @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 2.49/1.47 zero @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 2.49/1.47 one @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 2.49/1.47 size @ nat @ ( type2 @ nat ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Num_Onum___Quickcheck__Random_Orandom_55,axiom,
% 2.49/1.47 quickcheck_random @ num @ ( type2 @ num ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Num_Onum___Nat_Osize_56,axiom,
% 2.49/1.47 size @ num @ ( type2 @ num ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Set_Oset___Quickcheck__Random_Orandom_57,axiom,
% 2.49/1.47 ! [A6: $tType] :
% 2.49/1.47 ( ( quickcheck_random @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 => ( quickcheck_random @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_HOL_Obool___Quickcheck__Random_Orandom_58,axiom,
% 2.49/1.47 quickcheck_random @ $o @ ( type2 @ $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_HOL_Obool___Nat_Osize_59,axiom,
% 2.49/1.47 size @ $o @ ( type2 @ $o ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_List_Olist___Quickcheck__Random_Orandom_60,axiom,
% 2.49/1.47 ! [A6: $tType] :
% 2.49/1.47 ( ( quickcheck_random @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 => ( quickcheck_random @ ( list @ A6 ) @ ( type2 @ ( list @ A6 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_List_Olist___Nat_Osize_61,axiom,
% 2.49/1.47 ! [A6: $tType] : ( size @ ( list @ A6 ) @ ( type2 @ ( list @ A6 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Sum__Type_Osum___Quickcheck__Random_Orandom_62,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType] :
% 2.49/1.47 ( ( ( quickcheck_random @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 & ( quickcheck_random @ A7 @ ( type2 @ A7 ) ) )
% 2.49/1.47 => ( quickcheck_random @ ( sum_sum @ A6 @ A7 ) @ ( type2 @ ( sum_sum @ A6 @ A7 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Sum__Type_Osum___Nat_Osize_63,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType] : ( size @ ( sum_sum @ A6 @ A7 ) @ ( type2 @ ( sum_sum @ A6 @ A7 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Option_Ooption___Quickcheck__Random_Orandom_64,axiom,
% 2.49/1.47 ! [A6: $tType] :
% 2.49/1.47 ( ( quickcheck_random @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 => ( quickcheck_random @ ( option @ A6 ) @ ( type2 @ ( option @ A6 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Option_Ooption___Nat_Osize_65,axiom,
% 2.49/1.47 ! [A6: $tType] : ( size @ ( option @ A6 ) @ ( type2 @ ( option @ A6 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_String_Oliteral___Quickcheck__Random_Orandom_66,axiom,
% 2.49/1.47 quickcheck_random @ literal @ ( type2 @ literal ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_String_Oliteral___Nat_Osize_67,axiom,
% 2.49/1.47 size @ literal @ ( type2 @ literal ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Typerep_Otyperep___Nat_Osize_68,axiom,
% 2.49/1.47 size @ typerep @ ( type2 @ typerep ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Product__Type_Oprod___Quickcheck__Random_Orandom_69,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType] :
% 2.49/1.47 ( ( ( quickcheck_random @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 & ( quickcheck_random @ A7 @ ( type2 @ A7 ) ) )
% 2.49/1.47 => ( quickcheck_random @ ( product_prod @ A6 @ A7 ) @ ( type2 @ ( product_prod @ A6 @ A7 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Product__Type_Oprod___Nat_Osize_70,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType] : ( size @ ( product_prod @ A6 @ A7 ) @ ( type2 @ ( product_prod @ A6 @ A7 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Product__Type_Ounit___Quickcheck__Random_Orandom_71,axiom,
% 2.49/1.47 quickcheck_random @ product_unit @ ( type2 @ product_unit ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Product__Type_Ounit___Nat_Osize_72,axiom,
% 2.49/1.47 size @ product_unit @ ( type2 @ product_unit ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__add_73,axiom,
% 2.49/1.47 ordere779506340up_add @ code_natural @ ( type2 @ code_natural ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Numeral_Onatural___Groups_Ocancel__comm__monoid__add_74,axiom,
% 2.49/1.47 cancel1352612707id_add @ code_natural @ ( type2 @ code_natural ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Numeral_Onatural___Groups_Ocancel__semigroup__add_75,axiom,
% 2.49/1.47 cancel_semigroup_add @ code_natural @ ( type2 @ code_natural ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Numeral_Onatural___Quickcheck__Random_Orandom_76,axiom,
% 2.49/1.47 quickcheck_random @ code_natural @ ( type2 @ code_natural ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Numeral_Onatural___Groups_Oab__semigroup__add_77,axiom,
% 2.49/1.47 ab_semigroup_add @ code_natural @ ( type2 @ code_natural ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Numeral_Onatural___Groups_Ocomm__monoid__add_78,axiom,
% 2.49/1.47 comm_monoid_add @ code_natural @ ( type2 @ code_natural ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Numeral_Onatural___Rings_Ocomm__semiring__1_79,axiom,
% 2.49/1.47 comm_semiring_1 @ code_natural @ ( type2 @ code_natural ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Numeral_Onatural___Rings_Osemidom__divide_80,axiom,
% 2.49/1.47 semidom_divide @ code_natural @ ( type2 @ code_natural ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Numeral_Onatural___Groups_Osemigroup__add_81,axiom,
% 2.49/1.47 semigroup_add @ code_natural @ ( type2 @ code_natural ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Numeral_Onatural___Divides_Osemiring__div_82,axiom,
% 2.49/1.47 semiring_div @ code_natural @ ( type2 @ code_natural ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Numeral_Onatural___Rings_Ozero__neq__one_83,axiom,
% 2.49/1.47 zero_neq_one @ code_natural @ ( type2 @ code_natural ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Numeral_Onatural___Groups_Omonoid__add_84,axiom,
% 2.49/1.47 monoid_add @ code_natural @ ( type2 @ code_natural ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Numeral_Onatural___Num_Onumeral_85,axiom,
% 2.49/1.47 numeral @ code_natural @ ( type2 @ code_natural ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Numeral_Onatural___Groups_Ozero_86,axiom,
% 2.49/1.47 zero @ code_natural @ ( type2 @ code_natural ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Numeral_Onatural___Groups_Oone_87,axiom,
% 2.49/1.47 one @ code_natural @ ( type2 @ code_natural ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Code__Numeral_Onatural___Nat_Osize_88,axiom,
% 2.49/1.47 size @ code_natural @ ( type2 @ code_natural ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Record_Otuple__isomorphism___Quickcheck__Random_Orandom_89,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType,A8: $tType] :
% 2.49/1.47 ( ( ( code_term_of @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 & ( cl_HOL_Oequal @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 & ( quickcheck_random @ A6 @ ( type2 @ A6 ) )
% 2.49/1.47 & ( quickcheck_random @ A7 @ ( type2 @ A7 ) )
% 2.49/1.47 & ( quickcheck_random @ A8 @ ( type2 @ A8 ) ) )
% 2.49/1.47 => ( quickcheck_random @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) @ ( type2 @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_Record_Otuple__isomorphism___Nat_Osize_90,axiom,
% 2.49/1.47 ! [A6: $tType,A7: $tType,A8: $tType] : ( size @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) @ ( type2 @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(tcon_BinDag__Mirabelle__rybootvolr_Odag___Nat_Osize_91,axiom,
% 2.49/1.47 size @ binDag_Mirabelle_dag @ ( type2 @ binDag_Mirabelle_dag ) ).
% 2.49/1.47
% 2.49/1.47 thf(help_If_3_1_T,axiom,
% 2.49/1.47 ! [P: $o] :
% 2.49/1.47 ( ( P = $true )
% 2.49/1.47 | ( P = $false ) ) ).
% 2.49/1.47
% 2.49/1.47 thf(help_If_2_1_T,axiom,
% 2.49/1.47 ! [A: $tType,X4: A,Y: A] :
% 2.49/1.47 ( ( if @ A @ $false @ X4 @ Y )
% 2.49/1.47 = Y ) ).
% 2.49/1.47
% 2.49/1.47 thf(help_If_1_1_T,axiom,
% 2.49/1.47 ! [A: $tType,X4: A,Y: A] :
% 2.49/1.47 ( ( if @ A @ $true @ X4 @ Y )
% 2.49/1.47 = X4 ) ).
% 2.49/1.47
% 2.49/1.47 thf(conj_0,conjecture,
% 2.49/1.47 ( ( binDag476092410e_Node @ lt @ a @ rt )
% 2.49/1.47 != lt ) ).
% 2.49/1.47 ------------------------
% 2.67/1.50 % (32247)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/4Mi)
% 2.67/1.50 % (32248)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/27Mi)
% 2.67/1.50 % (32249)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/2Mi)
% 2.67/1.50 % (32247)Instruction limit reached!
% 2.67/1.50 % (32247)------------------------------
% 2.67/1.50 % (32247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.50 % (32247)Termination reason: Unknown
% 2.67/1.50 % (32247)Termination phase: shuffling
% 2.67/1.50
% 2.67/1.50 % (32247)Memory used [KB]: 1535
% 2.67/1.50 % (32247)Time elapsed: 0.003 s
% 2.67/1.50 % (32247)Instructions burned: 5 (million)
% 2.67/1.50 % (32247)------------------------------
% 2.67/1.50 % (32247)------------------------------
% 2.67/1.50 % (32249)Instruction limit reached!
% 2.67/1.50 % (32249)------------------------------
% 2.67/1.50 % (32249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.50 % (32249)Termination reason: Unknown
% 2.67/1.50 % (32249)Termination phase: shuffling
% 2.67/1.50
% 2.67/1.50 % (32249)Memory used [KB]: 1407
% 2.67/1.50 % (32249)Time elapsed: 0.002 s
% 2.67/1.50 % (32249)Instructions burned: 3 (million)
% 2.67/1.50 % (32249)------------------------------
% 2.67/1.50 % (32249)------------------------------
% 2.67/1.51 % (32246)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/183Mi)
% 2.67/1.51 % (32250)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/2Mi)
% 2.67/1.51 % (32251)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/275Mi)
% 2.67/1.51 % (32252)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/18Mi)
% 2.67/1.51 % (32248)Instruction limit reached!
% 2.67/1.51 % (32248)------------------------------
% 2.67/1.51 % (32248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.51 % (32248)Termination reason: Unknown
% 2.67/1.51 % (32248)Termination phase: Preprocessing 1
% 2.67/1.51
% 2.67/1.51 % (32248)Memory used [KB]: 1918
% 2.67/1.51 % (32248)Time elapsed: 0.010 s
% 2.67/1.51 % (32248)Instructions burned: 27 (million)
% 2.67/1.51 % (32248)------------------------------
% 2.67/1.51 % (32248)------------------------------
% 2.67/1.51 % (32250)Instruction limit reached!
% 2.67/1.51 % (32250)------------------------------
% 2.67/1.51 % (32250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.51 % (32250)Termination reason: Unknown
% 2.67/1.51 % (32250)Termination phase: shuffling
% 2.67/1.51
% 2.67/1.51 % (32250)Memory used [KB]: 1407
% 2.67/1.51 % (32250)Time elapsed: 0.004 s
% 2.67/1.51 % (32250)Instructions burned: 3 (million)
% 2.67/1.51 % (32250)------------------------------
% 2.67/1.51 % (32250)------------------------------
% 2.67/1.51 % (32253)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/3Mi)
% 2.67/1.51 % (32254)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/37Mi)
% 2.67/1.51 % (32253)Instruction limit reached!
% 2.67/1.51 % (32253)------------------------------
% 2.67/1.51 % (32253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.51 % (32253)Termination reason: Unknown
% 2.67/1.51 % (32253)Termination phase: shuffling
% 2.67/1.51
% 2.67/1.51 % (32253)Memory used [KB]: 1535
% 2.67/1.51 % (32253)Time elapsed: 0.002 s
% 2.67/1.51 % (32253)Instructions burned: 3 (million)
% 2.67/1.51 % (32253)------------------------------
% 2.67/1.51 % (32253)------------------------------
% 2.67/1.52 % (32252)Instruction limit reached!
% 2.67/1.52 % (32252)------------------------------
% 2.67/1.52 % (32252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.52 % (32252)Termination reason: Unknown
% 2.67/1.52 % (32252)Termination phase: Property scanning
% 2.67/1.52
% 2.67/1.52 % (32252)Memory used [KB]: 1663
% 2.67/1.52 % (32252)Time elapsed: 0.013 s
% 2.67/1.52 % (32252)Instructions burned: 18 (million)
% 2.67/1.52 % (32252)------------------------------
% 2.67/1.52 % (32252)------------------------------
% 2.67/1.52 % (32255)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/15Mi)
% 2.67/1.52 % (32257)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/1041Mi)
% 2.67/1.52 % (32254)Instruction limit reached!
% 2.67/1.52 % (32254)------------------------------
% 2.67/1.52 % (32254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.52 % (32254)Termination reason: Unknown
% 2.67/1.52 % (32254)Termination phase: Property scanning
% 2.67/1.52
% 2.67/1.52 % (32254)Memory used [KB]: 2174
% 2.67/1.52 % (32254)Time elapsed: 0.013 s
% 2.67/1.52 % (32254)Instructions burned: 37 (million)
% 2.67/1.52 % (32254)------------------------------
% 2.67/1.52 % (32254)------------------------------
% 2.67/1.52 % (32255)Instruction limit reached!
% 2.67/1.52 % (32255)------------------------------
% 2.67/1.52 % (32255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.52 % (32255)Termination reason: Unknown
% 2.67/1.52 % (32255)Termination phase: Property scanning
% 2.67/1.52
% 2.67/1.52 % (32255)Memory used [KB]: 1663
% 2.67/1.52 % (32255)Time elapsed: 0.007 s
% 2.67/1.52 % (32255)Instructions burned: 16 (million)
% 2.67/1.52 % (32255)------------------------------
% 2.67/1.52 % (32255)------------------------------
% 2.67/1.52 % (32256)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/3Mi)
% 2.67/1.53 % (32256)Instruction limit reached!
% 2.67/1.53 % (32256)------------------------------
% 2.67/1.53 % (32256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.53 % (32256)Termination reason: Unknown
% 2.67/1.53 % (32256)Termination phase: shuffling
% 2.67/1.53
% 2.67/1.53 % (32256)Memory used [KB]: 1535
% 2.67/1.53 % (32256)Time elapsed: 0.004 s
% 2.67/1.53 % (32256)Instructions burned: 3 (million)
% 2.67/1.53 % (32256)------------------------------
% 2.67/1.53 % (32256)------------------------------
% 2.67/1.53 % (32251)Refutation not found, incomplete strategy
% 2.67/1.53 % (32251)------------------------------
% 2.67/1.53 % (32251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.53 % (32251)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.53
% 2.67/1.53
% 2.67/1.53 % (32251)Memory used [KB]: 6524
% 2.67/1.53 % (32251)Time elapsed: 0.025 s
% 2.67/1.53 % (32251)Instructions burned: 37 (million)
% 2.67/1.53 % (32251)------------------------------
% 2.67/1.53 % (32251)------------------------------
% 2.67/1.53 % (32259)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/16Mi)
% 2.67/1.53 % (32260)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/3Mi)
% 2.67/1.53 % (32260)Instruction limit reached!
% 2.67/1.53 % (32260)------------------------------
% 2.67/1.53 % (32260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.53 % (32260)Termination reason: Unknown
% 2.67/1.53 % (32260)Termination phase: shuffling
% 2.67/1.53
% 2.67/1.53 % (32260)Memory used [KB]: 1407
% 2.67/1.53 % (32260)Time elapsed: 0.002 s
% 2.67/1.53 % (32260)Instructions burned: 3 (million)
% 2.67/1.53 % (32260)------------------------------
% 2.67/1.53 % (32260)------------------------------
% 2.67/1.53 % (32258)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/7Mi)
% 2.67/1.54 % (32261)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/3Mi)
% 2.67/1.54 % (32259)Instruction limit reached!
% 2.67/1.54 % (32259)------------------------------
% 2.67/1.54 % (32259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.54 % (32259)Termination reason: Unknown
% 2.67/1.54 % (32259)Termination phase: Property scanning
% 2.67/1.54
% 2.67/1.54 % (32259)Memory used [KB]: 1791
% 2.67/1.54 % (32259)Time elapsed: 0.008 s
% 2.67/1.54 % (32259)Instructions burned: 18 (million)
% 2.67/1.54 % (32259)------------------------------
% 2.67/1.54 % (32259)------------------------------
% 2.67/1.54 % (32261)Instruction limit reached!
% 2.67/1.54 % (32261)------------------------------
% 2.67/1.54 % (32261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.54 % (32261)Termination reason: Unknown
% 2.67/1.54 % (32261)Termination phase: shuffling
% 2.67/1.54
% 2.67/1.54 % (32261)Memory used [KB]: 1535
% 2.67/1.54 % (32261)Time elapsed: 0.003 s
% 2.67/1.54 % (32261)Instructions burned: 3 (million)
% 2.67/1.54 % (32261)------------------------------
% 2.67/1.54 % (32261)------------------------------
% 2.67/1.54 % (32258)Instruction limit reached!
% 2.67/1.54 % (32258)------------------------------
% 2.67/1.54 % (32258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.54 % (32258)Termination reason: Unknown
% 2.67/1.54 % (32258)Termination phase: shuffling
% 2.67/1.54
% 2.67/1.54 % (32258)Memory used [KB]: 1535
% 2.67/1.54 % (32258)Time elapsed: 0.007 s
% 2.67/1.54 % (32258)Instructions burned: 8 (million)
% 2.67/1.54 % (32258)------------------------------
% 2.67/1.54 % (32258)------------------------------
% 2.67/1.54 % (32263)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/3Mi)
% 2.67/1.54 % (32263)Instruction limit reached!
% 2.67/1.54 % (32263)------------------------------
% 2.67/1.54 % (32263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.54 % (32263)Termination reason: Unknown
% 2.67/1.54 % (32263)Termination phase: shuffling
% 2.67/1.54
% 2.67/1.54 % (32263)Memory used [KB]: 1407
% 2.67/1.54 % (32263)Time elapsed: 0.002 s
% 2.67/1.54 % (32263)Instructions burned: 3 (million)
% 2.67/1.54 % (32263)------------------------------
% 2.67/1.54 % (32263)------------------------------
% 2.67/1.55 % (32262)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/7Mi)
% 2.67/1.55 % (32264)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/4Mi)
% 2.67/1.55 % (32265)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/18Mi)
% 2.67/1.55 % (32264)Instruction limit reached!
% 2.67/1.55 % (32264)------------------------------
% 2.67/1.55 % (32264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.55 % (32264)Termination reason: Unknown
% 2.67/1.55 % (32264)Termination phase: shuffling
% 2.67/1.55
% 2.67/1.55 % (32264)Memory used [KB]: 1535
% 2.67/1.55 % (32264)Time elapsed: 0.004 s
% 2.67/1.55 % (32264)Instructions burned: 6 (million)
% 2.67/1.55 % (32264)------------------------------
% 2.67/1.55 % (32264)------------------------------
% 2.67/1.55 % (32262)Instruction limit reached!
% 2.67/1.55 % (32262)------------------------------
% 2.67/1.55 % (32262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.55 % (32262)Termination reason: Unknown
% 2.67/1.55 % (32262)Termination phase: shuffling
% 2.67/1.55
% 2.67/1.55 % (32262)Memory used [KB]: 1535
% 2.67/1.55 % (32262)Time elapsed: 0.007 s
% 2.67/1.55 % (32262)Instructions burned: 8 (million)
% 2.67/1.55 % (32262)------------------------------
% 2.67/1.55 % (32262)------------------------------
% 2.67/1.55 % (32267)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/6Mi)
% 2.67/1.55 % (32265)Instruction limit reached!
% 2.67/1.55 % (32265)------------------------------
% 2.67/1.55 % (32265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.55 % (32265)Termination reason: Unknown
% 2.67/1.55 % (32265)Termination phase: Property scanning
% 2.67/1.55
% 2.67/1.55 % (32265)Memory used [KB]: 1791
% 2.67/1.55 % (32265)Time elapsed: 0.008 s
% 2.67/1.55 % (32265)Instructions burned: 18 (million)
% 2.67/1.55 % (32265)------------------------------
% 2.67/1.55 % (32265)------------------------------
% 2.67/1.56 % (32267)Instruction limit reached!
% 2.67/1.56 % (32267)------------------------------
% 2.67/1.56 % (32267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.56 % (32267)Termination reason: Unknown
% 2.67/1.56 % (32267)Termination phase: shuffling
% 2.67/1.56
% 2.67/1.56 % (32267)Memory used [KB]: 1535
% 2.67/1.56 % (32267)Time elapsed: 0.003 s
% 2.67/1.56 % (32267)Instructions burned: 6 (million)
% 2.67/1.56 % (32267)------------------------------
% 2.67/1.56 % (32267)------------------------------
% 2.67/1.56 % (32266)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/710Mi)
% 2.67/1.56 % (32268)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/902Mi)
% 2.67/1.56 % (32270)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/5Mi)
% 2.67/1.56 % (32271)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/6Mi)
% 2.67/1.57 % (32271)Instruction limit reached!
% 2.67/1.57 % (32271)------------------------------
% 2.67/1.57 % (32271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.57 % (32271)Termination reason: Unknown
% 2.67/1.57 % (32271)Termination phase: shuffling
% 2.67/1.57
% 2.67/1.57 % (32271)Memory used [KB]: 1535
% 2.67/1.57 % (32271)Time elapsed: 0.003 s
% 2.67/1.57 % (32271)Instructions burned: 7 (million)
% 2.67/1.57 % (32271)------------------------------
% 2.67/1.57 % (32271)------------------------------
% 2.67/1.57 % (32270)Instruction limit reached!
% 2.67/1.57 % (32270)------------------------------
% 2.67/1.57 % (32270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.57 % (32270)Termination reason: Unknown
% 2.67/1.57 % (32270)Termination phase: shuffling
% 2.67/1.57
% 2.67/1.57 % (32270)Memory used [KB]: 1663
% 2.67/1.57 % (32270)Time elapsed: 0.004 s
% 2.67/1.57 % (32270)Instructions burned: 7 (million)
% 2.67/1.57 % (32270)------------------------------
% 2.67/1.57 % (32270)------------------------------
% 2.67/1.57 % (32269)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/21Mi)
% 2.67/1.58 % (32272)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/377Mi)
% 2.67/1.58 % (32246)Instruction limit reached!
% 2.67/1.58 % (32246)------------------------------
% 2.67/1.58 % (32246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.58 % (32246)Termination reason: Unknown
% 2.67/1.58 % (32246)Termination phase: Saturation
% 2.67/1.58
% 2.67/1.58 % (32246)Memory used [KB]: 7164
% 2.67/1.58 % (32246)Time elapsed: 0.073 s
% 2.67/1.58 % (32246)Instructions burned: 184 (million)
% 2.67/1.58 % (32246)------------------------------
% 2.67/1.58 % (32246)------------------------------
% 2.67/1.58 % (32273)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/779Mi)
% 2.67/1.58 % (32269)Instruction limit reached!
% 2.67/1.58 % (32269)------------------------------
% 2.67/1.58 % (32269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.58 % (32269)Termination reason: Unknown
% 2.67/1.58 % (32269)Termination phase: Property scanning
% 2.67/1.58
% 2.67/1.58 % (32269)Memory used [KB]: 1918
% 2.67/1.58 % (32269)Time elapsed: 0.015 s
% 2.67/1.58 % (32269)Instructions burned: 22 (million)
% 2.67/1.58 % (32269)------------------------------
% 2.67/1.58 % (32269)------------------------------
% 2.67/1.59 % (32274)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/19Mi)
% 2.67/1.59 % (32274)Instruction limit reached!
% 2.67/1.59 % (32274)------------------------------
% 2.67/1.59 % (32274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.59 % (32274)Termination reason: Unknown
% 2.67/1.59 % (32274)Termination phase: shuffling
% 2.67/1.59
% 2.67/1.59 % (32274)Memory used [KB]: 1791
% 2.67/1.59 % (32274)Time elapsed: 0.008 s
% 2.67/1.59 % (32274)Instructions burned: 20 (million)
% 2.67/1.59 % (32274)------------------------------
% 2.67/1.59 % (32274)------------------------------
% 2.67/1.60 % (32275)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_32018 for (2999ds/879Mi)
% 2.67/1.60 % (32276)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_32018 for (2998ds/17Mi)
% 2.67/1.61 % (32276)Instruction limit reached!
% 2.67/1.61 % (32276)------------------------------
% 2.67/1.61 % (32276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.61 % (32276)Termination reason: Unknown
% 2.67/1.61 % (32276)Termination phase: Property scanning
% 2.67/1.61
% 2.67/1.61 % (32276)Memory used [KB]: 1791
% 2.67/1.61 % (32276)Time elapsed: 0.008 s
% 2.67/1.61 % (32276)Instructions burned: 18 (million)
% 2.67/1.61 % (32276)------------------------------
% 2.67/1.61 % (32276)------------------------------
% 2.67/1.62 % (32277)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_32018 for (2998ds/3Mi)
% 2.67/1.62 % (32277)Instruction limit reached!
% 2.67/1.62 % (32277)------------------------------
% 2.67/1.62 % (32277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.62 % (32277)Termination reason: Unknown
% 2.67/1.62 % (32277)Termination phase: shuffling
% 2.67/1.62
% 2.67/1.62 % (32277)Memory used [KB]: 1535
% 2.67/1.62 % (32277)Time elapsed: 0.003 s
% 2.67/1.62 % (32277)Instructions burned: 4 (million)
% 2.67/1.62 % (32277)------------------------------
% 2.67/1.62 % (32277)------------------------------
% 2.67/1.63 % (32278)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_32018 for (2998ds/30Mi)
% 2.67/1.64 % (32278)Instruction limit reached!
% 2.67/1.64 % (32278)------------------------------
% 2.67/1.64 % (32278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.64 % (32278)Termination reason: Unknown
% 2.67/1.64 % (32278)Termination phase: Preprocessing 1
% 2.67/1.64
% 2.67/1.64 % (32278)Memory used [KB]: 1918
% 2.67/1.64 % (32278)Time elapsed: 0.012 s
% 2.67/1.64 % (32278)Instructions burned: 30 (million)
% 2.67/1.64 % (32278)------------------------------
% 2.67/1.64 % (32278)------------------------------
% 2.67/1.65 % (32279)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_32018 for (2998ds/127Mi)
% 2.67/1.69 % (32279)Instruction limit reached!
% 2.67/1.69 % (32279)------------------------------
% 2.67/1.69 % (32279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.69 % (32279)Termination reason: Unknown
% 2.67/1.69 % (32279)Termination phase: Saturation
% 2.67/1.69
% 2.67/1.69 % (32279)Memory used [KB]: 7036
% 2.67/1.69 % (32279)Time elapsed: 0.045 s
% 2.67/1.69 % (32279)Instructions burned: 127 (million)
% 2.67/1.69 % (32279)------------------------------
% 2.67/1.69 % (32279)------------------------------
% 2.67/1.70 % (32272)Instruction limit reached!
% 2.67/1.70 % (32272)------------------------------
% 2.67/1.70 % (32272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.70 % (32272)Termination reason: Unknown
% 2.67/1.70 % (32272)Termination phase: Saturation
% 2.67/1.70
% 2.67/1.70 % (32272)Memory used [KB]: 7803
% 2.67/1.70 % (32272)Time elapsed: 0.143 s
% 2.67/1.70 % (32272)Instructions burned: 377 (million)
% 2.67/1.70 % (32272)------------------------------
% 2.67/1.70 % (32272)------------------------------
% 2.67/1.70 % (32280)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_32018 for (2997ds/100Mi)
% 2.67/1.71 % (32281)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_32018 for (2997ds/3Mi)
% 2.67/1.71 % (32281)Instruction limit reached!
% 2.67/1.71 % (32281)------------------------------
% 2.67/1.71 % (32281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.71 % (32281)Termination reason: Unknown
% 2.67/1.71 % (32281)Termination phase: shuffling
% 2.67/1.71
% 2.67/1.71 % (32281)Memory used [KB]: 1407
% 2.67/1.71 % (32281)Time elapsed: 0.002 s
% 2.67/1.71 % (32281)Instructions burned: 4 (million)
% 2.67/1.71 % (32281)------------------------------
% 2.67/1.71 % (32281)------------------------------
% 2.67/1.72 % (32282)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_32018 for (2997ds/20Mi)
% 2.67/1.72 % (32282)Instruction limit reached!
% 2.67/1.72 % (32282)------------------------------
% 2.67/1.72 % (32282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.72 % (32282)Termination reason: Unknown
% 2.67/1.72 % (32282)Termination phase: Property scanning
% 2.67/1.72
% 2.67/1.72 % (32282)Memory used [KB]: 1663
% 2.67/1.72 % (32282)Time elapsed: 0.008 s
% 2.67/1.72 % (32282)Instructions burned: 21 (million)
% 2.67/1.72 % (32282)------------------------------
% 2.67/1.72 % (32282)------------------------------
% 2.67/1.73 % (32283)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_32018 for (2997ds/86Mi)
% 2.67/1.74 % (32280)Instruction limit reached!
% 2.67/1.74 % (32280)------------------------------
% 2.67/1.74 % (32280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.74 % (32280)Termination reason: Unknown
% 2.67/1.74 % (32280)Termination phase: Property scanning
% 2.67/1.74
% 2.67/1.74 % (32280)Memory used [KB]: 2302
% 2.67/1.74 % (32280)Time elapsed: 0.032 s
% 2.67/1.74 % (32280)Instructions burned: 103 (million)
% 2.67/1.74 % (32280)------------------------------
% 2.67/1.74 % (32280)------------------------------
% 2.67/1.75 % (32284)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_32018 for (2997ds/107Mi)
% 2.67/1.76 % (32283)Instruction limit reached!
% 2.67/1.76 % (32283)------------------------------
% 2.67/1.76 % (32283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.76 % (32283)Termination reason: Unknown
% 2.67/1.76 % (32283)Termination phase: Saturation
% 2.67/1.76
% 2.67/1.76 % (32283)Memory used [KB]: 6780
% 2.67/1.76 % (32283)Time elapsed: 0.027 s
% 2.67/1.76 % (32283)Instructions burned: 88 (million)
% 2.67/1.76 % (32283)------------------------------
% 2.67/1.76 % (32283)------------------------------
% 2.67/1.77 % (32285)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_32018 for (2997ds/39Mi)
% 2.67/1.78 % (32285)Instruction limit reached!
% 2.67/1.78 % (32285)------------------------------
% 2.67/1.78 % (32285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.78 % (32285)Termination reason: Unknown
% 2.67/1.78 % (32285)Termination phase: Property scanning
% 2.67/1.78
% 2.67/1.78 % (32285)Memory used [KB]: 2174
% 2.67/1.78 % (32285)Time elapsed: 0.012 s
% 2.67/1.78 % (32285)Instructions burned: 40 (million)
% 2.67/1.78 % (32285)------------------------------
% 2.67/1.78 % (32285)------------------------------
% 2.67/1.78 % (32284)Instruction limit reached!
% 2.67/1.78 % (32284)------------------------------
% 2.67/1.78 % (32284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.78 % (32284)Termination reason: Unknown
% 2.67/1.78 % (32284)Termination phase: Saturation
% 2.67/1.78
% 2.67/1.78 % (32284)Memory used [KB]: 6780
% 2.67/1.78 % (32284)Time elapsed: 0.038 s
% 2.67/1.78 % (32284)Instructions burned: 108 (million)
% 2.67/1.78 % (32284)------------------------------
% 2.67/1.78 % (32284)------------------------------
% 2.67/1.79 % (32286)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_32018 for (2996ds/448Mi)
% 2.67/1.79 % (32287)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_32018 for (2996ds/46Mi)
% 2.67/1.81 % (32287)Instruction limit reached!
% 2.67/1.81 % (32287)------------------------------
% 2.67/1.81 % (32287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.81 % (32287)Termination reason: Unknown
% 2.67/1.81 % (32287)Termination phase: Property scanning
% 2.67/1.81
% 2.67/1.81 % (32287)Memory used [KB]: 2046
% 2.67/1.81 % (32287)Time elapsed: 0.016 s
% 2.67/1.81 % (32287)Instructions burned: 48 (million)
% 2.67/1.81 % (32287)------------------------------
% 2.67/1.81 % (32287)------------------------------
% 2.67/1.81 % (32266)Instruction limit reached!
% 2.67/1.81 % (32266)------------------------------
% 2.67/1.81 % (32266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.81 % (32266)Termination reason: Unknown
% 2.67/1.81 % (32266)Termination phase: Saturation
% 2.67/1.81
% 2.67/1.81 % (32266)Memory used [KB]: 7931
% 2.67/1.81 % (32266)Time elapsed: 0.254 s
% 2.67/1.81 % (32266)Instructions burned: 710 (million)
% 2.67/1.81 % (32266)------------------------------
% 2.67/1.81 % (32266)------------------------------
% 2.67/1.82 % (32288)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_32018 for (2996ds/98Mi)
% 2.67/1.82 % (32289)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_32018 for (2996ds/507Mi)
% 2.67/1.84 % (32268)Instruction limit reached!
% 2.67/1.84 % (32268)------------------------------
% 2.67/1.84 % (32268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.84 % (32268)Termination reason: Unknown
% 2.67/1.84 % (32268)Termination phase: Saturation
% 2.67/1.84
% 2.67/1.84 % (32268)Memory used [KB]: 8059
% 2.67/1.84 % (32268)Time elapsed: 0.277 s
% 2.67/1.84 % (32268)Instructions burned: 904 (million)
% 2.67/1.84 % (32268)------------------------------
% 2.67/1.84 % (32268)------------------------------
% 2.67/1.84 % (32257)Instruction limit reached!
% 2.67/1.84 % (32257)------------------------------
% 2.67/1.84 % (32257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.84 % (32257)Termination reason: Unknown
% 2.67/1.84 % (32257)Termination phase: Saturation
% 2.67/1.84
% 2.67/1.84 % (32257)Memory used [KB]: 9210
% 2.67/1.84 % (32257)Time elapsed: 0.321 s
% 2.67/1.84 % (32257)Instructions burned: 1042 (million)
% 2.67/1.84 % (32257)------------------------------
% 2.67/1.84 % (32257)------------------------------
% 2.67/1.84 % (32273)Instruction limit reached!
% 2.67/1.84 % (32273)------------------------------
% 2.67/1.84 % (32273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.84 % (32273)Termination reason: Unknown
% 2.67/1.84 % (32273)Termination phase: Saturation
% 2.67/1.84
% 2.67/1.84 % (32273)Memory used [KB]: 7419
% 2.67/1.84 % (32273)Time elapsed: 0.288 s
% 2.67/1.84 % (32273)Instructions burned: 779 (million)
% 2.67/1.84 % (32273)------------------------------
% 2.67/1.84 % (32273)------------------------------
% 2.67/1.84 % (32288)Instruction limit reached!
% 2.67/1.84 % (32288)------------------------------
% 2.67/1.84 % (32288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.84 % (32288)Termination reason: Unknown
% 2.67/1.84 % (32288)Termination phase: Property scanning
% 2.67/1.84
% 2.67/1.84 % (32288)Memory used [KB]: 2302
% 2.67/1.84 % (32288)Time elapsed: 0.028 s
% 2.67/1.84 % (32288)Instructions burned: 99 (million)
% 2.67/1.84 % (32288)------------------------------
% 2.67/1.84 % (32288)------------------------------
% 2.67/1.85 % (32290)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_32018 for (2996ds/149Mi)
% 2.67/1.85 % (32291)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_32018 for (2996ds/39Mi)
% 2.67/1.85 % (32293)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_32018 for (2996ds/1087Mi)
% 2.67/1.85 % (32292)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_32018 for (2996ds/6Mi)
% 2.67/1.85 % (32292)Instruction limit reached!
% 2.67/1.85 % (32292)------------------------------
% 2.67/1.85 % (32292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.85 % (32292)Termination reason: Unknown
% 2.67/1.85 % (32292)Termination phase: shuffling
% 2.67/1.85
% 2.67/1.85 % (32292)Memory used [KB]: 1535
% 2.67/1.85 % (32292)Time elapsed: 0.004 s
% 2.67/1.85 % (32292)Instructions burned: 7 (million)
% 2.67/1.85 % (32292)------------------------------
% 2.67/1.85 % (32292)------------------------------
% 2.67/1.86 % (32291)Instruction limit reached!
% 2.67/1.86 % (32291)------------------------------
% 2.67/1.86 % (32291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.86 % (32291)Termination reason: Unknown
% 2.67/1.86 % (32291)Termination phase: Property scanning
% 2.67/1.86
% 2.67/1.86 % (32291)Memory used [KB]: 2046
% 2.67/1.86 % (32291)Time elapsed: 0.014 s
% 2.67/1.86 % (32291)Instructions burned: 42 (million)
% 2.67/1.86 % (32291)------------------------------
% 2.67/1.86 % (32291)------------------------------
% 2.67/1.86 % (32294)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_32018 for (2996ds/47Mi)
% 2.67/1.87 % (32295)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_32018 for (2996ds/44Mi)
% 2.67/1.88 % (32294)Instruction limit reached!
% 2.67/1.88 % (32294)------------------------------
% 2.67/1.88 % (32294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.88 % (32294)Termination reason: Unknown
% 2.67/1.88 % (32294)Termination phase: Function definition elimination
% 2.67/1.88
% 2.67/1.88 % (32294)Memory used [KB]: 2046
% 2.67/1.88 % (32294)Time elapsed: 0.017 s
% 2.67/1.88 % (32294)Instructions burned: 47 (million)
% 2.67/1.88 % (32294)------------------------------
% 2.67/1.88 % (32294)------------------------------
% 2.67/1.88 % (32295)Instruction limit reached!
% 2.67/1.88 % (32295)------------------------------
% 2.67/1.88 % (32295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.88 % (32295)Termination reason: Unknown
% 2.67/1.88 % (32295)Termination phase: Property scanning
% 2.67/1.88
% 2.67/1.88 % (32295)Memory used [KB]: 2174
% 2.67/1.88 % (32295)Time elapsed: 0.013 s
% 2.67/1.88 % (32295)Instructions burned: 44 (million)
% 2.67/1.88 % (32295)------------------------------
% 2.67/1.88 % (32295)------------------------------
% 2.67/1.89 % (32275)Instruction limit reached!
% 2.67/1.89 % (32275)------------------------------
% 2.67/1.89 % (32275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.89 % (32275)Termination reason: Unknown
% 2.67/1.89 % (32275)Termination phase: Saturation
% 2.67/1.89
% 2.67/1.89 % (32275)Memory used [KB]: 8059
% 2.67/1.89 % (32275)Time elapsed: 0.311 s
% 2.67/1.89 % (32275)Instructions burned: 880 (million)
% 2.67/1.89 % (32275)------------------------------
% 2.67/1.89 % (32275)------------------------------
% 2.67/1.89 % (32296)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_32018 for (2995ds/432Mi)
% 2.67/1.89 % (32290)Instruction limit reached!
% 2.67/1.89 % (32290)------------------------------
% 2.67/1.89 % (32290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.89 % (32290)Termination reason: Unknown
% 2.67/1.89 % (32290)Termination phase: Saturation
% 2.67/1.89
% 2.67/1.89 % (32290)Memory used [KB]: 7164
% 2.67/1.89 % (32290)Time elapsed: 0.047 s
% 2.67/1.89 % (32290)Instructions burned: 150 (million)
% 2.67/1.89 % (32290)------------------------------
% 2.67/1.89 % (32290)------------------------------
% 2.67/1.89 % (32297)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_32018 for (2995ds/62Mi)
% 2.67/1.90 % (32298)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_32018 for (2995ds/31Mi)
% 2.67/1.90 % (32299)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_32018 for (2995ds/96Mi)
% 2.67/1.91 % (32298)Instruction limit reached!
% 2.67/1.91 % (32298)------------------------------
% 2.67/1.91 % (32298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.91 % (32298)Termination reason: Unknown
% 2.67/1.91 % (32298)Termination phase: Preprocessing 3
% 2.67/1.91
% 2.67/1.91 % (32298)Memory used [KB]: 1918
% 2.67/1.91 % (32298)Time elapsed: 0.013 s
% 2.67/1.91 % (32298)Instructions burned: 33 (million)
% 2.67/1.91 % (32298)------------------------------
% 2.67/1.91 % (32298)------------------------------
% 2.67/1.91 % (32297)Instruction limit reached!
% 2.67/1.91 % (32297)------------------------------
% 2.67/1.91 % (32297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.91 % (32297)Termination reason: Unknown
% 2.67/1.91 % (32297)Termination phase: Property scanning
% 2.67/1.91
% 2.67/1.91 % (32297)Memory used [KB]: 2302
% 2.67/1.91 % (32297)Time elapsed: 0.018 s
% 2.67/1.91 % (32297)Instructions burned: 62 (million)
% 2.67/1.91 % (32297)------------------------------
% 2.67/1.91 % (32297)------------------------------
% 2.67/1.92 % (32300)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_32018 for (2995ds/453Mi)
% 2.67/1.92 % (32301)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_32018 for (2995ds/71Mi)
% 2.67/1.92 % (32286)Instruction limit reached!
% 2.67/1.92 % (32286)------------------------------
% 2.67/1.92 % (32286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.92 % (32286)Termination reason: Unknown
% 2.67/1.92 % (32286)Termination phase: Saturation
% 2.67/1.92
% 2.67/1.92 % (32286)Memory used [KB]: 7547
% 2.67/1.92 % (32286)Time elapsed: 0.134 s
% 2.67/1.92 % (32286)Instructions burned: 448 (million)
% 2.67/1.92 % (32286)------------------------------
% 2.67/1.92 % (32286)------------------------------
% 2.67/1.93 % (32299)Instruction limit reached!
% 2.67/1.93 % (32299)------------------------------
% 2.67/1.93 % (32299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.93 % (32299)Termination reason: Unknown
% 2.67/1.93 % (32299)Termination phase: Saturation
% 2.67/1.93
% 2.67/1.93 % (32299)Memory used [KB]: 6780
% 2.67/1.93 % (32299)Time elapsed: 0.030 s
% 2.67/1.93 % (32299)Instructions burned: 96 (million)
% 2.67/1.93 % (32299)------------------------------
% 2.67/1.93 % (32299)------------------------------
% 2.67/1.93 % (32302)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_32018 for (2995ds/83Mi)
% 2.67/1.94 % (32303)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_32018 for (2995ds/11Mi)
% 2.67/1.94 % (32301)Instruction limit reached!
% 2.67/1.94 % (32301)------------------------------
% 2.67/1.94 % (32301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.94 % (32301)Termination reason: Unknown
% 2.67/1.94 % (32301)Termination phase: Saturation
% 2.67/1.94
% 2.67/1.94 % (32301)Memory used [KB]: 6652
% 2.67/1.94 % (32301)Time elapsed: 0.022 s
% 2.67/1.94 % (32301)Instructions burned: 71 (million)
% 2.67/1.94 % (32301)------------------------------
% 2.67/1.94 % (32301)------------------------------
% 2.67/1.94 % (32303)Instruction limit reached!
% 2.67/1.94 % (32303)------------------------------
% 2.67/1.94 % (32303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.94 % (32303)Termination reason: Unknown
% 2.67/1.94 % (32303)Termination phase: shuffling
% 2.67/1.94
% 2.67/1.94 % (32303)Memory used [KB]: 1663
% 2.67/1.94 % (32303)Time elapsed: 0.005 s
% 2.67/1.94 % (32303)Instructions burned: 13 (million)
% 2.67/1.94 % (32303)------------------------------
% 2.67/1.94 % (32303)------------------------------
% 2.67/1.95 % (32304)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_32018 for (2995ds/41Mi)
% 2.67/1.95 % (32305)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32018 for (2995ds/6Mi)
% 2.67/1.95 % (32305)Instruction limit reached!
% 2.67/1.95 % (32305)------------------------------
% 2.67/1.95 % (32305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.95 % (32305)Termination reason: Unknown
% 2.67/1.95 % (32305)Termination phase: shuffling
% 2.67/1.95
% 2.67/1.95 % (32305)Memory used [KB]: 1535
% 2.67/1.95 % (32305)Time elapsed: 0.003 s
% 2.67/1.95 % (32305)Instructions burned: 7 (million)
% 2.67/1.95 % (32305)------------------------------
% 2.67/1.95 % (32305)------------------------------
% 2.67/1.96 % (32302)Instruction limit reached!
% 2.67/1.96 % (32302)------------------------------
% 2.67/1.96 % (32302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.96 % (32302)Termination reason: Unknown
% 2.67/1.96 % (32302)Termination phase: Saturation
% 2.67/1.96
% 2.67/1.96 % (32302)Memory used [KB]: 6524
% 2.67/1.96 % (32302)Time elapsed: 0.028 s
% 2.67/1.96 % (32302)Instructions burned: 84 (million)
% 2.67/1.96 % (32302)------------------------------
% 2.67/1.96 % (32302)------------------------------
% 2.67/1.96 % (32304)Instruction limit reached!
% 2.67/1.96 % (32304)------------------------------
% 2.67/1.96 % (32304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.96 % (32304)Termination reason: Unknown
% 2.67/1.96 % (32304)Termination phase: Property scanning
% 2.67/1.96
% 2.67/1.96 % (32304)Memory used [KB]: 2174
% 2.67/1.96 % (32304)Time elapsed: 0.013 s
% 2.67/1.96 % (32304)Instructions burned: 44 (million)
% 2.67/1.96 % (32304)------------------------------
% 2.67/1.96 % (32304)------------------------------
% 2.67/1.96 % (32306)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_32018 for (2995ds/150Mi)
% 2.67/1.97 % (32307)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_32018 for (2995ds/343Mi)
% 2.67/1.97 % (32308)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_32018 for (2995ds/109Mi)
% 2.67/1.98 % (32289)Instruction limit reached!
% 2.67/1.98 % (32289)------------------------------
% 2.67/1.98 % (32289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.98 % (32289)Termination reason: Unknown
% 2.67/1.98 % (32289)Termination phase: Saturation
% 2.67/1.98
% 2.67/1.98 % (32289)Memory used [KB]: 8443
% 2.67/1.98 % (32289)Time elapsed: 0.166 s
% 2.67/1.98 % (32289)Instructions burned: 507 (million)
% 2.67/1.98 % (32289)------------------------------
% 2.67/1.98 % (32289)------------------------------
% 2.67/1.99 % (32309)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_32018 for (2994ds/253Mi)
% 2.67/2.01 % (32308)Instruction limit reached!
% 2.67/2.01 % (32308)------------------------------
% 2.67/2.01 % (32308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/2.01 % (32308)Termination reason: Unknown
% 2.67/2.01 % (32308)Termination phase: Saturation
% 2.67/2.01
% 2.67/2.01 % (32308)Memory used [KB]: 6908
% 2.67/2.01 % (32308)Time elapsed: 0.035 s
% 2.67/2.01 % (32308)Instructions burned: 111 (million)
% 2.67/2.01 % (32308)------------------------------
% 2.67/2.01 % (32308)------------------------------
% 2.67/2.01 % (32309)Refutation not found, incomplete strategy
% 2.67/2.01 % (32309)------------------------------
% 2.67/2.01 % (32309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/2.01 % (32309)Termination reason: Refutation not found, incomplete strategy
% 2.67/2.01
% 2.67/2.01
% 2.67/2.01 % (32309)Memory used [KB]: 6524
% 2.67/2.01 % (32309)Time elapsed: 0.014 s
% 2.67/2.01 % (32309)Instructions burned: 41 (million)
% 2.67/2.01 % (32309)------------------------------
% 2.67/2.01 % (32309)------------------------------
% 2.67/2.01 % (32306)Instruction limit reached!
% 2.67/2.01 % (32306)------------------------------
% 2.67/2.01 % (32306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/2.01 % (32306)Termination reason: Unknown
% 2.67/2.01 % (32306)Termination phase: Saturation
% 2.67/2.01
% 2.67/2.01 % (32306)Memory used [KB]: 7291
% 2.67/2.01 % (32306)Time elapsed: 0.046 s
% 2.67/2.01 % (32306)Instructions burned: 150 (million)
% 2.67/2.01 % (32306)------------------------------
% 2.67/2.01 % (32306)------------------------------
% 2.67/2.01 % (32311)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_32018 for (2994ds/140Mi)
% 2.67/2.02 % (32312)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_32018 for (2994ds/614Mi)
% 2.67/2.02 % (32313)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_32018 for (2994ds/202Mi)
% 6.35/2.02 % (32296)Instruction limit reached!
% 6.35/2.02 % (32296)------------------------------
% 6.35/2.02 % (32296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.35/2.02 % (32296)Termination reason: Unknown
% 6.35/2.02 % (32296)Termination phase: Saturation
% 6.35/2.02
% 6.35/2.02 % (32296)Memory used [KB]: 3965
% 6.35/2.02 % (32296)Time elapsed: 0.135 s
% 6.35/2.02 % (32296)Instructions burned: 432 (million)
% 6.35/2.02 % (32296)------------------------------
% 6.35/2.02 % (32296)------------------------------
% 6.35/2.03 % (32314)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_32018 for (2994ds/339Mi)
% 6.35/2.05 % (32300)Instruction limit reached!
% 6.35/2.05 % (32300)------------------------------
% 6.35/2.05 % (32300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.35/2.05 % (32300)Termination reason: Unknown
% 6.35/2.05 % (32300)Termination phase: Saturation
% 6.35/2.05
% 6.35/2.05 % (32300)Memory used [KB]: 8059
% 6.35/2.05 % (32300)Time elapsed: 0.139 s
% 6.35/2.05 % (32300)Instructions burned: 454 (million)
% 6.35/2.05 % (32300)------------------------------
% 6.35/2.05 % (32300)------------------------------
% 6.35/2.06 % (32311)Instruction limit reached!
% 6.35/2.06 % (32311)------------------------------
% 6.35/2.06 % (32311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.35/2.06 % (32311)Termination reason: Unknown
% 6.35/2.06 % (32311)Termination phase: Saturation
% 6.35/2.06
% 6.35/2.06 % (32311)Memory used [KB]: 7036
% 6.35/2.06 % (32311)Time elapsed: 0.046 s
% 6.35/2.06 % (32311)Instructions burned: 142 (million)
% 6.35/2.06 % (32311)------------------------------
% 6.35/2.06 % (32311)------------------------------
% 6.35/2.06 % (32315)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_32018 for (2994ds/283Mi)
% 6.35/2.07 % (32316)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_32018 for (2994ds/134Mi)
% 6.35/2.08 % (32307)Instruction limit reached!
% 6.35/2.08 % (32307)------------------------------
% 6.35/2.08 % (32307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.35/2.08 % (32307)Termination reason: Unknown
% 6.35/2.08 % (32307)Termination phase: Saturation
% 6.35/2.08
% 6.35/2.08 % (32307)Memory used [KB]: 7675
% 6.35/2.08 % (32307)Time elapsed: 0.109 s
% 6.35/2.08 % (32307)Instructions burned: 344 (million)
% 6.35/2.08 % (32307)------------------------------
% 6.35/2.08 % (32307)------------------------------
% 6.35/2.08 % (32313)Instruction limit reached!
% 6.35/2.08 % (32313)------------------------------
% 6.35/2.08 % (32313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.35/2.08 % (32313)Termination reason: Unknown
% 6.35/2.08 % (32313)Termination phase: Saturation
% 6.35/2.08
% 6.35/2.08 % (32313)Memory used [KB]: 6652
% 6.35/2.08 % (32313)Time elapsed: 0.064 s
% 6.35/2.08 % (32313)Instructions burned: 202 (million)
% 6.35/2.08 % (32313)------------------------------
% 6.35/2.08 % (32313)------------------------------
% 6.35/2.09 % (32317)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_32018 for (2993ds/298Mi)
% 6.35/2.09 % (32318)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_32018 for (2993ds/192Mi)
% 6.35/2.11 % (32316)Instruction limit reached!
% 6.35/2.11 % (32316)------------------------------
% 6.35/2.11 % (32316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.35/2.11 % (32316)Termination reason: Unknown
% 6.35/2.11 % (32316)Termination phase: Saturation
% 6.35/2.11
% 6.35/2.11 % (32316)Memory used [KB]: 7164
% 6.35/2.11 % (32316)Time elapsed: 0.043 s
% 6.35/2.11 % (32316)Instructions burned: 137 (million)
% 6.35/2.11 % (32316)------------------------------
% 6.35/2.11 % (32316)------------------------------
% 6.35/2.12 % (32319)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_32018 for (2993ds/258Mi)
% 6.73/2.13 % (32314)Instruction limit reached!
% 6.73/2.13 % (32314)------------------------------
% 6.73/2.13 % (32314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.13 % (32314)Termination reason: Unknown
% 6.73/2.13 % (32314)Termination phase: Saturation
% 6.73/2.13
% 6.73/2.13 % (32314)Memory used [KB]: 7291
% 6.73/2.13 % (32314)Time elapsed: 0.100 s
% 6.73/2.13 % (32314)Instructions burned: 340 (million)
% 6.73/2.13 % (32314)------------------------------
% 6.73/2.13 % (32314)------------------------------
% 6.73/2.14 % (32320)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_32018 for (2993ds/90Mi)
% 6.73/2.15 % (32318)Instruction limit reached!
% 6.73/2.15 % (32318)------------------------------
% 6.73/2.15 % (32318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.15 % (32318)Termination reason: Unknown
% 6.73/2.15 % (32318)Termination phase: Saturation
% 6.73/2.15
% 6.73/2.15 % (32318)Memory used [KB]: 7931
% 6.73/2.15 % (32318)Time elapsed: 0.060 s
% 6.73/2.15 % (32318)Instructions burned: 193 (million)
% 6.73/2.15 % (32318)------------------------------
% 6.73/2.15 % (32318)------------------------------
% 6.73/2.15 % (32315)Instruction limit reached!
% 6.73/2.15 % (32315)------------------------------
% 6.73/2.15 % (32315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.15 % (32315)Termination reason: Unknown
% 6.73/2.15 % (32315)Termination phase: Saturation
% 6.73/2.15
% 6.73/2.15 % (32315)Memory used [KB]: 7675
% 6.73/2.15 % (32315)Time elapsed: 0.090 s
% 6.73/2.15 % (32315)Instructions burned: 285 (million)
% 6.73/2.15 % (32315)------------------------------
% 6.73/2.15 % (32315)------------------------------
% 6.73/2.16 % (32321)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_32018 for (2993ds/231Mi)
% 6.73/2.16 % (32322)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_32018 for (2993ds/458Mi)
% 6.73/2.17 % (32320)Instruction limit reached!
% 6.73/2.17 % (32320)------------------------------
% 6.73/2.17 % (32320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.17 % (32320)Termination reason: Unknown
% 6.73/2.17 % (32320)Termination phase: Saturation
% 6.73/2.17
% 6.73/2.17 % (32320)Memory used [KB]: 6780
% 6.73/2.17 % (32320)Time elapsed: 0.028 s
% 6.73/2.17 % (32320)Instructions burned: 90 (million)
% 6.73/2.17 % (32320)------------------------------
% 6.73/2.17 % (32320)------------------------------
% 6.73/2.17 % (32317)Instruction limit reached!
% 6.73/2.17 % (32317)------------------------------
% 6.73/2.17 % (32317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.17 % (32317)Termination reason: Unknown
% 6.73/2.17 % (32317)Termination phase: Saturation
% 6.73/2.17
% 6.73/2.17 % (32317)Memory used [KB]: 8059
% 6.73/2.17 % (32317)Time elapsed: 0.088 s
% 6.73/2.17 % (32317)Instructions burned: 298 (million)
% 6.73/2.17 % (32317)------------------------------
% 6.73/2.17 % (32317)------------------------------
% 6.73/2.18 % (32323)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_32018 for (2993ds/31Mi)
% 6.73/2.18 % (32324)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_32018 for (2993ds/297Mi)
% 6.73/2.19 % (32323)Instruction limit reached!
% 6.73/2.19 % (32323)------------------------------
% 6.73/2.19 % (32323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.19 % (32323)Termination reason: Unknown
% 6.73/2.19 % (32323)Termination phase: Preprocessing 3
% 6.73/2.19
% 6.73/2.19 % (32323)Memory used [KB]: 1918
% 6.73/2.19 % (32323)Time elapsed: 0.011 s
% 6.73/2.19 % (32323)Instructions burned: 32 (million)
% 6.73/2.19 % (32323)------------------------------
% 6.73/2.19 % (32323)------------------------------
% 6.73/2.19 % (32293)Instruction limit reached!
% 6.73/2.19 % (32293)------------------------------
% 6.73/2.19 % (32293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.19 % (32293)Termination reason: Unknown
% 6.73/2.19 % (32293)Termination phase: Saturation
% 6.73/2.19
% 6.73/2.19 % (32293)Memory used [KB]: 7675
% 6.73/2.19 % (32293)Time elapsed: 0.342 s
% 6.73/2.19 % (32293)Instructions burned: 1088 (million)
% 6.73/2.19 % (32293)------------------------------
% 6.73/2.19 % (32293)------------------------------
% 7.24/2.20 % (32325)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_32018 for (2992ds/987Mi)
% 7.24/2.20 % (32319)Instruction limit reached!
% 7.24/2.20 % (32319)------------------------------
% 7.24/2.20 % (32319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.20 % (32319)Termination reason: Unknown
% 7.24/2.20 % (32319)Termination phase: Saturation
% 7.24/2.20
% 7.24/2.20 % (32319)Memory used [KB]: 7547
% 7.24/2.20 % (32319)Time elapsed: 0.079 s
% 7.24/2.20 % (32319)Instructions burned: 258 (million)
% 7.24/2.20 % (32319)------------------------------
% 7.24/2.20 % (32319)------------------------------
% 7.24/2.20 % (32312)Instruction limit reached!
% 7.24/2.20 % (32312)------------------------------
% 7.24/2.20 % (32312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.20 % (32312)Termination reason: Unknown
% 7.24/2.20 % (32312)Termination phase: Saturation
% 7.24/2.20
% 7.24/2.20 % (32312)Memory used [KB]: 9083
% 7.24/2.20 % (32312)Time elapsed: 0.184 s
% 7.24/2.20 % (32312)Instructions burned: 616 (million)
% 7.24/2.20 % (32312)------------------------------
% 7.24/2.20 % (32312)------------------------------
% 7.24/2.20 % (32326)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_32018 for (2992ds/182Mi)
% 7.24/2.21 % (32327)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_32018 for (2992ds/182Mi)
% 7.24/2.21 % (32328)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_32018 for (2992ds/154Mi)
% 7.24/2.22 % (32321)Instruction limit reached!
% 7.24/2.22 % (32321)------------------------------
% 7.24/2.22 % (32321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.22 % (32321)Termination reason: Unknown
% 7.24/2.22 % (32321)Termination phase: Saturation
% 7.24/2.22
% 7.24/2.22 % (32321)Memory used [KB]: 7291
% 7.24/2.22 % (32321)Time elapsed: 0.066 s
% 7.24/2.22 % (32321)Instructions burned: 231 (million)
% 7.24/2.22 % (32321)------------------------------
% 7.24/2.22 % (32321)------------------------------
% 7.24/2.23 % (32329)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_32018 for (2992ds/79Mi)
% 7.24/2.25 % (32328)Instruction limit reached!
% 7.24/2.25 % (32328)------------------------------
% 7.24/2.25 % (32328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.25 % (32328)Termination reason: Unknown
% 7.24/2.25 % (32328)Termination phase: Saturation
% 7.24/2.25
% 7.24/2.25 % (32328)Memory used [KB]: 2942
% 7.24/2.25 % (32328)Time elapsed: 0.045 s
% 7.24/2.25 % (32328)Instructions burned: 154 (million)
% 7.24/2.25 % (32328)------------------------------
% 7.24/2.25 % (32328)------------------------------
% 7.24/2.26 % (32329)Instruction limit reached!
% 7.24/2.26 % (32329)------------------------------
% 7.24/2.26 % (32329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.26 % (32329)Termination reason: Unknown
% 7.24/2.26 % (32329)Termination phase: Saturation
% 7.24/2.26
% 7.24/2.26 % (32329)Memory used [KB]: 6652
% 7.24/2.26 % (32329)Time elapsed: 0.026 s
% 7.24/2.26 % (32329)Instructions burned: 82 (million)
% 7.24/2.26 % (32329)------------------------------
% 7.24/2.26 % (32329)------------------------------
% 7.24/2.26 % (32326)Instruction limit reached!
% 7.24/2.26 % (32326)------------------------------
% 7.24/2.26 % (32326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.26 % (32326)Termination reason: Unknown
% 7.24/2.26 % (32326)Termination phase: Saturation
% 7.24/2.26
% 7.24/2.26 % (32326)Memory used [KB]: 7164
% 7.24/2.26 % (32326)Time elapsed: 0.060 s
% 7.24/2.26 % (32326)Instructions burned: 184 (million)
% 7.24/2.26 % (32326)------------------------------
% 7.24/2.26 % (32326)------------------------------
% 7.24/2.26 % (32330)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_32018 for (2992ds/216Mi)
% 7.24/2.27 % (32327)Instruction limit reached!
% 7.24/2.27 % (32327)------------------------------
% 7.24/2.27 % (32327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.27 % (32327)Termination reason: Unknown
% 7.24/2.27 % (32327)Termination phase: Saturation
% 7.24/2.27
% 7.24/2.27 % (32327)Memory used [KB]: 7036
% 7.24/2.27 % (32327)Time elapsed: 0.061 s
% 7.24/2.27 % (32327)Instructions burned: 182 (million)
% 7.24/2.27 % (32327)------------------------------
% 7.24/2.27 % (32327)------------------------------
% 7.24/2.27 % (32331)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_32018 for (2992ds/114Mi)
% 7.24/2.27 % (32332)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_32018 for (2992ds/922Mi)
% 7.24/2.28 % (32324)Instruction limit reached!
% 7.24/2.28 % (32324)------------------------------
% 7.24/2.28 % (32324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.28 % (32324)Termination reason: Unknown
% 7.24/2.28 % (32324)Termination phase: Saturation
% 7.24/2.28
% 7.24/2.28 % (32324)Memory used [KB]: 7291
% 7.24/2.28 % (32324)Time elapsed: 0.096 s
% 7.24/2.28 % (32324)Instructions burned: 299 (million)
% 7.24/2.28 % (32324)------------------------------
% 7.24/2.28 % (32324)------------------------------
% 7.24/2.28 % (32333)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_32018 for (2992ds/182Mi)
% 7.24/2.29 % (32334)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_32018 for (2992ds/164Mi)
% 7.94/2.30 % (32331)Instruction limit reached!
% 7.94/2.30 % (32331)------------------------------
% 7.94/2.30 % (32331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.94/2.30 % (32331)Termination reason: Unknown
% 7.94/2.30 % (32331)Termination phase: Saturation
% 7.94/2.30
% 7.94/2.30 % (32331)Memory used [KB]: 7036
% 7.94/2.30 % (32331)Time elapsed: 0.036 s
% 7.94/2.30 % (32331)Instructions burned: 115 (million)
% 7.94/2.30 % (32331)------------------------------
% 7.94/2.30 % (32331)------------------------------
% 7.94/2.31 % (32322)Instruction limit reached!
% 7.94/2.31 % (32322)------------------------------
% 7.94/2.31 % (32322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.94/2.31 % (32322)Termination reason: Unknown
% 7.94/2.31 % (32322)Termination phase: Saturation
% 7.94/2.31
% 7.94/2.31 % (32322)Memory used [KB]: 7931
% 7.94/2.31 % (32322)Time elapsed: 0.150 s
% 7.94/2.31 % (32322)Instructions burned: 460 (million)
% 7.94/2.31 % (32322)------------------------------
% 7.94/2.31 % (32322)------------------------------
% 7.94/2.31 % (32335)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_32018 for (2991ds/50Mi)
% 7.94/2.32 % (32336)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_32018 for (2991ds/368Mi)
% 7.94/2.33 % (32335)Instruction limit reached!
% 7.94/2.33 % (32335)------------------------------
% 7.94/2.33 % (32335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.94/2.33 % (32335)Termination reason: Unknown
% 7.94/2.33 % (32335)Termination phase: Preprocessing 1
% 7.94/2.33
% 7.94/2.33 % (32335)Memory used [KB]: 2174
% 7.94/2.33 % (32335)Time elapsed: 0.015 s
% 7.94/2.33 % (32335)Instructions burned: 51 (million)
% 7.94/2.33 % (32335)------------------------------
% 7.94/2.33 % (32335)------------------------------
% 7.94/2.33 % (32333)Instruction limit reached!
% 7.94/2.33 % (32333)------------------------------
% 7.94/2.33 % (32333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.94/2.33 % (32333)Termination reason: Unknown
% 7.94/2.33 % (32333)Termination phase: Saturation
% 7.94/2.33
% 7.94/2.33 % (32333)Memory used [KB]: 7291
% 7.94/2.33 % (32333)Time elapsed: 0.053 s
% 7.94/2.33 % (32333)Instructions burned: 182 (million)
% 7.94/2.33 % (32333)------------------------------
% 7.94/2.33 % (32333)------------------------------
% 7.94/2.33 % (32330)Instruction limit reached!
% 7.94/2.33 % (32330)------------------------------
% 7.94/2.33 % (32330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.94/2.33 % (32330)Termination reason: Unknown
% 7.94/2.33 % (32330)Termination phase: Saturation
% 7.94/2.33
% 7.94/2.33 % (32330)Memory used [KB]: 7419
% 7.94/2.33 % (32330)Time elapsed: 0.068 s
% 7.94/2.33 % (32330)Instructions burned: 219 (million)
% 7.94/2.33 % (32330)------------------------------
% 7.94/2.33 % (32330)------------------------------
% 7.94/2.34 % (32337)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_32018 for (2991ds/1021Mi)
% 7.94/2.34 % (32334)Instruction limit reached!
% 7.94/2.34 % (32334)------------------------------
% 7.94/2.34 % (32334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.94/2.34 % (32334)Termination reason: Unknown
% 7.94/2.34 % (32334)Termination phase: Saturation
% 7.94/2.34
% 7.94/2.34 % (32334)Memory used [KB]: 2430
% 7.94/2.34 % (32334)Time elapsed: 0.052 s
% 7.94/2.34 % (32334)Instructions burned: 166 (million)
% 7.94/2.34 % (32334)------------------------------
% 7.94/2.34 % (32334)------------------------------
% 7.94/2.34 % (32339)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_32018 for (2991ds/204Mi)
% 7.94/2.35 % (32338)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_32018 for (2991ds/267Mi)
% 7.94/2.35 % (32340)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_32018 for (2991ds/26Mi)
% 7.94/2.35 % (32340)Instruction limit reached!
% 7.94/2.35 % (32340)------------------------------
% 7.94/2.35 % (32340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.94/2.35 % (32340)Termination reason: Unknown
% 7.94/2.35 % (32340)Termination phase: shuffling
% 7.94/2.35
% 7.94/2.35 % (32340)Memory used [KB]: 2046
% 7.94/2.35 % (32340)Time elapsed: 0.009 s
% 7.94/2.35 % (32340)Instructions burned: 26 (million)
% 7.94/2.35 % (32340)------------------------------
% 7.94/2.35 % (32340)------------------------------
% 7.94/2.36 % (32341)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_32018 for (2991ds/53Mi)
% 7.94/2.38 % (32341)Instruction limit reached!
% 7.94/2.38 % (32341)------------------------------
% 7.94/2.38 % (32341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.94/2.38 % (32341)Termination reason: Unknown
% 7.94/2.38 % (32341)Termination phase: Preprocessing 3
% 7.94/2.38
% 7.94/2.38 % (32341)Memory used [KB]: 2174
% 7.94/2.38 % (32341)Time elapsed: 0.016 s
% 7.94/2.38 % (32341)Instructions burned: 55 (million)
% 7.94/2.38 % (32341)------------------------------
% 7.94/2.38 % (32341)------------------------------
% 7.94/2.39 % (32342)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_32018 for (2991ds/4436Mi)
% 8.40/2.41 % (32339)Instruction limit reached!
% 8.40/2.41 % (32339)------------------------------
% 8.40/2.41 % (32339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.40/2.41 % (32339)Termination reason: Unknown
% 8.40/2.41 % (32339)Termination phase: Saturation
% 8.40/2.41
% 8.40/2.41 % (32339)Memory used [KB]: 7164
% 8.40/2.41 % (32339)Time elapsed: 0.067 s
% 8.40/2.41 % (32339)Instructions burned: 204 (million)
% 8.40/2.41 % (32339)------------------------------
% 8.40/2.41 % (32339)------------------------------
% 8.40/2.42 % (32343)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_32018 for (2990ds/1539Mi)
% 8.40/2.44 % (32336)Instruction limit reached!
% 8.40/2.44 % (32336)------------------------------
% 8.40/2.44 % (32336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.40/2.44 % (32336)Termination reason: Unknown
% 8.40/2.44 % (32336)Termination phase: Saturation
% 8.40/2.44
% 8.40/2.44 % (32336)Memory used [KB]: 8571
% 8.40/2.44 % (32336)Time elapsed: 0.122 s
% 8.40/2.44 % (32336)Instructions burned: 369 (million)
% 8.40/2.44 % (32336)------------------------------
% 8.40/2.44 % (32336)------------------------------
% 8.40/2.45 % (32344)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_32018 for (2990ds/408Mi)
% 8.40/2.49 % (32338)Instruction limit reached!
% 8.40/2.49 % (32338)------------------------------
% 8.40/2.49 % (32338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.40/2.49 % (32338)Termination reason: Unknown
% 8.40/2.49 % (32338)Termination phase: Saturation
% 8.40/2.49
% 8.40/2.49 % (32338)Memory used [KB]: 7675
% 8.40/2.49 % (32338)Time elapsed: 0.144 s
% 8.40/2.49 % (32338)Instructions burned: 268 (million)
% 8.40/2.49 % (32338)------------------------------
% 8.40/2.49 % (32338)------------------------------
% 8.77/2.50 % (32345)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_32018 for (2989ds/5205Mi)
% 8.77/2.51 % (32325)Instruction limit reached!
% 8.77/2.51 % (32325)------------------------------
% 8.77/2.51 % (32325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.77/2.51 % (32325)Termination reason: Unknown
% 8.77/2.51 % (32325)Termination phase: Saturation
% 8.77/2.51
% 8.77/2.51 % (32325)Memory used [KB]: 8443
% 8.77/2.51 % (32325)Time elapsed: 0.309 s
% 8.77/2.51 % (32325)Instructions burned: 987 (million)
% 8.77/2.51 % (32325)------------------------------
% 8.77/2.51 % (32325)------------------------------
% 8.77/2.52 % (32346)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_32018 for (2989ds/1913Mi)
% 8.77/2.57 % (32332)Instruction limit reached!
% 8.77/2.57 % (32332)------------------------------
% 8.77/2.57 % (32332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.77/2.57 % (32332)Termination reason: Unknown
% 8.77/2.57 % (32332)Termination phase: Saturation
% 8.77/2.57
% 8.77/2.57 % (32332)Memory used [KB]: 7803
% 8.77/2.57 % (32332)Time elapsed: 0.297 s
% 8.77/2.57 % (32332)Instructions burned: 923 (million)
% 8.77/2.57 % (32332)------------------------------
% 8.77/2.57 % (32332)------------------------------
% 8.77/2.58 % (32344)Instruction limit reached!
% 8.77/2.58 % (32344)------------------------------
% 8.77/2.58 % (32344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.77/2.58 % (32344)Termination reason: Unknown
% 8.77/2.58 % (32344)Termination phase: Saturation
% 8.77/2.58
% 8.77/2.58 % (32344)Memory used [KB]: 8315
% 8.77/2.58 % (32344)Time elapsed: 0.124 s
% 8.77/2.58 % (32344)Instructions burned: 408 (million)
% 8.77/2.58 % (32344)------------------------------
% 8.77/2.58 % (32344)------------------------------
% 8.77/2.58 % (32347)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_32018 for (2989ds/4350Mi)
% 8.77/2.59 % (32348)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_32018 for (2989ds/68Mi)
% 9.52/2.61 % (32348)Instruction limit reached!
% 9.52/2.61 % (32348)------------------------------
% 9.52/2.61 % (32348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.52/2.61 % (32348)Termination reason: Unknown
% 9.52/2.61 % (32348)Termination phase: Saturation
% 9.52/2.61
% 9.52/2.61 % (32348)Memory used [KB]: 6524
% 9.52/2.61 % (32348)Time elapsed: 0.023 s
% 9.52/2.61 % (32348)Instructions burned: 70 (million)
% 9.52/2.61 % (32348)------------------------------
% 9.52/2.61 % (32348)------------------------------
% 9.52/2.62 % (32349)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_32018 for (2988ds/358Mi)
% 9.52/2.65 % (32337)Instruction limit reached!
% 9.52/2.65 % (32337)------------------------------
% 9.52/2.65 % (32337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.52/2.65 % (32337)Termination reason: Unknown
% 9.52/2.65 % (32337)Termination phase: Saturation
% 9.52/2.65
% 9.52/2.65 % (32337)Memory used [KB]: 9338
% 9.52/2.65 % (32337)Time elapsed: 0.318 s
% 9.52/2.65 % (32337)Instructions burned: 1023 (million)
% 9.52/2.65 % (32337)------------------------------
% 9.52/2.65 % (32337)------------------------------
% 9.52/2.66 % (32350)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_32018 for (2988ds/31Mi)
% 9.52/2.67 % (32350)Instruction limit reached!
% 9.52/2.67 % (32350)------------------------------
% 9.52/2.67 % (32350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.52/2.67 % (32350)Termination reason: Unknown
% 9.52/2.67 % (32350)Termination phase: Preprocessing 3
% 9.52/2.67
% 9.52/2.67 % (32350)Memory used [KB]: 1918
% 9.52/2.67 % (32350)Time elapsed: 0.012 s
% 9.52/2.67 % (32350)Instructions burned: 33 (million)
% 9.52/2.67 % (32350)------------------------------
% 9.52/2.67 % (32350)------------------------------
% 9.52/2.68 % (32351)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_32018 for (2987ds/279Mi)
% 9.91/2.70 % (32351)Refutation not found, incomplete strategy
% 9.91/2.70 % (32351)------------------------------
% 9.91/2.70 % (32351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.91/2.70 % (32351)Termination reason: Refutation not found, incomplete strategy
% 9.91/2.70
% 9.91/2.70
% 9.91/2.70 % (32351)Memory used [KB]: 6780
% 9.91/2.70 % (32351)Time elapsed: 0.019 s
% 9.91/2.70 % (32351)Instructions burned: 65 (million)
% 9.91/2.70 % (32351)------------------------------
% 9.91/2.70 % (32351)------------------------------
% 9.91/2.71 % (32352)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_32018 for (2987ds/258Mi)
% 9.91/2.73 % (32349)Instruction limit reached!
% 9.91/2.73 % (32349)------------------------------
% 9.91/2.73 % (32349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.91/2.73 % (32349)Termination reason: Unknown
% 9.91/2.73 % (32349)Termination phase: Saturation
% 9.91/2.73
% 9.91/2.73 % (32349)Memory used [KB]: 7547
% 9.91/2.73 % (32349)Time elapsed: 0.137 s
% 9.91/2.73 % (32349)Instructions burned: 359 (million)
% 9.91/2.73 % (32349)------------------------------
% 9.91/2.73 % (32349)------------------------------
% 9.91/2.74 % (32353)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_32018 for (2987ds/26Mi)
% 9.91/2.75 % (32353)Instruction limit reached!
% 9.91/2.75 % (32353)------------------------------
% 9.91/2.75 % (32353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.91/2.75 % (32353)Termination reason: Unknown
% 9.91/2.75 % (32353)Termination phase: shuffling
% 9.91/2.75
% 9.91/2.75 % (32353)Memory used [KB]: 2046
% 9.91/2.75 % (32353)Time elapsed: 0.009 s
% 9.91/2.75 % (32353)Instructions burned: 26 (million)
% 9.91/2.75 % (32353)------------------------------
% 9.91/2.75 % (32353)------------------------------
% 9.91/2.76 % (32354)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_32018 for (2987ds/995Mi)
% 9.91/2.79 % (32352)Instruction limit reached!
% 9.91/2.79 % (32352)------------------------------
% 9.91/2.79 % (32352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.91/2.79 % (32352)Termination reason: Unknown
% 9.91/2.79 % (32352)Termination phase: Saturation
% 9.91/2.79
% 9.91/2.79 % (32352)Memory used [KB]: 7419
% 9.91/2.79 % (32352)Time elapsed: 0.083 s
% 9.91/2.79 % (32352)Instructions burned: 258 (million)
% 9.91/2.79 % (32352)------------------------------
% 9.91/2.79 % (32352)------------------------------
% 10.17/2.80 % (32355)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_32018 for (2986ds/373Mi)
% 10.17/2.88 % (32343)Instruction limit reached!
% 10.17/2.88 % (32343)------------------------------
% 10.17/2.88 % (32343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.17/2.88 % (32343)Termination reason: Unknown
% 10.17/2.88 % (32343)Termination phase: Saturation
% 10.17/2.88
% 10.17/2.88 % (32343)Memory used [KB]: 11129
% 10.17/2.88 % (32343)Time elapsed: 0.487 s
% 10.17/2.88 % (32343)Instructions burned: 1540 (million)
% 10.17/2.88 % (32343)------------------------------
% 10.17/2.88 % (32343)------------------------------
% 10.17/2.89 % (32356)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_32018 for (2985ds/253Mi)
% 10.64/2.92 % (32355)Instruction limit reached!
% 10.64/2.92 % (32355)------------------------------
% 10.64/2.92 % (32355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.64/2.92 % (32355)Termination reason: Unknown
% 10.64/2.92 % (32355)Termination phase: Saturation
% 10.64/2.92
% 10.64/2.92 % (32355)Memory used [KB]: 8059
% 10.64/2.92 % (32355)Time elapsed: 0.118 s
% 10.64/2.92 % (32355)Instructions burned: 373 (million)
% 10.64/2.92 % (32355)------------------------------
% 10.64/2.92 % (32355)------------------------------
% 10.64/2.93 % (32357)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_32018 for (2985ds/832Mi)
% 10.64/2.96 % (32356)Instruction limit reached!
% 10.64/2.96 % (32356)------------------------------
% 10.64/2.96 % (32356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.64/2.96 % (32356)Termination reason: Unknown
% 10.64/2.96 % (32356)Termination phase: Saturation
% 10.64/2.96
% 10.64/2.96 % (32356)Memory used [KB]: 7803
% 10.64/2.96 % (32356)Time elapsed: 0.075 s
% 10.64/2.96 % (32356)Instructions burned: 253 (million)
% 10.64/2.96 % (32356)------------------------------
% 10.64/2.96 % (32356)------------------------------
% 10.64/2.97 % (32346)First to succeed.
% 10.64/2.97 % (32358)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_32018 for (2985ds/668Mi)
% 10.64/2.98 % (32346)Refutation found. Thanks to Tanya!
% 10.64/2.98 % SZS status Theorem for DTF2THF_32018
% 10.64/2.98 % SZS output start Proof for DTF2THF_32018
% 10.64/2.98 thf(type_def_5, type, itself: ($tType) > $tType).
% 10.64/2.98 thf(type_def_7, type, list: ($tType) > $tType).
% 10.64/2.98 thf(type_def_8, type, set: ($tType) > $tType).
% 10.64/2.98 thf(type_def_9, type, nat: $tType).
% 10.64/2.98 thf(type_def_10, type, sum_sum: ($tType * $tType) > $tType).
% 10.64/2.98 thf(type_def_11, type, binDag_Mirabelle_dag: $tType).
% 10.64/2.98 thf(type_def_12, type, simpl_ref: $tType).
% 10.64/2.98 thf(type_def_13, type, code_natural: $tType).
% 10.64/2.98 thf(type_def_14, type, num: $tType).
% 10.64/2.98 thf(type_def_15, type, option: ($tType) > $tType).
% 10.64/2.98 thf(type_def_16, type, product_unit: $tType).
% 10.64/2.98 thf(type_def_17, type, product_prod: ($tType * $tType) > $tType).
% 10.64/2.98 thf(type_def_18, type, tuple_isomorphism: ($tType * $tType * $tType) > $tType).
% 10.64/2.98 thf(type_def_19, type, literal: $tType).
% 10.64/2.98 thf(type_def_20, type, typerep: $tType).
% 10.64/2.98 thf(type_def_21, type, code_term: $tType).
% 10.64/2.98 thf(func_def_0, type, binDag_Mirabelle_dag: $tType).
% 10.64/2.98 thf(func_def_1, type, tuple_isomorphism: ($tType * $tType * $tType) > $tType).
% 10.64/2.98 thf(func_def_2, type, code_natural: $tType).
% 10.64/2.98 thf(func_def_3, type, code_term: $tType).
% 10.64/2.98 thf(func_def_4, type, product_unit: $tType).
% 10.64/2.98 thf(func_def_5, type, product_prod: ($tType * $tType) > $tType).
% 10.64/2.98 thf(func_def_6, type, typerep: $tType).
% 10.64/2.98 thf(func_def_7, type, simpl_ref: $tType).
% 10.64/2.98 thf(func_def_8, type, literal: $tType).
% 10.64/2.98 thf(func_def_9, type, sum_sum: ($tType * $tType) > $tType).
% 10.64/2.98 thf(func_def_10, type, option: ($tType) > $tType).
% 10.64/2.98 thf(func_def_11, type, list: ($tType) > $tType).
% 10.64/2.98 thf(func_def_12, type, set: ($tType) > $tType).
% 10.64/2.98 thf(func_def_13, type, num: $tType).
% 10.64/2.98 thf(func_def_14, type, nat: $tType).
% 10.64/2.98 thf(func_def_15, type, itself: ($tType) > $tType).
% 10.64/2.98 thf(func_def_16, type, enum: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_17, type, typerep2: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_18, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_19, type, cl_HOL_Oequal: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_20, type, code_term_of: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_21, type, size: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_22, type, one: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_23, type, zero: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_24, type, numeral: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_25, type, field: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_26, type, neg_numeral: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_27, type, group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_28, type, monoid_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_29, type, zero_neq_one: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_30, type, semiring_char_0: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_31, type, semiring_div: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_32, type, division_ring: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_33, type, semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_34, type, semidom_divide: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_35, type, comm_semiring_1: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_36, type, comm_monoid_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_37, type, linordered_field: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_38, type, ab_semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_39, type, quickcheck_random: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_40, type, semiring_div_parity: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_41, type, cancel_semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_42, type, cancel1352612707id_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_43, type, linord219039673up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_44, type, ordere779506340up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_45, type, canoni770627133id_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_46, type, semiri456707255roduct: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.64/2.98 thf(func_def_47, type, bNF_Greatest_Shift: !>[X0: $tType]:(set @ list @ X0 > X0 > set @ list @ X0)).
% 10.64/2.98 thf(func_def_48, type, basic_BNF_size_sum: !>[X0: $tType, X1: $tType]:((X0 > nat) > (X1 > nat) > sum_sum @ X0 @ X1 > nat)).
% 10.64/2.98 thf(func_def_49, type, binDag476092410e_Node: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > binDag_Mirabelle_dag).
% 10.64/2.98 thf(func_def_50, type, binDag_Mirabelle_Tip: binDag_Mirabelle_dag).
% 10.64/2.98 thf(func_def_51, type, binDag1297733282se_dag: !>[X0: $tType]:(X0 > (binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > X0) > binDag_Mirabelle_dag > X0)).
% 10.64/2.98 thf(func_def_52, type, binDag1442713106ec_dag: !>[X0: $tType]:(X0 > (binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > X0 > X0 > X0) > binDag_Mirabelle_dag > X0)).
% 10.64/2.98 thf(func_def_53, type, binDag1924123185ze_dag: binDag_Mirabelle_dag > nat).
% 10.64/2.98 thf(func_def_54, type, code_Suc: code_natural > code_natural).
% 10.64/2.98 thf(func_def_55, type, code_case_natural: !>[X0: $tType]:(X0 > (code_natural > X0) > code_natural > X0)).
% 10.64/2.98 thf(func_def_56, type, code_rec_natural: !>[X0: $tType]:(X0 > (code_natural > X0 > X0) > code_natural > X0)).
% 10.64/2.98 thf(func_def_57, type, code_size_natural: code_natural > nat).
% 10.64/2.98 thf(func_def_58, type, one_one: !>[X0: $tType]:(X0)).
% 10.64/2.98 thf(func_def_59, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 10.64/2.98 thf(func_def_60, type, zero_zero: !>[X0: $tType]:(X0)).
% 10.64/2.98 thf(func_def_61, type, size_bool: $o > nat).
% 10.64/2.98 thf(func_def_62, type, default_default: !>[X0: $tType]:(X0)).
% 10.64/2.98 thf(func_def_63, type, undefined: !>[X0: $tType]:(X0)).
% 10.64/2.98 thf(func_def_64, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 10.64/2.98 thf(func_def_65, type, gen_length: !>[X0: $tType]:(nat > list @ X0 > nat)).
% 10.64/2.98 thf(func_def_66, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 10.64/2.98 thf(func_def_67, type, size_list: !>[X0: $tType]:((X0 > nat) > list @ X0 > nat)).
% 10.64/2.98 thf(func_def_68, type, splice: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 10.64/2.98 thf(func_def_69, type, suc: nat > nat).
% 10.64/2.98 thf(func_def_70, type, size_size: !>[X0: $tType]:(X0 > nat)).
% 10.64/2.98 thf(func_def_71, type, inc: num > num).
% 10.64/2.98 thf(func_def_72, type, nat_of_num: num > nat).
% 10.64/2.98 thf(func_def_73, type, neg_numeral_dbl_inc: !>[X0: $tType]:(X0 > X0)).
% 10.64/2.98 thf(func_def_74, type, bit0: num > num).
% 10.64/2.98 thf(func_def_75, type, bit1: num > num).
% 10.64/2.98 thf(func_def_76, type, one2: num).
% 10.64/2.98 thf(func_def_77, type, size_num: num > nat).
% 10.64/2.98 thf(func_def_78, type, numeral_numeral: !>[X0: $tType]:(num > X0)).
% 10.64/2.98 thf(func_def_79, type, none: !>[X0: $tType]:(option @ X0)).
% 10.64/2.98 thf(func_def_80, type, some: !>[X0: $tType]:(X0 > option @ X0)).
% 10.64/2.98 thf(func_def_81, type, case_option: !>[X0: $tType, X1: $tType]:(X0 > (X1 > X0) > option @ X1 > X0)).
% 10.64/2.98 thf(func_def_82, type, size_option: !>[X0: $tType]:((X0 > nat) > option @ X0 > nat)).
% 10.64/2.98 thf(func_def_83, type, the: !>[X0: $tType]:(option @ X0 > X0)).
% 10.64/2.98 thf(func_def_84, type, product_Unity: product_unit).
% 10.64/2.98 thf(func_def_85, type, product_rec_bool: !>[X0: $tType]:(X0 > X0 > $o > X0)).
% 10.64/2.98 thf(func_def_86, type, product_rec_unit: !>[X0: $tType]:(X0 > product_unit > X0)).
% 10.64/2.98 thf(func_def_87, type, product_case_unit: !>[X0: $tType]:(X0 > product_unit > X0)).
% 10.64/2.98 thf(func_def_88, type, product_size_unit: product_unit > nat).
% 10.64/2.98 thf(func_def_89, type, type2: !>[X0: $tType]:(itself @ X0)).
% 10.64/2.98 thf(func_def_90, type, tuple_742722141rphism: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > product_prod @ X1 @ X2) > (product_prod @ X1 @ X2 > X0) > tuple_isomorphism @ X0 @ X1 @ X2)).
% 10.64/2.98 thf(func_def_91, type, tuple_1907371454rphism: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > nat) > (X1 > nat) > (X2 > nat) > tuple_isomorphism @ X0 @ X1 @ X2 > nat)).
% 10.64/2.98 thf(func_def_92, type, divide_divide: !>[X0: $tType]:(X0 > X0 > X0)).
% 10.64/2.98 thf(func_def_93, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 10.64/2.98 thf(func_def_94, type, sum_Inl: !>[X0: $tType, X1: $tType]:(X0 > sum_sum @ X0 @ X1)).
% 10.64/2.98 thf(func_def_95, type, sum_Inr: !>[X0: $tType, X1: $tType]:(X0 > sum_sum @ X1 @ X0)).
% 10.64/2.98 thf(func_def_96, type, transitive_ntrancl: !>[X0: $tType]:(nat > set @ product_prod @ X0 @ X0 > set @ product_prod @ X0 @ X0)).
% 10.64/2.98 thf(func_def_97, type, typerep3: literal > list @ typerep > typerep).
% 10.64/2.98 thf(func_def_98, type, size_typerep: typerep > nat).
% 10.64/2.98 thf(func_def_99, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 10.64/2.98 thf(func_def_100, type, a: simpl_ref).
% 10.64/2.98 thf(func_def_101, type, lt: binDag_Mirabelle_dag).
% 10.64/2.98 thf(func_def_102, type, rt: binDag_Mirabelle_dag).
% 10.64/2.98 thf(func_def_117, type, sK0: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > X0)).
% 10.64/2.98 thf(func_def_118, type, sK1: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat)).
% 10.64/2.98 thf(func_def_119, type, sK2: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat > X0)).
% 10.64/2.98 thf(func_def_120, type, sK3: (binDag_Mirabelle_dag > $o) > binDag_Mirabelle_dag).
% 10.64/2.98 thf(func_def_121, type, sK4: (binDag_Mirabelle_dag > $o) > simpl_ref).
% 10.64/2.98 thf(func_def_122, type, sK5: (binDag_Mirabelle_dag > $o) > binDag_Mirabelle_dag).
% 10.64/2.98 thf(func_def_123, type, sK6: (nat > $o) > nat).
% 10.64/2.98 thf(func_def_124, type, sK7: (nat > $o) > nat).
% 10.64/2.98 thf(func_def_125, type, sK8: binDag_Mirabelle_dag > binDag_Mirabelle_dag).
% 10.64/2.98 thf(func_def_126, type, sK9: binDag_Mirabelle_dag > simpl_ref).
% 10.64/2.98 thf(func_def_127, type, sK10: binDag_Mirabelle_dag > binDag_Mirabelle_dag).
% 10.64/2.98 thf(func_def_128, type, sK11: nat > nat).
% 10.64/2.98 thf(func_def_129, type, sK12: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 10.64/2.98 thf(func_def_130, type, sK13: nat > nat).
% 10.64/2.98 thf(func_def_131, type, sK14: (nat > nat > $o) > nat).
% 10.64/2.98 thf(func_def_132, type, sK15: (nat > nat > $o) > nat).
% 10.64/2.98 thf(func_def_133, type, sK16: (nat > nat > $o) > nat).
% 10.64/2.98 thf(func_def_134, type, sK17: (nat > nat > $o) > nat).
% 10.64/2.98 thf(func_def_135, type, sK18: (nat > $o) > nat).
% 10.64/2.98 thf(func_def_136, type, sK19: !>[X0: $tType]:(nat > list @ X0 > list @ X0)).
% 10.64/2.98 thf(func_def_137, type, sK20: !>[X0: $tType]:(nat > list @ X0 > X0)).
% 10.64/2.98 thf(func_def_138, type, sK21: !>[X0: $tType]:(option @ X0 > X0)).
% 10.64/2.98 thf(func_def_139, type, sK22: !>[X0: $tType]:(list @ X0 > nat > list @ X0)).
% 10.64/2.98 thf(func_def_140, type, sK23: !>[X0: $tType]:(list @ X0 > nat > X0)).
% 10.64/2.98 thf(func_def_141, type, ph24: !>[X0: $tType]:(X0)).
% 10.64/2.98 thf(f3660,plain,(
% 10.64/2.98 $false),
% 10.64/2.98 inference(subsumption_resolution,[status(thm)],[f3653,f3494])).
% 10.64/2.98 thf(f3494,plain,(
% 10.64/2.98 ( ! [X0 : nat,X1 : nat] : (((plus_plus @ nat @ one_one @ nat @ (plus_plus @ nat @ X0 @ X1)) != X0)) )),
% 10.64/2.98 inference(subsumption_resolution,[status(thm)],[f1524,f1165])).
% 10.64/2.98 thf(f1165,plain,(
% 10.64/2.98 ( ! [X0 : nat] : ((zero_zero @ nat != (plus_plus @ nat @ one_one @ nat @ X0))) )),
% 10.64/2.98 inference(definition_unfolding,[status(thm)],[f1008,f1033])).
% 10.64/2.98 thf(f1033,plain,(
% 10.64/2.98 (suc = (plus_plus @ nat @ one_one @ nat))),
% 10.64/2.98 inference(cnf_transformation,[status(thm)],[f222])).
% 10.64/2.98 thf(f222,axiom,(
% 10.64/2.98 (suc = (plus_plus @ nat @ one_one @ nat))),
% 10.64/2.98 file('/export/starexec/sandbox2/tmp/tmp.m3AuIGZJso/DTF2THF_32018.p',fact_221_Suc__eq__plus1__left)).
% 10.64/2.98 thf(f1008,plain,(
% 10.64/2.98 ( ! [X0 : nat] : ((zero_zero @ nat != (suc @ X0))) )),
% 10.64/2.98 inference(cnf_transformation,[status(thm)],[f895])).
% 10.64/2.98 thf(f895,plain,(
% 10.64/2.98 ! [X0 : nat] : (zero_zero @ nat != (suc @ X0))),
% 10.64/2.98 inference(rectify,[status(thm)],[f71])).
% 10.64/2.98 thf(f71,axiom,(
% 10.64/2.98 ! [X37 : nat] : (zero_zero @ nat != (suc @ X37))),
% 10.64/2.98 file('/export/starexec/sandbox2/tmp/tmp.m3AuIGZJso/DTF2THF_32018.p',fact_70_Suc__neq__Zero)).
% 10.64/2.98 thf(f1524,plain,(
% 10.64/2.98 ( ! [X0 : nat,X1 : nat] : ((zero_zero @ nat = (plus_plus @ nat @ one_one @ nat @ X1)) | ((plus_plus @ nat @ one_one @ nat @ (plus_plus @ nat @ X0 @ X1)) != X0)) )),
% 10.64/2.98 inference(superposition,[status(thm)],[f998,f1203])).
% 10.64/2.98 thf(f1203,plain,(
% 10.64/2.98 ( ! [X0 : nat,X1 : nat] : (((plus_plus @ nat @ one_one @ nat @ (plus_plus @ nat @ X0 @ X1)) = (plus_plus @ nat @ X0 @ (plus_plus @ nat @ one_one @ nat @ X1)))) )),
% 10.64/2.98 inference(definition_unfolding,[status(thm)],[f1142,f1033,f1033])).
% 10.64/2.98 thf(f1142,plain,(
% 10.64/2.98 ( ! [X0 : nat,X1 : nat] : (((suc @ (plus_plus @ nat @ X0 @ X1)) = (plus_plus @ nat @ X0 @ (suc @ X1)))) )),
% 10.64/2.98 inference(cnf_transformation,[status(thm)],[f875])).
% 10.64/2.98 thf(f875,plain,(
% 10.64/2.98 ! [X0 : nat,X1 : nat] : ((suc @ (plus_plus @ nat @ X0 @ X1)) = (plus_plus @ nat @ X0 @ (suc @ X1)))),
% 10.64/2.98 inference(rectify,[status(thm)],[f38])).
% 10.64/2.98 thf(f38,axiom,(
% 10.64/2.98 ! [X37 : nat,X38 : nat] : ((plus_plus @ nat @ X37 @ (suc @ X38)) = (suc @ (plus_plus @ nat @ X37 @ X38)))),
% 10.64/2.98 file('/export/starexec/sandbox2/tmp/tmp.m3AuIGZJso/DTF2THF_32018.p',fact_37_add__Suc__right)).
% 10.64/2.98 thf(f998,plain,(
% 10.64/2.98 ( ! [X0 : nat,X1 : nat] : (((plus_plus @ nat @ X0 @ X1) != X0) | (zero_zero @ nat = X1)) )),
% 10.64/2.98 inference(cnf_transformation,[status(thm)],[f961])).
% 10.64/2.98 thf(f961,plain,(
% 10.64/2.98 ! [X0 : nat,X1 : nat] : (((plus_plus @ nat @ X0 @ X1) != X0) | (zero_zero @ nat = X1))),
% 10.64/2.98 inference(ennf_transformation,[status(thm)],[f873])).
% 10.64/2.98 thf(f873,plain,(
% 10.64/2.98 ! [X0 : nat,X1 : nat] : (((plus_plus @ nat @ X0 @ X1) = X0) => (zero_zero @ nat = X1))),
% 10.64/2.98 inference(rectify,[status(thm)],[f78])).
% 10.64/2.98 thf(f78,axiom,(
% 10.64/2.98 ! [X37 : nat,X38 : nat] : (((plus_plus @ nat @ X37 @ X38) = X37) => (zero_zero @ nat = X38))),
% 10.64/2.98 file('/export/starexec/sandbox2/tmp/tmp.m3AuIGZJso/DTF2THF_32018.p',fact_77_add__eq__self__zero)).
% 10.64/2.98 thf(f3653,plain,(
% 10.64/2.98 ((plus_plus @ nat @ one_one @ nat @ (plus_plus @ nat @ (size_size @ binDag_Mirabelle_dag @ lt) @ (size_size @ binDag_Mirabelle_dag @ rt))) = (size_size @ binDag_Mirabelle_dag @ lt))),
% 10.64/2.98 inference(superposition,[status(thm)],[f3633,f1499])).
% 10.64/2.98 thf(f1499,plain,(
% 10.64/2.98 ( ! [X0 : nat] : (((plus_plus @ nat @ one_one @ nat @ X0) = (plus_plus @ nat @ X0 @ one_one @ nat))) )),
% 10.64/2.98 inference(forward_demodulation,[status(thm)],[f1497,f1085])).
% 10.64/2.98 thf(f1085,plain,(
% 10.64/2.98 ( ! [X0 : nat] : (((plus_plus @ nat @ X0 @ zero_zero @ nat) = X0)) )),
% 10.64/2.98 inference(cnf_transformation,[status(thm)],[f870])).
% 10.64/2.98 thf(f870,plain,(
% 10.64/2.98 ! [X0 : nat] : ((plus_plus @ nat @ X0 @ zero_zero @ nat) = X0)),
% 10.64/2.98 inference(rectify,[status(thm)],[f37])).
% 10.64/2.98 thf(f37,axiom,(
% 10.64/2.98 ! [X37 : nat] : ((plus_plus @ nat @ X37 @ zero_zero @ nat) = X37)),
% 10.64/2.98 file('/export/starexec/sandbox2/tmp/tmp.m3AuIGZJso/DTF2THF_32018.p',fact_36_Nat_Oadd__0__right)).
% 10.64/2.98 thf(f1497,plain,(
% 10.64/2.98 ( ! [X0 : nat] : (((plus_plus @ nat @ X0 @ (plus_plus @ nat @ one_one @ nat @ zero_zero @ nat)) = (plus_plus @ nat @ one_one @ nat @ X0))) )),
% 10.64/2.98 inference(superposition,[status(thm)],[f1085,f1171])).
% 10.64/2.98 thf(f1171,plain,(
% 10.64/2.98 ( ! [X0 : nat,X1 : nat] : (((plus_plus @ nat @ X0 @ (plus_plus @ nat @ one_one @ nat @ X1)) = (plus_plus @ nat @ (plus_plus @ nat @ one_one @ nat @ X0) @ X1))) )),
% 10.64/2.98 inference(definition_unfolding,[status(thm)],[f1026,f1033,f1033])).
% 10.64/2.98 thf(f1026,plain,(
% 10.64/2.98 ( ! [X0 : nat,X1 : nat] : (((plus_plus @ nat @ (suc @ X0) @ X1) = (plus_plus @ nat @ X0 @ (suc @ X1)))) )),
% 10.64/2.98 inference(cnf_transformation,[status(thm)],[f876])).
% 10.64/2.98 thf(f876,plain,(
% 10.64/2.98 ! [X0 : nat,X1 : nat] : ((plus_plus @ nat @ (suc @ X0) @ X1) = (plus_plus @ nat @ X0 @ (suc @ X1)))),
% 10.64/2.98 inference(rectify,[status(thm)],[f49])).
% 10.64/2.98 thf(f49,axiom,(
% 10.64/2.98 ! [X37 : nat,X38 : nat] : ((plus_plus @ nat @ X37 @ (suc @ X38)) = (plus_plus @ nat @ (suc @ X37) @ X38))),
% 10.64/2.98 file('/export/starexec/sandbox2/tmp/tmp.m3AuIGZJso/DTF2THF_32018.p',fact_48_add__Suc__shift)).
% 10.64/2.98 thf(f3633,plain,(
% 10.64/2.98 ((size_size @ binDag_Mirabelle_dag @ lt) = (plus_plus @ nat @ (plus_plus @ nat @ (size_size @ binDag_Mirabelle_dag @ lt) @ (size_size @ binDag_Mirabelle_dag @ rt)) @ one_one @ nat))),
% 10.64/2.98 inference(superposition,[status(thm)],[f3601,f1610])).
% 10.64/2.98 thf(f1610,plain,(
% 10.64/2.98 ( ! [X2 : binDag_Mirabelle_dag,X0 : binDag_Mirabelle_dag,X1 : simpl_ref] : (((size_size @ binDag_Mirabelle_dag @ (binDag476092410e_Node @ X0 @ X1 @ X2)) = (plus_plus @ nat @ (plus_plus @ nat @ (size_size @ binDag_Mirabelle_dag @ X0) @ (size_size @ binDag_Mirabelle_dag @ X2)) @ one_one @ nat))) )),
% 10.64/2.98 inference(forward_demodulation,[status(thm)],[f1170,f1085])).
% 10.64/2.98 thf(f1170,plain,(
% 10.64/2.98 ( ! [X2 : binDag_Mirabelle_dag,X0 : binDag_Mirabelle_dag,X1 : simpl_ref] : (((plus_plus @ nat @ (plus_plus @ nat @ (size_size @ binDag_Mirabelle_dag @ X0) @ (size_size @ binDag_Mirabelle_dag @ X2)) @ (plus_plus @ nat @ one_one @ nat @ zero_zero @ nat)) = (size_size @ binDag_Mirabelle_dag @ (binDag476092410e_Node @ X0 @ X1 @ X2)))) )),
% 10.64/2.98 inference(definition_unfolding,[status(thm)],[f1023,f1033])).
% 10.64/2.98 thf(f1023,plain,(
% 10.64/2.98 ( ! [X2 : binDag_Mirabelle_dag,X0 : binDag_Mirabelle_dag,X1 : simpl_ref] : (((size_size @ binDag_Mirabelle_dag @ (binDag476092410e_Node @ X0 @ X1 @ X2)) = (plus_plus @ nat @ (plus_plus @ nat @ (size_size @ binDag_Mirabelle_dag @ X0) @ (size_size @ binDag_Mirabelle_dag @ X2)) @ (suc @ zero_zero @ nat)))) )),
% 10.64/2.98 inference(cnf_transformation,[status(thm)],[f877])).
% 10.64/2.98 thf(f877,plain,(
% 10.64/2.98 ! [X0 : binDag_Mirabelle_dag,X1 : simpl_ref,X2 : binDag_Mirabelle_dag] : ((size_size @ binDag_Mirabelle_dag @ (binDag476092410e_Node @ X0 @ X1 @ X2)) = (plus_plus @ nat @ (plus_plus @ nat @ (size_size @ binDag_Mirabelle_dag @ X0) @ (size_size @ binDag_Mirabelle_dag @ X2)) @ (suc @ zero_zero @ nat)))),
% 10.64/2.98 inference(rectify,[status(thm)],[f19])).
% 10.64/2.98 thf(f19,axiom,(
% 10.64/2.98 ! [X4 : binDag_Mirabelle_dag,X5 : simpl_ref,X6 : binDag_Mirabelle_dag] : ((size_size @ binDag_Mirabelle_dag @ (binDag476092410e_Node @ X4 @ X5 @ X6)) = (plus_plus @ nat @ (plus_plus @ nat @ (size_size @ binDag_Mirabelle_dag @ X4) @ (size_size @ binDag_Mirabelle_dag @ X6)) @ (suc @ zero_zero @ nat)))),
% 10.64/2.98 file('/export/starexec/sandbox2/tmp/tmp.m3AuIGZJso/DTF2THF_32018.p',fact_18_dag_Osize_I4_J)).
% 10.64/2.98 thf(f3601,plain,(
% 10.64/2.98 ( ! [X0 : simpl_ref] : (((size_size @ binDag_Mirabelle_dag @ lt) = (size_size @ binDag_Mirabelle_dag @ (binDag476092410e_Node @ lt @ X0 @ rt)))) )),
% 10.64/2.98 inference(superposition,[status(thm)],[f1668,f1090])).
% 10.64/2.98 thf(f1090,plain,(
% 10.64/2.98 (lt = (binDag476092410e_Node @ lt @ a @ rt))),
% 10.64/2.98 inference(cnf_transformation,[status(thm)],[f869])).
% 10.64/2.98 thf(f869,plain,(
% 10.64/2.98 (lt = (binDag476092410e_Node @ lt @ a @ rt))),
% 10.64/2.98 inference(flattening,[status(thm)],[f371])).
% 10.64/2.98 thf(f371,negated_conjecture,(
% 10.64/2.98 ~(lt != (binDag476092410e_Node @ lt @ a @ rt))),
% 10.64/2.98 inference(negated_conjecture,[status(cth)],[f370])).
% 10.64/2.98 thf(f370,conjecture,(
% 10.64/2.98 (lt != (binDag476092410e_Node @ lt @ a @ rt))),
% 10.64/2.98 file('/export/starexec/sandbox2/tmp/tmp.m3AuIGZJso/DTF2THF_32018.p',conj_0)).
% 10.64/2.98 thf(f1668,plain,(
% 10.64/2.98 ( ! [X2 : simpl_ref,X3 : simpl_ref,X0 : binDag_Mirabelle_dag,X1 : binDag_Mirabelle_dag] : (((size_size @ binDag_Mirabelle_dag @ (binDag476092410e_Node @ X0 @ X2 @ X1)) = (size_size @ binDag_Mirabelle_dag @ (binDag476092410e_Node @ X0 @ X3 @ X1)))) )),
% 10.64/2.98 inference(superposition,[status(thm)],[f1610,f1610])).
% 10.64/2.98 % SZS output end Proof for DTF2THF_32018
% 10.64/2.98 % (32346)------------------------------
% 10.64/2.98 % (32346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.64/2.98 % (32346)Termination reason: Refutation
% 10.64/2.98
% 10.64/2.98 % (32346)Memory used [KB]: 3454
% 10.64/2.98 % (32346)Time elapsed: 0.482 s
% 10.64/2.98 % (32346)Instructions burned: 1518 (million)
% 10.64/2.98 % (32346)------------------------------
% 10.64/2.98 % (32346)------------------------------
% 10.64/2.98 % (32245)Success in time 1.507 s
%------------------------------------------------------------------------------