%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP199^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n031.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 08:56:21 AM UTC 2026
% Result : Theorem 50.07s 8.73s
% Output : Refutation 50.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP199^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n031.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue Feb 24 08:31:18 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : ITP199^2 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.47 % Domain : Interactive Theorem Proving
% 0.30/0.47 % Problem : Sledgehammer USubst problem prob_1246__6349986_1
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.47 % Source : [Des21]
% 0.30/0.47 % Names : USubst/prob_1246__6349986_1 [Des21]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.00 v8.1.0, 0.25 v7.5.0
% 0.30/0.47 % Syntax : Number of formulae : 373 ( 160 unt; 71 typ; 0 def)
% 0.30/0.47 % Number of atoms : 698 ( 380 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 9 ( 2 avg)
% 0.30/0.47 % Number of connectives : 3287 ( 80 ~; 14 |; 43 &;2948 @)
% 0.30/0.47 % ( 0 <=>; 202 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 18 ( 6 avg)
% 0.30/0.47 % Number of types : 9 ( 8 usr)
% 0.30/0.47 % Number of type conns : 354 ( 354 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 66 ( 63 usr; 7 con; 0-7 aty)
% 0.30/0.47 % Number of variables : 900 ( 58 ^; 791 !; 14 ?; 900 :)
% 0.30/0.47 % ( 37 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.47 % SPC : TH1_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 16:22:53.994
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % Could-be-implicit typings (11)
% 0.30/0.47 thf(ty_t_Denotational__Semantics_Ointerp,type,
% 0.30/0.47 denotational_interp: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Product__Type_Oprod,type,
% 0.30/0.47 product_prod: $tType > $tType > $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Syntax_Ovariable,type,
% 0.30/0.47 variable: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Option_Ooption,type,
% 0.30/0.47 option: $tType > $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Syntax_Ogame,type,
% 0.30/0.47 game: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_String_Ochar,type,
% 0.30/0.47 char: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Syntax_Otrm,type,
% 0.30/0.47 trm: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Syntax_Ofml,type,
% 0.30/0.47 fml: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Real_Oreal,type,
% 0.30/0.47 real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Set_Oset,type,
% 0.30/0.47 set: $tType > $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Nat_Onat,type,
% 0.30/0.47 nat: $tType ).
% 0.30/0.47
% 0.30/0.47 % Explicit typings (60)
% 0.30/0.47 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.30/0.47 bounded_lattice:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_HOL_Otype,type,
% 0.30/0.47 type:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Groups_Ozero,type,
% 0.30/0.47 zero:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Groups_Ouminus,type,
% 0.30/0.47 uminus:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Obot,type,
% 0.30/0.47 bot:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Groups_Ogroup__add,type,
% 0.30/0.47 group_add:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Lattices_Olattice,type,
% 0.30/0.47 lattice:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Opreorder,type,
% 0.30/0.47 preorder:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 0.30/0.47 boolean_algebra:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 0.30/0.47 semilattice_inf:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.30/0.47 semilattice_sup:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.30/0.47 ordered_ab_group_add:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 0.30/0.47 linord219039673up_add:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 0.30/0.47 bounde1808546759up_bot:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.30/0.47 canoni770627133id_add:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Coincidence_Ostatediff,type,
% 0.30/0.47 statediff: ( variable > real ) > ( variable > real ) > ( set @ variable ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Coincidence_Ostateinterpol,type,
% 0.30/0.47 stateinterpol: ( variable > real ) > ( variable > real ) > ( set @ variable ) > variable > real ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Denotational__Semantics_OUvariation,type,
% 0.30/0.47 denota1419872369iation: ( variable > real ) > ( variable > real ) > ( set @ variable ) > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Denotational__Semantics_OVagree,type,
% 0.30/0.47 denotational_Vagree: ( variable > real ) > ( variable > real ) > ( set @ variable ) > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Denotational__Semantics_Orepv,type,
% 0.30/0.47 denotational_repv: ( variable > real ) > variable > real > variable > real ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Denotational__Semantics_Osolves__ODE,type,
% 0.30/0.47 denota1778088425es_ODE: denotational_interp > ( real > variable > real ) > char > trm > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Denotational__Semantics_Oterm__sem,type,
% 0.30/0.47 denota1863255036rm_sem: denotational_interp > trm > ( variable > real ) > real ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.30/0.47 uminus_uminus:
% 0.30/0.47 !>[A: $tType] : ( A > A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.30/0.47 zero_zero:
% 0.30/0.47 !>[A: $tType] : A ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_If,type,
% 0.30/0.47 if:
% 0.30/0.47 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.30/0.47 inf_inf:
% 0.30/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.30/0.47 sup_sup:
% 0.30/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.30/0.47 size_size:
% 0.30/0.47 !>[A: $tType] : ( A > nat ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Option_Ooption_ONone,type,
% 0.30/0.47 none:
% 0.30/0.47 !>[A: $tType] : ( option @ A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Option_Ooption_OSome,type,
% 0.30/0.47 some:
% 0.30/0.47 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Option_Ooption_Ocase__option,type,
% 0.30/0.47 case_option:
% 0.30/0.47 !>[B: $tType,A: $tType] : ( B > ( A > B ) > ( option @ A ) > B ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Option_Ooption_Oset__option,type,
% 0.30/0.47 set_option:
% 0.30/0.47 !>[A: $tType] : ( ( option @ A ) > ( set @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Option_Ooption_Othe,type,
% 0.30/0.47 the:
% 0.30/0.47 !>[A: $tType] : ( ( option @ A ) > A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Option_Othese,type,
% 0.30/0.47 these:
% 0.30/0.47 !>[A: $tType] : ( ( set @ ( option @ A ) ) > ( set @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.30/0.47 bot_bot:
% 0.30/0.47 !>[A: $tType] : A ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.30/0.47 ord_less_eq:
% 0.30/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_OCollect,type,
% 0.30/0.47 collect:
% 0.30/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oinsert,type,
% 0.30/0.47 insert:
% 0.30/0.47 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Ois__empty,type,
% 0.30/0.47 is_empty:
% 0.30/0.47 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Ois__singleton,type,
% 0.30/0.47 is_singleton:
% 0.30/0.47 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Othe__elem,type,
% 0.30/0.47 the_elem:
% 0.30/0.47 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Static__Semantics_OFVT,type,
% 0.30/0.47 static_FVT: trm > ( set @ variable ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Static__Semantics_Oselectlike,type,
% 0.30/0.47 static_selectlike: ( set @ ( variable > real ) ) > ( variable > real ) > ( set @ variable ) > ( set @ ( variable > real ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Syntax_Otrm_OTimes,type,
% 0.30/0.47 times: trm > trm > trm ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Syntax_Ovariable_ODVar,type,
% 0.30/0.47 dVar: char > variable ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Syntax_Ovariable_ORVar,type,
% 0.30/0.47 rVar: char > variable ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Syntax_Ovariable_Orec__variable,type,
% 0.30/0.47 rec_variable:
% 0.30/0.47 !>[A: $tType] : ( ( char > A ) > ( char > A ) > variable > A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Syntax_Ovariable_Osize__variable,type,
% 0.30/0.47 size_variable: variable > nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTimeso,type,
% 0.30/0.47 uSubst277968634Timeso: ( option @ trm ) > ( option @ trm ) > ( option @ trm ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Oadjoint,type,
% 0.30/0.47 uSubst2091380086djoint: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > denotational_interp > ( variable > real ) > denotational_interp ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappt,type,
% 0.30/0.47 uSubst95898992stappt: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > trm > ( option @ trm ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_member,type,
% 0.30/0.47 member:
% 0.30/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_F,type,
% 0.30/0.47 f: real > variable > real ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_I,type,
% 0.30/0.47 i: denotational_interp ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_U,type,
% 0.30/0.47 u: set @ variable ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v__092_060omega_062,type,
% 0.30/0.47 omega: variable > real ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v__092_060sigma_062,type,
% 0.30/0.47 sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v__092_060theta_062,type,
% 0.30/0.47 theta: trm ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_rr____,type,
% 0.30/0.47 rr: trm > denotational_interp > trm > denotational_interp > char > ( real > variable > real ) > variable > real ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_x,type,
% 0.30/0.47 x: char ).
% 0.30/0.47
% 0.30/0.47 % Relevant facts (254)
% 0.30/0.47 thf(fact_0_uv,axiom,
% 0.30/0.47 denota1419872369iation @ ( f @ ( zero_zero @ real ) ) @ omega @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % uv
% 0.30/0.47 thf(fact_1_Uvariation__empty,axiom,
% 0.30/0.47 ! [Nu: variable > real,Nu2: variable > real] :
% 0.30/0.47 ( ( denota1419872369iation @ Nu @ Nu2 @ ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.47 = ( Nu = Nu2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Uvariation_empty
% 0.30/0.47 thf(fact_2_Un__insert__left,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,B2: set @ A,C: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A2 @ B2 ) @ C )
% 0.30/0.47 = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_insert_left
% 0.30/0.47 thf(fact_3_Un__insert__right,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,A2: A,B2: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ A3 @ ( insert @ A @ A2 @ B2 ) )
% 0.30/0.47 = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_insert_right
% 0.30/0.47 thf(fact_4_Un__empty,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 0.30/0.47 ( ( ( sup_sup @ ( set @ A ) @ A3 @ B2 )
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = ( ( A3
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 & ( B2
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_empty
% 0.30/0.47 thf(fact_5_sup__bot__left,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [X: A] :
% 0.30/0.47 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 0.30/0.47 = X ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_bot_left
% 0.30/0.47 thf(fact_6_sup__bot__right,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [X: A] :
% 0.30/0.47 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 0.30/0.47 = X ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_bot_right
% 0.30/0.47 thf(fact_7_bot__eq__sup__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( ( bot_bot @ A )
% 0.30/0.47 = ( sup_sup @ A @ X @ Y ) )
% 0.30/0.47 = ( ( X
% 0.30/0.47 = ( bot_bot @ A ) )
% 0.30/0.47 & ( Y
% 0.30/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bot_eq_sup_iff
% 0.30/0.47 thf(fact_8_sup__eq__bot__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( ( sup_sup @ A @ X @ Y )
% 0.30/0.47 = ( bot_bot @ A ) )
% 0.30/0.47 = ( ( X
% 0.30/0.47 = ( bot_bot @ A ) )
% 0.30/0.47 & ( Y
% 0.30/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_eq_bot_iff
% 0.30/0.47 thf(fact_9_sup__bot_Oeq__neutr__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [A2: A,B3: A] :
% 0.30/0.47 ( ( ( sup_sup @ A @ A2 @ B3 )
% 0.30/0.47 = ( bot_bot @ A ) )
% 0.30/0.47 = ( ( A2
% 0.30/0.47 = ( bot_bot @ A ) )
% 0.30/0.47 & ( B3
% 0.30/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_bot.eq_neutr_iff
% 0.30/0.47 thf(fact_10_sup__bot_Oleft__neutral,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [A2: A] :
% 0.30/0.47 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A2 )
% 0.30/0.47 = A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_bot.left_neutral
% 0.30/0.47 thf(fact_11_sup__bot_Oneutr__eq__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [A2: A,B3: A] :
% 0.30/0.47 ( ( ( bot_bot @ A )
% 0.30/0.47 = ( sup_sup @ A @ A2 @ B3 ) )
% 0.30/0.47 = ( ( A2
% 0.30/0.47 = ( bot_bot @ A ) )
% 0.30/0.47 & ( B3
% 0.30/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_bot.neutr_eq_iff
% 0.30/0.47 thf(fact_12_sup__bot_Oright__neutral,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [A2: A] :
% 0.30/0.47 ( ( sup_sup @ A @ A2 @ ( bot_bot @ A ) )
% 0.30/0.47 = A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_bot.right_neutral
% 0.30/0.47 thf(fact_13_empty__Collect__eq,axiom,
% 0.30/0.47 ! [A: $tType,P: A > $o] :
% 0.30/0.47 ( ( ( bot_bot @ ( set @ A ) )
% 0.30/0.47 = ( collect @ A @ P ) )
% 0.30/0.47 = ( ! [X2: A] :
% 0.30/0.47 ~ ( P @ X2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % empty_Collect_eq
% 0.30/0.47 thf(fact_14_Collect__empty__eq,axiom,
% 0.30/0.47 ! [A: $tType,P: A > $o] :
% 0.30/0.47 ( ( ( collect @ A @ P )
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = ( ! [X2: A] :
% 0.30/0.47 ~ ( P @ X2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_empty_eq
% 0.30/0.47 thf(fact_15_all__not__in__conv,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A] :
% 0.30/0.47 ( ( ! [X2: A] :
% 0.30/0.47 ~ ( member @ A @ X2 @ A3 ) )
% 0.30/0.47 = ( A3
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % all_not_in_conv
% 0.30/0.47 thf(fact_16_empty__iff,axiom,
% 0.30/0.47 ! [A: $tType,C2: A] :
% 0.30/0.47 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % empty_iff
% 0.30/0.47 thf(fact_17_insert__absorb2,axiom,
% 0.30/0.47 ! [A: $tType,X: A,A3: set @ A] :
% 0.30/0.47 ( ( insert @ A @ X @ ( insert @ A @ X @ A3 ) )
% 0.30/0.47 = ( insert @ A @ X @ A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_absorb2
% 0.30/0.47 thf(fact_18_insert__iff,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,B3: A,A3: set @ A] :
% 0.30/0.47 ( ( member @ A @ A2 @ ( insert @ A @ B3 @ A3 ) )
% 0.30/0.47 = ( ( A2 = B3 )
% 0.30/0.47 | ( member @ A @ A2 @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_iff
% 0.30/0.47 thf(fact_19_insertCI,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,B2: set @ A,B3: A] :
% 0.30/0.47 ( ( ~ ( member @ A @ A2 @ B2 )
% 0.30/0.47 => ( A2 = B3 ) )
% 0.30/0.47 => ( member @ A @ A2 @ ( insert @ A @ B3 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insertCI
% 0.30/0.47 thf(fact_20_sup_Oright__idem,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [A2: A,B3: A] :
% 0.30/0.47 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B3 ) @ B3 )
% 0.30/0.47 = ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.right_idem
% 0.30/0.47 thf(fact_21_sup__left__idem,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.30/0.47 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_left_idem
% 0.30/0.47 thf(fact_22_sup_Oleft__idem,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [A2: A,B3: A] :
% 0.30/0.47 ( ( sup_sup @ A @ A2 @ ( sup_sup @ A @ A2 @ B3 ) )
% 0.30/0.47 = ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.left_idem
% 0.30/0.47 thf(fact_23_sup__idem,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [X: A] :
% 0.30/0.47 ( ( sup_sup @ A @ X @ X )
% 0.30/0.47 = X ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_idem
% 0.30/0.47 thf(fact_24_sup_Oidem,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [A2: A] :
% 0.30/0.47 ( ( sup_sup @ A @ A2 @ A2 )
% 0.30/0.47 = A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.idem
% 0.30/0.47 thf(fact_25_sup__apply,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ B )
% 0.30/0.47 => ( ( sup_sup @ ( A > B ) )
% 0.30/0.47 = ( ^ [F: A > B,G: A > B,X2: A] : ( sup_sup @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_apply
% 0.30/0.47 thf(fact_26_UnCI,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,B2: set @ A,A3: set @ A] :
% 0.30/0.47 ( ( ~ ( member @ A @ C2 @ B2 )
% 0.30/0.47 => ( member @ A @ C2 @ A3 ) )
% 0.30/0.47 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % UnCI
% 0.30/0.47 thf(fact_27_singletonI,axiom,
% 0.30/0.47 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % singletonI
% 0.30/0.47 thf(fact_28_bot__set__def,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bot_bot @ ( set @ A ) )
% 0.30/0.47 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bot_set_def
% 0.30/0.47 thf(fact_29_ex__in__conv,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A] :
% 0.30/0.47 ( ( ? [X2: A] : ( member @ A @ X2 @ A3 ) )
% 0.30/0.47 = ( A3
% 0.30/0.47 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ex_in_conv
% 0.30/0.47 thf(fact_30_equals0I,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A] :
% 0.30/0.47 ( ! [Y2: A] :
% 0.30/0.47 ~ ( member @ A @ Y2 @ A3 )
% 0.30/0.47 => ( A3
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % equals0I
% 0.30/0.47 thf(fact_31_equals0D,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,A2: A] :
% 0.30/0.47 ( ( A3
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 => ~ ( member @ A @ A2 @ A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % equals0D
% 0.30/0.47 thf(fact_32_emptyE,axiom,
% 0.30/0.47 ! [A: $tType,A2: A] :
% 0.30/0.47 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % emptyE
% 0.30/0.47 thf(fact_33_mk__disjoint__insert,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,A3: set @ A] :
% 0.30/0.47 ( ( member @ A @ A2 @ A3 )
% 0.30/0.47 => ? [B4: set @ A] :
% 0.30/0.47 ( ( A3
% 0.30/0.47 = ( insert @ A @ A2 @ B4 ) )
% 0.30/0.47 & ~ ( member @ A @ A2 @ B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % mk_disjoint_insert
% 0.30/0.47 thf(fact_34_insert__commute,axiom,
% 0.30/0.47 ! [A: $tType,X: A,Y: A,A3: set @ A] :
% 0.30/0.47 ( ( insert @ A @ X @ ( insert @ A @ Y @ A3 ) )
% 0.30/0.47 = ( insert @ A @ Y @ ( insert @ A @ X @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_commute
% 0.30/0.47 thf(fact_35_insert__eq__iff,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,A3: set @ A,B3: A,B2: set @ A] :
% 0.30/0.47 ( ~ ( member @ A @ A2 @ A3 )
% 0.30/0.47 => ( ~ ( member @ A @ B3 @ B2 )
% 0.30/0.47 => ( ( ( insert @ A @ A2 @ A3 )
% 0.30/0.47 = ( insert @ A @ B3 @ B2 ) )
% 0.30/0.47 = ( ( ( A2 = B3 )
% 0.30/0.47 => ( A3 = B2 ) )
% 0.30/0.47 & ( ( A2 != B3 )
% 0.30/0.47 => ? [C3: set @ A] :
% 0.30/0.47 ( ( A3
% 0.30/0.47 = ( insert @ A @ B3 @ C3 ) )
% 0.30/0.47 & ~ ( member @ A @ B3 @ C3 )
% 0.30/0.47 & ( B2
% 0.30/0.47 = ( insert @ A @ A2 @ C3 ) )
% 0.30/0.47 & ~ ( member @ A @ A2 @ C3 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_eq_iff
% 0.30/0.47 thf(fact_36_insert__absorb,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,A3: set @ A] :
% 0.30/0.47 ( ( member @ A @ A2 @ A3 )
% 0.30/0.47 => ( ( insert @ A @ A2 @ A3 )
% 0.30/0.47 = A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_absorb
% 0.30/0.47 thf(fact_37_insert__ident,axiom,
% 0.30/0.47 ! [A: $tType,X: A,A3: set @ A,B2: set @ A] :
% 0.30/0.47 ( ~ ( member @ A @ X @ A3 )
% 0.30/0.47 => ( ~ ( member @ A @ X @ B2 )
% 0.30/0.47 => ( ( ( insert @ A @ X @ A3 )
% 0.30/0.47 = ( insert @ A @ X @ B2 ) )
% 0.30/0.47 = ( A3 = B2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_ident
% 0.30/0.47 thf(fact_38_Set_Oset__insert,axiom,
% 0.30/0.47 ! [A: $tType,X: A,A3: set @ A] :
% 0.30/0.47 ( ( member @ A @ X @ A3 )
% 0.30/0.47 => ~ ! [B4: set @ A] :
% 0.30/0.47 ( ( A3
% 0.30/0.47 = ( insert @ A @ X @ B4 ) )
% 0.30/0.47 => ( member @ A @ X @ B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Set.set_insert
% 0.30/0.47 thf(fact_39_insertI2,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,B2: set @ A,B3: A] :
% 0.30/0.47 ( ( member @ A @ A2 @ B2 )
% 0.30/0.47 => ( member @ A @ A2 @ ( insert @ A @ B3 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insertI2
% 0.30/0.47 thf(fact_40_insertI1,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,B2: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % insertI1
% 0.30/0.47 thf(fact_41_insertE,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,B3: A,A3: set @ A] :
% 0.30/0.47 ( ( member @ A @ A2 @ ( insert @ A @ B3 @ A3 ) )
% 0.30/0.47 => ( ( A2 != B3 )
% 0.30/0.47 => ( member @ A @ A2 @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insertE
% 0.30/0.47 thf(fact_42_sup__left__commute,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [X: A,Y: A,Z: A] :
% 0.30/0.47 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.30/0.47 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_left_commute
% 0.30/0.47 thf(fact_43_sup_Oleft__commute,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [B3: A,A2: A,C2: A] :
% 0.30/0.47 ( ( sup_sup @ A @ B3 @ ( sup_sup @ A @ A2 @ C2 ) )
% 0.30/0.47 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B3 @ C2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.left_commute
% 0.30/0.47 thf(fact_44_sup__commute,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ( ( sup_sup @ A )
% 0.30/0.47 = ( ^ [X2: A,Y3: A] : ( sup_sup @ A @ Y3 @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_commute
% 0.30/0.47 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,P: A > $o] :
% 0.30/0.47 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.30/0.47 = ( P @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % mem_Collect_eq
% 0.30/0.47 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A] :
% 0.30/0.47 ( ( collect @ A
% 0.30/0.47 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 0.30/0.47 = A3 ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_mem_eq
% 0.30/0.47 thf(fact_47_Collect__cong,axiom,
% 0.30/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.47 ( ! [X3: A] :
% 0.30/0.47 ( ( P @ X3 )
% 0.30/0.47 = ( Q @ X3 ) )
% 0.30/0.47 => ( ( collect @ A @ P )
% 0.30/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_cong
% 0.30/0.47 thf(fact_48_ext,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,F2: A > B,G2: A > B] :
% 0.30/0.47 ( ! [X3: A] :
% 0.30/0.47 ( ( F2 @ X3 )
% 0.30/0.47 = ( G2 @ X3 ) )
% 0.30/0.47 => ( F2 = G2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % ext
% 0.30/0.47 thf(fact_49_sup_Ocommute,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ( ( sup_sup @ A )
% 0.30/0.47 = ( ^ [A4: A,B5: A] : ( sup_sup @ A @ B5 @ A4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.commute
% 0.30/0.47 thf(fact_50_sup__assoc,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [X: A,Y: A,Z: A] :
% 0.30/0.47 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.30/0.47 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_assoc
% 0.30/0.47 thf(fact_51_sup_Oassoc,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [A2: A,B3: A,C2: A] :
% 0.30/0.47 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B3 ) @ C2 )
% 0.30/0.47 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B3 @ C2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.assoc
% 0.30/0.47 thf(fact_52_boolean__algebra__cancel_Osup2,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [B2: A,K: A,B3: A,A2: A] :
% 0.30/0.47 ( ( B2
% 0.30/0.47 = ( sup_sup @ A @ K @ B3 ) )
% 0.30/0.47 => ( ( sup_sup @ A @ A2 @ B2 )
% 0.30/0.47 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % boolean_algebra_cancel.sup2
% 0.30/0.47 thf(fact_53_boolean__algebra__cancel_Osup1,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [A3: A,K: A,A2: A,B3: A] :
% 0.30/0.47 ( ( A3
% 0.30/0.47 = ( sup_sup @ A @ K @ A2 ) )
% 0.30/0.47 => ( ( sup_sup @ A @ A3 @ B3 )
% 0.30/0.47 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % boolean_algebra_cancel.sup1
% 0.30/0.47 thf(fact_54_sup__fun__def,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ B )
% 0.30/0.47 => ( ( sup_sup @ ( A > B ) )
% 0.30/0.47 = ( ^ [F: A > B,G: A > B,X2: A] : ( sup_sup @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_fun_def
% 0.30/0.47 thf(fact_55_inf__sup__aci_I5_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( lattice @ A )
% 0.30/0.47 => ( ( sup_sup @ A )
% 0.30/0.47 = ( ^ [X2: A,Y3: A] : ( sup_sup @ A @ Y3 @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inf_sup_aci(5)
% 0.30/0.47 thf(fact_56_inf__sup__aci_I6_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( lattice @ A )
% 0.30/0.47 => ! [X: A,Y: A,Z: A] :
% 0.30/0.47 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.30/0.47 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inf_sup_aci(6)
% 0.30/0.47 thf(fact_57_inf__sup__aci_I7_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( lattice @ A )
% 0.30/0.47 => ! [X: A,Y: A,Z: A] :
% 0.30/0.47 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.30/0.47 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inf_sup_aci(7)
% 0.30/0.47 thf(fact_58_inf__sup__aci_I8_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( lattice @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.30/0.47 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inf_sup_aci(8)
% 0.30/0.47 thf(fact_59_Un__left__commute,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,B2: set @ A,C: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B2 @ C ) )
% 0.30/0.47 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A3 @ C ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_left_commute
% 0.30/0.47 thf(fact_60_Un__left__absorb,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 0.30/0.47 = ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_left_absorb
% 0.30/0.47 thf(fact_61_Un__commute,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) )
% 0.30/0.47 = ( ^ [A5: set @ A,B6: set @ A] : ( sup_sup @ ( set @ A ) @ B6 @ A5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_commute
% 0.30/0.47 thf(fact_62_Un__absorb,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ A3 @ A3 )
% 0.30/0.47 = A3 ) ).
% 0.30/0.47
% 0.30/0.47 % Un_absorb
% 0.30/0.47 thf(fact_63_Un__assoc,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,B2: set @ A,C: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) @ C )
% 0.30/0.47 = ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B2 @ C ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_assoc
% 0.30/0.47 thf(fact_64_ball__Un,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,B2: set @ A,P: A > $o] :
% 0.30/0.47 ( ( ! [X2: A] :
% 0.30/0.47 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 0.30/0.47 => ( P @ X2 ) ) )
% 0.30/0.47 = ( ! [X2: A] :
% 0.30/0.47 ( ( member @ A @ X2 @ A3 )
% 0.30/0.47 => ( P @ X2 ) )
% 0.30/0.47 & ! [X2: A] :
% 0.30/0.47 ( ( member @ A @ X2 @ B2 )
% 0.30/0.47 => ( P @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ball_Un
% 0.30/0.47 thf(fact_65_bex__Un,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,B2: set @ A,P: A > $o] :
% 0.30/0.47 ( ( ? [X2: A] :
% 0.30/0.47 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 0.30/0.47 & ( P @ X2 ) ) )
% 0.30/0.47 = ( ? [X2: A] :
% 0.30/0.47 ( ( member @ A @ X2 @ A3 )
% 0.30/0.47 & ( P @ X2 ) )
% 0.30/0.47 | ? [X2: A] :
% 0.30/0.47 ( ( member @ A @ X2 @ B2 )
% 0.30/0.47 & ( P @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bex_Un
% 0.30/0.47 thf(fact_66_UnI2,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,B2: set @ A,A3: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ B2 )
% 0.30/0.47 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % UnI2
% 0.30/0.47 thf(fact_67_UnI1,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A3: set @ A,B2: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ A3 )
% 0.30/0.47 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % UnI1
% 0.30/0.47 thf(fact_68_UnE,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A3: set @ A,B2: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 0.30/0.47 => ( ~ ( member @ A @ C2 @ A3 )
% 0.30/0.47 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % UnE
% 0.30/0.47 thf(fact_69_Uvariation__sym__rel,axiom,
% 0.30/0.47 ! [Omega: variable > real,Nu: variable > real,U: set @ variable] :
% 0.30/0.47 ( ( denota1419872369iation @ Omega @ Nu @ U )
% 0.30/0.47 => ( denota1419872369iation @ Nu @ Omega @ U ) ) ).
% 0.30/0.47
% 0.30/0.47 % Uvariation_sym_rel
% 0.30/0.47 thf(fact_70_Uvariation__refl,axiom,
% 0.30/0.47 ! [Nu: variable > real,V: set @ variable] : ( denota1419872369iation @ Nu @ Nu @ V ) ).
% 0.30/0.47
% 0.30/0.47 % Uvariation_refl
% 0.30/0.47 thf(fact_71_Uvariation__sym,axiom,
% 0.30/0.47 ( denota1419872369iation
% 0.30/0.47 = ( ^ [Omega2: variable > real,Nu3: variable > real] : ( denota1419872369iation @ Nu3 @ Omega2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Uvariation_sym
% 0.30/0.47 thf(fact_72_Uvariation__def,axiom,
% 0.30/0.47 ( denota1419872369iation
% 0.30/0.47 = ( ^ [Nu3: variable > real,Nu4: variable > real,U2: set @ variable] :
% 0.30/0.47 ! [I: variable] :
% 0.30/0.47 ( ~ ( member @ variable @ I @ U2 )
% 0.30/0.47 => ( ( Nu3 @ I )
% 0.30/0.47 = ( Nu4 @ I ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Uvariation_def
% 0.30/0.47 thf(fact_73_singleton__inject,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,B3: A] :
% 0.30/0.47 ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 => ( A2 = B3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % singleton_inject
% 0.30/0.47 thf(fact_74_insert__not__empty,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,A3: set @ A] :
% 0.30/0.47 ( ( insert @ A @ A2 @ A3 )
% 0.30/0.47 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_not_empty
% 0.30/0.47 thf(fact_75_doubleton__eq__iff,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,B3: A,C2: A,D: A] :
% 0.30/0.47 ( ( ( insert @ A @ A2 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 = ( insert @ A @ C2 @ ( insert @ A @ D @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.47 = ( ( ( A2 = C2 )
% 0.30/0.47 & ( B3 = D ) )
% 0.30/0.47 | ( ( A2 = D )
% 0.30/0.47 & ( B3 = C2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % doubleton_eq_iff
% 0.30/0.47 thf(fact_76_singleton__iff,axiom,
% 0.30/0.47 ! [A: $tType,B3: A,A2: A] :
% 0.30/0.47 ( ( member @ A @ B3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 = ( B3 = A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % singleton_iff
% 0.30/0.47 thf(fact_77_singletonD,axiom,
% 0.30/0.47 ! [A: $tType,B3: A,A2: A] :
% 0.30/0.47 ( ( member @ A @ B3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 => ( B3 = A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % singletonD
% 0.30/0.47 thf(fact_78_Un__empty__right,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = A3 ) ).
% 0.30/0.47
% 0.30/0.47 % Un_empty_right
% 0.30/0.47 thf(fact_79_Un__empty__left,axiom,
% 0.30/0.47 ! [A: $tType,B2: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B2 )
% 0.30/0.47 = B2 ) ).
% 0.30/0.47
% 0.30/0.47 % Un_empty_left
% 0.30/0.47 thf(fact_80_Uvariation__trans,axiom,
% 0.30/0.47 ! [Omega: variable > real,Nu: variable > real,U: set @ variable,Mu: variable > real,V: set @ variable] :
% 0.30/0.47 ( ( denota1419872369iation @ Omega @ Nu @ U )
% 0.30/0.47 => ( ( denota1419872369iation @ Nu @ Mu @ V )
% 0.30/0.47 => ( denota1419872369iation @ Omega @ Mu @ ( sup_sup @ ( set @ variable ) @ U @ V ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Uvariation_trans
% 0.30/0.47 thf(fact_81_singleton__Un__iff,axiom,
% 0.30/0.47 ! [A: $tType,X: A,A3: set @ A,B2: set @ A] :
% 0.30/0.47 ( ( ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 0.30/0.47 = ( ( ( A3
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 & ( B2
% 0.30/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.47 | ( ( A3
% 0.30/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 & ( B2
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 | ( ( A3
% 0.30/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 & ( B2
% 0.30/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % singleton_Un_iff
% 0.30/0.47 thf(fact_82_Un__singleton__iff,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,B2: set @ A,X: A] :
% 0.30/0.47 ( ( ( sup_sup @ ( set @ A ) @ A3 @ B2 )
% 0.30/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 = ( ( ( A3
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 & ( B2
% 0.30/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.47 | ( ( A3
% 0.30/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 & ( B2
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 | ( ( A3
% 0.30/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 & ( B2
% 0.30/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_singleton_iff
% 0.30/0.47 thf(fact_83_insert__is__Un,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( insert @ A )
% 0.30/0.47 = ( ^ [A4: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_is_Un
% 0.30/0.47 thf(fact_84__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rr_O_A_092_060forall_062x0_Ax1_Ax2_Ax3_Ax4_Ax5_O_A_I_092_060exists_062v6_O_AUvariation_Av6_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_Av6_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_Av6_J_A_061_A_IUvariation_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.30/0.47 ~ ! [Rr: trm > denotational_interp > trm > denotational_interp > char > ( real > variable > real ) > variable > real] :
% 0.30/0.47 ~ ! [X0: trm,X1: denotational_interp,X22: trm,X32: denotational_interp,X4: char,X5: real > variable > real] :
% 0.30/0.47 ( ( ? [V6: variable > real] :
% 0.30/0.47 ( ( denota1419872369iation @ V6 @ ( X5 @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ X4 ) @ ( insert @ variable @ ( dVar @ X4 ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
% 0.30/0.47 & ( ( denota1863255036rm_sem @ X32 @ X22 @ V6 )
% 0.30/0.47 != ( denota1863255036rm_sem @ X1 @ X0 @ V6 ) ) ) )
% 0.30/0.47 = ( ( denota1419872369iation @ ( Rr @ X0 @ X1 @ X22 @ X32 @ X4 @ X5 ) @ ( X5 @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ X4 ) @ ( insert @ variable @ ( dVar @ X4 ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
% 0.30/0.47 & ( ( denota1863255036rm_sem @ X32 @ X22 @ ( Rr @ X0 @ X1 @ X22 @ X32 @ X4 @ X5 ) )
% 0.30/0.47 != ( denota1863255036rm_sem @ X1 @ X0 @ ( Rr @ X0 @ X1 @ X22 @ X32 @ X4 @ X5 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % \<open>\<And>thesis. (\<And>rr. \<forall>x0 x1 x2 x3 x4 x5. (\<exists>v6. Uvariation v6 (x5 0) {RVar x4, DVar x4} \<and> term_sem x3 x2 v6 \<noteq> term_sem x1 x0 v6) = (Uvariation (rr x0 x1 x2 x3 x4 x5) (x5 0) {RVar x4, DVar x4} \<and> term_sem x3 x2 (rr x0 x1 x2 x3 x4 x5) \<noteq> term_sem x1 x0 (rr x0 x1 x2 x3 x4 x5)) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.30/0.47 thf(fact_85_solves__Vagree__trans,axiom,
% 0.30/0.47 ! [F3: real > variable > real,Omega: variable > real,U: set @ variable,I2: denotational_interp,X: char,Theta: trm,Zeta: real] :
% 0.30/0.47 ( ( denota1419872369iation @ ( F3 @ ( zero_zero @ real ) ) @ Omega @ U )
% 0.30/0.47 => ( ( denota1778088425es_ODE @ I2 @ F3 @ X @ Theta )
% 0.30/0.47 => ( denota1419872369iation @ ( F3 @ Zeta ) @ Omega @ ( sup_sup @ ( set @ variable ) @ U @ ( insert @ variable @ ( rVar @ X ) @ ( insert @ variable @ ( dVar @ X ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % solves_Vagree_trans
% 0.30/0.47 thf(fact_86__092_060open_062_092_060forall_062x0_Ax1_Ax2_Ax3_Ax4_Ax5_O_A_I_092_060exists_062v6_O_AUvariation_Av6_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_Av6_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_Av6_J_A_061_A_IUvariation_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_J_092_060close_062,axiom,
% 0.30/0.47 ! [X0: trm,X1: denotational_interp,X22: trm,X32: denotational_interp,X4: char,X5: real > variable > real] :
% 0.30/0.47 ( ( ? [V6: variable > real] :
% 0.30/0.47 ( ( denota1419872369iation @ V6 @ ( X5 @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ X4 ) @ ( insert @ variable @ ( dVar @ X4 ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
% 0.30/0.47 & ( ( denota1863255036rm_sem @ X32 @ X22 @ V6 )
% 0.30/0.47 != ( denota1863255036rm_sem @ X1 @ X0 @ V6 ) ) ) )
% 0.30/0.47 = ( ( denota1419872369iation @ ( rr @ X0 @ X1 @ X22 @ X32 @ X4 @ X5 ) @ ( X5 @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ X4 ) @ ( insert @ variable @ ( dVar @ X4 ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
% 0.30/0.47 & ( ( denota1863255036rm_sem @ X32 @ X22 @ ( rr @ X0 @ X1 @ X22 @ X32 @ X4 @ X5 ) )
% 0.30/0.47 != ( denota1863255036rm_sem @ X1 @ X0 @ ( rr @ X0 @ X1 @ X22 @ X32 @ X4 @ X5 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % \<open>\<forall>x0 x1 x2 x3 x4 x5. (\<exists>v6. Uvariation v6 (x5 0) {RVar x4, DVar x4} \<and> term_sem x3 x2 v6 \<noteq> term_sem x1 x0 v6) = (Uvariation (rr x0 x1 x2 x3 x4 x5) (x5 0) {RVar x4, DVar x4} \<and> term_sem x3 x2 (rr x0 x1 x2 x3 x4 x5) \<noteq> term_sem x1 x0 (rr x0 x1 x2 x3 x4 x5))\<close>
% 0.30/0.47 thf(fact_87_variable_Oinject_I1_J,axiom,
% 0.30/0.47 ! [X12: char,Y1: char] :
% 0.30/0.47 ( ( ( rVar @ X12 )
% 0.30/0.47 = ( rVar @ Y1 ) )
% 0.30/0.47 = ( X12 = Y1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % variable.inject(1)
% 0.30/0.47 thf(fact_88_set__zero,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( zero @ A )
% 0.30/0.47 => ( ( zero_zero @ ( set @ A ) )
% 0.30/0.47 = ( insert @ A @ ( zero_zero @ A ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % set_zero
% 0.30/0.47 thf(fact_89_variable_Oinject_I2_J,axiom,
% 0.30/0.47 ! [X23: char,Y22: char] :
% 0.30/0.47 ( ( ( dVar @ X23 )
% 0.30/0.47 = ( dVar @ Y22 ) )
% 0.30/0.47 = ( X23 = Y22 ) ) ).
% 0.30/0.47
% 0.30/0.47 % variable.inject(2)
% 0.30/0.47 thf(fact_90_union__or,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A3: set @ A,B2: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 0.30/0.47 = ( ( member @ A @ C2 @ A3 )
% 0.30/0.47 | ( member @ A @ C2 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % union_or
% 0.30/0.47 thf(fact_91_ball__insert,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,B2: set @ A,P: A > $o] :
% 0.30/0.47 ( ( ! [X2: A] :
% 0.30/0.47 ( ( member @ A @ X2 @ ( insert @ A @ A2 @ B2 ) )
% 0.30/0.47 => ( P @ X2 ) ) )
% 0.30/0.47 = ( ( P @ A2 )
% 0.30/0.47 & ! [X2: A] :
% 0.30/0.47 ( ( member @ A @ X2 @ B2 )
% 0.30/0.47 => ( P @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ball_insert
% 0.30/0.47 thf(fact_92_the__elem__eq,axiom,
% 0.30/0.47 ! [A: $tType,X: A] :
% 0.30/0.47 ( ( the_elem @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 = X ) ).
% 0.30/0.47
% 0.30/0.47 % the_elem_eq
% 0.30/0.47 thf(fact_93_bot__apply,axiom,
% 0.30/0.47 ! [C4: $tType,D2: $tType] :
% 0.30/0.47 ( ( bot @ C4 )
% 0.30/0.47 => ( ( bot_bot @ ( D2 > C4 ) )
% 0.30/0.47 = ( ^ [X2: D2] : ( bot_bot @ C4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bot_apply
% 0.30/0.47 thf(fact_94_f2,axiom,
% 0.30/0.47 ! [F4: real > variable > real,C5: char,I3: denotational_interp,T: trm,Ia: denotational_interp,Ta: trm] :
% 0.30/0.47 ( ( ( denota1419872369iation @ ( rr @ Ta @ Ia @ T @ I3 @ C5 @ F4 ) @ ( F4 @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ C5 ) @ ( insert @ variable @ ( dVar @ C5 ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
% 0.30/0.47 & ( ( denota1863255036rm_sem @ I3 @ T @ ( rr @ Ta @ Ia @ T @ I3 @ C5 @ F4 ) )
% 0.30/0.47 != ( denota1863255036rm_sem @ Ia @ Ta @ ( rr @ Ta @ Ia @ T @ I3 @ C5 @ F4 ) ) ) )
% 0.30/0.47 | ( ( denota1778088425es_ODE @ I3 @ F4 @ C5 @ T )
% 0.30/0.47 = ( denota1778088425es_ODE @ Ia @ F4 @ C5 @ Ta ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f2
% 0.30/0.47 thf(fact_95_zero__reorient,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( zero @ A )
% 0.30/0.47 => ! [X: A] :
% 0.30/0.47 ( ( ( zero_zero @ A )
% 0.30/0.47 = X )
% 0.30/0.47 = ( X
% 0.30/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % zero_reorient
% 0.30/0.47 thf(fact_96_bot__fun__def,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( bot @ B )
% 0.30/0.47 => ( ( bot_bot @ ( A > B ) )
% 0.30/0.47 = ( ^ [X2: A] : ( bot_bot @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bot_fun_def
% 0.30/0.47 thf(fact_97_not__union__or,axiom,
% 0.30/0.47 ! [A: $tType,X: A,A3: set @ A,B2: set @ A] :
% 0.30/0.47 ( ( ~ ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) )
% 0.30/0.47 = ( ~ ( member @ A @ X @ A3 )
% 0.30/0.47 & ~ ( member @ A @ X @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_union_or
% 0.30/0.47 thf(fact_98_same__ODE__same__sol,axiom,
% 0.30/0.47 ! [F3: real > variable > real,X: char,I2: denotational_interp,Theta: trm,J: denotational_interp,Eta: trm] :
% 0.30/0.47 ( ! [Nu5: variable > real] :
% 0.30/0.47 ( ( denota1419872369iation @ Nu5 @ ( F3 @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ X ) @ ( insert @ variable @ ( dVar @ X ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
% 0.30/0.47 => ( ( denota1863255036rm_sem @ I2 @ Theta @ Nu5 )
% 0.30/0.47 = ( denota1863255036rm_sem @ J @ Eta @ Nu5 ) ) )
% 0.30/0.47 => ( ( denota1778088425es_ODE @ I2 @ F3 @ X @ Theta )
% 0.30/0.47 = ( denota1778088425es_ODE @ J @ F3 @ X @ Eta ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % same_ODE_same_sol
% 0.30/0.47 thf(fact_99_variable_Odistinct_I1_J,axiom,
% 0.30/0.47 ! [X12: char,X23: char] :
% 0.30/0.47 ( ( rVar @ X12 )
% 0.30/0.47 != ( dVar @ X23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % variable.distinct(1)
% 0.30/0.47 thf(fact_100_variable_Oinduct,axiom,
% 0.30/0.47 ! [P: variable > $o,Variable: variable] :
% 0.30/0.47 ( ! [X3: char] : ( P @ ( rVar @ X3 ) )
% 0.30/0.47 => ( ! [X3: char] : ( P @ ( dVar @ X3 ) )
% 0.30/0.47 => ( P @ Variable ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % variable.induct
% 0.30/0.47 thf(fact_101_variable_Oexhaust,axiom,
% 0.30/0.47 ! [Y: variable] :
% 0.30/0.47 ( ! [X13: char] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( rVar @ X13 ) )
% 0.30/0.47 => ~ ! [X24: char] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( dVar @ X24 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % variable.exhaust
% 0.30/0.47 thf(fact_102_bot__empty__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bot_bot @ ( A > $o ) )
% 0.30/0.47 = ( ^ [X2: A] : ( member @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bot_empty_eq
% 0.30/0.47 thf(fact_103_Collect__empty__eq__bot,axiom,
% 0.30/0.47 ! [A: $tType,P: A > $o] :
% 0.30/0.47 ( ( ( collect @ A @ P )
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = ( P
% 0.30/0.47 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_empty_eq_bot
% 0.30/0.47 thf(fact_104_is__singleton__the__elem,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( is_singleton @ A )
% 0.30/0.47 = ( ^ [A5: set @ A] :
% 0.30/0.47 ( A5
% 0.30/0.47 = ( insert @ A @ ( the_elem @ A @ A5 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % is_singleton_the_elem
% 0.30/0.47 thf(fact_105_vaflow2,axiom,
% 0.30/0.47 ! [F3: real > variable > real,Theta: trm,Zeta: real] :
% 0.30/0.47 ( ( denota1778088425es_ODE @ ( uSubst2091380086djoint @ sigma @ i @ omega ) @ F3 @ x @ Theta )
% 0.30/0.47 => ( denota1419872369iation @ ( F3 @ Zeta ) @ ( F3 @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % vaflow2
% 0.30/0.47 thf(fact_106_is__singletonI,axiom,
% 0.30/0.47 ! [A: $tType,X: A] : ( is_singleton @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % is_singletonI
% 0.30/0.47 thf(fact_107_a1,axiom,
% 0.30/0.47 denota1778088425es_ODE @ ( uSubst2091380086djoint @ sigma @ i @ omega ) @ f @ x @ theta ).
% 0.30/0.47
% 0.30/0.47 % a1
% 0.30/0.47 thf(fact_108_is__singletonI_H,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A] :
% 0.30/0.47 ( ( A3
% 0.30/0.47 != ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 => ( ! [X3: A,Y2: A] :
% 0.30/0.47 ( ( member @ A @ X3 @ A3 )
% 0.30/0.47 => ( ( member @ A @ Y2 @ A3 )
% 0.30/0.47 => ( X3 = Y2 ) ) )
% 0.30/0.47 => ( is_singleton @ A @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % is_singletonI'
% 0.30/0.47 thf(fact_109_is__singleton__def,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( is_singleton @ A )
% 0.30/0.47 = ( ^ [A5: set @ A] :
% 0.30/0.47 ? [X2: A] :
% 0.30/0.47 ( A5
% 0.30/0.47 = ( insert @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % is_singleton_def
% 0.30/0.47 thf(fact_110_is__singletonE,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A] :
% 0.30/0.47 ( ( is_singleton @ A @ A3 )
% 0.30/0.47 => ~ ! [X3: A] :
% 0.30/0.47 ( A3
% 0.30/0.47 != ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % is_singletonE
% 0.30/0.47 thf(fact_111_vaflow1,axiom,
% 0.30/0.47 ! [F3: real > variable > real,Theta: trm,Zeta: real] :
% 0.30/0.47 ( ( denota1778088425es_ODE @ i @ F3 @ x @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) @ Theta ) ) )
% 0.30/0.47 => ( denota1419872369iation @ ( F3 @ Zeta ) @ ( F3 @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % vaflow1
% 0.30/0.47 thf(fact_112_l2r,axiom,
% 0.30/0.47 ( ( denota1778088425es_ODE @ i @ f @ x @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) @ theta ) ) )
% 0.30/0.47 => ( denota1778088425es_ODE @ ( uSubst2091380086djoint @ sigma @ i @ omega ) @ f @ x @ theta ) ) ).
% 0.30/0.47
% 0.30/0.47 % l2r
% 0.30/0.47 thf(fact_113_IH,axiom,
% 0.30/0.47 ! [Nu: variable > real] :
% 0.30/0.47 ( ( denota1419872369iation @ Nu @ ( f @ ( zero_zero @ real ) ) @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) )
% 0.30/0.47 => ( ( denota1863255036rm_sem @ i @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) @ theta ) ) @ Nu )
% 0.30/0.47 = ( denota1863255036rm_sem @ ( uSubst2091380086djoint @ sigma @ i @ ( f @ ( zero_zero @ real ) ) ) @ theta @ Nu ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % IH
% 0.30/0.47 thf(fact_114_subdef,axiom,
% 0.30/0.47 ( ( uSubst95898992stappt @ sigma @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) @ theta )
% 0.30/0.47 != ( none @ trm ) ) ).
% 0.30/0.47
% 0.30/0.47 % subdef
% 0.30/0.47 thf(fact_115_variable_Osize__gen_I1_J,axiom,
% 0.30/0.47 ! [X12: char] :
% 0.30/0.47 ( ( size_variable @ ( rVar @ X12 ) )
% 0.30/0.47 = ( zero_zero @ nat ) ) ).
% 0.30/0.47
% 0.30/0.47 % variable.size_gen(1)
% 0.30/0.47 thf(fact_116_usubst__term,axiom,
% 0.30/0.47 ! [Nu: variable > real,Omega: variable > real,U: set @ variable,Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),Theta: trm,I2: denotational_interp] :
% 0.30/0.47 ( ( denota1419872369iation @ Nu @ Omega @ U )
% 0.30/0.47 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.30/0.47 != ( none @ trm ) )
% 0.30/0.47 => ( ( denota1863255036rm_sem @ I2 @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) @ Nu )
% 0.30/0.47 = ( denota1863255036rm_sem @ ( uSubst2091380086djoint @ Sigma @ I2 @ Omega ) @ Theta @ Nu ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % usubst_term
% 0.30/0.47 thf(fact_117_usubstappt__det,axiom,
% 0.30/0.47 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,V: set @ variable] :
% 0.30/0.47 ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.30/0.47 != ( none @ trm ) )
% 0.30/0.47 => ( ( ( uSubst95898992stappt @ Sigma @ V @ Theta )
% 0.30/0.47 != ( none @ trm ) )
% 0.30/0.47 => ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.30/0.47 = ( uSubst95898992stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % usubstappt_det
% 0.30/0.47 thf(fact_118_undeft__None,axiom,
% 0.30/0.47 ( ( none @ trm )
% 0.30/0.47 = ( none @ trm ) ) ).
% 0.30/0.47
% 0.30/0.47 % undeft_None
% 0.30/0.47 thf(fact_119_usubst__ode,axiom,
% 0.30/0.47 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),X: char,Theta: trm,I2: denotational_interp,F3: real > variable > real] :
% 0.30/0.47 ( ( ( uSubst95898992stappt @ Sigma @ ( insert @ variable @ ( rVar @ X ) @ ( insert @ variable @ ( dVar @ X ) @ ( bot_bot @ ( set @ variable ) ) ) ) @ Theta )
% 0.30/0.47 != ( none @ trm ) )
% 0.30/0.47 => ( ( denota1778088425es_ODE @ I2 @ F3 @ X @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ ( insert @ variable @ ( rVar @ X ) @ ( insert @ variable @ ( dVar @ X ) @ ( bot_bot @ ( set @ variable ) ) ) ) @ Theta ) ) )
% 0.30/0.47 = ( denota1778088425es_ODE @ ( uSubst2091380086djoint @ Sigma @ I2 @ ( F3 @ ( zero_zero @ real ) ) ) @ F3 @ X @ Theta ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % usubst_ode
% 0.30/0.47 thf(fact_120_variable_Osize__gen_I2_J,axiom,
% 0.30/0.47 ! [X23: char] :
% 0.30/0.47 ( ( size_variable @ ( dVar @ X23 ) )
% 0.30/0.47 = ( zero_zero @ nat ) ) ).
% 0.30/0.47
% 0.30/0.47 % variable.size_gen(2)
% 0.30/0.47 thf(fact_121_option_Oexpand,axiom,
% 0.30/0.47 ! [A: $tType,Option: option @ A,Option2: option @ A] :
% 0.30/0.47 ( ( ( Option
% 0.30/0.47 = ( none @ A ) )
% 0.30/0.47 = ( Option2
% 0.30/0.47 = ( none @ A ) ) )
% 0.30/0.47 => ( ( ( Option
% 0.30/0.47 != ( none @ A ) )
% 0.30/0.47 => ( ( Option2
% 0.30/0.47 != ( none @ A ) )
% 0.30/0.47 => ( ( the @ A @ Option )
% 0.30/0.47 = ( the @ A @ Option2 ) ) ) )
% 0.30/0.47 => ( Option = Option2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.expand
% 0.30/0.47 thf(fact_122_variable_Osize_I3_J,axiom,
% 0.30/0.47 ! [X12: char] :
% 0.30/0.47 ( ( size_size @ variable @ ( rVar @ X12 ) )
% 0.30/0.47 = ( zero_zero @ nat ) ) ).
% 0.30/0.47
% 0.30/0.47 % variable.size(3)
% 0.30/0.47 thf(fact_123_variable_Osize_I4_J,axiom,
% 0.30/0.47 ! [X23: char] :
% 0.30/0.47 ( ( size_size @ variable @ ( dVar @ X23 ) )
% 0.30/0.47 = ( zero_zero @ nat ) ) ).
% 0.30/0.47
% 0.30/0.47 % variable.size(4)
% 0.30/0.47 thf(fact_124_Set_Ois__empty__def,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( is_empty @ A )
% 0.30/0.47 = ( ^ [A5: set @ A] :
% 0.30/0.47 ( A5
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Set.is_empty_def
% 0.30/0.47 thf(fact_125_Uvariation__repv,axiom,
% 0.30/0.47 ! [Omega: variable > real,X: variable,D: real] : ( denota1419872369iation @ Omega @ ( denotational_repv @ Omega @ X @ D ) @ ( insert @ variable @ X @ ( bot_bot @ ( set @ variable ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Uvariation_repv
% 0.30/0.47 thf(fact_126_these__empty__eq,axiom,
% 0.30/0.47 ! [A: $tType,B2: set @ ( option @ A )] :
% 0.30/0.47 ( ( ( these @ A @ B2 )
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = ( ( B2
% 0.30/0.47 = ( bot_bot @ ( set @ ( option @ A ) ) ) )
% 0.30/0.47 | ( B2
% 0.30/0.47 = ( insert @ ( option @ A ) @ ( none @ A ) @ ( bot_bot @ ( set @ ( option @ A ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % these_empty_eq
% 0.30/0.47 thf(fact_127_these__not__empty__eq,axiom,
% 0.30/0.47 ! [A: $tType,B2: set @ ( option @ A )] :
% 0.30/0.47 ( ( ( these @ A @ B2 )
% 0.30/0.47 != ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = ( ( B2
% 0.30/0.47 != ( bot_bot @ ( set @ ( option @ A ) ) ) )
% 0.30/0.47 & ( B2
% 0.30/0.47 != ( insert @ ( option @ A ) @ ( none @ A ) @ ( bot_bot @ ( set @ ( option @ A ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % these_not_empty_eq
% 0.30/0.47 thf(fact_128_variable_Osimps_I7_J,axiom,
% 0.30/0.47 ! [A: $tType,F1: char > A,F22: char > A,X12: char] :
% 0.30/0.47 ( ( rec_variable @ A @ F1 @ F22 @ ( rVar @ X12 ) )
% 0.30/0.47 = ( F1 @ X12 ) ) ).
% 0.30/0.47
% 0.30/0.47 % variable.simps(7)
% 0.30/0.47 thf(fact_129_repv__self,axiom,
% 0.30/0.47 ! [Omega: variable > real,X: variable] :
% 0.30/0.47 ( ( denotational_repv @ Omega @ X @ ( Omega @ X ) )
% 0.30/0.47 = Omega ) ).
% 0.30/0.47
% 0.30/0.47 % repv_self
% 0.30/0.47 thf(fact_130_repv__access,axiom,
% 0.30/0.47 ( denotational_repv
% 0.30/0.47 = ( ^ [Omega2: variable > real,X2: variable,R: real,Y3: variable] : ( if @ real @ ( X2 = Y3 ) @ R @ ( Omega2 @ Y3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % repv_access
% 0.30/0.47 thf(fact_131_these__empty,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( these @ A @ ( bot_bot @ ( set @ ( option @ A ) ) ) )
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % these_empty
% 0.30/0.47 thf(fact_132_these__insert__None,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ ( option @ A )] :
% 0.30/0.47 ( ( these @ A @ ( insert @ ( option @ A ) @ ( none @ A ) @ A3 ) )
% 0.30/0.47 = ( these @ A @ A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % these_insert_None
% 0.30/0.47 thf(fact_133_repv__def__correct,axiom,
% 0.30/0.47 ( denotational_repv
% 0.30/0.47 = ( ^ [Omega2: variable > real,X2: variable,R: real,Y3: variable] : ( if @ real @ ( X2 = Y3 ) @ R @ ( Omega2 @ Y3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % repv_def_correct
% 0.30/0.47 thf(fact_134_variable_Osimps_I8_J,axiom,
% 0.30/0.47 ! [A: $tType,F1: char > A,F22: char > A,X23: char] :
% 0.30/0.47 ( ( rec_variable @ A @ F1 @ F22 @ ( dVar @ X23 ) )
% 0.30/0.47 = ( F22 @ X23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % variable.simps(8)
% 0.30/0.47 thf(fact_135_these__insert__Some,axiom,
% 0.30/0.47 ! [A: $tType,X: A,A3: set @ ( option @ A )] :
% 0.30/0.47 ( ( these @ A @ ( insert @ ( option @ A ) @ ( some @ A @ X ) @ A3 ) )
% 0.30/0.47 = ( insert @ A @ X @ ( these @ A @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % these_insert_Some
% 0.30/0.47 thf(fact_136_repv__selectlike__other__converse,axiom,
% 0.30/0.47 ! [X: variable,Y: variable,Omega: variable > real,D: real,X6: set @ ( variable > real )] :
% 0.30/0.47 ( ( X != Y )
% 0.30/0.47 => ( ( member @ ( variable > real ) @ ( denotational_repv @ Omega @ X @ D ) @ X6 )
% 0.30/0.47 = ( member @ ( variable > real ) @ ( denotational_repv @ Omega @ X @ D ) @ ( static_selectlike @ X6 @ Omega @ ( insert @ variable @ Y @ ( bot_bot @ ( set @ variable ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % repv_selectlike_other_converse
% 0.30/0.47 thf(fact_137_repv__selectlike__other,axiom,
% 0.30/0.47 ! [X: variable,Y: variable,Omega: variable > real,D: real,X6: set @ ( variable > real )] :
% 0.30/0.47 ( ( X != Y )
% 0.30/0.47 => ( ( member @ ( variable > real ) @ ( denotational_repv @ Omega @ X @ D ) @ ( static_selectlike @ X6 @ Omega @ ( insert @ variable @ Y @ ( bot_bot @ ( set @ variable ) ) ) ) )
% 0.30/0.47 = ( member @ ( variable > real ) @ ( denotational_repv @ Omega @ X @ D ) @ X6 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % repv_selectlike_other
% 0.30/0.47 thf(fact_138_repv__selectlike__self,axiom,
% 0.30/0.47 ! [Omega: variable > real,X: variable,D: real,X6: set @ ( variable > real )] :
% 0.30/0.47 ( ( member @ ( variable > real ) @ ( denotational_repv @ Omega @ X @ D ) @ ( static_selectlike @ X6 @ Omega @ ( insert @ variable @ X @ ( bot_bot @ ( set @ variable ) ) ) ) )
% 0.30/0.47 = ( ( D
% 0.30/0.47 = ( Omega @ X ) )
% 0.30/0.47 & ( member @ ( variable > real ) @ Omega @ X6 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % repv_selectlike_self
% 0.30/0.47 thf(fact_139_option_Oinject,axiom,
% 0.30/0.47 ! [A: $tType,X23: A,Y22: A] :
% 0.30/0.47 ( ( ( some @ A @ X23 )
% 0.30/0.47 = ( some @ A @ Y22 ) )
% 0.30/0.47 = ( X23 = Y22 ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.inject
% 0.30/0.47 thf(fact_140_selectlike__self,axiom,
% 0.30/0.47 ! [Nu: variable > real,X6: set @ ( variable > real ),V: set @ variable] :
% 0.30/0.47 ( ( member @ ( variable > real ) @ Nu @ ( static_selectlike @ X6 @ Nu @ V ) )
% 0.30/0.47 = ( member @ ( variable > real ) @ Nu @ X6 ) ) ).
% 0.30/0.47
% 0.30/0.47 % selectlike_self
% 0.30/0.47 thf(fact_141_not__None__eq,axiom,
% 0.30/0.47 ! [A: $tType,X: option @ A] :
% 0.30/0.47 ( ( X
% 0.30/0.47 != ( none @ A ) )
% 0.30/0.47 = ( ? [Y3: A] :
% 0.30/0.47 ( X
% 0.30/0.47 = ( some @ A @ Y3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_None_eq
% 0.30/0.47 thf(fact_142_not__Some__eq,axiom,
% 0.30/0.47 ! [A: $tType,X: option @ A] :
% 0.30/0.47 ( ( ! [Y3: A] :
% 0.30/0.47 ( X
% 0.30/0.47 != ( some @ A @ Y3 ) ) )
% 0.30/0.47 = ( X
% 0.30/0.47 = ( none @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_Some_eq
% 0.30/0.47 thf(fact_143_selectlike__empty,axiom,
% 0.30/0.47 ! [X6: set @ ( variable > real ),Nu: variable > real] :
% 0.30/0.47 ( ( static_selectlike @ X6 @ Nu @ ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.47 = X6 ) ).
% 0.30/0.47
% 0.30/0.47 % selectlike_empty
% 0.30/0.47 thf(fact_144_selectlike__compose,axiom,
% 0.30/0.47 ! [X6: set @ ( variable > real ),Nu: variable > real,V: set @ variable,W: set @ variable] :
% 0.30/0.47 ( ( static_selectlike @ ( static_selectlike @ X6 @ Nu @ V ) @ Nu @ W )
% 0.30/0.47 = ( static_selectlike @ X6 @ Nu @ ( sup_sup @ ( set @ variable ) @ V @ W ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % selectlike_compose
% 0.30/0.47 thf(fact_145_option_Ocollapse,axiom,
% 0.30/0.47 ! [A: $tType,Option: option @ A] :
% 0.30/0.47 ( ( Option
% 0.30/0.47 != ( none @ A ) )
% 0.30/0.47 => ( ( some @ A @ ( the @ A @ Option ) )
% 0.30/0.47 = Option ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.collapse
% 0.30/0.47 thf(fact_146_in__these__eq,axiom,
% 0.30/0.47 ! [A: $tType,X: A,A3: set @ ( option @ A )] :
% 0.30/0.47 ( ( member @ A @ X @ ( these @ A @ A3 ) )
% 0.30/0.47 = ( member @ ( option @ A ) @ ( some @ A @ X ) @ A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % in_these_eq
% 0.30/0.47 thf(fact_147_selectlike__union,axiom,
% 0.30/0.47 ! [X6: set @ ( variable > real ),Y4: set @ ( variable > real ),Nu: variable > real,V: set @ variable] :
% 0.30/0.47 ( ( static_selectlike @ ( sup_sup @ ( set @ ( variable > real ) ) @ X6 @ Y4 ) @ Nu @ V )
% 0.30/0.47 = ( sup_sup @ ( set @ ( variable > real ) ) @ ( static_selectlike @ X6 @ Nu @ V ) @ ( static_selectlike @ Y4 @ Nu @ V ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % selectlike_union
% 0.30/0.47 thf(fact_148_option_Odistinct_I1_J,axiom,
% 0.30/0.47 ! [A: $tType,X23: A] :
% 0.30/0.47 ( ( none @ A )
% 0.30/0.47 != ( some @ A @ X23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.distinct(1)
% 0.30/0.47 thf(fact_149_option_Osel,axiom,
% 0.30/0.47 ! [A: $tType,X23: A] :
% 0.30/0.47 ( ( the @ A @ ( some @ A @ X23 ) )
% 0.30/0.47 = X23 ) ).
% 0.30/0.47
% 0.30/0.47 % option.sel
% 0.30/0.47 thf(fact_150_option_OdiscI,axiom,
% 0.30/0.47 ! [A: $tType,Option: option @ A,X23: A] :
% 0.30/0.47 ( ( Option
% 0.30/0.47 = ( some @ A @ X23 ) )
% 0.30/0.47 => ( Option
% 0.30/0.47 != ( none @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.discI
% 0.30/0.47 thf(fact_151_option_Oexhaust,axiom,
% 0.30/0.47 ! [A: $tType,Y: option @ A] :
% 0.30/0.47 ( ( Y
% 0.30/0.47 != ( none @ A ) )
% 0.30/0.47 => ~ ! [X24: A] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( some @ A @ X24 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.exhaust
% 0.30/0.47 thf(fact_152_option_Oinducts,axiom,
% 0.30/0.47 ! [A: $tType,P: ( option @ A ) > $o,Option: option @ A] :
% 0.30/0.47 ( ( P @ ( none @ A ) )
% 0.30/0.47 => ( ! [X3: A] : ( P @ ( some @ A @ X3 ) )
% 0.30/0.47 => ( P @ Option ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.inducts
% 0.30/0.47 thf(fact_153_split__option__ex,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ^ [P2: ( option @ A ) > $o] :
% 0.30/0.47 ? [X7: option @ A] : ( P2 @ X7 ) )
% 0.30/0.47 = ( ^ [P3: ( option @ A ) > $o] :
% 0.30/0.47 ( ( P3 @ ( none @ A ) )
% 0.30/0.47 | ? [X2: A] : ( P3 @ ( some @ A @ X2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % split_option_ex
% 0.30/0.47 thf(fact_154_split__option__all,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ^ [P2: ( option @ A ) > $o] :
% 0.30/0.47 ! [X7: option @ A] : ( P2 @ X7 ) )
% 0.30/0.47 = ( ^ [P3: ( option @ A ) > $o] :
% 0.30/0.47 ( ( P3 @ ( none @ A ) )
% 0.30/0.47 & ! [X2: A] : ( P3 @ ( some @ A @ X2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % split_option_all
% 0.30/0.47 thf(fact_155_combine__options__cases,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,X: option @ A,P: ( option @ A ) > ( option @ B ) > $o,Y: option @ B] :
% 0.30/0.47 ( ( ( X
% 0.30/0.47 = ( none @ A ) )
% 0.30/0.47 => ( P @ X @ Y ) )
% 0.30/0.47 => ( ( ( Y
% 0.30/0.47 = ( none @ B ) )
% 0.30/0.47 => ( P @ X @ Y ) )
% 0.30/0.47 => ( ! [A6: A,B7: B] :
% 0.30/0.47 ( ( X
% 0.30/0.47 = ( some @ A @ A6 ) )
% 0.30/0.47 => ( ( Y
% 0.30/0.47 = ( some @ B @ B7 ) )
% 0.30/0.47 => ( P @ X @ Y ) ) )
% 0.30/0.47 => ( P @ X @ Y ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % combine_options_cases
% 0.30/0.47 thf(fact_156_ODEo_Oinduct,axiom,
% 0.30/0.47 ! [P: char > ( option @ trm ) > $o,A0: char,A1: option @ trm] :
% 0.30/0.47 ( ! [X3: char,Theta2: trm] : ( P @ X3 @ ( some @ trm @ Theta2 ) )
% 0.30/0.47 => ( ! [X3: char] : ( P @ X3 @ ( none @ trm ) )
% 0.30/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ODEo.induct
% 0.30/0.47 thf(fact_157_undeft__equiv,axiom,
% 0.30/0.47 ! [Theta: option @ trm] :
% 0.30/0.47 ( ( Theta
% 0.30/0.47 != ( none @ trm ) )
% 0.30/0.47 = ( ? [T2: trm] :
% 0.30/0.47 ( Theta
% 0.30/0.47 = ( some @ trm @ T2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % undeft_equiv
% 0.30/0.47 thf(fact_158_Timeso_Oinduct,axiom,
% 0.30/0.47 ! [P: ( option @ trm ) > ( option @ trm ) > $o,A0: option @ trm,A1: option @ trm] :
% 0.30/0.47 ( ! [Theta2: trm,Eta2: trm] : ( P @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta2 ) )
% 0.30/0.47 => ( ! [X_1: option @ trm] : ( P @ ( none @ trm ) @ X_1 )
% 0.30/0.47 => ( ! [V2: trm] : ( P @ ( some @ trm @ V2 ) @ ( none @ trm ) )
% 0.30/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Timeso.induct
% 0.30/0.47 thf(fact_159_Assigno_Oinduct,axiom,
% 0.30/0.47 ! [P: variable > ( option @ trm ) > $o,A0: variable,A1: option @ trm] :
% 0.30/0.47 ( ! [X3: variable,Theta2: trm] : ( P @ X3 @ ( some @ trm @ Theta2 ) )
% 0.30/0.47 => ( ! [X3: variable] : ( P @ X3 @ ( none @ trm ) )
% 0.30/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Assigno.induct
% 0.30/0.47 thf(fact_160_Differentialo_Ocases,axiom,
% 0.30/0.47 ! [X: option @ trm] :
% 0.30/0.47 ( ! [Theta2: trm] :
% 0.30/0.47 ( X
% 0.30/0.47 != ( some @ trm @ Theta2 ) )
% 0.30/0.47 => ( X
% 0.30/0.47 = ( none @ trm ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Differentialo.cases
% 0.30/0.47 thf(fact_161_Differentialo_Oinduct,axiom,
% 0.30/0.47 ! [P: ( option @ trm ) > $o,A0: option @ trm] :
% 0.30/0.47 ( ! [Theta2: trm] : ( P @ ( some @ trm @ Theta2 ) )
% 0.30/0.47 => ( ( P @ ( none @ trm ) )
% 0.30/0.47 => ( P @ A0 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Differentialo.induct
% 0.30/0.47 thf(fact_162_option_Oexhaust__sel,axiom,
% 0.30/0.47 ! [A: $tType,Option: option @ A] :
% 0.30/0.47 ( ( Option
% 0.30/0.47 != ( none @ A ) )
% 0.30/0.47 => ( Option
% 0.30/0.47 = ( some @ A @ ( the @ A @ Option ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.exhaust_sel
% 0.30/0.47 thf(fact_163_option_Osplit__sel,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 0.30/0.47 ( ( P @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 0.30/0.47 = ( ( ( Option
% 0.30/0.47 = ( none @ A ) )
% 0.30/0.47 => ( P @ F1 ) )
% 0.30/0.47 & ( ( Option
% 0.30/0.47 = ( some @ A @ ( the @ A @ Option ) ) )
% 0.30/0.47 => ( P @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.split_sel
% 0.30/0.47 thf(fact_164_option_Osplit__sel__asm,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 0.30/0.47 ( ( P @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 0.30/0.47 = ( ~ ( ( ( Option
% 0.30/0.47 = ( none @ A ) )
% 0.30/0.47 & ~ ( P @ F1 ) )
% 0.30/0.47 | ( ( Option
% 0.30/0.47 = ( some @ A @ ( the @ A @ Option ) ) )
% 0.30/0.47 & ~ ( P @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.split_sel_asm
% 0.30/0.47 thf(fact_165_option_Osimps_I15_J,axiom,
% 0.30/0.47 ! [A: $tType,X23: A] :
% 0.30/0.47 ( ( set_option @ A @ ( some @ A @ X23 ) )
% 0.30/0.47 = ( insert @ A @ X23 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.simps(15)
% 0.30/0.47 thf(fact_166_Vagree__repv__self,axiom,
% 0.30/0.47 ! [Omega: variable > real,X: variable,D: real] :
% 0.30/0.47 ( ( denotational_Vagree @ Omega @ ( denotational_repv @ Omega @ X @ D ) @ ( insert @ variable @ X @ ( bot_bot @ ( set @ variable ) ) ) )
% 0.30/0.47 = ( D
% 0.30/0.47 = ( Omega @ X ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Vagree_repv_self
% 0.30/0.47 thf(fact_167_elem__set,axiom,
% 0.30/0.47 ! [A: $tType,X: A,Xo: option @ A] :
% 0.30/0.47 ( ( member @ A @ X @ ( set_option @ A @ Xo ) )
% 0.30/0.47 = ( Xo
% 0.30/0.47 = ( some @ A @ X ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % elem_set
% 0.30/0.47 thf(fact_168_Vagree__and,axiom,
% 0.30/0.47 ! [Nu: variable > real,Nu2: variable > real,V: set @ variable,W: set @ variable] :
% 0.30/0.47 ( ( ( denotational_Vagree @ Nu @ Nu2 @ V )
% 0.30/0.47 & ( denotational_Vagree @ Nu @ Nu2 @ W ) )
% 0.30/0.47 = ( denotational_Vagree @ Nu @ Nu2 @ ( sup_sup @ ( set @ variable ) @ V @ W ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Vagree_and
% 0.30/0.47 thf(fact_169_set__empty__eq,axiom,
% 0.30/0.47 ! [A: $tType,Xo: option @ A] :
% 0.30/0.47 ( ( ( set_option @ A @ Xo )
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = ( Xo
% 0.30/0.47 = ( none @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % set_empty_eq
% 0.30/0.47 thf(fact_170_similar__selectlike__mem,axiom,
% 0.30/0.47 ! [Nu: variable > real,Omega: variable > real,V: set @ variable,X6: set @ ( variable > real )] :
% 0.30/0.47 ( ( denotational_Vagree @ Nu @ Omega @ V )
% 0.30/0.47 => ( ( member @ ( variable > real ) @ Nu @ ( static_selectlike @ X6 @ Omega @ V ) )
% 0.30/0.47 = ( member @ ( variable > real ) @ Nu @ X6 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % similar_selectlike_mem
% 0.30/0.47 thf(fact_171_selectlike__Vagree,axiom,
% 0.30/0.47 ! [Nu: variable > real,Omega: variable > real,V: set @ variable,X6: set @ ( variable > real )] :
% 0.30/0.47 ( ( denotational_Vagree @ Nu @ Omega @ V )
% 0.30/0.47 => ( ( static_selectlike @ X6 @ Nu @ V )
% 0.30/0.47 = ( static_selectlike @ X6 @ Omega @ V ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % selectlike_Vagree
% 0.30/0.47 thf(fact_172_Aterm__Some,axiom,
% 0.30/0.47 ( ( some @ trm )
% 0.30/0.47 = ( some @ trm ) ) ).
% 0.30/0.47
% 0.30/0.47 % Aterm_Some
% 0.30/0.47 thf(fact_173_option_Oset__intros,axiom,
% 0.30/0.47 ! [A: $tType,X23: A] : ( member @ A @ X23 @ ( set_option @ A @ ( some @ A @ X23 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.set_intros
% 0.30/0.47 thf(fact_174_option_Oset__cases,axiom,
% 0.30/0.47 ! [A: $tType,E: A,A2: option @ A] :
% 0.30/0.47 ( ( member @ A @ E @ ( set_option @ A @ A2 ) )
% 0.30/0.47 => ( A2
% 0.30/0.47 = ( some @ A @ E ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.set_cases
% 0.30/0.47 thf(fact_175_ospec,axiom,
% 0.30/0.47 ! [A: $tType,A3: option @ A,P: A > $o,X: A] :
% 0.30/0.47 ( ! [X3: A] :
% 0.30/0.47 ( ( member @ A @ X3 @ ( set_option @ A @ A3 ) )
% 0.30/0.47 => ( P @ X3 ) )
% 0.30/0.47 => ( ( A3
% 0.30/0.47 = ( some @ A @ X ) )
% 0.30/0.47 => ( P @ X ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ospec
% 0.30/0.47 thf(fact_176_Vagree__union,axiom,
% 0.30/0.47 ! [Nu: variable > real,Nu2: variable > real,V: set @ variable,W: set @ variable] :
% 0.30/0.47 ( ( denotational_Vagree @ Nu @ Nu2 @ V )
% 0.30/0.47 => ( ( denotational_Vagree @ Nu @ Nu2 @ W )
% 0.30/0.47 => ( denotational_Vagree @ Nu @ Nu2 @ ( sup_sup @ ( set @ variable ) @ V @ W ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Vagree_union
% 0.30/0.47 thf(fact_177_Vagree__def,axiom,
% 0.30/0.47 ( denotational_Vagree
% 0.30/0.47 = ( ^ [Nu3: variable > real,Nu4: variable > real,V3: set @ variable] :
% 0.30/0.47 ! [I: variable] :
% 0.30/0.47 ( ( member @ variable @ I @ V3 )
% 0.30/0.47 => ( ( Nu3 @ I )
% 0.30/0.47 = ( Nu4 @ I ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Vagree_def
% 0.30/0.47 thf(fact_178_Vagree__sym,axiom,
% 0.30/0.47 ( denotational_Vagree
% 0.30/0.47 = ( ^ [Nu3: variable > real,Nu4: variable > real] : ( denotational_Vagree @ Nu4 @ Nu3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Vagree_sym
% 0.30/0.47 thf(fact_179_Vagree__refl,axiom,
% 0.30/0.47 ! [Nu: variable > real,V: set @ variable] : ( denotational_Vagree @ Nu @ Nu @ V ) ).
% 0.30/0.47
% 0.30/0.47 % Vagree_refl
% 0.30/0.47 thf(fact_180_Vagree__sym__rel,axiom,
% 0.30/0.47 ! [Nu: variable > real,Nu2: variable > real,V: set @ variable] :
% 0.30/0.47 ( ( denotational_Vagree @ Nu @ Nu2 @ V )
% 0.30/0.47 => ( denotational_Vagree @ Nu2 @ Nu @ V ) ) ).
% 0.30/0.47
% 0.30/0.47 % Vagree_sym_rel
% 0.30/0.47 thf(fact_181_Vagree__empty,axiom,
% 0.30/0.47 ! [Nu: variable > real,Nu2: variable > real] : ( denotational_Vagree @ Nu @ Nu2 @ ( bot_bot @ ( set @ variable ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Vagree_empty
% 0.30/0.47 thf(fact_182_option_Osimps_I4_J,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,F1: B,F22: A > B] :
% 0.30/0.47 ( ( case_option @ B @ A @ F1 @ F22 @ ( none @ A ) )
% 0.30/0.47 = F1 ) ).
% 0.30/0.47
% 0.30/0.47 % option.simps(4)
% 0.30/0.47 thf(fact_183_option_Osimps_I5_J,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,F1: B,F22: A > B,X23: A] :
% 0.30/0.47 ( ( case_option @ B @ A @ F1 @ F22 @ ( some @ A @ X23 ) )
% 0.30/0.47 = ( F22 @ X23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.simps(5)
% 0.30/0.47 thf(fact_184_option_Osimps_I14_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( set_option @ A @ ( none @ A ) )
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.simps(14)
% 0.30/0.47 thf(fact_185_option_Oset__sel,axiom,
% 0.30/0.47 ! [A: $tType,A2: option @ A] :
% 0.30/0.47 ( ( A2
% 0.30/0.47 != ( none @ A ) )
% 0.30/0.47 => ( member @ A @ ( the @ A @ A2 ) @ ( set_option @ A @ A2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.set_sel
% 0.30/0.47 thf(fact_186_option_Ocase__eq__if,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( case_option @ B @ A )
% 0.30/0.47 = ( ^ [F12: B,F23: A > B,Option3: option @ A] :
% 0.30/0.47 ( if @ B
% 0.30/0.47 @ ( Option3
% 0.30/0.47 = ( none @ A ) )
% 0.30/0.47 @ F12
% 0.30/0.47 @ ( F23 @ ( the @ A @ Option3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.case_eq_if
% 0.30/0.47 thf(fact_187_solves__Vagree,axiom,
% 0.30/0.47 ! [I2: denotational_interp,F3: real > variable > real,X: char,Theta: trm,Zeta: real] :
% 0.30/0.47 ( ( denota1778088425es_ODE @ I2 @ F3 @ X @ Theta )
% 0.30/0.47 => ( denotational_Vagree @ ( F3 @ Zeta ) @ ( F3 @ ( zero_zero @ real ) ) @ ( uminus_uminus @ ( set @ variable ) @ ( insert @ variable @ ( rVar @ X ) @ ( insert @ variable @ ( dVar @ X ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % solves_Vagree
% 0.30/0.47 thf(fact_188_Vagree__repv,axiom,
% 0.30/0.47 ! [Omega: variable > real,X: variable,D: real] : ( denotational_Vagree @ Omega @ ( denotational_repv @ Omega @ X @ D ) @ ( uminus_uminus @ ( set @ variable ) @ ( insert @ variable @ X @ ( bot_bot @ ( set @ variable ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Vagree_repv
% 0.30/0.47 thf(fact_189_Timeso_Osimps_I3_J,axiom,
% 0.30/0.47 ! [V4: trm] :
% 0.30/0.47 ( ( uSubst277968634Timeso @ ( some @ trm @ V4 ) @ ( none @ trm ) )
% 0.30/0.47 = ( none @ trm ) ) ).
% 0.30/0.47
% 0.30/0.47 % Timeso.simps(3)
% 0.30/0.47 thf(fact_190_neg__equal__iff__equal,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( group_add @ A )
% 0.30/0.47 => ! [A2: A,B3: A] :
% 0.30/0.47 ( ( ( uminus_uminus @ A @ A2 )
% 0.30/0.47 = ( uminus_uminus @ A @ B3 ) )
% 0.30/0.47 = ( A2 = B3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % neg_equal_iff_equal
% 0.30/0.47 thf(fact_191_add_Oinverse__inverse,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( group_add @ A )
% 0.30/0.47 => ! [A2: A] :
% 0.30/0.47 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ A2 ) )
% 0.30/0.47 = A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % add.inverse_inverse
% 0.30/0.47 thf(fact_192_compl__eq__compl__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( boolean_algebra @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( ( uminus_uminus @ A @ X )
% 0.30/0.47 = ( uminus_uminus @ A @ Y ) )
% 0.30/0.47 = ( X = Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % compl_eq_compl_iff
% 0.30/0.47 thf(fact_193_double__compl,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( boolean_algebra @ A )
% 0.30/0.47 => ! [X: A] :
% 0.30/0.47 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ X ) )
% 0.30/0.47 = X ) ) ).
% 0.30/0.47
% 0.30/0.47 % double_compl
% 0.30/0.47 thf(fact_194_uminus__apply,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( uminus @ B )
% 0.30/0.47 => ( ( uminus_uminus @ ( A > B ) )
% 0.30/0.47 = ( ^ [A5: A > B,X2: A] : ( uminus_uminus @ B @ ( A5 @ X2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % uminus_apply
% 0.30/0.47 thf(fact_195_Compl__eq__Compl__iff,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 0.30/0.47 ( ( ( uminus_uminus @ ( set @ A ) @ A3 )
% 0.30/0.47 = ( uminus_uminus @ ( set @ A ) @ B2 ) )
% 0.30/0.47 = ( A3 = B2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Compl_eq_Compl_iff
% 0.30/0.47 thf(fact_196_Compl__iff,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A3: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A3 ) )
% 0.30/0.47 = ( ~ ( member @ A @ C2 @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Compl_iff
% 0.30/0.47 thf(fact_197_ComplI,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A3: set @ A] :
% 0.30/0.47 ( ~ ( member @ A @ C2 @ A3 )
% 0.30/0.47 => ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ComplI
% 0.30/0.47 thf(fact_198_add_Oinverse__neutral,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( group_add @ A )
% 0.30/0.47 => ( ( uminus_uminus @ A @ ( zero_zero @ A ) )
% 0.30/0.47 = ( zero_zero @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % add.inverse_neutral
% 0.30/0.47 thf(fact_199_neg__0__equal__iff__equal,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( group_add @ A )
% 0.30/0.47 => ! [A2: A] :
% 0.30/0.47 ( ( ( zero_zero @ A )
% 0.30/0.47 = ( uminus_uminus @ A @ A2 ) )
% 0.30/0.47 = ( ( zero_zero @ A )
% 0.30/0.47 = A2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % neg_0_equal_iff_equal
% 0.30/0.47 thf(fact_200_neg__equal__0__iff__equal,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( group_add @ A )
% 0.30/0.47 => ! [A2: A] :
% 0.30/0.47 ( ( ( uminus_uminus @ A @ A2 )
% 0.30/0.47 = ( zero_zero @ A ) )
% 0.30/0.47 = ( A2
% 0.30/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % neg_equal_0_iff_equal
% 0.30/0.47 thf(fact_201_equal__neg__zero,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linord219039673up_add @ A )
% 0.30/0.47 => ! [A2: A] :
% 0.30/0.47 ( ( A2
% 0.30/0.47 = ( uminus_uminus @ A @ A2 ) )
% 0.30/0.47 = ( A2
% 0.30/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % equal_neg_zero
% 0.30/0.47 thf(fact_202_neg__equal__zero,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linord219039673up_add @ A )
% 0.30/0.47 => ! [A2: A] :
% 0.30/0.47 ( ( ( uminus_uminus @ A @ A2 )
% 0.30/0.47 = A2 )
% 0.30/0.47 = ( A2
% 0.30/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % neg_equal_zero
% 0.30/0.47 thf(fact_203_Uvariation__Vagree,axiom,
% 0.30/0.47 ! [Nu: variable > real,Nu2: variable > real,V: set @ variable] :
% 0.30/0.47 ( ( denota1419872369iation @ Nu @ Nu2 @ ( uminus_uminus @ ( set @ variable ) @ V ) )
% 0.30/0.47 = ( denotational_Vagree @ Nu @ Nu2 @ V ) ) ).
% 0.30/0.47
% 0.30/0.47 % Uvariation_Vagree
% 0.30/0.47 thf(fact_204_minus__equation__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( group_add @ A )
% 0.30/0.47 => ! [A2: A,B3: A] :
% 0.30/0.47 ( ( ( uminus_uminus @ A @ A2 )
% 0.30/0.47 = B3 )
% 0.30/0.47 = ( ( uminus_uminus @ A @ B3 )
% 0.30/0.47 = A2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minus_equation_iff
% 0.30/0.47 thf(fact_205_equation__minus__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( group_add @ A )
% 0.30/0.47 => ! [A2: A,B3: A] :
% 0.30/0.47 ( ( A2
% 0.30/0.47 = ( uminus_uminus @ A @ B3 ) )
% 0.30/0.47 = ( B3
% 0.30/0.47 = ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % equation_minus_iff
% 0.30/0.47 thf(fact_206_fun__Compl__def,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( uminus @ B )
% 0.30/0.47 => ( ( uminus_uminus @ ( A > B ) )
% 0.30/0.47 = ( ^ [A5: A > B,X2: A] : ( uminus_uminus @ B @ ( A5 @ X2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % fun_Compl_def
% 0.30/0.47 thf(fact_207_double__complement,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A] :
% 0.30/0.47 ( ( uminus_uminus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A3 ) )
% 0.30/0.47 = A3 ) ).
% 0.30/0.47
% 0.30/0.47 % double_complement
% 0.30/0.47 thf(fact_208_ComplD,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A3: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A3 ) )
% 0.30/0.47 => ~ ( member @ A @ C2 @ A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % ComplD
% 0.30/0.47 thf(fact_209_Timeso_Osimps_I2_J,axiom,
% 0.30/0.47 ! [Eta: option @ trm] :
% 0.30/0.47 ( ( uSubst277968634Timeso @ ( none @ trm ) @ Eta )
% 0.30/0.47 = ( none @ trm ) ) ).
% 0.30/0.47
% 0.30/0.47 % Timeso.simps(2)
% 0.30/0.47 thf(fact_210_Timeso__undef,axiom,
% 0.30/0.47 ! [Theta: option @ trm,Eta: option @ trm] :
% 0.30/0.47 ( ( ( uSubst277968634Timeso @ Theta @ Eta )
% 0.30/0.47 = ( none @ trm ) )
% 0.30/0.47 = ( ( Theta
% 0.30/0.47 = ( none @ trm ) )
% 0.30/0.47 | ( Eta
% 0.30/0.47 = ( none @ trm ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Timeso_undef
% 0.30/0.47 thf(fact_211_selectlike__equal__cocond__corule,axiom,
% 0.30/0.47 ! [Nu: variable > real,V: set @ variable,X6: set @ ( variable > real ),Y4: set @ ( variable > real )] :
% 0.30/0.47 ( ! [Mu2: variable > real] :
% 0.30/0.47 ( ( denota1419872369iation @ Mu2 @ Nu @ V )
% 0.30/0.47 => ( ( member @ ( variable > real ) @ Mu2 @ X6 )
% 0.30/0.47 = ( member @ ( variable > real ) @ Mu2 @ Y4 ) ) )
% 0.30/0.47 => ( ( static_selectlike @ X6 @ Nu @ ( uminus_uminus @ ( set @ variable ) @ V ) )
% 0.30/0.47 = ( static_selectlike @ Y4 @ Nu @ ( uminus_uminus @ ( set @ variable ) @ V ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % selectlike_equal_cocond_corule
% 0.30/0.47 thf(fact_212_selectlike__equal__cocond__rule,axiom,
% 0.30/0.47 ! [Nu: variable > real,V: set @ variable,X6: set @ ( variable > real ),Y4: set @ ( variable > real )] :
% 0.30/0.47 ( ! [Mu2: variable > real] :
% 0.30/0.47 ( ( denota1419872369iation @ Mu2 @ Nu @ ( uminus_uminus @ ( set @ variable ) @ V ) )
% 0.30/0.47 => ( ( member @ ( variable > real ) @ Mu2 @ X6 )
% 0.30/0.47 = ( member @ ( variable > real ) @ Mu2 @ Y4 ) ) )
% 0.30/0.47 => ( ( static_selectlike @ X6 @ Nu @ V )
% 0.30/0.47 = ( static_selectlike @ Y4 @ Nu @ V ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % selectlike_equal_cocond_rule
% 0.30/0.47 thf(fact_213_selectlike__equal__cocond,axiom,
% 0.30/0.47 ! [X6: set @ ( variable > real ),Nu: variable > real,V: set @ variable,Y4: set @ ( variable > real )] :
% 0.30/0.47 ( ( ( static_selectlike @ X6 @ Nu @ ( uminus_uminus @ ( set @ variable ) @ V ) )
% 0.30/0.47 = ( static_selectlike @ Y4 @ Nu @ ( uminus_uminus @ ( set @ variable ) @ V ) ) )
% 0.30/0.47 = ( ! [Mu3: variable > real] :
% 0.30/0.47 ( ( denota1419872369iation @ Mu3 @ Nu @ V )
% 0.30/0.47 => ( ( member @ ( variable > real ) @ Mu3 @ X6 )
% 0.30/0.47 = ( member @ ( variable > real ) @ Mu3 @ Y4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % selectlike_equal_cocond
% 0.30/0.47 thf(fact_214_selectlike__equal__cond,axiom,
% 0.30/0.47 ! [X6: set @ ( variable > real ),Nu: variable > real,V: set @ variable,Y4: set @ ( variable > real )] :
% 0.30/0.47 ( ( ( static_selectlike @ X6 @ Nu @ V )
% 0.30/0.47 = ( static_selectlike @ Y4 @ Nu @ V ) )
% 0.30/0.47 = ( ! [Mu3: variable > real] :
% 0.30/0.47 ( ( denota1419872369iation @ Mu3 @ Nu @ ( uminus_uminus @ ( set @ variable ) @ V ) )
% 0.30/0.47 => ( ( member @ ( variable > real ) @ Mu3 @ X6 )
% 0.30/0.47 = ( member @ ( variable > real ) @ Mu3 @ Y4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % selectlike_equal_cond
% 0.30/0.47 thf(fact_215_stateinterpol__insert,axiom,
% 0.30/0.47 ! [V4: variable > real,W2: variable > real,S: set @ variable,Z: variable] : ( denotational_Vagree @ ( stateinterpol @ V4 @ W2 @ S ) @ ( stateinterpol @ V4 @ W2 @ ( insert @ variable @ Z @ S ) ) @ ( uminus_uminus @ ( set @ variable ) @ ( insert @ variable @ Z @ ( bot_bot @ ( set @ variable ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % stateinterpol_insert
% 0.30/0.47 thf(fact_216_Timeso_Oelims,axiom,
% 0.30/0.47 ! [X: option @ trm,Xa: option @ trm,Y: option @ trm] :
% 0.30/0.47 ( ( ( uSubst277968634Timeso @ X @ Xa )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ! [Theta2: trm] :
% 0.30/0.47 ( ( X
% 0.30/0.47 = ( some @ trm @ Theta2 ) )
% 0.30/0.47 => ! [Eta2: trm] :
% 0.30/0.47 ( ( Xa
% 0.30/0.47 = ( some @ trm @ Eta2 ) )
% 0.30/0.47 => ( Y
% 0.30/0.47 != ( some @ trm @ ( times @ Theta2 @ Eta2 ) ) ) ) )
% 0.30/0.47 => ( ( ( X
% 0.30/0.47 = ( none @ trm ) )
% 0.30/0.47 => ( Y
% 0.30/0.47 != ( none @ trm ) ) )
% 0.30/0.47 => ~ ( ? [V2: trm] :
% 0.30/0.47 ( X
% 0.30/0.47 = ( some @ trm @ V2 ) )
% 0.30/0.47 => ( ( Xa
% 0.30/0.47 = ( none @ trm ) )
% 0.30/0.47 => ( Y
% 0.30/0.47 != ( none @ trm ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Timeso.elims
% 0.30/0.47 thf(fact_217_trm_Oinject_I6_J,axiom,
% 0.30/0.47 ! [X61: trm,X62: trm,Y61: trm,Y62: trm] :
% 0.30/0.47 ( ( ( times @ X61 @ X62 )
% 0.30/0.47 = ( times @ Y61 @ Y62 ) )
% 0.30/0.47 = ( ( X61 = Y61 )
% 0.30/0.47 & ( X62 = Y62 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % trm.inject(6)
% 0.30/0.47 thf(fact_218_stateinterpol__left,axiom,
% 0.30/0.47 ! [X: variable,S: set @ variable,Nu: variable > real,Omega: variable > real] :
% 0.30/0.47 ( ( member @ variable @ X @ S )
% 0.30/0.47 => ( ( stateinterpol @ Nu @ Omega @ S @ X )
% 0.30/0.47 = ( Nu @ X ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % stateinterpol_left
% 0.30/0.47 thf(fact_219_stateinterpol__right,axiom,
% 0.30/0.47 ! [X: variable,S: set @ variable,Nu: variable > real,Omega: variable > real] :
% 0.30/0.47 ( ~ ( member @ variable @ X @ S )
% 0.30/0.47 => ( ( stateinterpol @ Nu @ Omega @ S @ X )
% 0.30/0.47 = ( Omega @ X ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % stateinterpol_right
% 0.30/0.47 thf(fact_220_selectlike__co__selectlike,axiom,
% 0.30/0.47 ! [X6: set @ ( variable > real ),Nu: variable > real,V: set @ variable] :
% 0.30/0.47 ( ( static_selectlike @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ ( static_selectlike @ X6 @ Nu @ V ) ) @ Nu @ V )
% 0.30/0.47 = ( static_selectlike @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ X6 ) @ Nu @ V ) ) ).
% 0.30/0.47
% 0.30/0.47 % selectlike_co_selectlike
% 0.30/0.47 thf(fact_221_stateinterpol__empty,axiom,
% 0.30/0.47 ! [Nu: variable > real,Omega: variable > real] :
% 0.30/0.47 ( ( stateinterpol @ Nu @ Omega @ ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.47 = Omega ) ).
% 0.30/0.47
% 0.30/0.47 % stateinterpol_empty
% 0.30/0.47 thf(fact_222_Vagree__stateinterpol,axiom,
% 0.30/0.47 ! [Nu: variable > real,Omega: variable > real,S: set @ variable] : ( denotational_Vagree @ ( stateinterpol @ Nu @ Omega @ S ) @ Nu @ S ) ).
% 0.30/0.47
% 0.30/0.47 % Vagree_stateinterpol
% 0.30/0.47 thf(fact_223_stateinterpol__def,axiom,
% 0.30/0.47 ( stateinterpol
% 0.30/0.47 = ( ^ [Nu3: variable > real,Omega2: variable > real,S2: set @ variable,X2: variable] : ( if @ real @ ( member @ variable @ X2 @ S2 ) @ ( Nu3 @ X2 ) @ ( Omega2 @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % stateinterpol_def
% 0.30/0.47 thf(fact_224_usubstappt__times__conv,axiom,
% 0.30/0.47 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,Eta: trm] :
% 0.30/0.47 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 0.30/0.47 != ( none @ trm ) )
% 0.30/0.47 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.30/0.47 != ( none @ trm ) )
% 0.30/0.47 & ( ( uSubst95898992stappt @ Sigma @ U @ Eta )
% 0.30/0.47 != ( none @ trm ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % usubstappt_times_conv
% 0.30/0.47 thf(fact_225_usubstappt_Osimps_I6_J,axiom,
% 0.30/0.47 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,Eta: trm] :
% 0.30/0.47 ( ( uSubst95898992stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 0.30/0.47 = ( uSubst277968634Timeso @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) @ ( uSubst95898992stappt @ Sigma @ U @ Eta ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % usubstappt.simps(6)
% 0.30/0.47 thf(fact_226_Timeso_Osimps_I1_J,axiom,
% 0.30/0.47 ! [Theta: trm,Eta: trm] :
% 0.30/0.47 ( ( uSubst277968634Timeso @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta ) )
% 0.30/0.47 = ( some @ trm @ ( times @ Theta @ Eta ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Timeso.simps(1)
% 0.30/0.47 thf(fact_227_stateinterpol__diff,axiom,
% 0.30/0.47 ! [Nu: variable > real,Omega: variable > real] :
% 0.30/0.47 ( ( stateinterpol @ Nu @ Omega @ ( statediff @ Nu @ Omega ) )
% 0.30/0.47 = Nu ) ).
% 0.30/0.47
% 0.30/0.47 % stateinterpol_diff
% 0.30/0.47 thf(fact_228_stateinterpol__FVT,axiom,
% 0.30/0.47 ! [Z: variable,T3: trm,I2: denotational_interp,Omega: variable > real,Omega3: variable > real,S: set @ variable] :
% 0.30/0.47 ( ~ ( member @ variable @ Z @ ( static_FVT @ T3 ) )
% 0.30/0.47 => ( ( denota1863255036rm_sem @ I2 @ T3 @ ( stateinterpol @ Omega @ Omega3 @ S ) )
% 0.30/0.47 = ( denota1863255036rm_sem @ I2 @ T3 @ ( stateinterpol @ Omega @ Omega3 @ ( insert @ variable @ Z @ S ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % stateinterpol_FVT
% 0.30/0.47 thf(fact_229_nostatediff,axiom,
% 0.30/0.47 ! [X: variable,Nu: variable > real,Omega: variable > real] :
% 0.30/0.47 ( ~ ( member @ variable @ X @ ( statediff @ Nu @ Omega ) )
% 0.30/0.47 => ( ( Nu @ X )
% 0.30/0.47 = ( Omega @ X ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nostatediff
% 0.30/0.47 thf(fact_230_coincidence__term,axiom,
% 0.30/0.47 ! [Omega: variable > real,Omega3: variable > real,Theta: trm,I2: denotational_interp] :
% 0.30/0.47 ( ( denotational_Vagree @ Omega @ Omega3 @ ( static_FVT @ Theta ) )
% 0.30/0.47 => ( ( denota1863255036rm_sem @ I2 @ Theta @ Omega )
% 0.30/0.47 = ( denota1863255036rm_sem @ I2 @ Theta @ Omega3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % coincidence_term
% 0.30/0.47 thf(fact_231_coincidence__term__cor,axiom,
% 0.30/0.47 ! [Omega: variable > real,Omega3: variable > real,U: set @ variable,Theta: trm,I2: denotational_interp] :
% 0.30/0.47 ( ( denota1419872369iation @ Omega @ Omega3 @ U )
% 0.30/0.47 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ Theta ) @ U )
% 0.30/0.47 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.47 => ( ( denota1863255036rm_sem @ I2 @ Theta @ Omega )
% 0.30/0.47 = ( denota1863255036rm_sem @ I2 @ Theta @ Omega3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % coincidence_term_cor
% 0.30/0.47 thf(fact_232_Vagree__statediff,axiom,
% 0.30/0.47 ! [Omega: variable > real,Omega3: variable > real,S: set @ variable] :
% 0.30/0.47 ( ( denotational_Vagree @ Omega @ Omega3 @ S )
% 0.30/0.47 => ( ord_less_eq @ ( set @ variable ) @ ( statediff @ Omega @ Omega3 ) @ ( uminus_uminus @ ( set @ variable ) @ S ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Vagree_statediff
% 0.30/0.47 thf(fact_233_order__refl,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_refl
% 0.30/0.47 thf(fact_234_subsetI,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 0.30/0.47 ( ! [X3: A] :
% 0.30/0.47 ( ( member @ A @ X3 @ A3 )
% 0.30/0.47 => ( member @ A @ X3 @ B2 ) )
% 0.30/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ B2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % subsetI
% 0.30/0.47 thf(fact_235_subset__antisym,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 0.30/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ A3 )
% 0.30/0.47 => ( A3 = B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_antisym
% 0.30/0.47 thf(fact_236_inf__apply,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( semilattice_inf @ B )
% 0.30/0.47 => ( ( inf_inf @ ( A > B ) )
% 0.30/0.47 = ( ^ [F: A > B,G: A > B,X2: A] : ( inf_inf @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inf_apply
% 0.30/0.47 thf(fact_237_inf_Oidem,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_inf @ A )
% 0.30/0.47 => ! [A2: A] :
% 0.30/0.47 ( ( inf_inf @ A @ A2 @ A2 )
% 0.30/0.47 = A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % inf.idem
% 0.30/0.47 thf(fact_238_inf__idem,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_inf @ A )
% 0.30/0.47 => ! [X: A] :
% 0.30/0.47 ( ( inf_inf @ A @ X @ X )
% 0.30/0.47 = X ) ) ).
% 0.30/0.47
% 0.30/0.47 % inf_idem
% 0.30/0.47 thf(fact_239_inf_Oleft__idem,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_inf @ A )
% 0.30/0.47 => ! [A2: A,B3: A] :
% 0.30/0.47 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B3 ) )
% 0.30/0.47 = ( inf_inf @ A @ A2 @ B3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inf.left_idem
% 0.30/0.47 thf(fact_240_inf__left__idem,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_inf @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 0.30/0.47 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inf_left_idem
% 0.30/0.47 thf(fact_241_inf_Oright__idem,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_inf @ A )
% 0.30/0.47 => ! [A2: A,B3: A] :
% 0.30/0.47 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B3 ) @ B3 )
% 0.30/0.47 = ( inf_inf @ A @ A2 @ B3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inf.right_idem
% 0.30/0.47 thf(fact_242_inf__right__idem,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_inf @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Y )
% 0.30/0.47 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inf_right_idem
% 0.30/0.47 thf(fact_243_IntI,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A3: set @ A,B2: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ A3 )
% 0.30/0.47 => ( ( member @ A @ C2 @ B2 )
% 0.30/0.47 => ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % IntI
% 0.30/0.47 thf(fact_244_Int__iff,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A3: set @ A,B2: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B2 ) )
% 0.30/0.47 = ( ( member @ A @ C2 @ A3 )
% 0.30/0.47 & ( member @ A @ C2 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Int_iff
% 0.30/0.47 thf(fact_245_le__zero__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( canoni770627133id_add @ A )
% 0.30/0.47 => ! [N: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 0.30/0.47 = ( N
% 0.30/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_zero_eq
% 0.30/0.47 thf(fact_246_neg__le__iff__le,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordered_ab_group_add @ A )
% 0.30/0.47 => ! [B3: A,A2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ B3 ) @ ( uminus_uminus @ A @ A2 ) )
% 0.30/0.47 = ( ord_less_eq @ A @ A2 @ B3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % neg_le_iff_le
% 0.30/0.47 thf(fact_247_compl__le__compl__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( boolean_algebra @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ X ) @ ( uminus_uminus @ A @ Y ) )
% 0.30/0.47 = ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % compl_le_compl_iff
% 0.30/0.47 thf(fact_248_le__inf__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_inf @ A )
% 0.30/0.47 => ! [X: A,Y: A,Z: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ X @ ( inf_inf @ A @ Y @ Z ) )
% 0.30/0.47 = ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.47 & ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_inf_iff
% 0.30/0.47 thf(fact_249_inf_Obounded__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_inf @ A )
% 0.30/0.47 => ! [A2: A,B3: A,C2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B3 @ C2 ) )
% 0.30/0.47 = ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.30/0.47 & ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inf.bounded_iff
% 0.30/0.47 thf(fact_250_le__sup__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [X: A,Y: A,Z: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.30/0.47 = ( ( ord_less_eq @ A @ X @ Z )
% 0.30/0.47 & ( ord_less_eq @ A @ Y @ Z ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_sup_iff
% 0.30/0.47 thf(fact_251_sup_Obounded__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [B3: A,C2: A,A2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C2 ) @ A2 )
% 0.30/0.47 = ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.30/0.47 & ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.bounded_iff
% 0.30/0.47 thf(fact_252_empty__subsetI,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A3 ) ).
% 0.30/0.47
% 0.30/0.47 % empty_subsetI
% 0.30/0.47 thf(fact_253_subset__empty,axiom,
% 0.30/0.47 ! [A: $tType,A3: set @ A] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = ( A3
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_empty
% 0.30/0.47
% 0.30/0.47 % Type constructors (44)
% 0.30/0.47 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.30/0.47 bounded_lattice @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.30/0.47 ! [A7: $tType] : ( bounded_lattice @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( bounded_lattice @ A8 )
% 0.30/0.47 => ( bounded_lattice @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( bounded_lattice @ A8 )
% 0.30/0.47 => ( bounde1808546759up_bot @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A8 )
% 0.30/0.47 => ( semilattice_sup @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( semilattice_inf @ A8 )
% 0.30/0.47 => ( semilattice_inf @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( boolean_algebra @ A8 )
% 0.30/0.47 => ( boolean_algebra @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( preorder @ A8 )
% 0.30/0.47 => ( preorder @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( lattice @ A8 )
% 0.30/0.47 => ( lattice @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Orderings_Obot,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( bot @ A8 )
% 0.30/0.47 => ( bot @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Groups_Ouminus,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( uminus @ A8 )
% 0.30/0.47 => ( uminus @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.30/0.47 canoni770627133id_add @ nat ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Nat_Onat___Lattices_Osemilattice__sup_3,axiom,
% 0.30/0.47 semilattice_sup @ nat ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Nat_Onat___Lattices_Osemilattice__inf_4,axiom,
% 0.30/0.47 semilattice_inf @ nat ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Nat_Onat___Orderings_Opreorder_5,axiom,
% 0.30/0.47 preorder @ nat ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Nat_Onat___Lattices_Olattice_6,axiom,
% 0.30/0.47 lattice @ nat ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Nat_Onat___Orderings_Obot_7,axiom,
% 0.30/0.47 bot @ nat ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 0.30/0.47 zero @ nat ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_8,axiom,
% 0.30/0.47 ! [A7: $tType] : ( bounde1808546759up_bot @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_9,axiom,
% 0.30/0.47 ! [A7: $tType] : ( semilattice_sup @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_10,axiom,
% 0.30/0.47 ! [A7: $tType] : ( semilattice_inf @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_11,axiom,
% 0.30/0.47 ! [A7: $tType] : ( boolean_algebra @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Orderings_Opreorder_12,axiom,
% 0.30/0.47 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Lattices_Olattice_13,axiom,
% 0.30/0.47 ! [A7: $tType] : ( lattice @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Orderings_Obot_14,axiom,
% 0.30/0.47 ! [A7: $tType] : ( bot @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Groups_Ouminus_15,axiom,
% 0.30/0.47 ! [A7: $tType] : ( uminus @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Groups_Ozero_16,axiom,
% 0.30/0.47 ! [A7: $tType] :
% 0.30/0.47 ( ( zero @ A7 )
% 0.30/0.47 => ( zero @ ( set @ A7 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_17,axiom,
% 0.30/0.47 bounde1808546759up_bot @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_18,axiom,
% 0.30/0.47 semilattice_sup @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_19,axiom,
% 0.30/0.47 semilattice_inf @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_20,axiom,
% 0.30/0.48 boolean_algebra @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Orderings_Opreorder_21,axiom,
% 0.30/0.48 preorder @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Lattices_Olattice_22,axiom,
% 0.30/0.48 lattice @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Orderings_Obot_23,axiom,
% 0.30/0.48 bot @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Groups_Ouminus_24,axiom,
% 0.30/0.48 uminus @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add,axiom,
% 0.30/0.48 linord219039673up_add @ real ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add,axiom,
% 0.30/0.48 ordered_ab_group_add @ real ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Real_Oreal___Lattices_Osemilattice__sup_25,axiom,
% 0.30/0.48 semilattice_sup @ real ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Real_Oreal___Lattices_Osemilattice__inf_26,axiom,
% 0.30/0.48 semilattice_inf @ real ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Real_Oreal___Orderings_Opreorder_27,axiom,
% 0.30/0.48 preorder @ real ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Real_Oreal___Lattices_Olattice_28,axiom,
% 0.30/0.48 lattice @ real ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Real_Oreal___Groups_Ogroup__add,axiom,
% 0.30/0.48 group_add @ real ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Real_Oreal___Groups_Ouminus_29,axiom,
% 0.30/0.48 uminus @ real ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Real_Oreal___Groups_Ozero_30,axiom,
% 0.30/0.48 zero @ real ).
% 0.30/0.48
% 0.30/0.48 % Helper facts (3)
% 0.30/0.48 thf(help_If_3_1_T,axiom,
% 0.30/0.48 ! [P: $o] :
% 0.30/0.48 ( ( P = $true )
% 0.30/0.48 | ( P = $false ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(help_If_2_1_T,axiom,
% 0.30/0.48 ! [A: $tType,X: A,Y: A] :
% 0.30/0.48 ( ( if @ A @ $false @ X @ Y )
% 0.30/0.48 = Y ) ).
% 0.30/0.48
% 0.30/0.48 thf(help_If_1_1_T,axiom,
% 0.30/0.48 ! [A: $tType,X: A,Y: A] :
% 0.30/0.48 ( ( if @ A @ $true @ X @ Y )
% 0.30/0.48 = X ) ).
% 0.30/0.48
% 0.30/0.48 % Conjectures (1)
% 0.30/0.48 thf(conj_0,conjecture,
% 0.30/0.48 denota1419872369iation @ ( f @ ( zero_zero @ real ) ) @ omega @ ( sup_sup @ ( set @ variable ) @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) @ u ) ).
% 0.30/0.48
% 0.30/0.48 %------------------------------------------------------------------------------
% 0.30/0.48 ------------------------
% 3.26/1.73 ---- Embedded in THF ---
% 3.26/1.73 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.26/1.73 %%% Generated on Tue Feb 24 08:31:19 EST 2026
% 3.26/1.73 %%% using '$$dhol' embedding, version 1.3.0.
% 3.26/1.73 %%% Logic specification used:
% 3.26/1.73 %%% thf(spec, logic, $$dhol).
% 3.26/1.73
% 3.26/1.73 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.FtwHsTTgu9/DTF2DTF7422.p
% 3.26/1.73 thf(ty_t_Denotational__Semantics_Ointerp, type, denotational_interp: $tType).
% 3.26/1.73 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 3.26/1.73 thf(ty_t_Syntax_Ovariable, type, variable: $tType).
% 3.26/1.73 thf(ty_t_Option_Ooption, type, option: ($tType > $tType)).
% 3.26/1.73 thf(ty_t_Syntax_Ogame, type, game: $tType).
% 3.26/1.73 thf(ty_t_String_Ochar, type, char: $tType).
% 3.26/1.73 thf(ty_t_Syntax_Otrm, type, trm: $tType).
% 3.26/1.73 thf(ty_t_Syntax_Ofml, type, fml: $tType).
% 3.26/1.73 thf(ty_t_Real_Oreal, type, real: $tType).
% 3.26/1.73 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.26/1.73 thf(ty_t_Nat_Onat, type, nat: $tType).
% 3.26/1.73 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: ($o))).
% 3.26/1.73 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 3.26/1.73 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 3.26/1.73 thf(sy_cl_Groups_Ouminus, type, uminus: (!> [A:$tType]: ($o))).
% 3.26/1.73 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: ($o))).
% 3.26/1.73 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 3.26/1.73 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: ($o))).
% 3.26/1.73 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 3.26/1.73 thf(sy_cl_Lattices_Oboolean__algebra, type, boolean_algebra: (!> [A:$tType]: ($o))).
% 3.26/1.73 thf(sy_cl_Lattices_Osemilattice__inf, type, semilattice_inf: (!> [A:$tType]: ($o))).
% 3.26/1.73 thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: ($o))).
% 3.26/1.73 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: ($o))).
% 3.26/1.73 thf(sy_cl_Groups_Olinordered__ab__group__add, type, linord219039673up_add: (!> [A:$tType]: ($o))).
% 3.26/1.73 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot, type, bounde1808546759up_bot: (!> [A:$tType]: ($o))).
% 3.26/1.73 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 3.26/1.73 thf(sy_c_Coincidence_Ostatediff, type, statediff: ((variable > real) > ((variable > real) > (set @ variable)))).
% 3.26/1.73 thf(sy_c_Coincidence_Ostateinterpol, type, stateinterpol: ((variable > real) > ((variable > real) > ((set @ variable) > (variable > real))))).
% 3.26/1.73 thf(sy_c_Denotational__Semantics_OUvariation, type, denota1419872369iation: ((variable > real) > ((variable > real) > ((set @ variable) > $o)))).
% 3.26/1.73 thf(sy_c_Denotational__Semantics_OVagree, type, denotational_Vagree: ((variable > real) > ((variable > real) > ((set @ variable) > $o)))).
% 3.26/1.73 thf(sy_c_Denotational__Semantics_Orepv, type, denotational_repv: ((variable > real) > (variable > (real > (variable > real))))).
% 3.26/1.73 thf(sy_c_Denotational__Semantics_Osolves__ODE, type, denota1778088425es_ODE: (denotational_interp > ((real > (variable > real)) > (char > (trm > $o))))).
% 3.26/1.73 thf(sy_c_Denotational__Semantics_Oterm__sem, type, denota1863255036rm_sem: (denotational_interp > (trm > ((variable > real) > real)))).
% 3.26/1.73 thf(sy_c_Groups_Ouminus__class_Ouminus, type, uminus_uminus: (!> [A:$tType]: ((A > A)))).
% 3.26/1.73 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 3.26/1.73 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 3.26/1.73 thf(sy_c_Lattices_Oinf__class_Oinf, type, inf_inf: (!> [A:$tType]: ((A > (A > A))))).
% 3.26/1.73 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 3.26/1.73 thf(sy_c_Nat_Osize__class_Osize, type, size_size: (!> [A:$tType]: ((A > nat)))).
% 3.26/1.73 thf(sy_c_Option_Ooption_ONone, type, none: (!> [A:$tType]: ((option @ A)))).
% 3.26/1.73 thf(sy_c_Option_Ooption_OSome, type, some: (!> [A:$tType]: ((A > (option @ A))))).
% 3.26/1.73 thf(sy_c_Option_Ooption_Ocase__option, type, case_option: (!> [B:$tType,A:$tType]: ((B > ((A > B) > ((option @ A) > B)))))).
% 3.26/1.73 thf(sy_c_Option_Ooption_Oset__option, type, set_option: (!> [A:$tType]: (((option @ A) > (set @ A))))).
% 3.26/1.73 thf(sy_c_Option_Ooption_Othe, type, the: (!> [A:$tType]: (((option @ A) > A)))).
% 3.26/1.73 thf(sy_c_Option_Othese, type, these: (!> [A:$tType]: (((set @ (option @ A)) > (set @ A))))).
% 3.26/1.73 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 3.26/1.73 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 3.26/1.73 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.26/1.73 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 3.26/1.73 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 3.26/1.73 thf(sy_c_Set_Ois__singleton, type, is_singleton: (!> [A:$tType]: (((set @ A) > $o)))).
% 3.26/1.73 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 3.26/1.73 thf(sy_c_Static__Semantics_OFVT, type, static_FVT: (trm > (set @ variable))).
% 3.26/1.73 thf(sy_c_Static__Semantics_Oselectlike, type, static_selectlike: ((set @ (variable > real)) > ((variable > real) > ((set @ variable) > (set @ (variable > real)))))).
% 3.26/1.73 thf(sy_c_Syntax_Otrm_OTimes, type, times: (trm > (trm > trm))).
% 3.26/1.73 thf(sy_c_Syntax_Ovariable_ODVar, type, dVar: (char > variable)).
% 3.26/1.73 thf(sy_c_Syntax_Ovariable_ORVar, type, rVar: (char > variable)).
% 3.26/1.73 thf(sy_c_Syntax_Ovariable_Orec__variable, type, rec_variable: (!> [A:$tType]: (((char > A) > ((char > A) > (variable > A)))))).
% 3.26/1.73 thf(sy_c_Syntax_Ovariable_Osize__variable, type, size_variable: (variable > nat)).
% 3.26/1.73 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTimeso, type, uSubst277968634Timeso: ((option @ trm) > ((option @ trm) > (option @ trm)))).
% 3.26/1.73 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Oadjoint, type, uSubst2091380086djoint: (((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) > (denotational_interp > ((variable > real) > denotational_interp)))).
% 3.26/1.73 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappt, type, uSubst95898992stappt: (((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) > ((set @ variable) > (trm > (option @ trm))))).
% 3.26/1.73 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.26/1.73 thf(sy_v_F, type, f: (real > (variable > real))).
% 3.26/1.73 thf(sy_v_I, type, i: denotational_interp).
% 3.26/1.73 thf(sy_v_U, type, u: (set @ variable)).
% 3.26/1.73 thf(sy_v__092_060omega_062, type, omega: (variable > real)).
% 3.26/1.73 thf(sy_v__092_060sigma_062, type, sigma: ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))).
% 3.26/1.73 thf(sy_v__092_060theta_062, type, theta: trm).
% 3.26/1.73 thf(sy_v_rr____, type, rr: (trm > (denotational_interp > (trm > (denotational_interp > (char > ((real > (variable > real)) > (variable > real)))))))).
% 3.26/1.73 thf(sy_v_x, type, x: char).
% 3.26/1.73 thf(fact_0_uv, axiom, (((denota1419872369iation @ (f @ (zero_zero @ real))) @ omega) @ (((sup_sup @ (set @ variable)) @ u) @ (((insert @ variable) @ (rVar @ x)) @ (((insert @ variable) @ (dVar @ x)) @ (bot_bot @ (set @ variable))))))).
% 3.26/1.73 thf(fact_1_Uvariation__empty, axiom, (! [Nu:(variable > real),Nu2:(variable > real)]: (((((denota1419872369iation @ Nu) @ Nu2) @ (bot_bot @ (set @ variable))) = (Nu = Nu2))))).
% 3.26/1.73 thf(fact_2_Un__insert__left, axiom, (! [A:$tType,A2:A,B2:(set @ A),C:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((insert @ A) @ A2) @ B2)) @ C) = (((insert @ A) @ A2) @ (((sup_sup @ (set @ A)) @ B2) @ C)))))).
% 3.26/1.73 thf(fact_3_Un__insert__right, axiom, (! [A:$tType,A3:(set @ A),A2:A,B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((insert @ A) @ A2) @ B2)) = (((insert @ A) @ A2) @ (((sup_sup @ (set @ A)) @ A3) @ B2)))))).
% 3.26/1.73 thf(fact_4_Un__empty, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A)]: ((((((sup_sup @ (set @ A)) @ A3) @ B2) = (bot_bot @ (set @ A))) = ((A3 = (bot_bot @ (set @ A))) & (B2 = (bot_bot @ (set @ A)))))))).
% 3.26/1.73 thf(fact_5_sup__bot__left, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ X) = X))))))).
% 3.26/1.73 thf(fact_6_sup__bot__right, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A]: (((((sup_sup @ A) @ X) @ (bot_bot @ A)) = X))))))).
% 3.26/1.73 thf(fact_7_bot__eq__sup__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A,Y:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ X) @ Y)) = ((X = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 3.26/1.73 thf(fact_8_sup__eq__bot__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A,Y:A]: ((((((sup_sup @ A) @ X) @ Y) = (bot_bot @ A)) = ((X = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 3.26/1.73 thf(fact_9_sup__bot_Oeq__neutr__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A,B3:A]: ((((((sup_sup @ A) @ A2) @ B3) = (bot_bot @ A)) = ((A2 = (bot_bot @ A)) & (B3 = (bot_bot @ A)))))))))).
% 3.26/1.73 thf(fact_10_sup__bot_Oleft__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ A2) = A2))))))).
% 3.26/1.73 thf(fact_11_sup__bot_Oneutr__eq__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A,B3:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ A2) @ B3)) = ((A2 = (bot_bot @ A)) & (B3 = (bot_bot @ A)))))))))).
% 3.26/1.73 thf(fact_12_sup__bot_Oright__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A]: (((((sup_sup @ A) @ A2) @ (bot_bot @ A)) = A2))))))).
% 3.26/1.73 thf(fact_13_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X2:A]: ((~ ((P @ X2))))))))).
% 3.26/1.73 thf(fact_14_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X2:A]: ((~ ((P @ X2))))))))).
% 3.26/1.73 thf(fact_15_all__not__in__conv, axiom, (! [A:$tType,A3:(set @ A)]: (((! [X2:A]: ((~ ((((member @ A) @ X2) @ A3))))) = (A3 = (bot_bot @ (set @ A))))))).
% 3.26/1.73 thf(fact_16_empty__iff, axiom, (! [A:$tType,C2:A]: ((~ ((((member @ A) @ C2) @ (bot_bot @ (set @ A)))))))).
% 3.26/1.73 thf(fact_17_insert__absorb2, axiom, (! [A:$tType,X:A,A3:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ X) @ A3)) = (((insert @ A) @ X) @ A3))))).
% 3.26/1.73 thf(fact_18_insert__iff, axiom, (! [A:$tType,A2:A,B3:A,A3:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B3) @ A3)) = ((A2 = B3) | (((member @ A) @ A2) @ A3)))))).
% 3.26/1.73 thf(fact_19_insertCI, axiom, (! [A:$tType,A2:A,B2:(set @ A),B3:A]: ((((~ ((((member @ A) @ A2) @ B2))) => (A2 = B3)) => (((member @ A) @ A2) @ (((insert @ A) @ B3) @ B2)))))).
% 3.26/1.73 thf(fact_20_sup_Oright__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B3:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A2) @ B3)) @ B3) = (((sup_sup @ A) @ A2) @ B3)))))))).
% 3.26/1.73 thf(fact_21_sup__left__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = (((sup_sup @ A) @ X) @ Y)))))))).
% 3.26/1.73 thf(fact_22_sup_Oleft__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B3:A]: (((((sup_sup @ A) @ A2) @ (((sup_sup @ A) @ A2) @ B3)) = (((sup_sup @ A) @ A2) @ B3)))))))).
% 3.26/1.73 thf(fact_23_sup__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X:A]: (((((sup_sup @ A) @ X) @ X) = X))))))).
% 3.26/1.73 thf(fact_24_sup_Oidem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A]: (((((sup_sup @ A) @ A2) @ A2) = A2))))))).
% 3.26/1.73 thf(fact_25_sup__apply, axiom, (! [B:$tType,A:$tType]: (((semilattice_sup @ B) => ((sup_sup @ (A > B)) = (^ [F:(A > B),G:(A > B),X2:A]: ((((sup_sup @ B) @ (F @ X2)) @ (G @ X2))))))))).
% 3.26/1.73 thf(fact_26_UnCI, axiom, (! [A:$tType,C2:A,B2:(set @ A),A3:(set @ A)]: ((((~ ((((member @ A) @ C2) @ B2))) => (((member @ A) @ C2) @ A3)) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B2)))))).
% 3.26/1.73 thf(fact_27_singletonI, axiom, (! [A:$tType,A2:A]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 3.26/1.73 thf(fact_28_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 3.26/1.73 thf(fact_29_ex__in__conv, axiom, (! [A:$tType,A3:(set @ A)]: (((? [X2:A]: ((((member @ A) @ X2) @ A3))) = (A3 != (bot_bot @ (set @ A))))))).
% 3.26/1.73 thf(fact_30_equals0I, axiom, (! [A:$tType,A3:(set @ A)]: (((! [Y2:A]: ((~ ((((member @ A) @ Y2) @ A3))))) => (A3 = (bot_bot @ (set @ A))))))).
% 3.26/1.73 thf(fact_31_equals0D, axiom, (! [A:$tType,A3:(set @ A),A2:A]: (((A3 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A2) @ A3))))))).
% 3.26/1.73 thf(fact_32_emptyE, axiom, (! [A:$tType,A2:A]: ((~ ((((member @ A) @ A2) @ (bot_bot @ (set @ A)))))))).
% 3.26/1.73 thf(fact_33_mk__disjoint__insert, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: (((((member @ A) @ A2) @ A3) => (? [B4:(set @ A)]: (((A3 = (((insert @ A) @ A2) @ B4)) & (~ ((((member @ A) @ A2) @ B4)))))))))).
% 3.26/1.73 thf(fact_34_insert__commute, axiom, (! [A:$tType,X:A,Y:A,A3:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ Y) @ A3)) = (((insert @ A) @ Y) @ (((insert @ A) @ X) @ A3)))))).
% 3.26/1.73 thf(fact_35_insert__eq__iff, axiom, (! [A:$tType,A2:A,A3:(set @ A),B3:A,B2:(set @ A)]: (((~ ((((member @ A) @ A2) @ A3))) => ((~ ((((member @ A) @ B3) @ B2))) => (((((insert @ A) @ A2) @ A3) = (((insert @ A) @ B3) @ B2)) = (((A2 = B3) => (A3 = B2)) & ((A2 != B3) => (? [C3:(set @ A)]: (((A3 = (((insert @ A) @ B3) @ C3)) & ((~ ((((member @ A) @ B3) @ C3))) & ((B2 = (((insert @ A) @ A2) @ C3)) & (~ ((((member @ A) @ A2) @ C3)))))))))))))))).
% 3.26/1.73 thf(fact_36_insert__absorb, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: (((((member @ A) @ A2) @ A3) => ((((insert @ A) @ A2) @ A3) = A3))))).
% 3.26/1.73 thf(fact_37_insert__ident, axiom, (! [A:$tType,X:A,A3:(set @ A),B2:(set @ A)]: (((~ ((((member @ A) @ X) @ A3))) => ((~ ((((member @ A) @ X) @ B2))) => (((((insert @ A) @ X) @ A3) = (((insert @ A) @ X) @ B2)) = (A3 = B2))))))).
% 3.26/1.73 thf(fact_38_Set_Oset__insert, axiom, (! [A:$tType,X:A,A3:(set @ A)]: (((((member @ A) @ X) @ A3) => (~ ((! [B4:(set @ A)]: (((A3 = (((insert @ A) @ X) @ B4)) => (((member @ A) @ X) @ B4)))))))))).
% 3.26/1.73 thf(fact_39_insertI2, axiom, (! [A:$tType,A2:A,B2:(set @ A),B3:A]: (((((member @ A) @ A2) @ B2) => (((member @ A) @ A2) @ (((insert @ A) @ B3) @ B2)))))).
% 3.26/1.73 thf(fact_40_insertI1, axiom, (! [A:$tType,A2:A,B2:(set @ A)]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ B2))))).
% 3.26/1.73 thf(fact_41_insertE, axiom, (! [A:$tType,A2:A,B3:A,A3:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B3) @ A3)) => ((A2 != B3) => (((member @ A) @ A2) @ A3)))))).
% 3.26/1.73 thf(fact_42_sup__left__commute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X) @ Z))))))))).
% 3.26/1.73 thf(fact_43_sup_Oleft__commute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B3:A,A2:A,C2:A]: (((((sup_sup @ A) @ B3) @ (((sup_sup @ A) @ A2) @ C2)) = (((sup_sup @ A) @ A2) @ (((sup_sup @ A) @ B3) @ C2))))))))).
% 3.26/1.73 thf(fact_44_sup__commute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((sup_sup @ A) = (^ [X2:A,Y3:A]: ((((sup_sup @ A) @ Y3) @ X2)))))))).
% 3.26/1.73 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 3.26/1.73 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A3)))) = A3)))).
% 3.26/1.73 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 3.26/1.73 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F2:(A > B),G2:(A > B)]: (((! [X3:A]: (((F2 @ X3) = (G2 @ X3)))) => (F2 = G2))))).
% 3.26/1.73 thf(fact_49_sup_Ocommute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((sup_sup @ A) = (^ [A4:A,B5:A]: ((((sup_sup @ A) @ B5) @ A4)))))))).
% 3.26/1.73 thf(fact_50_sup__assoc, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z) = (((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z))))))))).
% 3.26/1.73 thf(fact_51_sup_Oassoc, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B3:A,C2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A2) @ B3)) @ C2) = (((sup_sup @ A) @ A2) @ (((sup_sup @ A) @ B3) @ C2))))))))).
% 3.26/1.73 thf(fact_52_boolean__algebra__cancel_Osup2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B2:A,K:A,B3:A,A2:A]: (((B2 = (((sup_sup @ A) @ K) @ B3)) => ((((sup_sup @ A) @ A2) @ B2) = (((sup_sup @ A) @ K) @ (((sup_sup @ A) @ A2) @ B3)))))))))).
% 3.26/1.73 thf(fact_53_boolean__algebra__cancel_Osup1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A3:A,K:A,A2:A,B3:A]: (((A3 = (((sup_sup @ A) @ K) @ A2)) => ((((sup_sup @ A) @ A3) @ B3) = (((sup_sup @ A) @ K) @ (((sup_sup @ A) @ A2) @ B3)))))))))).
% 3.26/1.73 thf(fact_54_sup__fun__def, axiom, (! [B:$tType,A:$tType]: (((semilattice_sup @ B) => ((sup_sup @ (A > B)) = (^ [F:(A > B),G:(A > B),X2:A]: ((((sup_sup @ B) @ (F @ X2)) @ (G @ X2))))))))).
% 3.26/1.73 thf(fact_55_inf__sup__aci_I5_J, axiom, (! [A:$tType]: (((lattice @ A) => ((sup_sup @ A) = (^ [X2:A,Y3:A]: ((((sup_sup @ A) @ Y3) @ X2)))))))).
% 3.26/1.73 thf(fact_56_inf__sup__aci_I6_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z) = (((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z))))))))).
% 3.26/1.73 thf(fact_57_inf__sup__aci_I7_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X) @ Z))))))))).
% 3.26/1.73 thf(fact_58_inf__sup__aci_I8_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = (((sup_sup @ A) @ X) @ Y)))))))).
% 3.26/1.73 thf(fact_59_Un__left__commute, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),C:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ B2) @ C)) = (((sup_sup @ (set @ A)) @ B2) @ (((sup_sup @ (set @ A)) @ A3) @ C)))))).
% 3.26/1.73 thf(fact_60_Un__left__absorb, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) = (((sup_sup @ (set @ A)) @ A3) @ B2))))).
% 3.26/1.73 thf(fact_61_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A5:(set @ A),B6:(set @ A)]: ((((sup_sup @ (set @ A)) @ B6) @ A5))))))).
% 3.26/1.73 thf(fact_62_Un__absorb, axiom, (! [A:$tType,A3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ A3) = A3)))).
% 3.26/1.73 thf(fact_63_Un__assoc, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),C:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) @ C) = (((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ B2) @ C)))))).
% 3.26/1.73 thf(fact_64_ball__Un, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),P:(A > $o)]: (((! [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) => (P @ X2)))) = ((! [X2:A]: (((((member @ A) @ X2) @ A3) => (P @ X2)))) & (! [X2:A]: (((((member @ A) @ X2) @ B2) => (P @ X2))))))))).
% 3.26/1.73 thf(fact_65_bex__Un, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) & (P @ X2)))) = ((? [X2:A]: (((((member @ A) @ X2) @ A3) & (P @ X2)))) | (? [X2:A]: (((((member @ A) @ X2) @ B2) & (P @ X2))))))))).
% 3.26/1.73 thf(fact_66_UnI2, axiom, (! [A:$tType,C2:A,B2:(set @ A),A3:(set @ A)]: (((((member @ A) @ C2) @ B2) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B2)))))).
% 3.26/1.73 thf(fact_67_UnI1, axiom, (! [A:$tType,C2:A,A3:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ A3) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B2)))))).
% 3.26/1.73 thf(fact_68_UnE, axiom, (! [A:$tType,C2:A,A3:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) => ((~ ((((member @ A) @ C2) @ A3))) => (((member @ A) @ C2) @ B2)))))).
% 3.26/1.73 thf(fact_69_Uvariation__sym__rel, axiom, (! [Omega:(variable > real),Nu:(variable > real),U:(set @ variable)]: (((((denota1419872369iation @ Omega) @ Nu) @ U) => (((denota1419872369iation @ Nu) @ Omega) @ U))))).
% 3.26/1.73 thf(fact_70_Uvariation__refl, axiom, (! [Nu:(variable > real),V:(set @ variable)]: ((((denota1419872369iation @ Nu) @ Nu) @ V)))).
% 3.26/1.73 thf(fact_71_Uvariation__sym, axiom, (denota1419872369iation = (^ [Omega2:(variable > real),Nu3:(variable > real)]: (((denota1419872369iation @ Nu3) @ Omega2))))).
% 3.26/1.73 thf(fact_72_Uvariation__def, axiom, (denota1419872369iation = (^ [Nu3:(variable > real),Nu4:(variable > real),U2:(set @ variable)]: ((! [I:variable]: (((~ ((((member @ variable) @ I) @ U2))) => ((Nu3 @ I) = (Nu4 @ I))))))))).
% 3.26/1.73 thf(fact_73_singleton__inject, axiom, (! [A:$tType,A2:A,B3:A]: ((((((insert @ A) @ A2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B3) @ (bot_bot @ (set @ A)))) => (A2 = B3))))).
% 3.26/1.73 thf(fact_74_insert__not__empty, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: (((((insert @ A) @ A2) @ A3) != (bot_bot @ (set @ A)))))).
% 3.26/1.73 thf(fact_75_doubleton__eq__iff, axiom, (! [A:$tType,A2:A,B3:A,C2:A,D:A]: ((((((insert @ A) @ A2) @ (((insert @ A) @ B3) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C2) @ (((insert @ A) @ D) @ (bot_bot @ (set @ A))))) = (((A2 = C2) & (B3 = D)) | ((A2 = D) & (B3 = C2))))))).
% 3.26/1.73 thf(fact_76_singleton__iff, axiom, (! [A:$tType,B3:A,A2:A]: (((((member @ A) @ B3) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) = (B3 = A2))))).
% 3.26/1.73 thf(fact_77_singletonD, axiom, (! [A:$tType,B3:A,A2:A]: (((((member @ A) @ B3) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) => (B3 = A2))))).
% 3.26/1.73 thf(fact_78_Un__empty__right, axiom, (! [A:$tType,A3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (bot_bot @ (set @ A))) = A3)))).
% 3.26/1.73 thf(fact_79_Un__empty__left, axiom, (! [A:$tType,B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (bot_bot @ (set @ A))) @ B2) = B2)))).
% 3.26/1.73 thf(fact_80_Uvariation__trans, axiom, (! [Omega:(variable > real),Nu:(variable > real),U:(set @ variable),Mu:(variable > real),V:(set @ variable)]: (((((denota1419872369iation @ Omega) @ Nu) @ U) => ((((denota1419872369iation @ Nu) @ Mu) @ V) => (((denota1419872369iation @ Omega) @ Mu) @ (((sup_sup @ (set @ variable)) @ U) @ V))))))).
% 3.26/1.73 thf(fact_81_singleton__Un__iff, axiom, (! [A:$tType,X:A,A3:(set @ A),B2:(set @ A)]: ((((((insert @ A) @ X) @ (bot_bot @ (set @ A))) = (((sup_sup @ (set @ A)) @ A3) @ B2)) = (((A3 = (bot_bot @ (set @ A))) & (B2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) | (((A3 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B2 = (bot_bot @ (set @ A)))) | ((A3 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))))).
% 3.26/1.73 thf(fact_82_Un__singleton__iff, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),X:A]: ((((((sup_sup @ (set @ A)) @ A3) @ B2) = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = (((A3 = (bot_bot @ (set @ A))) & (B2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) | (((A3 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B2 = (bot_bot @ (set @ A)))) | ((A3 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))))).
% 3.26/1.73 thf(fact_83_insert__is__Un, axiom, (! [A:$tType]: (((insert @ A) = (^ [A4:A]: (((sup_sup @ (set @ A)) @ (((insert @ A) @ A4) @ (bot_bot @ (set @ A)))))))))).
% 3.26/1.73 thf(fact_84__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rr_O_A_092_060forall_062x0_Ax1_Ax2_Ax3_Ax4_Ax5_O_A_I_092_060exists_062v6_O_AUvariation_Av6_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_Av6_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_Av6_J_A_061_A_IUvariation_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [Rr:(trm > (denotational_interp > (trm > (denotational_interp > (char > ((real > (variable > real)) > (variable > real)))))))]: ((~ ((! [X0:trm,X1:denotational_interp,X22:trm,X32:denotational_interp,X4:char,X5:(real > (variable > real))]: (((? [V6:(variable > real)]: (((((denota1419872369iation @ V6) @ (X5 @ (zero_zero @ real))) @ (((insert @ variable) @ (rVar @ X4)) @ (((insert @ variable) @ (dVar @ X4)) @ (bot_bot @ (set @ variable))))) & ((((denota1863255036rm_sem @ X32) @ X22) @ V6) != (((denota1863255036rm_sem @ X1) @ X0) @ V6))))) = ((((denota1419872369iation @ ((((((Rr @ X0) @ X1) @ X22) @ X32) @ X4) @ X5)) @ (X5 @ (zero_zero @ real))) @ (((insert @ variable) @ (rVar @ X4)) @ (((insert @ variable) @ (dVar @ X4)) @ (bot_bot @ (set @ variable))))) & ((((denota1863255036rm_sem @ X32) @ X22) @ ((((((Rr @ X0) @ X1) @ X22) @ X32) @ X4) @ X5)) != (((denota1863255036rm_sem @ X1) @ X0) @ ((((((Rr @ X0) @ X1) @ X22) @ X32) @ X4) @ X5)))))))))))))).
% 3.26/1.73 thf(fact_85_solves__Vagree__trans, axiom, (! [F3:(real > (variable > real)),Omega:(variable > real),U:(set @ variable),I2:denotational_interp,X:char,Theta:trm,Zeta:real]: (((((denota1419872369iation @ (F3 @ (zero_zero @ real))) @ Omega) @ U) => (((((denota1778088425es_ODE @ I2) @ F3) @ X) @ Theta) => (((denota1419872369iation @ (F3 @ Zeta)) @ Omega) @ (((sup_sup @ (set @ variable)) @ U) @ (((insert @ variable) @ (rVar @ X)) @ (((insert @ variable) @ (dVar @ X)) @ (bot_bot @ (set @ variable))))))))))).
% 3.26/1.73 thf(fact_86__092_060open_062_092_060forall_062x0_Ax1_Ax2_Ax3_Ax4_Ax5_O_A_I_092_060exists_062v6_O_AUvariation_Av6_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_Av6_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_Av6_J_A_061_A_IUvariation_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_J_092_060close_062, axiom, (! [X0:trm,X1:denotational_interp,X22:trm,X32:denotational_interp,X4:char,X5:(real > (variable > real))]: (((? [V6:(variable > real)]: (((((denota1419872369iation @ V6) @ (X5 @ (zero_zero @ real))) @ (((insert @ variable) @ (rVar @ X4)) @ (((insert @ variable) @ (dVar @ X4)) @ (bot_bot @ (set @ variable))))) & ((((denota1863255036rm_sem @ X32) @ X22) @ V6) != (((denota1863255036rm_sem @ X1) @ X0) @ V6))))) = ((((denota1419872369iation @ ((((((rr @ X0) @ X1) @ X22) @ X32) @ X4) @ X5)) @ (X5 @ (zero_zero @ real))) @ (((insert @ variable) @ (rVar @ X4)) @ (((insert @ variable) @ (dVar @ X4)) @ (bot_bot @ (set @ variable))))) & ((((denota1863255036rm_sem @ X32) @ X22) @ ((((((rr @ X0) @ X1) @ X22) @ X32) @ X4) @ X5)) != (((denota1863255036rm_sem @ X1) @ X0) @ ((((((rr @ X0) @ X1) @ X22) @ X32) @ X4) @ X5)))))))).
% 3.26/1.73 thf(fact_87_variable_Oinject_I1_J, axiom, (! [X12:char,Y1:char]: ((((rVar @ X12) = (rVar @ Y1)) = (X12 = Y1))))).
% 3.26/1.73 thf(fact_88_set__zero, axiom, (! [A:$tType]: (((zero @ A) => ((zero_zero @ (set @ A)) = (((insert @ A) @ (zero_zero @ A)) @ (bot_bot @ (set @ A)))))))).
% 3.26/1.73 thf(fact_89_variable_Oinject_I2_J, axiom, (! [X23:char,Y22:char]: ((((dVar @ X23) = (dVar @ Y22)) = (X23 = Y22))))).
% 3.26/1.73 thf(fact_90_union__or, axiom, (! [A:$tType,C2:A,A3:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) = ((((member @ A) @ C2) @ A3) | (((member @ A) @ C2) @ B2)))))).
% 3.26/1.73 thf(fact_91_ball__insert, axiom, (! [A:$tType,A2:A,B2:(set @ A),P:(A > $o)]: (((! [X2:A]: (((((member @ A) @ X2) @ (((insert @ A) @ A2) @ B2)) => (P @ X2)))) = ((P @ A2) & (! [X2:A]: (((((member @ A) @ X2) @ B2) => (P @ X2))))))))).
% 3.26/1.73 thf(fact_92_the__elem__eq, axiom, (! [A:$tType,X:A]: ((((the_elem @ A) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = X)))).
% 3.26/1.73 thf(fact_93_bot__apply, axiom, (! [C4:$tType,D2:$tType]: (((bot @ C4) => ((bot_bot @ (D2 > C4)) = (^ [X2:D2]: ((bot_bot @ C4)))))))).
% 3.26/1.73 thf(fact_94_f2, axiom, (! [F4:(real > (variable > real)),C5:char,I3:denotational_interp,T:trm,Ia:denotational_interp,Ta:trm]: ((((((denota1419872369iation @ ((((((rr @ Ta) @ Ia) @ T) @ I3) @ C5) @ F4)) @ (F4 @ (zero_zero @ real))) @ (((insert @ variable) @ (rVar @ C5)) @ (((insert @ variable) @ (dVar @ C5)) @ (bot_bot @ (set @ variable))))) & ((((denota1863255036rm_sem @ I3) @ T) @ ((((((rr @ Ta) @ Ia) @ T) @ I3) @ C5) @ F4)) != (((denota1863255036rm_sem @ Ia) @ Ta) @ ((((((rr @ Ta) @ Ia) @ T) @ I3) @ C5) @ F4)))) | (((((denota1778088425es_ODE @ I3) @ F4) @ C5) @ T) = ((((denota1778088425es_ODE @ Ia) @ F4) @ C5) @ Ta)))))).
% 3.26/1.73 thf(fact_95_zero__reorient, axiom, (! [A:$tType]: (((zero @ A) => (! [X:A]: ((((zero_zero @ A) = X) = (X = (zero_zero @ A))))))))).
% 3.26/1.73 thf(fact_96_bot__fun__def, axiom, (! [B:$tType,A:$tType]: (((bot @ B) => ((bot_bot @ (A > B)) = (^ [X2:A]: ((bot_bot @ B)))))))).
% 3.26/1.73 thf(fact_97_not__union__or, axiom, (! [A:$tType,X:A,A3:(set @ A),B2:(set @ A)]: (((~ ((((member @ A) @ X) @ (((sup_sup @ (set @ A)) @ A3) @ B2)))) = ((~ ((((member @ A) @ X) @ A3))) & (~ ((((member @ A) @ X) @ B2)))))))).
% 3.26/1.73 thf(fact_98_same__ODE__same__sol, axiom, (! [F3:(real > (variable > real)),X:char,I2:denotational_interp,Theta:trm,J:denotational_interp,Eta:trm]: (((! [Nu5:(variable > real)]: (((((denota1419872369iation @ Nu5) @ (F3 @ (zero_zero @ real))) @ (((insert @ variable) @ (rVar @ X)) @ (((insert @ variable) @ (dVar @ X)) @ (bot_bot @ (set @ variable))))) => ((((denota1863255036rm_sem @ I2) @ Theta) @ Nu5) = (((denota1863255036rm_sem @ J) @ Eta) @ Nu5))))) => (((((denota1778088425es_ODE @ I2) @ F3) @ X) @ Theta) = ((((denota1778088425es_ODE @ J) @ F3) @ X) @ Eta)))))).
% 3.26/1.73 thf(fact_99_variable_Odistinct_I1_J, axiom, (! [X12:char,X23:char]: (((rVar @ X12) != (dVar @ X23))))).
% 3.26/1.73 thf(fact_100_variable_Oinduct, axiom, (! [P:(variable > $o),Variable:variable]: (((! [X3:char]: ((P @ (rVar @ X3)))) => ((! [X3:char]: ((P @ (dVar @ X3)))) => (P @ Variable)))))).
% 3.26/1.73 thf(fact_101_variable_Oexhaust, axiom, (! [Y:variable]: (((! [X13:char]: ((Y != (rVar @ X13)))) => (~ ((! [X24:char]: ((Y != (dVar @ X24)))))))))).
% 3.26/1.73 thf(fact_102_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X2:A]: ((((member @ A) @ X2) @ (bot_bot @ (set @ A))))))))).
% 3.26/1.73 thf(fact_103_Collect__empty__eq__bot, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (P = (bot_bot @ (A > $o))))))).
% 3.26/1.73 thf(fact_104_is__singleton__the__elem, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A5:(set @ A)]: ((A5 = (((insert @ A) @ ((the_elem @ A) @ A5)) @ (bot_bot @ (set @ A)))))))))).
% 3.26/1.73 thf(fact_105_vaflow2, axiom, (! [F3:(real > (variable > real)),Theta:trm,Zeta:real]: ((((((denota1778088425es_ODE @ (((uSubst2091380086djoint @ sigma) @ i) @ omega)) @ F3) @ x) @ Theta) => (((denota1419872369iation @ (F3 @ Zeta)) @ (F3 @ (zero_zero @ real))) @ (((insert @ variable) @ (rVar @ x)) @ (((insert @ variable) @ (dVar @ x)) @ (bot_bot @ (set @ variable))))))))).
% 3.26/1.73 thf(fact_106_is__singletonI, axiom, (! [A:$tType,X:A]: (((is_singleton @ A) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))).
% 3.26/1.73 thf(fact_107_a1, axiom, ((((denota1778088425es_ODE @ (((uSubst2091380086djoint @ sigma) @ i) @ omega)) @ f) @ x) @ theta)).
% 3.26/1.73 thf(fact_108_is__singletonI_H, axiom, (! [A:$tType,A3:(set @ A)]: (((A3 != (bot_bot @ (set @ A))) => ((! [X3:A,Y2:A]: (((((member @ A) @ X3) @ A3) => ((((member @ A) @ Y2) @ A3) => (X3 = Y2))))) => ((is_singleton @ A) @ A3)))))).
% 3.26/1.73 thf(fact_109_is__singleton__def, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A5:(set @ A)]: ((? [X2:A]: ((A5 = (((insert @ A) @ X2) @ (bot_bot @ (set @ A)))))))))))).
% 3.26/1.73 thf(fact_110_is__singletonE, axiom, (! [A:$tType,A3:(set @ A)]: ((((is_singleton @ A) @ A3) => (~ ((! [X3:A]: ((A3 != (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))))))))))).
% 3.26/1.73 thf(fact_111_vaflow1, axiom, (! [F3:(real > (variable > real)),Theta:trm,Zeta:real]: ((((((denota1778088425es_ODE @ i) @ F3) @ x) @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ (((sup_sup @ (set @ variable)) @ u) @ (((insert @ variable) @ (rVar @ x)) @ (((insert @ variable) @ (dVar @ x)) @ (bot_bot @ (set @ variable)))))) @ Theta))) => (((denota1419872369iation @ (F3 @ Zeta)) @ (F3 @ (zero_zero @ real))) @ (((insert @ variable) @ (rVar @ x)) @ (((insert @ variable) @ (dVar @ x)) @ (bot_bot @ (set @ variable))))))))).
% 3.26/1.73 thf(fact_112_l2r, axiom, (((((denota1778088425es_ODE @ i) @ f) @ x) @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ (((sup_sup @ (set @ variable)) @ u) @ (((insert @ variable) @ (rVar @ x)) @ (((insert @ variable) @ (dVar @ x)) @ (bot_bot @ (set @ variable)))))) @ theta))) => ((((denota1778088425es_ODE @ (((uSubst2091380086djoint @ sigma) @ i) @ omega)) @ f) @ x) @ theta))).
% 3.26/1.73 thf(fact_113_IH, axiom, (! [Nu:(variable > real)]: (((((denota1419872369iation @ Nu) @ (f @ (zero_zero @ real))) @ (((sup_sup @ (set @ variable)) @ u) @ (((insert @ variable) @ (rVar @ x)) @ (((insert @ variable) @ (dVar @ x)) @ (bot_bot @ (set @ variable)))))) => ((((denota1863255036rm_sem @ i) @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ (((sup_sup @ (set @ variable)) @ u) @ (((insert @ variable) @ (rVar @ x)) @ (((insert @ variable) @ (dVar @ x)) @ (bot_bot @ (set @ variable)))))) @ theta))) @ Nu) = (((denota1863255036rm_sem @ (((uSubst2091380086djoint @ sigma) @ i) @ (f @ (zero_zero @ real)))) @ theta) @ Nu)))))).
% 3.26/1.73 thf(fact_114_subdef, axiom, ((((uSubst95898992stappt @ sigma) @ (((sup_sup @ (set @ variable)) @ u) @ (((insert @ variable) @ (rVar @ x)) @ (((insert @ variable) @ (dVar @ x)) @ (bot_bot @ (set @ variable)))))) @ theta) != (none @ trm))).
% 3.26/1.73 thf(fact_115_variable_Osize__gen_I1_J, axiom, (! [X12:char]: (((size_variable @ (rVar @ X12)) = (zero_zero @ nat))))).
% 3.26/1.73 thf(fact_116_usubst__term, axiom, (! [Nu:(variable > real),Omega:(variable > real),U:(set @ variable),Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),Theta:trm,I2:denotational_interp]: (((((denota1419872369iation @ Nu) @ Omega) @ U) => (((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (none @ trm)) => ((((denota1863255036rm_sem @ I2) @ ((the @ trm) @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta))) @ Nu) = (((denota1863255036rm_sem @ (((uSubst2091380086djoint @ Sigma) @ I2) @ Omega)) @ Theta) @ Nu))))))).
% 3.26/1.73 thf(fact_117_usubstappt__det, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm,V:(set @ variable)]: ((((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (none @ trm)) => (((((uSubst95898992stappt @ Sigma) @ V) @ Theta) != (none @ trm)) => ((((uSubst95898992stappt @ Sigma) @ U) @ Theta) = (((uSubst95898992stappt @ Sigma) @ V) @ Theta))))))).
% 3.26/1.73 thf(fact_118_undeft__None, axiom, ((none @ trm) = (none @ trm))).
% 3.26/1.73 thf(fact_119_usubst__ode, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),X:char,Theta:trm,I2:denotational_interp,F3:(real > (variable > real))]: ((((((uSubst95898992stappt @ Sigma) @ (((insert @ variable) @ (rVar @ X)) @ (((insert @ variable) @ (dVar @ X)) @ (bot_bot @ (set @ variable))))) @ Theta) != (none @ trm)) => (((((denota1778088425es_ODE @ I2) @ F3) @ X) @ ((the @ trm) @ (((uSubst95898992stappt @ Sigma) @ (((insert @ variable) @ (rVar @ X)) @ (((insert @ variable) @ (dVar @ X)) @ (bot_bot @ (set @ variable))))) @ Theta))) = ((((denota1778088425es_ODE @ (((uSubst2091380086djoint @ Sigma) @ I2) @ (F3 @ (zero_zero @ real)))) @ F3) @ X) @ Theta)))))).
% 3.26/1.73 thf(fact_120_variable_Osize__gen_I2_J, axiom, (! [X23:char]: (((size_variable @ (dVar @ X23)) = (zero_zero @ nat))))).
% 3.26/1.73 thf(fact_121_option_Oexpand, axiom, (! [A:$tType,Option:(option @ A),Option2:(option @ A)]: ((((Option = (none @ A)) = (Option2 = (none @ A))) => (((Option != (none @ A)) => ((Option2 != (none @ A)) => (((the @ A) @ Option) = ((the @ A) @ Option2)))) => (Option = Option2)))))).
% 3.26/1.73 thf(fact_122_variable_Osize_I3_J, axiom, (! [X12:char]: ((((size_size @ variable) @ (rVar @ X12)) = (zero_zero @ nat))))).
% 3.26/1.73 thf(fact_123_variable_Osize_I4_J, axiom, (! [X23:char]: ((((size_size @ variable) @ (dVar @ X23)) = (zero_zero @ nat))))).
% 3.26/1.73 thf(fact_124_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A5:(set @ A)]: ((A5 = (bot_bot @ (set @ A))))))))).
% 3.26/1.73 thf(fact_125_Uvariation__repv, axiom, (! [Omega:(variable > real),X:variable,D:real]: ((((denota1419872369iation @ Omega) @ (((denotational_repv @ Omega) @ X) @ D)) @ (((insert @ variable) @ X) @ (bot_bot @ (set @ variable))))))).
% 3.26/1.73 thf(fact_126_these__empty__eq, axiom, (! [A:$tType,B2:(set @ (option @ A))]: (((((these @ A) @ B2) = (bot_bot @ (set @ A))) = ((B2 = (bot_bot @ (set @ (option @ A)))) | (B2 = (((insert @ (option @ A)) @ (none @ A)) @ (bot_bot @ (set @ (option @ A)))))))))).
% 3.26/1.73 thf(fact_127_these__not__empty__eq, axiom, (! [A:$tType,B2:(set @ (option @ A))]: (((((these @ A) @ B2) != (bot_bot @ (set @ A))) = ((B2 != (bot_bot @ (set @ (option @ A)))) & (B2 != (((insert @ (option @ A)) @ (none @ A)) @ (bot_bot @ (set @ (option @ A)))))))))).
% 3.26/1.73 thf(fact_128_variable_Osimps_I7_J, axiom, (! [A:$tType,F1:(char > A),F22:(char > A),X12:char]: ((((((rec_variable @ A) @ F1) @ F22) @ (rVar @ X12)) = (F1 @ X12))))).
% 3.26/1.73 thf(fact_129_repv__self, axiom, (! [Omega:(variable > real),X:variable]: (((((denotational_repv @ Omega) @ X) @ (Omega @ X)) = Omega)))).
% 3.26/1.73 thf(fact_130_repv__access, axiom, (denotational_repv = (^ [Omega2:(variable > real),X2:variable,R:real,Y3:variable]: (((((if @ real) @ (X2 = Y3)) @ R) @ (Omega2 @ Y3)))))).
% 3.26/1.73 thf(fact_131_these__empty, axiom, (! [A:$tType]: ((((these @ A) @ (bot_bot @ (set @ (option @ A)))) = (bot_bot @ (set @ A)))))).
% 3.26/1.73 thf(fact_132_these__insert__None, axiom, (! [A:$tType,A3:(set @ (option @ A))]: ((((these @ A) @ (((insert @ (option @ A)) @ (none @ A)) @ A3)) = ((these @ A) @ A3))))).
% 3.26/1.73 thf(fact_133_repv__def__correct, axiom, (denotational_repv = (^ [Omega2:(variable > real),X2:variable,R:real,Y3:variable]: (((((if @ real) @ (X2 = Y3)) @ R) @ (Omega2 @ Y3)))))).
% 3.26/1.73 thf(fact_134_variable_Osimps_I8_J, axiom, (! [A:$tType,F1:(char > A),F22:(char > A),X23:char]: ((((((rec_variable @ A) @ F1) @ F22) @ (dVar @ X23)) = (F22 @ X23))))).
% 3.26/1.73 thf(fact_135_these__insert__Some, axiom, (! [A:$tType,X:A,A3:(set @ (option @ A))]: ((((these @ A) @ (((insert @ (option @ A)) @ ((some @ A) @ X)) @ A3)) = (((insert @ A) @ X) @ ((these @ A) @ A3)))))).
% 3.26/1.73 thf(fact_136_repv__selectlike__other__converse, axiom, (! [X:variable,Y:variable,Omega:(variable > real),D:real,X6:(set @ (variable > real))]: (((X != Y) => ((((member @ (variable > real)) @ (((denotational_repv @ Omega) @ X) @ D)) @ X6) = (((member @ (variable > real)) @ (((denotational_repv @ Omega) @ X) @ D)) @ (((static_selectlike @ X6) @ Omega) @ (((insert @ variable) @ Y) @ (bot_bot @ (set @ variable)))))))))).
% 3.26/1.73 thf(fact_137_repv__selectlike__other, axiom, (! [X:variable,Y:variable,Omega:(variable > real),D:real,X6:(set @ (variable > real))]: (((X != Y) => ((((member @ (variable > real)) @ (((denotational_repv @ Omega) @ X) @ D)) @ (((static_selectlike @ X6) @ Omega) @ (((insert @ variable) @ Y) @ (bot_bot @ (set @ variable))))) = (((member @ (variable > real)) @ (((denotational_repv @ Omega) @ X) @ D)) @ X6)))))).
% 3.26/1.73 thf(fact_138_repv__selectlike__self, axiom, (! [Omega:(variable > real),X:variable,D:real,X6:(set @ (variable > real))]: (((((member @ (variable > real)) @ (((denotational_repv @ Omega) @ X) @ D)) @ (((static_selectlike @ X6) @ Omega) @ (((insert @ variable) @ X) @ (bot_bot @ (set @ variable))))) = ((D = (Omega @ X)) & (((member @ (variable > real)) @ Omega) @ X6)))))).
% 3.26/1.73 thf(fact_139_option_Oinject, axiom, (! [A:$tType,X23:A,Y22:A]: (((((some @ A) @ X23) = ((some @ A) @ Y22)) = (X23 = Y22))))).
% 3.26/1.73 thf(fact_140_selectlike__self, axiom, (! [Nu:(variable > real),X6:(set @ (variable > real)),V:(set @ variable)]: (((((member @ (variable > real)) @ Nu) @ (((static_selectlike @ X6) @ Nu) @ V)) = (((member @ (variable > real)) @ Nu) @ X6))))).
% 3.26/1.73 thf(fact_141_not__None__eq, axiom, (! [A:$tType,X:(option @ A)]: (((X != (none @ A)) = (? [Y3:A]: ((X = ((some @ A) @ Y3)))))))).
% 3.26/1.73 thf(fact_142_not__Some__eq, axiom, (! [A:$tType,X:(option @ A)]: (((! [Y3:A]: ((X != ((some @ A) @ Y3)))) = (X = (none @ A)))))).
% 3.26/1.73 thf(fact_143_selectlike__empty, axiom, (! [X6:(set @ (variable > real)),Nu:(variable > real)]: (((((static_selectlike @ X6) @ Nu) @ (bot_bot @ (set @ variable))) = X6)))).
% 3.26/1.73 thf(fact_144_selectlike__compose, axiom, (! [X6:(set @ (variable > real)),Nu:(variable > real),V:(set @ variable),W:(set @ variable)]: (((((static_selectlike @ (((static_selectlike @ X6) @ Nu) @ V)) @ Nu) @ W) = (((static_selectlike @ X6) @ Nu) @ (((sup_sup @ (set @ variable)) @ V) @ W)))))).
% 3.26/1.73 thf(fact_145_option_Ocollapse, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) => (((some @ A) @ ((the @ A) @ Option)) = Option))))).
% 3.26/1.73 thf(fact_146_in__these__eq, axiom, (! [A:$tType,X:A,A3:(set @ (option @ A))]: (((((member @ A) @ X) @ ((these @ A) @ A3)) = (((member @ (option @ A)) @ ((some @ A) @ X)) @ A3))))).
% 3.26/1.73 thf(fact_147_selectlike__union, axiom, (! [X6:(set @ (variable > real)),Y4:(set @ (variable > real)),Nu:(variable > real),V:(set @ variable)]: (((((static_selectlike @ (((sup_sup @ (set @ (variable > real))) @ X6) @ Y4)) @ Nu) @ V) = (((sup_sup @ (set @ (variable > real))) @ (((static_selectlike @ X6) @ Nu) @ V)) @ (((static_selectlike @ Y4) @ Nu) @ V)))))).
% 3.26/1.73 thf(fact_148_option_Odistinct_I1_J, axiom, (! [A:$tType,X23:A]: (((none @ A) != ((some @ A) @ X23))))).
% 3.26/1.73 thf(fact_149_option_Osel, axiom, (! [A:$tType,X23:A]: ((((the @ A) @ ((some @ A) @ X23)) = X23)))).
% 3.26/1.73 thf(fact_150_option_OdiscI, axiom, (! [A:$tType,Option:(option @ A),X23:A]: (((Option = ((some @ A) @ X23)) => (Option != (none @ A)))))).
% 3.26/1.73 thf(fact_151_option_Oexhaust, axiom, (! [A:$tType,Y:(option @ A)]: (((Y != (none @ A)) => (~ ((! [X24:A]: ((Y != ((some @ A) @ X24)))))))))).
% 3.26/1.73 thf(fact_152_option_Oinducts, axiom, (! [A:$tType,P:((option @ A) > $o),Option:(option @ A)]: (((P @ (none @ A)) => ((! [X3:A]: ((P @ ((some @ A) @ X3)))) => (P @ Option)))))).
% 3.26/1.73 thf(fact_153_split__option__ex, axiom, (! [A:$tType]: (((^ [P2:((option @ A) > $o)]: ((? [X7:(option @ A)]: ((P2 @ X7))))) = (^ [P3:((option @ A) > $o)]: (((P3 @ (none @ A)) | (? [X2:A]: ((P3 @ ((some @ A) @ X2))))))))))).
% 3.26/1.73 thf(fact_154_split__option__all, axiom, (! [A:$tType]: (((^ [P2:((option @ A) > $o)]: ((! [X7:(option @ A)]: ((P2 @ X7))))) = (^ [P3:((option @ A) > $o)]: (((P3 @ (none @ A)) & (! [X2:A]: ((P3 @ ((some @ A) @ X2))))))))))).
% 3.26/1.73 thf(fact_155_combine__options__cases, axiom, (! [A:$tType,B:$tType,X:(option @ A),P:((option @ A) > ((option @ B) > $o)),Y:(option @ B)]: ((((X = (none @ A)) => ((P @ X) @ Y)) => (((Y = (none @ B)) => ((P @ X) @ Y)) => ((! [A6:A,B7:B]: (((X = ((some @ A) @ A6)) => ((Y = ((some @ B) @ B7)) => ((P @ X) @ Y))))) => ((P @ X) @ Y))))))).
% 3.26/1.73 thf(fact_156_ODEo_Oinduct, axiom, (! [P:(char > ((option @ trm) > $o)),A0:char,A1:(option @ trm)]: (((! [X3:char,Theta2:trm]: (((P @ X3) @ ((some @ trm) @ Theta2)))) => ((! [X3:char]: (((P @ X3) @ (none @ trm)))) => ((P @ A0) @ A1)))))).
% 3.26/1.73 thf(fact_157_undeft__equiv, axiom, (! [Theta:(option @ trm)]: (((Theta != (none @ trm)) = (? [T2:trm]: ((Theta = ((some @ trm) @ T2)))))))).
% 3.26/1.73 thf(fact_158_Timeso_Oinduct, axiom, (! [P:((option @ trm) > ((option @ trm) > $o)),A0:(option @ trm),A1:(option @ trm)]: (((! [Theta2:trm,Eta2:trm]: (((P @ ((some @ trm) @ Theta2)) @ ((some @ trm) @ Eta2)))) => ((! [X_1:(option @ trm)]: (((P @ (none @ trm)) @ X_1))) => ((! [V2:trm]: (((P @ ((some @ trm) @ V2)) @ (none @ trm)))) => ((P @ A0) @ A1))))))).
% 3.26/1.73 thf(fact_159_Assigno_Oinduct, axiom, (! [P:(variable > ((option @ trm) > $o)),A0:variable,A1:(option @ trm)]: (((! [X3:variable,Theta2:trm]: (((P @ X3) @ ((some @ trm) @ Theta2)))) => ((! [X3:variable]: (((P @ X3) @ (none @ trm)))) => ((P @ A0) @ A1)))))).
% 3.26/1.73 thf(fact_160_Differentialo_Ocases, axiom, (! [X:(option @ trm)]: (((! [Theta2:trm]: ((X != ((some @ trm) @ Theta2)))) => (X = (none @ trm)))))).
% 3.26/1.73 thf(fact_161_Differentialo_Oinduct, axiom, (! [P:((option @ trm) > $o),A0:(option @ trm)]: (((! [Theta2:trm]: ((P @ ((some @ trm) @ Theta2)))) => ((P @ (none @ trm)) => (P @ A0)))))).
% 3.26/1.73 thf(fact_162_option_Oexhaust__sel, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) => (Option = ((some @ A) @ ((the @ A) @ Option))))))).
% 3.26/1.73 thf(fact_163_option_Osplit__sel, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F22:(A > B),Option:(option @ A)]: (((P @ (((((case_option @ B) @ A) @ F1) @ F22) @ Option)) = (((Option = (none @ A)) => (P @ F1)) & ((Option = ((some @ A) @ ((the @ A) @ Option))) => (P @ (F22 @ ((the @ A) @ Option))))))))).
% 3.26/1.73 thf(fact_164_option_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F22:(A > B),Option:(option @ A)]: (((P @ (((((case_option @ B) @ A) @ F1) @ F22) @ Option)) = (~ ((((Option = (none @ A)) & (~ ((P @ F1)))) | ((Option = ((some @ A) @ ((the @ A) @ Option))) & (~ ((P @ (F22 @ ((the @ A) @ Option))))))))))))).
% 3.26/1.73 thf(fact_165_option_Osimps_I15_J, axiom, (! [A:$tType,X23:A]: ((((set_option @ A) @ ((some @ A) @ X23)) = (((insert @ A) @ X23) @ (bot_bot @ (set @ A))))))).
% 3.26/1.73 thf(fact_166_Vagree__repv__self, axiom, (! [Omega:(variable > real),X:variable,D:real]: (((((denotational_Vagree @ Omega) @ (((denotational_repv @ Omega) @ X) @ D)) @ (((insert @ variable) @ X) @ (bot_bot @ (set @ variable)))) = (D = (Omega @ X)))))).
% 3.26/1.73 thf(fact_167_elem__set, axiom, (! [A:$tType,X:A,Xo:(option @ A)]: (((((member @ A) @ X) @ ((set_option @ A) @ Xo)) = (Xo = ((some @ A) @ X)))))).
% 3.26/1.73 thf(fact_168_Vagree__and, axiom, (! [Nu:(variable > real),Nu2:(variable > real),V:(set @ variable),W:(set @ variable)]: ((((((denotational_Vagree @ Nu) @ Nu2) @ V) & (((denotational_Vagree @ Nu) @ Nu2) @ W)) = (((denotational_Vagree @ Nu) @ Nu2) @ (((sup_sup @ (set @ variable)) @ V) @ W)))))).
% 3.26/1.73 thf(fact_169_set__empty__eq, axiom, (! [A:$tType,Xo:(option @ A)]: (((((set_option @ A) @ Xo) = (bot_bot @ (set @ A))) = (Xo = (none @ A)))))).
% 3.26/1.73 thf(fact_170_similar__selectlike__mem, axiom, (! [Nu:(variable > real),Omega:(variable > real),V:(set @ variable),X6:(set @ (variable > real))]: (((((denotational_Vagree @ Nu) @ Omega) @ V) => ((((member @ (variable > real)) @ Nu) @ (((static_selectlike @ X6) @ Omega) @ V)) = (((member @ (variable > real)) @ Nu) @ X6)))))).
% 3.26/1.73 thf(fact_171_selectlike__Vagree, axiom, (! [Nu:(variable > real),Omega:(variable > real),V:(set @ variable),X6:(set @ (variable > real))]: (((((denotational_Vagree @ Nu) @ Omega) @ V) => ((((static_selectlike @ X6) @ Nu) @ V) = (((static_selectlike @ X6) @ Omega) @ V)))))).
% 3.26/1.73 thf(fact_172_Aterm__Some, axiom, ((some @ trm) = (some @ trm))).
% 3.26/1.73 thf(fact_173_option_Oset__intros, axiom, (! [A:$tType,X23:A]: ((((member @ A) @ X23) @ ((set_option @ A) @ ((some @ A) @ X23)))))).
% 3.26/1.73 thf(fact_174_option_Oset__cases, axiom, (! [A:$tType,E:A,A2:(option @ A)]: (((((member @ A) @ E) @ ((set_option @ A) @ A2)) => (A2 = ((some @ A) @ E)))))).
% 3.26/1.73 thf(fact_175_ospec, axiom, (! [A:$tType,A3:(option @ A),P:(A > $o),X:A]: (((! [X3:A]: (((((member @ A) @ X3) @ ((set_option @ A) @ A3)) => (P @ X3)))) => ((A3 = ((some @ A) @ X)) => (P @ X)))))).
% 3.26/1.73 thf(fact_176_Vagree__union, axiom, (! [Nu:(variable > real),Nu2:(variable > real),V:(set @ variable),W:(set @ variable)]: (((((denotational_Vagree @ Nu) @ Nu2) @ V) => ((((denotational_Vagree @ Nu) @ Nu2) @ W) => (((denotational_Vagree @ Nu) @ Nu2) @ (((sup_sup @ (set @ variable)) @ V) @ W))))))).
% 3.26/1.73 thf(fact_177_Vagree__def, axiom, (denotational_Vagree = (^ [Nu3:(variable > real),Nu4:(variable > real),V3:(set @ variable)]: ((! [I:variable]: (((((member @ variable) @ I) @ V3) => ((Nu3 @ I) = (Nu4 @ I))))))))).
% 3.26/1.73 thf(fact_178_Vagree__sym, axiom, (denotational_Vagree = (^ [Nu3:(variable > real),Nu4:(variable > real)]: (((denotational_Vagree @ Nu4) @ Nu3))))).
% 3.26/1.73 thf(fact_179_Vagree__refl, axiom, (! [Nu:(variable > real),V:(set @ variable)]: ((((denotational_Vagree @ Nu) @ Nu) @ V)))).
% 3.26/1.73 thf(fact_180_Vagree__sym__rel, axiom, (! [Nu:(variable > real),Nu2:(variable > real),V:(set @ variable)]: (((((denotational_Vagree @ Nu) @ Nu2) @ V) => (((denotational_Vagree @ Nu2) @ Nu) @ V))))).
% 3.26/1.73 thf(fact_181_Vagree__empty, axiom, (! [Nu:(variable > real),Nu2:(variable > real)]: ((((denotational_Vagree @ Nu) @ Nu2) @ (bot_bot @ (set @ variable)))))).
% 3.26/1.73 thf(fact_182_option_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F1:B,F22:(A > B)]: (((((((case_option @ B) @ A) @ F1) @ F22) @ (none @ A)) = F1)))).
% 3.26/1.73 thf(fact_183_option_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:B,F22:(A > B),X23:A]: (((((((case_option @ B) @ A) @ F1) @ F22) @ ((some @ A) @ X23)) = (F22 @ X23))))).
% 3.26/1.73 thf(fact_184_option_Osimps_I14_J, axiom, (! [A:$tType]: ((((set_option @ A) @ (none @ A)) = (bot_bot @ (set @ A)))))).
% 3.26/1.73 thf(fact_185_option_Oset__sel, axiom, (! [A:$tType,A2:(option @ A)]: (((A2 != (none @ A)) => (((member @ A) @ ((the @ A) @ A2)) @ ((set_option @ A) @ A2)))))).
% 3.26/1.73 thf(fact_186_option_Ocase__eq__if, axiom, (! [A:$tType,B:$tType]: ((((case_option @ B) @ A) = (^ [F12:B,F23:(A > B),Option3:(option @ A)]: (((((if @ B) @ (Option3 = (none @ A))) @ F12) @ (F23 @ ((the @ A) @ Option3))))))))).
% 3.26/1.73 thf(fact_187_solves__Vagree, axiom, (! [I2:denotational_interp,F3:(real > (variable > real)),X:char,Theta:trm,Zeta:real]: ((((((denota1778088425es_ODE @ I2) @ F3) @ X) @ Theta) => (((denotational_Vagree @ (F3 @ Zeta)) @ (F3 @ (zero_zero @ real))) @ ((uminus_uminus @ (set @ variable)) @ (((insert @ variable) @ (rVar @ X)) @ (((insert @ variable) @ (dVar @ X)) @ (bot_bot @ (set @ variable)))))))))).
% 3.26/1.73 thf(fact_188_Vagree__repv, axiom, (! [Omega:(variable > real),X:variable,D:real]: ((((denotational_Vagree @ Omega) @ (((denotational_repv @ Omega) @ X) @ D)) @ ((uminus_uminus @ (set @ variable)) @ (((insert @ variable) @ X) @ (bot_bot @ (set @ variable)))))))).
% 3.26/1.73 thf(fact_189_Timeso_Osimps_I3_J, axiom, (! [V4:trm]: ((((uSubst277968634Timeso @ ((some @ trm) @ V4)) @ (none @ trm)) = (none @ trm))))).
% 3.26/1.73 thf(fact_190_neg__equal__iff__equal, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B3:A]: (((((uminus_uminus @ A) @ A2) = ((uminus_uminus @ A) @ B3)) = (A2 = B3)))))))).
% 3.26/1.73 thf(fact_191_add_Oinverse__inverse, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A]: ((((uminus_uminus @ A) @ ((uminus_uminus @ A) @ A2)) = A2))))))).
% 3.26/1.73 thf(fact_192_compl__eq__compl__iff, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [X:A,Y:A]: (((((uminus_uminus @ A) @ X) = ((uminus_uminus @ A) @ Y)) = (X = Y)))))))).
% 3.26/1.73 thf(fact_193_double__compl, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [X:A]: ((((uminus_uminus @ A) @ ((uminus_uminus @ A) @ X)) = X))))))).
% 3.26/1.73 thf(fact_194_uminus__apply, axiom, (! [B:$tType,A:$tType]: (((uminus @ B) => ((uminus_uminus @ (A > B)) = (^ [A5:(A > B),X2:A]: (((uminus_uminus @ B) @ (A5 @ X2))))))))).
% 3.26/1.73 thf(fact_195_Compl__eq__Compl__iff, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A)]: (((((uminus_uminus @ (set @ A)) @ A3) = ((uminus_uminus @ (set @ A)) @ B2)) = (A3 = B2))))).
% 3.26/1.73 thf(fact_196_Compl__iff, axiom, (! [A:$tType,C2:A,A3:(set @ A)]: (((((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A3)) = (~ ((((member @ A) @ C2) @ A3))))))).
% 3.26/1.73 thf(fact_197_ComplI, axiom, (! [A:$tType,C2:A,A3:(set @ A)]: (((~ ((((member @ A) @ C2) @ A3))) => (((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A3)))))).
% 3.26/1.73 thf(fact_198_add_Oinverse__neutral, axiom, (! [A:$tType]: (((group_add @ A) => (((uminus_uminus @ A) @ (zero_zero @ A)) = (zero_zero @ A)))))).
% 3.26/1.73 thf(fact_199_neg__0__equal__iff__equal, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A]: ((((zero_zero @ A) = ((uminus_uminus @ A) @ A2)) = ((zero_zero @ A) = A2)))))))).
% 3.26/1.73 thf(fact_200_neg__equal__0__iff__equal, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A]: (((((uminus_uminus @ A) @ A2) = (zero_zero @ A)) = (A2 = (zero_zero @ A))))))))).
% 3.26/1.73 thf(fact_201_equal__neg__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((A2 = ((uminus_uminus @ A) @ A2)) = (A2 = (zero_zero @ A))))))))).
% 3.26/1.73 thf(fact_202_neg__equal__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((uminus_uminus @ A) @ A2) = A2) = (A2 = (zero_zero @ A))))))))).
% 3.26/1.73 thf(fact_203_Uvariation__Vagree, axiom, (! [Nu:(variable > real),Nu2:(variable > real),V:(set @ variable)]: (((((denota1419872369iation @ Nu) @ Nu2) @ ((uminus_uminus @ (set @ variable)) @ V)) = (((denotational_Vagree @ Nu) @ Nu2) @ V))))).
% 3.26/1.73 thf(fact_204_minus__equation__iff, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B3:A]: (((((uminus_uminus @ A) @ A2) = B3) = (((uminus_uminus @ A) @ B3) = A2)))))))).
% 3.26/1.73 thf(fact_205_equation__minus__iff, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B3:A]: (((A2 = ((uminus_uminus @ A) @ B3)) = (B3 = ((uminus_uminus @ A) @ A2))))))))).
% 3.26/1.73 thf(fact_206_fun__Compl__def, axiom, (! [B:$tType,A:$tType]: (((uminus @ B) => ((uminus_uminus @ (A > B)) = (^ [A5:(A > B),X2:A]: (((uminus_uminus @ B) @ (A5 @ X2))))))))).
% 3.26/1.73 thf(fact_207_double__complement, axiom, (! [A:$tType,A3:(set @ A)]: ((((uminus_uminus @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A3)) = A3)))).
% 3.26/1.73 thf(fact_208_ComplD, axiom, (! [A:$tType,C2:A,A3:(set @ A)]: (((((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A3)) => (~ ((((member @ A) @ C2) @ A3))))))).
% 3.26/1.73 thf(fact_209_Timeso_Osimps_I2_J, axiom, (! [Eta:(option @ trm)]: ((((uSubst277968634Timeso @ (none @ trm)) @ Eta) = (none @ trm))))).
% 3.26/1.73 thf(fact_210_Timeso__undef, axiom, (! [Theta:(option @ trm),Eta:(option @ trm)]: (((((uSubst277968634Timeso @ Theta) @ Eta) = (none @ trm)) = ((Theta = (none @ trm)) | (Eta = (none @ trm))))))).
% 3.26/1.73 thf(fact_211_selectlike__equal__cocond__corule, axiom, (! [Nu:(variable > real),V:(set @ variable),X6:(set @ (variable > real)),Y4:(set @ (variable > real))]: (((! [Mu2:(variable > real)]: (((((denota1419872369iation @ Mu2) @ Nu) @ V) => ((((member @ (variable > real)) @ Mu2) @ X6) = (((member @ (variable > real)) @ Mu2) @ Y4))))) => ((((static_selectlike @ X6) @ Nu) @ ((uminus_uminus @ (set @ variable)) @ V)) = (((static_selectlike @ Y4) @ Nu) @ ((uminus_uminus @ (set @ variable)) @ V))))))).
% 3.26/1.73 thf(fact_212_selectlike__equal__cocond__rule, axiom, (! [Nu:(variable > real),V:(set @ variable),X6:(set @ (variable > real)),Y4:(set @ (variable > real))]: (((! [Mu2:(variable > real)]: (((((denota1419872369iation @ Mu2) @ Nu) @ ((uminus_uminus @ (set @ variable)) @ V)) => ((((member @ (variable > real)) @ Mu2) @ X6) = (((member @ (variable > real)) @ Mu2) @ Y4))))) => ((((static_selectlike @ X6) @ Nu) @ V) = (((static_selectlike @ Y4) @ Nu) @ V)))))).
% 3.26/1.73 thf(fact_213_selectlike__equal__cocond, axiom, (! [X6:(set @ (variable > real)),Nu:(variable > real),V:(set @ variable),Y4:(set @ (variable > real))]: ((((((static_selectlike @ X6) @ Nu) @ ((uminus_uminus @ (set @ variable)) @ V)) = (((static_selectlike @ Y4) @ Nu) @ ((uminus_uminus @ (set @ variable)) @ V))) = (! [Mu3:(variable > real)]: (((((denota1419872369iation @ Mu3) @ Nu) @ V) => ((((member @ (variable > real)) @ Mu3) @ X6) = (((member @ (variable > real)) @ Mu3) @ Y4))))))))).
% 3.26/1.73 thf(fact_214_selectlike__equal__cond, axiom, (! [X6:(set @ (variable > real)),Nu:(variable > real),V:(set @ variable),Y4:(set @ (variable > real))]: ((((((static_selectlike @ X6) @ Nu) @ V) = (((static_selectlike @ Y4) @ Nu) @ V)) = (! [Mu3:(variable > real)]: (((((denota1419872369iation @ Mu3) @ Nu) @ ((uminus_uminus @ (set @ variable)) @ V)) => ((((member @ (variable > real)) @ Mu3) @ X6) = (((member @ (variable > real)) @ Mu3) @ Y4))))))))).
% 3.26/1.73 thf(fact_215_stateinterpol__insert, axiom, (! [V4:(variable > real),W2:(variable > real),S:(set @ variable),Z:variable]: ((((denotational_Vagree @ (((stateinterpol @ V4) @ W2) @ S)) @ (((stateinterpol @ V4) @ W2) @ (((insert @ variable) @ Z) @ S))) @ ((uminus_uminus @ (set @ variable)) @ (((insert @ variable) @ Z) @ (bot_bot @ (set @ variable)))))))).
% 3.26/1.73 thf(fact_216_Timeso_Oelims, axiom, (! [X:(option @ trm),Xa:(option @ trm),Y:(option @ trm)]: (((((uSubst277968634Timeso @ X) @ Xa) = Y) => ((! [Theta2:trm]: (((X = ((some @ trm) @ Theta2)) => (! [Eta2:trm]: (((Xa = ((some @ trm) @ Eta2)) => (Y != ((some @ trm) @ ((times @ Theta2) @ Eta2))))))))) => (((X = (none @ trm)) => (Y != (none @ trm))) => (~ (((? [V2:trm]: ((X = ((some @ trm) @ V2)))) => ((Xa = (none @ trm)) => (Y != (none @ trm)))))))))))).
% 3.26/1.73 thf(fact_217_trm_Oinject_I6_J, axiom, (! [X61:trm,X62:trm,Y61:trm,Y62:trm]: (((((times @ X61) @ X62) = ((times @ Y61) @ Y62)) = ((X61 = Y61) & (X62 = Y62)))))).
% 3.26/1.73 thf(fact_218_stateinterpol__left, axiom, (! [X:variable,S:(set @ variable),Nu:(variable > real),Omega:(variable > real)]: (((((member @ variable) @ X) @ S) => (((((stateinterpol @ Nu) @ Omega) @ S) @ X) = (Nu @ X)))))).
% 3.26/1.73 thf(fact_219_stateinterpol__right, axiom, (! [X:variable,S:(set @ variable),Nu:(variable > real),Omega:(variable > real)]: (((~ ((((member @ variable) @ X) @ S))) => (((((stateinterpol @ Nu) @ Omega) @ S) @ X) = (Omega @ X)))))).
% 3.26/1.73 thf(fact_220_selectlike__co__selectlike, axiom, (! [X6:(set @ (variable > real)),Nu:(variable > real),V:(set @ variable)]: (((((static_selectlike @ ((uminus_uminus @ (set @ (variable > real))) @ (((static_selectlike @ X6) @ Nu) @ V))) @ Nu) @ V) = (((static_selectlike @ ((uminus_uminus @ (set @ (variable > real))) @ X6)) @ Nu) @ V))))).
% 3.26/1.73 thf(fact_221_stateinterpol__empty, axiom, (! [Nu:(variable > real),Omega:(variable > real)]: (((((stateinterpol @ Nu) @ Omega) @ (bot_bot @ (set @ variable))) = Omega)))).
% 3.26/1.73 thf(fact_222_Vagree__stateinterpol, axiom, (! [Nu:(variable > real),Omega:(variable > real),S:(set @ variable)]: ((((denotational_Vagree @ (((stateinterpol @ Nu) @ Omega) @ S)) @ Nu) @ S)))).
% 3.26/1.73 thf(fact_223_stateinterpol__def, axiom, (stateinterpol = (^ [Nu3:(variable > real),Omega2:(variable > real),S2:(set @ variable),X2:variable]: (((((if @ real) @ (((member @ variable) @ X2) @ S2)) @ (Nu3 @ X2)) @ (Omega2 @ X2)))))).
% 3.26/1.73 thf(fact_224_usubstappt__times__conv, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm,Eta:trm]: ((((((uSubst95898992stappt @ Sigma) @ U) @ ((times @ Theta) @ Eta)) != (none @ trm)) => (((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (none @ trm)) & ((((uSubst95898992stappt @ Sigma) @ U) @ Eta) != (none @ trm))))))).
% 3.26/1.73 thf(fact_225_usubstappt_Osimps_I6_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm,Eta:trm]: (((((uSubst95898992stappt @ Sigma) @ U) @ ((times @ Theta) @ Eta)) = ((uSubst277968634Timeso @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta)) @ (((uSubst95898992stappt @ Sigma) @ U) @ Eta)))))).
% 3.26/1.73 thf(fact_226_Timeso_Osimps_I1_J, axiom, (! [Theta:trm,Eta:trm]: ((((uSubst277968634Timeso @ ((some @ trm) @ Theta)) @ ((some @ trm) @ Eta)) = ((some @ trm) @ ((times @ Theta) @ Eta)))))).
% 3.26/1.73 thf(fact_227_stateinterpol__diff, axiom, (! [Nu:(variable > real),Omega:(variable > real)]: (((((stateinterpol @ Nu) @ Omega) @ ((statediff @ Nu) @ Omega)) = Nu)))).
% 3.26/1.73 thf(fact_228_stateinterpol__FVT, axiom, (! [Z:variable,T3:trm,I2:denotational_interp,Omega:(variable > real),Omega3:(variable > real),S:(set @ variable)]: (((~ ((((member @ variable) @ Z) @ (static_FVT @ T3)))) => ((((denota1863255036rm_sem @ I2) @ T3) @ (((stateinterpol @ Omega) @ Omega3) @ S)) = (((denota1863255036rm_sem @ I2) @ T3) @ (((stateinterpol @ Omega) @ Omega3) @ (((insert @ variable) @ Z) @ S)))))))).
% 3.26/1.73 thf(fact_229_nostatediff, axiom, (! [X:variable,Nu:(variable > real),Omega:(variable > real)]: (((~ ((((member @ variable) @ X) @ ((statediff @ Nu) @ Omega)))) => ((Nu @ X) = (Omega @ X)))))).
% 3.26/1.73 thf(fact_230_coincidence__term, axiom, (! [Omega:(variable > real),Omega3:(variable > real),Theta:trm,I2:denotational_interp]: (((((denotational_Vagree @ Omega) @ Omega3) @ (static_FVT @ Theta)) => ((((denota1863255036rm_sem @ I2) @ Theta) @ Omega) = (((denota1863255036rm_sem @ I2) @ Theta) @ Omega3)))))).
% 3.26/1.73 thf(fact_231_coincidence__term__cor, axiom, (! [Omega:(variable > real),Omega3:(variable > real),U:(set @ variable),Theta:trm,I2:denotational_interp]: (((((denota1419872369iation @ Omega) @ Omega3) @ U) => (((((inf_inf @ (set @ variable)) @ (static_FVT @ Theta)) @ U) = (bot_bot @ (set @ variable))) => ((((denota1863255036rm_sem @ I2) @ Theta) @ Omega) = (((denota1863255036rm_sem @ I2) @ Theta) @ Omega3))))))).
% 3.26/1.73 thf(fact_232_Vagree__statediff, axiom, (! [Omega:(variable > real),Omega3:(variable > real),S:(set @ variable)]: (((((denotational_Vagree @ Omega) @ Omega3) @ S) => (((ord_less_eq @ (set @ variable)) @ ((statediff @ Omega) @ Omega3)) @ ((uminus_uminus @ (set @ variable)) @ S)))))).
% 3.26/1.73 thf(fact_233_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 3.26/1.73 thf(fact_234_subsetI, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A3) => (((member @ A) @ X3) @ B2)))) => (((ord_less_eq @ (set @ A)) @ A3) @ B2))))).
% 3.26/1.73 thf(fact_235_subset__antisym, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B2) => ((((ord_less_eq @ (set @ A)) @ B2) @ A3) => (A3 = B2)))))).
% 3.26/1.73 thf(fact_236_inf__apply, axiom, (! [B:$tType,A:$tType]: (((semilattice_inf @ B) => ((inf_inf @ (A > B)) = (^ [F:(A > B),G:(A > B),X2:A]: ((((inf_inf @ B) @ (F @ X2)) @ (G @ X2))))))))).
% 3.26/1.73 thf(fact_237_inf_Oidem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A]: (((((inf_inf @ A) @ A2) @ A2) = A2))))))).
% 3.26/1.73 thf(fact_238_inf__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X:A]: (((((inf_inf @ A) @ X) @ X) = X))))))).
% 3.26/1.73 thf(fact_239_inf_Oleft__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B3:A]: (((((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ A2) @ B3)) = (((inf_inf @ A) @ A2) @ B3)))))))).
% 3.26/1.73 thf(fact_240_inf__left__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X:A,Y:A]: (((((inf_inf @ A) @ X) @ (((inf_inf @ A) @ X) @ Y)) = (((inf_inf @ A) @ X) @ Y)))))))).
% 3.26/1.73 thf(fact_241_inf_Oright__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B3:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A2) @ B3)) @ B3) = (((inf_inf @ A) @ A2) @ B3)))))))).
% 3.26/1.73 thf(fact_242_inf__right__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X:A,Y:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X) @ Y)) @ Y) = (((inf_inf @ A) @ X) @ Y)))))))).
% 3.26/1.73 thf(fact_243_IntI, axiom, (! [A:$tType,C2:A,A3:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ A3) => ((((member @ A) @ C2) @ B2) => (((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A3) @ B2))))))).
% 3.26/1.73 thf(fact_244_Int__iff, axiom, (! [A:$tType,C2:A,A3:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A3) @ B2)) = ((((member @ A) @ C2) @ A3) & (((member @ A) @ C2) @ B2)))))).
% 3.26/1.73 thf(fact_245_le__zero__eq, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less_eq @ A) @ N) @ (zero_zero @ A)) = (N = (zero_zero @ A))))))))).
% 3.26/1.73 thf(fact_246_neg__le__iff__le, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B3:A,A2:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ B3)) @ ((uminus_uminus @ A) @ A2)) = (((ord_less_eq @ A) @ A2) @ B3)))))))).
% 3.26/1.73 thf(fact_247_compl__le__compl__iff, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ X)) @ ((uminus_uminus @ A) @ Y)) = (((ord_less_eq @ A) @ Y) @ X)))))))).
% 3.26/1.73 thf(fact_248_le__inf__iff, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ X) @ (((inf_inf @ A) @ Y) @ Z)) = ((((ord_less_eq @ A) @ X) @ Y) & (((ord_less_eq @ A) @ X) @ Z))))))))).
% 3.26/1.73 thf(fact_249_inf_Obounded__iff, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B3:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ (((inf_inf @ A) @ B3) @ C2)) = ((((ord_less_eq @ A) @ A2) @ B3) & (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 3.26/1.73 thf(fact_250_le__sup__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z) = ((((ord_less_eq @ A) @ X) @ Z) & (((ord_less_eq @ A) @ Y) @ Z))))))))).
% 3.26/1.73 thf(fact_251_sup_Obounded__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B3:A,C2:A,A2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ B3) @ C2)) @ A2) = ((((ord_less_eq @ A) @ B3) @ A2) & (((ord_less_eq @ A) @ C2) @ A2))))))))).
% 3.26/1.73 thf(fact_252_empty__subsetI, axiom, (! [A:$tType,A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A3)))).
% 3.26/1.73 thf(fact_253_subset__empty, axiom, (! [A:$tType,A3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ (bot_bot @ (set @ A))) = (A3 = (bot_bot @ (set @ A))))))).
% 3.26/1.73 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, (bounded_lattice @ $o)).
% 3.26/1.73 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A7:$tType]: ((bounded_lattice @ (set @ A7))))).
% 3.26/1.73 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A7:$tType,A8:$tType]: (((bounded_lattice @ A8) => (bounded_lattice @ (A7 > A8)))))).
% 3.26/1.73 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot, axiom, (! [A7:$tType,A8:$tType]: (((bounded_lattice @ A8) => (bounde1808546759up_bot @ (A7 > A8)))))).
% 3.26/1.73 thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A7:$tType,A8:$tType]: (((semilattice_sup @ A8) => (semilattice_sup @ (A7 > A8)))))).
% 3.26/1.73 thf(tcon_fun___Lattices_Osemilattice__inf, axiom, (! [A7:$tType,A8:$tType]: (((semilattice_inf @ A8) => (semilattice_inf @ (A7 > A8)))))).
% 3.26/1.73 thf(tcon_fun___Lattices_Oboolean__algebra, axiom, (! [A7:$tType,A8:$tType]: (((boolean_algebra @ A8) => (boolean_algebra @ (A7 > A8)))))).
% 3.26/1.73 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A8:$tType]: (((preorder @ A8) => (preorder @ (A7 > A8)))))).
% 3.26/1.73 thf(tcon_fun___Lattices_Olattice, axiom, (! [A7:$tType,A8:$tType]: (((lattice @ A8) => (lattice @ (A7 > A8)))))).
% 3.26/1.73 thf(tcon_fun___Orderings_Obot, axiom, (! [A7:$tType,A8:$tType]: (((bot @ A8) => (bot @ (A7 > A8)))))).
% 3.26/1.73 thf(tcon_fun___Groups_Ouminus, axiom, (! [A7:$tType,A8:$tType]: (((uminus @ A8) => (uminus @ (A7 > A8)))))).
% 3.26/1.73 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, (canoni770627133id_add @ nat)).
% 3.26/1.73 thf(tcon_Nat_Onat___Lattices_Osemilattice__sup_3, axiom, (semilattice_sup @ nat)).
% 3.26/1.73 thf(tcon_Nat_Onat___Lattices_Osemilattice__inf_4, axiom, (semilattice_inf @ nat)).
% 3.26/1.73 thf(tcon_Nat_Onat___Orderings_Opreorder_5, axiom, (preorder @ nat)).
% 3.26/1.73 thf(tcon_Nat_Onat___Lattices_Olattice_6, axiom, (lattice @ nat)).
% 3.26/1.73 thf(tcon_Nat_Onat___Orderings_Obot_7, axiom, (bot @ nat)).
% 3.26/1.73 thf(tcon_Nat_Onat___Groups_Ozero, axiom, (zero @ nat)).
% 3.26/1.73 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_8, axiom, (! [A7:$tType]: ((bounde1808546759up_bot @ (set @ A7))))).
% 3.26/1.73 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_9, axiom, (! [A7:$tType]: ((semilattice_sup @ (set @ A7))))).
% 3.26/1.73 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_10, axiom, (! [A7:$tType]: ((semilattice_inf @ (set @ A7))))).
% 3.26/1.73 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_11, axiom, (! [A7:$tType]: ((boolean_algebra @ (set @ A7))))).
% 3.26/1.73 thf(tcon_Set_Oset___Orderings_Opreorder_12, axiom, (! [A7:$tType]: ((preorder @ (set @ A7))))).
% 3.26/1.73 thf(tcon_Set_Oset___Lattices_Olattice_13, axiom, (! [A7:$tType]: ((lattice @ (set @ A7))))).
% 3.26/1.73 thf(tcon_Set_Oset___Orderings_Obot_14, axiom, (! [A7:$tType]: ((bot @ (set @ A7))))).
% 3.26/1.73 thf(tcon_Set_Oset___Groups_Ouminus_15, axiom, (! [A7:$tType]: ((uminus @ (set @ A7))))).
% 3.26/1.73 thf(tcon_Set_Oset___Groups_Ozero_16, axiom, (! [A7:$tType]: (((zero @ A7) => (zero @ (set @ A7)))))).
% 3.26/1.73 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_17, axiom, (bounde1808546759up_bot @ $o)).
% 3.26/1.73 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_18, axiom, (semilattice_sup @ $o)).
% 3.26/1.73 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_19, axiom, (semilattice_inf @ $o)).
% 3.26/1.73 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_20, axiom, (boolean_algebra @ $o)).
% 3.26/1.73 thf(tcon_HOL_Obool___Orderings_Opreorder_21, axiom, (preorder @ $o)).
% 3.26/1.73 thf(tcon_HOL_Obool___Lattices_Olattice_22, axiom, (lattice @ $o)).
% 3.26/1.73 thf(tcon_HOL_Obool___Orderings_Obot_23, axiom, (bot @ $o)).
% 3.26/1.73 thf(tcon_HOL_Obool___Groups_Ouminus_24, axiom, (uminus @ $o)).
% 3.26/1.73 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add, axiom, (linord219039673up_add @ real)).
% 3.26/1.73 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add, axiom, (ordered_ab_group_add @ real)).
% 3.26/1.73 thf(tcon_Real_Oreal___Lattices_Osemilattice__sup_25, axiom, (semilattice_sup @ real)).
% 3.26/1.73 thf(tcon_Real_Oreal___Lattices_Osemilattice__inf_26, axiom, (semilattice_inf @ real)).
% 3.26/1.73 thf(tcon_Real_Oreal___Orderings_Opreorder_27, axiom, (preorder @ real)).
% 3.26/1.73 thf(tcon_Real_Oreal___Lattices_Olattice_28, axiom, (lattice @ real)).
% 3.26/1.73 thf(tcon_Real_Oreal___Groups_Ogroup__add, axiom, (group_add @ real)).
% 3.26/1.73 thf(tcon_Real_Oreal___Groups_Ouminus_29, axiom, (uminus @ real)).
% 3.26/1.73 thf(tcon_Real_Oreal___Groups_Ozero_30, axiom, (zero @ real)).
% 3.26/1.73 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 3.26/1.73 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 3.26/1.73 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 3.26/1.73 thf(conj_0, conjecture, (((denota1419872369iation @ (f @ (zero_zero @ real))) @ omega) @ (((sup_sup @ (set @ variable)) @ (((insert @ variable) @ (rVar @ x)) @ (((insert @ variable) @ (dVar @ x)) @ (bot_bot @ (set @ variable))))) @ u))).
% 3.26/1.73 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.FtwHsTTgu9/DTF2DTF7422.p
% 3.26/1.73 ------------------------
% 3.26/1.78 ---- Cleaned THF ---
% 3.26/1.78 thf(ty_t_Denotational__Semantics_Ointerp,type,
% 3.26/1.78 denotational_interp: $tType ).
% 3.26/1.78
% 3.26/1.78 thf(ty_t_Product__Type_Oprod,type,
% 3.26/1.78 product_prod: $tType > $tType > $tType ).
% 3.26/1.78
% 3.26/1.78 thf(ty_t_Syntax_Ovariable,type,
% 3.26/1.78 variable: $tType ).
% 3.26/1.78
% 3.26/1.78 thf(ty_t_Option_Ooption,type,
% 3.26/1.78 option: $tType > $tType ).
% 3.26/1.78
% 3.26/1.78 thf(ty_t_Syntax_Ogame,type,
% 3.26/1.78 game: $tType ).
% 3.26/1.78
% 3.26/1.78 thf(ty_t_String_Ochar,type,
% 3.26/1.78 char: $tType ).
% 3.26/1.78
% 3.26/1.78 thf(ty_t_Syntax_Otrm,type,
% 3.26/1.78 trm: $tType ).
% 3.26/1.78
% 3.26/1.78 thf(ty_t_Syntax_Ofml,type,
% 3.26/1.78 fml: $tType ).
% 3.26/1.78
% 3.26/1.78 thf(ty_t_Real_Oreal,type,
% 3.26/1.78 real: $tType ).
% 3.26/1.78
% 3.26/1.78 thf(ty_t_Set_Oset,type,
% 3.26/1.78 set: $tType > $tType ).
% 3.26/1.78
% 3.26/1.78 thf(ty_t_Nat_Onat,type,
% 3.26/1.78 nat: $tType ).
% 3.26/1.78
% 3.26/1.78 thf(sy_cl_Lattices_Obounded__lattice,type,
% 3.26/1.78 bounded_lattice:
% 3.26/1.78 !>[A: $tType] : $o ).
% 3.26/1.78
% 3.26/1.78 thf(sy_cl_HOL_Otype,type,
% 3.26/1.78 type:
% 3.26/1.78 !>[A: $tType] : $o ).
% 3.26/1.78
% 3.26/1.78 thf(sy_cl_Groups_Ozero,type,
% 3.26/1.78 zero:
% 3.26/1.78 !>[A: $tType] : $o ).
% 3.26/1.78
% 3.26/1.78 thf(sy_cl_Groups_Ouminus,type,
% 3.26/1.78 uminus:
% 3.26/1.78 !>[A: $tType] : $o ).
% 3.26/1.78
% 3.26/1.78 thf(sy_cl_Orderings_Obot,type,
% 3.26/1.78 bot:
% 3.26/1.78 !>[A: $tType] : $o ).
% 3.26/1.78
% 3.26/1.78 thf(sy_cl_Groups_Ogroup__add,type,
% 3.26/1.78 group_add:
% 3.26/1.78 !>[A: $tType] : $o ).
% 3.26/1.78
% 3.26/1.78 thf(sy_cl_Lattices_Olattice,type,
% 3.26/1.78 lattice:
% 3.26/1.78 !>[A: $tType] : $o ).
% 3.26/1.78
% 3.26/1.78 thf(sy_cl_Orderings_Opreorder,type,
% 3.26/1.78 preorder:
% 3.26/1.78 !>[A: $tType] : $o ).
% 3.26/1.78
% 3.26/1.78 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 3.26/1.78 boolean_algebra:
% 3.26/1.78 !>[A: $tType] : $o ).
% 3.26/1.78
% 3.26/1.78 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 3.26/1.78 semilattice_inf:
% 3.26/1.78 !>[A: $tType] : $o ).
% 3.26/1.78
% 3.26/1.78 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 3.26/1.78 semilattice_sup:
% 3.26/1.78 !>[A: $tType] : $o ).
% 3.26/1.78
% 3.26/1.78 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 3.26/1.78 ordered_ab_group_add:
% 3.26/1.78 !>[A: $tType] : $o ).
% 3.26/1.78
% 3.26/1.78 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 3.26/1.78 linord219039673up_add:
% 3.26/1.78 !>[A: $tType] : $o ).
% 3.26/1.78
% 3.26/1.78 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 3.26/1.78 bounde1808546759up_bot:
% 3.26/1.78 !>[A: $tType] : $o ).
% 3.26/1.78
% 3.26/1.78 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 3.26/1.78 canoni770627133id_add:
% 3.26/1.78 !>[A: $tType] : $o ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Coincidence_Ostatediff,type,
% 3.26/1.78 statediff: ( variable > real ) > ( variable > real ) > ( set @ variable ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Coincidence_Ostateinterpol,type,
% 3.26/1.78 stateinterpol: ( variable > real ) > ( variable > real ) > ( set @ variable ) > variable > real ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Denotational__Semantics_OUvariation,type,
% 3.26/1.78 denota1419872369iation: ( variable > real ) > ( variable > real ) > ( set @ variable ) > $o ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Denotational__Semantics_OVagree,type,
% 3.26/1.78 denotational_Vagree: ( variable > real ) > ( variable > real ) > ( set @ variable ) > $o ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Denotational__Semantics_Orepv,type,
% 3.26/1.78 denotational_repv: ( variable > real ) > variable > real > variable > real ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Denotational__Semantics_Osolves__ODE,type,
% 3.26/1.78 denota1778088425es_ODE: denotational_interp > ( real > variable > real ) > char > trm > $o ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Denotational__Semantics_Oterm__sem,type,
% 3.26/1.78 denota1863255036rm_sem: denotational_interp > trm > ( variable > real ) > real ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 3.26/1.78 uminus_uminus:
% 3.26/1.78 !>[A: $tType] : ( A > A ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 3.26/1.78 zero_zero:
% 3.26/1.78 !>[A: $tType] : A ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_If,type,
% 3.26/1.78 if:
% 3.26/1.78 !>[A: $tType] : ( $o > A > A > A ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 3.26/1.78 inf_inf:
% 3.26/1.78 !>[A: $tType] : ( A > A > A ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Lattices_Osup__class_Osup,type,
% 3.26/1.78 sup_sup:
% 3.26/1.78 !>[A: $tType] : ( A > A > A ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Nat_Osize__class_Osize,type,
% 3.26/1.78 size_size:
% 3.26/1.78 !>[A: $tType] : ( A > nat ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Option_Ooption_ONone,type,
% 3.26/1.78 none:
% 3.26/1.78 !>[A: $tType] : ( option @ A ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Option_Ooption_OSome,type,
% 3.26/1.78 some:
% 3.26/1.78 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Option_Ooption_Ocase__option,type,
% 3.26/1.78 case_option:
% 3.26/1.78 !>[B: $tType,A: $tType] : ( B > ( A > B ) > ( option @ A ) > B ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Option_Ooption_Oset__option,type,
% 3.26/1.78 set_option:
% 3.26/1.78 !>[A: $tType] : ( ( option @ A ) > ( set @ A ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Option_Ooption_Othe,type,
% 3.26/1.78 the:
% 3.26/1.78 !>[A: $tType] : ( ( option @ A ) > A ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Option_Othese,type,
% 3.26/1.78 these:
% 3.26/1.78 !>[A: $tType] : ( ( set @ ( option @ A ) ) > ( set @ A ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Orderings_Obot__class_Obot,type,
% 3.26/1.78 bot_bot:
% 3.26/1.78 !>[A: $tType] : A ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 3.26/1.78 ord_less_eq:
% 3.26/1.78 !>[A: $tType] : ( A > A > $o ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Set_OCollect,type,
% 3.26/1.78 collect:
% 3.26/1.78 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Set_Oinsert,type,
% 3.26/1.78 insert:
% 3.26/1.78 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Set_Ois__empty,type,
% 3.26/1.78 is_empty:
% 3.26/1.78 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Set_Ois__singleton,type,
% 3.26/1.78 is_singleton:
% 3.26/1.78 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Set_Othe__elem,type,
% 3.26/1.78 the_elem:
% 3.26/1.78 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Static__Semantics_OFVT,type,
% 3.26/1.78 static_FVT: trm > ( set @ variable ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Static__Semantics_Oselectlike,type,
% 3.26/1.78 static_selectlike: ( set @ ( variable > real ) ) > ( variable > real ) > ( set @ variable ) > ( set @ ( variable > real ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Syntax_Otrm_OTimes,type,
% 3.26/1.78 times: trm > trm > trm ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Syntax_Ovariable_ODVar,type,
% 3.26/1.78 dVar: char > variable ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Syntax_Ovariable_ORVar,type,
% 3.26/1.78 rVar: char > variable ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Syntax_Ovariable_Orec__variable,type,
% 3.26/1.78 rec_variable:
% 3.26/1.78 !>[A: $tType] : ( ( char > A ) > ( char > A ) > variable > A ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_Syntax_Ovariable_Osize__variable,type,
% 3.26/1.78 size_variable: variable > nat ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTimeso,type,
% 3.26/1.78 uSubst277968634Timeso: ( option @ trm ) > ( option @ trm ) > ( option @ trm ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Oadjoint,type,
% 3.26/1.78 uSubst2091380086djoint: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > denotational_interp > ( variable > real ) > denotational_interp ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappt,type,
% 3.26/1.78 uSubst95898992stappt: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > trm > ( option @ trm ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_c_member,type,
% 3.26/1.78 member:
% 3.26/1.78 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_v_F,type,
% 3.26/1.78 f: real > variable > real ).
% 3.26/1.78
% 3.26/1.78 thf(sy_v_I,type,
% 3.26/1.78 i: denotational_interp ).
% 3.26/1.78
% 3.26/1.78 thf(sy_v_U,type,
% 3.26/1.78 u: set @ variable ).
% 3.26/1.78
% 3.26/1.78 thf(sy_v__092_060omega_062,type,
% 3.26/1.78 omega: variable > real ).
% 3.26/1.78
% 3.26/1.78 thf(sy_v__092_060sigma_062,type,
% 3.26/1.78 sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(sy_v__092_060theta_062,type,
% 3.26/1.78 theta: trm ).
% 3.26/1.78
% 3.26/1.78 thf(sy_v_rr____,type,
% 3.26/1.78 rr: trm > denotational_interp > trm > denotational_interp > char > ( real > variable > real ) > variable > real ).
% 3.26/1.78
% 3.26/1.78 thf(sy_v_x,type,
% 3.26/1.78 x: char ).
% 3.26/1.78
% 3.26/1.78 thf(fact_0_uv,axiom,
% 3.26/1.78 denota1419872369iation @ ( f @ ( zero_zero @ real ) ) @ omega @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_1_Uvariation__empty,axiom,
% 3.26/1.78 ! [Nu: variable > real,Nu2: variable > real] :
% 3.26/1.78 ( ( denota1419872369iation @ Nu @ Nu2 @ ( bot_bot @ ( set @ variable ) ) )
% 3.26/1.78 = ( Nu = Nu2 ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_2_Un__insert__left,axiom,
% 3.26/1.78 ! [A: $tType,A2: A,B2: set @ A,C: set @ A] :
% 3.26/1.78 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A2 @ B2 ) @ C )
% 3.26/1.78 = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C ) ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_3_Un__insert__right,axiom,
% 3.26/1.78 ! [A: $tType,A3: set @ A,A2: A,B2: set @ A] :
% 3.26/1.78 ( ( sup_sup @ ( set @ A ) @ A3 @ ( insert @ A @ A2 @ B2 ) )
% 3.26/1.78 = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_4_Un__empty,axiom,
% 3.26/1.78 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 3.26/1.78 ( ( ( sup_sup @ ( set @ A ) @ A3 @ B2 )
% 3.26/1.78 = ( bot_bot @ ( set @ A ) ) )
% 3.26/1.78 = ( ( A3
% 3.26/1.78 = ( bot_bot @ ( set @ A ) ) )
% 3.26/1.78 & ( B2
% 3.26/1.78 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_5_sup__bot__left,axiom,
% 3.26/1.78 ! [A: $tType] :
% 3.26/1.78 ( ( bounde1808546759up_bot @ A )
% 3.26/1.78 => ! [X: A] :
% 3.26/1.78 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 3.26/1.78 = X ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_6_sup__bot__right,axiom,
% 3.26/1.78 ! [A: $tType] :
% 3.26/1.78 ( ( bounde1808546759up_bot @ A )
% 3.26/1.78 => ! [X: A] :
% 3.26/1.78 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 3.26/1.78 = X ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_7_bot__eq__sup__iff,axiom,
% 3.26/1.78 ! [A: $tType] :
% 3.26/1.78 ( ( bounde1808546759up_bot @ A )
% 3.26/1.78 => ! [X: A,Y: A] :
% 3.26/1.78 ( ( ( bot_bot @ A )
% 3.26/1.78 = ( sup_sup @ A @ X @ Y ) )
% 3.26/1.78 = ( ( X
% 3.26/1.78 = ( bot_bot @ A ) )
% 3.26/1.78 & ( Y
% 3.26/1.78 = ( bot_bot @ A ) ) ) ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_8_sup__eq__bot__iff,axiom,
% 3.26/1.78 ! [A: $tType] :
% 3.26/1.78 ( ( bounde1808546759up_bot @ A )
% 3.26/1.78 => ! [X: A,Y: A] :
% 3.26/1.78 ( ( ( sup_sup @ A @ X @ Y )
% 3.26/1.78 = ( bot_bot @ A ) )
% 3.26/1.78 = ( ( X
% 3.26/1.78 = ( bot_bot @ A ) )
% 3.26/1.78 & ( Y
% 3.26/1.78 = ( bot_bot @ A ) ) ) ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_9_sup__bot_Oeq__neutr__iff,axiom,
% 3.26/1.78 ! [A: $tType] :
% 3.26/1.78 ( ( bounde1808546759up_bot @ A )
% 3.26/1.78 => ! [A2: A,B3: A] :
% 3.26/1.78 ( ( ( sup_sup @ A @ A2 @ B3 )
% 3.26/1.78 = ( bot_bot @ A ) )
% 3.26/1.78 = ( ( A2
% 3.26/1.78 = ( bot_bot @ A ) )
% 3.26/1.78 & ( B3
% 3.26/1.78 = ( bot_bot @ A ) ) ) ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_10_sup__bot_Oleft__neutral,axiom,
% 3.26/1.78 ! [A: $tType] :
% 3.26/1.78 ( ( bounde1808546759up_bot @ A )
% 3.26/1.78 => ! [A2: A] :
% 3.26/1.78 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A2 )
% 3.26/1.78 = A2 ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_11_sup__bot_Oneutr__eq__iff,axiom,
% 3.26/1.78 ! [A: $tType] :
% 3.26/1.78 ( ( bounde1808546759up_bot @ A )
% 3.26/1.78 => ! [A2: A,B3: A] :
% 3.26/1.78 ( ( ( bot_bot @ A )
% 3.26/1.78 = ( sup_sup @ A @ A2 @ B3 ) )
% 3.26/1.78 = ( ( A2
% 3.26/1.78 = ( bot_bot @ A ) )
% 3.26/1.78 & ( B3
% 3.26/1.78 = ( bot_bot @ A ) ) ) ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_12_sup__bot_Oright__neutral,axiom,
% 3.26/1.78 ! [A: $tType] :
% 3.26/1.78 ( ( bounde1808546759up_bot @ A )
% 3.26/1.78 => ! [A2: A] :
% 3.26/1.78 ( ( sup_sup @ A @ A2 @ ( bot_bot @ A ) )
% 3.26/1.78 = A2 ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_13_empty__Collect__eq,axiom,
% 3.26/1.78 ! [A: $tType,P: A > $o] :
% 3.26/1.78 ( ( ( bot_bot @ ( set @ A ) )
% 3.26/1.78 = ( collect @ A @ P ) )
% 3.26/1.78 = ( ! [X2: A] :
% 3.26/1.78 ~ ( P @ X2 ) ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_14_Collect__empty__eq,axiom,
% 3.26/1.78 ! [A: $tType,P: A > $o] :
% 3.26/1.78 ( ( ( collect @ A @ P )
% 3.26/1.78 = ( bot_bot @ ( set @ A ) ) )
% 3.26/1.78 = ( ! [X2: A] :
% 3.26/1.78 ~ ( P @ X2 ) ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_15_all__not__in__conv,axiom,
% 3.26/1.78 ! [A: $tType,A3: set @ A] :
% 3.26/1.78 ( ( ! [X2: A] :
% 3.26/1.78 ~ ( member @ A @ X2 @ A3 ) )
% 3.26/1.78 = ( A3
% 3.26/1.78 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_16_empty__iff,axiom,
% 3.26/1.78 ! [A: $tType,C2: A] :
% 3.26/1.78 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_17_insert__absorb2,axiom,
% 3.26/1.78 ! [A: $tType,X: A,A3: set @ A] :
% 3.26/1.78 ( ( insert @ A @ X @ ( insert @ A @ X @ A3 ) )
% 3.26/1.78 = ( insert @ A @ X @ A3 ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_18_insert__iff,axiom,
% 3.26/1.78 ! [A: $tType,A2: A,B3: A,A3: set @ A] :
% 3.26/1.78 ( ( member @ A @ A2 @ ( insert @ A @ B3 @ A3 ) )
% 3.26/1.78 = ( ( A2 = B3 )
% 3.26/1.78 | ( member @ A @ A2 @ A3 ) ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_19_insertCI,axiom,
% 3.26/1.78 ! [A: $tType,A2: A,B2: set @ A,B3: A] :
% 3.26/1.78 ( ( ~ ( member @ A @ A2 @ B2 )
% 3.26/1.78 => ( A2 = B3 ) )
% 3.26/1.78 => ( member @ A @ A2 @ ( insert @ A @ B3 @ B2 ) ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_20_sup_Oright__idem,axiom,
% 3.26/1.78 ! [A: $tType] :
% 3.26/1.78 ( ( semilattice_sup @ A )
% 3.26/1.78 => ! [A2: A,B3: A] :
% 3.26/1.78 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B3 ) @ B3 )
% 3.26/1.78 = ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_21_sup__left__idem,axiom,
% 3.26/1.78 ! [A: $tType] :
% 3.26/1.78 ( ( semilattice_sup @ A )
% 3.26/1.78 => ! [X: A,Y: A] :
% 3.26/1.78 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 3.26/1.78 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_22_sup_Oleft__idem,axiom,
% 3.26/1.78 ! [A: $tType] :
% 3.26/1.78 ( ( semilattice_sup @ A )
% 3.26/1.78 => ! [A2: A,B3: A] :
% 3.26/1.78 ( ( sup_sup @ A @ A2 @ ( sup_sup @ A @ A2 @ B3 ) )
% 3.26/1.78 = ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_23_sup__idem,axiom,
% 3.26/1.78 ! [A: $tType] :
% 3.26/1.78 ( ( semilattice_sup @ A )
% 3.26/1.78 => ! [X: A] :
% 3.26/1.78 ( ( sup_sup @ A @ X @ X )
% 3.26/1.78 = X ) ) ).
% 3.26/1.78
% 3.26/1.78 thf(fact_24_sup_Oidem,axiom,
% 3.26/1.78 ! [A: $tType] :
% 3.26/1.78 ( ( semilattice_sup @ A )
% 3.26/1.78 => ! [A2: A] :
% 3.26/1.79 ( ( sup_sup @ A @ A2 @ A2 )
% 3.26/1.79 = A2 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_25_sup__apply,axiom,
% 3.26/1.79 ! [B: $tType,A: $tType] :
% 3.26/1.79 ( ( semilattice_sup @ B )
% 3.26/1.79 => ( ( sup_sup @ ( A > B ) )
% 3.26/1.79 = ( ^ [F: A > B,G: A > B,X2: A] : ( sup_sup @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_26_UnCI,axiom,
% 3.26/1.79 ! [A: $tType,C2: A,B2: set @ A,A3: set @ A] :
% 3.26/1.79 ( ( ~ ( member @ A @ C2 @ B2 )
% 3.26/1.79 => ( member @ A @ C2 @ A3 ) )
% 3.26/1.79 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_27_singletonI,axiom,
% 3.26/1.79 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_28_bot__set__def,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( bot_bot @ ( set @ A ) )
% 3.26/1.79 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_29_ex__in__conv,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A] :
% 3.26/1.79 ( ( ? [X2: A] : ( member @ A @ X2 @ A3 ) )
% 3.26/1.79 = ( A3
% 3.26/1.79 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_30_equals0I,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A] :
% 3.26/1.79 ( ! [Y2: A] :
% 3.26/1.79 ~ ( member @ A @ Y2 @ A3 )
% 3.26/1.79 => ( A3
% 3.26/1.79 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_31_equals0D,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A,A2: A] :
% 3.26/1.79 ( ( A3
% 3.26/1.79 = ( bot_bot @ ( set @ A ) ) )
% 3.26/1.79 => ~ ( member @ A @ A2 @ A3 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_32_emptyE,axiom,
% 3.26/1.79 ! [A: $tType,A2: A] :
% 3.26/1.79 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_33_mk__disjoint__insert,axiom,
% 3.26/1.79 ! [A: $tType,A2: A,A3: set @ A] :
% 3.26/1.79 ( ( member @ A @ A2 @ A3 )
% 3.26/1.79 => ? [B4: set @ A] :
% 3.26/1.79 ( ( A3
% 3.26/1.79 = ( insert @ A @ A2 @ B4 ) )
% 3.26/1.79 & ~ ( member @ A @ A2 @ B4 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_34_insert__commute,axiom,
% 3.26/1.79 ! [A: $tType,X: A,Y: A,A3: set @ A] :
% 3.26/1.79 ( ( insert @ A @ X @ ( insert @ A @ Y @ A3 ) )
% 3.26/1.79 = ( insert @ A @ Y @ ( insert @ A @ X @ A3 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_35_insert__eq__iff,axiom,
% 3.26/1.79 ! [A: $tType,A2: A,A3: set @ A,B3: A,B2: set @ A] :
% 3.26/1.79 ( ~ ( member @ A @ A2 @ A3 )
% 3.26/1.79 => ( ~ ( member @ A @ B3 @ B2 )
% 3.26/1.79 => ( ( ( insert @ A @ A2 @ A3 )
% 3.26/1.79 = ( insert @ A @ B3 @ B2 ) )
% 3.26/1.79 = ( ( ( A2 = B3 )
% 3.26/1.79 => ( A3 = B2 ) )
% 3.26/1.79 & ( ( A2 != B3 )
% 3.26/1.79 => ? [C3: set @ A] :
% 3.26/1.79 ( ( A3
% 3.26/1.79 = ( insert @ A @ B3 @ C3 ) )
% 3.26/1.79 & ~ ( member @ A @ B3 @ C3 )
% 3.26/1.79 & ( B2
% 3.26/1.79 = ( insert @ A @ A2 @ C3 ) )
% 3.26/1.79 & ~ ( member @ A @ A2 @ C3 ) ) ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_36_insert__absorb,axiom,
% 3.26/1.79 ! [A: $tType,A2: A,A3: set @ A] :
% 3.26/1.79 ( ( member @ A @ A2 @ A3 )
% 3.26/1.79 => ( ( insert @ A @ A2 @ A3 )
% 3.26/1.79 = A3 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_37_insert__ident,axiom,
% 3.26/1.79 ! [A: $tType,X: A,A3: set @ A,B2: set @ A] :
% 3.26/1.79 ( ~ ( member @ A @ X @ A3 )
% 3.26/1.79 => ( ~ ( member @ A @ X @ B2 )
% 3.26/1.79 => ( ( ( insert @ A @ X @ A3 )
% 3.26/1.79 = ( insert @ A @ X @ B2 ) )
% 3.26/1.79 = ( A3 = B2 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_38_Set_Oset__insert,axiom,
% 3.26/1.79 ! [A: $tType,X: A,A3: set @ A] :
% 3.26/1.79 ( ( member @ A @ X @ A3 )
% 3.26/1.79 => ~ ! [B4: set @ A] :
% 3.26/1.79 ( ( A3
% 3.26/1.79 = ( insert @ A @ X @ B4 ) )
% 3.26/1.79 => ( member @ A @ X @ B4 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_39_insertI2,axiom,
% 3.26/1.79 ! [A: $tType,A2: A,B2: set @ A,B3: A] :
% 3.26/1.79 ( ( member @ A @ A2 @ B2 )
% 3.26/1.79 => ( member @ A @ A2 @ ( insert @ A @ B3 @ B2 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_40_insertI1,axiom,
% 3.26/1.79 ! [A: $tType,A2: A,B2: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B2 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_41_insertE,axiom,
% 3.26/1.79 ! [A: $tType,A2: A,B3: A,A3: set @ A] :
% 3.26/1.79 ( ( member @ A @ A2 @ ( insert @ A @ B3 @ A3 ) )
% 3.26/1.79 => ( ( A2 != B3 )
% 3.26/1.79 => ( member @ A @ A2 @ A3 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_42_sup__left__commute,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( semilattice_sup @ A )
% 3.26/1.79 => ! [X: A,Y: A,Z: A] :
% 3.26/1.79 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 3.26/1.79 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_43_sup_Oleft__commute,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( semilattice_sup @ A )
% 3.26/1.79 => ! [B3: A,A2: A,C2: A] :
% 3.26/1.79 ( ( sup_sup @ A @ B3 @ ( sup_sup @ A @ A2 @ C2 ) )
% 3.26/1.79 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B3 @ C2 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_44_sup__commute,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( semilattice_sup @ A )
% 3.26/1.79 => ( ( sup_sup @ A )
% 3.26/1.79 = ( ^ [X2: A,Y3: A] : ( sup_sup @ A @ Y3 @ X2 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_45_mem__Collect__eq,axiom,
% 3.26/1.79 ! [A: $tType,A2: A,P: A > $o] :
% 3.26/1.79 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 3.26/1.79 = ( P @ A2 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_46_Collect__mem__eq,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A] :
% 3.26/1.79 ( ( collect @ A
% 3.26/1.79 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 3.26/1.79 = A3 ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_47_Collect__cong,axiom,
% 3.26/1.79 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.26/1.79 ( ! [X3: A] :
% 3.26/1.79 ( ( P @ X3 )
% 3.26/1.79 = ( Q @ X3 ) )
% 3.26/1.79 => ( ( collect @ A @ P )
% 3.26/1.79 = ( collect @ A @ Q ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_48_ext,axiom,
% 3.26/1.79 ! [B: $tType,A: $tType,F2: A > B,G2: A > B] :
% 3.26/1.79 ( ! [X3: A] :
% 3.26/1.79 ( ( F2 @ X3 )
% 3.26/1.79 = ( G2 @ X3 ) )
% 3.26/1.79 => ( F2 = G2 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_49_sup_Ocommute,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( semilattice_sup @ A )
% 3.26/1.79 => ( ( sup_sup @ A )
% 3.26/1.79 = ( ^ [A4: A,B5: A] : ( sup_sup @ A @ B5 @ A4 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_50_sup__assoc,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( semilattice_sup @ A )
% 3.26/1.79 => ! [X: A,Y: A,Z: A] :
% 3.26/1.79 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 3.26/1.79 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_51_sup_Oassoc,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( semilattice_sup @ A )
% 3.26/1.79 => ! [A2: A,B3: A,C2: A] :
% 3.26/1.79 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B3 ) @ C2 )
% 3.26/1.79 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B3 @ C2 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_52_boolean__algebra__cancel_Osup2,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( semilattice_sup @ A )
% 3.26/1.79 => ! [B2: A,K: A,B3: A,A2: A] :
% 3.26/1.79 ( ( B2
% 3.26/1.79 = ( sup_sup @ A @ K @ B3 ) )
% 3.26/1.79 => ( ( sup_sup @ A @ A2 @ B2 )
% 3.26/1.79 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_53_boolean__algebra__cancel_Osup1,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( semilattice_sup @ A )
% 3.26/1.79 => ! [A3: A,K: A,A2: A,B3: A] :
% 3.26/1.79 ( ( A3
% 3.26/1.79 = ( sup_sup @ A @ K @ A2 ) )
% 3.26/1.79 => ( ( sup_sup @ A @ A3 @ B3 )
% 3.26/1.79 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_54_sup__fun__def,axiom,
% 3.26/1.79 ! [B: $tType,A: $tType] :
% 3.26/1.79 ( ( semilattice_sup @ B )
% 3.26/1.79 => ( ( sup_sup @ ( A > B ) )
% 3.26/1.79 = ( ^ [F: A > B,G: A > B,X2: A] : ( sup_sup @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_55_inf__sup__aci_I5_J,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( lattice @ A )
% 3.26/1.79 => ( ( sup_sup @ A )
% 3.26/1.79 = ( ^ [X2: A,Y3: A] : ( sup_sup @ A @ Y3 @ X2 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_56_inf__sup__aci_I6_J,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( lattice @ A )
% 3.26/1.79 => ! [X: A,Y: A,Z: A] :
% 3.26/1.79 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 3.26/1.79 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_57_inf__sup__aci_I7_J,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( lattice @ A )
% 3.26/1.79 => ! [X: A,Y: A,Z: A] :
% 3.26/1.79 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 3.26/1.79 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_58_inf__sup__aci_I8_J,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( lattice @ A )
% 3.26/1.79 => ! [X: A,Y: A] :
% 3.26/1.79 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 3.26/1.79 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_59_Un__left__commute,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A,B2: set @ A,C: set @ A] :
% 3.26/1.79 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B2 @ C ) )
% 3.26/1.79 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A3 @ C ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_60_Un__left__absorb,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 3.26/1.79 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 3.26/1.79 = ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_61_Un__commute,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( sup_sup @ ( set @ A ) )
% 3.26/1.79 = ( ^ [A5: set @ A,B6: set @ A] : ( sup_sup @ ( set @ A ) @ B6 @ A5 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_62_Un__absorb,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A] :
% 3.26/1.79 ( ( sup_sup @ ( set @ A ) @ A3 @ A3 )
% 3.26/1.79 = A3 ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_63_Un__assoc,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A,B2: set @ A,C: set @ A] :
% 3.26/1.79 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) @ C )
% 3.26/1.79 = ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B2 @ C ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_64_ball__Un,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A,B2: set @ A,P: A > $o] :
% 3.26/1.79 ( ( ! [X2: A] :
% 3.26/1.79 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 3.26/1.79 => ( P @ X2 ) ) )
% 3.26/1.79 = ( ! [X2: A] :
% 3.26/1.79 ( ( member @ A @ X2 @ A3 )
% 3.26/1.79 => ( P @ X2 ) )
% 3.26/1.79 & ! [X2: A] :
% 3.26/1.79 ( ( member @ A @ X2 @ B2 )
% 3.26/1.79 => ( P @ X2 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_65_bex__Un,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A,B2: set @ A,P: A > $o] :
% 3.26/1.79 ( ( ? [X2: A] :
% 3.26/1.79 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 3.26/1.79 & ( P @ X2 ) ) )
% 3.26/1.79 = ( ? [X2: A] :
% 3.26/1.79 ( ( member @ A @ X2 @ A3 )
% 3.26/1.79 & ( P @ X2 ) )
% 3.26/1.79 | ? [X2: A] :
% 3.26/1.79 ( ( member @ A @ X2 @ B2 )
% 3.26/1.79 & ( P @ X2 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_66_UnI2,axiom,
% 3.26/1.79 ! [A: $tType,C2: A,B2: set @ A,A3: set @ A] :
% 3.26/1.79 ( ( member @ A @ C2 @ B2 )
% 3.26/1.79 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_67_UnI1,axiom,
% 3.26/1.79 ! [A: $tType,C2: A,A3: set @ A,B2: set @ A] :
% 3.26/1.79 ( ( member @ A @ C2 @ A3 )
% 3.26/1.79 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_68_UnE,axiom,
% 3.26/1.79 ! [A: $tType,C2: A,A3: set @ A,B2: set @ A] :
% 3.26/1.79 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 3.26/1.79 => ( ~ ( member @ A @ C2 @ A3 )
% 3.26/1.79 => ( member @ A @ C2 @ B2 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_69_Uvariation__sym__rel,axiom,
% 3.26/1.79 ! [Omega: variable > real,Nu: variable > real,U: set @ variable] :
% 3.26/1.79 ( ( denota1419872369iation @ Omega @ Nu @ U )
% 3.26/1.79 => ( denota1419872369iation @ Nu @ Omega @ U ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_70_Uvariation__refl,axiom,
% 3.26/1.79 ! [Nu: variable > real,V: set @ variable] : ( denota1419872369iation @ Nu @ Nu @ V ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_71_Uvariation__sym,axiom,
% 3.26/1.79 ( denota1419872369iation
% 3.26/1.79 = ( ^ [Omega2: variable > real,Nu3: variable > real] : ( denota1419872369iation @ Nu3 @ Omega2 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_72_Uvariation__def,axiom,
% 3.26/1.79 ( denota1419872369iation
% 3.26/1.79 = ( ^ [Nu3: variable > real,Nu4: variable > real,U2: set @ variable] :
% 3.26/1.79 ! [I: variable] :
% 3.26/1.79 ( ~ ( member @ variable @ I @ U2 )
% 3.26/1.79 => ( ( Nu3 @ I )
% 3.26/1.79 = ( Nu4 @ I ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_73_singleton__inject,axiom,
% 3.26/1.79 ! [A: $tType,A2: A,B3: A] :
% 3.26/1.79 ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 3.26/1.79 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.79 => ( A2 = B3 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_74_insert__not__empty,axiom,
% 3.26/1.79 ! [A: $tType,A2: A,A3: set @ A] :
% 3.26/1.79 ( ( insert @ A @ A2 @ A3 )
% 3.26/1.79 != ( bot_bot @ ( set @ A ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_75_doubleton__eq__iff,axiom,
% 3.26/1.79 ! [A: $tType,A2: A,B3: A,C2: A,D: A] :
% 3.26/1.79 ( ( ( insert @ A @ A2 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.79 = ( insert @ A @ C2 @ ( insert @ A @ D @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.26/1.79 = ( ( ( A2 = C2 )
% 3.26/1.79 & ( B3 = D ) )
% 3.26/1.79 | ( ( A2 = D )
% 3.26/1.79 & ( B3 = C2 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_76_singleton__iff,axiom,
% 3.26/1.79 ! [A: $tType,B3: A,A2: A] :
% 3.26/1.79 ( ( member @ A @ B3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.79 = ( B3 = A2 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_77_singletonD,axiom,
% 3.26/1.79 ! [A: $tType,B3: A,A2: A] :
% 3.26/1.79 ( ( member @ A @ B3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.79 => ( B3 = A2 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_78_Un__empty__right,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A] :
% 3.26/1.79 ( ( sup_sup @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 3.26/1.79 = A3 ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_79_Un__empty__left,axiom,
% 3.26/1.79 ! [A: $tType,B2: set @ A] :
% 3.26/1.79 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B2 )
% 3.26/1.79 = B2 ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_80_Uvariation__trans,axiom,
% 3.26/1.79 ! [Omega: variable > real,Nu: variable > real,U: set @ variable,Mu: variable > real,V: set @ variable] :
% 3.26/1.79 ( ( denota1419872369iation @ Omega @ Nu @ U )
% 3.26/1.79 => ( ( denota1419872369iation @ Nu @ Mu @ V )
% 3.26/1.79 => ( denota1419872369iation @ Omega @ Mu @ ( sup_sup @ ( set @ variable ) @ U @ V ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_81_singleton__Un__iff,axiom,
% 3.26/1.79 ! [A: $tType,X: A,A3: set @ A,B2: set @ A] :
% 3.26/1.79 ( ( ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 3.26/1.79 = ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 3.26/1.79 = ( ( ( A3
% 3.26/1.79 = ( bot_bot @ ( set @ A ) ) )
% 3.26/1.79 & ( B2
% 3.26/1.79 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.26/1.79 | ( ( A3
% 3.26/1.79 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.79 & ( B2
% 3.26/1.79 = ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.79 | ( ( A3
% 3.26/1.79 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.79 & ( B2
% 3.26/1.79 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_82_Un__singleton__iff,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A,B2: set @ A,X: A] :
% 3.26/1.79 ( ( ( sup_sup @ ( set @ A ) @ A3 @ B2 )
% 3.26/1.79 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.79 = ( ( ( A3
% 3.26/1.79 = ( bot_bot @ ( set @ A ) ) )
% 3.26/1.79 & ( B2
% 3.26/1.79 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.26/1.79 | ( ( A3
% 3.26/1.79 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.79 & ( B2
% 3.26/1.79 = ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.79 | ( ( A3
% 3.26/1.79 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.79 & ( B2
% 3.26/1.79 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_83_insert__is__Un,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( insert @ A )
% 3.26/1.79 = ( ^ [A4: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_84__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rr_O_A_092_060forall_062x0_Ax1_Ax2_Ax3_Ax4_Ax5_O_A_I_092_060exists_062v6_O_AUvariation_Av6_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_Av6_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_Av6_J_A_061_A_IUvariation_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 3.26/1.79 ~ ! [Rr: trm > denotational_interp > trm > denotational_interp > char > ( real > variable > real ) > variable > real] :
% 3.26/1.79 ~ ! [X0: trm,X1: denotational_interp,X22: trm,X32: denotational_interp,X4: char,X5: real > variable > real] :
% 3.26/1.79 ( ( ? [V6: variable > real] :
% 3.26/1.79 ( ( denota1419872369iation @ V6 @ ( X5 @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ X4 ) @ ( insert @ variable @ ( dVar @ X4 ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
% 3.26/1.79 & ( ( denota1863255036rm_sem @ X32 @ X22 @ V6 )
% 3.26/1.79 != ( denota1863255036rm_sem @ X1 @ X0 @ V6 ) ) ) )
% 3.26/1.79 = ( ( denota1419872369iation @ ( Rr @ X0 @ X1 @ X22 @ X32 @ X4 @ X5 ) @ ( X5 @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ X4 ) @ ( insert @ variable @ ( dVar @ X4 ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
% 3.26/1.79 & ( ( denota1863255036rm_sem @ X32 @ X22 @ ( Rr @ X0 @ X1 @ X22 @ X32 @ X4 @ X5 ) )
% 3.26/1.79 != ( denota1863255036rm_sem @ X1 @ X0 @ ( Rr @ X0 @ X1 @ X22 @ X32 @ X4 @ X5 ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_85_solves__Vagree__trans,axiom,
% 3.26/1.79 ! [F3: real > variable > real,Omega: variable > real,U: set @ variable,I2: denotational_interp,X: char,Theta: trm,Zeta: real] :
% 3.26/1.79 ( ( denota1419872369iation @ ( F3 @ ( zero_zero @ real ) ) @ Omega @ U )
% 3.26/1.79 => ( ( denota1778088425es_ODE @ I2 @ F3 @ X @ Theta )
% 3.26/1.79 => ( denota1419872369iation @ ( F3 @ Zeta ) @ Omega @ ( sup_sup @ ( set @ variable ) @ U @ ( insert @ variable @ ( rVar @ X ) @ ( insert @ variable @ ( dVar @ X ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_86__092_060open_062_092_060forall_062x0_Ax1_Ax2_Ax3_Ax4_Ax5_O_A_I_092_060exists_062v6_O_AUvariation_Av6_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_Av6_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_Av6_J_A_061_A_IUvariation_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_J_092_060close_062,axiom,
% 3.26/1.79 ! [X0: trm,X1: denotational_interp,X22: trm,X32: denotational_interp,X4: char,X5: real > variable > real] :
% 3.26/1.79 ( ( ? [V6: variable > real] :
% 3.26/1.79 ( ( denota1419872369iation @ V6 @ ( X5 @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ X4 ) @ ( insert @ variable @ ( dVar @ X4 ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
% 3.26/1.79 & ( ( denota1863255036rm_sem @ X32 @ X22 @ V6 )
% 3.26/1.79 != ( denota1863255036rm_sem @ X1 @ X0 @ V6 ) ) ) )
% 3.26/1.79 = ( ( denota1419872369iation @ ( rr @ X0 @ X1 @ X22 @ X32 @ X4 @ X5 ) @ ( X5 @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ X4 ) @ ( insert @ variable @ ( dVar @ X4 ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
% 3.26/1.79 & ( ( denota1863255036rm_sem @ X32 @ X22 @ ( rr @ X0 @ X1 @ X22 @ X32 @ X4 @ X5 ) )
% 3.26/1.79 != ( denota1863255036rm_sem @ X1 @ X0 @ ( rr @ X0 @ X1 @ X22 @ X32 @ X4 @ X5 ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_87_variable_Oinject_I1_J,axiom,
% 3.26/1.79 ! [X12: char,Y1: char] :
% 3.26/1.79 ( ( ( rVar @ X12 )
% 3.26/1.79 = ( rVar @ Y1 ) )
% 3.26/1.79 = ( X12 = Y1 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_88_set__zero,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( zero @ A )
% 3.26/1.79 => ( ( zero_zero @ ( set @ A ) )
% 3.26/1.79 = ( insert @ A @ ( zero_zero @ A ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_89_variable_Oinject_I2_J,axiom,
% 3.26/1.79 ! [X23: char,Y22: char] :
% 3.26/1.79 ( ( ( dVar @ X23 )
% 3.26/1.79 = ( dVar @ Y22 ) )
% 3.26/1.79 = ( X23 = Y22 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_90_union__or,axiom,
% 3.26/1.79 ! [A: $tType,C2: A,A3: set @ A,B2: set @ A] :
% 3.26/1.79 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 3.26/1.79 = ( ( member @ A @ C2 @ A3 )
% 3.26/1.79 | ( member @ A @ C2 @ B2 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_91_ball__insert,axiom,
% 3.26/1.79 ! [A: $tType,A2: A,B2: set @ A,P: A > $o] :
% 3.26/1.79 ( ( ! [X2: A] :
% 3.26/1.79 ( ( member @ A @ X2 @ ( insert @ A @ A2 @ B2 ) )
% 3.26/1.79 => ( P @ X2 ) ) )
% 3.26/1.79 = ( ( P @ A2 )
% 3.26/1.79 & ! [X2: A] :
% 3.26/1.79 ( ( member @ A @ X2 @ B2 )
% 3.26/1.79 => ( P @ X2 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_92_the__elem__eq,axiom,
% 3.26/1.79 ! [A: $tType,X: A] :
% 3.26/1.79 ( ( the_elem @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.26/1.79 = X ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_93_bot__apply,axiom,
% 3.26/1.79 ! [C4: $tType,D2: $tType] :
% 3.26/1.79 ( ( bot @ C4 )
% 3.26/1.79 => ( ( bot_bot @ ( D2 > C4 ) )
% 3.26/1.79 = ( ^ [X2: D2] : ( bot_bot @ C4 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_94_f2,axiom,
% 3.26/1.79 ! [F4: real > variable > real,C5: char,I3: denotational_interp,T: trm,Ia: denotational_interp,Ta: trm] :
% 3.26/1.79 ( ( ( denota1419872369iation @ ( rr @ Ta @ Ia @ T @ I3 @ C5 @ F4 ) @ ( F4 @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ C5 ) @ ( insert @ variable @ ( dVar @ C5 ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
% 3.26/1.79 & ( ( denota1863255036rm_sem @ I3 @ T @ ( rr @ Ta @ Ia @ T @ I3 @ C5 @ F4 ) )
% 3.26/1.79 != ( denota1863255036rm_sem @ Ia @ Ta @ ( rr @ Ta @ Ia @ T @ I3 @ C5 @ F4 ) ) ) )
% 3.26/1.79 | ( ( denota1778088425es_ODE @ I3 @ F4 @ C5 @ T )
% 3.26/1.79 = ( denota1778088425es_ODE @ Ia @ F4 @ C5 @ Ta ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_95_zero__reorient,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( zero @ A )
% 3.26/1.79 => ! [X: A] :
% 3.26/1.79 ( ( ( zero_zero @ A )
% 3.26/1.79 = X )
% 3.26/1.79 = ( X
% 3.26/1.79 = ( zero_zero @ A ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_96_bot__fun__def,axiom,
% 3.26/1.79 ! [B: $tType,A: $tType] :
% 3.26/1.79 ( ( bot @ B )
% 3.26/1.79 => ( ( bot_bot @ ( A > B ) )
% 3.26/1.79 = ( ^ [X2: A] : ( bot_bot @ B ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_97_not__union__or,axiom,
% 3.26/1.79 ! [A: $tType,X: A,A3: set @ A,B2: set @ A] :
% 3.26/1.79 ( ( ~ ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) )
% 3.26/1.79 = ( ~ ( member @ A @ X @ A3 )
% 3.26/1.79 & ~ ( member @ A @ X @ B2 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_98_same__ODE__same__sol,axiom,
% 3.26/1.79 ! [F3: real > variable > real,X: char,I2: denotational_interp,Theta: trm,J: denotational_interp,Eta: trm] :
% 3.26/1.79 ( ! [Nu5: variable > real] :
% 3.26/1.79 ( ( denota1419872369iation @ Nu5 @ ( F3 @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ X ) @ ( insert @ variable @ ( dVar @ X ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
% 3.26/1.79 => ( ( denota1863255036rm_sem @ I2 @ Theta @ Nu5 )
% 3.26/1.79 = ( denota1863255036rm_sem @ J @ Eta @ Nu5 ) ) )
% 3.26/1.79 => ( ( denota1778088425es_ODE @ I2 @ F3 @ X @ Theta )
% 3.26/1.79 = ( denota1778088425es_ODE @ J @ F3 @ X @ Eta ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_99_variable_Odistinct_I1_J,axiom,
% 3.26/1.79 ! [X12: char,X23: char] :
% 3.26/1.79 ( ( rVar @ X12 )
% 3.26/1.79 != ( dVar @ X23 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_100_variable_Oinduct,axiom,
% 3.26/1.79 ! [P: variable > $o,Variable: variable] :
% 3.26/1.79 ( ! [X3: char] : ( P @ ( rVar @ X3 ) )
% 3.26/1.79 => ( ! [X3: char] : ( P @ ( dVar @ X3 ) )
% 3.26/1.79 => ( P @ Variable ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_101_variable_Oexhaust,axiom,
% 3.26/1.79 ! [Y: variable] :
% 3.26/1.79 ( ! [X13: char] :
% 3.26/1.79 ( Y
% 3.26/1.79 != ( rVar @ X13 ) )
% 3.26/1.79 => ~ ! [X24: char] :
% 3.26/1.79 ( Y
% 3.26/1.79 != ( dVar @ X24 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_102_bot__empty__eq,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( bot_bot @ ( A > $o ) )
% 3.26/1.79 = ( ^ [X2: A] : ( member @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_103_Collect__empty__eq__bot,axiom,
% 3.26/1.79 ! [A: $tType,P: A > $o] :
% 3.26/1.79 ( ( ( collect @ A @ P )
% 3.26/1.79 = ( bot_bot @ ( set @ A ) ) )
% 3.26/1.79 = ( P
% 3.26/1.79 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_104_is__singleton__the__elem,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( is_singleton @ A )
% 3.26/1.79 = ( ^ [A5: set @ A] :
% 3.26/1.79 ( A5
% 3.26/1.79 = ( insert @ A @ ( the_elem @ A @ A5 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_105_vaflow2,axiom,
% 3.26/1.79 ! [F3: real > variable > real,Theta: trm,Zeta: real] :
% 3.26/1.79 ( ( denota1778088425es_ODE @ ( uSubst2091380086djoint @ sigma @ i @ omega ) @ F3 @ x @ Theta )
% 3.26/1.79 => ( denota1419872369iation @ ( F3 @ Zeta ) @ ( F3 @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_106_is__singletonI,axiom,
% 3.26/1.79 ! [A: $tType,X: A] : ( is_singleton @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_107_a1,axiom,
% 3.26/1.79 denota1778088425es_ODE @ ( uSubst2091380086djoint @ sigma @ i @ omega ) @ f @ x @ theta ).
% 3.26/1.79
% 3.26/1.79 thf(fact_108_is__singletonI_H,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A] :
% 3.26/1.79 ( ( A3
% 3.26/1.79 != ( bot_bot @ ( set @ A ) ) )
% 3.26/1.79 => ( ! [X3: A,Y2: A] :
% 3.26/1.79 ( ( member @ A @ X3 @ A3 )
% 3.26/1.79 => ( ( member @ A @ Y2 @ A3 )
% 3.26/1.79 => ( X3 = Y2 ) ) )
% 3.26/1.79 => ( is_singleton @ A @ A3 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_109_is__singleton__def,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( is_singleton @ A )
% 3.26/1.79 = ( ^ [A5: set @ A] :
% 3.26/1.79 ? [X2: A] :
% 3.26/1.79 ( A5
% 3.26/1.79 = ( insert @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_110_is__singletonE,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A] :
% 3.26/1.79 ( ( is_singleton @ A @ A3 )
% 3.26/1.79 => ~ ! [X3: A] :
% 3.26/1.79 ( A3
% 3.26/1.79 != ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_111_vaflow1,axiom,
% 3.26/1.79 ! [F3: real > variable > real,Theta: trm,Zeta: real] :
% 3.26/1.79 ( ( denota1778088425es_ODE @ i @ F3 @ x @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) @ Theta ) ) )
% 3.26/1.79 => ( denota1419872369iation @ ( F3 @ Zeta ) @ ( F3 @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_112_l2r,axiom,
% 3.26/1.79 ( ( denota1778088425es_ODE @ i @ f @ x @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) @ theta ) ) )
% 3.26/1.79 => ( denota1778088425es_ODE @ ( uSubst2091380086djoint @ sigma @ i @ omega ) @ f @ x @ theta ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_113_IH,axiom,
% 3.26/1.79 ! [Nu: variable > real] :
% 3.26/1.79 ( ( denota1419872369iation @ Nu @ ( f @ ( zero_zero @ real ) ) @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) )
% 3.26/1.79 => ( ( denota1863255036rm_sem @ i @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) @ theta ) ) @ Nu )
% 3.26/1.79 = ( denota1863255036rm_sem @ ( uSubst2091380086djoint @ sigma @ i @ ( f @ ( zero_zero @ real ) ) ) @ theta @ Nu ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_114_subdef,axiom,
% 3.26/1.79 ( ( uSubst95898992stappt @ sigma @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) @ theta )
% 3.26/1.79 != ( none @ trm ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_115_variable_Osize__gen_I1_J,axiom,
% 3.26/1.79 ! [X12: char] :
% 3.26/1.79 ( ( size_variable @ ( rVar @ X12 ) )
% 3.26/1.79 = ( zero_zero @ nat ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_116_usubst__term,axiom,
% 3.26/1.79 ! [Nu: variable > real,Omega: variable > real,U: set @ variable,Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),Theta: trm,I2: denotational_interp] :
% 3.26/1.79 ( ( denota1419872369iation @ Nu @ Omega @ U )
% 3.26/1.79 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 3.26/1.79 != ( none @ trm ) )
% 3.26/1.79 => ( ( denota1863255036rm_sem @ I2 @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) @ Nu )
% 3.26/1.79 = ( denota1863255036rm_sem @ ( uSubst2091380086djoint @ Sigma @ I2 @ Omega ) @ Theta @ Nu ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_117_usubstappt__det,axiom,
% 3.26/1.79 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,V: set @ variable] :
% 3.26/1.79 ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 3.26/1.79 != ( none @ trm ) )
% 3.26/1.79 => ( ( ( uSubst95898992stappt @ Sigma @ V @ Theta )
% 3.26/1.79 != ( none @ trm ) )
% 3.26/1.79 => ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 3.26/1.79 = ( uSubst95898992stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_118_undeft__None,axiom,
% 3.26/1.79 ( ( none @ trm )
% 3.26/1.79 = ( none @ trm ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_119_usubst__ode,axiom,
% 3.26/1.79 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),X: char,Theta: trm,I2: denotational_interp,F3: real > variable > real] :
% 3.26/1.79 ( ( ( uSubst95898992stappt @ Sigma @ ( insert @ variable @ ( rVar @ X ) @ ( insert @ variable @ ( dVar @ X ) @ ( bot_bot @ ( set @ variable ) ) ) ) @ Theta )
% 3.26/1.79 != ( none @ trm ) )
% 3.26/1.79 => ( ( denota1778088425es_ODE @ I2 @ F3 @ X @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ ( insert @ variable @ ( rVar @ X ) @ ( insert @ variable @ ( dVar @ X ) @ ( bot_bot @ ( set @ variable ) ) ) ) @ Theta ) ) )
% 3.26/1.79 = ( denota1778088425es_ODE @ ( uSubst2091380086djoint @ Sigma @ I2 @ ( F3 @ ( zero_zero @ real ) ) ) @ F3 @ X @ Theta ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_120_variable_Osize__gen_I2_J,axiom,
% 3.26/1.79 ! [X23: char] :
% 3.26/1.79 ( ( size_variable @ ( dVar @ X23 ) )
% 3.26/1.79 = ( zero_zero @ nat ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_121_option_Oexpand,axiom,
% 3.26/1.79 ! [A: $tType,Option: option @ A,Option2: option @ A] :
% 3.26/1.79 ( ( ( Option
% 3.26/1.79 = ( none @ A ) )
% 3.26/1.79 = ( Option2
% 3.26/1.79 = ( none @ A ) ) )
% 3.26/1.79 => ( ( ( Option
% 3.26/1.79 != ( none @ A ) )
% 3.26/1.79 => ( ( Option2
% 3.26/1.79 != ( none @ A ) )
% 3.26/1.79 => ( ( the @ A @ Option )
% 3.26/1.79 = ( the @ A @ Option2 ) ) ) )
% 3.26/1.79 => ( Option = Option2 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_122_variable_Osize_I3_J,axiom,
% 3.26/1.79 ! [X12: char] :
% 3.26/1.79 ( ( size_size @ variable @ ( rVar @ X12 ) )
% 3.26/1.79 = ( zero_zero @ nat ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_123_variable_Osize_I4_J,axiom,
% 3.26/1.79 ! [X23: char] :
% 3.26/1.79 ( ( size_size @ variable @ ( dVar @ X23 ) )
% 3.26/1.79 = ( zero_zero @ nat ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_124_Set_Ois__empty__def,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( is_empty @ A )
% 3.26/1.79 = ( ^ [A5: set @ A] :
% 3.26/1.79 ( A5
% 3.26/1.79 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_125_Uvariation__repv,axiom,
% 3.26/1.79 ! [Omega: variable > real,X: variable,D: real] : ( denota1419872369iation @ Omega @ ( denotational_repv @ Omega @ X @ D ) @ ( insert @ variable @ X @ ( bot_bot @ ( set @ variable ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_126_these__empty__eq,axiom,
% 3.26/1.79 ! [A: $tType,B2: set @ ( option @ A )] :
% 3.26/1.79 ( ( ( these @ A @ B2 )
% 3.26/1.79 = ( bot_bot @ ( set @ A ) ) )
% 3.26/1.79 = ( ( B2
% 3.26/1.79 = ( bot_bot @ ( set @ ( option @ A ) ) ) )
% 3.26/1.79 | ( B2
% 3.26/1.79 = ( insert @ ( option @ A ) @ ( none @ A ) @ ( bot_bot @ ( set @ ( option @ A ) ) ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_127_these__not__empty__eq,axiom,
% 3.26/1.79 ! [A: $tType,B2: set @ ( option @ A )] :
% 3.26/1.79 ( ( ( these @ A @ B2 )
% 3.26/1.79 != ( bot_bot @ ( set @ A ) ) )
% 3.26/1.79 = ( ( B2
% 3.26/1.79 != ( bot_bot @ ( set @ ( option @ A ) ) ) )
% 3.26/1.79 & ( B2
% 3.26/1.79 != ( insert @ ( option @ A ) @ ( none @ A ) @ ( bot_bot @ ( set @ ( option @ A ) ) ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_128_variable_Osimps_I7_J,axiom,
% 3.26/1.79 ! [A: $tType,F1: char > A,F22: char > A,X12: char] :
% 3.26/1.79 ( ( rec_variable @ A @ F1 @ F22 @ ( rVar @ X12 ) )
% 3.26/1.79 = ( F1 @ X12 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_129_repv__self,axiom,
% 3.26/1.79 ! [Omega: variable > real,X: variable] :
% 3.26/1.79 ( ( denotational_repv @ Omega @ X @ ( Omega @ X ) )
% 3.26/1.79 = Omega ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_130_repv__access,axiom,
% 3.26/1.79 ( denotational_repv
% 3.26/1.79 = ( ^ [Omega2: variable > real,X2: variable,R: real,Y3: variable] : ( if @ real @ ( X2 = Y3 ) @ R @ ( Omega2 @ Y3 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_131_these__empty,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( these @ A @ ( bot_bot @ ( set @ ( option @ A ) ) ) )
% 3.26/1.79 = ( bot_bot @ ( set @ A ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_132_these__insert__None,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ ( option @ A )] :
% 3.26/1.79 ( ( these @ A @ ( insert @ ( option @ A ) @ ( none @ A ) @ A3 ) )
% 3.26/1.79 = ( these @ A @ A3 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_133_repv__def__correct,axiom,
% 3.26/1.79 ( denotational_repv
% 3.26/1.79 = ( ^ [Omega2: variable > real,X2: variable,R: real,Y3: variable] : ( if @ real @ ( X2 = Y3 ) @ R @ ( Omega2 @ Y3 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_134_variable_Osimps_I8_J,axiom,
% 3.26/1.79 ! [A: $tType,F1: char > A,F22: char > A,X23: char] :
% 3.26/1.79 ( ( rec_variable @ A @ F1 @ F22 @ ( dVar @ X23 ) )
% 3.26/1.79 = ( F22 @ X23 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_135_these__insert__Some,axiom,
% 3.26/1.79 ! [A: $tType,X: A,A3: set @ ( option @ A )] :
% 3.26/1.79 ( ( these @ A @ ( insert @ ( option @ A ) @ ( some @ A @ X ) @ A3 ) )
% 3.26/1.79 = ( insert @ A @ X @ ( these @ A @ A3 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_136_repv__selectlike__other__converse,axiom,
% 3.26/1.79 ! [X: variable,Y: variable,Omega: variable > real,D: real,X6: set @ ( variable > real )] :
% 3.26/1.79 ( ( X != Y )
% 3.26/1.79 => ( ( member @ ( variable > real ) @ ( denotational_repv @ Omega @ X @ D ) @ X6 )
% 3.26/1.79 = ( member @ ( variable > real ) @ ( denotational_repv @ Omega @ X @ D ) @ ( static_selectlike @ X6 @ Omega @ ( insert @ variable @ Y @ ( bot_bot @ ( set @ variable ) ) ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_137_repv__selectlike__other,axiom,
% 3.26/1.79 ! [X: variable,Y: variable,Omega: variable > real,D: real,X6: set @ ( variable > real )] :
% 3.26/1.79 ( ( X != Y )
% 3.26/1.79 => ( ( member @ ( variable > real ) @ ( denotational_repv @ Omega @ X @ D ) @ ( static_selectlike @ X6 @ Omega @ ( insert @ variable @ Y @ ( bot_bot @ ( set @ variable ) ) ) ) )
% 3.26/1.79 = ( member @ ( variable > real ) @ ( denotational_repv @ Omega @ X @ D ) @ X6 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_138_repv__selectlike__self,axiom,
% 3.26/1.79 ! [Omega: variable > real,X: variable,D: real,X6: set @ ( variable > real )] :
% 3.26/1.79 ( ( member @ ( variable > real ) @ ( denotational_repv @ Omega @ X @ D ) @ ( static_selectlike @ X6 @ Omega @ ( insert @ variable @ X @ ( bot_bot @ ( set @ variable ) ) ) ) )
% 3.26/1.79 = ( ( D
% 3.26/1.79 = ( Omega @ X ) )
% 3.26/1.79 & ( member @ ( variable > real ) @ Omega @ X6 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_139_option_Oinject,axiom,
% 3.26/1.79 ! [A: $tType,X23: A,Y22: A] :
% 3.26/1.79 ( ( ( some @ A @ X23 )
% 3.26/1.79 = ( some @ A @ Y22 ) )
% 3.26/1.79 = ( X23 = Y22 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_140_selectlike__self,axiom,
% 3.26/1.79 ! [Nu: variable > real,X6: set @ ( variable > real ),V: set @ variable] :
% 3.26/1.79 ( ( member @ ( variable > real ) @ Nu @ ( static_selectlike @ X6 @ Nu @ V ) )
% 3.26/1.79 = ( member @ ( variable > real ) @ Nu @ X6 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_141_not__None__eq,axiom,
% 3.26/1.79 ! [A: $tType,X: option @ A] :
% 3.26/1.79 ( ( X
% 3.26/1.79 != ( none @ A ) )
% 3.26/1.79 = ( ? [Y3: A] :
% 3.26/1.79 ( X
% 3.26/1.79 = ( some @ A @ Y3 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_142_not__Some__eq,axiom,
% 3.26/1.79 ! [A: $tType,X: option @ A] :
% 3.26/1.79 ( ( ! [Y3: A] :
% 3.26/1.79 ( X
% 3.26/1.79 != ( some @ A @ Y3 ) ) )
% 3.26/1.79 = ( X
% 3.26/1.79 = ( none @ A ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_143_selectlike__empty,axiom,
% 3.26/1.79 ! [X6: set @ ( variable > real ),Nu: variable > real] :
% 3.26/1.79 ( ( static_selectlike @ X6 @ Nu @ ( bot_bot @ ( set @ variable ) ) )
% 3.26/1.79 = X6 ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_144_selectlike__compose,axiom,
% 3.26/1.79 ! [X6: set @ ( variable > real ),Nu: variable > real,V: set @ variable,W: set @ variable] :
% 3.26/1.79 ( ( static_selectlike @ ( static_selectlike @ X6 @ Nu @ V ) @ Nu @ W )
% 3.26/1.79 = ( static_selectlike @ X6 @ Nu @ ( sup_sup @ ( set @ variable ) @ V @ W ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_145_option_Ocollapse,axiom,
% 3.26/1.79 ! [A: $tType,Option: option @ A] :
% 3.26/1.79 ( ( Option
% 3.26/1.79 != ( none @ A ) )
% 3.26/1.79 => ( ( some @ A @ ( the @ A @ Option ) )
% 3.26/1.79 = Option ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_146_in__these__eq,axiom,
% 3.26/1.79 ! [A: $tType,X: A,A3: set @ ( option @ A )] :
% 3.26/1.79 ( ( member @ A @ X @ ( these @ A @ A3 ) )
% 3.26/1.79 = ( member @ ( option @ A ) @ ( some @ A @ X ) @ A3 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_147_selectlike__union,axiom,
% 3.26/1.79 ! [X6: set @ ( variable > real ),Y4: set @ ( variable > real ),Nu: variable > real,V: set @ variable] :
% 3.26/1.79 ( ( static_selectlike @ ( sup_sup @ ( set @ ( variable > real ) ) @ X6 @ Y4 ) @ Nu @ V )
% 3.26/1.79 = ( sup_sup @ ( set @ ( variable > real ) ) @ ( static_selectlike @ X6 @ Nu @ V ) @ ( static_selectlike @ Y4 @ Nu @ V ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_148_option_Odistinct_I1_J,axiom,
% 3.26/1.79 ! [A: $tType,X23: A] :
% 3.26/1.79 ( ( none @ A )
% 3.26/1.79 != ( some @ A @ X23 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_149_option_Osel,axiom,
% 3.26/1.79 ! [A: $tType,X23: A] :
% 3.26/1.79 ( ( the @ A @ ( some @ A @ X23 ) )
% 3.26/1.79 = X23 ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_150_option_OdiscI,axiom,
% 3.26/1.79 ! [A: $tType,Option: option @ A,X23: A] :
% 3.26/1.79 ( ( Option
% 3.26/1.79 = ( some @ A @ X23 ) )
% 3.26/1.79 => ( Option
% 3.26/1.79 != ( none @ A ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_151_option_Oexhaust,axiom,
% 3.26/1.79 ! [A: $tType,Y: option @ A] :
% 3.26/1.79 ( ( Y
% 3.26/1.79 != ( none @ A ) )
% 3.26/1.79 => ~ ! [X24: A] :
% 3.26/1.79 ( Y
% 3.26/1.79 != ( some @ A @ X24 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_152_option_Oinducts,axiom,
% 3.26/1.79 ! [A: $tType,P: ( option @ A ) > $o,Option: option @ A] :
% 3.26/1.79 ( ( P @ ( none @ A ) )
% 3.26/1.79 => ( ! [X3: A] : ( P @ ( some @ A @ X3 ) )
% 3.26/1.79 => ( P @ Option ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_153_split__option__ex,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( ^ [P2: ( option @ A ) > $o] :
% 3.26/1.79 ? [X7: option @ A] : ( P2 @ X7 ) )
% 3.26/1.79 = ( ^ [P3: ( option @ A ) > $o] :
% 3.26/1.79 ( ( P3 @ ( none @ A ) )
% 3.26/1.79 | ? [X2: A] : ( P3 @ ( some @ A @ X2 ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_154_split__option__all,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( ^ [P2: ( option @ A ) > $o] :
% 3.26/1.79 ! [X7: option @ A] : ( P2 @ X7 ) )
% 3.26/1.79 = ( ^ [P3: ( option @ A ) > $o] :
% 3.26/1.79 ( ( P3 @ ( none @ A ) )
% 3.26/1.79 & ! [X2: A] : ( P3 @ ( some @ A @ X2 ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_155_combine__options__cases,axiom,
% 3.26/1.79 ! [A: $tType,B: $tType,X: option @ A,P: ( option @ A ) > ( option @ B ) > $o,Y: option @ B] :
% 3.26/1.79 ( ( ( X
% 3.26/1.79 = ( none @ A ) )
% 3.26/1.79 => ( P @ X @ Y ) )
% 3.26/1.79 => ( ( ( Y
% 3.26/1.79 = ( none @ B ) )
% 3.26/1.79 => ( P @ X @ Y ) )
% 3.26/1.79 => ( ! [A6: A,B7: B] :
% 3.26/1.79 ( ( X
% 3.26/1.79 = ( some @ A @ A6 ) )
% 3.26/1.79 => ( ( Y
% 3.26/1.79 = ( some @ B @ B7 ) )
% 3.26/1.79 => ( P @ X @ Y ) ) )
% 3.26/1.79 => ( P @ X @ Y ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_156_ODEo_Oinduct,axiom,
% 3.26/1.79 ! [P: char > ( option @ trm ) > $o,A0: char,A1: option @ trm] :
% 3.26/1.79 ( ! [X3: char,Theta2: trm] : ( P @ X3 @ ( some @ trm @ Theta2 ) )
% 3.26/1.79 => ( ! [X3: char] : ( P @ X3 @ ( none @ trm ) )
% 3.26/1.79 => ( P @ A0 @ A1 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_157_undeft__equiv,axiom,
% 3.26/1.79 ! [Theta: option @ trm] :
% 3.26/1.79 ( ( Theta
% 3.26/1.79 != ( none @ trm ) )
% 3.26/1.79 = ( ? [T2: trm] :
% 3.26/1.79 ( Theta
% 3.26/1.79 = ( some @ trm @ T2 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_158_Timeso_Oinduct,axiom,
% 3.26/1.79 ! [P: ( option @ trm ) > ( option @ trm ) > $o,A0: option @ trm,A1: option @ trm] :
% 3.26/1.79 ( ! [Theta2: trm,Eta2: trm] : ( P @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta2 ) )
% 3.26/1.79 => ( ! [X_1: option @ trm] : ( P @ ( none @ trm ) @ X_1 )
% 3.26/1.79 => ( ! [V2: trm] : ( P @ ( some @ trm @ V2 ) @ ( none @ trm ) )
% 3.26/1.79 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_159_Assigno_Oinduct,axiom,
% 3.26/1.79 ! [P: variable > ( option @ trm ) > $o,A0: variable,A1: option @ trm] :
% 3.26/1.79 ( ! [X3: variable,Theta2: trm] : ( P @ X3 @ ( some @ trm @ Theta2 ) )
% 3.26/1.79 => ( ! [X3: variable] : ( P @ X3 @ ( none @ trm ) )
% 3.26/1.79 => ( P @ A0 @ A1 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_160_Differentialo_Ocases,axiom,
% 3.26/1.79 ! [X: option @ trm] :
% 3.26/1.79 ( ! [Theta2: trm] :
% 3.26/1.79 ( X
% 3.26/1.79 != ( some @ trm @ Theta2 ) )
% 3.26/1.79 => ( X
% 3.26/1.79 = ( none @ trm ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_161_Differentialo_Oinduct,axiom,
% 3.26/1.79 ! [P: ( option @ trm ) > $o,A0: option @ trm] :
% 3.26/1.79 ( ! [Theta2: trm] : ( P @ ( some @ trm @ Theta2 ) )
% 3.26/1.79 => ( ( P @ ( none @ trm ) )
% 3.26/1.79 => ( P @ A0 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_162_option_Oexhaust__sel,axiom,
% 3.26/1.79 ! [A: $tType,Option: option @ A] :
% 3.26/1.79 ( ( Option
% 3.26/1.79 != ( none @ A ) )
% 3.26/1.79 => ( Option
% 3.26/1.79 = ( some @ A @ ( the @ A @ Option ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_163_option_Osplit__sel,axiom,
% 3.26/1.79 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 3.26/1.79 ( ( P @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 3.26/1.79 = ( ( ( Option
% 3.26/1.79 = ( none @ A ) )
% 3.26/1.79 => ( P @ F1 ) )
% 3.26/1.79 & ( ( Option
% 3.26/1.79 = ( some @ A @ ( the @ A @ Option ) ) )
% 3.26/1.79 => ( P @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_164_option_Osplit__sel__asm,axiom,
% 3.26/1.79 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 3.26/1.79 ( ( P @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 3.26/1.79 = ( ~ ( ( ( Option
% 3.26/1.79 = ( none @ A ) )
% 3.26/1.79 & ~ ( P @ F1 ) )
% 3.26/1.79 | ( ( Option
% 3.26/1.79 = ( some @ A @ ( the @ A @ Option ) ) )
% 3.26/1.79 & ~ ( P @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_165_option_Osimps_I15_J,axiom,
% 3.26/1.79 ! [A: $tType,X23: A] :
% 3.26/1.79 ( ( set_option @ A @ ( some @ A @ X23 ) )
% 3.26/1.79 = ( insert @ A @ X23 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_166_Vagree__repv__self,axiom,
% 3.26/1.79 ! [Omega: variable > real,X: variable,D: real] :
% 3.26/1.79 ( ( denotational_Vagree @ Omega @ ( denotational_repv @ Omega @ X @ D ) @ ( insert @ variable @ X @ ( bot_bot @ ( set @ variable ) ) ) )
% 3.26/1.79 = ( D
% 3.26/1.79 = ( Omega @ X ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_167_elem__set,axiom,
% 3.26/1.79 ! [A: $tType,X: A,Xo: option @ A] :
% 3.26/1.79 ( ( member @ A @ X @ ( set_option @ A @ Xo ) )
% 3.26/1.79 = ( Xo
% 3.26/1.79 = ( some @ A @ X ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_168_Vagree__and,axiom,
% 3.26/1.79 ! [Nu: variable > real,Nu2: variable > real,V: set @ variable,W: set @ variable] :
% 3.26/1.79 ( ( ( denotational_Vagree @ Nu @ Nu2 @ V )
% 3.26/1.79 & ( denotational_Vagree @ Nu @ Nu2 @ W ) )
% 3.26/1.79 = ( denotational_Vagree @ Nu @ Nu2 @ ( sup_sup @ ( set @ variable ) @ V @ W ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_169_set__empty__eq,axiom,
% 3.26/1.79 ! [A: $tType,Xo: option @ A] :
% 3.26/1.79 ( ( ( set_option @ A @ Xo )
% 3.26/1.79 = ( bot_bot @ ( set @ A ) ) )
% 3.26/1.79 = ( Xo
% 3.26/1.79 = ( none @ A ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_170_similar__selectlike__mem,axiom,
% 3.26/1.79 ! [Nu: variable > real,Omega: variable > real,V: set @ variable,X6: set @ ( variable > real )] :
% 3.26/1.79 ( ( denotational_Vagree @ Nu @ Omega @ V )
% 3.26/1.79 => ( ( member @ ( variable > real ) @ Nu @ ( static_selectlike @ X6 @ Omega @ V ) )
% 3.26/1.79 = ( member @ ( variable > real ) @ Nu @ X6 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_171_selectlike__Vagree,axiom,
% 3.26/1.79 ! [Nu: variable > real,Omega: variable > real,V: set @ variable,X6: set @ ( variable > real )] :
% 3.26/1.79 ( ( denotational_Vagree @ Nu @ Omega @ V )
% 3.26/1.79 => ( ( static_selectlike @ X6 @ Nu @ V )
% 3.26/1.79 = ( static_selectlike @ X6 @ Omega @ V ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_172_Aterm__Some,axiom,
% 3.26/1.79 ( ( some @ trm )
% 3.26/1.79 = ( some @ trm ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_173_option_Oset__intros,axiom,
% 3.26/1.79 ! [A: $tType,X23: A] : ( member @ A @ X23 @ ( set_option @ A @ ( some @ A @ X23 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_174_option_Oset__cases,axiom,
% 3.26/1.79 ! [A: $tType,E: A,A2: option @ A] :
% 3.26/1.79 ( ( member @ A @ E @ ( set_option @ A @ A2 ) )
% 3.26/1.79 => ( A2
% 3.26/1.79 = ( some @ A @ E ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_175_ospec,axiom,
% 3.26/1.79 ! [A: $tType,A3: option @ A,P: A > $o,X: A] :
% 3.26/1.79 ( ! [X3: A] :
% 3.26/1.79 ( ( member @ A @ X3 @ ( set_option @ A @ A3 ) )
% 3.26/1.79 => ( P @ X3 ) )
% 3.26/1.79 => ( ( A3
% 3.26/1.79 = ( some @ A @ X ) )
% 3.26/1.79 => ( P @ X ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_176_Vagree__union,axiom,
% 3.26/1.79 ! [Nu: variable > real,Nu2: variable > real,V: set @ variable,W: set @ variable] :
% 3.26/1.79 ( ( denotational_Vagree @ Nu @ Nu2 @ V )
% 3.26/1.79 => ( ( denotational_Vagree @ Nu @ Nu2 @ W )
% 3.26/1.79 => ( denotational_Vagree @ Nu @ Nu2 @ ( sup_sup @ ( set @ variable ) @ V @ W ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_177_Vagree__def,axiom,
% 3.26/1.79 ( denotational_Vagree
% 3.26/1.79 = ( ^ [Nu3: variable > real,Nu4: variable > real,V3: set @ variable] :
% 3.26/1.79 ! [I: variable] :
% 3.26/1.79 ( ( member @ variable @ I @ V3 )
% 3.26/1.79 => ( ( Nu3 @ I )
% 3.26/1.79 = ( Nu4 @ I ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_178_Vagree__sym,axiom,
% 3.26/1.79 ( denotational_Vagree
% 3.26/1.79 = ( ^ [Nu3: variable > real,Nu4: variable > real] : ( denotational_Vagree @ Nu4 @ Nu3 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_179_Vagree__refl,axiom,
% 3.26/1.79 ! [Nu: variable > real,V: set @ variable] : ( denotational_Vagree @ Nu @ Nu @ V ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_180_Vagree__sym__rel,axiom,
% 3.26/1.79 ! [Nu: variable > real,Nu2: variable > real,V: set @ variable] :
% 3.26/1.79 ( ( denotational_Vagree @ Nu @ Nu2 @ V )
% 3.26/1.79 => ( denotational_Vagree @ Nu2 @ Nu @ V ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_181_Vagree__empty,axiom,
% 3.26/1.79 ! [Nu: variable > real,Nu2: variable > real] : ( denotational_Vagree @ Nu @ Nu2 @ ( bot_bot @ ( set @ variable ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_182_option_Osimps_I4_J,axiom,
% 3.26/1.79 ! [A: $tType,B: $tType,F1: B,F22: A > B] :
% 3.26/1.79 ( ( case_option @ B @ A @ F1 @ F22 @ ( none @ A ) )
% 3.26/1.79 = F1 ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_183_option_Osimps_I5_J,axiom,
% 3.26/1.79 ! [B: $tType,A: $tType,F1: B,F22: A > B,X23: A] :
% 3.26/1.79 ( ( case_option @ B @ A @ F1 @ F22 @ ( some @ A @ X23 ) )
% 3.26/1.79 = ( F22 @ X23 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_184_option_Osimps_I14_J,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( set_option @ A @ ( none @ A ) )
% 3.26/1.79 = ( bot_bot @ ( set @ A ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_185_option_Oset__sel,axiom,
% 3.26/1.79 ! [A: $tType,A2: option @ A] :
% 3.26/1.79 ( ( A2
% 3.26/1.79 != ( none @ A ) )
% 3.26/1.79 => ( member @ A @ ( the @ A @ A2 ) @ ( set_option @ A @ A2 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_186_option_Ocase__eq__if,axiom,
% 3.26/1.79 ! [A: $tType,B: $tType] :
% 3.26/1.79 ( ( case_option @ B @ A )
% 3.26/1.79 = ( ^ [F12: B,F23: A > B,Option3: option @ A] :
% 3.26/1.79 ( if @ B
% 3.26/1.79 @ ( Option3
% 3.26/1.79 = ( none @ A ) )
% 3.26/1.79 @ F12
% 3.26/1.79 @ ( F23 @ ( the @ A @ Option3 ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_187_solves__Vagree,axiom,
% 3.26/1.79 ! [I2: denotational_interp,F3: real > variable > real,X: char,Theta: trm,Zeta: real] :
% 3.26/1.79 ( ( denota1778088425es_ODE @ I2 @ F3 @ X @ Theta )
% 3.26/1.79 => ( denotational_Vagree @ ( F3 @ Zeta ) @ ( F3 @ ( zero_zero @ real ) ) @ ( uminus_uminus @ ( set @ variable ) @ ( insert @ variable @ ( rVar @ X ) @ ( insert @ variable @ ( dVar @ X ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_188_Vagree__repv,axiom,
% 3.26/1.79 ! [Omega: variable > real,X: variable,D: real] : ( denotational_Vagree @ Omega @ ( denotational_repv @ Omega @ X @ D ) @ ( uminus_uminus @ ( set @ variable ) @ ( insert @ variable @ X @ ( bot_bot @ ( set @ variable ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_189_Timeso_Osimps_I3_J,axiom,
% 3.26/1.79 ! [V4: trm] :
% 3.26/1.79 ( ( uSubst277968634Timeso @ ( some @ trm @ V4 ) @ ( none @ trm ) )
% 3.26/1.79 = ( none @ trm ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_190_neg__equal__iff__equal,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( group_add @ A )
% 3.26/1.79 => ! [A2: A,B3: A] :
% 3.26/1.79 ( ( ( uminus_uminus @ A @ A2 )
% 3.26/1.79 = ( uminus_uminus @ A @ B3 ) )
% 3.26/1.79 = ( A2 = B3 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_191_add_Oinverse__inverse,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( group_add @ A )
% 3.26/1.79 => ! [A2: A] :
% 3.26/1.79 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ A2 ) )
% 3.26/1.79 = A2 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_192_compl__eq__compl__iff,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( boolean_algebra @ A )
% 3.26/1.79 => ! [X: A,Y: A] :
% 3.26/1.79 ( ( ( uminus_uminus @ A @ X )
% 3.26/1.79 = ( uminus_uminus @ A @ Y ) )
% 3.26/1.79 = ( X = Y ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_193_double__compl,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( boolean_algebra @ A )
% 3.26/1.79 => ! [X: A] :
% 3.26/1.79 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ X ) )
% 3.26/1.79 = X ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_194_uminus__apply,axiom,
% 3.26/1.79 ! [B: $tType,A: $tType] :
% 3.26/1.79 ( ( uminus @ B )
% 3.26/1.79 => ( ( uminus_uminus @ ( A > B ) )
% 3.26/1.79 = ( ^ [A5: A > B,X2: A] : ( uminus_uminus @ B @ ( A5 @ X2 ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_195_Compl__eq__Compl__iff,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 3.26/1.79 ( ( ( uminus_uminus @ ( set @ A ) @ A3 )
% 3.26/1.79 = ( uminus_uminus @ ( set @ A ) @ B2 ) )
% 3.26/1.79 = ( A3 = B2 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_196_Compl__iff,axiom,
% 3.26/1.79 ! [A: $tType,C2: A,A3: set @ A] :
% 3.26/1.79 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A3 ) )
% 3.26/1.79 = ( ~ ( member @ A @ C2 @ A3 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_197_ComplI,axiom,
% 3.26/1.79 ! [A: $tType,C2: A,A3: set @ A] :
% 3.26/1.79 ( ~ ( member @ A @ C2 @ A3 )
% 3.26/1.79 => ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A3 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_198_add_Oinverse__neutral,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( group_add @ A )
% 3.26/1.79 => ( ( uminus_uminus @ A @ ( zero_zero @ A ) )
% 3.26/1.79 = ( zero_zero @ A ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_199_neg__0__equal__iff__equal,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( group_add @ A )
% 3.26/1.79 => ! [A2: A] :
% 3.26/1.79 ( ( ( zero_zero @ A )
% 3.26/1.79 = ( uminus_uminus @ A @ A2 ) )
% 3.26/1.79 = ( ( zero_zero @ A )
% 3.26/1.79 = A2 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_200_neg__equal__0__iff__equal,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( group_add @ A )
% 3.26/1.79 => ! [A2: A] :
% 3.26/1.79 ( ( ( uminus_uminus @ A @ A2 )
% 3.26/1.79 = ( zero_zero @ A ) )
% 3.26/1.79 = ( A2
% 3.26/1.79 = ( zero_zero @ A ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_201_equal__neg__zero,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( linord219039673up_add @ A )
% 3.26/1.79 => ! [A2: A] :
% 3.26/1.79 ( ( A2
% 3.26/1.79 = ( uminus_uminus @ A @ A2 ) )
% 3.26/1.79 = ( A2
% 3.26/1.79 = ( zero_zero @ A ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_202_neg__equal__zero,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( linord219039673up_add @ A )
% 3.26/1.79 => ! [A2: A] :
% 3.26/1.79 ( ( ( uminus_uminus @ A @ A2 )
% 3.26/1.79 = A2 )
% 3.26/1.79 = ( A2
% 3.26/1.79 = ( zero_zero @ A ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_203_Uvariation__Vagree,axiom,
% 3.26/1.79 ! [Nu: variable > real,Nu2: variable > real,V: set @ variable] :
% 3.26/1.79 ( ( denota1419872369iation @ Nu @ Nu2 @ ( uminus_uminus @ ( set @ variable ) @ V ) )
% 3.26/1.79 = ( denotational_Vagree @ Nu @ Nu2 @ V ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_204_minus__equation__iff,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( group_add @ A )
% 3.26/1.79 => ! [A2: A,B3: A] :
% 3.26/1.79 ( ( ( uminus_uminus @ A @ A2 )
% 3.26/1.79 = B3 )
% 3.26/1.79 = ( ( uminus_uminus @ A @ B3 )
% 3.26/1.79 = A2 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_205_equation__minus__iff,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( group_add @ A )
% 3.26/1.79 => ! [A2: A,B3: A] :
% 3.26/1.79 ( ( A2
% 3.26/1.79 = ( uminus_uminus @ A @ B3 ) )
% 3.26/1.79 = ( B3
% 3.26/1.79 = ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_206_fun__Compl__def,axiom,
% 3.26/1.79 ! [B: $tType,A: $tType] :
% 3.26/1.79 ( ( uminus @ B )
% 3.26/1.79 => ( ( uminus_uminus @ ( A > B ) )
% 3.26/1.79 = ( ^ [A5: A > B,X2: A] : ( uminus_uminus @ B @ ( A5 @ X2 ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_207_double__complement,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A] :
% 3.26/1.79 ( ( uminus_uminus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A3 ) )
% 3.26/1.79 = A3 ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_208_ComplD,axiom,
% 3.26/1.79 ! [A: $tType,C2: A,A3: set @ A] :
% 3.26/1.79 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A3 ) )
% 3.26/1.79 => ~ ( member @ A @ C2 @ A3 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_209_Timeso_Osimps_I2_J,axiom,
% 3.26/1.79 ! [Eta: option @ trm] :
% 3.26/1.79 ( ( uSubst277968634Timeso @ ( none @ trm ) @ Eta )
% 3.26/1.79 = ( none @ trm ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_210_Timeso__undef,axiom,
% 3.26/1.79 ! [Theta: option @ trm,Eta: option @ trm] :
% 3.26/1.79 ( ( ( uSubst277968634Timeso @ Theta @ Eta )
% 3.26/1.79 = ( none @ trm ) )
% 3.26/1.79 = ( ( Theta
% 3.26/1.79 = ( none @ trm ) )
% 3.26/1.79 | ( Eta
% 3.26/1.79 = ( none @ trm ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_211_selectlike__equal__cocond__corule,axiom,
% 3.26/1.79 ! [Nu: variable > real,V: set @ variable,X6: set @ ( variable > real ),Y4: set @ ( variable > real )] :
% 3.26/1.79 ( ! [Mu2: variable > real] :
% 3.26/1.79 ( ( denota1419872369iation @ Mu2 @ Nu @ V )
% 3.26/1.79 => ( ( member @ ( variable > real ) @ Mu2 @ X6 )
% 3.26/1.79 = ( member @ ( variable > real ) @ Mu2 @ Y4 ) ) )
% 3.26/1.79 => ( ( static_selectlike @ X6 @ Nu @ ( uminus_uminus @ ( set @ variable ) @ V ) )
% 3.26/1.79 = ( static_selectlike @ Y4 @ Nu @ ( uminus_uminus @ ( set @ variable ) @ V ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_212_selectlike__equal__cocond__rule,axiom,
% 3.26/1.79 ! [Nu: variable > real,V: set @ variable,X6: set @ ( variable > real ),Y4: set @ ( variable > real )] :
% 3.26/1.79 ( ! [Mu2: variable > real] :
% 3.26/1.79 ( ( denota1419872369iation @ Mu2 @ Nu @ ( uminus_uminus @ ( set @ variable ) @ V ) )
% 3.26/1.79 => ( ( member @ ( variable > real ) @ Mu2 @ X6 )
% 3.26/1.79 = ( member @ ( variable > real ) @ Mu2 @ Y4 ) ) )
% 3.26/1.79 => ( ( static_selectlike @ X6 @ Nu @ V )
% 3.26/1.79 = ( static_selectlike @ Y4 @ Nu @ V ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_213_selectlike__equal__cocond,axiom,
% 3.26/1.79 ! [X6: set @ ( variable > real ),Nu: variable > real,V: set @ variable,Y4: set @ ( variable > real )] :
% 3.26/1.79 ( ( ( static_selectlike @ X6 @ Nu @ ( uminus_uminus @ ( set @ variable ) @ V ) )
% 3.26/1.79 = ( static_selectlike @ Y4 @ Nu @ ( uminus_uminus @ ( set @ variable ) @ V ) ) )
% 3.26/1.79 = ( ! [Mu3: variable > real] :
% 3.26/1.79 ( ( denota1419872369iation @ Mu3 @ Nu @ V )
% 3.26/1.79 => ( ( member @ ( variable > real ) @ Mu3 @ X6 )
% 3.26/1.79 = ( member @ ( variable > real ) @ Mu3 @ Y4 ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_214_selectlike__equal__cond,axiom,
% 3.26/1.79 ! [X6: set @ ( variable > real ),Nu: variable > real,V: set @ variable,Y4: set @ ( variable > real )] :
% 3.26/1.79 ( ( ( static_selectlike @ X6 @ Nu @ V )
% 3.26/1.79 = ( static_selectlike @ Y4 @ Nu @ V ) )
% 3.26/1.79 = ( ! [Mu3: variable > real] :
% 3.26/1.79 ( ( denota1419872369iation @ Mu3 @ Nu @ ( uminus_uminus @ ( set @ variable ) @ V ) )
% 3.26/1.79 => ( ( member @ ( variable > real ) @ Mu3 @ X6 )
% 3.26/1.79 = ( member @ ( variable > real ) @ Mu3 @ Y4 ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_215_stateinterpol__insert,axiom,
% 3.26/1.79 ! [V4: variable > real,W2: variable > real,S: set @ variable,Z: variable] : ( denotational_Vagree @ ( stateinterpol @ V4 @ W2 @ S ) @ ( stateinterpol @ V4 @ W2 @ ( insert @ variable @ Z @ S ) ) @ ( uminus_uminus @ ( set @ variable ) @ ( insert @ variable @ Z @ ( bot_bot @ ( set @ variable ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_216_Timeso_Oelims,axiom,
% 3.26/1.79 ! [X: option @ trm,Xa: option @ trm,Y: option @ trm] :
% 3.26/1.79 ( ( ( uSubst277968634Timeso @ X @ Xa )
% 3.26/1.79 = Y )
% 3.26/1.79 => ( ! [Theta2: trm] :
% 3.26/1.79 ( ( X
% 3.26/1.79 = ( some @ trm @ Theta2 ) )
% 3.26/1.79 => ! [Eta2: trm] :
% 3.26/1.79 ( ( Xa
% 3.26/1.79 = ( some @ trm @ Eta2 ) )
% 3.26/1.79 => ( Y
% 3.26/1.79 != ( some @ trm @ ( times @ Theta2 @ Eta2 ) ) ) ) )
% 3.26/1.79 => ( ( ( X
% 3.26/1.79 = ( none @ trm ) )
% 3.26/1.79 => ( Y
% 3.26/1.79 != ( none @ trm ) ) )
% 3.26/1.79 => ~ ( ? [V2: trm] :
% 3.26/1.79 ( X
% 3.26/1.79 = ( some @ trm @ V2 ) )
% 3.26/1.79 => ( ( Xa
% 3.26/1.79 = ( none @ trm ) )
% 3.26/1.79 => ( Y
% 3.26/1.79 != ( none @ trm ) ) ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_217_trm_Oinject_I6_J,axiom,
% 3.26/1.79 ! [X61: trm,X62: trm,Y61: trm,Y62: trm] :
% 3.26/1.79 ( ( ( times @ X61 @ X62 )
% 3.26/1.79 = ( times @ Y61 @ Y62 ) )
% 3.26/1.79 = ( ( X61 = Y61 )
% 3.26/1.79 & ( X62 = Y62 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_218_stateinterpol__left,axiom,
% 3.26/1.79 ! [X: variable,S: set @ variable,Nu: variable > real,Omega: variable > real] :
% 3.26/1.79 ( ( member @ variable @ X @ S )
% 3.26/1.79 => ( ( stateinterpol @ Nu @ Omega @ S @ X )
% 3.26/1.79 = ( Nu @ X ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_219_stateinterpol__right,axiom,
% 3.26/1.79 ! [X: variable,S: set @ variable,Nu: variable > real,Omega: variable > real] :
% 3.26/1.79 ( ~ ( member @ variable @ X @ S )
% 3.26/1.79 => ( ( stateinterpol @ Nu @ Omega @ S @ X )
% 3.26/1.79 = ( Omega @ X ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_220_selectlike__co__selectlike,axiom,
% 3.26/1.79 ! [X6: set @ ( variable > real ),Nu: variable > real,V: set @ variable] :
% 3.26/1.79 ( ( static_selectlike @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ ( static_selectlike @ X6 @ Nu @ V ) ) @ Nu @ V )
% 3.26/1.79 = ( static_selectlike @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ X6 ) @ Nu @ V ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_221_stateinterpol__empty,axiom,
% 3.26/1.79 ! [Nu: variable > real,Omega: variable > real] :
% 3.26/1.79 ( ( stateinterpol @ Nu @ Omega @ ( bot_bot @ ( set @ variable ) ) )
% 3.26/1.79 = Omega ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_222_Vagree__stateinterpol,axiom,
% 3.26/1.79 ! [Nu: variable > real,Omega: variable > real,S: set @ variable] : ( denotational_Vagree @ ( stateinterpol @ Nu @ Omega @ S ) @ Nu @ S ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_223_stateinterpol__def,axiom,
% 3.26/1.79 ( stateinterpol
% 3.26/1.79 = ( ^ [Nu3: variable > real,Omega2: variable > real,S2: set @ variable,X2: variable] : ( if @ real @ ( member @ variable @ X2 @ S2 ) @ ( Nu3 @ X2 ) @ ( Omega2 @ X2 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_224_usubstappt__times__conv,axiom,
% 3.26/1.79 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,Eta: trm] :
% 3.26/1.79 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 3.26/1.79 != ( none @ trm ) )
% 3.26/1.79 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 3.26/1.79 != ( none @ trm ) )
% 3.26/1.79 & ( ( uSubst95898992stappt @ Sigma @ U @ Eta )
% 3.26/1.79 != ( none @ trm ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_225_usubstappt_Osimps_I6_J,axiom,
% 3.26/1.79 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,Eta: trm] :
% 3.26/1.79 ( ( uSubst95898992stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 3.26/1.79 = ( uSubst277968634Timeso @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) @ ( uSubst95898992stappt @ Sigma @ U @ Eta ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_226_Timeso_Osimps_I1_J,axiom,
% 3.26/1.79 ! [Theta: trm,Eta: trm] :
% 3.26/1.79 ( ( uSubst277968634Timeso @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta ) )
% 3.26/1.79 = ( some @ trm @ ( times @ Theta @ Eta ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_227_stateinterpol__diff,axiom,
% 3.26/1.79 ! [Nu: variable > real,Omega: variable > real] :
% 3.26/1.79 ( ( stateinterpol @ Nu @ Omega @ ( statediff @ Nu @ Omega ) )
% 3.26/1.79 = Nu ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_228_stateinterpol__FVT,axiom,
% 3.26/1.79 ! [Z: variable,T3: trm,I2: denotational_interp,Omega: variable > real,Omega3: variable > real,S: set @ variable] :
% 3.26/1.79 ( ~ ( member @ variable @ Z @ ( static_FVT @ T3 ) )
% 3.26/1.79 => ( ( denota1863255036rm_sem @ I2 @ T3 @ ( stateinterpol @ Omega @ Omega3 @ S ) )
% 3.26/1.79 = ( denota1863255036rm_sem @ I2 @ T3 @ ( stateinterpol @ Omega @ Omega3 @ ( insert @ variable @ Z @ S ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_229_nostatediff,axiom,
% 3.26/1.79 ! [X: variable,Nu: variable > real,Omega: variable > real] :
% 3.26/1.79 ( ~ ( member @ variable @ X @ ( statediff @ Nu @ Omega ) )
% 3.26/1.79 => ( ( Nu @ X )
% 3.26/1.79 = ( Omega @ X ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_230_coincidence__term,axiom,
% 3.26/1.79 ! [Omega: variable > real,Omega3: variable > real,Theta: trm,I2: denotational_interp] :
% 3.26/1.79 ( ( denotational_Vagree @ Omega @ Omega3 @ ( static_FVT @ Theta ) )
% 3.26/1.79 => ( ( denota1863255036rm_sem @ I2 @ Theta @ Omega )
% 3.26/1.79 = ( denota1863255036rm_sem @ I2 @ Theta @ Omega3 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_231_coincidence__term__cor,axiom,
% 3.26/1.79 ! [Omega: variable > real,Omega3: variable > real,U: set @ variable,Theta: trm,I2: denotational_interp] :
% 3.26/1.79 ( ( denota1419872369iation @ Omega @ Omega3 @ U )
% 3.26/1.79 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ Theta ) @ U )
% 3.26/1.79 = ( bot_bot @ ( set @ variable ) ) )
% 3.26/1.79 => ( ( denota1863255036rm_sem @ I2 @ Theta @ Omega )
% 3.26/1.79 = ( denota1863255036rm_sem @ I2 @ Theta @ Omega3 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_232_Vagree__statediff,axiom,
% 3.26/1.79 ! [Omega: variable > real,Omega3: variable > real,S: set @ variable] :
% 3.26/1.79 ( ( denotational_Vagree @ Omega @ Omega3 @ S )
% 3.26/1.79 => ( ord_less_eq @ ( set @ variable ) @ ( statediff @ Omega @ Omega3 ) @ ( uminus_uminus @ ( set @ variable ) @ S ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_233_order__refl,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( preorder @ A )
% 3.26/1.79 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_234_subsetI,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 3.26/1.79 ( ! [X3: A] :
% 3.26/1.79 ( ( member @ A @ X3 @ A3 )
% 3.26/1.79 => ( member @ A @ X3 @ B2 ) )
% 3.26/1.79 => ( ord_less_eq @ ( set @ A ) @ A3 @ B2 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_235_subset__antisym,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 3.26/1.79 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 3.26/1.79 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ A3 )
% 3.26/1.79 => ( A3 = B2 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_236_inf__apply,axiom,
% 3.26/1.79 ! [B: $tType,A: $tType] :
% 3.26/1.79 ( ( semilattice_inf @ B )
% 3.26/1.79 => ( ( inf_inf @ ( A > B ) )
% 3.26/1.79 = ( ^ [F: A > B,G: A > B,X2: A] : ( inf_inf @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_237_inf_Oidem,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( semilattice_inf @ A )
% 3.26/1.79 => ! [A2: A] :
% 3.26/1.79 ( ( inf_inf @ A @ A2 @ A2 )
% 3.26/1.79 = A2 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_238_inf__idem,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( semilattice_inf @ A )
% 3.26/1.79 => ! [X: A] :
% 3.26/1.79 ( ( inf_inf @ A @ X @ X )
% 3.26/1.79 = X ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_239_inf_Oleft__idem,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( semilattice_inf @ A )
% 3.26/1.79 => ! [A2: A,B3: A] :
% 3.26/1.79 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B3 ) )
% 3.26/1.79 = ( inf_inf @ A @ A2 @ B3 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_240_inf__left__idem,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( semilattice_inf @ A )
% 3.26/1.79 => ! [X: A,Y: A] :
% 3.26/1.79 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 3.26/1.79 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_241_inf_Oright__idem,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( semilattice_inf @ A )
% 3.26/1.79 => ! [A2: A,B3: A] :
% 3.26/1.79 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B3 ) @ B3 )
% 3.26/1.79 = ( inf_inf @ A @ A2 @ B3 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_242_inf__right__idem,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( semilattice_inf @ A )
% 3.26/1.79 => ! [X: A,Y: A] :
% 3.26/1.79 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Y )
% 3.26/1.79 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_243_IntI,axiom,
% 3.26/1.79 ! [A: $tType,C2: A,A3: set @ A,B2: set @ A] :
% 3.26/1.79 ( ( member @ A @ C2 @ A3 )
% 3.26/1.79 => ( ( member @ A @ C2 @ B2 )
% 3.26/1.79 => ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B2 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_244_Int__iff,axiom,
% 3.26/1.79 ! [A: $tType,C2: A,A3: set @ A,B2: set @ A] :
% 3.26/1.79 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B2 ) )
% 3.26/1.79 = ( ( member @ A @ C2 @ A3 )
% 3.26/1.79 & ( member @ A @ C2 @ B2 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_245_le__zero__eq,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( canoni770627133id_add @ A )
% 3.26/1.79 => ! [N: A] :
% 3.26/1.79 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 3.26/1.79 = ( N
% 3.26/1.79 = ( zero_zero @ A ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_246_neg__le__iff__le,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( ordered_ab_group_add @ A )
% 3.26/1.79 => ! [B3: A,A2: A] :
% 3.26/1.79 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ B3 ) @ ( uminus_uminus @ A @ A2 ) )
% 3.26/1.79 = ( ord_less_eq @ A @ A2 @ B3 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_247_compl__le__compl__iff,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( boolean_algebra @ A )
% 3.26/1.79 => ! [X: A,Y: A] :
% 3.26/1.79 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ X ) @ ( uminus_uminus @ A @ Y ) )
% 3.26/1.79 = ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_248_le__inf__iff,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( semilattice_inf @ A )
% 3.26/1.79 => ! [X: A,Y: A,Z: A] :
% 3.26/1.79 ( ( ord_less_eq @ A @ X @ ( inf_inf @ A @ Y @ Z ) )
% 3.26/1.79 = ( ( ord_less_eq @ A @ X @ Y )
% 3.26/1.79 & ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_249_inf_Obounded__iff,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( semilattice_inf @ A )
% 3.26/1.79 => ! [A2: A,B3: A,C2: A] :
% 3.26/1.79 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B3 @ C2 ) )
% 3.26/1.79 = ( ( ord_less_eq @ A @ A2 @ B3 )
% 3.26/1.79 & ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_250_le__sup__iff,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( semilattice_sup @ A )
% 3.26/1.79 => ! [X: A,Y: A,Z: A] :
% 3.26/1.79 ( ( ord_less_eq @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 3.26/1.79 = ( ( ord_less_eq @ A @ X @ Z )
% 3.26/1.79 & ( ord_less_eq @ A @ Y @ Z ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_251_sup_Obounded__iff,axiom,
% 3.26/1.79 ! [A: $tType] :
% 3.26/1.79 ( ( semilattice_sup @ A )
% 3.26/1.79 => ! [B3: A,C2: A,A2: A] :
% 3.26/1.79 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C2 ) @ A2 )
% 3.26/1.79 = ( ( ord_less_eq @ A @ B3 @ A2 )
% 3.26/1.79 & ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_252_empty__subsetI,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A3 ) ).
% 3.26/1.79
% 3.26/1.79 thf(fact_253_subset__empty,axiom,
% 3.26/1.79 ! [A: $tType,A3: set @ A] :
% 3.26/1.79 ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 3.26/1.79 = ( A3
% 3.26/1.79 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 3.26/1.79 bounded_lattice @ $o ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 3.26/1.79 ! [A7: $tType] : ( bounded_lattice @ ( set @ A7 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 3.26/1.79 ! [A7: $tType,A8: $tType] :
% 3.26/1.79 ( ( bounded_lattice @ A8 )
% 3.26/1.79 => ( bounded_lattice @ ( A7 > A8 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 3.26/1.79 ! [A7: $tType,A8: $tType] :
% 3.26/1.79 ( ( bounded_lattice @ A8 )
% 3.26/1.79 => ( bounde1808546759up_bot @ ( A7 > A8 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 3.26/1.79 ! [A7: $tType,A8: $tType] :
% 3.26/1.79 ( ( semilattice_sup @ A8 )
% 3.26/1.79 => ( semilattice_sup @ ( A7 > A8 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 3.26/1.79 ! [A7: $tType,A8: $tType] :
% 3.26/1.79 ( ( semilattice_inf @ A8 )
% 3.26/1.79 => ( semilattice_inf @ ( A7 > A8 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 3.26/1.79 ! [A7: $tType,A8: $tType] :
% 3.26/1.79 ( ( boolean_algebra @ A8 )
% 3.26/1.79 => ( boolean_algebra @ ( A7 > A8 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_fun___Orderings_Opreorder,axiom,
% 3.26/1.79 ! [A7: $tType,A8: $tType] :
% 3.26/1.79 ( ( preorder @ A8 )
% 3.26/1.79 => ( preorder @ ( A7 > A8 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_fun___Lattices_Olattice,axiom,
% 3.26/1.79 ! [A7: $tType,A8: $tType] :
% 3.26/1.79 ( ( lattice @ A8 )
% 3.26/1.79 => ( lattice @ ( A7 > A8 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_fun___Orderings_Obot,axiom,
% 3.26/1.79 ! [A7: $tType,A8: $tType] :
% 3.26/1.79 ( ( bot @ A8 )
% 3.26/1.79 => ( bot @ ( A7 > A8 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_fun___Groups_Ouminus,axiom,
% 3.26/1.79 ! [A7: $tType,A8: $tType] :
% 3.26/1.79 ( ( uminus @ A8 )
% 3.26/1.79 => ( uminus @ ( A7 > A8 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 3.26/1.79 canoni770627133id_add @ nat ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Nat_Onat___Lattices_Osemilattice__sup_3,axiom,
% 3.26/1.79 semilattice_sup @ nat ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Nat_Onat___Lattices_Osemilattice__inf_4,axiom,
% 3.26/1.79 semilattice_inf @ nat ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Nat_Onat___Orderings_Opreorder_5,axiom,
% 3.26/1.79 preorder @ nat ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Nat_Onat___Lattices_Olattice_6,axiom,
% 3.26/1.79 lattice @ nat ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Nat_Onat___Orderings_Obot_7,axiom,
% 3.26/1.79 bot @ nat ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 3.26/1.79 zero @ nat ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_8,axiom,
% 3.26/1.79 ! [A7: $tType] : ( bounde1808546759up_bot @ ( set @ A7 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_9,axiom,
% 3.26/1.79 ! [A7: $tType] : ( semilattice_sup @ ( set @ A7 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_10,axiom,
% 3.26/1.79 ! [A7: $tType] : ( semilattice_inf @ ( set @ A7 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_11,axiom,
% 3.26/1.79 ! [A7: $tType] : ( boolean_algebra @ ( set @ A7 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Set_Oset___Orderings_Opreorder_12,axiom,
% 3.26/1.79 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Set_Oset___Lattices_Olattice_13,axiom,
% 3.26/1.79 ! [A7: $tType] : ( lattice @ ( set @ A7 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Set_Oset___Orderings_Obot_14,axiom,
% 3.26/1.79 ! [A7: $tType] : ( bot @ ( set @ A7 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Set_Oset___Groups_Ouminus_15,axiom,
% 3.26/1.79 ! [A7: $tType] : ( uminus @ ( set @ A7 ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Set_Oset___Groups_Ozero_16,axiom,
% 3.26/1.79 ! [A7: $tType] :
% 3.26/1.79 ( ( zero @ A7 )
% 3.26/1.79 => ( zero @ ( set @ A7 ) ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_17,axiom,
% 3.26/1.79 bounde1808546759up_bot @ $o ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_18,axiom,
% 3.26/1.79 semilattice_sup @ $o ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_19,axiom,
% 3.26/1.79 semilattice_inf @ $o ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_20,axiom,
% 3.26/1.79 boolean_algebra @ $o ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_HOL_Obool___Orderings_Opreorder_21,axiom,
% 3.26/1.79 preorder @ $o ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_HOL_Obool___Lattices_Olattice_22,axiom,
% 3.26/1.79 lattice @ $o ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_HOL_Obool___Orderings_Obot_23,axiom,
% 3.26/1.79 bot @ $o ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_HOL_Obool___Groups_Ouminus_24,axiom,
% 3.26/1.79 uminus @ $o ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add,axiom,
% 3.26/1.79 linord219039673up_add @ real ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add,axiom,
% 3.26/1.79 ordered_ab_group_add @ real ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Real_Oreal___Lattices_Osemilattice__sup_25,axiom,
% 3.26/1.79 semilattice_sup @ real ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Real_Oreal___Lattices_Osemilattice__inf_26,axiom,
% 3.26/1.79 semilattice_inf @ real ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Real_Oreal___Orderings_Opreorder_27,axiom,
% 3.26/1.79 preorder @ real ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Real_Oreal___Lattices_Olattice_28,axiom,
% 3.26/1.79 lattice @ real ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Real_Oreal___Groups_Ogroup__add,axiom,
% 3.26/1.79 group_add @ real ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Real_Oreal___Groups_Ouminus_29,axiom,
% 3.26/1.79 uminus @ real ).
% 3.26/1.79
% 3.26/1.79 thf(tcon_Real_Oreal___Groups_Ozero_30,axiom,
% 3.26/1.79 zero @ real ).
% 3.26/1.79
% 3.26/1.79 thf(help_If_3_1_T,axiom,
% 3.26/1.79 ! [P: $o] :
% 3.26/1.79 ( ( P = $true )
% 3.26/1.79 | ( P = $false ) ) ).
% 3.26/1.79
% 3.26/1.79 thf(help_If_2_1_T,axiom,
% 3.26/1.79 ! [A: $tType,X: A,Y: A] :
% 3.26/1.79 ( ( if @ A @ $false @ X @ Y )
% 3.26/1.79 = Y ) ).
% 3.26/1.79
% 3.26/1.79 thf(help_If_1_1_T,axiom,
% 3.26/1.79 ! [A: $tType,X: A,Y: A] :
% 3.26/1.79 ( ( if @ A @ $true @ X @ Y )
% 3.26/1.79 = X ) ).
% 3.26/1.79
% 3.26/1.79 thf(conj_0,conjecture,
% 3.26/1.79 denota1419872369iation @ ( f @ ( zero_zero @ real ) ) @ omega @ ( sup_sup @ ( set @ variable ) @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) @ u ) ).
% 3.26/1.79 ------------------------
% 3.36/1.83 % (7539)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7422 for (2999ds/2Mi)
% 3.36/1.83 % (7538)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_7422 for (2999ds/27Mi)
% 3.36/1.83 % (7537)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_7422 for (2999ds/4Mi)
% 3.36/1.83 % (7540)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_7422 for (2999ds/2Mi)
% 3.36/1.83 % (7536)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7422 for (2999ds/183Mi)
% 3.36/1.83 % (7541)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_7422 for (2999ds/275Mi)
% 3.36/1.83 % (7542)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7422 for (2999ds/18Mi)
% 3.36/1.83 % (7539)Instruction limit reached!
% 3.36/1.83 % (7539)------------------------------
% 3.36/1.83 % (7539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.83 % (7539)Termination reason: Unknown
% 3.36/1.83 % (7539)Termination phase: shuffling
% 3.36/1.83 % (7540)Instruction limit reached!
% 3.36/1.83 % (7540)------------------------------
% 3.36/1.83 % (7540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.83
% 3.36/1.83 % (7539)Memory used [KB]: 1407
% 3.36/1.83 % (7539)Time elapsed: 0.003 s
% 3.36/1.83 % (7539)Instructions burned: 2 (million)
% 3.36/1.83 % (7539)------------------------------
% 3.36/1.83 % (7539)------------------------------
% 3.36/1.83 % (7540)Termination reason: Unknown
% 3.36/1.83 % (7540)Termination phase: shuffling
% 3.36/1.83
% 3.36/1.83 % (7540)Memory used [KB]: 1407
% 3.36/1.83 % (7540)Time elapsed: 0.003 s
% 3.36/1.83 % (7540)Instructions burned: 3 (million)
% 3.36/1.83 % (7540)------------------------------
% 3.36/1.83 % (7540)------------------------------
% 3.36/1.83 % (7537)Instruction limit reached!
% 3.36/1.83 % (7537)------------------------------
% 3.36/1.83 % (7537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.83 % (7537)Termination reason: Unknown
% 3.36/1.83 % (7537)Termination phase: shuffling
% 3.36/1.83
% 3.36/1.83 % (7537)Memory used [KB]: 1407
% 3.36/1.83 % (7537)Time elapsed: 0.004 s
% 3.36/1.83 % (7537)Instructions burned: 4 (million)
% 3.36/1.83 % (7537)------------------------------
% 3.36/1.83 % (7537)------------------------------
% 3.36/1.84 % (7542)Instruction limit reached!
% 3.36/1.84 % (7542)------------------------------
% 3.36/1.84 % (7542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.84 % (7542)Termination reason: Unknown
% 3.36/1.84 % (7542)Termination phase: shuffling
% 3.36/1.84
% 3.36/1.84 % (7542)Memory used [KB]: 1663
% 3.36/1.84 % (7542)Time elapsed: 0.012 s
% 3.36/1.84 % (7542)Instructions burned: 19 (million)
% 3.36/1.84 % (7542)------------------------------
% 3.36/1.84 % (7542)------------------------------
% 3.36/1.84 % (7538)Instruction limit reached!
% 3.36/1.84 % (7538)------------------------------
% 3.36/1.84 % (7538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.84 % (7538)Termination reason: Unknown
% 3.36/1.84 % (7538)Termination phase: Property scanning
% 3.36/1.84
% 3.36/1.84 % (7538)Memory used [KB]: 1791
% 3.36/1.84 % (7538)Time elapsed: 0.016 s
% 3.36/1.84 % (7538)Instructions burned: 27 (million)
% 3.36/1.84 % (7538)------------------------------
% 3.36/1.84 % (7538)------------------------------
% 3.36/1.85 % (7543)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7422 for (2999ds/3Mi)
% 3.36/1.85 % (7545)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_7422 for (2999ds/15Mi)
% 3.36/1.85 % (7544)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_7422 for (2999ds/37Mi)
% 3.36/1.85 % (7543)Instruction limit reached!
% 3.36/1.85 % (7543)------------------------------
% 3.36/1.85 % (7543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.85 % (7543)Termination reason: Unknown
% 3.36/1.85 % (7543)Termination phase: shuffling
% 3.36/1.85
% 3.36/1.85 % (7543)Memory used [KB]: 1407
% 3.36/1.85 % (7543)Time elapsed: 0.003 s
% 3.36/1.85 % (7543)Instructions burned: 3 (million)
% 3.36/1.85 % (7543)------------------------------
% 3.36/1.85 % (7543)------------------------------
% 3.36/1.85 % (7545)Instruction limit reached!
% 3.36/1.85 % (7545)------------------------------
% 3.36/1.85 % (7545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.85 % (7545)Termination reason: Unknown
% 3.36/1.85 % (7545)Termination phase: shuffling
% 3.36/1.85
% 3.36/1.85 % (7545)Memory used [KB]: 1535
% 3.36/1.85 % (7545)Time elapsed: 0.010 s
% 3.36/1.85 % (7545)Instructions burned: 15 (million)
% 3.36/1.85 % (7545)------------------------------
% 3.36/1.85 % (7545)------------------------------
% 3.36/1.86 % (7546)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_7422 for (2999ds/3Mi)
% 3.36/1.86 % (7546)Instruction limit reached!
% 3.36/1.86 % (7546)------------------------------
% 3.36/1.86 % (7546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.86 % (7546)Termination reason: Unknown
% 3.36/1.86 % (7546)Termination phase: shuffling
% 3.36/1.86
% 3.36/1.86 % (7546)Memory used [KB]: 1407
% 3.36/1.86 % (7546)Time elapsed: 0.003 s
% 3.36/1.86 % (7546)Instructions burned: 3 (million)
% 3.36/1.86 % (7546)------------------------------
% 3.36/1.86 % (7546)------------------------------
% 3.36/1.86 % (7547)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_7422 for (2999ds/1041Mi)
% 3.36/1.86 % (7544)Instruction limit reached!
% 3.36/1.86 % (7544)------------------------------
% 3.36/1.86 % (7544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.86 % (7544)Termination reason: Unknown
% 3.36/1.87 % (7544)Termination phase: shuffling
% 3.36/1.87
% 3.36/1.87 % (7544)Memory used [KB]: 2174
% 3.36/1.87 % (7544)Time elapsed: 0.020 s
% 3.36/1.87 % (7544)Instructions burned: 37 (million)
% 3.36/1.87 % (7544)------------------------------
% 3.36/1.87 % (7544)------------------------------
% 3.36/1.87 % (7548)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7422 for (2999ds/7Mi)
% 3.36/1.87 % (7548)Instruction limit reached!
% 3.36/1.87 % (7548)------------------------------
% 3.36/1.87 % (7548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.87 % (7548)Termination reason: Unknown
% 3.36/1.87 % (7548)Termination phase: shuffling
% 3.36/1.87
% 3.36/1.87 % (7548)Memory used [KB]: 1407
% 3.36/1.87 % (7548)Time elapsed: 0.006 s
% 3.36/1.87 % (7548)Instructions burned: 8 (million)
% 3.36/1.87 % (7548)------------------------------
% 3.36/1.87 % (7548)------------------------------
% 3.36/1.87 % (7549)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7422 for (2999ds/16Mi)
% 3.36/1.87 % (7541)Refutation not found, incomplete strategy
% 3.36/1.87 % (7541)------------------------------
% 3.36/1.87 % (7541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.87 % (7541)Termination reason: Refutation not found, incomplete strategy
% 3.36/1.87
% 3.36/1.87
% 3.36/1.87 % (7541)Memory used [KB]: 6652
% 3.36/1.87 % (7541)Time elapsed: 0.048 s
% 3.36/1.87 % (7541)Instructions burned: 84 (million)
% 3.36/1.87 % (7541)------------------------------
% 3.36/1.87 % (7541)------------------------------
% 3.36/1.87 % (7550)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_7422 for (2999ds/3Mi)
% 3.36/1.88 % (7550)Instruction limit reached!
% 3.36/1.88 % (7550)------------------------------
% 3.36/1.88 % (7550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.88 % (7550)Termination reason: Unknown
% 3.36/1.88 % (7550)Termination phase: shuffling
% 3.36/1.88
% 3.36/1.88 % (7550)Memory used [KB]: 1407
% 3.36/1.88 % (7550)Time elapsed: 0.004 s
% 3.36/1.88 % (7550)Instructions burned: 4 (million)
% 3.36/1.88 % (7550)------------------------------
% 3.36/1.88 % (7550)------------------------------
% 3.36/1.88 % (7549)Instruction limit reached!
% 3.36/1.88 % (7549)------------------------------
% 3.36/1.88 % (7549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.88 % (7549)Termination reason: Unknown
% 3.36/1.88 % (7549)Termination phase: shuffling
% 3.36/1.88
% 3.36/1.88 % (7549)Memory used [KB]: 1663
% 3.36/1.88 % (7549)Time elapsed: 0.010 s
% 3.36/1.88 % (7549)Instructions burned: 16 (million)
% 3.36/1.88 % (7549)------------------------------
% 3.36/1.88 % (7549)------------------------------
% 3.36/1.88 % (7551)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_7422 for (2999ds/3Mi)
% 3.36/1.88 % (7551)Instruction limit reached!
% 3.36/1.88 % (7551)------------------------------
% 3.36/1.88 % (7551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.88 % (7551)Termination reason: Unknown
% 3.36/1.88 % (7551)Termination phase: shuffling
% 3.36/1.88
% 3.36/1.88 % (7551)Memory used [KB]: 1407
% 3.36/1.88 % (7551)Time elapsed: 0.003 s
% 3.36/1.88 % (7551)Instructions burned: 3 (million)
% 3.36/1.88 % (7551)------------------------------
% 3.36/1.88 % (7551)------------------------------
% 3.36/1.89 % (7552)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7422 for (2999ds/7Mi)
% 3.36/1.89 % (7553)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7422 for (2999ds/3Mi)
% 3.36/1.89 % (7552)Instruction limit reached!
% 3.36/1.89 % (7552)------------------------------
% 3.36/1.89 % (7552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.89 % (7552)Termination reason: Unknown
% 3.36/1.89 % (7552)Termination phase: shuffling
% 3.36/1.89
% 3.36/1.89 % (7552)Memory used [KB]: 1407
% 3.36/1.89 % (7552)Time elapsed: 0.006 s
% 3.36/1.89 % (7552)Instructions burned: 7 (million)
% 3.36/1.89 % (7552)------------------------------
% 3.36/1.89 % (7552)------------------------------
% 3.36/1.89 % (7553)Instruction limit reached!
% 3.36/1.89 % (7553)------------------------------
% 3.36/1.89 % (7553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.89 % (7553)Termination reason: Unknown
% 3.36/1.89 % (7553)Termination phase: shuffling
% 3.36/1.89
% 3.36/1.89 % (7553)Memory used [KB]: 1407
% 3.36/1.89 % (7553)Time elapsed: 0.004 s
% 3.36/1.89 % (7553)Instructions burned: 4 (million)
% 3.36/1.89 % (7553)------------------------------
% 3.36/1.89 % (7553)------------------------------
% 3.36/1.89 % (7554)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7422 for (2999ds/4Mi)
% 3.36/1.90 % (7554)Instruction limit reached!
% 3.36/1.90 % (7554)------------------------------
% 3.36/1.90 % (7554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.90 % (7554)Termination reason: Unknown
% 3.36/1.90 % (7554)Termination phase: shuffling
% 3.36/1.90
% 3.36/1.90 % (7554)Memory used [KB]: 1407
% 3.36/1.90 % (7554)Time elapsed: 0.004 s
% 3.36/1.90 % (7554)Instructions burned: 4 (million)
% 3.36/1.90 % (7554)------------------------------
% 3.36/1.90 % (7554)------------------------------
% 3.36/1.90 % (7555)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7422 for (2999ds/18Mi)
% 3.36/1.90 % (7556)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7422 for (2999ds/710Mi)
% 3.36/1.91 % (7555)Instruction limit reached!
% 3.36/1.91 % (7555)------------------------------
% 3.36/1.91 % (7555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.91 % (7555)Termination reason: Unknown
% 3.36/1.91 % (7555)Termination phase: shuffling
% 3.36/1.91
% 3.36/1.91 % (7555)Memory used [KB]: 1663
% 3.36/1.91 % (7555)Time elapsed: 0.011 s
% 3.36/1.91 % (7555)Instructions burned: 18 (million)
% 3.36/1.91 % (7555)------------------------------
% 3.36/1.91 % (7555)------------------------------
% 3.36/1.91 % (7557)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7422 for (2999ds/6Mi)
% 3.36/1.91 % (7558)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_7422 for (2999ds/902Mi)
% 3.36/1.91 % (7557)Instruction limit reached!
% 3.36/1.91 % (7557)------------------------------
% 3.36/1.91 % (7557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.91 % (7557)Termination reason: Unknown
% 3.36/1.91 % (7557)Termination phase: shuffling
% 3.36/1.91
% 3.36/1.91 % (7557)Memory used [KB]: 1407
% 3.36/1.91 % (7557)Time elapsed: 0.005 s
% 3.36/1.91 % (7557)Instructions burned: 6 (million)
% 3.36/1.91 % (7559)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_7422 for (2999ds/21Mi)
% 3.36/1.91 % (7557)------------------------------
% 3.36/1.91 % (7557)------------------------------
% 3.36/1.92 % (7536)Instruction limit reached!
% 3.36/1.92 % (7536)------------------------------
% 3.36/1.92 % (7536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.92 % (7536)Termination reason: Unknown
% 3.36/1.92 % (7536)Termination phase: Saturation
% 3.36/1.92
% 3.36/1.92 % (7536)Memory used [KB]: 7164
% 3.36/1.92 % (7536)Time elapsed: 0.098 s
% 3.36/1.92 % (7536)Instructions burned: 183 (million)
% 3.36/1.92 % (7536)------------------------------
% 3.36/1.92 % (7536)------------------------------
% 3.36/1.93 % (7559)Instruction limit reached!
% 3.36/1.93 % (7559)------------------------------
% 3.36/1.93 % (7559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.93 % (7559)Termination reason: Unknown
% 3.36/1.93 % (7559)Termination phase: shuffling
% 3.36/1.93
% 3.36/1.93 % (7559)Memory used [KB]: 1791
% 3.36/1.93 % (7559)Time elapsed: 0.014 s
% 3.36/1.93 % (7559)Instructions burned: 22 (million)
% 3.36/1.93 % (7559)------------------------------
% 3.36/1.93 % (7559)------------------------------
% 3.36/1.93 % (7560)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7422 for (2998ds/5Mi)
% 3.36/1.93 % (7560)Instruction limit reached!
% 3.36/1.93 % (7560)------------------------------
% 3.36/1.93 % (7560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.93 % (7560)Termination reason: Unknown
% 3.36/1.93 % (7560)Termination phase: shuffling
% 3.36/1.93
% 3.36/1.93 % (7560)Memory used [KB]: 1407
% 3.36/1.93 % (7560)Time elapsed: 0.005 s
% 3.36/1.93 % (7560)Instructions burned: 6 (million)
% 3.36/1.93 % (7560)------------------------------
% 3.36/1.93 % (7560)------------------------------
% 3.36/1.93 % (7561)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_7422 for (2998ds/6Mi)
% 3.36/1.94 % (7561)Instruction limit reached!
% 3.36/1.94 % (7561)------------------------------
% 3.36/1.94 % (7561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.94 % (7561)Termination reason: Unknown
% 3.36/1.94 % (7561)Termination phase: shuffling
% 3.36/1.94
% 3.36/1.94 % (7561)Memory used [KB]: 1407
% 3.36/1.94 % (7561)Time elapsed: 0.005 s
% 3.36/1.94 % (7561)Instructions burned: 7 (million)
% 3.36/1.94 % (7561)------------------------------
% 3.36/1.94 % (7561)------------------------------
% 3.36/1.94 % (7562)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_7422 for (2998ds/377Mi)
% 3.36/1.94 % (7563)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_7422 for (2998ds/779Mi)
% 3.36/1.95 % (7564)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_7422 for (2998ds/19Mi)
% 3.36/1.95 % (7565)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_7422 for (2998ds/879Mi)
% 3.36/1.96 % (7564)Instruction limit reached!
% 3.36/1.96 % (7564)------------------------------
% 3.36/1.96 % (7564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.96 % (7564)Termination reason: Unknown
% 3.36/1.96 % (7564)Termination phase: shuffling
% 3.36/1.96
% 3.36/1.96 % (7564)Memory used [KB]: 1663
% 3.36/1.96 % (7564)Time elapsed: 0.011 s
% 3.36/1.96 % (7564)Instructions burned: 19 (million)
% 3.36/1.96 % (7564)------------------------------
% 3.36/1.96 % (7564)------------------------------
% 3.36/1.98 % (7566)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_7422 for (2998ds/17Mi)
% 3.36/1.99 % (7566)Instruction limit reached!
% 3.36/1.99 % (7566)------------------------------
% 3.36/1.99 % (7566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.99 % (7566)Termination reason: Unknown
% 3.36/1.99 % (7566)Termination phase: shuffling
% 3.36/1.99
% 3.36/1.99 % (7566)Memory used [KB]: 1663
% 3.36/1.99 % (7566)Time elapsed: 0.011 s
% 3.36/1.99 % (7566)Instructions burned: 17 (million)
% 3.36/1.99 % (7566)------------------------------
% 3.36/1.99 % (7566)------------------------------
% 3.36/2.01 % (7567)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7422 for (2998ds/3Mi)
% 3.36/2.01 % (7567)Instruction limit reached!
% 3.36/2.01 % (7567)------------------------------
% 3.36/2.01 % (7567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/2.01 % (7567)Termination reason: Unknown
% 3.36/2.01 % (7567)Termination phase: shuffling
% 3.36/2.01
% 3.36/2.01 % (7567)Memory used [KB]: 1407
% 3.36/2.01 % (7567)Time elapsed: 0.005 s
% 3.36/2.01 % (7567)Instructions burned: 4 (million)
% 3.36/2.01 % (7567)------------------------------
% 3.36/2.01 % (7567)------------------------------
% 4.79/2.03 % (7568)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_7422 for (2997ds/30Mi)
% 4.79/2.05 % (7568)Instruction limit reached!
% 4.79/2.05 % (7568)------------------------------
% 4.79/2.05 % (7568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.79/2.05 % (7568)Termination reason: Unknown
% 4.79/2.05 % (7568)Termination phase: Property scanning
% 4.79/2.05
% 4.79/2.05 % (7568)Memory used [KB]: 1791
% 4.79/2.05 % (7568)Time elapsed: 0.019 s
% 4.79/2.05 % (7568)Instructions burned: 31 (million)
% 4.79/2.05 % (7568)------------------------------
% 4.79/2.05 % (7568)------------------------------
% 4.79/2.07 % (7569)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_7422 for (2997ds/127Mi)
% 5.47/2.14 % (7569)Instruction limit reached!
% 5.47/2.14 % (7569)------------------------------
% 5.47/2.14 % (7569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.47/2.14 % (7569)Termination reason: Unknown
% 5.47/2.14 % (7569)Termination phase: Saturation
% 5.47/2.14
% 5.47/2.14 % (7569)Memory used [KB]: 6908
% 5.47/2.14 % (7569)Time elapsed: 0.071 s
% 5.47/2.14 % (7569)Instructions burned: 127 (million)
% 5.47/2.14 % (7569)------------------------------
% 5.47/2.14 % (7569)------------------------------
% 5.47/2.15 % (7562)Instruction limit reached!
% 5.47/2.15 % (7562)------------------------------
% 5.47/2.15 % (7562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.47/2.15 % (7562)Termination reason: Unknown
% 5.47/2.15 % (7562)Termination phase: Saturation
% 5.47/2.15
% 5.47/2.15 % (7562)Memory used [KB]: 7931
% 5.47/2.15 % (7562)Time elapsed: 0.209 s
% 5.47/2.15 % (7562)Instructions burned: 377 (million)
% 5.47/2.15 % (7562)------------------------------
% 5.47/2.15 % (7562)------------------------------
% 5.47/2.16 % (7570)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_7422 for (2996ds/100Mi)
% 5.47/2.17 % (7571)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_7422 for (2996ds/3Mi)
% 5.47/2.17 % (7571)Instruction limit reached!
% 5.47/2.17 % (7571)------------------------------
% 5.47/2.17 % (7571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.47/2.17 % (7571)Termination reason: Unknown
% 5.47/2.17 % (7571)Termination phase: shuffling
% 5.47/2.17
% 5.47/2.17 % (7571)Memory used [KB]: 1407
% 5.47/2.17 % (7571)Time elapsed: 0.004 s
% 5.47/2.17 % (7571)Instructions burned: 3 (million)
% 5.47/2.17 % (7571)------------------------------
% 5.47/2.17 % (7571)------------------------------
% 5.47/2.19 % (7572)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_7422 for (2996ds/20Mi)
% 5.94/2.20 % (7572)Instruction limit reached!
% 5.94/2.20 % (7572)------------------------------
% 5.94/2.20 % (7572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.94/2.20 % (7572)Termination reason: Unknown
% 5.94/2.20 % (7572)Termination phase: shuffling
% 5.94/2.20
% 5.94/2.20 % (7572)Memory used [KB]: 1663
% 5.94/2.20 % (7572)Time elapsed: 0.014 s
% 5.94/2.20 % (7572)Instructions burned: 21 (million)
% 5.94/2.20 % (7572)------------------------------
% 5.94/2.20 % (7572)------------------------------
% 5.94/2.21 % (7570)Instruction limit reached!
% 5.94/2.21 % (7570)------------------------------
% 5.94/2.21 % (7570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.94/2.21 % (7570)Termination reason: Unknown
% 5.94/2.21 % (7570)Termination phase: Function definition elimination
% 5.94/2.21
% 5.94/2.21 % (7570)Memory used [KB]: 2302
% 5.94/2.21 % (7570)Time elapsed: 0.052 s
% 5.94/2.21 % (7570)Instructions burned: 100 (million)
% 5.94/2.21 % (7570)------------------------------
% 5.94/2.21 % (7570)------------------------------
% 5.94/2.22 % (7573)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_7422 for (2995ds/86Mi)
% 5.94/2.22 % (7574)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_7422 for (2995ds/107Mi)
% 5.94/2.27 % (7573)Instruction limit reached!
% 5.94/2.27 % (7573)------------------------------
% 5.94/2.27 % (7573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.94/2.27 % (7573)Termination reason: Unknown
% 5.94/2.27 % (7573)Termination phase: Saturation
% 5.94/2.27
% 5.94/2.27 % (7573)Memory used [KB]: 6524
% 5.94/2.27 % (7573)Time elapsed: 0.048 s
% 5.94/2.27 % (7573)Instructions burned: 87 (million)
% 5.94/2.27 % (7573)------------------------------
% 5.94/2.27 % (7573)------------------------------
% 5.94/2.28 % (7574)Instruction limit reached!
% 5.94/2.28 % (7574)------------------------------
% 5.94/2.28 % (7574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.94/2.28 % (7574)Termination reason: Unknown
% 5.94/2.28 % (7574)Termination phase: Saturation
% 5.94/2.28
% 5.94/2.28 % (7574)Memory used [KB]: 6652
% 5.94/2.28 % (7574)Time elapsed: 0.057 s
% 5.94/2.28 % (7574)Instructions burned: 107 (million)
% 5.94/2.28 % (7574)------------------------------
% 5.94/2.28 % (7574)------------------------------
% 5.94/2.28 % (7556)Instruction limit reached!
% 5.94/2.28 % (7556)------------------------------
% 5.94/2.28 % (7556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.94/2.28 % (7556)Termination reason: Unknown
% 5.94/2.28 % (7556)Termination phase: Saturation
% 5.94/2.28
% 5.94/2.28 % (7556)Memory used [KB]: 7291
% 5.94/2.28 % (7556)Time elapsed: 0.379 s
% 5.94/2.28 % (7556)Instructions burned: 710 (million)
% 5.94/2.28 % (7556)------------------------------
% 5.94/2.28 % (7556)------------------------------
% 5.94/2.29 % (7575)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_7422 for (2995ds/39Mi)
% 6.67/2.30 % (7577)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_7422 for (2995ds/46Mi)
% 6.67/2.30 % (7576)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_7422 for (2995ds/448Mi)
% 6.67/2.31 % (7575)Instruction limit reached!
% 6.67/2.31 % (7575)------------------------------
% 6.67/2.31 % (7575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.67/2.31 % (7575)Termination reason: Unknown
% 6.67/2.31 % (7575)Termination phase: Property scanning
% 6.67/2.31
% 6.67/2.31 % (7575)Memory used [KB]: 2174
% 6.67/2.31 % (7575)Time elapsed: 0.023 s
% 6.67/2.31 % (7575)Instructions burned: 40 (million)
% 6.67/2.31 % (7575)------------------------------
% 6.67/2.31 % (7575)------------------------------
% 6.67/2.32 % (7577)Instruction limit reached!
% 6.67/2.32 % (7577)------------------------------
% 6.67/2.32 % (7577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.67/2.32 % (7577)Termination reason: Unknown
% 6.67/2.32 % (7577)Termination phase: Preprocessing 1
% 6.67/2.32
% 6.67/2.32 % (7577)Memory used [KB]: 1791
% 6.67/2.32 % (7577)Time elapsed: 0.026 s
% 6.67/2.32 % (7577)Instructions burned: 46 (million)
% 6.67/2.32 % (7577)------------------------------
% 6.67/2.32 % (7577)------------------------------
% 6.67/2.33 % (7578)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_7422 for (2994ds/98Mi)
% 6.67/2.34 % (7579)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_7422 for (2994ds/507Mi)
% 6.67/2.37 % (7563)Instruction limit reached!
% 6.67/2.37 % (7563)------------------------------
% 6.67/2.37 % (7563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.67/2.37 % (7563)Termination reason: Unknown
% 6.67/2.37 % (7563)Termination phase: Saturation
% 6.67/2.37
% 6.67/2.37 % (7563)Memory used [KB]: 7803
% 6.67/2.37 % (7563)Time elapsed: 0.425 s
% 6.67/2.37 % (7563)Instructions burned: 779 (million)
% 6.67/2.37 % (7563)------------------------------
% 6.67/2.37 % (7563)------------------------------
% 6.67/2.38 % (7578)Instruction limit reached!
% 6.67/2.38 % (7578)------------------------------
% 6.67/2.38 % (7578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.67/2.38 % (7578)Termination reason: Unknown
% 6.67/2.38 % (7578)Termination phase: Function definition elimination
% 6.67/2.38
% 6.67/2.38 % (7578)Memory used [KB]: 2302
% 6.67/2.38 % (7578)Time elapsed: 0.051 s
% 6.67/2.38 % (7578)Instructions burned: 99 (million)
% 6.67/2.38 % (7578)------------------------------
% 6.67/2.38 % (7578)------------------------------
% 6.67/2.38 % (7558)Instruction limit reached!
% 6.67/2.38 % (7558)------------------------------
% 6.67/2.38 % (7558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.67/2.38 % (7558)Termination reason: Unknown
% 6.67/2.38 % (7558)Termination phase: Saturation
% 6.67/2.38
% 6.67/2.38 % (7558)Memory used [KB]: 7291
% 6.67/2.38 % (7558)Time elapsed: 0.473 s
% 6.67/2.38 % (7558)Instructions burned: 903 (million)
% 6.67/2.38 % (7558)------------------------------
% 6.67/2.38 % (7558)------------------------------
% 6.67/2.39 % (7580)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_7422 for (2994ds/149Mi)
% 7.20/2.40 % (7581)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_7422 for (2994ds/39Mi)
% 7.20/2.40 % (7582)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_7422 for (2994ds/6Mi)
% 7.20/2.41 % (7582)Instruction limit reached!
% 7.20/2.41 % (7582)------------------------------
% 7.20/2.41 % (7582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.20/2.41 % (7582)Termination reason: Unknown
% 7.20/2.41 % (7582)Termination phase: shuffling
% 7.20/2.41
% 7.20/2.41 % (7582)Memory used [KB]: 1407
% 7.20/2.41 % (7582)Time elapsed: 0.005 s
% 7.20/2.41 % (7582)Instructions burned: 6 (million)
% 7.20/2.41 % (7582)------------------------------
% 7.20/2.41 % (7582)------------------------------
% 7.20/2.42 % (7581)Instruction limit reached!
% 7.20/2.42 % (7581)------------------------------
% 7.20/2.42 % (7581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.20/2.42 % (7581)Termination reason: Unknown
% 7.20/2.42 % (7581)Termination phase: Preprocessing 3
% 7.20/2.42
% 7.20/2.42 % (7581)Memory used [KB]: 1918
% 7.20/2.42 % (7581)Time elapsed: 0.023 s
% 7.20/2.42 % (7581)Instructions burned: 39 (million)
% 7.20/2.42 % (7581)------------------------------
% 7.20/2.42 % (7581)------------------------------
% 7.20/2.42 % (7565)Refutation not found, non-redundant clauses discarded% (7565)------------------------------
% 7.20/2.42 % (7565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.20/2.42 % (7565)Termination reason: Refutation not found, non-redundant clauses discarded
% 7.20/2.42
% 7.20/2.42 % (7565)Memory used [KB]: 7675
% 7.20/2.42 % (7565)Time elapsed: 0.471 s
% 7.20/2.42 % (7565)Instructions burned: 875 (million)
% 7.20/2.42 % (7565)------------------------------
% 7.20/2.42 % (7565)------------------------------
% 7.20/2.43 % (7583)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_7422 for (2993ds/1087Mi)
% 7.20/2.44 % (7584)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_7422 for (2993ds/47Mi)
% 7.20/2.44 % (7585)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_7422 for (2993ds/44Mi)
% 7.20/2.45 % (7547)Instruction limit reached!
% 7.20/2.45 % (7547)------------------------------
% 7.20/2.45 % (7547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.20/2.45 % (7547)Termination reason: Unknown
% 7.20/2.45 % (7547)Termination phase: Saturation
% 7.20/2.45
% 7.20/2.45 % (7547)Memory used [KB]: 9850
% 7.20/2.45 % (7547)Time elapsed: 0.593 s
% 7.20/2.45 % (7547)Instructions burned: 1041 (million)
% 7.20/2.45 % (7547)------------------------------
% 7.20/2.45 % (7547)------------------------------
% 7.20/2.46 % (7584)Instruction limit reached!
% 7.20/2.46 % (7584)------------------------------
% 7.20/2.46 % (7584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.20/2.46 % (7584)Termination reason: Unknown
% 7.20/2.46 % (7584)Termination phase: Property scanning
% 7.20/2.46
% 7.20/2.46 % (7584)Memory used [KB]: 1918
% 7.20/2.46 % (7584)Time elapsed: 0.027 s
% 7.20/2.46 % (7584)Instructions burned: 47 (million)
% 7.20/2.46 % (7584)------------------------------
% 7.20/2.46 % (7584)------------------------------
% 7.20/2.47 % (7580)Instruction limit reached!
% 7.20/2.47 % (7580)------------------------------
% 7.20/2.47 % (7580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.20/2.47 % (7580)Termination reason: Unknown
% 7.20/2.47 % (7580)Termination phase: Saturation
% 7.20/2.47
% 7.20/2.47 % (7580)Memory used [KB]: 7036
% 7.20/2.47 % (7580)Time elapsed: 0.081 s
% 7.20/2.47 % (7580)Instructions burned: 150 (million)
% 7.20/2.47 % (7580)------------------------------
% 7.20/2.47 % (7580)------------------------------
% 7.20/2.47 % (7585)Instruction limit reached!
% 7.20/2.47 % (7585)------------------------------
% 7.20/2.47 % (7585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.20/2.47 % (7585)Termination reason: Unknown
% 7.20/2.47 % (7585)Termination phase: Property scanning
% 7.20/2.47
% 7.20/2.47 % (7585)Memory used [KB]: 2174
% 7.20/2.47 % (7585)Time elapsed: 0.025 s
% 7.20/2.47 % (7585)Instructions burned: 45 (million)
% 7.20/2.47 % (7585)------------------------------
% 7.20/2.47 % (7585)------------------------------
% 7.20/2.47 % (7586)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_7422 for (2993ds/432Mi)
% 7.20/2.48 % (7587)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_7422 for (2993ds/62Mi)
% 7.20/2.48 % (7588)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_7422 for (2993ds/31Mi)
% 7.20/2.49 % (7589)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_7422 for (2993ds/96Mi)
% 7.55/2.50 % (7588)Instruction limit reached!
% 7.55/2.50 % (7588)------------------------------
% 7.55/2.50 % (7588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.55/2.50 % (7588)Termination reason: Unknown
% 7.55/2.50 % (7588)Termination phase: Property scanning
% 7.55/2.50
% 7.55/2.50 % (7588)Memory used [KB]: 1791
% 7.55/2.50 % (7588)Time elapsed: 0.018 s
% 7.55/2.50 % (7588)Instructions burned: 32 (million)
% 7.55/2.50 % (7588)------------------------------
% 7.55/2.50 % (7588)------------------------------
% 7.55/2.52 % (7587)Instruction limit reached!
% 7.55/2.52 % (7587)------------------------------
% 7.55/2.52 % (7587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.55/2.52 % (7587)Termination reason: Unknown
% 7.55/2.52 % (7587)Termination phase: Preprocessing 1
% 7.55/2.52
% 7.55/2.52 % (7587)Memory used [KB]: 2174
% 7.55/2.52 % (7587)Time elapsed: 0.034 s
% 7.55/2.52 % (7587)Instructions burned: 63 (million)
% 7.55/2.52 % (7587)------------------------------
% 7.55/2.52 % (7587)------------------------------
% 7.55/2.52 % (7590)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_7422 for (2993ds/453Mi)
% 7.55/2.54 % (7591)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_7422 for (2992ds/71Mi)
% 7.55/2.54 % (7589)Instruction limit reached!
% 7.55/2.54 % (7589)------------------------------
% 7.55/2.54 % (7589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.55/2.54 % (7589)Termination reason: Unknown
% 7.55/2.54 % (7589)Termination phase: Saturation
% 7.55/2.54
% 7.55/2.54 % (7589)Memory used [KB]: 6652
% 7.55/2.54 % (7589)Time elapsed: 0.053 s
% 7.55/2.54 % (7589)Instructions burned: 97 (million)
% 7.55/2.54 % (7589)------------------------------
% 7.55/2.54 % (7589)------------------------------
% 7.55/2.54 % (7576)Instruction limit reached!
% 7.55/2.54 % (7576)------------------------------
% 7.55/2.54 % (7576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.55/2.54 % (7576)Termination reason: Unknown
% 7.55/2.54 % (7576)Termination phase: Saturation
% 7.55/2.54
% 7.55/2.54 % (7576)Memory used [KB]: 7803
% 7.55/2.54 % (7576)Time elapsed: 0.243 s
% 7.55/2.54 % (7576)Instructions burned: 448 (million)
% 7.55/2.54 % (7576)------------------------------
% 7.55/2.54 % (7576)------------------------------
% 7.55/2.56 % (7592)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_7422 for (2992ds/83Mi)
% 7.55/2.56 % (7593)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_7422 for (2992ds/11Mi)
% 7.55/2.56 % (7593)Instruction limit reached!
% 7.55/2.56 % (7593)------------------------------
% 7.55/2.56 % (7593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.55/2.56 % (7593)Termination reason: Unknown
% 7.55/2.56 % (7593)Termination phase: shuffling
% 7.55/2.56
% 7.55/2.56 % (7593)Memory used [KB]: 1535
% 7.55/2.56 % (7593)Time elapsed: 0.008 s
% 7.55/2.56 % (7593)Instructions burned: 11 (million)
% 7.55/2.56 % (7593)------------------------------
% 7.55/2.56 % (7593)------------------------------
% 7.55/2.57 % (7591)Instruction limit reached!
% 7.55/2.57 % (7591)------------------------------
% 7.55/2.57 % (7591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.55/2.57 % (7591)Termination reason: Unknown
% 7.55/2.57 % (7591)Termination phase: Property scanning
% 7.55/2.57
% 7.55/2.57 % (7591)Memory used [KB]: 2046
% 7.55/2.57 % (7591)Time elapsed: 0.040 s
% 7.55/2.57 % (7591)Instructions burned: 72 (million)
% 7.55/2.57 % (7591)------------------------------
% 7.55/2.57 % (7591)------------------------------
% 7.55/2.58 % (7594)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_7422 for (2992ds/41Mi)
% 7.55/2.59 % (7595)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7422 for (2992ds/6Mi)
% 8.05/2.60 % (7595)Instruction limit reached!
% 8.05/2.60 % (7595)------------------------------
% 8.05/2.60 % (7595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.60 % (7595)Termination reason: Unknown
% 8.05/2.60 % (7595)Termination phase: shuffling
% 8.05/2.60
% 8.05/2.60 % (7595)Memory used [KB]: 1407
% 8.05/2.60 % (7595)Time elapsed: 0.006 s
% 8.05/2.60 % (7595)Instructions burned: 7 (million)
% 8.05/2.60 % (7595)------------------------------
% 8.05/2.60 % (7595)------------------------------
% 8.05/2.60 % (7592)Instruction limit reached!
% 8.05/2.60 % (7592)------------------------------
% 8.05/2.60 % (7592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.60 % (7592)Termination reason: Unknown
% 8.05/2.60 % (7592)Termination phase: Saturation
% 8.05/2.60
% 8.05/2.60 % (7592)Memory used [KB]: 6524
% 8.05/2.60 % (7592)Time elapsed: 0.047 s
% 8.05/2.60 % (7592)Instructions burned: 83 (million)
% 8.05/2.60 % (7592)------------------------------
% 8.05/2.60 % (7592)------------------------------
% 8.05/2.61 % (7594)Instruction limit reached!
% 8.05/2.61 % (7594)------------------------------
% 8.05/2.61 % (7594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.61 % (7594)Termination reason: Unknown
% 8.05/2.61 % (7594)Termination phase: Property scanning
% 8.05/2.61
% 8.05/2.61 % (7594)Memory used [KB]: 2174
% 8.05/2.61 % (7594)Time elapsed: 0.023 s
% 8.05/2.61 % (7594)Instructions burned: 42 (million)
% 8.05/2.61 % (7594)------------------------------
% 8.05/2.61 % (7594)------------------------------
% 8.05/2.62 % (7579)Instruction limit reached!
% 8.05/2.62 % (7579)------------------------------
% 8.05/2.62 % (7579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.62 % (7579)Termination reason: Unknown
% 8.05/2.62 % (7579)Termination phase: Saturation
% 8.05/2.62
% 8.05/2.62 % (7579)Memory used [KB]: 8187
% 8.05/2.62 % (7579)Time elapsed: 0.274 s
% 8.05/2.62 % (7579)Instructions burned: 508 (million)
% 8.05/2.62 % (7579)------------------------------
% 8.05/2.62 % (7579)------------------------------
% 8.05/2.62 % (7596)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_7422 for (2992ds/150Mi)
% 8.05/2.62 % (7597)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_7422 for (2992ds/343Mi)
% 8.05/2.62 % (7598)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_7422 for (2992ds/109Mi)
% 8.05/2.64 % (7599)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_7422 for (2991ds/253Mi)
% 8.05/2.68 % (7598)Instruction limit reached!
% 8.05/2.68 % (7598)------------------------------
% 8.05/2.68 % (7598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.68 % (7598)Termination reason: Unknown
% 8.05/2.68 % (7598)Termination phase: Saturation
% 8.05/2.68
% 8.05/2.68 % (7598)Memory used [KB]: 6652
% 8.05/2.68 % (7598)Time elapsed: 0.059 s
% 8.05/2.68 % (7598)Instructions burned: 109 (million)
% 8.05/2.68 % (7598)------------------------------
% 8.05/2.68 % (7598)------------------------------
% 8.56/2.70 % (7596)Instruction limit reached!
% 8.56/2.70 % (7596)------------------------------
% 8.56/2.70 % (7596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.56/2.70 % (7596)Termination reason: Unknown
% 8.56/2.70 % (7596)Termination phase: Saturation
% 8.56/2.70
% 8.56/2.70 % (7596)Memory used [KB]: 7164
% 8.56/2.70 % (7596)Time elapsed: 0.105 s
% 8.56/2.70 % (7596)Instructions burned: 150 (million)
% 8.56/2.70 % (7596)------------------------------
% 8.56/2.70 % (7596)------------------------------
% 8.56/2.70 % (7600)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_7422 for (2991ds/140Mi)
% 8.56/2.71 % (7586)Instruction limit reached!
% 8.56/2.71 % (7586)------------------------------
% 8.56/2.71 % (7586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.56/2.71 % (7586)Termination reason: Unknown
% 8.56/2.71 % (7586)Termination phase: Saturation
% 8.56/2.71
% 8.56/2.71 % (7586)Memory used [KB]: 3709
% 8.56/2.71 % (7586)Time elapsed: 0.242 s
% 8.56/2.71 % (7586)Instructions burned: 432 (million)
% 8.56/2.71 % (7586)------------------------------
% 8.56/2.71 % (7586)------------------------------
% 8.56/2.72 % (7601)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_7422 for (2990ds/614Mi)
% 8.56/2.73 % (7602)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_7422 for (2990ds/202Mi)
% 8.56/2.77 % (7590)Instruction limit reached!
% 8.56/2.77 % (7590)------------------------------
% 8.56/2.77 % (7590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.56/2.77 % (7590)Termination reason: Unknown
% 8.56/2.77 % (7590)Termination phase: Saturation
% 8.56/2.77
% 8.56/2.77 % (7590)Memory used [KB]: 7803
% 8.56/2.77 % (7590)Time elapsed: 0.248 s
% 8.56/2.77 % (7590)Instructions burned: 454 (million)
% 8.56/2.77 % (7590)------------------------------
% 8.56/2.77 % (7590)------------------------------
% 8.56/2.77 % (7599)Instruction limit reached!
% 8.56/2.77 % (7599)------------------------------
% 8.56/2.77 % (7599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.56/2.77 % (7599)Termination reason: Unknown
% 8.56/2.77 % (7599)Termination phase: Saturation
% 8.56/2.77
% 8.56/2.77 % (7599)Memory used [KB]: 7419
% 8.56/2.77 % (7599)Time elapsed: 0.139 s
% 8.56/2.77 % (7599)Instructions burned: 253 (million)
% 8.56/2.77 % (7599)------------------------------
% 8.56/2.77 % (7599)------------------------------
% 8.56/2.78 % (7600)Instruction limit reached!
% 8.56/2.78 % (7600)------------------------------
% 8.56/2.78 % (7600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.56/2.78 % (7600)Termination reason: Unknown
% 8.56/2.78 % (7600)Termination phase: Saturation
% 8.56/2.78
% 8.56/2.78 % (7600)Memory used [KB]: 6652
% 8.56/2.78 % (7600)Time elapsed: 0.079 s
% 8.56/2.78 % (7600)Instructions burned: 141 (million)
% 8.56/2.78 % (7600)------------------------------
% 8.56/2.78 % (7600)------------------------------
% 8.56/2.79 % (7603)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_7422 for (2990ds/339Mi)
% 8.56/2.79 % (7604)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_7422 for (2990ds/283Mi)
% 9.44/2.80 % (7605)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_7422 for (2990ds/134Mi)
% 9.44/2.81 % (7597)Instruction limit reached!
% 9.44/2.81 % (7597)------------------------------
% 9.44/2.81 % (7597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.44/2.81 % (7597)Termination reason: Unknown
% 9.44/2.81 % (7597)Termination phase: Saturation
% 9.44/2.81
% 9.44/2.81 % (7597)Memory used [KB]: 7291
% 9.44/2.81 % (7597)Time elapsed: 0.211 s
% 9.44/2.81 % (7597)Instructions burned: 344 (million)
% 9.44/2.81 % (7597)------------------------------
% 9.44/2.81 % (7597)------------------------------
% 9.44/2.83 % (7606)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_7422 for (2989ds/298Mi)
% 9.44/2.84 % (7602)Instruction limit reached!
% 9.44/2.84 % (7602)------------------------------
% 9.44/2.84 % (7602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.44/2.84 % (7602)Termination reason: Unknown
% 9.44/2.84 % (7602)Termination phase: Saturation
% 9.44/2.84
% 9.44/2.84 % (7602)Memory used [KB]: 7164
% 9.44/2.84 % (7602)Time elapsed: 0.115 s
% 9.44/2.84 % (7602)Instructions burned: 203 (million)
% 9.44/2.84 % (7602)------------------------------
% 9.44/2.84 % (7602)------------------------------
% 9.44/2.86 % (7607)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_7422 for (2989ds/192Mi)
% 9.44/2.87 % (7605)Instruction limit reached!
% 9.44/2.87 % (7605)------------------------------
% 9.44/2.87 % (7605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.44/2.87 % (7605)Termination reason: Unknown
% 9.44/2.87 % (7605)Termination phase: Saturation
% 9.44/2.87
% 9.44/2.87 % (7605)Memory used [KB]: 6908
% 9.44/2.87 % (7605)Time elapsed: 0.071 s
% 9.44/2.87 % (7605)Instructions burned: 134 (million)
% 9.44/2.87 % (7605)------------------------------
% 9.44/2.87 % (7605)------------------------------
% 9.44/2.89 % (7608)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_7422 for (2989ds/258Mi)
% 9.87/2.95 % (7604)Instruction limit reached!
% 9.87/2.95 % (7604)------------------------------
% 9.87/2.95 % (7604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/2.95 % (7604)Termination reason: Unknown
% 9.87/2.95 % (7604)Termination phase: Saturation
% 9.87/2.95
% 9.87/2.95 % (7604)Memory used [KB]: 7675
% 9.87/2.95 % (7604)Time elapsed: 0.159 s
% 9.87/2.95 % (7604)Instructions burned: 284 (million)
% 9.87/2.95 % (7604)------------------------------
% 9.87/2.95 % (7604)------------------------------
% 9.87/2.96 % (7603)Instruction limit reached!
% 9.87/2.96 % (7603)------------------------------
% 9.87/2.96 % (7603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/2.96 % (7603)Termination reason: Unknown
% 9.87/2.96 % (7603)Termination phase: Saturation
% 9.87/2.96
% 9.87/2.96 % (7603)Memory used [KB]: 7547
% 9.87/2.96 % (7603)Time elapsed: 0.179 s
% 9.87/2.96 % (7603)Instructions burned: 340 (million)
% 9.87/2.96 % (7603)------------------------------
% 9.87/2.96 % (7603)------------------------------
% 9.87/2.97 % (7609)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_7422 for (2988ds/90Mi)
% 9.87/2.97 % (7607)Instruction limit reached!
% 9.87/2.97 % (7607)------------------------------
% 9.87/2.97 % (7607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/2.97 % (7607)Termination reason: Unknown
% 9.87/2.97 % (7607)Termination phase: Saturation
% 9.87/2.97
% 9.87/2.97 % (7607)Memory used [KB]: 7803
% 9.87/2.97 % (7607)Time elapsed: 0.106 s
% 9.87/2.97 % (7607)Instructions burned: 193 (million)
% 9.87/2.97 % (7607)------------------------------
% 9.87/2.97 % (7607)------------------------------
% 9.87/2.98 % (7610)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_7422 for (2988ds/231Mi)
% 9.87/2.99 % (7606)Instruction limit reached!
% 9.87/2.99 % (7606)------------------------------
% 9.87/2.99 % (7606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/2.99 % (7606)Termination reason: Unknown
% 9.87/2.99 % (7606)Termination phase: Saturation
% 9.87/2.99
% 9.87/2.99 % (7606)Memory used [KB]: 7803
% 9.87/2.99 % (7606)Time elapsed: 0.161 s
% 9.87/2.99 % (7606)Instructions burned: 299 (million)
% 9.87/2.99 % (7606)------------------------------
% 9.87/2.99 % (7606)------------------------------
% 9.87/2.99 % (7611)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_7422 for (2988ds/458Mi)
% 9.87/3.01 % (7612)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_7422 for (2988ds/31Mi)
% 9.87/3.02 % (7609)Instruction limit reached!
% 9.87/3.02 % (7609)------------------------------
% 9.87/3.02 % (7609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/3.02 % (7609)Termination reason: Unknown
% 9.87/3.02 % (7609)Termination phase: Saturation
% 9.87/3.02
% 9.87/3.02 % (7609)Memory used [KB]: 6652
% 9.87/3.02 % (7609)Time elapsed: 0.050 s
% 9.87/3.02 % (7609)Instructions burned: 90 (million)
% 9.87/3.02 % (7609)------------------------------
% 9.87/3.02 % (7609)------------------------------
% 9.87/3.02 % (7583)Instruction limit reached!
% 9.87/3.02 % (7583)------------------------------
% 9.87/3.02 % (7583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/3.02 % (7583)Termination reason: Unknown
% 9.87/3.02 % (7583)Termination phase: Saturation
% 9.87/3.02
% 9.87/3.02 % (7583)Memory used [KB]: 7931
% 9.87/3.02 % (7583)Time elapsed: 0.600 s
% 9.87/3.02 % (7583)Instructions burned: 1088 (million)
% 9.87/3.02 % (7583)------------------------------
% 9.87/3.02 % (7583)------------------------------
% 9.87/3.03 % (7612)Instruction limit reached!
% 9.87/3.03 % (7612)------------------------------
% 9.87/3.03 % (7612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/3.03 % (7612)Termination reason: Unknown
% 9.87/3.03 % (7612)Termination phase: Property scanning
% 9.87/3.03
% 9.87/3.03 % (7612)Memory used [KB]: 1791
% 9.87/3.03 % (7612)Time elapsed: 0.019 s
% 9.87/3.03 % (7612)Instructions burned: 32 (million)
% 9.87/3.03 % (7612)------------------------------
% 9.87/3.03 % (7612)------------------------------
% 11.80/3.03 % (7608)Instruction limit reached!
% 11.80/3.03 % (7608)------------------------------
% 11.80/3.03 % (7608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.80/3.03 % (7608)Termination reason: Unknown
% 11.80/3.03 % (7608)Termination phase: Saturation
% 11.80/3.03
% 11.80/3.03 % (7608)Memory used [KB]: 7419
% 11.80/3.03 % (7608)Time elapsed: 0.144 s
% 11.80/3.03 % (7608)Instructions burned: 258 (million)
% 11.80/3.03 % (7608)------------------------------
% 11.80/3.03 % (7608)------------------------------
% 11.80/3.04 % (7613)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_7422 for (2987ds/297Mi)
% 11.80/3.04 % (7614)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_7422 for (2987ds/987Mi)
% 11.80/3.05 % (7615)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_7422 for (2987ds/182Mi)
% 11.80/3.05 % (7616)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_7422 for (2987ds/182Mi)
% 11.80/3.06 % (7601)Instruction limit reached!
% 11.80/3.06 % (7601)------------------------------
% 11.80/3.06 % (7601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.80/3.06 % (7601)Termination reason: Unknown
% 11.80/3.06 % (7601)Termination phase: Saturation
% 11.80/3.06
% 11.80/3.06 % (7601)Memory used [KB]: 8699
% 11.80/3.06 % (7601)Time elapsed: 0.341 s
% 11.80/3.06 % (7601)Instructions burned: 615 (million)
% 11.80/3.06 % (7601)------------------------------
% 11.80/3.06 % (7601)------------------------------
% 11.80/3.08 % (7617)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_7422 for (2987ds/154Mi)
% 11.80/3.10 % (7610)Instruction limit reached!
% 11.80/3.10 % (7610)------------------------------
% 11.80/3.10 % (7610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.80/3.10 % (7610)Termination reason: Unknown
% 11.80/3.10 % (7610)Termination phase: Saturation
% 11.80/3.10
% 11.80/3.10 % (7610)Memory used [KB]: 7419
% 11.80/3.10 % (7610)Time elapsed: 0.124 s
% 11.80/3.10 % (7610)Instructions burned: 231 (million)
% 11.80/3.10 % (7610)------------------------------
% 11.80/3.10 % (7610)------------------------------
% 11.80/3.13 % (7618)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_7422 for (2986ds/79Mi)
% 12.07/3.14 % (7615)Instruction limit reached!
% 12.07/3.14 % (7615)------------------------------
% 12.07/3.14 % (7615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.07/3.14 % (7615)Termination reason: Unknown
% 12.07/3.14 % (7615)Termination phase: Saturation
% 12.07/3.14
% 12.07/3.14 % (7615)Memory used [KB]: 7291
% 12.07/3.14 % (7615)Time elapsed: 0.099 s
% 12.07/3.14 % (7615)Instructions burned: 182 (million)
% 12.07/3.14 % (7615)------------------------------
% 12.07/3.14 % (7615)------------------------------
% 12.07/3.15 % (7616)Instruction limit reached!
% 12.07/3.15 % (7616)------------------------------
% 12.07/3.15 % (7616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.07/3.15 % (7616)Termination reason: Unknown
% 12.07/3.15 % (7616)Termination phase: Saturation
% 12.07/3.15
% 12.07/3.15 % (7616)Memory used [KB]: 7036
% 12.07/3.15 % (7616)Time elapsed: 0.105 s
% 12.07/3.15 % (7616)Instructions burned: 183 (million)
% 12.07/3.15 % (7616)------------------------------
% 12.07/3.15 % (7616)------------------------------
% 12.07/3.16 % (7617)Instruction limit reached!
% 12.07/3.16 % (7617)------------------------------
% 12.07/3.16 % (7617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.07/3.16 % (7617)Termination reason: Unknown
% 12.07/3.16 % (7617)Termination phase: Saturation
% 12.07/3.16
% 12.07/3.16 % (7617)Memory used [KB]: 2558
% 12.07/3.16 % (7617)Time elapsed: 0.081 s
% 12.07/3.16 % (7617)Instructions burned: 155 (million)
% 12.07/3.16 % (7617)------------------------------
% 12.07/3.16 % (7617)------------------------------
% 12.07/3.16 % (7619)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_7422 for (2986ds/216Mi)
% 12.07/3.17 % (7618)Instruction limit reached!
% 12.07/3.17 % (7618)------------------------------
% 12.07/3.17 % (7618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.07/3.17 % (7618)Termination reason: Unknown
% 12.07/3.17 % (7618)Termination phase: Property scanning
% 12.07/3.17
% 12.07/3.17 % (7618)Memory used [KB]: 2046
% 12.07/3.17 % (7618)Time elapsed: 0.044 s
% 12.07/3.17 % (7618)Instructions burned: 79 (million)
% 12.07/3.17 % (7618)------------------------------
% 12.07/3.17 % (7618)------------------------------
% 12.07/3.17 % (7620)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_7422 for (2986ds/114Mi)
% 12.07/3.18 % (7621)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_7422 for (2986ds/922Mi)
% 12.07/3.19 % (7622)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_7422 for (2986ds/182Mi)
% 12.54/3.20 % (7613)Instruction limit reached!
% 12.54/3.20 % (7613)------------------------------
% 12.54/3.20 % (7613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.54/3.20 % (7613)Termination reason: Unknown
% 12.54/3.20 % (7613)Termination phase: Saturation
% 12.54/3.20
% 12.54/3.20 % (7613)Memory used [KB]: 7419
% 12.54/3.20 % (7613)Time elapsed: 0.163 s
% 12.54/3.20 % (7613)Instructions burned: 297 (million)
% 12.54/3.20 % (7613)------------------------------
% 12.54/3.20 % (7613)------------------------------
% 12.54/3.22 % (7623)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_7422 for (2986ds/164Mi)
% 12.54/3.23 % (7620)Instruction limit reached!
% 12.54/3.23 % (7620)------------------------------
% 12.54/3.23 % (7620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.54/3.23 % (7620)Termination reason: Unknown
% 12.54/3.23 % (7620)Termination phase: Saturation
% 12.54/3.23
% 12.54/3.23 % (7620)Memory used [KB]: 6780
% 12.54/3.23 % (7620)Time elapsed: 0.062 s
% 12.54/3.23 % (7620)Instructions burned: 114 (million)
% 12.54/3.23 % (7620)------------------------------
% 12.54/3.23 % (7620)------------------------------
% 12.54/3.24 % (7611)Instruction limit reached!
% 12.54/3.24 % (7611)------------------------------
% 12.54/3.24 % (7611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.54/3.24 % (7611)Termination reason: Unknown
% 12.54/3.24 % (7611)Termination phase: Saturation
% 12.54/3.24
% 12.54/3.24 % (7611)Memory used [KB]: 8059
% 12.54/3.24 % (7611)Time elapsed: 0.258 s
% 12.54/3.24 % (7611)Instructions burned: 458 (million)
% 12.54/3.24 % (7611)------------------------------
% 12.54/3.24 % (7611)------------------------------
% 12.54/3.25 % (7624)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_7422 for (2985ds/50Mi)
% 12.54/3.27 % (7625)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_7422 for (2985ds/368Mi)
% 12.54/3.28 % (7619)Instruction limit reached!
% 12.54/3.28 % (7619)------------------------------
% 12.54/3.28 % (7619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.54/3.28 % (7619)Termination reason: Unknown
% 12.54/3.28 % (7619)Termination phase: Saturation
% 12.54/3.28
% 12.54/3.28 % (7619)Memory used [KB]: 7419
% 12.54/3.28 % (7619)Time elapsed: 0.117 s
% 12.54/3.28 % (7619)Instructions burned: 217 (million)
% 12.54/3.28 % (7619)------------------------------
% 12.54/3.28 % (7619)------------------------------
% 12.54/3.28 % (7624)Instruction limit reached!
% 12.54/3.28 % (7624)------------------------------
% 12.54/3.28 % (7624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.54/3.28 % (7624)Termination reason: Unknown
% 12.54/3.28 % (7624)Termination phase: Property scanning
% 12.54/3.28
% 12.54/3.28 % (7624)Memory used [KB]: 2174
% 12.54/3.28 % (7624)Time elapsed: 0.028 s
% 12.54/3.28 % (7624)Instructions burned: 50 (million)
% 12.54/3.28 % (7624)------------------------------
% 12.54/3.28 % (7624)------------------------------
% 12.54/3.28 % (7622)Instruction limit reached!
% 12.54/3.28 % (7622)------------------------------
% 12.54/3.28 % (7622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.54/3.28 % (7622)Termination reason: Unknown
% 12.54/3.28 % (7622)Termination phase: Saturation
% 12.54/3.28
% 12.54/3.28 % (7622)Memory used [KB]: 7164
% 12.54/3.28 % (7622)Time elapsed: 0.094 s
% 12.54/3.28 % (7622)Instructions burned: 182 (million)
% 12.54/3.28 % (7622)------------------------------
% 12.54/3.28 % (7622)------------------------------
% 13.16/3.30 % (7626)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_7422 for (2985ds/1021Mi)
% 13.16/3.30 % (7628)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_7422 for (2985ds/204Mi)
% 13.16/3.30 % (7627)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_7422 for (2985ds/267Mi)
% 13.16/3.30 % (7623)Instruction limit reached!
% 13.16/3.30 % (7623)------------------------------
% 13.16/3.30 % (7623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.16/3.30 % (7623)Termination reason: Unknown
% 13.16/3.30 % (7623)Termination phase: Saturation
% 13.16/3.30
% 13.16/3.30 % (7623)Memory used [KB]: 2430
% 13.16/3.30 % (7623)Time elapsed: 0.087 s
% 13.16/3.30 % (7623)Instructions burned: 165 (million)
% 13.16/3.30 % (7623)------------------------------
% 13.16/3.30 % (7623)------------------------------
% 13.16/3.33 % (7629)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_7422 for (2985ds/26Mi)
% 13.16/3.34 % (7629)Instruction limit reached!
% 13.16/3.34 % (7629)------------------------------
% 13.16/3.34 % (7629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.16/3.34 % (7629)Termination reason: Unknown
% 13.16/3.34 % (7629)Termination phase: shuffling
% 13.16/3.34
% 13.16/3.34 % (7629)Memory used [KB]: 1918
% 13.16/3.34 % (7629)Time elapsed: 0.016 s
% 13.16/3.34 % (7629)Instructions burned: 27 (million)
% 13.16/3.34 % (7629)------------------------------
% 13.16/3.34 % (7629)------------------------------
% 13.16/3.36 % (7630)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_7422 for (2984ds/53Mi)
% 13.16/3.39 % (7630)Instruction limit reached!
% 13.16/3.39 % (7630)------------------------------
% 13.16/3.39 % (7630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.16/3.39 % (7630)Termination reason: Unknown
% 13.16/3.39 % (7630)Termination phase: Property scanning
% 13.16/3.39
% 13.16/3.39 % (7630)Memory used [KB]: 2174
% 13.16/3.39 % (7630)Time elapsed: 0.030 s
% 13.16/3.39 % (7630)Instructions burned: 53 (million)
% 13.16/3.39 % (7630)------------------------------
% 13.16/3.39 % (7630)------------------------------
% 13.35/3.41 % (7628)Instruction limit reached!
% 13.35/3.41 % (7628)------------------------------
% 13.35/3.41 % (7628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.35/3.41 % (7628)Termination reason: Unknown
% 13.35/3.41 % (7628)Termination phase: Saturation
% 13.35/3.41
% 13.35/3.41 % (7628)Memory used [KB]: 7164
% 13.35/3.41 % (7628)Time elapsed: 0.114 s
% 13.35/3.41 % (7628)Instructions burned: 204 (million)
% 13.35/3.41 % (7628)------------------------------
% 13.35/3.41 % (7628)------------------------------
% 13.35/3.41 % (7631)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_7422 for (2984ds/4436Mi)
% 13.35/3.43 % (7632)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_7422 for (2983ds/1539Mi)
% 13.35/3.44 % (7627)Instruction limit reached!
% 13.35/3.44 % (7627)------------------------------
% 13.35/3.44 % (7627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.35/3.44 % (7627)Termination reason: Unknown
% 13.35/3.44 % (7627)Termination phase: Saturation
% 13.35/3.45
% 13.35/3.45 % (7627)Memory used [KB]: 7547
% 13.35/3.45 % (7627)Time elapsed: 0.149 s
% 13.35/3.45 % (7627)Instructions burned: 267 (million)
% 13.35/3.45 % (7627)------------------------------
% 13.35/3.45 % (7627)------------------------------
% 13.35/3.47 % (7633)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_7422 for (2983ds/408Mi)
% 13.35/3.47 % (7625)Instruction limit reached!
% 13.35/3.47 % (7625)------------------------------
% 13.35/3.47 % (7625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.35/3.47 % (7625)Termination reason: Unknown
% 13.35/3.47 % (7625)Termination phase: Saturation
% 13.35/3.47
% 13.35/3.47 % (7625)Memory used [KB]: 8059
% 13.35/3.47 % (7625)Time elapsed: 0.207 s
% 13.35/3.47 % (7625)Instructions burned: 368 (million)
% 13.35/3.47 % (7625)------------------------------
% 13.35/3.47 % (7625)------------------------------
% 13.35/3.49 % (7634)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_7422 for (2983ds/5205Mi)
% 13.87/3.61 % (7614)Instruction limit reached!
% 13.87/3.61 % (7614)------------------------------
% 13.87/3.61 % (7614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.87/3.61 % (7614)Termination reason: Unknown
% 13.87/3.61 % (7614)Termination phase: Saturation
% 13.87/3.61
% 13.87/3.61 % (7614)Memory used [KB]: 9594
% 13.87/3.61 % (7614)Time elapsed: 0.563 s
% 13.87/3.61 % (7614)Instructions burned: 987 (million)
% 13.87/3.61 % (7614)------------------------------
% 13.87/3.61 % (7614)------------------------------
% 13.87/3.63 % (7635)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_7422 for (2981ds/1913Mi)
% 13.87/3.69 % (7621)Instruction limit reached!
% 13.87/3.69 % (7621)------------------------------
% 13.87/3.69 % (7621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.87/3.69 % (7621)Termination reason: Unknown
% 13.87/3.69 % (7621)Termination phase: Saturation
% 13.87/3.69
% 13.87/3.69 % (7621)Memory used [KB]: 7675
% 13.87/3.69 % (7621)Time elapsed: 0.516 s
% 13.87/3.69 % (7621)Instructions burned: 923 (million)
% 13.87/3.69 % (7621)------------------------------
% 13.87/3.69 % (7621)------------------------------
% 13.87/3.69 % (7633)Instruction limit reached!
% 13.87/3.69 % (7633)------------------------------
% 13.87/3.69 % (7633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.87/3.69 % (7633)Termination reason: Unknown
% 13.87/3.69 % (7633)Termination phase: Saturation
% 13.87/3.69
% 13.87/3.69 % (7633)Memory used [KB]: 7803
% 13.87/3.69 % (7633)Time elapsed: 0.253 s
% 13.87/3.69 % (7633)Instructions burned: 409 (million)
% 13.87/3.69 % (7633)------------------------------
% 13.87/3.69 % (7633)------------------------------
% 15.24/3.71 % (7636)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_7422 for (2980ds/4350Mi)
% 15.24/3.71 % (7637)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_7422 for (2980ds/68Mi)
% 15.24/3.75 % (7637)Instruction limit reached!
% 15.24/3.75 % (7637)------------------------------
% 15.24/3.75 % (7637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.24/3.75 % (7637)Termination reason: Unknown
% 15.24/3.75 % (7637)Termination phase: Function definition elimination
% 15.24/3.75
% 15.24/3.75 % (7637)Memory used [KB]: 1918
% 15.24/3.75 % (7637)Time elapsed: 0.038 s
% 15.24/3.75 % (7637)Instructions burned: 68 (million)
% 15.24/3.75 % (7637)------------------------------
% 15.24/3.75 % (7637)------------------------------
% 15.24/3.77 % (7638)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_7422 for (2980ds/358Mi)
% 15.29/3.86 % (7626)Instruction limit reached!
% 15.29/3.86 % (7626)------------------------------
% 15.29/3.86 % (7626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.29/3.86 % (7626)Termination reason: Unknown
% 15.29/3.86 % (7626)Termination phase: Saturation
% 15.29/3.86
% 15.29/3.86 % (7626)Memory used [KB]: 8699
% 15.29/3.86 % (7626)Time elapsed: 0.569 s
% 15.29/3.86 % (7626)Instructions burned: 1022 (million)
% 15.29/3.86 % (7626)------------------------------
% 15.29/3.86 % (7626)------------------------------
% 15.29/3.89 % (7639)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_7422 for (2979ds/31Mi)
% 15.88/3.90 % (7639)Instruction limit reached!
% 15.88/3.90 % (7639)------------------------------
% 15.88/3.90 % (7639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.88/3.90 % (7639)Termination reason: Unknown
% 15.88/3.90 % (7639)Termination phase: Property scanning
% 15.88/3.90
% 15.88/3.90 % (7639)Memory used [KB]: 1791
% 15.88/3.90 % (7639)Time elapsed: 0.019 s
% 15.88/3.90 % (7639)Instructions burned: 32 (million)
% 15.88/3.90 % (7639)------------------------------
% 15.88/3.90 % (7639)------------------------------
% 15.88/3.92 % (7640)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_7422 for (2978ds/279Mi)
% 15.88/3.97 % (7638)Instruction limit reached!
% 15.88/3.97 % (7638)------------------------------
% 15.88/3.97 % (7638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.88/3.97 % (7638)Termination reason: Unknown
% 15.88/3.97 % (7638)Termination phase: Saturation
% 15.88/3.97
% 15.88/3.97 % (7638)Memory used [KB]: 7419
% 15.88/3.97 % (7638)Time elapsed: 0.199 s
% 15.88/3.97 % (7638)Instructions burned: 358 (million)
% 15.88/3.97 % (7638)------------------------------
% 15.88/3.97 % (7638)------------------------------
% 15.88/3.99 % (7640)Refutation not found, incomplete strategy
% 15.88/3.99 % (7640)------------------------------
% 15.88/3.99 % (7640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.88/3.99 % (7640)Termination reason: Refutation not found, incomplete strategy
% 15.88/3.99
% 15.88/3.99
% 15.88/3.99 % (7640)Memory used [KB]: 6908
% 15.88/3.99 % (7640)Time elapsed: 0.067 s
% 15.88/3.99 % (7640)Instructions burned: 122 (million)
% 15.88/3.99 % (7640)------------------------------
% 15.88/3.99 % (7640)------------------------------
% 15.88/3.99 % (7641)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_7422 for (2978ds/258Mi)
% 15.88/4.01 % (7642)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_7422 for (2978ds/26Mi)
% 15.88/4.02 % (7642)Instruction limit reached!
% 15.88/4.02 % (7642)------------------------------
% 15.88/4.02 % (7642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.88/4.02 % (7642)Termination reason: Unknown
% 15.88/4.02 % (7642)Termination phase: shuffling
% 15.88/4.02
% 15.88/4.02 % (7642)Memory used [KB]: 1918
% 15.88/4.02 % (7642)Time elapsed: 0.016 s
% 15.88/4.02 % (7642)Instructions burned: 27 (million)
% 15.88/4.02 % (7642)------------------------------
% 15.88/4.02 % (7642)------------------------------
% 18.78/4.04 % (7643)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_7422 for (2977ds/995Mi)
% 19.43/4.13 % (7641)Instruction limit reached!
% 19.43/4.13 % (7641)------------------------------
% 19.43/4.13 % (7641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.43/4.13 % (7641)Termination reason: Unknown
% 19.43/4.13 % (7641)Termination phase: Saturation
% 19.43/4.13
% 19.43/4.13 % (7641)Memory used [KB]: 7419
% 19.43/4.13 % (7641)Time elapsed: 0.144 s
% 19.43/4.13 % (7641)Instructions burned: 258 (million)
% 19.43/4.13 % (7641)------------------------------
% 19.43/4.13 % (7641)------------------------------
% 19.43/4.15 % (7644)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_7422 for (2976ds/373Mi)
% 19.78/4.28 % (7632)Instruction limit reached!
% 19.78/4.28 % (7632)------------------------------
% 19.78/4.28 % (7632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.78/4.28 % (7632)Termination reason: Unknown
% 19.78/4.28 % (7632)Termination phase: Saturation
% 19.78/4.28
% 19.78/4.28 % (7632)Memory used [KB]: 10490
% 19.78/4.28 % (7632)Time elapsed: 0.869 s
% 19.78/4.28 % (7632)Instructions burned: 1540 (million)
% 19.78/4.28 % (7632)------------------------------
% 19.78/4.28 % (7632)------------------------------
% 20.27/4.30 % (7645)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_7422 for (2975ds/253Mi)
% 20.27/4.36 % (7644)Instruction limit reached!
% 20.27/4.36 % (7644)------------------------------
% 20.27/4.36 % (7644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.27/4.36 % (7644)Termination reason: Unknown
% 20.27/4.36 % (7644)Termination phase: Saturation
% 20.27/4.36
% 20.27/4.36 % (7644)Memory used [KB]: 8059
% 20.27/4.36 % (7644)Time elapsed: 0.206 s
% 20.27/4.36 % (7644)Instructions burned: 373 (million)
% 20.27/4.36 % (7644)------------------------------
% 20.27/4.36 % (7644)------------------------------
% 20.27/4.38 % (7646)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_7422 for (2974ds/832Mi)
% 20.89/4.43 % (7645)Instruction limit reached!
% 20.89/4.43 % (7645)------------------------------
% 20.89/4.43 % (7645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.89/4.43 % (7645)Termination reason: Unknown
% 20.89/4.43 % (7645)Termination phase: Saturation
% 20.89/4.43
% 20.89/4.43 % (7645)Memory used [KB]: 7675
% 20.89/4.43 % (7645)Time elapsed: 0.137 s
% 20.89/4.43 % (7645)Instructions burned: 254 (million)
% 20.89/4.43 % (7645)------------------------------
% 20.89/4.43 % (7645)------------------------------
% 20.89/4.45 % (7647)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_7422 for (2973ds/668Mi)
% 20.89/4.47 % (7646)Refutation not found, incomplete strategy
% 20.89/4.47 % (7646)------------------------------
% 20.89/4.47 % (7646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.89/4.47 % (7646)Termination reason: Refutation not found, incomplete strategy
% 20.89/4.47
% 20.89/4.47
% 20.89/4.47 % (7646)Memory used [KB]: 7419
% 20.89/4.47 % (7646)Time elapsed: 0.092 s
% 20.89/4.47 % (7646)Instructions burned: 162 (million)
% 20.89/4.47 % (7646)------------------------------
% 20.89/4.47 % (7646)------------------------------
% 20.89/4.49 % (7648)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=40:si=on:rtra=on_0 on DTF2THF_7422 for (2973ds/40Mi)
% 21.56/4.51 % (7648)Instruction limit reached!
% 21.56/4.51 % (7648)------------------------------
% 21.56/4.51 % (7648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.56/4.51 % (7648)Termination reason: Unknown
% 21.56/4.51 % (7648)Termination phase: Property scanning
% 21.56/4.51
% 21.56/4.51 % (7648)Memory used [KB]: 2174
% 21.56/4.51 % (7648)Time elapsed: 0.023 s
% 21.56/4.51 % (7648)Instructions burned: 41 (million)
% 21.56/4.51 % (7648)------------------------------
% 21.56/4.51 % (7648)------------------------------
% 21.56/4.53 % (7649)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_7422 for (2972ds/294Mi)
% 21.56/4.60 % (7643)Instruction limit reached!
% 21.56/4.60 % (7643)------------------------------
% 21.56/4.60 % (7643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.56/4.60 % (7643)Termination reason: Unknown
% 21.56/4.60 % (7643)Termination phase: Saturation
% 21.56/4.60
% 21.56/4.60 % (7643)Memory used [KB]: 9722
% 21.56/4.60 % (7643)Time elapsed: 0.554 s
% 21.56/4.60 % (7643)Instructions burned: 996 (million)
% 21.99/4.60 % (7643)------------------------------
% 21.99/4.60 % (7643)------------------------------
% 21.99/4.62 % (7650)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_7422 for (2971ds/187Mi)
% 21.99/4.68 % (7635)Instruction limit reached!
% 21.99/4.68 % (7635)------------------------------
% 21.99/4.68 % (7635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.99/4.68 % (7635)Termination reason: Unknown
% 21.99/4.68 % (7635)Termination phase: Saturation
% 21.99/4.68
% 21.99/4.68 % (7635)Memory used [KB]: 4477
% 21.99/4.68 % (7635)Time elapsed: 1.056 s
% 21.99/4.68 % (7635)Instructions burned: 1913 (million)
% 21.99/4.68 % (7635)------------------------------
% 21.99/4.68 % (7635)------------------------------
% 21.99/4.69 % (7649)Instruction limit reached!
% 21.99/4.69 % (7649)------------------------------
% 21.99/4.69 % (7649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.99/4.69 % (7649)Termination reason: Unknown
% 21.99/4.69 % (7649)Termination phase: Saturation
% 21.99/4.69
% 21.99/4.69 % (7649)Memory used [KB]: 7291
% 21.99/4.69 % (7649)Time elapsed: 0.159 s
% 21.99/4.69 % (7649)Instructions burned: 295 (million)
% 21.99/4.69 % (7649)------------------------------
% 21.99/4.69 % (7649)------------------------------
% 23.15/4.70 % (7651)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_7422 for (2971ds/371Mi)
% 23.15/4.71 % (7652)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_7422 for (2971ds/1827Mi)
% 23.15/4.72 % (7650)Instruction limit reached!
% 23.15/4.72 % (7650)------------------------------
% 23.15/4.72 % (7650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.15/4.72 % (7650)Termination reason: Unknown
% 23.15/4.72 % (7650)Termination phase: Saturation
% 23.15/4.72
% 23.15/4.72 % (7650)Memory used [KB]: 7291
% 23.15/4.72 % (7650)Time elapsed: 0.107 s
% 23.15/4.72 % (7650)Instructions burned: 187 (million)
% 23.15/4.72 % (7650)------------------------------
% 23.15/4.72 % (7650)------------------------------
% 23.15/4.75 % (7653)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_7422 for (2970ds/70Mi)
% 23.15/4.78 % (7653)Instruction limit reached!
% 23.15/4.78 % (7653)------------------------------
% 23.15/4.78 % (7653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.15/4.78 % (7653)Termination reason: Unknown
% 23.15/4.78 % (7653)Termination phase: Property scanning
% 23.15/4.78
% 23.15/4.78 % (7653)Memory used [KB]: 2302
% 23.15/4.78 % (7653)Time elapsed: 0.038 s
% 23.15/4.78 % (7653)Instructions burned: 71 (million)
% 23.15/4.78 % (7653)------------------------------
% 23.15/4.78 % (7653)------------------------------
% 23.64/4.80 % (7654)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_7422 for (2970ds/316Mi)
% 23.64/4.82 % (7647)Instruction limit reached!
% 23.64/4.82 % (7647)------------------------------
% 23.64/4.82 % (7647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.64/4.82 % (7647)Termination reason: Unknown
% 23.64/4.82 % (7647)Termination phase: Saturation
% 23.64/4.82
% 23.64/4.82 % (7647)Memory used [KB]: 14328
% 23.64/4.82 % (7647)Time elapsed: 0.371 s
% 23.64/4.82 % (7647)Instructions burned: 669 (million)
% 23.64/4.82 % (7647)------------------------------
% 23.64/4.82 % (7647)------------------------------
% 23.64/4.85 % (7655)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_7422 for (2969ds/932Mi)
% 24.32/4.91 % (7651)Instruction limit reached!
% 24.32/4.91 % (7651)------------------------------
% 24.32/4.91 % (7651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.32/4.91 % (7651)Termination reason: Unknown
% 24.32/4.91 % (7651)Termination phase: Saturation
% 24.32/4.91
% 24.32/4.91 % (7651)Memory used [KB]: 7675
% 24.32/4.91 % (7651)Time elapsed: 0.212 s
% 24.32/4.91 % (7651)Instructions burned: 372 (million)
% 24.32/4.91 % (7651)------------------------------
% 24.32/4.91 % (7651)------------------------------
% 24.32/4.91 % (7654)Refutation not found, incomplete strategy
% 24.32/4.91 % (7654)------------------------------
% 24.32/4.91 % (7654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.32/4.91 % (7654)Termination reason: Refutation not found, incomplete strategy
% 24.32/4.91
% 24.32/4.91
% 24.32/4.91 % (7654)Memory used [KB]: 7547
% 24.32/4.91 % (7654)Time elapsed: 0.112 s
% 24.32/4.91 % (7654)Instructions burned: 201 (million)
% 24.32/4.91 % (7654)------------------------------
% 24.32/4.91 % (7654)------------------------------
% 24.32/4.93 % (7656)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_7422 for (2968ds/4714Mi)
% 24.32/4.93 % (7657)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_7422 for (2968ds/8250Mi)
% 25.76/5.05 % (7656)Refutation not found, incomplete strategy
% 25.76/5.05 % (7656)------------------------------
% 25.76/5.05 % (7656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.76/5.05 % (7656)Termination reason: Refutation not found, incomplete strategy
% 25.76/5.05
% 25.76/5.05
% 25.76/5.05 % (7656)Memory used [KB]: 7675
% 25.76/5.05 % (7656)Time elapsed: 0.117 s
% 25.76/5.05 % (7656)Instructions burned: 218 (million)
% 25.76/5.05 % (7656)------------------------------
% 25.76/5.05 % (7656)------------------------------
% 25.76/5.07 % (7658)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_7422 for (2967ds/770Mi)
% 26.44/5.14 % (7658)Refutation not found, incomplete strategy
% 26.44/5.14 % (7658)------------------------------
% 26.44/5.14 % (7658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.44/5.14 % (7658)Termination reason: Refutation not found, incomplete strategy
% 26.44/5.14
% 26.44/5.14
% 26.44/5.14 % (7658)Memory used [KB]: 6652
% 26.44/5.14 % (7658)Time elapsed: 0.068 s
% 26.44/5.14 % (7658)Instructions burned: 116 (million)
% 26.44/5.14 % (7658)------------------------------
% 26.44/5.14 % (7658)------------------------------
% 26.44/5.16 % (7659)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_7422 for (2966ds/794Mi)
% 27.51/5.37 % (7655)Instruction limit reached!
% 27.51/5.37 % (7655)------------------------------
% 27.51/5.37 % (7655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.51/5.37 % (7655)Termination reason: Unknown
% 27.51/5.37 % (7655)Termination phase: Saturation
% 27.51/5.37
% 27.51/5.37 % (7655)Memory used [KB]: 9978
% 27.51/5.37 % (7655)Time elapsed: 0.523 s
% 27.51/5.37 % (7655)Instructions burned: 932 (million)
% 27.51/5.37 % (7655)------------------------------
% 27.51/5.37 % (7655)------------------------------
% 27.51/5.39 % (7660)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_7422 for (2964ds/464Mi)
% 29.10/5.62 % (7659)Instruction limit reached!
% 29.10/5.62 % (7659)------------------------------
% 29.10/5.62 % (7659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.10/5.62 % (7659)Termination reason: Unknown
% 29.10/5.62 % (7659)Termination phase: Saturation
% 29.10/5.62
% 29.10/5.62 % (7659)Memory used [KB]: 4733
% 29.10/5.62 % (7659)Time elapsed: 0.464 s
% 29.10/5.62 % (7659)Instructions burned: 794 (million)
% 29.10/5.62 % (7659)------------------------------
% 29.10/5.62 % (7659)------------------------------
% 29.10/5.62 % (7660)Instruction limit reached!
% 29.10/5.62 % (7660)------------------------------
% 29.10/5.62 % (7660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.10/5.62 % (7660)Termination reason: Unknown
% 29.10/5.62 % (7660)Termination phase: Saturation
% 29.10/5.62
% 29.10/5.62 % (7660)Memory used [KB]: 7291
% 29.10/5.62 % (7660)Time elapsed: 0.236 s
% 29.10/5.62 % (7660)Instructions burned: 464 (million)
% 29.10/5.62 % (7660)------------------------------
% 29.10/5.62 % (7660)------------------------------
% 29.10/5.64 % (7661)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_7422 for (2961ds/1376Mi)
% 29.10/5.64 % (7662)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_7422 for (2961ds/906Mi)
% 30.35/5.75 % (7652)Instruction limit reached!
% 30.35/5.75 % (7652)------------------------------
% 30.35/5.75 % (7652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.35/5.75 % (7652)Termination reason: Unknown
% 30.35/5.75 % (7652)Termination phase: Saturation
% 30.35/5.75
% 30.35/5.75 % (7652)Memory used [KB]: 10234
% 30.35/5.75 % (7652)Time elapsed: 1.044 s
% 30.35/5.75 % (7652)Instructions burned: 1827 (million)
% 30.35/5.75 % (7652)------------------------------
% 30.35/5.75 % (7652)------------------------------
% 30.35/5.78 % (7663)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_7422 for (2960ds/434Mi)
% 30.82/5.88 % (7631)Instruction limit reached!
% 30.82/5.88 % (7631)------------------------------
% 30.82/5.88 % (7631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.82/5.88 % (7631)Termination reason: Unknown
% 30.82/5.88 % (7631)Termination phase: Saturation
% 30.82/5.88
% 30.82/5.88 % (7631)Memory used [KB]: 10362
% 30.82/5.88 % (7631)Time elapsed: 2.493 s
% 30.82/5.88 % (7631)Instructions burned: 4437 (million)
% 30.82/5.88 % (7631)------------------------------
% 30.82/5.88 % (7631)------------------------------
% 31.22/5.90 % (7664)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_7422 for (2959ds/865Mi)
% 31.22/5.97 % (7636)Instruction limit reached!
% 31.22/5.97 % (7636)------------------------------
% 31.22/5.97 % (7636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.22/5.97 % (7636)Termination reason: Unknown
% 31.22/5.97 % (7636)Termination phase: Saturation
% 31.22/5.97
% 31.22/5.97 % (7636)Memory used [KB]: 12409
% 31.22/5.97 % (7636)Time elapsed: 2.259 s
% 31.22/5.97 % (7636)Instructions burned: 4351 (million)
% 31.22/5.97 % (7636)------------------------------
% 31.22/5.97 % (7636)------------------------------
% 31.22/5.99 % (7665)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_7422 for (2958ds/593Mi)
% 31.22/6.01 % (7663)Instruction limit reached!
% 31.22/6.01 % (7663)------------------------------
% 31.22/6.01 % (7663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.22/6.01 % (7663)Termination reason: Unknown
% 31.22/6.01 % (7663)Termination phase: Saturation
% 31.22/6.01
% 31.22/6.01 % (7663)Memory used [KB]: 7291
% 31.22/6.01 % (7663)Time elapsed: 0.240 s
% 31.22/6.01 % (7663)Instructions burned: 435 (million)
% 31.22/6.01 % (7663)------------------------------
% 31.22/6.01 % (7663)------------------------------
% 32.76/6.03 % (7666)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_7422 for (2957ds/443Mi)
% 33.40/6.18 % (7662)Instruction limit reached!
% 33.40/6.18 % (7662)------------------------------
% 33.40/6.18 % (7662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.40/6.18 % (7662)Termination reason: Unknown
% 33.40/6.18 % (7662)Termination phase: Saturation
% 33.40/6.18
% 33.40/6.18 % (7662)Memory used [KB]: 11001
% 33.40/6.18 % (7662)Time elapsed: 0.540 s
% 33.40/6.18 % (7662)Instructions burned: 906 (million)
% 33.40/6.18 % (7662)------------------------------
% 33.40/6.18 % (7662)------------------------------
% 33.79/6.20 % (7667)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_7422 for (2956ds/594Mi)
% 33.79/6.29 % (7666)Instruction limit reached!
% 33.79/6.29 % (7666)------------------------------
% 33.79/6.29 % (7666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.79/6.29 % (7666)Termination reason: Unknown
% 33.79/6.29 % (7666)Termination phase: Saturation
% 33.79/6.29
% 33.79/6.29 % (7666)Memory used [KB]: 8187
% 33.79/6.29 % (7666)Time elapsed: 0.277 s
% 33.79/6.29 % (7666)Instructions burned: 443 (million)
% 33.79/6.29 % (7666)------------------------------
% 33.79/6.29 % (7666)------------------------------
% 34.56/6.31 % (7668)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_7422 for (2955ds/327Mi)
% 34.56/6.32 % (7665)Instruction limit reached!
% 34.56/6.32 % (7665)------------------------------
% 34.56/6.32 % (7665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.56/6.32 % (7665)Termination reason: Unknown
% 34.56/6.32 % (7665)Termination phase: Saturation
% 34.56/6.32
% 34.56/6.32 % (7665)Memory used [KB]: 9210
% 34.56/6.32 % (7665)Time elapsed: 0.328 s
% 34.56/6.32 % (7665)Instructions burned: 593 (million)
% 34.56/6.32 % (7665)------------------------------
% 34.56/6.32 % (7665)------------------------------
% 34.56/6.34 % (7669)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_7422 for (2954ds/5411Mi)
% 34.56/6.37 % (7664)Instruction limit reached!
% 34.56/6.37 % (7664)------------------------------
% 34.56/6.37 % (7664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.56/6.37 % (7664)Termination reason: Unknown
% 34.56/6.37 % (7664)Termination phase: Saturation
% 34.56/6.37
% 34.56/6.37 % (7664)Memory used [KB]: 8955
% 34.56/6.37 % (7664)Time elapsed: 0.471 s
% 34.56/6.37 % (7664)Instructions burned: 865 (million)
% 34.56/6.37 % (7664)------------------------------
% 34.56/6.37 % (7664)------------------------------
% 34.56/6.39 % (7669)Refutation not found, incomplete strategy
% 34.56/6.39 % (7669)------------------------------
% 34.56/6.39 % (7669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.56/6.39 % (7669)Termination reason: Refutation not found, incomplete strategy
% 34.56/6.39
% 34.56/6.39
% 34.56/6.39 % (7669)Memory used [KB]: 6652
% 34.56/6.39 % (7669)Time elapsed: 0.071 s
% 34.56/6.39 % (7669)Instructions burned: 82 (million)
% 34.56/6.39 % (7669)------------------------------
% 34.56/6.39 % (7669)------------------------------
% 34.56/6.39 % (7670)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_7422 for (2954ds/1762Mi)
% 35.05/6.41 % (7671)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_7422 for (2954ds/96Mi)
% 35.05/6.44 % (7661)Instruction limit reached!
% 35.05/6.44 % (7661)------------------------------
% 35.05/6.44 % (7661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.05/6.44 % (7661)Termination reason: Unknown
% 35.05/6.44 % (7661)Termination phase: Saturation
% 35.05/6.44
% 35.05/6.44 % (7661)Memory used [KB]: 13304
% 35.05/6.44 % (7661)Time elapsed: 0.800 s
% 35.05/6.44 % (7661)Instructions burned: 1377 (million)
% 35.05/6.44 % (7661)------------------------------
% 35.05/6.44 % (7661)------------------------------
% 35.05/6.45 % (7672)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_7422 for (2953ds/503Mi)
% 35.05/6.46 % (7671)Instruction limit reached!
% 35.05/6.46 % (7671)------------------------------
% 35.05/6.46 % (7671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.05/6.46 % (7671)Termination reason: Unknown
% 35.05/6.46 % (7671)Termination phase: Function definition elimination
% 35.05/6.46
% 35.05/6.46 % (7671)Memory used [KB]: 2302
% 35.05/6.46 % (7671)Time elapsed: 0.052 s
% 35.05/6.46 % (7671)Instructions burned: 96 (million)
% 35.05/6.46 % (7671)------------------------------
% 35.05/6.46 % (7671)------------------------------
% 35.05/6.48 % (7673)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_7422 for (2953ds/90Mi)
% 35.37/6.50 % (7668)Instruction limit reached!
% 35.37/6.50 % (7668)------------------------------
% 35.37/6.50 % (7668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.37/6.50 % (7668)Termination reason: Unknown
% 35.37/6.50 % (7668)Termination phase: Saturation
% 35.37/6.50
% 35.37/6.50 % (7668)Memory used [KB]: 7547
% 35.37/6.50 % (7668)Time elapsed: 0.210 s
% 35.37/6.50 % (7668)Instructions burned: 327 (million)
% 35.37/6.50 % (7668)------------------------------
% 35.37/6.50 % (7668)------------------------------
% 35.37/6.51 % (7673)Instruction limit reached!
% 35.37/6.51 % (7673)------------------------------
% 35.37/6.51 % (7673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.37/6.51 % (7673)Termination reason: Unknown
% 35.37/6.51 % (7673)Termination phase: Saturation
% 35.37/6.51
% 35.37/6.51 % (7673)Memory used [KB]: 6524
% 35.37/6.51 % (7673)Time elapsed: 0.029 s
% 35.37/6.51 % (7673)Instructions burned: 92 (million)
% 35.37/6.51 % (7673)------------------------------
% 35.37/6.51 % (7673)------------------------------
% 35.37/6.52 % (7674)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_7422 for (2952ds/593Mi)
% 35.37/6.53 % (7634)Instruction limit reached!
% 35.37/6.53 % (7634)------------------------------
% 35.37/6.53 % (7634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.37/6.53 % (7634)Termination reason: Unknown
% 35.37/6.53 % (7634)Termination phase: Saturation
% 35.37/6.53
% 35.37/6.53 % (7634)Memory used [KB]: 15863
% 35.37/6.53 % (7634)Time elapsed: 3.051 s
% 35.37/6.53 % (7634)Instructions burned: 5205 (million)
% 35.37/6.53 % (7634)------------------------------
% 35.37/6.53 % (7634)------------------------------
% 35.37/6.53 % (7667)Instruction limit reached!
% 35.37/6.53 % (7667)------------------------------
% 35.37/6.53 % (7667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.37/6.53 % (7667)Termination reason: Unknown
% 35.37/6.53 % (7667)Termination phase: Saturation
% 35.37/6.53
% 35.37/6.53 % (7667)Memory used [KB]: 8059
% 35.37/6.53 % (7667)Time elapsed: 0.351 s
% 35.37/6.53 % (7667)Instructions burned: 595 (million)
% 35.37/6.53 % (7667)------------------------------
% 35.37/6.53 % (7667)------------------------------
% 35.37/6.53 % (7675)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_7422 for (2952ds/1512Mi)
% 35.37/6.55 % (7676)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_7422 for (2952ds/569Mi)
% 35.37/6.56 % (7677)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_7422 for (2952ds/501Mi)
% 36.10/6.61 % (7677)Refutation not found, incomplete strategy
% 36.10/6.61 % (7677)------------------------------
% 36.10/6.61 % (7677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.10/6.61 % (7677)Termination reason: Refutation not found, incomplete strategy
% 36.10/6.61
% 36.10/6.61
% 36.10/6.61 % (7677)Memory used [KB]: 7547
% 36.10/6.61 % (7677)Time elapsed: 0.073 s
% 36.10/6.61 % (7677)Instructions burned: 160 (million)
% 36.10/6.61 % (7677)------------------------------
% 36.10/6.61 % (7677)------------------------------
% 36.10/6.62 % (7678)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_7422 for (2951ds/562Mi)
% 36.27/6.71 % (7672)Instruction limit reached!
% 36.27/6.71 % (7672)------------------------------
% 36.27/6.71 % (7672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.27/6.71 % (7672)Termination reason: Unknown
% 36.27/6.71 % (7672)Termination phase: Saturation
% 36.27/6.71
% 36.27/6.71 % (7672)Memory used [KB]: 7547
% 36.27/6.71 % (7672)Time elapsed: 0.263 s
% 36.27/6.71 % (7672)Instructions burned: 503 (million)
% 36.27/6.71 % (7672)------------------------------
% 36.27/6.71 % (7672)------------------------------
% 36.27/6.74 % (7679)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_7422 for (2950ds/406Mi)
% 36.27/6.79 % (7678)Instruction limit reached!
% 36.27/6.79 % (7678)------------------------------
% 36.27/6.79 % (7678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.27/6.79 % (7678)Termination reason: Unknown
% 36.27/6.79 % (7678)Termination phase: Saturation
% 36.27/6.79
% 36.27/6.79 % (7678)Memory used [KB]: 7931
% 36.27/6.79 % (7678)Time elapsed: 0.171 s
% 36.27/6.79 % (7678)Instructions burned: 565 (million)
% 36.27/6.79 % (7678)------------------------------
% 36.27/6.79 % (7678)------------------------------
% 36.83/6.80 % (7680)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_7422 for (2950ds/582Mi)
% 36.83/6.86 % (7676)Instruction limit reached!
% 36.83/6.86 % (7676)------------------------------
% 36.83/6.86 % (7676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.83/6.86 % (7676)Termination reason: Unknown
% 36.83/6.86 % (7676)Termination phase: Saturation
% 36.83/6.86
% 36.83/6.86 % (7676)Memory used [KB]: 8955
% 36.83/6.86 % (7676)Time elapsed: 0.309 s
% 36.83/6.86 % (7676)Instructions burned: 569 (million)
% 36.83/6.86 % (7676)------------------------------
% 36.83/6.86 % (7676)------------------------------
% 36.83/6.86 % (7674)Instruction limit reached!
% 36.83/6.86 % (7674)------------------------------
% 36.83/6.86 % (7674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.83/6.86 % (7674)Termination reason: Unknown
% 36.83/6.86 % (7674)Termination phase: Saturation
% 36.83/6.86
% 36.83/6.86 % (7674)Memory used [KB]: 8187
% 36.83/6.86 % (7674)Time elapsed: 0.339 s
% 36.83/6.86 % (7674)Instructions burned: 593 (million)
% 36.83/6.86 % (7674)------------------------------
% 36.83/6.86 % (7674)------------------------------
% 36.83/6.88 % (7682)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_7422 for (2949ds/393Mi)
% 37.60/6.90 % (7681)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_7422 for (2949ds/456Mi)
% 37.60/6.97 % (7679)Instruction limit reached!
% 37.60/6.97 % (7679)------------------------------
% 37.60/6.97 % (7679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.60/6.97 % (7679)Termination reason: Unknown
% 37.60/6.97 % (7679)Termination phase: Saturation
% 37.60/6.97
% 37.60/6.97 % (7679)Memory used [KB]: 7675
% 37.60/6.97 % (7679)Time elapsed: 0.236 s
% 37.60/6.97 % (7679)Instructions burned: 407 (million)
% 37.60/6.97 % (7679)------------------------------
% 37.60/6.97 % (7679)------------------------------
% 37.60/6.99 % (7683)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_7422 for (2948ds/1335Mi)
% 37.60/7.01 % (7680)Instruction limit reached!
% 37.60/7.01 % (7680)------------------------------
% 37.60/7.01 % (7680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.60/7.01 % (7680)Termination reason: Unknown
% 37.60/7.01 % (7680)Termination phase: Saturation
% 37.60/7.01
% 37.60/7.01 % (7680)Memory used [KB]: 8187
% 37.60/7.01 % (7680)Time elapsed: 0.216 s
% 37.60/7.01 % (7680)Instructions burned: 584 (million)
% 37.60/7.01 % (7680)------------------------------
% 37.60/7.01 % (7680)------------------------------
% 39.52/7.03 % (7684)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_7422 for (2947ds/3373Mi)
% 39.52/7.09 % (7682)Instruction limit reached!
% 39.52/7.09 % (7682)------------------------------
% 39.52/7.09 % (7682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.52/7.09 % (7682)Termination reason: Unknown
% 39.52/7.09 % (7682)Termination phase: Saturation
% 39.52/7.09
% 39.52/7.09 % (7682)Memory used [KB]: 7675
% 39.52/7.09 % (7682)Time elapsed: 0.210 s
% 39.52/7.09 % (7682)Instructions burned: 394 (million)
% 39.52/7.09 % (7682)------------------------------
% 39.52/7.09 % (7682)------------------------------
% 39.52/7.11 % (7685)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_7422 for (2947ds/474Mi)
% 40.15/7.16 % (7681)Instruction limit reached!
% 40.15/7.16 % (7681)------------------------------
% 40.15/7.16 % (7681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.15/7.16 % (7681)Termination reason: Unknown
% 40.15/7.16 % (7681)Termination phase: Saturation
% 40.15/7.16
% 40.15/7.16 % (7681)Memory used [KB]: 7931
% 40.15/7.16 % (7681)Time elapsed: 0.282 s
% 40.15/7.16 % (7681)Instructions burned: 457 (million)
% 40.15/7.16 % (7681)------------------------------
% 40.15/7.16 % (7681)------------------------------
% 40.15/7.18 % (7686)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_7422 for (2946ds/157Mi)
% 40.53/7.25 % (7686)Instruction limit reached!
% 40.53/7.25 % (7686)------------------------------
% 40.53/7.25 % (7686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.53/7.25 % (7686)Termination reason: Unknown
% 40.53/7.25 % (7686)Termination phase: Saturation
% 40.53/7.25
% 40.53/7.25 % (7686)Memory used [KB]: 6908
% 40.53/7.25 % (7686)Time elapsed: 0.079 s
% 40.53/7.25 % (7686)Instructions burned: 157 (million)
% 40.53/7.25 % (7686)------------------------------
% 40.53/7.25 % (7686)------------------------------
% 40.53/7.28 % (7687)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_7422 for (2945ds/590Mi)
% 41.02/7.38 % (7675)Instruction limit reached!
% 41.02/7.38 % (7675)------------------------------
% 41.02/7.38 % (7675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.02/7.38 % (7675)Termination reason: Unknown
% 41.02/7.38 % (7675)Termination phase: Saturation
% 41.02/7.38
% 41.02/7.38 % (7675)Memory used [KB]: 8059
% 41.02/7.38 % (7675)Time elapsed: 0.859 s
% 41.02/7.38 % (7675)Instructions burned: 1513 (million)
% 41.02/7.38 % (7675)------------------------------
% 41.02/7.38 % (7675)------------------------------
% 41.02/7.38 % (7670)Instruction limit reached!
% 41.02/7.38 % (7670)------------------------------
% 41.02/7.38 % (7670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.02/7.38 % (7670)Termination reason: Unknown
% 41.02/7.38 % (7670)Termination phase: Saturation
% 41.02/7.38
% 41.02/7.38 % (7670)Memory used [KB]: 10362
% 41.02/7.38 % (7670)Time elapsed: 1.014 s
% 41.02/7.38 % (7670)Instructions burned: 1763 (million)
% 41.02/7.38 % (7670)------------------------------
% 41.02/7.38 % (7670)------------------------------
% 41.02/7.38 % (7685)Instruction limit reached!
% 41.02/7.38 % (7685)------------------------------
% 41.02/7.38 % (7685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.02/7.38 % (7685)Termination reason: Unknown
% 41.02/7.38 % (7685)Termination phase: Saturation
% 41.02/7.38
% 41.02/7.38 % (7685)Memory used [KB]: 8315
% 41.02/7.38 % (7685)Time elapsed: 0.268 s
% 41.02/7.38 % (7685)Instructions burned: 474 (million)
% 41.02/7.38 % (7685)------------------------------
% 41.02/7.38 % (7685)------------------------------
% 41.71/7.40 % (7688)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_7422 for (2944ds/104Mi)
% 41.71/7.40 % (7689)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_7422 for (2944ds/414Mi)
% 41.71/7.40 % (7690)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_7422 for (2944ds/715Mi)
% 41.71/7.45 % (7688)Instruction limit reached!
% 41.71/7.45 % (7688)------------------------------
% 41.71/7.45 % (7688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.71/7.45 % (7688)Termination reason: Unknown
% 41.71/7.45 % (7688)Termination phase: Saturation
% 41.71/7.45
% 41.71/7.45 % (7688)Memory used [KB]: 2558
% 41.71/7.45 % (7688)Time elapsed: 0.059 s
% 41.71/7.45 % (7688)Instructions burned: 104 (million)
% 41.71/7.45 % (7688)------------------------------
% 41.71/7.45 % (7688)------------------------------
% 41.71/7.48 % (7691)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_7422 for (2943ds/961Mi)
% 41.99/7.58 % (7687)Instruction limit reached!
% 41.99/7.58 % (7687)------------------------------
% 41.99/7.58 % (7687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.99/7.58 % (7687)Termination reason: Unknown
% 41.99/7.58 % (7687)Termination phase: Saturation
% 41.99/7.58
% 41.99/7.58 % (7687)Memory used [KB]: 7803
% 41.99/7.58 % (7687)Time elapsed: 0.306 s
% 41.99/7.58 % (7687)Instructions burned: 591 (million)
% 41.99/7.58 % (7687)------------------------------
% 41.99/7.58 % (7687)------------------------------
% 42.51/7.60 % (7692)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_7422 for (2942ds/1213Mi)
% 42.51/7.62 % (7689)Instruction limit reached!
% 42.51/7.62 % (7689)------------------------------
% 42.51/7.62 % (7689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.51/7.62 % (7689)Termination reason: Unknown
% 42.51/7.62 % (7689)Termination phase: Saturation
% 42.51/7.62
% 42.51/7.62 % (7689)Memory used [KB]: 7675
% 42.51/7.62 % (7689)Time elapsed: 0.225 s
% 42.51/7.62 % (7689)Instructions burned: 415 (million)
% 42.51/7.62 % (7689)------------------------------
% 42.51/7.62 % (7689)------------------------------
% 42.51/7.64 % (7693)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_7422 for (2941ds/1979Mi)
% 42.96/7.72 % (7683)Instruction limit reached!
% 42.96/7.72 % (7683)------------------------------
% 42.96/7.72 % (7683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.96/7.72 % (7683)Termination reason: Unknown
% 42.96/7.72 % (7683)Termination phase: Saturation
% 42.96/7.72
% 42.96/7.72 % (7683)Memory used [KB]: 8571
% 42.96/7.72 % (7683)Time elapsed: 0.744 s
% 42.96/7.72 % (7683)Instructions burned: 1336 (million)
% 42.96/7.72 % (7683)------------------------------
% 42.96/7.72 % (7683)------------------------------
% 42.96/7.74 % (7694)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_7422 for (2940ds/481Mi)
% 43.09/7.80 % (7690)Instruction limit reached!
% 43.09/7.80 % (7690)------------------------------
% 43.09/7.80 % (7690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.09/7.80 % (7690)Termination reason: Unknown
% 43.09/7.80 % (7690)Termination phase: Saturation
% 43.09/7.80
% 43.09/7.80 % (7690)Memory used [KB]: 4989
% 43.09/7.80 % (7690)Time elapsed: 0.407 s
% 43.09/7.80 % (7690)Instructions burned: 715 (million)
% 43.09/7.80 % (7690)------------------------------
% 43.09/7.80 % (7690)------------------------------
% 43.09/7.82 % (7695)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_7422 for (2939ds/783Mi)
% 43.62/8.00 % (7691)Instruction limit reached!
% 43.62/8.00 % (7691)------------------------------
% 43.62/8.00 % (7691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.62/8.00 % (7691)Termination reason: Unknown
% 43.62/8.00 % (7691)Termination phase: Saturation
% 43.62/8.00
% 43.62/8.00 % (7691)Memory used [KB]: 8187
% 43.62/8.00 % (7691)Time elapsed: 0.532 s
% 43.62/8.01 % (7691)Instructions burned: 962 (million)
% 43.62/8.01 % (7691)------------------------------
% 43.62/8.01 % (7691)------------------------------
% 43.62/8.01 % (7694)Instruction limit reached!
% 43.62/8.01 % (7694)------------------------------
% 43.62/8.01 % (7694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.62/8.01 % (7694)Termination reason: Unknown
% 43.62/8.01 % (7694)Termination phase: Saturation
% 43.62/8.01
% 43.62/8.01 % (7694)Memory used [KB]: 8187
% 43.62/8.01 % (7694)Time elapsed: 0.273 s
% 43.62/8.01 % (7694)Instructions burned: 481 (million)
% 43.62/8.01 % (7694)------------------------------
% 43.62/8.01 % (7694)------------------------------
% 43.62/8.03 % (7696)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_7422 for (2937ds/432Mi)
% 46.61/8.03 % (7697)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_7422 for (2937ds/1670Mi)
% 47.47/8.25 % (7695)Instruction limit reached!
% 47.47/8.25 % (7695)------------------------------
% 47.47/8.25 % (7695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.47/8.25 % (7695)Termination reason: Unknown
% 47.47/8.25 % (7695)Termination phase: Saturation
% 47.47/8.25
% 47.47/8.25 % (7695)Memory used [KB]: 8187
% 47.47/8.25 % (7695)Time elapsed: 0.428 s
% 47.47/8.25 % (7695)Instructions burned: 783 (million)
% 47.47/8.25 % (7695)------------------------------
% 47.47/8.25 % (7695)------------------------------
% 47.47/8.26 % (7696)Instruction limit reached!
% 47.47/8.26 % (7696)------------------------------
% 47.47/8.26 % (7696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.47/8.26 % (7696)Termination reason: Unknown
% 47.47/8.26 % (7696)Termination phase: Saturation
% 47.47/8.26
% 47.47/8.26 % (7696)Memory used [KB]: 7164
% 47.47/8.26 % (7696)Time elapsed: 0.239 s
% 47.47/8.26 % (7696)Instructions burned: 433 (million)
% 47.47/8.26 % (7696)------------------------------
% 47.47/8.26 % (7696)------------------------------
% 47.47/8.27 % (7698)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_7422 for (2935ds/90Mi)
% 47.47/8.28 % (7692)Instruction limit reached!
% 47.47/8.28 % (7692)------------------------------
% 47.47/8.28 % (7692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.47/8.28 % (7692)Termination reason: Unknown
% 47.47/8.28 % (7692)Termination phase: Saturation
% 47.47/8.28
% 47.47/8.28 % (7692)Memory used [KB]: 8315
% 47.47/8.28 % (7692)Time elapsed: 0.679 s
% 47.47/8.28 % (7692)Instructions burned: 1214 (million)
% 47.47/8.28 % (7692)------------------------------
% 47.47/8.28 % (7692)------------------------------
% 47.47/8.28 % (7699)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_7422 for (2935ds/346Mi)
% 47.47/8.29 % (7700)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_7422 for (2935ds/401Mi)
% 48.17/8.32 % (7698)Instruction limit reached!
% 48.17/8.32 % (7698)------------------------------
% 48.17/8.32 % (7698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.17/8.32 % (7698)Termination reason: Unknown
% 48.17/8.32 % (7698)Termination phase: Saturation
% 48.17/8.32
% 48.17/8.32 % (7698)Memory used [KB]: 6524
% 48.17/8.32 % (7698)Time elapsed: 0.050 s
% 48.17/8.32 % (7698)Instructions burned: 91 (million)
% 48.17/8.32 % (7698)------------------------------
% 48.17/8.32 % (7698)------------------------------
% 48.17/8.34 % (7701)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_7422 for (2934ds/6454Mi)
% 48.55/8.48 % (7699)Instruction limit reached!
% 48.55/8.48 % (7699)------------------------------
% 48.55/8.48 % (7699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.55/8.48 % (7699)Termination reason: Unknown
% 48.55/8.48 % (7699)Termination phase: Saturation
% 48.55/8.48
% 48.55/8.48 % (7699)Memory used [KB]: 7803
% 48.55/8.48 % (7699)Time elapsed: 0.197 s
% 48.55/8.48 % (7699)Instructions burned: 347 (million)
% 48.55/8.48 % (7699)------------------------------
% 48.55/8.48 % (7699)------------------------------
% 49.06/8.50 % (7702)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_7422 for (2933ds/283Mi)
% 49.06/8.51 % (7700)Instruction limit reached!
% 49.06/8.51 % (7700)------------------------------
% 49.06/8.51 % (7700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.06/8.51 % (7700)Termination reason: Unknown
% 49.06/8.51 % (7700)Termination phase: Saturation
% 49.06/8.51
% 49.06/8.51 % (7700)Memory used [KB]: 8827
% 49.06/8.51 % (7700)Time elapsed: 0.222 s
% 49.06/8.51 % (7700)Instructions burned: 402 (million)
% 49.06/8.51 % (7700)------------------------------
% 49.06/8.51 % (7700)------------------------------
% 49.06/8.53 % (7703)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_7422 for (2932ds/865Mi)
% 49.59/8.66 % (7702)Instruction limit reached!
% 49.59/8.66 % (7702)------------------------------
% 49.59/8.66 % (7702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.59/8.66 % (7702)Termination reason: Unknown
% 49.59/8.66 % (7702)Termination phase: Saturation
% 49.59/8.66
% 49.59/8.66 % (7702)Memory used [KB]: 7803
% 49.59/8.66 % (7702)Time elapsed: 0.182 s
% 49.59/8.66 % (7702)Instructions burned: 283 (million)
% 49.59/8.66 % (7702)------------------------------
% 49.59/8.66 % (7702)------------------------------
% 49.59/8.68 % (7704)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_7422 for (2931ds/4528Mi)
% 50.07/8.73 % (7701)First to succeed.
% 50.07/8.73 % (7701)Refutation found. Thanks to Tanya!
% 50.07/8.73 % SZS status Theorem for DTF2THF_7422
% 50.07/8.73 % SZS output start Proof for DTF2THF_7422
% 50.07/8.73 thf(type_def_5, type, variable: $tType).
% 50.07/8.73 thf(type_def_6, type, real: $tType).
% 50.07/8.73 thf(type_def_8, type, set: ($tType) > $tType).
% 50.07/8.73 thf(type_def_9, type, denotational_interp: $tType).
% 50.07/8.73 thf(type_def_10, type, char: $tType).
% 50.07/8.73 thf(type_def_11, type, trm: $tType).
% 50.07/8.73 thf(type_def_12, type, nat: $tType).
% 50.07/8.73 thf(type_def_13, type, option: ($tType) > $tType).
% 50.07/8.73 thf(type_def_14, type, fml: $tType).
% 50.07/8.73 thf(type_def_15, type, game: $tType).
% 50.07/8.73 thf(type_def_16, type, product_prod: ($tType * $tType) > $tType).
% 50.07/8.73 thf(func_def_0, type, denotational_interp: $tType).
% 50.07/8.73 thf(func_def_1, type, product_prod: ($tType * $tType) > $tType).
% 50.07/8.73 thf(func_def_2, type, variable: $tType).
% 50.07/8.73 thf(func_def_3, type, option: ($tType) > $tType).
% 50.07/8.73 thf(func_def_4, type, game: $tType).
% 50.07/8.73 thf(func_def_5, type, char: $tType).
% 50.07/8.73 thf(func_def_6, type, trm: $tType).
% 50.07/8.73 thf(func_def_7, type, fml: $tType).
% 50.07/8.73 thf(func_def_8, type, real: $tType).
% 50.07/8.73 thf(func_def_9, type, set: ($tType) > $tType).
% 50.07/8.73 thf(func_def_10, type, nat: $tType).
% 50.07/8.73 thf(func_def_11, type, bounded_lattice: !>[X0: $tType]:($o)).
% 50.07/8.73 thf(func_def_12, type, type: !>[X0: $tType]:($o)).
% 50.07/8.73 thf(func_def_13, type, zero: !>[X0: $tType]:($o)).
% 50.07/8.73 thf(func_def_14, type, uminus: !>[X0: $tType]:($o)).
% 50.07/8.73 thf(func_def_15, type, bot: !>[X0: $tType]:($o)).
% 50.07/8.73 thf(func_def_16, type, group_add: !>[X0: $tType]:($o)).
% 50.07/8.73 thf(func_def_17, type, lattice: !>[X0: $tType]:($o)).
% 50.07/8.73 thf(func_def_18, type, preorder: !>[X0: $tType]:($o)).
% 50.07/8.73 thf(func_def_19, type, boolean_algebra: !>[X0: $tType]:($o)).
% 50.07/8.73 thf(func_def_20, type, semilattice_inf: !>[X0: $tType]:($o)).
% 50.07/8.73 thf(func_def_21, type, semilattice_sup: !>[X0: $tType]:($o)).
% 50.07/8.73 thf(func_def_22, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 50.07/8.73 thf(func_def_23, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 50.07/8.73 thf(func_def_24, type, bounde1808546759up_bot: !>[X0: $tType]:($o)).
% 50.07/8.73 thf(func_def_25, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 50.07/8.73 thf(func_def_26, type, statediff: (variable > real) > (variable > real) > set @ variable).
% 50.07/8.73 thf(func_def_27, type, stateinterpol: (variable > real) > (variable > real) > set @ variable > variable > real).
% 50.07/8.73 thf(func_def_28, type, denota1419872369iation: (variable > real) > (variable > real) > set @ variable > $o).
% 50.07/8.73 thf(func_def_29, type, denotational_Vagree: (variable > real) > (variable > real) > set @ variable > $o).
% 50.07/8.73 thf(func_def_30, type, denotational_repv: (variable > real) > variable > real > variable > real).
% 50.07/8.73 thf(func_def_31, type, denota1778088425es_ODE: denotational_interp > (real > variable > real) > char > trm > $o).
% 50.07/8.73 thf(func_def_32, type, denota1863255036rm_sem: denotational_interp > trm > (variable > real) > real).
% 50.07/8.73 thf(func_def_33, type, uminus_uminus: !>[X0: $tType]:(X0 > X0)).
% 50.07/8.73 thf(func_def_34, type, zero_zero: !>[X0: $tType]:(X0)).
% 50.07/8.73 thf(func_def_35, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 50.07/8.73 thf(func_def_36, type, inf_inf: !>[X0: $tType]:(X0 > X0 > X0)).
% 50.07/8.73 thf(func_def_37, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 50.07/8.73 thf(func_def_38, type, size_size: !>[X0: $tType]:(X0 > nat)).
% 50.07/8.73 thf(func_def_39, type, none: !>[X0: $tType]:(option @ X0)).
% 50.07/8.73 thf(func_def_40, type, some: !>[X0: $tType]:(X0 > option @ X0)).
% 50.07/8.73 thf(func_def_41, type, case_option: !>[X0: $tType, X1: $tType]:(X0 > (X1 > X0) > option @ X1 > X0)).
% 50.07/8.73 thf(func_def_42, type, set_option: !>[X0: $tType]:(option @ X0 > set @ X0)).
% 50.07/8.73 thf(func_def_43, type, the: !>[X0: $tType]:(option @ X0 > X0)).
% 50.07/8.73 thf(func_def_44, type, these: !>[X0: $tType]:(set @ option @ X0 > set @ X0)).
% 50.07/8.73 thf(func_def_45, type, bot_bot: !>[X0: $tType]:(X0)).
% 50.07/8.73 thf(func_def_46, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 50.07/8.73 thf(func_def_47, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 50.07/8.73 thf(func_def_48, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 50.07/8.73 thf(func_def_49, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 50.07/8.73 thf(func_def_50, type, is_singleton: !>[X0: $tType]:(set @ X0 > $o)).
% 50.07/8.73 thf(func_def_51, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 50.07/8.73 thf(func_def_52, type, static_FVT: trm > set @ variable).
% 50.07/8.73 thf(func_def_53, type, static_selectlike: set @ (variable > real) > (variable > real) > set @ variable > set @ (variable > real)).
% 50.07/8.73 thf(func_def_54, type, times: trm > trm > trm).
% 50.07/8.73 thf(func_def_55, type, dVar: char > variable).
% 50.07/8.73 thf(func_def_56, type, rVar: char > variable).
% 50.07/8.73 thf(func_def_57, type, rec_variable: !>[X0: $tType]:((char > X0) > (char > X0) > variable > X0)).
% 50.07/8.73 thf(func_def_58, type, size_variable: variable > nat).
% 50.07/8.73 thf(func_def_59, type, uSubst277968634Timeso: option @ trm > option @ trm > option @ trm).
% 50.07/8.73 thf(func_def_60, type, uSubst2091380086djoint: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > denotational_interp > (variable > real) > denotational_interp).
% 50.07/8.73 thf(func_def_61, type, uSubst95898992stappt: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > option @ trm).
% 50.07/8.73 thf(func_def_62, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 50.07/8.73 thf(func_def_63, type, f: real > variable > real).
% 50.07/8.73 thf(func_def_64, type, i: denotational_interp).
% 50.07/8.73 thf(func_def_65, type, u: set @ variable).
% 50.07/8.73 thf(func_def_66, type, omega: variable > real).
% 50.07/8.73 thf(func_def_67, type, sigma: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 50.07/8.73 thf(func_def_68, type, theta: trm).
% 50.07/8.73 thf(func_def_69, type, rr: trm > denotational_interp > trm > denotational_interp > char > (real > variable > real) > variable > real).
% 50.07/8.73 thf(func_def_70, type, x: char).
% 50.07/8.73 thf(func_def_86, type, sK0: variable > char).
% 50.07/8.73 thf(func_def_87, type, sK1: variable > char).
% 50.07/8.73 thf(func_def_88, type, sK2: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 50.07/8.73 thf(func_def_89, type, sK3: set @ (variable > real) > set @ (variable > real) > set @ variable > (variable > real) > variable > real).
% 50.07/8.73 thf(func_def_90, type, sK4: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 50.07/8.73 thf(func_def_91, type, sK5: trm > denotational_interp > trm > denotational_interp > char > (real > variable > real) > variable > real).
% 50.07/8.73 thf(func_def_92, type, sK6: (variable > $o) > char).
% 50.07/8.73 thf(func_def_93, type, sK7: (variable > $o) > char).
% 50.07/8.73 thf(func_def_94, type, sK8: set @ (variable > real) > set @ (variable > real) > set @ variable > (variable > real) > variable > real).
% 50.07/8.73 thf(func_def_95, type, sK9: (char > option @ trm > $o) > char).
% 50.07/8.73 thf(func_def_96, type, sK10: (char > option @ trm > $o) > char).
% 50.07/8.73 thf(func_def_97, type, sK11: (char > option @ trm > $o) > trm).
% 50.07/8.73 thf(func_def_98, type, sK12: trm > denotational_interp > trm > denotational_interp > char > (real > variable > real) > variable > real).
% 50.07/8.73 thf(func_def_99, type, sK13: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 50.07/8.73 thf(func_def_101, type, sK15: (variable > real) > (variable > real) > set @ variable > variable).
% 50.07/8.73 thf(func_def_102, type, sK16: (variable > real) > (variable > real) > set @ variable > variable).
% 50.07/8.73 thf(func_def_103, type, sK17: variable).
% 50.07/8.73 thf(func_def_104, type, sK18: (variable > real) > (variable > real) > set @ variable > variable).
% 50.07/8.73 thf(func_def_105, type, sK19: (variable > real) > (variable > real) > set @ variable > variable).
% 50.07/8.73 thf(func_def_106, type, sK20: set @ (variable > real) > (variable > real) > set @ (variable > real) > set @ variable > variable > real).
% 50.07/8.73 thf(func_def_107, type, sK21: set @ (variable > real) > (variable > real) > set @ (variable > real) > set @ variable > variable > real).
% 50.07/8.73 thf(func_def_108, type, sK22: (variable > real) > (variable > real) > set @ variable > variable).
% 50.07/8.73 thf(func_def_109, type, sK23: (variable > real) > (variable > real) > set @ variable > variable).
% 50.07/8.73 thf(func_def_110, type, sK24: (variable > real) > (variable > real) > variable).
% 50.07/8.73 thf(func_def_111, type, sK25: (variable > real) > (real > variable > real) > set @ variable > variable).
% 50.07/8.73 thf(func_def_112, type, sK26: (variable > real) > (variable > real) > set @ variable > variable).
% 50.07/8.73 thf(func_def_113, type, sK27: (variable > real) > (variable > real) > set @ variable > variable).
% 50.07/8.73 thf(func_def_114, type, sK28: (variable > real) > (variable > real) > set @ variable > variable).
% 50.07/8.73 thf(func_def_115, type, sK29: (variable > real) > variable).
% 50.07/8.73 thf(func_def_116, type, sK30: (real > variable > real) > char > (variable > real) > variable).
% 50.07/8.73 thf(func_def_117, type, sK31: (real > variable > real) > char > (variable > real) > variable).
% 50.07/8.73 thf(func_def_118, type, sK32: denotational_interp > trm > (real > variable > real) > trm > char > denotational_interp > variable > real).
% 50.07/8.73 thf(func_def_119, type, sK33: denotational_interp > (real > variable > real) > denotational_interp > trm > char > trm > variable).
% 50.07/8.73 thf(func_def_120, type, sK34: denotational_interp > (real > variable > real) > denotational_interp > trm > char > trm > variable).
% 50.07/8.73 thf(func_def_121, type, sK35: (variable > real) > set @ variable > (variable > real) > variable).
% 50.07/8.73 thf(func_def_122, type, sK36: char > (variable > real) > (real > variable > real) > variable).
% 50.07/8.73 thf(func_def_123, type, sK37: (variable > real) > char > (real > variable > real) > variable).
% 50.07/8.73 thf(func_def_124, type, sK38: trm > denotational_interp > trm > denotational_interp > (real > variable > real) > char > variable > real).
% 50.07/8.73 thf(func_def_125, type, sK39: trm > char > (real > variable > real) > denotational_interp > trm > denotational_interp > variable).
% 50.07/8.73 thf(func_def_126, type, sK40: trm > char > (real > variable > real) > denotational_interp > trm > denotational_interp > variable).
% 50.07/8.73 thf(func_def_127, type, ph41: !>[X0: $tType]:(X0)).
% 50.07/8.73 thf(f2443,plain,(
% 50.07/8.73 $false),
% 50.07/8.73 inference(subsumption_resolution,[status(thm)],[f2442,f1055])).
% 50.07/8.73 thf(f1055,plain,(
% 50.07/8.73 ((omega @ sK17) != (f @ zero_zero @ real @ sK17))),
% 50.07/8.73 inference(equality_proxy_clausification,[status(thm)],[f1052])).
% 50.07/8.73 thf(f1052,plain,(
% 50.07/8.73 (((f @ zero_zero @ real @ sK17) = (omega @ sK17)) = $false)),
% 50.07/8.73 inference(binary_proxy_clausification,[status(thm)],[f1051])).
% 50.07/8.73 thf(f1051,plain,(
% 50.07/8.73 ($false = ((~ (member @ variable @ sK17 @ (sup_sup @ set @ variable @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable)) @ u))) => ((f @ zero_zero @ real @ sK17) = (omega @ sK17))))),
% 50.07/8.73 inference(beta_eta_normalization,[status(thm)],[f1050])).
% 50.07/8.73 thf(f1050,plain,(
% 50.07/8.73 ($false = ((^[Y0 : variable]: ((~ (member @ variable @ Y0 @ (sup_sup @ set @ variable @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable)) @ u))) => ((f @ zero_zero @ real @ Y0) = (omega @ Y0)))) @ sK17))),
% 50.07/8.73 inference(sigma_clausification,[status(thm)],[f1049])).
% 50.07/8.73 thf(f1049,plain,(
% 50.07/8.73 ($true != (!! @ variable @ (^[Y0 : variable]: ((~ (member @ variable @ Y0 @ (sup_sup @ set @ variable @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable)) @ u))) => ((f @ zero_zero @ real @ Y0) = (omega @ Y0))))))),
% 50.07/8.73 inference(beta_eta_normalization,[status(thm)],[f980])).
% 50.07/8.73 thf(f980,plain,(
% 50.07/8.73 ($true != ((^[Y0 : variable > real]: ((^[Y1 : variable > real]: ((^[Y2 : set @ variable]: (!! @ variable @ (^[Y3 : variable]: ((~ (member @ variable @ Y3 @ Y2)) => ((Y0 @ Y3) = (Y1 @ Y3)))))))))) @ (f @ zero_zero @ real) @ omega @ (sup_sup @ set @ variable @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable)) @ u)))),
% 50.07/8.73 inference(definition_unfolding,[status(thm)],[f916,f964])).
% 50.07/8.73 thf(f964,plain,(
% 50.07/8.73 (denota1419872369iation = (^[Y0 : variable > real]: ((^[Y1 : variable > real]: ((^[Y2 : set @ variable]: (!! @ variable @ (^[Y3 : variable]: ((~ (member @ variable @ Y3 @ Y2)) => ((Y0 @ Y3) = (Y1 @ Y3)))))))))))),
% 50.07/8.73 inference(cnf_transformation,[status(thm)],[f446])).
% 50.07/8.73 thf(f446,plain,(
% 50.07/8.73 (denota1419872369iation = (^[Y0 : variable > real]: ((^[Y1 : variable > real]: ((^[Y2 : set @ variable]: (!! @ variable @ (^[Y3 : variable]: ((~ (member @ variable @ Y3 @ Y2)) => ((Y0 @ Y3) = (Y1 @ Y3)))))))))))),
% 50.07/8.73 inference(fool_elimination,[status(thm)],[f445])).
% 50.07/8.73 thf(f445,plain,(
% 50.07/8.73 (denota1419872369iation = (^[X0 : variable > real, X1 : variable > real, X2 : set @ variable] : (! [X3 : variable] : (~(member @ variable @ X3 @ X2) => ((X0 @ X3) = (X1 @ X3))))))),
% 50.07/8.73 inference(rectify,[status(thm)],[f73])).
% 50.07/8.73 thf(f73,axiom,(
% 50.07/8.73 (denota1419872369iation = (^[X34 : variable > real, X35 : variable > real, X36 : set @ variable] : (! [X37 : variable] : (~(member @ variable @ X37 @ X36) => ((X34 @ X37) = (X35 @ X37))))))),
% 50.07/8.73 file('/export/starexec/sandbox/tmp/tmp.FtwHsTTgu9/DTF2THF_7422.p',fact_72_Uvariation__def)).
% 50.07/8.73 thf(f916,plain,(
% 50.07/8.73 ((denota1419872369iation @ (f @ zero_zero @ real) @ omega @ (sup_sup @ set @ variable @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable)) @ u)) != $true)),
% 50.07/8.73 inference(cnf_transformation,[status(thm)],[f783])).
% 50.07/8.73 thf(f783,plain,(
% 50.07/8.73 ((denota1419872369iation @ (f @ zero_zero @ real) @ omega @ (sup_sup @ set @ variable @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable)) @ u)) != $true)),
% 50.07/8.73 inference(flattening,[status(thm)],[f582])).
% 50.07/8.73 thf(f582,plain,(
% 50.07/8.73 ~((denota1419872369iation @ (f @ zero_zero @ real) @ omega @ (sup_sup @ set @ variable @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable)) @ u)) = $true)),
% 50.07/8.73 inference(fool_elimination,[status(thm)],[f581])).
% 50.07/8.73 thf(f581,plain,(
% 50.07/8.73 ~(denota1419872369iation @ (f @ zero_zero @ real) @ omega @ (sup_sup @ set @ variable @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable)) @ u))),
% 50.07/8.73 inference(rectify,[status(thm)],[f303])).
% 50.07/8.73 thf(f303,negated_conjecture,(
% 50.07/8.73 ~(denota1419872369iation @ (f @ zero_zero @ real) @ omega @ (sup_sup @ set @ variable @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable)) @ u))),
% 50.07/8.73 inference(negated_conjecture,[status(cth)],[f302])).
% 50.07/8.73 thf(f302,conjecture,(
% 50.07/8.73 (denota1419872369iation @ (f @ zero_zero @ real) @ omega @ (sup_sup @ set @ variable @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable)) @ u))),
% 50.07/8.73 file('/export/starexec/sandbox/tmp/tmp.FtwHsTTgu9/DTF2THF_7422.p',conj_0)).
% 50.07/8.73 thf(f2442,plain,(
% 50.07/8.73 ((omega @ sK17) = (f @ zero_zero @ real @ sK17))),
% 50.07/8.73 inference(trivial_inequality_removal,[status(thm)],[f2429])).
% 50.07/8.73 thf(f2429,plain,(
% 50.07/8.73 ($true = $false) | ((omega @ sK17) = (f @ zero_zero @ real @ sK17))),
% 50.07/8.73 inference(superposition,[status(thm)],[f2382,f1490])).
% 50.07/8.73 thf(f1490,plain,(
% 50.07/8.73 ($false = (member @ variable @ sK17 @ (insert @ variable @ (dVar @ x) @ (insert @ variable @ (rVar @ x) @ u))))),
% 50.07/8.73 inference(forward_demodulation,[status(thm)],[f1489,f959])).
% 50.07/8.73 thf(f959,plain,(
% 50.07/8.73 ( ! [X0 : $tType,X1 : set @ X0] : (((sup_sup @ set @ X0 @ bot_bot @ set @ X0 @ X1) = X1)) )),
% 50.07/8.73 inference(cnf_transformation,[status(thm)],[f800])).
% 50.07/8.73 thf(f800,plain,(
% 50.07/8.73 ! [X0 : $tType,X1 : set @ X0] : ((sup_sup @ set @ X0 @ bot_bot @ set @ X0 @ X1) = X1)),
% 50.07/8.73 inference(rectify,[status(thm)],[f80])).
% 50.07/8.73 thf(f80,axiom,(
% 50.07/8.73 ! [X0 : $tType,X5 : set @ X0] : ((sup_sup @ set @ X0 @ bot_bot @ set @ X0 @ X5) = X5)),
% 50.07/8.73 file('/export/starexec/sandbox/tmp/tmp.FtwHsTTgu9/DTF2THF_7422.p',fact_79_Un__empty__left)).
% 50.07/8.73 thf(f1489,plain,(
% 50.07/8.73 ($false = (member @ variable @ sK17 @ (insert @ variable @ (dVar @ x) @ (insert @ variable @ (rVar @ x) @ (sup_sup @ set @ variable @ bot_bot @ set @ variable @ u)))))),
% 50.07/8.73 inference(forward_demodulation,[status(thm)],[f1488,f954])).
% 50.07/8.73 thf(f954,plain,(
% 50.07/8.73 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : (((insert @ X0 @ X2 @ (insert @ X0 @ X1 @ X3)) = (insert @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)))) )),
% 50.07/8.73 inference(cnf_transformation,[status(thm)],[f809])).
% 50.07/8.73 thf(f809,plain,(
% 50.07/8.73 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : set @ X0] : ((insert @ X0 @ X2 @ (insert @ X0 @ X1 @ X3)) = (insert @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)))),
% 50.07/8.73 inference(rectify,[status(thm)],[f35])).
% 50.07/8.73 thf(f35,axiom,(
% 50.07/8.73 ! [X0 : $tType,X8 : X0,X9 : X0,X7 : set @ X0] : ((insert @ X0 @ X8 @ (insert @ X0 @ X9 @ X7)) = (insert @ X0 @ X9 @ (insert @ X0 @ X8 @ X7)))),
% 50.07/8.73 file('/export/starexec/sandbox/tmp/tmp.FtwHsTTgu9/DTF2THF_7422.p',fact_34_insert__commute)).
% 50.07/8.73 thf(f1488,plain,(
% 50.07/8.73 ((member @ variable @ sK17 @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ (sup_sup @ set @ variable @ bot_bot @ set @ variable @ u)))) = $false)),
% 50.07/8.73 inference(forward_demodulation,[status(thm)],[f1487,f929])).
% 50.07/8.73 thf(f929,plain,(
% 50.07/8.74 ( ! [X0 : $tType,X2 : set @ X0,X3 : set @ X0,X1 : X0] : (((sup_sup @ set @ X0 @ (insert @ X0 @ X1 @ X2) @ X3) = (insert @ X0 @ X1 @ (sup_sup @ set @ X0 @ X2 @ X3)))) )),
% 50.07/8.74 inference(cnf_transformation,[status(thm)],[f808])).
% 50.07/8.74 thf(f808,plain,(
% 50.07/8.74 ! [X0 : $tType,X1 : X0,X2 : set @ X0,X3 : set @ X0] : ((sup_sup @ set @ X0 @ (insert @ X0 @ X1 @ X2) @ X3) = (insert @ X0 @ X1 @ (sup_sup @ set @ X0 @ X2 @ X3)))),
% 50.07/8.74 inference(rectify,[status(thm)],[f3])).
% 50.07/8.74 thf(f3,axiom,(
% 50.07/8.74 ! [X0 : $tType,X4 : X0,X5 : set @ X0,X6 : set @ X0] : ((sup_sup @ set @ X0 @ (insert @ X0 @ X4 @ X5) @ X6) = (insert @ X0 @ X4 @ (sup_sup @ set @ X0 @ X5 @ X6)))),
% 50.07/8.74 file('/export/starexec/sandbox/tmp/tmp.FtwHsTTgu9/DTF2THF_7422.p',fact_2_Un__insert__left)).
% 50.07/8.74 thf(f1487,plain,(
% 50.07/8.74 ($false = (member @ variable @ sK17 @ (insert @ variable @ (rVar @ x) @ (sup_sup @ set @ variable @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable) @ u))))),
% 50.07/8.74 inference(forward_demodulation,[status(thm)],[f1054,f929])).
% 50.07/8.74 thf(f1054,plain,(
% 50.07/8.74 ((member @ variable @ sK17 @ (sup_sup @ set @ variable @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable)) @ u)) = $false)),
% 50.07/8.74 inference(not_proxy_clausification,[status(thm)],[f1053])).
% 50.07/8.74 thf(f1053,plain,(
% 50.07/8.74 ($true = (~ (member @ variable @ sK17 @ (sup_sup @ set @ variable @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable)) @ u))))),
% 50.07/8.74 inference(binary_proxy_clausification,[status(thm)],[f1051])).
% 50.07/8.74 thf(f2382,plain,(
% 50.07/8.74 ( ! [X1 : variable] : (($true = (member @ variable @ X1 @ (insert @ variable @ (dVar @ x) @ (insert @ variable @ (rVar @ x) @ u)))) | ((omega @ X1) = (f @ zero_zero @ real @ X1))) )),
% 50.07/8.74 inference(backward_demodulation,[status(thm)],[f1482,f2364])).
% 50.07/8.74 thf(f2364,plain,(
% 50.07/8.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : set @ X0] : (((insert @ X0 @ X3 @ (insert @ X0 @ X2 @ X1)) = (sup_sup @ set @ X0 @ X1 @ (insert @ X0 @ X3 @ (insert @ X0 @ X2 @ bot_bot @ set @ X0))))) )),
% 50.07/8.74 inference(superposition,[status(thm)],[f915,f1759])).
% 50.07/8.74 thf(f1759,plain,(
% 50.07/8.74 ( ! [X0 : $tType,X2 : X0,X1 : set @ X0] : (((insert @ X0 @ X2 @ X1) = (sup_sup @ set @ X0 @ X1 @ (insert @ X0 @ X2 @ bot_bot @ set @ X0)))) )),
% 50.07/8.74 inference(superposition,[status(thm)],[f915,f927])).
% 50.07/8.74 thf(f927,plain,(
% 50.07/8.74 ( ! [X0 : $tType,X1 : set @ X0] : (((sup_sup @ set @ X0 @ X1 @ bot_bot @ set @ X0) = X1)) )),
% 50.07/8.74 inference(cnf_transformation,[status(thm)],[f798])).
% 50.07/8.74 thf(f798,plain,(
% 50.07/8.74 ! [X0 : $tType,X1 : set @ X0] : ((sup_sup @ set @ X0 @ X1 @ bot_bot @ set @ X0) = X1)),
% 50.07/8.74 inference(rectify,[status(thm)],[f79])).
% 50.07/8.74 thf(f79,axiom,(
% 50.07/8.74 ! [X0 : $tType,X7 : set @ X0] : ((sup_sup @ set @ X0 @ X7 @ bot_bot @ set @ X0) = X7)),
% 50.07/8.74 file('/export/starexec/sandbox/tmp/tmp.FtwHsTTgu9/DTF2THF_7422.p',fact_78_Un__empty__right)).
% 50.07/8.74 thf(f915,plain,(
% 50.07/8.74 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : set @ X0] : (((insert @ X0 @ X2 @ (sup_sup @ set @ X0 @ X1 @ X3)) = (sup_sup @ set @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)))) )),
% 50.07/8.74 inference(cnf_transformation,[status(thm)],[f805])).
% 50.07/8.74 thf(f805,plain,(
% 50.07/8.74 ! [X0 : $tType,X1 : set @ X0,X2 : X0,X3 : set @ X0] : ((insert @ X0 @ X2 @ (sup_sup @ set @ X0 @ X1 @ X3)) = (sup_sup @ set @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)))),
% 50.07/8.74 inference(rectify,[status(thm)],[f4])).
% 50.07/8.74 thf(f4,axiom,(
% 50.07/8.74 ! [X0 : $tType,X7 : set @ X0,X4 : X0,X5 : set @ X0] : ((sup_sup @ set @ X0 @ X7 @ (insert @ X0 @ X4 @ X5)) = (insert @ X0 @ X4 @ (sup_sup @ set @ X0 @ X7 @ X5)))),
% 50.07/8.74 file('/export/starexec/sandbox/tmp/tmp.FtwHsTTgu9/DTF2THF_7422.p',fact_3_Un__insert__right)).
% 50.07/8.74 thf(f1482,plain,(
% 50.07/8.74 ( ! [X1 : variable] : (($true = (member @ variable @ X1 @ (sup_sup @ set @ variable @ u @ (insert @ variable @ (dVar @ x) @ (insert @ variable @ (rVar @ x) @ bot_bot @ set @ variable))))) | ((omega @ X1) = (f @ zero_zero @ real @ X1))) )),
% 50.07/8.74 inference(forward_demodulation,[status(thm)],[f1151,f954])).
% 50.07/8.74 thf(f1151,plain,(
% 50.07/8.74 ( ! [X1 : variable] : (((omega @ X1) = (f @ zero_zero @ real @ X1)) | ($true = (member @ variable @ X1 @ (sup_sup @ set @ variable @ u @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable)))))) )),
% 50.07/8.74 inference(not_proxy_clausification,[status(thm)],[f1150])).
% 50.07/8.74 thf(f1150,plain,(
% 50.07/8.74 ( ! [X1 : variable] : (($false = (~ (member @ variable @ X1 @ (sup_sup @ set @ variable @ u @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable)))))) | ((omega @ X1) = (f @ zero_zero @ real @ X1))) )),
% 50.07/8.74 inference(equality_proxy_clausification,[status(thm)],[f1149])).
% 50.07/8.74 thf(f1149,plain,(
% 50.07/8.74 ( ! [X1 : variable] : (($true = ((f @ zero_zero @ real @ X1) = (omega @ X1))) | ($false = (~ (member @ variable @ X1 @ (sup_sup @ set @ variable @ u @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable))))))) )),
% 50.07/8.74 inference(binary_proxy_clausification,[status(thm)],[f1148])).
% 50.07/8.74 thf(f1148,plain,(
% 50.07/8.74 ( ! [X1 : variable] : (($true = ((~ (member @ variable @ X1 @ (sup_sup @ set @ variable @ u @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable))))) => ((f @ zero_zero @ real @ X1) = (omega @ X1))))) )),
% 50.07/8.74 inference(beta_eta_normalization,[status(thm)],[f1147])).
% 50.07/8.74 thf(f1147,plain,(
% 50.07/8.74 ( ! [X1 : variable] : (($true = ((^[Y0 : variable]: ((~ (member @ variable @ Y0 @ (sup_sup @ set @ variable @ u @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable))))) => ((f @ zero_zero @ real @ Y0) = (omega @ Y0)))) @ X1))) )),
% 50.07/8.74 inference(pi_clausification,[status(thm)],[f1146])).
% 50.07/8.74 thf(f1146,plain,(
% 50.07/8.74 ($true = (!! @ variable @ (^[Y0 : variable]: ((~ (member @ variable @ Y0 @ (sup_sup @ set @ variable @ u @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable))))) => ((f @ zero_zero @ real @ Y0) = (omega @ Y0))))))),
% 50.07/8.74 inference(beta_eta_normalization,[status(thm)],[f970])).
% 50.07/8.74 thf(f970,plain,(
% 50.07/8.74 ($true = ((^[Y0 : variable > real]: ((^[Y1 : variable > real]: ((^[Y2 : set @ variable]: (!! @ variable @ (^[Y3 : variable]: ((~ (member @ variable @ Y3 @ Y2)) => ((Y0 @ Y3) = (Y1 @ Y3)))))))))) @ (f @ zero_zero @ real) @ omega @ (sup_sup @ set @ variable @ u @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable)))))),
% 50.07/8.74 inference(definition_unfolding,[status(thm)],[f886,f964])).
% 50.07/8.74 thf(f886,plain,(
% 50.07/8.74 ((denota1419872369iation @ (f @ zero_zero @ real) @ omega @ (sup_sup @ set @ variable @ u @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable)))) = $true)),
% 50.07/8.74 inference(cnf_transformation,[status(thm)],[f474])).
% 50.07/8.74 thf(f474,plain,(
% 50.07/8.74 ((denota1419872369iation @ (f @ zero_zero @ real) @ omega @ (sup_sup @ set @ variable @ u @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable)))) = $true)),
% 50.07/8.74 inference(fool_elimination,[status(thm)],[f473])).
% 50.07/8.74 thf(f473,plain,(
% 50.07/8.74 (denota1419872369iation @ (f @ zero_zero @ real) @ omega @ (sup_sup @ set @ variable @ u @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable))))),
% 50.07/8.74 inference(rectify,[status(thm)],[f1])).
% 50.07/8.74 thf(f1,axiom,(
% 50.07/8.74 (denota1419872369iation @ (f @ zero_zero @ real) @ omega @ (sup_sup @ set @ variable @ u @ (insert @ variable @ (rVar @ x) @ (insert @ variable @ (dVar @ x) @ bot_bot @ set @ variable))))),
% 50.07/8.74 file('/export/starexec/sandbox/tmp/tmp.FtwHsTTgu9/DTF2THF_7422.p',fact_0_uv)).
% 50.07/8.74 % SZS output end Proof for DTF2THF_7422
% 50.07/8.74 % (7701)------------------------------
% 50.07/8.74 % (7701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.07/8.74 % (7701)Termination reason: Refutation
% 50.07/8.74
% 50.07/8.74 % (7701)Memory used [KB]: 7675
% 50.07/8.74 % (7701)Time elapsed: 0.392 s
% 50.07/8.74 % (7701)Instructions burned: 696 (million)
% 50.07/8.74 % (7701)------------------------------
% 50.07/8.74 % (7701)------------------------------
% 50.07/8.74 % (7535)Success in time 6.927 s
%------------------------------------------------------------------------------