%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP200^2 : 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 : n002.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 08:56:22 AM UTC 2026
% Result : Theorem 5.16s 2.15s
% Output : Refutation 5.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP200^2 : 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
% 0.16/0.34 % Computer : n002.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:29:48 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : ITP200^2 : TPTP v9.2.1. Released v7.5.0.
% 0.20/0.46 % Domain : Interactive Theorem Proving
% 0.20/0.46 % Problem : Sledgehammer USubst problem prob_1407__6352118_1
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.20/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Des21]
% 0.20/0.46 % Names : USubst/prob_1407__6352118_1 [Des21]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.00 v9.1.0, 0.33 v9.0.0, 0.00 v8.1.0, 0.25 v7.5.0
% 0.20/0.46 % Syntax : Number of formulae : 352 ( 141 unt; 73 typ; 0 def)
% 0.20/0.46 % Number of atoms : 769 ( 414 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 17 ( 2 avg)
% 0.20/0.46 % Number of connectives : 4518 ( 179 ~; 9 |; 38 &;3861 @)
% 0.20/0.46 % ( 0 <=>; 431 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 20 ( 7 avg)
% 0.20/0.46 % Number of types : 8 ( 7 usr)
% 0.20/0.46 % Number of type conns : 515 ( 515 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 69 ( 66 usr; 7 con; 0-6 aty)
% 0.20/0.46 % Number of variables : 1091 ( 86 ^; 957 !; 17 ?;1091 :)
% 0.20/0.46 % ( 31 !>; 0 ?*; 0 @-; 0 @+)
% 0.20/0.46 % SPC : TH1_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:23:31.757
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % Could-be-implicit typings (10)
% 0.20/0.46 thf(ty_t_Denotational__Semantics_Ointerp,type,
% 0.20/0.46 denotational_interp: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Product__Type_Oprod,type,
% 0.20/0.46 product_prod: $tType > $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Syntax_Ovariable,type,
% 0.20/0.46 variable: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Option_Ooption,type,
% 0.20/0.46 option: $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Syntax_Ogame,type,
% 0.20/0.46 game: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_String_Ochar,type,
% 0.20/0.46 char: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Syntax_Otrm,type,
% 0.20/0.46 trm: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Syntax_Ofml,type,
% 0.20/0.46 fml: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Real_Oreal,type,
% 0.20/0.46 real: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Set_Oset,type,
% 0.20/0.46 set: $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 % Explicit typings (63)
% 0.20/0.46 thf(sy_cl_HOL_Otype,type,
% 0.20/0.46 type:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.20/0.46 ord:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Otop,type,
% 0.20/0.46 top:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.20/0.46 order:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.20/0.46 linorder:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Opreorder,type,
% 0.20/0.46 preorder:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Oorder__top,type,
% 0.20/0.46 order_top:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2,type,
% 0.20/0.46 bNF_Greatest_image2:
% 0.20/0.46 !>[C: $tType,A: $tType,B: $tType] : ( ( set @ C ) > ( C > A ) > ( C > B ) > ( set @ ( product_prod @ A @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_BNF__Greatest__Fixpoint_OrelImage,type,
% 0.20/0.46 bNF_Gr1317331620lImage:
% 0.20/0.46 !>[B: $tType,A: $tType] : ( ( set @ ( product_prod @ B @ B ) ) > ( B > A ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_BNF__Greatest__Fixpoint_OrelInvImage,type,
% 0.20/0.46 bNF_Gr2107612801vImage:
% 0.20/0.46 !>[A: $tType,B: $tType] : ( ( set @ A ) > ( set @ ( product_prod @ B @ B ) ) > ( A > B ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Denotational__Semantics_OUvariation,type,
% 0.20/0.46 denota1419872369iation: ( variable > real ) > ( variable > real ) > ( set @ variable ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_If,type,
% 0.20/0.46 if:
% 0.20/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Option_Ooption_ONone,type,
% 0.20/0.46 none:
% 0.20/0.46 !>[A: $tType] : ( option @ A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Option_Ooption_OSome,type,
% 0.20/0.46 some:
% 0.20/0.46 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Option_Ooption_Ocase__option,type,
% 0.20/0.46 case_option:
% 0.20/0.46 !>[B: $tType,A: $tType] : ( B > ( A > B ) > ( option @ A ) > B ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Option_Ooption_Othe,type,
% 0.20/0.46 the:
% 0.20/0.46 !>[A: $tType] : ( ( option @ A ) > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.20/0.46 ord_less_eq:
% 0.20/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Oorder__class_OGreatest,type,
% 0.20/0.46 order_Greatest:
% 0.20/0.46 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.20/0.46 top_top:
% 0.20/0.46 !>[A: $tType] : A ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Product__Type_OPair,type,
% 0.20/0.46 product_Pair:
% 0.20/0.46 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Relation_OPowp,type,
% 0.20/0.46 powp:
% 0.20/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_OCollect,type,
% 0.20/0.46 collect:
% 0.20/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Syntax_Ofml_OGeq,type,
% 0.20/0.46 geq: trm > trm > fml ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Syntax_Ogame_OAssign,type,
% 0.20/0.46 assign: variable > trm > game ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Syntax_Ogame_OODE,type,
% 0.20/0.46 ode: char > trm > game ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Syntax_Ogame_OTest,type,
% 0.20/0.46 test: fml > game ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Syntax_Otrm_OConst,type,
% 0.20/0.46 const: char > trm ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Syntax_Otrm_ODifferential,type,
% 0.20/0.46 differential: trm > trm ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Syntax_Otrm_OFunc,type,
% 0.20/0.46 func: char > trm > trm ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Syntax_Otrm_ONumber,type,
% 0.20/0.46 number: real > trm ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Syntax_Otrm_OPlus,type,
% 0.20/0.46 plus: trm > trm > trm ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Syntax_Otrm_OTimes,type,
% 0.20/0.46 times: trm > trm > trm ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Syntax_Otrm_OVar,type,
% 0.20/0.46 var: variable > trm ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OAssigno,type,
% 0.20/0.46 uSubst1326326671ssigno: variable > ( option @ trm ) > ( option @ game ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OAssigno__rel,type,
% 0.20/0.46 uSubst1741596714no_rel: ( product_prod @ variable @ ( option @ trm ) ) > ( product_prod @ variable @ ( option @ trm ) ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_ODifferentialo,type,
% 0.20/0.46 uSubst259074819ntialo: ( option @ trm ) > ( option @ trm ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_ODifferentialo__rel,type,
% 0.20/0.46 uSubst99643830lo_rel: ( option @ trm ) > ( option @ trm ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OGeqo,type,
% 0.20/0.46 uSubst1556497037e_Geqo: ( option @ trm ) > ( option @ trm ) > ( option @ fml ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OGeqo__rel,type,
% 0.20/0.46 uSubst864323244qo_rel: ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OODEo,type,
% 0.20/0.46 uSubst1083227664e_ODEo: char > ( option @ trm ) > ( option @ game ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OODEo__rel,type,
% 0.20/0.46 uSubst2007600873Eo_rel: ( product_prod @ char @ ( option @ trm ) ) > ( product_prod @ char @ ( option @ trm ) ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OPluso,type,
% 0.20/0.46 uSubst1112714340_Pluso: ( option @ trm ) > ( option @ trm ) > ( option @ trm ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OPluso__rel,type,
% 0.20/0.46 uSubst270600597so_rel: ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTesto,type,
% 0.20/0.46 uSubst190403692_Testo: ( option @ fml ) > ( option @ game ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTesto__rel,type,
% 0.20/0.46 uSubst533687181to_rel: ( option @ fml ) > ( option @ fml ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTimeso,type,
% 0.20/0.46 uSubst277968634Timeso: ( option @ trm ) > ( option @ trm ) > ( option @ trm ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTimeso__rel,type,
% 0.20/0.46 uSubst1377811071so_rel: ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousappconst,type,
% 0.20/0.46 uSubst1138577137pconst: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > char > ( option @ trm ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappf,type,
% 0.20/0.46 uSubst95898978stappf: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > fml > ( option @ fml ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappt,type,
% 0.20/0.46 uSubst95898992stappt: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > trm > ( option @ trm ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappt__rel,type,
% 0.20/0.46 uSubst2096773001pt_rel: ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) > ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Wellfounded_Oaccp,type,
% 0.20/0.46 accp:
% 0.20/0.46 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Wellfounded_Olex__prod,type,
% 0.20/0.46 lex_prod:
% 0.20/0.46 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ B @ B ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member,type,
% 0.20/0.46 member:
% 0.20/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_U,type,
% 0.20/0.46 u: set @ variable ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_Ua____,type,
% 0.20/0.46 ua: set @ variable ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v__092_060eta_062____,type,
% 0.20/0.46 eta: trm ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v__092_060nu_062,type,
% 0.20/0.46 nu: variable > real ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v__092_060nu_062_H____,type,
% 0.20/0.46 nu2: variable > real ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v__092_060omega_062,type,
% 0.20/0.46 omega: variable > real ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v__092_060omega_062_H____,type,
% 0.20/0.46 omega2: variable > real ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v__092_060sigma_062_H_H____,type,
% 0.20/0.46 sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v__092_060theta_062____,type,
% 0.20/0.46 theta: trm ).
% 0.20/0.46
% 0.20/0.46 % Relevant facts (255)
% 0.20/0.46 thf(fact_0_vaouter,axiom,
% 0.20/0.46 denota1419872369iation @ nu @ omega @ u ).
% 0.20/0.46
% 0.20/0.46 % vaouter
% 0.20/0.46 thf(fact_1_usubstappf__geq__conv,axiom,
% 0.20/0.46 ! [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] :
% 0.20/0.46 ( ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.20/0.46 != ( none @ fml ) )
% 0.20/0.46 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.20/0.46 != ( none @ trm ) )
% 0.20/0.46 & ( ( uSubst95898992stappt @ Sigma @ U @ Eta )
% 0.20/0.46 != ( none @ trm ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % usubstappf_geq_conv
% 0.20/0.46 thf(fact_2_Geq_Oprems_I1_J,axiom,
% 0.20/0.46 ( ( uSubst95898978stappf @ sigma @ ua @ ( geq @ theta @ eta ) )
% 0.20/0.46 != ( none @ fml ) ) ).
% 0.20/0.46
% 0.20/0.46 % Geq.prems(1)
% 0.20/0.46 thf(fact_3_undeft__None,axiom,
% 0.20/0.46 ( ( none @ trm )
% 0.20/0.46 = ( none @ trm ) ) ).
% 0.20/0.46
% 0.20/0.46 % undeft_None
% 0.20/0.46 thf(fact_4_usubstappt__det,axiom,
% 0.20/0.46 ! [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] :
% 0.20/0.46 ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.20/0.46 != ( none @ trm ) )
% 0.20/0.46 => ( ( ( uSubst95898992stappt @ Sigma @ V @ Theta )
% 0.20/0.46 != ( none @ trm ) )
% 0.20/0.46 => ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.20/0.46 = ( uSubst95898992stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % usubstappt_det
% 0.20/0.46 thf(fact_5_Geq_Oprems_I2_J,axiom,
% 0.20/0.46 denota1419872369iation @ nu2 @ omega2 @ ua ).
% 0.20/0.46
% 0.20/0.46 % Geq.prems(2)
% 0.20/0.46 thf(fact_6_usubstappt__plus__conv,axiom,
% 0.20/0.46 ! [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] :
% 0.20/0.46 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( plus @ Theta @ Eta ) )
% 0.20/0.46 != ( none @ trm ) )
% 0.20/0.46 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.20/0.46 != ( none @ trm ) )
% 0.20/0.46 & ( ( uSubst95898992stappt @ Sigma @ U @ Eta )
% 0.20/0.46 != ( none @ trm ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % usubstappt_plus_conv
% 0.20/0.46 thf(fact_7_usubstappt__times__conv,axiom,
% 0.20/0.46 ! [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] :
% 0.20/0.46 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 0.20/0.46 != ( none @ trm ) )
% 0.20/0.46 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.20/0.46 != ( none @ trm ) )
% 0.20/0.46 & ( ( uSubst95898992stappt @ Sigma @ U @ Eta )
% 0.20/0.46 != ( none @ trm ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % usubstappt_times_conv
% 0.20/0.46 thf(fact_8_usubstappt__antimon,axiom,
% 0.20/0.46 ! [V: set @ variable,U: set @ variable,Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),Theta: trm] :
% 0.20/0.46 ( ( ord_less_eq @ ( set @ variable ) @ V @ U )
% 0.20/0.46 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.20/0.46 != ( none @ trm ) )
% 0.20/0.46 => ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.20/0.46 = ( uSubst95898992stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % usubstappt_antimon
% 0.20/0.46 thf(fact_9_Differentialo_Osimps_I2_J,axiom,
% 0.20/0.46 ( ( uSubst259074819ntialo @ ( none @ trm ) )
% 0.20/0.46 = ( none @ trm ) ) ).
% 0.20/0.46
% 0.20/0.46 % Differentialo.simps(2)
% 0.20/0.46 thf(fact_10_Differentialo__undef,axiom,
% 0.20/0.46 ! [Theta: option @ trm] :
% 0.20/0.46 ( ( ( uSubst259074819ntialo @ Theta )
% 0.20/0.46 = ( none @ trm ) )
% 0.20/0.46 = ( Theta
% 0.20/0.46 = ( none @ trm ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Differentialo_undef
% 0.20/0.46 thf(fact_11_Pluso_Osimps_I2_J,axiom,
% 0.20/0.46 ! [Eta: option @ trm] :
% 0.20/0.46 ( ( uSubst1112714340_Pluso @ ( none @ trm ) @ Eta )
% 0.20/0.46 = ( none @ trm ) ) ).
% 0.20/0.46
% 0.20/0.46 % Pluso.simps(2)
% 0.20/0.46 thf(fact_12_Timeso_Osimps_I2_J,axiom,
% 0.20/0.46 ! [Eta: option @ trm] :
% 0.20/0.46 ( ( uSubst277968634Timeso @ ( none @ trm ) @ Eta )
% 0.20/0.46 = ( none @ trm ) ) ).
% 0.20/0.46
% 0.20/0.46 % Timeso.simps(2)
% 0.20/0.46 thf(fact_13_Pluso__undef,axiom,
% 0.20/0.46 ! [Theta: option @ trm,Eta: option @ trm] :
% 0.20/0.46 ( ( ( uSubst1112714340_Pluso @ Theta @ Eta )
% 0.20/0.46 = ( none @ trm ) )
% 0.20/0.46 = ( ( Theta
% 0.20/0.46 = ( none @ trm ) )
% 0.20/0.46 | ( Eta
% 0.20/0.46 = ( none @ trm ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Pluso_undef
% 0.20/0.46 thf(fact_14_Timeso__undef,axiom,
% 0.20/0.46 ! [Theta: option @ trm,Eta: option @ trm] :
% 0.20/0.46 ( ( ( uSubst277968634Timeso @ Theta @ Eta )
% 0.20/0.46 = ( none @ trm ) )
% 0.20/0.46 = ( ( Theta
% 0.20/0.46 = ( none @ trm ) )
% 0.20/0.46 | ( Eta
% 0.20/0.46 = ( none @ trm ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Timeso_undef
% 0.20/0.46 thf(fact_15_Geqo_Osimps_I2_J,axiom,
% 0.20/0.46 ! [Eta: option @ trm] :
% 0.20/0.46 ( ( uSubst1556497037e_Geqo @ ( none @ trm ) @ Eta )
% 0.20/0.46 = ( none @ fml ) ) ).
% 0.20/0.46
% 0.20/0.46 % Geqo.simps(2)
% 0.20/0.46 thf(fact_16_usubstappf__antimon,axiom,
% 0.20/0.46 ! [V: set @ variable,U: set @ variable,Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),Phi: fml] :
% 0.20/0.46 ( ( ord_less_eq @ ( set @ variable ) @ V @ U )
% 0.20/0.46 => ( ( ( uSubst95898978stappf @ Sigma @ U @ Phi )
% 0.20/0.46 != ( none @ fml ) )
% 0.20/0.46 => ( ( uSubst95898978stappf @ Sigma @ U @ Phi )
% 0.20/0.46 = ( uSubst95898978stappf @ Sigma @ V @ Phi ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % usubstappf_antimon
% 0.20/0.46 thf(fact_17_usubstappf__det,axiom,
% 0.20/0.46 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Phi: fml,V: set @ variable] :
% 0.20/0.46 ( ( ( uSubst95898978stappf @ Sigma @ U @ Phi )
% 0.20/0.46 != ( none @ fml ) )
% 0.20/0.46 => ( ( ( uSubst95898978stappf @ Sigma @ V @ Phi )
% 0.20/0.46 != ( none @ fml ) )
% 0.20/0.46 => ( ( uSubst95898978stappf @ Sigma @ U @ Phi )
% 0.20/0.46 = ( uSubst95898978stappf @ Sigma @ V @ Phi ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % usubstappf_det
% 0.20/0.46 thf(fact_18_usubstappt_Osimps_I5_J,axiom,
% 0.20/0.46 ! [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] :
% 0.20/0.46 ( ( uSubst95898992stappt @ Sigma @ U @ ( plus @ Theta @ Eta ) )
% 0.20/0.46 = ( uSubst1112714340_Pluso @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) @ ( uSubst95898992stappt @ Sigma @ U @ Eta ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % usubstappt.simps(5)
% 0.20/0.46 thf(fact_19_usubstappt_Osimps_I6_J,axiom,
% 0.20/0.46 ! [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] :
% 0.20/0.46 ( ( uSubst95898992stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 0.20/0.46 = ( uSubst277968634Timeso @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) @ ( uSubst95898992stappt @ Sigma @ U @ Eta ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % usubstappt.simps(6)
% 0.20/0.46 thf(fact_20_usubstappf_Osimps_I2_J,axiom,
% 0.20/0.46 ! [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] :
% 0.20/0.46 ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.20/0.46 = ( uSubst1556497037e_Geqo @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) @ ( uSubst95898992stappt @ Sigma @ U @ Eta ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % usubstappf.simps(2)
% 0.20/0.46 thf(fact_21_Geqo__undef,axiom,
% 0.20/0.46 ! [Theta: option @ trm,Eta: option @ trm] :
% 0.20/0.46 ( ( ( uSubst1556497037e_Geqo @ Theta @ Eta )
% 0.20/0.46 = ( none @ fml ) )
% 0.20/0.46 = ( ( Theta
% 0.20/0.46 = ( none @ trm ) )
% 0.20/0.46 | ( Eta
% 0.20/0.46 = ( none @ trm ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Geqo_undef
% 0.20/0.46 thf(fact_22_trm_Oinject_I6_J,axiom,
% 0.20/0.46 ! [X61: trm,X62: trm,Y61: trm,Y62: trm] :
% 0.20/0.46 ( ( ( times @ X61 @ X62 )
% 0.20/0.46 = ( times @ Y61 @ Y62 ) )
% 0.20/0.46 = ( ( X61 = Y61 )
% 0.20/0.46 & ( X62 = Y62 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % trm.inject(6)
% 0.20/0.46 thf(fact_23_trm_Oinject_I5_J,axiom,
% 0.20/0.46 ! [X51: trm,X52: trm,Y51: trm,Y52: trm] :
% 0.20/0.46 ( ( ( plus @ X51 @ X52 )
% 0.20/0.46 = ( plus @ Y51 @ Y52 ) )
% 0.20/0.46 = ( ( X51 = Y51 )
% 0.20/0.46 & ( X52 = Y52 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % trm.inject(5)
% 0.20/0.46 thf(fact_24_fml_Oinject_I2_J,axiom,
% 0.20/0.46 ! [X21: trm,X22: trm,Y21: trm,Y22: trm] :
% 0.20/0.46 ( ( ( geq @ X21 @ X22 )
% 0.20/0.46 = ( geq @ Y21 @ Y22 ) )
% 0.20/0.46 = ( ( X21 = Y21 )
% 0.20/0.46 & ( X22 = Y22 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % fml.inject(2)
% 0.20/0.46 thf(fact_25_Uvariation__mon,axiom,
% 0.20/0.46 ! [U: set @ variable,V: set @ variable,Omega: variable > real,Nu: variable > real] :
% 0.20/0.46 ( ( ord_less_eq @ ( set @ variable ) @ U @ V )
% 0.20/0.46 => ( ( denota1419872369iation @ Omega @ Nu @ U )
% 0.20/0.46 => ( denota1419872369iation @ Omega @ Nu @ V ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Uvariation_mon
% 0.20/0.46 thf(fact_26_subsetI,axiom,
% 0.20/0.46 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.20/0.46 ( ! [X: A] :
% 0.20/0.46 ( ( member @ A @ X @ A2 )
% 0.20/0.46 => ( member @ A @ X @ B2 ) )
% 0.20/0.46 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % subsetI
% 0.20/0.46 thf(fact_27_subset__antisym,axiom,
% 0.20/0.46 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.20/0.46 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 0.20/0.46 => ( A2 = B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_antisym
% 0.20/0.46 thf(fact_28_trm_Odistinct_I37_J,axiom,
% 0.20/0.46 ! [X51: trm,X52: trm,X61: trm,X62: trm] :
% 0.20/0.46 ( ( plus @ X51 @ X52 )
% 0.20/0.46 != ( times @ X61 @ X62 ) ) ).
% 0.20/0.46
% 0.20/0.46 % trm.distinct(37)
% 0.20/0.46 thf(fact_29_order__refl,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( preorder @ A )
% 0.20/0.46 => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_refl
% 0.20/0.46 thf(fact_30_Uvariation__univ,axiom,
% 0.20/0.46 ! [Nu: variable > real,Nu2: variable > real] :
% 0.20/0.46 ( denota1419872369iation @ Nu @ Nu2
% 0.20/0.46 @ ( collect @ variable
% 0.20/0.46 @ ^ [X3: variable] : $true ) ) ).
% 0.20/0.46
% 0.20/0.46 % Uvariation_univ
% 0.20/0.46 thf(fact_31_Collect__subset,axiom,
% 0.20/0.46 ! [A: $tType,A2: set @ A,P: A > $o] :
% 0.20/0.46 ( ord_less_eq @ ( set @ A )
% 0.20/0.46 @ ( collect @ A
% 0.20/0.46 @ ^ [X3: A] :
% 0.20/0.46 ( ( member @ A @ X3 @ A2 )
% 0.20/0.46 & ( P @ X3 ) ) )
% 0.20/0.46 @ A2 ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_subset
% 0.20/0.46 thf(fact_32_less__eq__set__def,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ord_less_eq @ ( set @ A ) )
% 0.20/0.46 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.20/0.46 ( ord_less_eq @ ( A > $o )
% 0.20/0.46 @ ^ [X3: A] : ( member @ A @ X3 @ A3 )
% 0.20/0.46 @ ^ [X3: A] : ( member @ A @ X3 @ B3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_eq_set_def
% 0.20/0.46 thf(fact_33_dual__order_Oantisym,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( order @ A )
% 0.20/0.46 => ! [B4: A,A4: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.20/0.46 => ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.20/0.46 => ( A4 = B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.antisym
% 0.20/0.46 thf(fact_34_dual__order_Oeq__iff,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( order @ A )
% 0.20/0.46 => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.20/0.46 = ( ^ [A5: A,B5: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ B5 @ A5 )
% 0.20/0.46 & ( ord_less_eq @ A @ A5 @ B5 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.eq_iff
% 0.20/0.46 thf(fact_35_dual__order_Otrans,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( order @ A )
% 0.20/0.46 => ! [B4: A,A4: A,C2: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.20/0.46 => ( ( ord_less_eq @ A @ C2 @ B4 )
% 0.20/0.46 => ( ord_less_eq @ A @ C2 @ A4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.trans
% 0.20/0.46 thf(fact_36_linorder__wlog,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A )
% 0.20/0.46 => ! [P: A > A > $o,A4: A,B4: A] :
% 0.20/0.46 ( ! [A6: A,B6: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ A6 @ B6 )
% 0.20/0.46 => ( P @ A6 @ B6 ) )
% 0.20/0.46 => ( ! [A6: A,B6: A] :
% 0.20/0.46 ( ( P @ B6 @ A6 )
% 0.20/0.46 => ( P @ A6 @ B6 ) )
% 0.20/0.46 => ( P @ A4 @ B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % linorder_wlog
% 0.20/0.46 thf(fact_37_dual__order_Orefl,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( order @ A )
% 0.20/0.46 => ! [A4: A] : ( ord_less_eq @ A @ A4 @ A4 ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.refl
% 0.20/0.46 thf(fact_38_order__trans,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( preorder @ A )
% 0.20/0.46 => ! [X2: A,Y2: A,Z2: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.20/0.46 => ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 0.20/0.46 => ( ord_less_eq @ A @ X2 @ Z2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_trans
% 0.20/0.46 thf(fact_39_order__class_Oorder_Oantisym,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( order @ A )
% 0.20/0.46 => ! [A4: A,B4: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.20/0.46 => ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.20/0.46 => ( A4 = B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_class.order.antisym
% 0.20/0.46 thf(fact_40_ord__le__eq__trans,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ord @ A )
% 0.20/0.46 => ! [A4: A,B4: A,C2: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.20/0.46 => ( ( B4 = C2 )
% 0.20/0.46 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_le_eq_trans
% 0.20/0.46 thf(fact_41_ord__eq__le__trans,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ord @ A )
% 0.20/0.46 => ! [A4: A,B4: A,C2: A] :
% 0.20/0.46 ( ( A4 = B4 )
% 0.20/0.46 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 0.20/0.46 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_trans
% 0.20/0.47 thf(fact_42_order__class_Oorder_Oeq__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( order @ A )
% 0.20/0.47 => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.20/0.47 = ( ^ [A5: A,B5: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ A5 @ B5 )
% 0.20/0.47 & ( ord_less_eq @ A @ B5 @ A5 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order_class.order.eq_iff
% 0.20/0.47 thf(fact_43_antisym__conv,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( order @ A )
% 0.20/0.47 => ! [Y2: A,X2: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.20/0.47 => ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.20/0.47 = ( X2 = Y2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % antisym_conv
% 0.20/0.47 thf(fact_44_mem__Collect__eq,axiom,
% 0.20/0.47 ! [A: $tType,A4: A,P: A > $o] :
% 0.20/0.47 ( ( member @ A @ A4 @ ( collect @ A @ P ) )
% 0.20/0.47 = ( P @ A4 ) ) ).
% 0.20/0.47
% 0.20/0.47 % mem_Collect_eq
% 0.20/0.47 thf(fact_45_Collect__mem__eq,axiom,
% 0.20/0.47 ! [A: $tType,A2: set @ A] :
% 0.20/0.47 ( ( collect @ A
% 0.20/0.47 @ ^ [X3: A] : ( member @ A @ X3 @ A2 ) )
% 0.20/0.47 = A2 ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mem_eq
% 0.20/0.47 thf(fact_46_Collect__cong,axiom,
% 0.20/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.20/0.47 ( ! [X: A] :
% 0.20/0.47 ( ( P @ X )
% 0.20/0.47 = ( Q @ X ) )
% 0.20/0.47 => ( ( collect @ A @ P )
% 0.20/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_cong
% 0.20/0.47 thf(fact_47_ext,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.20/0.47 ( ! [X: A] :
% 0.20/0.47 ( ( F @ X )
% 0.20/0.47 = ( G @ X ) )
% 0.20/0.47 => ( F = G ) ) ).
% 0.20/0.47
% 0.20/0.47 % ext
% 0.20/0.47 thf(fact_48_le__cases3,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linorder @ A )
% 0.20/0.47 => ! [X2: A,Y2: A,Z2: A] :
% 0.20/0.47 ( ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.20/0.47 => ~ ( ord_less_eq @ A @ Y2 @ Z2 ) )
% 0.20/0.47 => ( ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.20/0.47 => ~ ( ord_less_eq @ A @ X2 @ Z2 ) )
% 0.20/0.47 => ( ( ( ord_less_eq @ A @ X2 @ Z2 )
% 0.20/0.47 => ~ ( ord_less_eq @ A @ Z2 @ Y2 ) )
% 0.20/0.47 => ( ( ( ord_less_eq @ A @ Z2 @ Y2 )
% 0.20/0.47 => ~ ( ord_less_eq @ A @ Y2 @ X2 ) )
% 0.20/0.47 => ( ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 0.20/0.47 => ~ ( ord_less_eq @ A @ Z2 @ X2 ) )
% 0.20/0.47 => ~ ( ( ord_less_eq @ A @ Z2 @ X2 )
% 0.20/0.47 => ~ ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_cases3
% 0.20/0.47 thf(fact_49_order_Otrans,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( order @ A )
% 0.20/0.47 => ! [A4: A,B4: A,C2: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.20/0.47 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 0.20/0.47 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order.trans
% 0.20/0.47 thf(fact_50_le__cases,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linorder @ A )
% 0.20/0.47 => ! [X2: A,Y2: A] :
% 0.20/0.47 ( ~ ( ord_less_eq @ A @ X2 @ Y2 )
% 0.20/0.47 => ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_cases
% 0.20/0.47 thf(fact_51_eq__refl,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( preorder @ A )
% 0.20/0.47 => ! [X2: A,Y2: A] :
% 0.20/0.47 ( ( X2 = Y2 )
% 0.20/0.47 => ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % eq_refl
% 0.20/0.47 thf(fact_52_linear,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linorder @ A )
% 0.20/0.47 => ! [X2: A,Y2: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.20/0.47 | ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % linear
% 0.20/0.47 thf(fact_53_antisym,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( order @ A )
% 0.20/0.47 => ! [X2: A,Y2: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.20/0.47 => ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.20/0.47 => ( X2 = Y2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % antisym
% 0.20/0.47 thf(fact_54_eq__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( order @ A )
% 0.20/0.47 => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.20/0.47 = ( ^ [X3: A,Y3: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.20/0.47 & ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % eq_iff
% 0.20/0.47 thf(fact_55_ord__le__eq__subst,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType] :
% 0.20/0.47 ( ( ( ord @ B )
% 0.20/0.47 & ( ord @ A ) )
% 0.20/0.47 => ! [A4: A,B4: A,F: A > B,C2: B] :
% 0.20/0.47 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.20/0.47 => ( ( ( F @ B4 )
% 0.20/0.47 = C2 )
% 0.20/0.47 => ( ! [X: A,Y4: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ X @ Y4 )
% 0.20/0.47 => ( ord_less_eq @ B @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.20/0.47 => ( ord_less_eq @ B @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ord_le_eq_subst
% 0.20/0.47 thf(fact_56_ord__eq__le__subst,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType] :
% 0.20/0.47 ( ( ( ord @ B )
% 0.20/0.47 & ( ord @ A ) )
% 0.20/0.47 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 0.20/0.47 ( ( A4
% 0.20/0.47 = ( F @ B4 ) )
% 0.20/0.47 => ( ( ord_less_eq @ B @ B4 @ C2 )
% 0.20/0.47 => ( ! [X: B,Y4: B] :
% 0.20/0.47 ( ( ord_less_eq @ B @ X @ Y4 )
% 0.20/0.47 => ( ord_less_eq @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.20/0.47 => ( ord_less_eq @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ord_eq_le_subst
% 0.20/0.47 thf(fact_57_order__subst2,axiom,
% 0.20/0.47 ! [A: $tType,C: $tType] :
% 0.20/0.47 ( ( ( order @ C )
% 0.20/0.47 & ( order @ A ) )
% 0.20/0.47 => ! [A4: A,B4: A,F: A > C,C2: C] :
% 0.20/0.47 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.20/0.47 => ( ( ord_less_eq @ C @ ( F @ B4 ) @ C2 )
% 0.20/0.47 => ( ! [X: A,Y4: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ X @ Y4 )
% 0.20/0.47 => ( ord_less_eq @ C @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.20/0.47 => ( ord_less_eq @ C @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order_subst2
% 0.20/0.47 thf(fact_58_order__subst1,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType] :
% 0.20/0.47 ( ( ( order @ B )
% 0.20/0.47 & ( order @ A ) )
% 0.20/0.47 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 0.20/0.47 ( ( ord_less_eq @ A @ A4 @ ( F @ B4 ) )
% 0.20/0.47 => ( ( ord_less_eq @ B @ B4 @ C2 )
% 0.20/0.47 => ( ! [X: B,Y4: B] :
% 0.20/0.47 ( ( ord_less_eq @ B @ X @ Y4 )
% 0.20/0.47 => ( ord_less_eq @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.20/0.47 => ( ord_less_eq @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order_subst1
% 0.20/0.47 thf(fact_59_le__fun__def,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType] :
% 0.20/0.47 ( ( ord @ B )
% 0.20/0.47 => ( ( ord_less_eq @ ( A > B ) )
% 0.20/0.47 = ( ^ [F2: A > B,G2: A > B] :
% 0.20/0.47 ! [X3: A] : ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_fun_def
% 0.20/0.47 thf(fact_60_le__funI,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType] :
% 0.20/0.47 ( ( ord @ B )
% 0.20/0.47 => ! [F: A > B,G: A > B] :
% 0.20/0.47 ( ! [X: A] : ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) )
% 0.20/0.47 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_funI
% 0.20/0.47 thf(fact_61_le__funE,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType] :
% 0.20/0.47 ( ( ord @ B )
% 0.20/0.47 => ! [F: A > B,G: A > B,X2: A] :
% 0.20/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.20/0.47 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_funE
% 0.20/0.47 thf(fact_62_le__funD,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType] :
% 0.20/0.47 ( ( ord @ B )
% 0.20/0.47 => ! [F: A > B,G: A > B,X2: A] :
% 0.20/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.20/0.47 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_funD
% 0.20/0.47 thf(fact_63_Collect__mono__iff,axiom,
% 0.20/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.20/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.20/0.47 = ( ! [X3: A] :
% 0.20/0.47 ( ( P @ X3 )
% 0.20/0.47 => ( Q @ X3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mono_iff
% 0.20/0.47 thf(fact_64_set__eq__subset,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ^ [Y: set @ A,Z: set @ A] : ( Y = Z ) )
% 0.20/0.47 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.20/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.20/0.47 & ( ord_less_eq @ ( set @ A ) @ B3 @ A3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % set_eq_subset
% 0.20/0.47 thf(fact_65_subset__trans,axiom,
% 0.20/0.47 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.20/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.20/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C3 )
% 0.20/0.47 => ( ord_less_eq @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subset_trans
% 0.20/0.47 thf(fact_66_Collect__mono,axiom,
% 0.20/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.20/0.47 ( ! [X: A] :
% 0.20/0.47 ( ( P @ X )
% 0.20/0.47 => ( Q @ X ) )
% 0.20/0.47 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mono
% 0.20/0.47 thf(fact_67_subset__refl,axiom,
% 0.20/0.47 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 0.20/0.47
% 0.20/0.47 % subset_refl
% 0.20/0.47 thf(fact_68_subset__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.20/0.47 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.20/0.47 ! [T: A] :
% 0.20/0.47 ( ( member @ A @ T @ A3 )
% 0.20/0.47 => ( member @ A @ T @ B3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subset_iff
% 0.20/0.47 thf(fact_69_equalityD2,axiom,
% 0.20/0.47 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.20/0.47 ( ( A2 = B2 )
% 0.20/0.47 => ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % equalityD2
% 0.20/0.47 thf(fact_70_equalityD1,axiom,
% 0.20/0.47 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.20/0.47 ( ( A2 = B2 )
% 0.20/0.47 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % equalityD1
% 0.20/0.47 thf(fact_71_subset__eq,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.20/0.47 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.20/0.47 ! [X3: A] :
% 0.20/0.47 ( ( member @ A @ X3 @ A3 )
% 0.20/0.47 => ( member @ A @ X3 @ B3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subset_eq
% 0.20/0.47 thf(fact_72_equalityE,axiom,
% 0.20/0.47 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.20/0.47 ( ( A2 = B2 )
% 0.20/0.47 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.20/0.47 => ~ ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % equalityE
% 0.20/0.47 thf(fact_73_subsetD,axiom,
% 0.20/0.47 ! [A: $tType,A2: set @ A,B2: set @ A,C2: A] :
% 0.20/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.20/0.47 => ( ( member @ A @ C2 @ A2 )
% 0.20/0.47 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subsetD
% 0.20/0.47 thf(fact_74_in__mono,axiom,
% 0.20/0.47 ! [A: $tType,A2: set @ A,B2: set @ A,X2: A] :
% 0.20/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.20/0.47 => ( ( member @ A @ X2 @ A2 )
% 0.20/0.47 => ( member @ A @ X2 @ B2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % in_mono
% 0.20/0.47 thf(fact_75_Uvariation__sym__rel,axiom,
% 0.20/0.47 ! [Omega: variable > real,Nu: variable > real,U: set @ variable] :
% 0.20/0.47 ( ( denota1419872369iation @ Omega @ Nu @ U )
% 0.20/0.47 => ( denota1419872369iation @ Nu @ Omega @ U ) ) ).
% 0.20/0.47
% 0.20/0.47 % Uvariation_sym_rel
% 0.20/0.47 thf(fact_76_Uvariation__refl,axiom,
% 0.20/0.47 ! [Nu: variable > real,V: set @ variable] : ( denota1419872369iation @ Nu @ Nu @ V ) ).
% 0.20/0.47
% 0.20/0.47 % Uvariation_refl
% 0.20/0.47 thf(fact_77_Uvariation__sym,axiom,
% 0.20/0.47 ( denota1419872369iation
% 0.20/0.47 = ( ^ [Omega2: variable > real,Nu3: variable > real] : ( denota1419872369iation @ Nu3 @ Omega2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Uvariation_sym
% 0.20/0.47 thf(fact_78_Uvariation__def,axiom,
% 0.20/0.47 ( denota1419872369iation
% 0.20/0.47 = ( ^ [Nu3: variable > real,Nu4: variable > real,U2: set @ variable] :
% 0.20/0.47 ! [I: variable] :
% 0.20/0.47 ( ~ ( member @ variable @ I @ U2 )
% 0.20/0.47 => ( ( Nu3 @ I )
% 0.20/0.47 = ( Nu4 @ I ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Uvariation_def
% 0.20/0.47 thf(fact_79_pred__subset__eq,axiom,
% 0.20/0.47 ! [A: $tType,R: set @ A,S: set @ A] :
% 0.20/0.47 ( ( ord_less_eq @ ( A > $o )
% 0.20/0.47 @ ^ [X3: A] : ( member @ A @ X3 @ R )
% 0.20/0.47 @ ^ [X3: A] : ( member @ A @ X3 @ S ) )
% 0.20/0.47 = ( ord_less_eq @ ( set @ A ) @ R @ S ) ) ).
% 0.20/0.47
% 0.20/0.47 % pred_subset_eq
% 0.20/0.47 thf(fact_80_subset__Collect__iff,axiom,
% 0.20/0.47 ! [A: $tType,B2: set @ A,A2: set @ A,P: A > $o] :
% 0.20/0.47 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 0.20/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B2
% 0.20/0.47 @ ( collect @ A
% 0.20/0.47 @ ^ [X3: A] :
% 0.20/0.47 ( ( member @ A @ X3 @ A2 )
% 0.20/0.47 & ( P @ X3 ) ) ) )
% 0.20/0.47 = ( ! [X3: A] :
% 0.20/0.47 ( ( member @ A @ X3 @ B2 )
% 0.20/0.47 => ( P @ X3 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subset_Collect_iff
% 0.20/0.47 thf(fact_81_subset__CollectI,axiom,
% 0.20/0.47 ! [A: $tType,B2: set @ A,A2: set @ A,Q: A > $o,P: A > $o] :
% 0.20/0.47 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 0.20/0.47 => ( ! [X: A] :
% 0.20/0.47 ( ( member @ A @ X @ B2 )
% 0.20/0.47 => ( ( Q @ X )
% 0.20/0.47 => ( P @ X ) ) )
% 0.20/0.47 => ( ord_less_eq @ ( set @ A )
% 0.20/0.47 @ ( collect @ A
% 0.20/0.47 @ ^ [X3: A] :
% 0.20/0.47 ( ( member @ A @ X3 @ B2 )
% 0.20/0.47 & ( Q @ X3 ) ) )
% 0.20/0.47 @ ( collect @ A
% 0.20/0.47 @ ^ [X3: A] :
% 0.20/0.47 ( ( member @ A @ X3 @ A2 )
% 0.20/0.47 & ( P @ X3 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subset_CollectI
% 0.20/0.47 thf(fact_82_Collect__restrict,axiom,
% 0.20/0.47 ! [A: $tType,X4: set @ A,P: A > $o] :
% 0.20/0.47 ( ord_less_eq @ ( set @ A )
% 0.20/0.47 @ ( collect @ A
% 0.20/0.47 @ ^ [X3: A] :
% 0.20/0.47 ( ( member @ A @ X3 @ X4 )
% 0.20/0.47 & ( P @ X3 ) ) )
% 0.20/0.47 @ X4 ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_restrict
% 0.20/0.47 thf(fact_83_prop__restrict,axiom,
% 0.20/0.47 ! [A: $tType,X2: A,Z3: set @ A,X4: set @ A,P: A > $o] :
% 0.20/0.47 ( ( member @ A @ X2 @ Z3 )
% 0.20/0.47 => ( ( ord_less_eq @ ( set @ A ) @ Z3
% 0.20/0.47 @ ( collect @ A
% 0.20/0.47 @ ^ [X3: A] :
% 0.20/0.47 ( ( member @ A @ X3 @ X4 )
% 0.20/0.47 & ( P @ X3 ) ) ) )
% 0.20/0.47 => ( P @ X2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prop_restrict
% 0.20/0.47 thf(fact_84_conj__subset__def,axiom,
% 0.20/0.47 ! [A: $tType,A2: set @ A,P: A > $o,Q: A > $o] :
% 0.20/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2
% 0.20/0.47 @ ( collect @ A
% 0.20/0.47 @ ^ [X3: A] :
% 0.20/0.47 ( ( P @ X3 )
% 0.20/0.47 & ( Q @ X3 ) ) ) )
% 0.20/0.47 = ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( collect @ A @ P ) )
% 0.20/0.47 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( collect @ A @ Q ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % conj_subset_def
% 0.20/0.47 thf(fact_85_Pluso_Oelims,axiom,
% 0.20/0.47 ! [X2: option @ trm,Xa: option @ trm,Y2: option @ trm] :
% 0.20/0.47 ( ( ( uSubst1112714340_Pluso @ X2 @ Xa )
% 0.20/0.47 = Y2 )
% 0.20/0.47 => ( ! [Theta2: trm] :
% 0.20/0.47 ( ( X2
% 0.20/0.47 = ( some @ trm @ Theta2 ) )
% 0.20/0.47 => ! [Eta2: trm] :
% 0.20/0.47 ( ( Xa
% 0.20/0.47 = ( some @ trm @ Eta2 ) )
% 0.20/0.47 => ( Y2
% 0.20/0.47 != ( some @ trm @ ( plus @ Theta2 @ Eta2 ) ) ) ) )
% 0.20/0.47 => ( ( ( X2
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ( Y2
% 0.20/0.47 != ( none @ trm ) ) )
% 0.20/0.47 => ~ ( ? [V2: trm] :
% 0.20/0.47 ( X2
% 0.20/0.47 = ( some @ trm @ V2 ) )
% 0.20/0.47 => ( ( Xa
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ( Y2
% 0.20/0.47 != ( none @ trm ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pluso.elims
% 0.20/0.47 thf(fact_86_Timeso_Oelims,axiom,
% 0.20/0.47 ! [X2: option @ trm,Xa: option @ trm,Y2: option @ trm] :
% 0.20/0.47 ( ( ( uSubst277968634Timeso @ X2 @ Xa )
% 0.20/0.47 = Y2 )
% 0.20/0.47 => ( ! [Theta2: trm] :
% 0.20/0.47 ( ( X2
% 0.20/0.47 = ( some @ trm @ Theta2 ) )
% 0.20/0.47 => ! [Eta2: trm] :
% 0.20/0.47 ( ( Xa
% 0.20/0.47 = ( some @ trm @ Eta2 ) )
% 0.20/0.47 => ( Y2
% 0.20/0.47 != ( some @ trm @ ( times @ Theta2 @ Eta2 ) ) ) ) )
% 0.20/0.47 => ( ( ( X2
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ( Y2
% 0.20/0.47 != ( none @ trm ) ) )
% 0.20/0.47 => ~ ( ? [V2: trm] :
% 0.20/0.47 ( X2
% 0.20/0.47 = ( some @ trm @ V2 ) )
% 0.20/0.47 => ( ( Xa
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ( Y2
% 0.20/0.47 != ( none @ trm ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Timeso.elims
% 0.20/0.47 thf(fact_87_usubstappt_Osimps_I7_J,axiom,
% 0.20/0.47 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm] :
% 0.20/0.47 ( ( uSubst95898992stappt @ Sigma @ U @ ( differential @ Theta ) )
% 0.20/0.47 = ( uSubst259074819ntialo
% 0.20/0.47 @ ( uSubst95898992stappt @ Sigma
% 0.20/0.47 @ ( collect @ variable
% 0.20/0.47 @ ^ [X3: variable] : $true )
% 0.20/0.47 @ Theta ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % usubstappt.simps(7)
% 0.20/0.47 thf(fact_88_option_Oinject,axiom,
% 0.20/0.47 ! [A: $tType,X23: A,Y23: A] :
% 0.20/0.47 ( ( ( some @ A @ X23 )
% 0.20/0.47 = ( some @ A @ Y23 ) )
% 0.20/0.47 = ( X23 = Y23 ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.inject
% 0.20/0.47 thf(fact_89_trm_Oinject_I7_J,axiom,
% 0.20/0.47 ! [X7: trm,Y7: trm] :
% 0.20/0.47 ( ( ( differential @ X7 )
% 0.20/0.47 = ( differential @ Y7 ) )
% 0.20/0.47 = ( X7 = Y7 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.inject(7)
% 0.20/0.47 thf(fact_90_predicate1I,axiom,
% 0.20/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.20/0.47 ( ! [X: A] :
% 0.20/0.47 ( ( P @ X )
% 0.20/0.47 => ( Q @ X ) )
% 0.20/0.47 => ( ord_less_eq @ ( A > $o ) @ P @ Q ) ) ).
% 0.20/0.47
% 0.20/0.47 % predicate1I
% 0.20/0.47 thf(fact_91_not__Some__eq,axiom,
% 0.20/0.47 ! [A: $tType,X2: option @ A] :
% 0.20/0.47 ( ( ! [Y3: A] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( some @ A @ Y3 ) ) )
% 0.20/0.47 = ( X2
% 0.20/0.47 = ( none @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % not_Some_eq
% 0.20/0.47 thf(fact_92_not__None__eq,axiom,
% 0.20/0.47 ! [A: $tType,X2: option @ A] :
% 0.20/0.47 ( ( X2
% 0.20/0.47 != ( none @ A ) )
% 0.20/0.47 = ( ? [Y3: A] :
% 0.20/0.47 ( X2
% 0.20/0.47 = ( some @ A @ Y3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % not_None_eq
% 0.20/0.47 thf(fact_93_predicate1D,axiom,
% 0.20/0.47 ! [A: $tType,P: A > $o,Q: A > $o,X2: A] :
% 0.20/0.47 ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 0.20/0.47 => ( ( P @ X2 )
% 0.20/0.47 => ( Q @ X2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % predicate1D
% 0.20/0.47 thf(fact_94_rev__predicate1D,axiom,
% 0.20/0.47 ! [A: $tType,P: A > $o,X2: A,Q: A > $o] :
% 0.20/0.47 ( ( P @ X2 )
% 0.20/0.47 => ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 0.20/0.47 => ( Q @ X2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % rev_predicate1D
% 0.20/0.47 thf(fact_95_Aterm__Some,axiom,
% 0.20/0.47 ( ( some @ trm )
% 0.20/0.47 = ( some @ trm ) ) ).
% 0.20/0.47
% 0.20/0.47 % Aterm_Some
% 0.20/0.47 thf(fact_96_Differentialo_Osimps_I1_J,axiom,
% 0.20/0.47 ! [Theta: trm] :
% 0.20/0.47 ( ( uSubst259074819ntialo @ ( some @ trm @ Theta ) )
% 0.20/0.47 = ( some @ trm @ ( differential @ Theta ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Differentialo.simps(1)
% 0.20/0.47 thf(fact_97_combine__options__cases,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,X2: option @ A,P: ( option @ A ) > ( option @ B ) > $o,Y2: option @ B] :
% 0.20/0.47 ( ( ( X2
% 0.20/0.47 = ( none @ A ) )
% 0.20/0.47 => ( P @ X2 @ Y2 ) )
% 0.20/0.47 => ( ( ( Y2
% 0.20/0.47 = ( none @ B ) )
% 0.20/0.47 => ( P @ X2 @ Y2 ) )
% 0.20/0.47 => ( ! [A6: A,B6: B] :
% 0.20/0.47 ( ( X2
% 0.20/0.47 = ( some @ A @ A6 ) )
% 0.20/0.47 => ( ( Y2
% 0.20/0.47 = ( some @ B @ B6 ) )
% 0.20/0.47 => ( P @ X2 @ Y2 ) ) )
% 0.20/0.47 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % combine_options_cases
% 0.20/0.47 thf(fact_98_split__option__all,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ^ [P2: ( option @ A ) > $o] :
% 0.20/0.47 ! [X5: option @ A] : ( P2 @ X5 ) )
% 0.20/0.47 = ( ^ [P3: ( option @ A ) > $o] :
% 0.20/0.47 ( ( P3 @ ( none @ A ) )
% 0.20/0.47 & ! [X3: A] : ( P3 @ ( some @ A @ X3 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % split_option_all
% 0.20/0.47 thf(fact_99_split__option__ex,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ^ [P2: ( option @ A ) > $o] :
% 0.20/0.47 ? [X5: option @ A] : ( P2 @ X5 ) )
% 0.20/0.47 = ( ^ [P3: ( option @ A ) > $o] :
% 0.20/0.47 ( ( P3 @ ( none @ A ) )
% 0.20/0.47 | ? [X3: A] : ( P3 @ ( some @ A @ X3 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % split_option_ex
% 0.20/0.47 thf(fact_100_option_Oinducts,axiom,
% 0.20/0.47 ! [A: $tType,P: ( option @ A ) > $o,Option: option @ A] :
% 0.20/0.47 ( ( P @ ( none @ A ) )
% 0.20/0.47 => ( ! [X: A] : ( P @ ( some @ A @ X ) )
% 0.20/0.47 => ( P @ Option ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.inducts
% 0.20/0.47 thf(fact_101_option_Oexhaust,axiom,
% 0.20/0.47 ! [A: $tType,Y2: option @ A] :
% 0.20/0.47 ( ( Y2
% 0.20/0.47 != ( none @ A ) )
% 0.20/0.47 => ~ ! [X24: A] :
% 0.20/0.47 ( Y2
% 0.20/0.47 != ( some @ A @ X24 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.exhaust
% 0.20/0.47 thf(fact_102_option_OdiscI,axiom,
% 0.20/0.47 ! [A: $tType,Option: option @ A,X23: A] :
% 0.20/0.47 ( ( Option
% 0.20/0.47 = ( some @ A @ X23 ) )
% 0.20/0.47 => ( Option
% 0.20/0.47 != ( none @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.discI
% 0.20/0.47 thf(fact_103_option_Odistinct_I1_J,axiom,
% 0.20/0.47 ! [A: $tType,X23: A] :
% 0.20/0.47 ( ( none @ A )
% 0.20/0.47 != ( some @ A @ X23 ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.distinct(1)
% 0.20/0.47 thf(fact_104_Differentialo_Oinduct,axiom,
% 0.20/0.47 ! [P: ( option @ trm ) > $o,A0: option @ trm] :
% 0.20/0.47 ( ! [Theta2: trm] : ( P @ ( some @ trm @ Theta2 ) )
% 0.20/0.47 => ( ( P @ ( none @ trm ) )
% 0.20/0.47 => ( P @ A0 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Differentialo.induct
% 0.20/0.47 thf(fact_105_Differentialo_Ocases,axiom,
% 0.20/0.47 ! [X2: option @ trm] :
% 0.20/0.47 ( ! [Theta2: trm] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( some @ trm @ Theta2 ) )
% 0.20/0.47 => ( X2
% 0.20/0.47 = ( none @ trm ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Differentialo.cases
% 0.20/0.47 thf(fact_106_Assigno_Oinduct,axiom,
% 0.20/0.47 ! [P: variable > ( option @ trm ) > $o,A0: variable,A1: option @ trm] :
% 0.20/0.47 ( ! [X: variable,Theta2: trm] : ( P @ X @ ( some @ trm @ Theta2 ) )
% 0.20/0.47 => ( ! [X: variable] : ( P @ X @ ( none @ trm ) )
% 0.20/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Assigno.induct
% 0.20/0.47 thf(fact_107_Timeso_Oinduct,axiom,
% 0.20/0.47 ! [P: ( option @ trm ) > ( option @ trm ) > $o,A0: option @ trm,A1: option @ trm] :
% 0.20/0.47 ( ! [Theta2: trm,Eta2: trm] : ( P @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta2 ) )
% 0.20/0.47 => ( ! [X_1: option @ trm] : ( P @ ( none @ trm ) @ X_1 )
% 0.20/0.47 => ( ! [V2: trm] : ( P @ ( some @ trm @ V2 ) @ ( none @ trm ) )
% 0.20/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Timeso.induct
% 0.20/0.47 thf(fact_108_undeft__equiv,axiom,
% 0.20/0.47 ! [Theta: option @ trm] :
% 0.20/0.47 ( ( Theta
% 0.20/0.47 != ( none @ trm ) )
% 0.20/0.47 = ( ? [T: trm] :
% 0.20/0.47 ( Theta
% 0.20/0.47 = ( some @ trm @ T ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % undeft_equiv
% 0.20/0.47 thf(fact_109_ODEo_Oinduct,axiom,
% 0.20/0.47 ! [P: char > ( option @ trm ) > $o,A0: char,A1: option @ trm] :
% 0.20/0.47 ( ! [X: char,Theta2: trm] : ( P @ X @ ( some @ trm @ Theta2 ) )
% 0.20/0.47 => ( ! [X: char] : ( P @ X @ ( none @ trm ) )
% 0.20/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ODEo.induct
% 0.20/0.47 thf(fact_110_Differentialo_Oelims,axiom,
% 0.20/0.47 ! [X2: option @ trm,Y2: option @ trm] :
% 0.20/0.47 ( ( ( uSubst259074819ntialo @ X2 )
% 0.20/0.47 = Y2 )
% 0.20/0.47 => ( ! [Theta2: trm] :
% 0.20/0.47 ( ( X2
% 0.20/0.47 = ( some @ trm @ Theta2 ) )
% 0.20/0.47 => ( Y2
% 0.20/0.47 != ( some @ trm @ ( differential @ Theta2 ) ) ) )
% 0.20/0.47 => ~ ( ( X2
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ( Y2
% 0.20/0.47 != ( none @ trm ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Differentialo.elims
% 0.20/0.47 thf(fact_111_trm_Odistinct_I41_J,axiom,
% 0.20/0.47 ! [X61: trm,X62: trm,X7: trm] :
% 0.20/0.47 ( ( times @ X61 @ X62 )
% 0.20/0.47 != ( differential @ X7 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(41)
% 0.20/0.47 thf(fact_112_trm_Odistinct_I39_J,axiom,
% 0.20/0.47 ! [X51: trm,X52: trm,X7: trm] :
% 0.20/0.47 ( ( plus @ X51 @ X52 )
% 0.20/0.47 != ( differential @ X7 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(39)
% 0.20/0.47 thf(fact_113_Timeso_Osimps_I3_J,axiom,
% 0.20/0.47 ! [V3: trm] :
% 0.20/0.47 ( ( uSubst277968634Timeso @ ( some @ trm @ V3 ) @ ( none @ trm ) )
% 0.20/0.47 = ( none @ trm ) ) ).
% 0.20/0.47
% 0.20/0.47 % Timeso.simps(3)
% 0.20/0.47 thf(fact_114_Pluso_Osimps_I3_J,axiom,
% 0.20/0.47 ! [V3: trm] :
% 0.20/0.47 ( ( uSubst1112714340_Pluso @ ( some @ trm @ V3 ) @ ( none @ trm ) )
% 0.20/0.47 = ( none @ trm ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pluso.simps(3)
% 0.20/0.47 thf(fact_115_Pluso_Osimps_I1_J,axiom,
% 0.20/0.47 ! [Theta: trm,Eta: trm] :
% 0.20/0.47 ( ( uSubst1112714340_Pluso @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta ) )
% 0.20/0.47 = ( some @ trm @ ( plus @ Theta @ Eta ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pluso.simps(1)
% 0.20/0.47 thf(fact_116_Timeso_Osimps_I1_J,axiom,
% 0.20/0.47 ! [Theta: trm,Eta: trm] :
% 0.20/0.47 ( ( uSubst277968634Timeso @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta ) )
% 0.20/0.47 = ( some @ trm @ ( times @ Theta @ Eta ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Timeso.simps(1)
% 0.20/0.47 thf(fact_117_usubstappt__differential__conv,axiom,
% 0.20/0.47 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm] :
% 0.20/0.47 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( differential @ Theta ) )
% 0.20/0.47 != ( none @ trm ) )
% 0.20/0.47 => ( ( uSubst95898992stappt @ Sigma
% 0.20/0.47 @ ( collect @ variable
% 0.20/0.47 @ ^ [X3: variable] : $true )
% 0.20/0.47 @ Theta )
% 0.20/0.47 != ( none @ trm ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % usubstappt_differential_conv
% 0.20/0.47 thf(fact_118_Geqo_Osimps_I3_J,axiom,
% 0.20/0.47 ! [V3: trm] :
% 0.20/0.47 ( ( uSubst1556497037e_Geqo @ ( some @ trm @ V3 ) @ ( none @ trm ) )
% 0.20/0.47 = ( none @ fml ) ) ).
% 0.20/0.47
% 0.20/0.47 % Geqo.simps(3)
% 0.20/0.47 thf(fact_119_Geqo_Oelims,axiom,
% 0.20/0.47 ! [X2: option @ trm,Xa: option @ trm,Y2: option @ fml] :
% 0.20/0.47 ( ( ( uSubst1556497037e_Geqo @ X2 @ Xa )
% 0.20/0.47 = Y2 )
% 0.20/0.47 => ( ! [Theta2: trm] :
% 0.20/0.47 ( ( X2
% 0.20/0.47 = ( some @ trm @ Theta2 ) )
% 0.20/0.47 => ! [Eta2: trm] :
% 0.20/0.47 ( ( Xa
% 0.20/0.47 = ( some @ trm @ Eta2 ) )
% 0.20/0.47 => ( Y2
% 0.20/0.47 != ( some @ fml @ ( geq @ Theta2 @ Eta2 ) ) ) ) )
% 0.20/0.47 => ( ( ( X2
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ( Y2
% 0.20/0.47 != ( none @ fml ) ) )
% 0.20/0.47 => ~ ( ? [V2: trm] :
% 0.20/0.47 ( X2
% 0.20/0.47 = ( some @ trm @ V2 ) )
% 0.20/0.47 => ( ( Xa
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ( Y2
% 0.20/0.47 != ( none @ fml ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Geqo.elims
% 0.20/0.47 thf(fact_120_Differentialo_Opelims,axiom,
% 0.20/0.47 ! [X2: option @ trm,Y2: option @ trm] :
% 0.20/0.47 ( ( ( uSubst259074819ntialo @ X2 )
% 0.20/0.47 = Y2 )
% 0.20/0.47 => ( ( accp @ ( option @ trm ) @ uSubst99643830lo_rel @ X2 )
% 0.20/0.47 => ( ! [Theta2: trm] :
% 0.20/0.47 ( ( X2
% 0.20/0.47 = ( some @ trm @ Theta2 ) )
% 0.20/0.47 => ( ( Y2
% 0.20/0.47 = ( some @ trm @ ( differential @ Theta2 ) ) )
% 0.20/0.47 => ~ ( accp @ ( option @ trm ) @ uSubst99643830lo_rel @ ( some @ trm @ Theta2 ) ) ) )
% 0.20/0.47 => ~ ( ( X2
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ( ( Y2
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ~ ( accp @ ( option @ trm ) @ uSubst99643830lo_rel @ ( none @ trm ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Differentialo.pelims
% 0.20/0.47 thf(fact_121_Powp__mono,axiom,
% 0.20/0.47 ! [A: $tType,A2: A > $o,B2: A > $o] :
% 0.20/0.47 ( ( ord_less_eq @ ( A > $o ) @ A2 @ B2 )
% 0.20/0.47 => ( ord_less_eq @ ( ( set @ A ) > $o ) @ ( powp @ A @ A2 ) @ ( powp @ A @ B2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Powp_mono
% 0.20/0.47 thf(fact_122_Geqo_Osimps_I1_J,axiom,
% 0.20/0.47 ! [Theta: trm,Eta: trm] :
% 0.20/0.47 ( ( uSubst1556497037e_Geqo @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta ) )
% 0.20/0.47 = ( some @ fml @ ( geq @ Theta @ Eta ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Geqo.simps(1)
% 0.20/0.47 thf(fact_123_GreatestI2__order,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( order @ A )
% 0.20/0.47 => ! [P: A > $o,X2: A,Q: A > $o] :
% 0.20/0.47 ( ( P @ X2 )
% 0.20/0.47 => ( ! [Y4: A] :
% 0.20/0.47 ( ( P @ Y4 )
% 0.20/0.47 => ( ord_less_eq @ A @ Y4 @ X2 ) )
% 0.20/0.47 => ( ! [X: A] :
% 0.20/0.47 ( ( P @ X )
% 0.20/0.47 => ( ! [Y5: A] :
% 0.20/0.47 ( ( P @ Y5 )
% 0.20/0.47 => ( ord_less_eq @ A @ Y5 @ X ) )
% 0.20/0.47 => ( Q @ X ) ) )
% 0.20/0.47 => ( Q @ ( order_Greatest @ A @ P ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % GreatestI2_order
% 0.20/0.47 thf(fact_124_Greatest__equality,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( order @ A )
% 0.20/0.47 => ! [P: A > $o,X2: A] :
% 0.20/0.47 ( ( P @ X2 )
% 0.20/0.47 => ( ! [Y4: A] :
% 0.20/0.47 ( ( P @ Y4 )
% 0.20/0.47 => ( ord_less_eq @ A @ Y4 @ X2 ) )
% 0.20/0.47 => ( ( order_Greatest @ A @ P )
% 0.20/0.47 = X2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Greatest_equality
% 0.20/0.47 thf(fact_125_Diamondo_Oinduct,axiom,
% 0.20/0.47 ! [P: ( option @ game ) > ( option @ fml ) > $o,A0: option @ game,A1: option @ fml] :
% 0.20/0.47 ( ! [Alpha: game,Phi2: fml] : ( P @ ( some @ game @ Alpha ) @ ( some @ fml @ Phi2 ) )
% 0.20/0.47 => ( ! [X_1: option @ fml] : ( P @ ( none @ game ) @ X_1 )
% 0.20/0.47 => ( ! [V2: game] : ( P @ ( some @ game @ V2 ) @ ( none @ fml ) )
% 0.20/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Diamondo.induct
% 0.20/0.47 thf(fact_126_Existso_Oinduct,axiom,
% 0.20/0.47 ! [P: variable > ( option @ fml ) > $o,A0: variable,A1: option @ fml] :
% 0.20/0.47 ( ! [X: variable,Phi2: fml] : ( P @ X @ ( some @ fml @ Phi2 ) )
% 0.20/0.47 => ( ! [X: variable] : ( P @ X @ ( none @ fml ) )
% 0.20/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Existso.induct
% 0.20/0.47 thf(fact_127_undeff__equiv,axiom,
% 0.20/0.47 ! [Phi: option @ fml] :
% 0.20/0.47 ( ( Phi
% 0.20/0.47 != ( none @ fml ) )
% 0.20/0.47 = ( ? [F2: fml] :
% 0.20/0.47 ( Phi
% 0.20/0.47 = ( some @ fml @ F2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % undeff_equiv
% 0.20/0.47 thf(fact_128_Testo_Oinduct,axiom,
% 0.20/0.47 ! [P: ( option @ fml ) > $o,A0: option @ fml] :
% 0.20/0.47 ( ! [Phi2: fml] : ( P @ ( some @ fml @ Phi2 ) )
% 0.20/0.47 => ( ( P @ ( none @ fml ) )
% 0.20/0.47 => ( P @ A0 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Testo.induct
% 0.20/0.47 thf(fact_129_Testo_Ocases,axiom,
% 0.20/0.47 ! [X2: option @ fml] :
% 0.20/0.47 ( ! [Phi2: fml] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( some @ fml @ Phi2 ) )
% 0.20/0.47 => ( X2
% 0.20/0.47 = ( none @ fml ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Testo.cases
% 0.20/0.47 thf(fact_130_Ando_Oinduct,axiom,
% 0.20/0.47 ! [P: ( option @ fml ) > ( option @ fml ) > $o,A0: option @ fml,A1: option @ fml] :
% 0.20/0.47 ( ! [Phi2: fml,Psi: fml] : ( P @ ( some @ fml @ Phi2 ) @ ( some @ fml @ Psi ) )
% 0.20/0.47 => ( ! [X_1: option @ fml] : ( P @ ( none @ fml ) @ X_1 )
% 0.20/0.47 => ( ! [V2: fml] : ( P @ ( some @ fml @ V2 ) @ ( none @ fml ) )
% 0.20/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Ando.induct
% 0.20/0.47 thf(fact_131_accp__subset,axiom,
% 0.20/0.47 ! [A: $tType,R1: A > A > $o,R2: A > A > $o] :
% 0.20/0.47 ( ( ord_less_eq @ ( A > A > $o ) @ R1 @ R2 )
% 0.20/0.47 => ( ord_less_eq @ ( A > $o ) @ ( accp @ A @ R2 ) @ ( accp @ A @ R1 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % accp_subset
% 0.20/0.47 thf(fact_132_accp__subset__induct,axiom,
% 0.20/0.47 ! [A: $tType,D: A > $o,R: A > A > $o,X2: A,P: A > $o] :
% 0.20/0.47 ( ( ord_less_eq @ ( A > $o ) @ D @ ( accp @ A @ R ) )
% 0.20/0.47 => ( ! [X: A,Z4: A] :
% 0.20/0.47 ( ( D @ X )
% 0.20/0.47 => ( ( R @ Z4 @ X )
% 0.20/0.47 => ( D @ Z4 ) ) )
% 0.20/0.47 => ( ( D @ X2 )
% 0.20/0.47 => ( ! [X: A] :
% 0.20/0.47 ( ( D @ X )
% 0.20/0.47 => ( ! [Z5: A] :
% 0.20/0.47 ( ( R @ Z5 @ X )
% 0.20/0.47 => ( P @ Z5 ) )
% 0.20/0.47 => ( P @ X ) ) )
% 0.20/0.47 => ( P @ X2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % accp_subset_induct
% 0.20/0.47 thf(fact_133_usubstappf__geqr,axiom,
% 0.20/0.47 ! [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] :
% 0.20/0.47 ( ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.20/0.47 != ( none @ fml ) )
% 0.20/0.47 => ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.20/0.47 = ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Eta ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % usubstappf_geqr
% 0.20/0.47 thf(fact_134_usubstappf__geq,axiom,
% 0.20/0.47 ! [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] :
% 0.20/0.47 ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.20/0.47 != ( none @ trm ) )
% 0.20/0.47 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Eta )
% 0.20/0.47 != ( none @ trm ) )
% 0.20/0.47 => ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.20/0.47 = ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Eta ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % usubstappf_geq
% 0.20/0.47 thf(fact_135_predicate2I,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,P: A > B > $o,Q: A > B > $o] :
% 0.20/0.47 ( ! [X: A,Y4: B] :
% 0.20/0.47 ( ( P @ X @ Y4 )
% 0.20/0.47 => ( Q @ X @ Y4 ) )
% 0.20/0.47 => ( ord_less_eq @ ( A > B > $o ) @ P @ Q ) ) ).
% 0.20/0.47
% 0.20/0.47 % predicate2I
% 0.20/0.47 thf(fact_136_option_Ocollapse,axiom,
% 0.20/0.47 ! [A: $tType,Option: option @ A] :
% 0.20/0.47 ( ( Option
% 0.20/0.47 != ( none @ A ) )
% 0.20/0.47 => ( ( some @ A @ ( the @ A @ Option ) )
% 0.20/0.47 = Option ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.collapse
% 0.20/0.47 thf(fact_137_predicate2D,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,X2: A,Y2: B] :
% 0.20/0.47 ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 0.20/0.47 => ( ( P @ X2 @ Y2 )
% 0.20/0.47 => ( Q @ X2 @ Y2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % predicate2D
% 0.20/0.47 thf(fact_138_rev__predicate2D,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,P: A > B > $o,X2: A,Y2: B,Q: A > B > $o] :
% 0.20/0.47 ( ( P @ X2 @ Y2 )
% 0.20/0.47 => ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 0.20/0.47 => ( Q @ X2 @ Y2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % rev_predicate2D
% 0.20/0.47 thf(fact_139_Composeo_Oinduct,axiom,
% 0.20/0.47 ! [P: ( option @ game ) > ( option @ game ) > $o,A0: option @ game,A1: option @ game] :
% 0.20/0.47 ( ! [Alpha: game,Beta: game] : ( P @ ( some @ game @ Alpha ) @ ( some @ game @ Beta ) )
% 0.20/0.47 => ( ! [Alpha: option @ game] : ( P @ Alpha @ ( none @ game ) )
% 0.20/0.47 => ( ! [V2: game] : ( P @ ( none @ game ) @ ( some @ game @ V2 ) )
% 0.20/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Composeo.induct
% 0.20/0.47 thf(fact_140_undefg__equiv,axiom,
% 0.20/0.47 ! [Alpha2: option @ game] :
% 0.20/0.47 ( ( Alpha2
% 0.20/0.47 != ( none @ game ) )
% 0.20/0.47 = ( ? [G2: game] :
% 0.20/0.47 ( Alpha2
% 0.20/0.47 = ( some @ game @ G2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % undefg_equiv
% 0.20/0.47 thf(fact_141_Loopo_Oinduct,axiom,
% 0.20/0.47 ! [P: ( option @ game ) > $o,A0: option @ game] :
% 0.20/0.47 ( ! [Alpha: game] : ( P @ ( some @ game @ Alpha ) )
% 0.20/0.47 => ( ( P @ ( none @ game ) )
% 0.20/0.47 => ( P @ A0 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Loopo.induct
% 0.20/0.47 thf(fact_142_Loopo_Ocases,axiom,
% 0.20/0.47 ! [X2: option @ game] :
% 0.20/0.47 ( ! [Alpha: game] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( some @ game @ Alpha ) )
% 0.20/0.47 => ( X2
% 0.20/0.47 = ( none @ game ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Loopo.cases
% 0.20/0.47 thf(fact_143_option_Oexpand,axiom,
% 0.20/0.47 ! [A: $tType,Option: option @ A,Option2: option @ A] :
% 0.20/0.47 ( ( ( Option
% 0.20/0.47 = ( none @ A ) )
% 0.20/0.47 = ( Option2
% 0.20/0.47 = ( none @ A ) ) )
% 0.20/0.47 => ( ( ( Option
% 0.20/0.47 != ( none @ A ) )
% 0.20/0.47 => ( ( Option2
% 0.20/0.47 != ( none @ A ) )
% 0.20/0.47 => ( ( the @ A @ Option )
% 0.20/0.47 = ( the @ A @ Option2 ) ) ) )
% 0.20/0.47 => ( Option = Option2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.expand
% 0.20/0.47 thf(fact_144_option_Osel,axiom,
% 0.20/0.47 ! [A: $tType,X23: A] :
% 0.20/0.47 ( ( the @ A @ ( some @ A @ X23 ) )
% 0.20/0.47 = X23 ) ).
% 0.20/0.47
% 0.20/0.47 % option.sel
% 0.20/0.47 thf(fact_145_option_Oexhaust__sel,axiom,
% 0.20/0.47 ! [A: $tType,Option: option @ A] :
% 0.20/0.47 ( ( Option
% 0.20/0.47 != ( none @ A ) )
% 0.20/0.47 => ( Option
% 0.20/0.47 = ( some @ A @ ( the @ A @ Option ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.exhaust_sel
% 0.20/0.47 thf(fact_146_accp_Ocases,axiom,
% 0.20/0.47 ! [A: $tType,R3: A > A > $o,A4: A] :
% 0.20/0.47 ( ( accp @ A @ R3 @ A4 )
% 0.20/0.47 => ! [Y5: A] :
% 0.20/0.47 ( ( R3 @ Y5 @ A4 )
% 0.20/0.47 => ( accp @ A @ R3 @ Y5 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % accp.cases
% 0.20/0.47 thf(fact_147_accp_Osimps,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( accp @ A )
% 0.20/0.47 = ( ^ [R4: A > A > $o,A5: A] :
% 0.20/0.47 ? [X3: A] :
% 0.20/0.47 ( ( A5 = X3 )
% 0.20/0.47 & ! [Y3: A] :
% 0.20/0.47 ( ( R4 @ Y3 @ X3 )
% 0.20/0.47 => ( accp @ A @ R4 @ Y3 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % accp.simps
% 0.20/0.47 thf(fact_148_accp_Ointros,axiom,
% 0.20/0.47 ! [A: $tType,R3: A > A > $o,X2: A] :
% 0.20/0.47 ( ! [Y4: A] :
% 0.20/0.47 ( ( R3 @ Y4 @ X2 )
% 0.20/0.47 => ( accp @ A @ R3 @ Y4 ) )
% 0.20/0.47 => ( accp @ A @ R3 @ X2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % accp.intros
% 0.20/0.47 thf(fact_149_accp__induct,axiom,
% 0.20/0.47 ! [A: $tType,R3: A > A > $o,A4: A,P: A > $o] :
% 0.20/0.47 ( ( accp @ A @ R3 @ A4 )
% 0.20/0.47 => ( ! [X: A] :
% 0.20/0.47 ( ( accp @ A @ R3 @ X )
% 0.20/0.47 => ( ! [Y5: A] :
% 0.20/0.47 ( ( R3 @ Y5 @ X )
% 0.20/0.47 => ( P @ Y5 ) )
% 0.20/0.47 => ( P @ X ) ) )
% 0.20/0.47 => ( P @ A4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % accp_induct
% 0.20/0.47 thf(fact_150_accp_Oinducts,axiom,
% 0.20/0.47 ! [A: $tType,R3: A > A > $o,X2: A,P: A > $o] :
% 0.20/0.47 ( ( accp @ A @ R3 @ X2 )
% 0.20/0.47 => ( ! [X: A] :
% 0.20/0.47 ( ! [Y5: A] :
% 0.20/0.47 ( ( R3 @ Y5 @ X )
% 0.20/0.47 => ( accp @ A @ R3 @ Y5 ) )
% 0.20/0.47 => ( ! [Y5: A] :
% 0.20/0.47 ( ( R3 @ Y5 @ X )
% 0.20/0.47 => ( P @ Y5 ) )
% 0.20/0.47 => ( P @ X ) ) )
% 0.20/0.47 => ( P @ X2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % accp.inducts
% 0.20/0.47 thf(fact_151_accp__downward,axiom,
% 0.20/0.47 ! [A: $tType,R3: A > A > $o,B4: A,A4: A] :
% 0.20/0.47 ( ( accp @ A @ R3 @ B4 )
% 0.20/0.47 => ( ( R3 @ A4 @ B4 )
% 0.20/0.47 => ( accp @ A @ R3 @ A4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % accp_downward
% 0.20/0.47 thf(fact_152_not__accp__down,axiom,
% 0.20/0.47 ! [A: $tType,R: A > A > $o,X2: A] :
% 0.20/0.47 ( ~ ( accp @ A @ R @ X2 )
% 0.20/0.47 => ~ ! [Z4: A] :
% 0.20/0.47 ( ( R @ Z4 @ X2 )
% 0.20/0.47 => ( accp @ A @ R @ Z4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % not_accp_down
% 0.20/0.47 thf(fact_153_accp__induct__rule,axiom,
% 0.20/0.47 ! [A: $tType,R3: A > A > $o,A4: A,P: A > $o] :
% 0.20/0.47 ( ( accp @ A @ R3 @ A4 )
% 0.20/0.47 => ( ! [X: A] :
% 0.20/0.47 ( ( accp @ A @ R3 @ X )
% 0.20/0.47 => ( ! [Y5: A] :
% 0.20/0.47 ( ( R3 @ Y5 @ X )
% 0.20/0.47 => ( P @ Y5 ) )
% 0.20/0.47 => ( P @ X ) ) )
% 0.20/0.47 => ( P @ A4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % accp_induct_rule
% 0.20/0.47 thf(fact_154_eq__subset,axiom,
% 0.20/0.47 ! [A: $tType,P: A > A > $o] :
% 0.20/0.47 ( ord_less_eq @ ( A > A > $o )
% 0.20/0.47 @ ^ [Y: A,Z: A] : ( Y = Z )
% 0.20/0.47 @ ^ [A5: A,B5: A] :
% 0.20/0.47 ( ( P @ A5 @ B5 )
% 0.20/0.47 | ( A5 = B5 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % eq_subset
% 0.20/0.47 thf(fact_155_Geqo_Opelims,axiom,
% 0.20/0.47 ! [X2: option @ trm,Xa: option @ trm,Y2: option @ fml] :
% 0.20/0.47 ( ( ( uSubst1556497037e_Geqo @ X2 @ Xa )
% 0.20/0.47 = Y2 )
% 0.20/0.47 => ( ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst864323244qo_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ X2 @ Xa ) )
% 0.20/0.47 => ( ! [Theta2: trm] :
% 0.20/0.47 ( ( X2
% 0.20/0.47 = ( some @ trm @ Theta2 ) )
% 0.20/0.47 => ! [Eta2: trm] :
% 0.20/0.47 ( ( Xa
% 0.20/0.47 = ( some @ trm @ Eta2 ) )
% 0.20/0.47 => ( ( Y2
% 0.20/0.47 = ( some @ fml @ ( geq @ Theta2 @ Eta2 ) ) )
% 0.20/0.47 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst864323244qo_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta2 ) ) ) ) ) )
% 0.20/0.47 => ( ( ( X2
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ( ( Y2
% 0.20/0.47 = ( none @ fml ) )
% 0.20/0.47 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst864323244qo_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( none @ trm ) @ Xa ) ) ) )
% 0.20/0.47 => ~ ! [V2: trm] :
% 0.20/0.47 ( ( X2
% 0.20/0.47 = ( some @ trm @ V2 ) )
% 0.20/0.47 => ( ( Xa
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ( ( Y2
% 0.20/0.47 = ( none @ fml ) )
% 0.20/0.47 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst864323244qo_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ V2 ) @ ( none @ trm ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Geqo.pelims
% 0.20/0.47 thf(fact_156_Diamondo_Ocases,axiom,
% 0.20/0.47 ! [X2: product_prod @ ( option @ game ) @ ( option @ fml )] :
% 0.20/0.47 ( ! [Alpha: game,Phi2: fml] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ Alpha ) @ ( some @ fml @ Phi2 ) ) )
% 0.20/0.47 => ( ! [Phi2: option @ fml] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( none @ game ) @ Phi2 ) )
% 0.20/0.47 => ~ ! [V2: game] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ V2 ) @ ( none @ fml ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Diamondo.cases
% 0.20/0.47 thf(fact_157_option_Osplit__sel,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 0.20/0.47 ( ( P @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( ( ( Option
% 0.20/0.47 = ( none @ A ) )
% 0.20/0.47 => ( P @ F1 ) )
% 0.20/0.47 & ( ( Option
% 0.20/0.47 = ( some @ A @ ( the @ A @ Option ) ) )
% 0.20/0.47 => ( P @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.split_sel
% 0.20/0.47 thf(fact_158_subrelI,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),S2: set @ ( product_prod @ A @ B )] :
% 0.20/0.47 ( ! [X: A,Y4: B] :
% 0.20/0.47 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y4 ) @ R3 )
% 0.20/0.47 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y4 ) @ S2 ) )
% 0.20/0.47 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R3 @ S2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % subrelI
% 0.20/0.47 thf(fact_159_ssubst__Pair__rhs,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,R3: A,S2: B,R: set @ ( product_prod @ A @ B ),S3: B] :
% 0.20/0.47 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S2 ) @ R )
% 0.20/0.47 => ( ( S3 = S2 )
% 0.20/0.47 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S3 ) @ R ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ssubst_Pair_rhs
% 0.20/0.47 thf(fact_160_pred__equals__eq2,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.20/0.47 ( ( ( ^ [X3: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ R ) )
% 0.20/0.47 = ( ^ [X3: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ S ) ) )
% 0.20/0.47 = ( R = S ) ) ).
% 0.20/0.47
% 0.20/0.47 % pred_equals_eq2
% 0.20/0.47 thf(fact_161_option_Ocase__distrib,axiom,
% 0.20/0.47 ! [C: $tType,B: $tType,A: $tType,H: B > C,F1: B,F22: A > B,Option: option @ A] :
% 0.20/0.47 ( ( H @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( case_option @ C @ A @ ( H @ F1 )
% 0.20/0.47 @ ^ [X3: A] : ( H @ ( F22 @ X3 ) )
% 0.20/0.47 @ Option ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.case_distrib
% 0.20/0.47 thf(fact_162_option_Osimps_I4_J,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,F1: B,F22: A > B] :
% 0.20/0.47 ( ( case_option @ B @ A @ F1 @ F22 @ ( none @ A ) )
% 0.20/0.47 = F1 ) ).
% 0.20/0.47
% 0.20/0.47 % option.simps(4)
% 0.20/0.47 thf(fact_163_pred__subset__eq2,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.20/0.47 ( ( ord_less_eq @ ( A > B > $o )
% 0.20/0.47 @ ^ [X3: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ R )
% 0.20/0.47 @ ^ [X3: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ S ) )
% 0.20/0.47 = ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R @ S ) ) ).
% 0.20/0.47
% 0.20/0.47 % pred_subset_eq2
% 0.20/0.47 thf(fact_164_option_Osimps_I5_J,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,F1: B,F22: A > B,X23: A] :
% 0.20/0.47 ( ( case_option @ B @ A @ F1 @ F22 @ ( some @ A @ X23 ) )
% 0.20/0.47 = ( F22 @ X23 ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.simps(5)
% 0.20/0.47 thf(fact_165_option_Odisc__eq__case_I1_J,axiom,
% 0.20/0.47 ! [A: $tType,Option: option @ A] :
% 0.20/0.47 ( ( Option
% 0.20/0.47 = ( none @ A ) )
% 0.20/0.47 = ( case_option @ $o @ A @ $true
% 0.20/0.47 @ ^ [Uu: A] : $false
% 0.20/0.47 @ Option ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.disc_eq_case(1)
% 0.20/0.47 thf(fact_166_option_Odisc__eq__case_I2_J,axiom,
% 0.20/0.47 ! [A: $tType,Option: option @ A] :
% 0.20/0.47 ( ( Option
% 0.20/0.47 != ( none @ A ) )
% 0.20/0.47 = ( case_option @ $o @ A @ $false
% 0.20/0.47 @ ^ [Uu: A] : $true
% 0.20/0.47 @ Option ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.disc_eq_case(2)
% 0.20/0.47 thf(fact_167_Timeso_Ocases,axiom,
% 0.20/0.47 ! [X2: product_prod @ ( option @ trm ) @ ( option @ trm )] :
% 0.20/0.47 ( ! [Theta2: trm,Eta2: trm] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta2 ) ) )
% 0.20/0.47 => ( ! [Eta2: option @ trm] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( none @ trm ) @ Eta2 ) )
% 0.20/0.47 => ~ ! [V2: trm] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ V2 ) @ ( none @ trm ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Timeso.cases
% 0.20/0.47 thf(fact_168_case__optionE,axiom,
% 0.20/0.47 ! [A: $tType,P: $o,Q: A > $o,X2: option @ A] :
% 0.20/0.47 ( ( case_option @ $o @ A @ P @ Q @ X2 )
% 0.20/0.47 => ( ( ( X2
% 0.20/0.47 = ( none @ A ) )
% 0.20/0.47 => ~ P )
% 0.20/0.47 => ~ ! [Y4: A] :
% 0.20/0.47 ( ( X2
% 0.20/0.47 = ( some @ A @ Y4 ) )
% 0.20/0.47 => ~ ( Q @ Y4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_optionE
% 0.20/0.47 thf(fact_169_option_Ocase__eq__if,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType] :
% 0.20/0.47 ( ( case_option @ B @ A )
% 0.20/0.47 = ( ^ [F12: B,F23: A > B,Option3: option @ A] :
% 0.20/0.47 ( if @ B
% 0.20/0.47 @ ( Option3
% 0.20/0.47 = ( none @ A ) )
% 0.20/0.47 @ F12
% 0.20/0.47 @ ( F23 @ ( the @ A @ Option3 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.case_eq_if
% 0.20/0.47 thf(fact_170_predicate2D__conj,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,R: $o,X2: A,Y2: B] :
% 0.20/0.47 ( ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 0.20/0.47 & R )
% 0.20/0.47 => ( R
% 0.20/0.47 & ( ( P @ X2 @ Y2 )
% 0.20/0.47 => ( Q @ X2 @ Y2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % predicate2D_conj
% 0.20/0.47 thf(fact_171_option_Osplit__sel__asm,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 0.20/0.47 ( ( P @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( ~ ( ( ( Option
% 0.20/0.47 = ( none @ A ) )
% 0.20/0.47 & ~ ( P @ F1 ) )
% 0.20/0.47 | ( ( Option
% 0.20/0.47 = ( some @ A @ ( the @ A @ Option ) ) )
% 0.20/0.47 & ~ ( P @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.split_sel_asm
% 0.20/0.47 thf(fact_172_Timeso_Opelims,axiom,
% 0.20/0.47 ! [X2: option @ trm,Xa: option @ trm,Y2: option @ trm] :
% 0.20/0.47 ( ( ( uSubst277968634Timeso @ X2 @ Xa )
% 0.20/0.47 = Y2 )
% 0.20/0.47 => ( ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst1377811071so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ X2 @ Xa ) )
% 0.20/0.47 => ( ! [Theta2: trm] :
% 0.20/0.47 ( ( X2
% 0.20/0.47 = ( some @ trm @ Theta2 ) )
% 0.20/0.47 => ! [Eta2: trm] :
% 0.20/0.47 ( ( Xa
% 0.20/0.47 = ( some @ trm @ Eta2 ) )
% 0.20/0.47 => ( ( Y2
% 0.20/0.47 = ( some @ trm @ ( times @ Theta2 @ Eta2 ) ) )
% 0.20/0.47 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst1377811071so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta2 ) ) ) ) ) )
% 0.20/0.47 => ( ( ( X2
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ( ( Y2
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst1377811071so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( none @ trm ) @ Xa ) ) ) )
% 0.20/0.47 => ~ ! [V2: trm] :
% 0.20/0.47 ( ( X2
% 0.20/0.47 = ( some @ trm @ V2 ) )
% 0.20/0.47 => ( ( Xa
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ( ( Y2
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst1377811071so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ V2 ) @ ( none @ trm ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Timeso.pelims
% 0.20/0.47 thf(fact_173_Pluso_Opelims,axiom,
% 0.20/0.47 ! [X2: option @ trm,Xa: option @ trm,Y2: option @ trm] :
% 0.20/0.47 ( ( ( uSubst1112714340_Pluso @ X2 @ Xa )
% 0.20/0.47 = Y2 )
% 0.20/0.47 => ( ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst270600597so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ X2 @ Xa ) )
% 0.20/0.47 => ( ! [Theta2: trm] :
% 0.20/0.47 ( ( X2
% 0.20/0.47 = ( some @ trm @ Theta2 ) )
% 0.20/0.47 => ! [Eta2: trm] :
% 0.20/0.47 ( ( Xa
% 0.20/0.47 = ( some @ trm @ Eta2 ) )
% 0.20/0.47 => ( ( Y2
% 0.20/0.47 = ( some @ trm @ ( plus @ Theta2 @ Eta2 ) ) )
% 0.20/0.47 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst270600597so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta2 ) ) ) ) ) )
% 0.20/0.47 => ( ( ( X2
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ( ( Y2
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst270600597so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( none @ trm ) @ Xa ) ) ) )
% 0.20/0.47 => ~ ! [V2: trm] :
% 0.20/0.47 ( ( X2
% 0.20/0.47 = ( some @ trm @ V2 ) )
% 0.20/0.47 => ( ( Xa
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ( ( Y2
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst270600597so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ V2 ) @ ( none @ trm ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pluso.pelims
% 0.20/0.47 thf(fact_174_disjE__realizer2,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,P: $o,Q: A > $o,X2: option @ A,R: B > $o,F: B,G: A > B] :
% 0.20/0.47 ( ( case_option @ $o @ A @ P @ Q @ X2 )
% 0.20/0.47 => ( ( P
% 0.20/0.47 => ( R @ F ) )
% 0.20/0.47 => ( ! [Q2: A] :
% 0.20/0.47 ( ( Q @ Q2 )
% 0.20/0.47 => ( R @ ( G @ Q2 ) ) )
% 0.20/0.47 => ( R @ ( case_option @ B @ A @ F @ G @ X2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % disjE_realizer2
% 0.20/0.47 thf(fact_175_ODEo_Ocases,axiom,
% 0.20/0.47 ! [X2: product_prod @ char @ ( option @ trm )] :
% 0.20/0.47 ( ! [X: char,Theta2: trm] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ char @ ( option @ trm ) @ X @ ( some @ trm @ Theta2 ) ) )
% 0.20/0.47 => ~ ! [X: char] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ char @ ( option @ trm ) @ X @ ( none @ trm ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ODEo.cases
% 0.20/0.47 thf(fact_176_Assigno_Ocases,axiom,
% 0.20/0.47 ! [X2: product_prod @ variable @ ( option @ trm )] :
% 0.20/0.47 ( ! [X: variable,Theta2: trm] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ variable @ ( option @ trm ) @ X @ ( some @ trm @ Theta2 ) ) )
% 0.20/0.47 => ~ ! [X: variable] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ variable @ ( option @ trm ) @ X @ ( none @ trm ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Assigno.cases
% 0.20/0.47 thf(fact_177_Composeo_Ocases,axiom,
% 0.20/0.47 ! [X2: product_prod @ ( option @ game ) @ ( option @ game )] :
% 0.20/0.47 ( ! [Alpha: game,Beta: game] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ ( some @ game @ Alpha ) @ ( some @ game @ Beta ) ) )
% 0.20/0.47 => ( ! [Alpha: option @ game] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ Alpha @ ( none @ game ) ) )
% 0.20/0.47 => ~ ! [V2: game] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ ( none @ game ) @ ( some @ game @ V2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Composeo.cases
% 0.20/0.47 thf(fact_178_Existso_Ocases,axiom,
% 0.20/0.47 ! [X2: product_prod @ variable @ ( option @ fml )] :
% 0.20/0.47 ( ! [X: variable,Phi2: fml] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ variable @ ( option @ fml ) @ X @ ( some @ fml @ Phi2 ) ) )
% 0.20/0.47 => ~ ! [X: variable] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ variable @ ( option @ fml ) @ X @ ( none @ fml ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Existso.cases
% 0.20/0.47 thf(fact_179_Ando_Ocases,axiom,
% 0.20/0.47 ! [X2: product_prod @ ( option @ fml ) @ ( option @ fml )] :
% 0.20/0.47 ( ! [Phi2: fml,Psi: fml] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ ( option @ fml ) @ ( option @ fml ) @ ( some @ fml @ Phi2 ) @ ( some @ fml @ Psi ) ) )
% 0.20/0.47 => ( ! [Psi: option @ fml] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ ( option @ fml ) @ ( option @ fml ) @ ( none @ fml ) @ Psi ) )
% 0.20/0.47 => ~ ! [V2: fml] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ ( option @ fml ) @ ( option @ fml ) @ ( some @ fml @ V2 ) @ ( none @ fml ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Ando.cases
% 0.20/0.47 thf(fact_180_usubstappt_Opsimps_I7_J,axiom,
% 0.20/0.47 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm] :
% 0.20/0.47 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( differential @ Theta ) ) ) )
% 0.20/0.47 => ( ( uSubst95898992stappt @ Sigma @ U @ ( differential @ Theta ) )
% 0.20/0.47 = ( uSubst259074819ntialo
% 0.20/0.47 @ ( uSubst95898992stappt @ Sigma
% 0.20/0.47 @ ( collect @ variable
% 0.20/0.47 @ ^ [X3: variable] : $true )
% 0.20/0.47 @ Theta ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % usubstappt.psimps(7)
% 0.20/0.47 thf(fact_181_usubstappt_Opsimps_I6_J,axiom,
% 0.20/0.47 ! [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] :
% 0.20/0.47 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( times @ Theta @ Eta ) ) ) )
% 0.20/0.47 => ( ( uSubst95898992stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 0.20/0.47 = ( uSubst277968634Timeso @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) @ ( uSubst95898992stappt @ Sigma @ U @ Eta ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % usubstappt.psimps(6)
% 0.20/0.47 thf(fact_182_usubstappt_Opsimps_I5_J,axiom,
% 0.20/0.47 ! [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] :
% 0.20/0.47 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( plus @ Theta @ Eta ) ) ) )
% 0.20/0.47 => ( ( uSubst95898992stappt @ Sigma @ U @ ( plus @ Theta @ Eta ) )
% 0.20/0.47 = ( uSubst1112714340_Pluso @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) @ ( uSubst95898992stappt @ Sigma @ U @ Eta ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % usubstappt.psimps(5)
% 0.20/0.47 thf(fact_183_usubstappt_Opsimps_I1_J,axiom,
% 0.20/0.47 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,X2: variable] :
% 0.20/0.47 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( var @ X2 ) ) ) )
% 0.20/0.47 => ( ( uSubst95898992stappt @ Sigma @ U @ ( var @ X2 ) )
% 0.20/0.47 = ( some @ trm @ ( var @ X2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % usubstappt.psimps(1)
% 0.20/0.47 thf(fact_184_usubstappt_Opsimps_I2_J,axiom,
% 0.20/0.47 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,R3: real] :
% 0.20/0.47 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( number @ R3 ) ) ) )
% 0.20/0.47 => ( ( uSubst95898992stappt @ Sigma @ U @ ( number @ R3 ) )
% 0.20/0.47 = ( some @ trm @ ( number @ R3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % usubstappt.psimps(2)
% 0.20/0.47 thf(fact_185_in__lex__prod,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,A4: A,B4: B,A7: A,B7: B,R3: set @ ( product_prod @ A @ A ),S2: set @ ( product_prod @ B @ B )] :
% 0.20/0.47 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A4 @ B4 ) @ ( product_Pair @ A @ B @ A7 @ B7 ) ) @ ( lex_prod @ A @ B @ R3 @ S2 ) )
% 0.20/0.47 = ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A4 @ A7 ) @ R3 )
% 0.20/0.47 | ( ( A4 = A7 )
% 0.20/0.47 & ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ B4 @ B7 ) @ S2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % in_lex_prod
% 0.20/0.47 thf(fact_186_trm_Oinject_I2_J,axiom,
% 0.20/0.47 ! [X23: real,Y23: real] :
% 0.20/0.47 ( ( ( number @ X23 )
% 0.20/0.47 = ( number @ Y23 ) )
% 0.20/0.47 = ( X23 = Y23 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.inject(2)
% 0.20/0.47 thf(fact_187_trm_Oinject_I1_J,axiom,
% 0.20/0.47 ! [X1: variable,Y1: variable] :
% 0.20/0.47 ( ( ( var @ X1 )
% 0.20/0.47 = ( var @ Y1 ) )
% 0.20/0.47 = ( X1 = Y1 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.inject(1)
% 0.20/0.47 thf(fact_188_trm_Odistinct_I17_J,axiom,
% 0.20/0.47 ! [X23: real,X51: trm,X52: trm] :
% 0.20/0.47 ( ( number @ X23 )
% 0.20/0.47 != ( plus @ X51 @ X52 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(17)
% 0.20/0.47 thf(fact_189_trm_Odistinct_I19_J,axiom,
% 0.20/0.47 ! [X23: real,X61: trm,X62: trm] :
% 0.20/0.47 ( ( number @ X23 )
% 0.20/0.47 != ( times @ X61 @ X62 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(19)
% 0.20/0.47 thf(fact_190_trm_Odistinct_I21_J,axiom,
% 0.20/0.47 ! [X23: real,X7: trm] :
% 0.20/0.47 ( ( number @ X23 )
% 0.20/0.47 != ( differential @ X7 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(21)
% 0.20/0.47 thf(fact_191_trm_Odistinct_I7_J,axiom,
% 0.20/0.47 ! [X1: variable,X51: trm,X52: trm] :
% 0.20/0.47 ( ( var @ X1 )
% 0.20/0.47 != ( plus @ X51 @ X52 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(7)
% 0.20/0.47 thf(fact_192_trm_Odistinct_I9_J,axiom,
% 0.20/0.47 ! [X1: variable,X61: trm,X62: trm] :
% 0.20/0.47 ( ( var @ X1 )
% 0.20/0.47 != ( times @ X61 @ X62 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(9)
% 0.20/0.47 thf(fact_193_trm_Odistinct_I11_J,axiom,
% 0.20/0.47 ! [X1: variable,X7: trm] :
% 0.20/0.47 ( ( var @ X1 )
% 0.20/0.47 != ( differential @ X7 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(11)
% 0.20/0.47 thf(fact_194_trm_Odistinct_I1_J,axiom,
% 0.20/0.47 ! [X1: variable,X23: real] :
% 0.20/0.47 ( ( var @ X1 )
% 0.20/0.47 != ( number @ X23 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(1)
% 0.20/0.47 thf(fact_195_usubstappt_Osimps_I2_J,axiom,
% 0.20/0.47 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,R3: real] :
% 0.20/0.47 ( ( uSubst95898992stappt @ Sigma @ U @ ( number @ R3 ) )
% 0.20/0.47 = ( some @ trm @ ( number @ R3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % usubstappt.simps(2)
% 0.20/0.47 thf(fact_196_usubstappt_Osimps_I1_J,axiom,
% 0.20/0.47 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,X2: variable] :
% 0.20/0.47 ( ( uSubst95898992stappt @ Sigma @ U @ ( var @ X2 ) )
% 0.20/0.47 = ( some @ trm @ ( var @ X2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % usubstappt.simps(1)
% 0.20/0.47 thf(fact_197_usubstappt_Ocases,axiom,
% 0.20/0.47 ! [X2: product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm )] :
% 0.20/0.47 ( ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,X: variable] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( var @ X ) ) ) )
% 0.20/0.47 => ( ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,R5: real] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( number @ R5 ) ) ) )
% 0.20/0.47 => ( ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F3: char] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( const @ F3 ) ) ) )
% 0.20/0.47 => ( ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F3: char,Theta2: trm] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( func @ F3 @ Theta2 ) ) ) )
% 0.20/0.47 => ( ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm,Eta2: trm] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( plus @ Theta2 @ Eta2 ) ) ) )
% 0.20/0.47 => ( ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm,Eta2: trm] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( times @ Theta2 @ Eta2 ) ) ) )
% 0.20/0.47 => ~ ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( differential @ Theta2 ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % usubstappt.cases
% 0.20/0.47 thf(fact_198_Testo_Osimps_I2_J,axiom,
% 0.20/0.47 ( ( uSubst190403692_Testo @ ( none @ fml ) )
% 0.20/0.47 = ( none @ game ) ) ).
% 0.20/0.47
% 0.20/0.47 % Testo.simps(2)
% 0.20/0.47 thf(fact_199_Testo__undef,axiom,
% 0.20/0.47 ! [Phi: option @ fml] :
% 0.20/0.47 ( ( ( uSubst190403692_Testo @ Phi )
% 0.20/0.47 = ( none @ game ) )
% 0.20/0.47 = ( Phi
% 0.20/0.47 = ( none @ fml ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Testo_undef
% 0.20/0.47 thf(fact_200_trm_Oinject_I4_J,axiom,
% 0.20/0.47 ! [X41: char,X42: trm,Y41: char,Y42: trm] :
% 0.20/0.47 ( ( ( func @ X41 @ X42 )
% 0.20/0.47 = ( func @ Y41 @ Y42 ) )
% 0.20/0.47 = ( ( X41 = Y41 )
% 0.20/0.47 & ( X42 = Y42 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.inject(4)
% 0.20/0.47 thf(fact_201_trm_Oinject_I3_J,axiom,
% 0.20/0.47 ! [X32: char,Y32: char] :
% 0.20/0.47 ( ( ( const @ X32 )
% 0.20/0.47 = ( const @ Y32 ) )
% 0.20/0.47 = ( X32 = Y32 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.inject(3)
% 0.20/0.47 thf(fact_202_trm_Odistinct_I3_J,axiom,
% 0.20/0.47 ! [X1: variable,X32: char] :
% 0.20/0.47 ( ( var @ X1 )
% 0.20/0.47 != ( const @ X32 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(3)
% 0.20/0.47 thf(fact_203_trm_Odistinct_I5_J,axiom,
% 0.20/0.47 ! [X1: variable,X41: char,X42: trm] :
% 0.20/0.47 ( ( var @ X1 )
% 0.20/0.47 != ( func @ X41 @ X42 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(5)
% 0.20/0.47 thf(fact_204_trm_Odistinct_I13_J,axiom,
% 0.20/0.47 ! [X23: real,X32: char] :
% 0.20/0.47 ( ( number @ X23 )
% 0.20/0.47 != ( const @ X32 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(13)
% 0.20/0.47 thf(fact_205_trm_Odistinct_I15_J,axiom,
% 0.20/0.47 ! [X23: real,X41: char,X42: trm] :
% 0.20/0.47 ( ( number @ X23 )
% 0.20/0.47 != ( func @ X41 @ X42 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(15)
% 0.20/0.47 thf(fact_206_trm_Odistinct_I23_J,axiom,
% 0.20/0.47 ! [X32: char,X41: char,X42: trm] :
% 0.20/0.47 ( ( const @ X32 )
% 0.20/0.47 != ( func @ X41 @ X42 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(23)
% 0.20/0.47 thf(fact_207_trm_Odistinct_I29_J,axiom,
% 0.20/0.47 ! [X32: char,X7: trm] :
% 0.20/0.47 ( ( const @ X32 )
% 0.20/0.47 != ( differential @ X7 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(29)
% 0.20/0.47 thf(fact_208_trm_Odistinct_I27_J,axiom,
% 0.20/0.47 ! [X32: char,X61: trm,X62: trm] :
% 0.20/0.47 ( ( const @ X32 )
% 0.20/0.47 != ( times @ X61 @ X62 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(27)
% 0.20/0.47 thf(fact_209_trm_Odistinct_I25_J,axiom,
% 0.20/0.47 ! [X32: char,X51: trm,X52: trm] :
% 0.20/0.47 ( ( const @ X32 )
% 0.20/0.47 != ( plus @ X51 @ X52 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(25)
% 0.20/0.47 thf(fact_210_trm_Odistinct_I35_J,axiom,
% 0.20/0.47 ! [X41: char,X42: trm,X7: trm] :
% 0.20/0.47 ( ( func @ X41 @ X42 )
% 0.20/0.47 != ( differential @ X7 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(35)
% 0.20/0.47 thf(fact_211_trm_Odistinct_I33_J,axiom,
% 0.20/0.47 ! [X41: char,X42: trm,X61: trm,X62: trm] :
% 0.20/0.47 ( ( func @ X41 @ X42 )
% 0.20/0.47 != ( times @ X61 @ X62 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(33)
% 0.20/0.47 thf(fact_212_trm_Odistinct_I31_J,axiom,
% 0.20/0.47 ! [X41: char,X42: trm,X51: trm,X52: trm] :
% 0.20/0.47 ( ( func @ X41 @ X42 )
% 0.20/0.47 != ( plus @ X51 @ X52 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(31)
% 0.20/0.47 thf(fact_213_trm_Oinduct,axiom,
% 0.20/0.47 ! [P: trm > $o,Trm: trm] :
% 0.20/0.47 ( ! [X: variable] : ( P @ ( var @ X ) )
% 0.20/0.47 => ( ! [X: real] : ( P @ ( number @ X ) )
% 0.20/0.47 => ( ! [X: char] : ( P @ ( const @ X ) )
% 0.20/0.47 => ( ! [X1a: char,X2a: trm] :
% 0.20/0.47 ( ( P @ X2a )
% 0.20/0.47 => ( P @ ( func @ X1a @ X2a ) ) )
% 0.20/0.47 => ( ! [X1a: trm,X2a: trm] :
% 0.20/0.47 ( ( P @ X1a )
% 0.20/0.47 => ( ( P @ X2a )
% 0.20/0.47 => ( P @ ( plus @ X1a @ X2a ) ) ) )
% 0.20/0.47 => ( ! [X1a: trm,X2a: trm] :
% 0.20/0.47 ( ( P @ X1a )
% 0.20/0.47 => ( ( P @ X2a )
% 0.20/0.47 => ( P @ ( times @ X1a @ X2a ) ) ) )
% 0.20/0.47 => ( ! [X: trm] :
% 0.20/0.47 ( ( P @ X )
% 0.20/0.47 => ( P @ ( differential @ X ) ) )
% 0.20/0.47 => ( P @ Trm ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.induct
% 0.20/0.47 thf(fact_214_trm_Oexhaust,axiom,
% 0.20/0.47 ! [Y2: trm] :
% 0.20/0.47 ( ! [X12: variable] :
% 0.20/0.47 ( Y2
% 0.20/0.47 != ( var @ X12 ) )
% 0.20/0.47 => ( ! [X24: real] :
% 0.20/0.47 ( Y2
% 0.20/0.47 != ( number @ X24 ) )
% 0.20/0.47 => ( ! [X33: char] :
% 0.20/0.47 ( Y2
% 0.20/0.47 != ( const @ X33 ) )
% 0.20/0.47 => ( ! [X412: char,X422: trm] :
% 0.20/0.47 ( Y2
% 0.20/0.47 != ( func @ X412 @ X422 ) )
% 0.20/0.47 => ( ! [X512: trm,X522: trm] :
% 0.20/0.47 ( Y2
% 0.20/0.47 != ( plus @ X512 @ X522 ) )
% 0.20/0.47 => ( ! [X612: trm,X622: trm] :
% 0.20/0.47 ( Y2
% 0.20/0.47 != ( times @ X612 @ X622 ) )
% 0.20/0.47 => ~ ! [X72: trm] :
% 0.20/0.47 ( Y2
% 0.20/0.47 != ( differential @ X72 ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.exhaust
% 0.20/0.47 thf(fact_215_term__sem_Ocases,axiom,
% 0.20/0.47 ! [X2: product_prod @ denotational_interp @ trm] :
% 0.20/0.47 ( ! [I2: denotational_interp,X: variable] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ denotational_interp @ trm @ I2 @ ( var @ X ) ) )
% 0.20/0.47 => ( ! [I2: denotational_interp,R5: real] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ denotational_interp @ trm @ I2 @ ( number @ R5 ) ) )
% 0.20/0.47 => ( ! [I2: denotational_interp,F3: char] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ denotational_interp @ trm @ I2 @ ( const @ F3 ) ) )
% 0.20/0.47 => ( ! [I2: denotational_interp,F3: char,Theta2: trm] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ denotational_interp @ trm @ I2 @ ( func @ F3 @ Theta2 ) ) )
% 0.20/0.47 => ( ! [I2: denotational_interp,Theta2: trm,Eta2: trm] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ denotational_interp @ trm @ I2 @ ( plus @ Theta2 @ Eta2 ) ) )
% 0.20/0.47 => ( ! [I2: denotational_interp,Theta2: trm,Eta2: trm] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ denotational_interp @ trm @ I2 @ ( times @ Theta2 @ Eta2 ) ) )
% 0.20/0.47 => ~ ! [I2: denotational_interp,Theta2: trm] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( product_Pair @ denotational_interp @ trm @ I2 @ ( differential @ Theta2 ) ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % term_sem.cases
% 0.20/0.47 thf(fact_216_usubstappt_Opsimps_I3_J,axiom,
% 0.20/0.47 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F: char] :
% 0.20/0.47 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( const @ F ) ) ) )
% 0.20/0.47 => ( ( uSubst95898992stappt @ Sigma @ U @ ( const @ F ) )
% 0.20/0.47 = ( uSubst1138577137pconst @ Sigma @ U @ F ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % usubstappt.psimps(3)
% 0.20/0.47 thf(fact_217_term__sem_Oinduct,axiom,
% 0.20/0.47 ! [P: denotational_interp > trm > $o,A0: denotational_interp,A1: trm] :
% 0.20/0.47 ( ! [I2: denotational_interp,X: variable] : ( P @ I2 @ ( var @ X ) )
% 0.20/0.47 => ( ! [I2: denotational_interp,R5: real] : ( P @ I2 @ ( number @ R5 ) )
% 0.20/0.47 => ( ! [I2: denotational_interp,F3: char] : ( P @ I2 @ ( const @ F3 ) )
% 0.20/0.47 => ( ! [I2: denotational_interp,F3: char,Theta2: trm] :
% 0.20/0.47 ( ( P @ I2 @ Theta2 )
% 0.20/0.47 => ( P @ I2 @ ( func @ F3 @ Theta2 ) ) )
% 0.20/0.47 => ( ! [I2: denotational_interp,Theta2: trm] :
% 0.20/0.47 ( ( P @ I2 @ Theta2 )
% 0.20/0.47 => ! [Eta2: trm] :
% 0.20/0.47 ( ( P @ I2 @ Eta2 )
% 0.20/0.47 => ( P @ I2 @ ( plus @ Theta2 @ Eta2 ) ) ) )
% 0.20/0.47 => ( ! [I2: denotational_interp,Theta2: trm] :
% 0.20/0.47 ( ( P @ I2 @ Theta2 )
% 0.20/0.47 => ! [Eta2: trm] :
% 0.20/0.47 ( ( P @ I2 @ Eta2 )
% 0.20/0.47 => ( P @ I2 @ ( times @ Theta2 @ Eta2 ) ) ) )
% 0.20/0.47 => ( ! [I2: denotational_interp,Theta2: trm] :
% 0.20/0.47 ( ( ? [Xa2: char] :
% 0.20/0.47 ( member @ char @ Xa2
% 0.20/0.47 @ ( collect @ char
% 0.20/0.47 @ ^ [Uu: char] : $true ) )
% 0.20/0.47 => ( P @ I2 @ Theta2 ) )
% 0.20/0.47 => ( P @ I2 @ ( differential @ Theta2 ) ) )
% 0.20/0.47 => ( P @ A0 @ A1 ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % term_sem.induct
% 0.20/0.47 thf(fact_218_usubstappt_Osimps_I3_J,axiom,
% 0.20/0.47 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F: char] :
% 0.20/0.47 ( ( uSubst95898992stappt @ Sigma @ U @ ( const @ F ) )
% 0.20/0.47 = ( uSubst1138577137pconst @ Sigma @ U @ F ) ) ).
% 0.20/0.47
% 0.20/0.47 % usubstappt.simps(3)
% 0.20/0.47 thf(fact_219_image2__def,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,C: $tType] :
% 0.20/0.47 ( ( bNF_Greatest_image2 @ C @ A @ B )
% 0.20/0.47 = ( ^ [A3: set @ C,F2: C > A,G2: C > B] :
% 0.20/0.47 ( collect @ ( product_prod @ A @ B )
% 0.20/0.47 @ ^ [Uu: product_prod @ A @ B] :
% 0.20/0.47 ? [A5: C] :
% 0.20/0.47 ( ( Uu
% 0.20/0.47 = ( product_Pair @ A @ B @ ( F2 @ A5 ) @ ( G2 @ A5 ) ) )
% 0.20/0.47 & ( member @ C @ A5 @ A3 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % image2_def
% 0.20/0.47 thf(fact_220_Testo_Oelims,axiom,
% 0.20/0.47 ! [X2: option @ fml,Y2: option @ game] :
% 0.20/0.47 ( ( ( uSubst190403692_Testo @ X2 )
% 0.20/0.47 = Y2 )
% 0.20/0.47 => ( ! [Phi2: fml] :
% 0.20/0.47 ( ( X2
% 0.20/0.47 = ( some @ fml @ Phi2 ) )
% 0.20/0.47 => ( Y2
% 0.20/0.47 != ( some @ game @ ( test @ Phi2 ) ) ) )
% 0.20/0.47 => ~ ( ( X2
% 0.20/0.47 = ( none @ fml ) )
% 0.20/0.47 => ( Y2
% 0.20/0.47 != ( none @ game ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Testo.elims
% 0.20/0.47 thf(fact_221_game_Oinject_I3_J,axiom,
% 0.20/0.47 ! [X32: fml,Y32: fml] :
% 0.20/0.47 ( ( ( test @ X32 )
% 0.20/0.47 = ( test @ Y32 ) )
% 0.20/0.47 = ( X32 = Y32 ) ) ).
% 0.20/0.47
% 0.20/0.47 % game.inject(3)
% 0.20/0.47 thf(fact_222_image2__eqI,axiom,
% 0.20/0.47 ! [A: $tType,C: $tType,B: $tType,B4: A,F: B > A,X2: B,C2: C,G: B > C,A2: set @ B] :
% 0.20/0.47 ( ( B4
% 0.20/0.47 = ( F @ X2 ) )
% 0.20/0.47 => ( ( C2
% 0.20/0.47 = ( G @ X2 ) )
% 0.20/0.47 => ( ( member @ B @ X2 @ A2 )
% 0.20/0.47 => ( member @ ( product_prod @ A @ C ) @ ( product_Pair @ A @ C @ B4 @ C2 ) @ ( bNF_Greatest_image2 @ B @ A @ C @ A2 @ F @ G ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % image2_eqI
% 0.20/0.47 thf(fact_223_Testo_Osimps_I1_J,axiom,
% 0.20/0.47 ! [Phi: fml] :
% 0.20/0.47 ( ( uSubst190403692_Testo @ ( some @ fml @ Phi ) )
% 0.20/0.47 = ( some @ game @ ( test @ Phi ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Testo.simps(1)
% 0.20/0.47 thf(fact_224_Testo_Opelims,axiom,
% 0.20/0.47 ! [X2: option @ fml,Y2: option @ game] :
% 0.20/0.47 ( ( ( uSubst190403692_Testo @ X2 )
% 0.20/0.47 = Y2 )
% 0.20/0.47 => ( ( accp @ ( option @ fml ) @ uSubst533687181to_rel @ X2 )
% 0.20/0.47 => ( ! [Phi2: fml] :
% 0.20/0.47 ( ( X2
% 0.20/0.47 = ( some @ fml @ Phi2 ) )
% 0.20/0.47 => ( ( Y2
% 0.20/0.47 = ( some @ game @ ( test @ Phi2 ) ) )
% 0.20/0.47 => ~ ( accp @ ( option @ fml ) @ uSubst533687181to_rel @ ( some @ fml @ Phi2 ) ) ) )
% 0.20/0.47 => ~ ( ( X2
% 0.20/0.47 = ( none @ fml ) )
% 0.20/0.47 => ( ( Y2
% 0.20/0.47 = ( none @ game ) )
% 0.20/0.47 => ~ ( accp @ ( option @ fml ) @ uSubst533687181to_rel @ ( none @ fml ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Testo.pelims
% 0.20/0.47 thf(fact_225_relImage__def,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType] :
% 0.20/0.47 ( ( bNF_Gr1317331620lImage @ B @ A )
% 0.20/0.47 = ( ^ [R6: set @ ( product_prod @ B @ B ),F2: B > A] :
% 0.20/0.47 ( collect @ ( product_prod @ A @ A )
% 0.20/0.47 @ ^ [Uu: product_prod @ A @ A] :
% 0.20/0.47 ? [A12: B,A22: B] :
% 0.20/0.47 ( ( Uu
% 0.20/0.47 = ( product_Pair @ A @ A @ ( F2 @ A12 ) @ ( F2 @ A22 ) ) )
% 0.20/0.47 & ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ A12 @ A22 ) @ R6 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % relImage_def
% 0.20/0.47 thf(fact_226_relImage__mono,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,R1: set @ ( product_prod @ A @ A ),R2: set @ ( product_prod @ A @ A ),F: A > B] :
% 0.20/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ R1 @ R2 )
% 0.20/0.47 => ( ord_less_eq @ ( set @ ( product_prod @ B @ B ) ) @ ( bNF_Gr1317331620lImage @ A @ B @ R1 @ F ) @ ( bNF_Gr1317331620lImage @ A @ B @ R2 @ F ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % relImage_mono
% 0.20/0.47 thf(fact_227_relInvImage__def,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType] :
% 0.20/0.47 ( ( bNF_Gr2107612801vImage @ A @ B )
% 0.20/0.47 = ( ^ [A3: set @ A,R6: set @ ( product_prod @ B @ B ),F2: A > B] :
% 0.20/0.47 ( collect @ ( product_prod @ A @ A )
% 0.20/0.47 @ ^ [Uu: product_prod @ A @ A] :
% 0.20/0.47 ? [A12: A,A22: A] :
% 0.20/0.47 ( ( Uu
% 0.20/0.47 = ( product_Pair @ A @ A @ A12 @ A22 ) )
% 0.20/0.47 & ( member @ A @ A12 @ A3 )
% 0.20/0.47 & ( member @ A @ A22 @ A3 )
% 0.20/0.47 & ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ ( F2 @ A12 ) @ ( F2 @ A22 ) ) @ R6 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % relInvImage_def
% 0.20/0.47 thf(fact_228_Assigno__undef,axiom,
% 0.20/0.47 ! [X2: variable,Theta: option @ trm] :
% 0.20/0.47 ( ( ( uSubst1326326671ssigno @ X2 @ Theta )
% 0.20/0.47 = ( none @ game ) )
% 0.20/0.47 = ( Theta
% 0.20/0.47 = ( none @ trm ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Assigno_undef
% 0.20/0.47 thf(fact_229_relInvImage__mono,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,R1: set @ ( product_prod @ A @ A ),R2: set @ ( product_prod @ A @ A ),A2: set @ B,F: B > A] :
% 0.20/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ R1 @ R2 )
% 0.20/0.47 => ( ord_less_eq @ ( set @ ( product_prod @ B @ B ) ) @ ( bNF_Gr2107612801vImage @ B @ A @ A2 @ R1 @ F ) @ ( bNF_Gr2107612801vImage @ B @ A @ A2 @ R2 @ F ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % relInvImage_mono
% 0.20/0.47 thf(fact_230_Assigno_Osimps_I2_J,axiom,
% 0.20/0.47 ! [X2: variable] :
% 0.20/0.47 ( ( uSubst1326326671ssigno @ X2 @ ( none @ trm ) )
% 0.20/0.47 = ( none @ game ) ) ).
% 0.20/0.47
% 0.20/0.47 % Assigno.simps(2)
% 0.20/0.47 thf(fact_231_Assigno_Oelims,axiom,
% 0.20/0.47 ! [X2: variable,Xa: option @ trm,Y2: option @ game] :
% 0.20/0.47 ( ( ( uSubst1326326671ssigno @ X2 @ Xa )
% 0.20/0.47 = Y2 )
% 0.20/0.47 => ( ! [Theta2: trm] :
% 0.20/0.47 ( ( Xa
% 0.20/0.47 = ( some @ trm @ Theta2 ) )
% 0.20/0.47 => ( Y2
% 0.20/0.47 != ( some @ game @ ( assign @ X2 @ Theta2 ) ) ) )
% 0.20/0.47 => ~ ( ( Xa
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ( Y2
% 0.20/0.47 != ( none @ game ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Assigno.elims
% 0.20/0.47 thf(fact_232_Assigno_Opelims,axiom,
% 0.20/0.47 ! [X2: variable,Xa: option @ trm,Y2: option @ game] :
% 0.20/0.47 ( ( ( uSubst1326326671ssigno @ X2 @ Xa )
% 0.20/0.47 = Y2 )
% 0.20/0.47 => ( ( accp @ ( product_prod @ variable @ ( option @ trm ) ) @ uSubst1741596714no_rel @ ( product_Pair @ variable @ ( option @ trm ) @ X2 @ Xa ) )
% 0.20/0.47 => ( ! [Theta2: trm] :
% 0.20/0.47 ( ( Xa
% 0.20/0.47 = ( some @ trm @ Theta2 ) )
% 0.20/0.47 => ( ( Y2
% 0.20/0.47 = ( some @ game @ ( assign @ X2 @ Theta2 ) ) )
% 0.20/0.47 => ~ ( accp @ ( product_prod @ variable @ ( option @ trm ) ) @ uSubst1741596714no_rel @ ( product_Pair @ variable @ ( option @ trm ) @ X2 @ ( some @ trm @ Theta2 ) ) ) ) )
% 0.20/0.47 => ~ ( ( Xa
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ( ( Y2
% 0.20/0.47 = ( none @ game ) )
% 0.20/0.47 => ~ ( accp @ ( product_prod @ variable @ ( option @ trm ) ) @ uSubst1741596714no_rel @ ( product_Pair @ variable @ ( option @ trm ) @ X2 @ ( none @ trm ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Assigno.pelims
% 0.20/0.47 thf(fact_233_game_Oinject_I2_J,axiom,
% 0.20/0.47 ! [X21: variable,X22: trm,Y21: variable,Y22: trm] :
% 0.20/0.47 ( ( ( assign @ X21 @ X22 )
% 0.20/0.47 = ( assign @ Y21 @ Y22 ) )
% 0.20/0.47 = ( ( X21 = Y21 )
% 0.20/0.47 & ( X22 = Y22 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % game.inject(2)
% 0.20/0.47 thf(fact_234_game_Odistinct_I15_J,axiom,
% 0.20/0.47 ! [X21: variable,X22: trm,X32: fml] :
% 0.20/0.47 ( ( assign @ X21 @ X22 )
% 0.20/0.47 != ( test @ X32 ) ) ).
% 0.20/0.47
% 0.20/0.47 % game.distinct(15)
% 0.20/0.47 thf(fact_235_Assigno_Osimps_I1_J,axiom,
% 0.20/0.47 ! [X2: variable,Theta: trm] :
% 0.20/0.47 ( ( uSubst1326326671ssigno @ X2 @ ( some @ trm @ Theta ) )
% 0.20/0.47 = ( some @ game @ ( assign @ X2 @ Theta ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Assigno.simps(1)
% 0.20/0.47 thf(fact_236_relInvImage__UNIV__relImage,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ A ),F: A > B] : ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ R @ ( bNF_Gr2107612801vImage @ A @ B @ ( top_top @ ( set @ A ) ) @ ( bNF_Gr1317331620lImage @ A @ B @ R @ F ) @ F ) ) ).
% 0.20/0.47
% 0.20/0.47 % relInvImage_UNIV_relImage
% 0.20/0.47 thf(fact_237_ODEo__undef,axiom,
% 0.20/0.47 ! [X2: char,Theta: option @ trm] :
% 0.20/0.47 ( ( ( uSubst1083227664e_ODEo @ X2 @ Theta )
% 0.20/0.47 = ( none @ game ) )
% 0.20/0.47 = ( Theta
% 0.20/0.47 = ( none @ trm ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ODEo_undef
% 0.20/0.47 thf(fact_238_top__apply,axiom,
% 0.20/0.47 ! [C: $tType,D2: $tType] :
% 0.20/0.47 ( ( top @ C )
% 0.20/0.47 => ( ( top_top @ ( D2 > C ) )
% 0.20/0.47 = ( ^ [X3: D2] : ( top_top @ C ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % top_apply
% 0.20/0.47 thf(fact_239_UNIV__I,axiom,
% 0.20/0.47 ! [A: $tType,X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_I
% 0.20/0.47 thf(fact_240_subset__UNIV,axiom,
% 0.20/0.47 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subset_UNIV
% 0.20/0.47 thf(fact_241_top__greatest,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( order_top @ A )
% 0.20/0.47 => ! [A4: A] : ( ord_less_eq @ A @ A4 @ ( top_top @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % top_greatest
% 0.20/0.47 thf(fact_242_top_Oextremum__unique,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( order_top @ A )
% 0.20/0.47 => ! [A4: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A4 )
% 0.20/0.47 = ( A4
% 0.20/0.47 = ( top_top @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % top.extremum_unique
% 0.20/0.47 thf(fact_243_top_Oextremum__uniqueI,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( order_top @ A )
% 0.20/0.47 => ! [A4: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A4 )
% 0.20/0.47 => ( A4
% 0.20/0.47 = ( top_top @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % top.extremum_uniqueI
% 0.20/0.47 thf(fact_244_UNIV__def,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( top_top @ ( set @ A ) )
% 0.20/0.47 = ( collect @ A
% 0.20/0.47 @ ^ [X3: A] : $true ) ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_def
% 0.20/0.47 thf(fact_245_UNIV__eq__I,axiom,
% 0.20/0.47 ! [A: $tType,A2: set @ A] :
% 0.20/0.47 ( ! [X: A] : ( member @ A @ X @ A2 )
% 0.20/0.47 => ( ( top_top @ ( set @ A ) )
% 0.20/0.47 = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_eq_I
% 0.20/0.47 thf(fact_246_UNIV__witness,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ? [X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_witness
% 0.20/0.47 thf(fact_247_ODEo_Osimps_I2_J,axiom,
% 0.20/0.47 ! [X2: char] :
% 0.20/0.47 ( ( uSubst1083227664e_ODEo @ X2 @ ( none @ trm ) )
% 0.20/0.47 = ( none @ game ) ) ).
% 0.20/0.47
% 0.20/0.47 % ODEo.simps(2)
% 0.20/0.47 thf(fact_248_ODEo_Oelims,axiom,
% 0.20/0.47 ! [X2: char,Xa: option @ trm,Y2: option @ game] :
% 0.20/0.47 ( ( ( uSubst1083227664e_ODEo @ X2 @ Xa )
% 0.20/0.47 = Y2 )
% 0.20/0.47 => ( ! [Theta2: trm] :
% 0.20/0.47 ( ( Xa
% 0.20/0.47 = ( some @ trm @ Theta2 ) )
% 0.20/0.47 => ( Y2
% 0.20/0.47 != ( some @ game @ ( ode @ X2 @ Theta2 ) ) ) )
% 0.20/0.47 => ~ ( ( Xa
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ( Y2
% 0.20/0.47 != ( none @ game ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ODEo.elims
% 0.20/0.47 thf(fact_249_ODEo_Opelims,axiom,
% 0.20/0.47 ! [X2: char,Xa: option @ trm,Y2: option @ game] :
% 0.20/0.47 ( ( ( uSubst1083227664e_ODEo @ X2 @ Xa )
% 0.20/0.47 = Y2 )
% 0.20/0.47 => ( ( accp @ ( product_prod @ char @ ( option @ trm ) ) @ uSubst2007600873Eo_rel @ ( product_Pair @ char @ ( option @ trm ) @ X2 @ Xa ) )
% 0.20/0.47 => ( ! [Theta2: trm] :
% 0.20/0.47 ( ( Xa
% 0.20/0.47 = ( some @ trm @ Theta2 ) )
% 0.20/0.47 => ( ( Y2
% 0.20/0.47 = ( some @ game @ ( ode @ X2 @ Theta2 ) ) )
% 0.20/0.47 => ~ ( accp @ ( product_prod @ char @ ( option @ trm ) ) @ uSubst2007600873Eo_rel @ ( product_Pair @ char @ ( option @ trm ) @ X2 @ ( some @ trm @ Theta2 ) ) ) ) )
% 0.20/0.47 => ~ ( ( Xa
% 0.20/0.47 = ( none @ trm ) )
% 0.20/0.47 => ( ( Y2
% 0.20/0.47 = ( none @ game ) )
% 0.20/0.47 => ~ ( accp @ ( product_prod @ char @ ( option @ trm ) ) @ uSubst2007600873Eo_rel @ ( product_Pair @ char @ ( option @ trm ) @ X2 @ ( none @ trm ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ODEo.pelims
% 0.20/0.47 thf(fact_250_game_Oinject_I8_J,axiom,
% 0.20/0.47 ! [X81: char,X82: trm,Y81: char,Y82: trm] :
% 0.20/0.47 ( ( ( ode @ X81 @ X82 )
% 0.20/0.47 = ( ode @ Y81 @ Y82 ) )
% 0.20/0.47 = ( ( X81 = Y81 )
% 0.20/0.47 & ( X82 = Y82 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % game.inject(8)
% 0.20/0.47 thf(fact_251_top__empty__eq2,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType] :
% 0.20/0.47 ( ( top_top @ ( A > B > $o ) )
% 0.20/0.47 = ( ^ [X3: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % top_empty_eq2
% 0.20/0.47 thf(fact_252_top__empty__eq,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( top_top @ ( A > $o ) )
% 0.20/0.47 = ( ^ [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % top_empty_eq
% 0.20/0.47 thf(fact_253_top__set__def,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( top_top @ ( set @ A ) )
% 0.20/0.47 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % top_set_def
% 0.20/0.47 thf(fact_254_game_Odistinct_I35_J,axiom,
% 0.20/0.47 ! [X32: fml,X81: char,X82: trm] :
% 0.20/0.47 ( ( test @ X32 )
% 0.20/0.47 != ( ode @ X81 @ X82 ) ) ).
% 0.20/0.47
% 0.20/0.47 % game.distinct(35)
% 0.20/0.47
% 0.20/0.47 % Type constructors (20)
% 0.20/0.47 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 0.20/0.47 ! [A8: $tType,A9: $tType] :
% 0.20/0.47 ( ( order_top @ A9 )
% 0.20/0.47 => ( order_top @ ( A8 > A9 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.20/0.47 ! [A8: $tType,A9: $tType] :
% 0.20/0.47 ( ( preorder @ A9 )
% 0.20/0.47 => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.20/0.47 ! [A8: $tType,A9: $tType] :
% 0.20/0.47 ( ( order @ A9 )
% 0.20/0.47 => ( order @ ( A8 > A9 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_fun___Orderings_Otop,axiom,
% 0.20/0.47 ! [A8: $tType,A9: $tType] :
% 0.20/0.47 ( ( top @ A9 )
% 0.20/0.47 => ( top @ ( A8 > A9 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.20/0.47 ! [A8: $tType,A9: $tType] :
% 0.20/0.47 ( ( ord @ A9 )
% 0.20/0.47 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Set_Oset___Orderings_Oorder__top_1,axiom,
% 0.20/0.47 ! [A8: $tType] : ( order_top @ ( set @ A8 ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Set_Oset___Orderings_Opreorder_2,axiom,
% 0.20/0.47 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Set_Oset___Orderings_Oorder_3,axiom,
% 0.20/0.47 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Set_Oset___Orderings_Otop_4,axiom,
% 0.20/0.47 ! [A8: $tType] : ( top @ ( set @ A8 ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Set_Oset___Orderings_Oord_5,axiom,
% 0.20/0.47 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_HOL_Obool___Orderings_Oorder__top_6,axiom,
% 0.20/0.47 order_top @ $o ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_HOL_Obool___Orderings_Opreorder_7,axiom,
% 0.20/0.47 preorder @ $o ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.20/0.47 linorder @ $o ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_8,axiom,
% 0.20/0.47 order @ $o ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_HOL_Obool___Orderings_Otop_9,axiom,
% 0.20/0.47 top @ $o ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_HOL_Obool___Orderings_Oord_10,axiom,
% 0.20/0.47 ord @ $o ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Real_Oreal___Orderings_Opreorder_11,axiom,
% 0.20/0.47 preorder @ real ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Real_Oreal___Orderings_Olinorder_12,axiom,
% 0.31/0.47 linorder @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Orderings_Oorder_13,axiom,
% 0.31/0.47 order @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Orderings_Oord_14,axiom,
% 0.31/0.47 ord @ real ).
% 0.31/0.47
% 0.31/0.47 % Helper facts (3)
% 0.31/0.47 thf(help_If_3_1_T,axiom,
% 0.31/0.47 ! [P: $o] :
% 0.31/0.47 ( ( P = $true )
% 0.31/0.47 | ( P = $false ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(help_If_2_1_T,axiom,
% 0.31/0.47 ! [A: $tType,X2: A,Y2: A] :
% 0.31/0.47 ( ( if @ A @ $false @ X2 @ Y2 )
% 0.31/0.47 = Y2 ) ).
% 0.31/0.47
% 0.31/0.47 thf(help_If_1_1_T,axiom,
% 0.31/0.47 ! [A: $tType,X2: A,Y2: A] :
% 0.31/0.47 ( ( if @ A @ $true @ X2 @ Y2 )
% 0.31/0.47 = X2 ) ).
% 0.31/0.47
% 0.31/0.47 % Conjectures (1)
% 0.31/0.47 thf(conj_0,conjecture,
% 0.31/0.47 ( ( uSubst95898992stappt @ sigma @ ua @ theta )
% 0.31/0.47 != ( none @ trm ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 0.31/1.81 ---- Embedded in THF ---
% 0.31/1.81 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.81 %%% Generated on Tue Feb 24 08:29:49 EST 2026
% 0.31/1.81 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.81 %%% Logic specification used:
% 0.31/1.81 %%% thf(spec, logic, $$dhol).
% 0.31/1.81
% 0.31/1.81 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.LNgQuHokvE/DTF2DTF23487.p
% 0.31/1.81 thf(ty_t_Denotational__Semantics_Ointerp, type, denotational_interp: $tType).
% 0.31/1.81 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 0.31/1.81 thf(ty_t_Syntax_Ovariable, type, variable: $tType).
% 0.31/1.81 thf(ty_t_Option_Ooption, type, option: ($tType > $tType)).
% 0.31/1.81 thf(ty_t_Syntax_Ogame, type, game: $tType).
% 0.31/1.81 thf(ty_t_String_Ochar, type, char: $tType).
% 0.31/1.81 thf(ty_t_Syntax_Otrm, type, trm: $tType).
% 0.31/1.81 thf(ty_t_Syntax_Ofml, type, fml: $tType).
% 0.31/1.81 thf(ty_t_Real_Oreal, type, real: $tType).
% 0.31/1.81 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 0.31/1.81 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 0.31/1.81 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 0.31/1.81 thf(sy_cl_Orderings_Otop, type, top: (!> [A:$tType]: ($o))).
% 0.31/1.81 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 0.31/1.81 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 0.31/1.81 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 0.31/1.81 thf(sy_cl_Orderings_Oorder__top, type, order_top: (!> [A:$tType]: ($o))).
% 0.31/1.81 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2, type, bNF_Greatest_image2: (!> [C:$tType,A:$tType,B:$tType]: (((set @ C) > ((C > A) > ((C > B) > (set @ ((product_prod @ A) @ B)))))))).
% 0.31/1.81 thf(sy_c_BNF__Greatest__Fixpoint_OrelImage, type, bNF_Gr1317331620lImage: (!> [B:$tType,A:$tType]: (((set @ ((product_prod @ B) @ B)) > ((B > A) > (set @ ((product_prod @ A) @ A))))))).
% 0.31/1.81 thf(sy_c_BNF__Greatest__Fixpoint_OrelInvImage, type, bNF_Gr2107612801vImage: (!> [A:$tType,B:$tType]: (((set @ A) > ((set @ ((product_prod @ B) @ B)) > ((A > B) > (set @ ((product_prod @ A) @ A)))))))).
% 0.31/1.81 thf(sy_c_Denotational__Semantics_OUvariation, type, denota1419872369iation: ((variable > real) > ((variable > real) > ((set @ variable) > $o)))).
% 0.31/1.81 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 0.31/1.81 thf(sy_c_Option_Ooption_ONone, type, none: (!> [A:$tType]: ((option @ A)))).
% 0.31/1.81 thf(sy_c_Option_Ooption_OSome, type, some: (!> [A:$tType]: ((A > (option @ A))))).
% 0.31/1.81 thf(sy_c_Option_Ooption_Ocase__option, type, case_option: (!> [B:$tType,A:$tType]: ((B > ((A > B) > ((option @ A) > B)))))).
% 0.31/1.81 thf(sy_c_Option_Ooption_Othe, type, the: (!> [A:$tType]: (((option @ A) > A)))).
% 0.31/1.81 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 0.31/1.81 thf(sy_c_Orderings_Oorder__class_OGreatest, type, order_Greatest: (!> [A:$tType]: (((A > $o) > A)))).
% 0.31/1.81 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 0.31/1.81 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 0.31/1.81 thf(sy_c_Relation_OPowp, type, powp: (!> [A:$tType]: (((A > $o) > ((set @ A) > $o))))).
% 0.31/1.81 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 0.31/1.81 thf(sy_c_Syntax_Ofml_OGeq, type, geq: (trm > (trm > fml))).
% 0.31/1.81 thf(sy_c_Syntax_Ogame_OAssign, type, assign: (variable > (trm > game))).
% 0.31/1.81 thf(sy_c_Syntax_Ogame_OODE, type, ode: (char > (trm > game))).
% 0.31/1.81 thf(sy_c_Syntax_Ogame_OTest, type, test: (fml > game)).
% 0.31/1.81 thf(sy_c_Syntax_Otrm_OConst, type, const: (char > trm)).
% 0.31/1.81 thf(sy_c_Syntax_Otrm_ODifferential, type, differential: (trm > trm)).
% 0.31/1.81 thf(sy_c_Syntax_Otrm_OFunc, type, func: (char > (trm > trm))).
% 0.31/1.81 thf(sy_c_Syntax_Otrm_ONumber, type, number: (real > trm)).
% 0.31/1.81 thf(sy_c_Syntax_Otrm_OPlus, type, plus: (trm > (trm > trm))).
% 0.31/1.81 thf(sy_c_Syntax_Otrm_OTimes, type, times: (trm > (trm > trm))).
% 0.31/1.81 thf(sy_c_Syntax_Otrm_OVar, type, var: (variable > trm)).
% 0.31/1.81 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OAssigno, type, uSubst1326326671ssigno: (variable > ((option @ trm) > (option @ game)))).
% 0.31/1.81 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OAssigno__rel, type, uSubst1741596714no_rel: (((product_prod @ variable) @ (option @ trm)) > (((product_prod @ variable) @ (option @ trm)) > $o))).
% 0.31/1.81 thf(sy_c_USubst__Mirabelle__nnnzepxswx_ODifferentialo, type, uSubst259074819ntialo: ((option @ trm) > (option @ trm))).
% 0.31/1.81 thf(sy_c_USubst__Mirabelle__nnnzepxswx_ODifferentialo__rel, type, uSubst99643830lo_rel: ((option @ trm) > ((option @ trm) > $o))).
% 0.31/1.81 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OGeqo, type, uSubst1556497037e_Geqo: ((option @ trm) > ((option @ trm) > (option @ fml)))).
% 0.31/1.81 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OGeqo__rel, type, uSubst864323244qo_rel: (((product_prod @ (option @ trm)) @ (option @ trm)) > (((product_prod @ (option @ trm)) @ (option @ trm)) > $o))).
% 0.31/1.81 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OODEo, type, uSubst1083227664e_ODEo: (char > ((option @ trm) > (option @ game)))).
% 0.31/1.81 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OODEo__rel, type, uSubst2007600873Eo_rel: (((product_prod @ char) @ (option @ trm)) > (((product_prod @ char) @ (option @ trm)) > $o))).
% 0.31/1.81 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OPluso, type, uSubst1112714340_Pluso: ((option @ trm) > ((option @ trm) > (option @ trm)))).
% 0.31/1.81 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OPluso__rel, type, uSubst270600597so_rel: (((product_prod @ (option @ trm)) @ (option @ trm)) > (((product_prod @ (option @ trm)) @ (option @ trm)) > $o))).
% 0.31/1.81 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTesto, type, uSubst190403692_Testo: ((option @ fml) > (option @ game))).
% 0.31/1.81 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTesto__rel, type, uSubst533687181to_rel: ((option @ fml) > ((option @ fml) > $o))).
% 0.31/1.81 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTimeso, type, uSubst277968634Timeso: ((option @ trm) > ((option @ trm) > (option @ trm)))).
% 0.31/1.81 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTimeso__rel, type, uSubst1377811071so_rel: (((product_prod @ (option @ trm)) @ (option @ trm)) > (((product_prod @ (option @ trm)) @ (option @ trm)) > $o))).
% 0.31/1.81 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousappconst, type, uSubst1138577137pconst: (((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) > ((set @ variable) > (char > (option @ trm))))).
% 0.31/1.81 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappf, type, uSubst95898978stappf: (((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) > ((set @ variable) > (fml > (option @ fml))))).
% 0.31/1.81 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))))).
% 0.31/1.81 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappt__rel, type, uSubst2096773001pt_rel: (((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) > (((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) > $o))).
% 0.31/1.81 thf(sy_c_Wellfounded_Oaccp, type, accp: (!> [A:$tType]: (((A > (A > $o)) > (A > $o))))).
% 0.31/1.81 thf(sy_c_Wellfounded_Olex__prod, type, lex_prod: (!> [A:$tType,B:$tType]: (((set @ ((product_prod @ A) @ A)) > ((set @ ((product_prod @ B) @ B)) > (set @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)))))))).
% 0.31/1.81 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 0.31/1.81 thf(sy_v_U, type, u: (set @ variable)).
% 0.31/1.81 thf(sy_v_Ua____, type, ua: (set @ variable)).
% 0.31/1.81 thf(sy_v__092_060eta_062____, type, eta: trm).
% 0.31/1.81 thf(sy_v__092_060nu_062, type, nu: (variable > real)).
% 0.31/1.81 thf(sy_v__092_060nu_062_H____, type, nu2: (variable > real)).
% 0.31/1.81 thf(sy_v__092_060omega_062, type, omega: (variable > real)).
% 0.31/1.81 thf(sy_v__092_060omega_062_H____, type, omega2: (variable > real)).
% 0.31/1.81 thf(sy_v__092_060sigma_062_H_H____, type, sigma: ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))).
% 0.31/1.81 thf(sy_v__092_060theta_062____, type, theta: trm).
% 0.31/1.81 thf(fact_0_vaouter, axiom, (((denota1419872369iation @ nu) @ omega) @ u)).
% 0.31/1.81 thf(fact_1_usubstappf__geq__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]: ((((((uSubst95898978stappf @ Sigma) @ U) @ ((geq @ Theta) @ Eta)) != (none @ fml)) => (((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (none @ trm)) & ((((uSubst95898992stappt @ Sigma) @ U) @ Eta) != (none @ trm))))))).
% 0.31/1.81 thf(fact_2_Geq_Oprems_I1_J, axiom, ((((uSubst95898978stappf @ sigma) @ ua) @ ((geq @ theta) @ eta)) != (none @ fml))).
% 0.31/1.81 thf(fact_3_undeft__None, axiom, ((none @ trm) = (none @ trm))).
% 0.31/1.81 thf(fact_4_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))))))).
% 0.31/1.81 thf(fact_5_Geq_Oprems_I2_J, axiom, (((denota1419872369iation @ nu2) @ omega2) @ ua)).
% 0.31/1.81 thf(fact_6_usubstappt__plus__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) @ ((plus @ Theta) @ Eta)) != (none @ trm)) => (((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (none @ trm)) & ((((uSubst95898992stappt @ Sigma) @ U) @ Eta) != (none @ trm))))))).
% 0.31/1.81 thf(fact_7_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))))))).
% 0.31/1.81 thf(fact_8_usubstappt__antimon, axiom, (! [V:(set @ variable),U:(set @ variable),Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),Theta:trm]: (((((ord_less_eq @ (set @ variable)) @ V) @ U) => (((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (none @ trm)) => ((((uSubst95898992stappt @ Sigma) @ U) @ Theta) = (((uSubst95898992stappt @ Sigma) @ V) @ Theta))))))).
% 0.31/1.81 thf(fact_9_Differentialo_Osimps_I2_J, axiom, ((uSubst259074819ntialo @ (none @ trm)) = (none @ trm))).
% 0.31/1.81 thf(fact_10_Differentialo__undef, axiom, (! [Theta:(option @ trm)]: ((((uSubst259074819ntialo @ Theta) = (none @ trm)) = (Theta = (none @ trm)))))).
% 0.31/1.81 thf(fact_11_Pluso_Osimps_I2_J, axiom, (! [Eta:(option @ trm)]: ((((uSubst1112714340_Pluso @ (none @ trm)) @ Eta) = (none @ trm))))).
% 0.31/1.81 thf(fact_12_Timeso_Osimps_I2_J, axiom, (! [Eta:(option @ trm)]: ((((uSubst277968634Timeso @ (none @ trm)) @ Eta) = (none @ trm))))).
% 0.31/1.81 thf(fact_13_Pluso__undef, axiom, (! [Theta:(option @ trm),Eta:(option @ trm)]: (((((uSubst1112714340_Pluso @ Theta) @ Eta) = (none @ trm)) = ((Theta = (none @ trm)) | (Eta = (none @ trm))))))).
% 0.31/1.81 thf(fact_14_Timeso__undef, axiom, (! [Theta:(option @ trm),Eta:(option @ trm)]: (((((uSubst277968634Timeso @ Theta) @ Eta) = (none @ trm)) = ((Theta = (none @ trm)) | (Eta = (none @ trm))))))).
% 0.31/1.81 thf(fact_15_Geqo_Osimps_I2_J, axiom, (! [Eta:(option @ trm)]: ((((uSubst1556497037e_Geqo @ (none @ trm)) @ Eta) = (none @ fml))))).
% 0.31/1.81 thf(fact_16_usubstappf__antimon, axiom, (! [V:(set @ variable),U:(set @ variable),Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),Phi:fml]: (((((ord_less_eq @ (set @ variable)) @ V) @ U) => (((((uSubst95898978stappf @ Sigma) @ U) @ Phi) != (none @ fml)) => ((((uSubst95898978stappf @ Sigma) @ U) @ Phi) = (((uSubst95898978stappf @ Sigma) @ V) @ Phi))))))).
% 0.31/1.81 thf(fact_17_usubstappf__det, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Phi:fml,V:(set @ variable)]: ((((((uSubst95898978stappf @ Sigma) @ U) @ Phi) != (none @ fml)) => (((((uSubst95898978stappf @ Sigma) @ V) @ Phi) != (none @ fml)) => ((((uSubst95898978stappf @ Sigma) @ U) @ Phi) = (((uSubst95898978stappf @ Sigma) @ V) @ Phi))))))).
% 0.31/1.81 thf(fact_18_usubstappt_Osimps_I5_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) @ ((plus @ Theta) @ Eta)) = ((uSubst1112714340_Pluso @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta)) @ (((uSubst95898992stappt @ Sigma) @ U) @ Eta)))))).
% 0.31/1.81 thf(fact_19_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)))))).
% 0.31/1.81 thf(fact_20_usubstappf_Osimps_I2_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]: (((((uSubst95898978stappf @ Sigma) @ U) @ ((geq @ Theta) @ Eta)) = ((uSubst1556497037e_Geqo @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta)) @ (((uSubst95898992stappt @ Sigma) @ U) @ Eta)))))).
% 0.31/1.81 thf(fact_21_Geqo__undef, axiom, (! [Theta:(option @ trm),Eta:(option @ trm)]: (((((uSubst1556497037e_Geqo @ Theta) @ Eta) = (none @ fml)) = ((Theta = (none @ trm)) | (Eta = (none @ trm))))))).
% 0.31/1.81 thf(fact_22_trm_Oinject_I6_J, axiom, (! [X61:trm,X62:trm,Y61:trm,Y62:trm]: (((((times @ X61) @ X62) = ((times @ Y61) @ Y62)) = ((X61 = Y61) & (X62 = Y62)))))).
% 0.31/1.81 thf(fact_23_trm_Oinject_I5_J, axiom, (! [X51:trm,X52:trm,Y51:trm,Y52:trm]: (((((plus @ X51) @ X52) = ((plus @ Y51) @ Y52)) = ((X51 = Y51) & (X52 = Y52)))))).
% 0.31/1.81 thf(fact_24_fml_Oinject_I2_J, axiom, (! [X21:trm,X22:trm,Y21:trm,Y22:trm]: (((((geq @ X21) @ X22) = ((geq @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 0.31/1.81 thf(fact_25_Uvariation__mon, axiom, (! [U:(set @ variable),V:(set @ variable),Omega:(variable > real),Nu:(variable > real)]: (((((ord_less_eq @ (set @ variable)) @ U) @ V) => ((((denota1419872369iation @ Omega) @ Nu) @ U) => (((denota1419872369iation @ Omega) @ Nu) @ V)))))).
% 0.31/1.81 thf(fact_26_subsetI, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((! [X:A]: (((((member @ A) @ X) @ A2) => (((member @ A) @ X) @ B2)))) => (((ord_less_eq @ (set @ A)) @ A2) @ B2))))).
% 0.31/1.81 thf(fact_27_subset__antisym, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((ord_less_eq @ (set @ A)) @ B2) @ A2) => (A2 = B2)))))).
% 0.31/1.81 thf(fact_28_trm_Odistinct_I37_J, axiom, (! [X51:trm,X52:trm,X61:trm,X62:trm]: ((((plus @ X51) @ X52) != ((times @ X61) @ X62))))).
% 0.31/1.81 thf(fact_29_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A]: ((((ord_less_eq @ A) @ X2) @ X2))))))).
% 0.31/1.81 thf(fact_30_Uvariation__univ, axiom, (! [Nu:(variable > real),Nu2:(variable > real)]: ((((denota1419872369iation @ Nu) @ Nu2) @ ((collect @ variable) @ (^ [X3:variable]: ($true))))))).
% 0.31/1.81 thf(fact_31_Collect__subset, axiom, (! [A:$tType,A2:(set @ A),P:(A > $o)]: ((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X3:A]: (((((member @ A) @ X3) @ A2) & (P @ X3)))))) @ A2)))).
% 0.31/1.81 thf(fact_32_less__eq__set__def, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A3:(set @ A),B3:(set @ A)]: ((((ord_less_eq @ (A > $o)) @ (^ [X3:A]: ((((member @ A) @ X3) @ A3)))) @ (^ [X3:A]: ((((member @ A) @ X3) @ B3)))))))))).
% 0.31/1.81 thf(fact_33_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A4:A]: (((((ord_less_eq @ A) @ B4) @ A4) => ((((ord_less_eq @ A) @ A4) @ B4) => (A4 = B4))))))))).
% 0.31/1.81 thf(fact_34_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y:A,Z:A]: ((Y = Z))) = (^ [A5:A,B5:A]: (((((ord_less_eq @ A) @ B5) @ A5) & (((ord_less_eq @ A) @ A5) @ B5))))))))).
% 0.31/1.81 thf(fact_35_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A4:A,C2:A]: (((((ord_less_eq @ A) @ B4) @ A4) => ((((ord_less_eq @ A) @ C2) @ B4) => (((ord_less_eq @ A) @ C2) @ A4))))))))).
% 0.31/1.81 thf(fact_36_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A4:A,B4:A]: (((! [A6:A,B6:A]: (((((ord_less_eq @ A) @ A6) @ B6) => ((P @ A6) @ B6)))) => ((! [A6:A,B6:A]: ((((P @ B6) @ A6) => ((P @ A6) @ B6)))) => ((P @ A4) @ B4))))))))).
% 0.31/1.81 thf(fact_37_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A]: ((((ord_less_eq @ A) @ A4) @ A4))))))).
% 0.31/1.81 thf(fact_38_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A,Z2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ Z2) => (((ord_less_eq @ A) @ X2) @ Z2))))))))).
% 0.31/1.81 thf(fact_39_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B4:A]: (((((ord_less_eq @ A) @ A4) @ B4) => ((((ord_less_eq @ A) @ B4) @ A4) => (A4 = B4))))))))).
% 0.31/1.81 thf(fact_40_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A4:A,B4:A,C2:A]: (((((ord_less_eq @ A) @ A4) @ B4) => ((B4 = C2) => (((ord_less_eq @ A) @ A4) @ C2))))))))).
% 0.31/1.81 thf(fact_41_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A4:A,B4:A,C2:A]: (((A4 = B4) => ((((ord_less_eq @ A) @ B4) @ C2) => (((ord_less_eq @ A) @ A4) @ C2))))))))).
% 0.31/1.81 thf(fact_42_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y:A,Z:A]: ((Y = Z))) = (^ [A5:A,B5:A]: (((((ord_less_eq @ A) @ A5) @ B5) & (((ord_less_eq @ A) @ B5) @ A5))))))))).
% 0.31/1.81 thf(fact_43_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y2:A,X2:A]: (((((ord_less_eq @ A) @ Y2) @ X2) => ((((ord_less_eq @ A) @ X2) @ Y2) = (X2 = Y2))))))))).
% 0.31/1.81 thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A4:A,P:(A > $o)]: (((((member @ A) @ A4) @ ((collect @ A) @ P)) = (P @ A4))))).
% 0.31/1.81 thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A2)))) = A2)))).
% 0.31/1.81 thf(fact_46_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X:A]: (((P @ X) = (Q @ X)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 0.31/1.81 thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X:A]: (((F @ X) = (G @ X)))) => (F = G))))).
% 0.31/1.81 thf(fact_48_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A,Z2:A]: ((((((ord_less_eq @ A) @ X2) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ Z2)))) => (((((ord_less_eq @ A) @ Y2) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Z2)))) => (((((ord_less_eq @ A) @ X2) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y2)))) => (((((ord_less_eq @ A) @ Z2) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ X2)))) => (((((ord_less_eq @ A) @ Y2) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X2)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Y2))))))))))))))))).
% 0.31/1.81 thf(fact_49_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B4:A,C2:A]: (((((ord_less_eq @ A) @ A4) @ B4) => ((((ord_less_eq @ A) @ B4) @ C2) => (((ord_less_eq @ A) @ A4) @ C2))))))))).
% 0.31/1.81 thf(fact_50_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((~ ((((ord_less_eq @ A) @ X2) @ Y2))) => (((ord_less_eq @ A) @ Y2) @ X2)))))))).
% 0.31/1.81 thf(fact_51_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A]: (((X2 = Y2) => (((ord_less_eq @ A) @ X2) @ Y2)))))))).
% 0.31/1.81 thf(fact_52_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) | (((ord_less_eq @ A) @ Y2) @ X2)))))))).
% 0.31/1.81 thf(fact_53_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ X2) => (X2 = Y2))))))))).
% 0.31/1.81 thf(fact_54_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y:A,Z:A]: ((Y = Z))) = (^ [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) & (((ord_less_eq @ A) @ Y3) @ X3))))))))).
% 0.31/1.81 thf(fact_55_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A4:A,B4:A,F:(A > B),C2:B]: (((((ord_less_eq @ A) @ A4) @ B4) => (((F @ B4) = C2) => ((! [X:A,Y4:A]: (((((ord_less_eq @ A) @ X) @ Y4) => (((ord_less_eq @ B) @ (F @ X)) @ (F @ Y4))))) => (((ord_less_eq @ B) @ (F @ A4)) @ C2)))))))))).
% 0.31/1.81 thf(fact_56_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A4:A,F:(B > A),B4:B,C2:B]: (((A4 = (F @ B4)) => ((((ord_less_eq @ B) @ B4) @ C2) => ((! [X:B,Y4:B]: (((((ord_less_eq @ B) @ X) @ Y4) => (((ord_less_eq @ A) @ (F @ X)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A4) @ (F @ C2))))))))))).
% 0.31/1.81 thf(fact_57_order__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A4:A,B4:A,F:(A > C),C2:C]: (((((ord_less_eq @ A) @ A4) @ B4) => ((((ord_less_eq @ C) @ (F @ B4)) @ C2) => ((! [X:A,Y4:A]: (((((ord_less_eq @ A) @ X) @ Y4) => (((ord_less_eq @ C) @ (F @ X)) @ (F @ Y4))))) => (((ord_less_eq @ C) @ (F @ A4)) @ C2)))))))))).
% 0.31/1.81 thf(fact_58_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A4:A,F:(B > A),B4:B,C2:B]: (((((ord_less_eq @ A) @ A4) @ (F @ B4)) => ((((ord_less_eq @ B) @ B4) @ C2) => ((! [X:B,Y4:B]: (((((ord_less_eq @ B) @ X) @ Y4) => (((ord_less_eq @ A) @ (F @ X)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A4) @ (F @ C2))))))))))).
% 0.31/1.81 thf(fact_59_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: ((! [X3:A]: ((((ord_less_eq @ B) @ (F2 @ X3)) @ (G2 @ X3))))))))))).
% 0.31/1.81 thf(fact_60_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B)]: (((! [X:A]: ((((ord_less_eq @ B) @ (F @ X)) @ (G @ X)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 0.31/1.81 thf(fact_61_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X2:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X2)) @ (G @ X2))))))))).
% 0.31/1.81 thf(fact_62_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X2:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X2)) @ (G @ X2))))))))).
% 0.31/1.81 thf(fact_63_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X3:A]: (((P @ X3) => (Q @ X3)))))))).
% 0.31/1.81 thf(fact_64_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y:(set @ A),Z:(set @ A)]: ((Y = Z))) = (^ [A3:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B3) & (((ord_less_eq @ (set @ A)) @ B3) @ A3)))))))).
% 0.31/1.81 thf(fact_65_subset__trans, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((ord_less_eq @ (set @ A)) @ B2) @ C3) => (((ord_less_eq @ (set @ A)) @ A2) @ C3)))))).
% 0.31/1.81 thf(fact_66_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X:A]: (((P @ X) => (Q @ X)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 0.31/1.81 thf(fact_67_subset__refl, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ A2)))).
% 0.31/1.81 thf(fact_68_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A3:(set @ A),B3:(set @ A)]: ((! [T:A]: (((((member @ A) @ T) @ A3) => (((member @ A) @ T) @ B3)))))))))).
% 0.31/1.81 thf(fact_69_equalityD2, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((A2 = B2) => (((ord_less_eq @ (set @ A)) @ B2) @ A2))))).
% 0.31/1.81 thf(fact_70_equalityD1, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((A2 = B2) => (((ord_less_eq @ (set @ A)) @ A2) @ B2))))).
% 0.31/1.81 thf(fact_71_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A3:(set @ A),B3:(set @ A)]: ((! [X3:A]: (((((member @ A) @ X3) @ A3) => (((member @ A) @ X3) @ B3)))))))))).
% 0.31/1.81 thf(fact_72_equalityE, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((A2 = B2) => (~ (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => (~ ((((ord_less_eq @ (set @ A)) @ B2) @ A2)))))))))).
% 0.31/1.81 thf(fact_73_subsetD, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((member @ A) @ C2) @ A2) => (((member @ A) @ C2) @ B2)))))).
% 0.31/1.81 thf(fact_74_in__mono, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),X2:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((member @ A) @ X2) @ A2) => (((member @ A) @ X2) @ B2)))))).
% 0.31/1.81 thf(fact_75_Uvariation__sym__rel, axiom, (! [Omega:(variable > real),Nu:(variable > real),U:(set @ variable)]: (((((denota1419872369iation @ Omega) @ Nu) @ U) => (((denota1419872369iation @ Nu) @ Omega) @ U))))).
% 0.31/1.81 thf(fact_76_Uvariation__refl, axiom, (! [Nu:(variable > real),V:(set @ variable)]: ((((denota1419872369iation @ Nu) @ Nu) @ V)))).
% 0.31/1.81 thf(fact_77_Uvariation__sym, axiom, (denota1419872369iation = (^ [Omega2:(variable > real),Nu3:(variable > real)]: (((denota1419872369iation @ Nu3) @ Omega2))))).
% 0.31/1.81 thf(fact_78_Uvariation__def, axiom, (denota1419872369iation = (^ [Nu3:(variable > real),Nu4:(variable > real),U2:(set @ variable)]: ((! [I:variable]: (((~ ((((member @ variable) @ I) @ U2))) => ((Nu3 @ I) = (Nu4 @ I))))))))).
% 0.31/1.81 thf(fact_79_pred__subset__eq, axiom, (! [A:$tType,R:(set @ A),S:(set @ A)]: (((((ord_less_eq @ (A > $o)) @ (^ [X3:A]: ((((member @ A) @ X3) @ R)))) @ (^ [X3:A]: ((((member @ A) @ X3) @ S)))) = (((ord_less_eq @ (set @ A)) @ R) @ S))))).
% 0.31/1.81 thf(fact_80_subset__Collect__iff, axiom, (! [A:$tType,B2:(set @ A),A2:(set @ A),P:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ B2) @ A2) => ((((ord_less_eq @ (set @ A)) @ B2) @ ((collect @ A) @ (^ [X3:A]: (((((member @ A) @ X3) @ A2) & (P @ X3)))))) = (! [X3:A]: (((((member @ A) @ X3) @ B2) => (P @ X3))))))))).
% 0.31/1.81 thf(fact_81_subset__CollectI, axiom, (! [A:$tType,B2:(set @ A),A2:(set @ A),Q:(A > $o),P:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ B2) @ A2) => ((! [X:A]: (((((member @ A) @ X) @ B2) => ((Q @ X) => (P @ X))))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X3:A]: (((((member @ A) @ X3) @ B2) & (Q @ X3)))))) @ ((collect @ A) @ (^ [X3:A]: (((((member @ A) @ X3) @ A2) & (P @ X3))))))))))).
% 0.31/1.81 thf(fact_82_Collect__restrict, axiom, (! [A:$tType,X4:(set @ A),P:(A > $o)]: ((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X3:A]: (((((member @ A) @ X3) @ X4) & (P @ X3)))))) @ X4)))).
% 0.31/1.81 thf(fact_83_prop__restrict, axiom, (! [A:$tType,X2:A,Z3:(set @ A),X4:(set @ A),P:(A > $o)]: (((((member @ A) @ X2) @ Z3) => ((((ord_less_eq @ (set @ A)) @ Z3) @ ((collect @ A) @ (^ [X3:A]: (((((member @ A) @ X3) @ X4) & (P @ X3)))))) => (P @ X2)))))).
% 0.31/1.81 thf(fact_84_conj__subset__def, axiom, (! [A:$tType,A2:(set @ A),P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ A2) @ ((collect @ A) @ (^ [X3:A]: (((P @ X3) & (Q @ X3)))))) = ((((ord_less_eq @ (set @ A)) @ A2) @ ((collect @ A) @ P)) & (((ord_less_eq @ (set @ A)) @ A2) @ ((collect @ A) @ Q))))))).
% 0.31/1.81 thf(fact_85_Pluso_Oelims, axiom, (! [X2:(option @ trm),Xa:(option @ trm),Y2:(option @ trm)]: (((((uSubst1112714340_Pluso @ X2) @ Xa) = Y2) => ((! [Theta2:trm]: (((X2 = ((some @ trm) @ Theta2)) => (! [Eta2:trm]: (((Xa = ((some @ trm) @ Eta2)) => (Y2 != ((some @ trm) @ ((plus @ Theta2) @ Eta2))))))))) => (((X2 = (none @ trm)) => (Y2 != (none @ trm))) => (~ (((? [V2:trm]: ((X2 = ((some @ trm) @ V2)))) => ((Xa = (none @ trm)) => (Y2 != (none @ trm)))))))))))).
% 0.31/1.81 thf(fact_86_Timeso_Oelims, axiom, (! [X2:(option @ trm),Xa:(option @ trm),Y2:(option @ trm)]: (((((uSubst277968634Timeso @ X2) @ Xa) = Y2) => ((! [Theta2:trm]: (((X2 = ((some @ trm) @ Theta2)) => (! [Eta2:trm]: (((Xa = ((some @ trm) @ Eta2)) => (Y2 != ((some @ trm) @ ((times @ Theta2) @ Eta2))))))))) => (((X2 = (none @ trm)) => (Y2 != (none @ trm))) => (~ (((? [V2:trm]: ((X2 = ((some @ trm) @ V2)))) => ((Xa = (none @ trm)) => (Y2 != (none @ trm)))))))))))).
% 0.31/1.81 thf(fact_87_usubstappt_Osimps_I7_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm]: (((((uSubst95898992stappt @ Sigma) @ U) @ (differential @ Theta)) = (uSubst259074819ntialo @ (((uSubst95898992stappt @ Sigma) @ ((collect @ variable) @ (^ [X3:variable]: ($true)))) @ Theta)))))).
% 0.31/1.81 thf(fact_88_option_Oinject, axiom, (! [A:$tType,X23:A,Y23:A]: (((((some @ A) @ X23) = ((some @ A) @ Y23)) = (X23 = Y23))))).
% 0.31/1.81 thf(fact_89_trm_Oinject_I7_J, axiom, (! [X7:trm,Y7:trm]: ((((differential @ X7) = (differential @ Y7)) = (X7 = Y7))))).
% 0.31/1.81 thf(fact_90_predicate1I, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X:A]: (((P @ X) => (Q @ X)))) => (((ord_less_eq @ (A > $o)) @ P) @ Q))))).
% 0.31/1.81 thf(fact_91_not__Some__eq, axiom, (! [A:$tType,X2:(option @ A)]: (((! [Y3:A]: ((X2 != ((some @ A) @ Y3)))) = (X2 = (none @ A)))))).
% 0.31/1.81 thf(fact_92_not__None__eq, axiom, (! [A:$tType,X2:(option @ A)]: (((X2 != (none @ A)) = (? [Y3:A]: ((X2 = ((some @ A) @ Y3)))))))).
% 0.31/1.81 thf(fact_93_predicate1D, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o),X2:A]: (((((ord_less_eq @ (A > $o)) @ P) @ Q) => ((P @ X2) => (Q @ X2)))))).
% 0.31/1.81 thf(fact_94_rev__predicate1D, axiom, (! [A:$tType,P:(A > $o),X2:A,Q:(A > $o)]: (((P @ X2) => ((((ord_less_eq @ (A > $o)) @ P) @ Q) => (Q @ X2)))))).
% 0.31/1.81 thf(fact_95_Aterm__Some, axiom, ((some @ trm) = (some @ trm))).
% 0.31/1.81 thf(fact_96_Differentialo_Osimps_I1_J, axiom, (! [Theta:trm]: (((uSubst259074819ntialo @ ((some @ trm) @ Theta)) = ((some @ trm) @ (differential @ Theta)))))).
% 0.31/1.81 thf(fact_97_combine__options__cases, axiom, (! [A:$tType,B:$tType,X2:(option @ A),P:((option @ A) > ((option @ B) > $o)),Y2:(option @ B)]: ((((X2 = (none @ A)) => ((P @ X2) @ Y2)) => (((Y2 = (none @ B)) => ((P @ X2) @ Y2)) => ((! [A6:A,B6:B]: (((X2 = ((some @ A) @ A6)) => ((Y2 = ((some @ B) @ B6)) => ((P @ X2) @ Y2))))) => ((P @ X2) @ Y2))))))).
% 0.31/1.81 thf(fact_98_split__option__all, axiom, (! [A:$tType]: (((^ [P2:((option @ A) > $o)]: ((! [X5:(option @ A)]: ((P2 @ X5))))) = (^ [P3:((option @ A) > $o)]: (((P3 @ (none @ A)) & (! [X3:A]: ((P3 @ ((some @ A) @ X3))))))))))).
% 0.31/1.81 thf(fact_99_split__option__ex, axiom, (! [A:$tType]: (((^ [P2:((option @ A) > $o)]: ((? [X5:(option @ A)]: ((P2 @ X5))))) = (^ [P3:((option @ A) > $o)]: (((P3 @ (none @ A)) | (? [X3:A]: ((P3 @ ((some @ A) @ X3))))))))))).
% 0.31/1.81 thf(fact_100_option_Oinducts, axiom, (! [A:$tType,P:((option @ A) > $o),Option:(option @ A)]: (((P @ (none @ A)) => ((! [X:A]: ((P @ ((some @ A) @ X)))) => (P @ Option)))))).
% 0.31/1.81 thf(fact_101_option_Oexhaust, axiom, (! [A:$tType,Y2:(option @ A)]: (((Y2 != (none @ A)) => (~ ((! [X24:A]: ((Y2 != ((some @ A) @ X24)))))))))).
% 0.31/1.81 thf(fact_102_option_OdiscI, axiom, (! [A:$tType,Option:(option @ A),X23:A]: (((Option = ((some @ A) @ X23)) => (Option != (none @ A)))))).
% 0.31/1.81 thf(fact_103_option_Odistinct_I1_J, axiom, (! [A:$tType,X23:A]: (((none @ A) != ((some @ A) @ X23))))).
% 0.31/1.81 thf(fact_104_Differentialo_Oinduct, axiom, (! [P:((option @ trm) > $o),A0:(option @ trm)]: (((! [Theta2:trm]: ((P @ ((some @ trm) @ Theta2)))) => ((P @ (none @ trm)) => (P @ A0)))))).
% 0.31/1.81 thf(fact_105_Differentialo_Ocases, axiom, (! [X2:(option @ trm)]: (((! [Theta2:trm]: ((X2 != ((some @ trm) @ Theta2)))) => (X2 = (none @ trm)))))).
% 0.31/1.81 thf(fact_106_Assigno_Oinduct, axiom, (! [P:(variable > ((option @ trm) > $o)),A0:variable,A1:(option @ trm)]: (((! [X:variable,Theta2:trm]: (((P @ X) @ ((some @ trm) @ Theta2)))) => ((! [X:variable]: (((P @ X) @ (none @ trm)))) => ((P @ A0) @ A1)))))).
% 0.31/1.81 thf(fact_107_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))))))).
% 0.31/1.81 thf(fact_108_undeft__equiv, axiom, (! [Theta:(option @ trm)]: (((Theta != (none @ trm)) = (? [T:trm]: ((Theta = ((some @ trm) @ T)))))))).
% 0.31/1.81 thf(fact_109_ODEo_Oinduct, axiom, (! [P:(char > ((option @ trm) > $o)),A0:char,A1:(option @ trm)]: (((! [X:char,Theta2:trm]: (((P @ X) @ ((some @ trm) @ Theta2)))) => ((! [X:char]: (((P @ X) @ (none @ trm)))) => ((P @ A0) @ A1)))))).
% 0.31/1.81 thf(fact_110_Differentialo_Oelims, axiom, (! [X2:(option @ trm),Y2:(option @ trm)]: ((((uSubst259074819ntialo @ X2) = Y2) => ((! [Theta2:trm]: (((X2 = ((some @ trm) @ Theta2)) => (Y2 != ((some @ trm) @ (differential @ Theta2)))))) => (~ (((X2 = (none @ trm)) => (Y2 != (none @ trm)))))))))).
% 0.31/1.81 thf(fact_111_trm_Odistinct_I41_J, axiom, (! [X61:trm,X62:trm,X7:trm]: ((((times @ X61) @ X62) != (differential @ X7))))).
% 0.31/1.81 thf(fact_112_trm_Odistinct_I39_J, axiom, (! [X51:trm,X52:trm,X7:trm]: ((((plus @ X51) @ X52) != (differential @ X7))))).
% 0.31/1.81 thf(fact_113_Timeso_Osimps_I3_J, axiom, (! [V3:trm]: ((((uSubst277968634Timeso @ ((some @ trm) @ V3)) @ (none @ trm)) = (none @ trm))))).
% 0.31/1.81 thf(fact_114_Pluso_Osimps_I3_J, axiom, (! [V3:trm]: ((((uSubst1112714340_Pluso @ ((some @ trm) @ V3)) @ (none @ trm)) = (none @ trm))))).
% 0.31/1.81 thf(fact_115_Pluso_Osimps_I1_J, axiom, (! [Theta:trm,Eta:trm]: ((((uSubst1112714340_Pluso @ ((some @ trm) @ Theta)) @ ((some @ trm) @ Eta)) = ((some @ trm) @ ((plus @ Theta) @ Eta)))))).
% 0.31/1.81 thf(fact_116_Timeso_Osimps_I1_J, axiom, (! [Theta:trm,Eta:trm]: ((((uSubst277968634Timeso @ ((some @ trm) @ Theta)) @ ((some @ trm) @ Eta)) = ((some @ trm) @ ((times @ Theta) @ Eta)))))).
% 0.31/1.81 thf(fact_117_usubstappt__differential__conv, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm]: ((((((uSubst95898992stappt @ Sigma) @ U) @ (differential @ Theta)) != (none @ trm)) => ((((uSubst95898992stappt @ Sigma) @ ((collect @ variable) @ (^ [X3:variable]: ($true)))) @ Theta) != (none @ trm)))))).
% 0.31/1.81 thf(fact_118_Geqo_Osimps_I3_J, axiom, (! [V3:trm]: ((((uSubst1556497037e_Geqo @ ((some @ trm) @ V3)) @ (none @ trm)) = (none @ fml))))).
% 0.31/1.81 thf(fact_119_Geqo_Oelims, axiom, (! [X2:(option @ trm),Xa:(option @ trm),Y2:(option @ fml)]: (((((uSubst1556497037e_Geqo @ X2) @ Xa) = Y2) => ((! [Theta2:trm]: (((X2 = ((some @ trm) @ Theta2)) => (! [Eta2:trm]: (((Xa = ((some @ trm) @ Eta2)) => (Y2 != ((some @ fml) @ ((geq @ Theta2) @ Eta2))))))))) => (((X2 = (none @ trm)) => (Y2 != (none @ fml))) => (~ (((? [V2:trm]: ((X2 = ((some @ trm) @ V2)))) => ((Xa = (none @ trm)) => (Y2 != (none @ fml)))))))))))).
% 0.31/1.81 thf(fact_120_Differentialo_Opelims, axiom, (! [X2:(option @ trm),Y2:(option @ trm)]: ((((uSubst259074819ntialo @ X2) = Y2) => ((((accp @ (option @ trm)) @ uSubst99643830lo_rel) @ X2) => ((! [Theta2:trm]: (((X2 = ((some @ trm) @ Theta2)) => ((Y2 = ((some @ trm) @ (differential @ Theta2))) => (~ ((((accp @ (option @ trm)) @ uSubst99643830lo_rel) @ ((some @ trm) @ Theta2)))))))) => (~ (((X2 = (none @ trm)) => ((Y2 = (none @ trm)) => (~ ((((accp @ (option @ trm)) @ uSubst99643830lo_rel) @ (none @ trm)))))))))))))).
% 0.31/1.81 thf(fact_121_Powp__mono, axiom, (! [A:$tType,A2:(A > $o),B2:(A > $o)]: (((((ord_less_eq @ (A > $o)) @ A2) @ B2) => (((ord_less_eq @ ((set @ A) > $o)) @ ((powp @ A) @ A2)) @ ((powp @ A) @ B2)))))).
% 0.31/1.81 thf(fact_122_Geqo_Osimps_I1_J, axiom, (! [Theta:trm,Eta:trm]: ((((uSubst1556497037e_Geqo @ ((some @ trm) @ Theta)) @ ((some @ trm) @ Eta)) = ((some @ fml) @ ((geq @ Theta) @ Eta)))))).
% 0.31/1.81 thf(fact_123_GreatestI2__order, axiom, (! [A:$tType]: (((order @ A) => (! [P:(A > $o),X2:A,Q:(A > $o)]: (((P @ X2) => ((! [Y4:A]: (((P @ Y4) => (((ord_less_eq @ A) @ Y4) @ X2)))) => ((! [X:A]: (((P @ X) => ((! [Y5:A]: (((P @ Y5) => (((ord_less_eq @ A) @ Y5) @ X)))) => (Q @ X))))) => (Q @ ((order_Greatest @ A) @ P))))))))))).
% 0.31/1.81 thf(fact_124_Greatest__equality, axiom, (! [A:$tType]: (((order @ A) => (! [P:(A > $o),X2:A]: (((P @ X2) => ((! [Y4:A]: (((P @ Y4) => (((ord_less_eq @ A) @ Y4) @ X2)))) => (((order_Greatest @ A) @ P) = X2))))))))).
% 0.31/1.81 thf(fact_125_Diamondo_Oinduct, axiom, (! [P:((option @ game) > ((option @ fml) > $o)),A0:(option @ game),A1:(option @ fml)]: (((! [Alpha:game,Phi2:fml]: (((P @ ((some @ game) @ Alpha)) @ ((some @ fml) @ Phi2)))) => ((! [X_1:(option @ fml)]: (((P @ (none @ game)) @ X_1))) => ((! [V2:game]: (((P @ ((some @ game) @ V2)) @ (none @ fml)))) => ((P @ A0) @ A1))))))).
% 0.31/1.81 thf(fact_126_Existso_Oinduct, axiom, (! [P:(variable > ((option @ fml) > $o)),A0:variable,A1:(option @ fml)]: (((! [X:variable,Phi2:fml]: (((P @ X) @ ((some @ fml) @ Phi2)))) => ((! [X:variable]: (((P @ X) @ (none @ fml)))) => ((P @ A0) @ A1)))))).
% 0.31/1.81 thf(fact_127_undeff__equiv, axiom, (! [Phi:(option @ fml)]: (((Phi != (none @ fml)) = (? [F2:fml]: ((Phi = ((some @ fml) @ F2)))))))).
% 0.31/1.81 thf(fact_128_Testo_Oinduct, axiom, (! [P:((option @ fml) > $o),A0:(option @ fml)]: (((! [Phi2:fml]: ((P @ ((some @ fml) @ Phi2)))) => ((P @ (none @ fml)) => (P @ A0)))))).
% 0.31/1.81 thf(fact_129_Testo_Ocases, axiom, (! [X2:(option @ fml)]: (((! [Phi2:fml]: ((X2 != ((some @ fml) @ Phi2)))) => (X2 = (none @ fml)))))).
% 0.31/1.81 thf(fact_130_Ando_Oinduct, axiom, (! [P:((option @ fml) > ((option @ fml) > $o)),A0:(option @ fml),A1:(option @ fml)]: (((! [Phi2:fml,Psi:fml]: (((P @ ((some @ fml) @ Phi2)) @ ((some @ fml) @ Psi)))) => ((! [X_1:(option @ fml)]: (((P @ (none @ fml)) @ X_1))) => ((! [V2:fml]: (((P @ ((some @ fml) @ V2)) @ (none @ fml)))) => ((P @ A0) @ A1))))))).
% 0.31/1.81 thf(fact_131_accp__subset, axiom, (! [A:$tType,R1:(A > (A > $o)),R2:(A > (A > $o))]: (((((ord_less_eq @ (A > (A > $o))) @ R1) @ R2) => (((ord_less_eq @ (A > $o)) @ ((accp @ A) @ R2)) @ ((accp @ A) @ R1)))))).
% 0.31/1.81 thf(fact_132_accp__subset__induct, axiom, (! [A:$tType,D:(A > $o),R:(A > (A > $o)),X2:A,P:(A > $o)]: (((((ord_less_eq @ (A > $o)) @ D) @ ((accp @ A) @ R)) => ((! [X:A,Z4:A]: (((D @ X) => (((R @ Z4) @ X) => (D @ Z4))))) => ((D @ X2) => ((! [X:A]: (((D @ X) => ((! [Z5:A]: ((((R @ Z5) @ X) => (P @ Z5)))) => (P @ X))))) => (P @ X2)))))))).
% 0.31/1.81 thf(fact_133_usubstappf__geqr, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm,Eta:trm]: ((((((uSubst95898978stappf @ Sigma) @ U) @ ((geq @ Theta) @ Eta)) != (none @ fml)) => ((((uSubst95898978stappf @ Sigma) @ U) @ ((geq @ Theta) @ Eta)) = ((some @ fml) @ ((geq @ ((the @ trm) @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta))) @ ((the @ trm) @ (((uSubst95898992stappt @ Sigma) @ U) @ Eta))))))))).
% 0.31/1.81 thf(fact_134_usubstappf__geq, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm,Eta:trm]: ((((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (none @ trm)) => (((((uSubst95898992stappt @ Sigma) @ U) @ Eta) != (none @ trm)) => ((((uSubst95898978stappf @ Sigma) @ U) @ ((geq @ Theta) @ Eta)) = ((some @ fml) @ ((geq @ ((the @ trm) @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta))) @ ((the @ trm) @ (((uSubst95898992stappt @ Sigma) @ U) @ Eta)))))))))).
% 0.31/1.81 thf(fact_135_predicate2I, axiom, (! [B:$tType,A:$tType,P:(A > (B > $o)),Q:(A > (B > $o))]: (((! [X:A,Y4:B]: ((((P @ X) @ Y4) => ((Q @ X) @ Y4)))) => (((ord_less_eq @ (A > (B > $o))) @ P) @ Q))))).
% 0.31/1.81 thf(fact_136_option_Ocollapse, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) => (((some @ A) @ ((the @ A) @ Option)) = Option))))).
% 0.31/1.81 thf(fact_137_predicate2D, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Q:(A > (B > $o)),X2:A,Y2:B]: (((((ord_less_eq @ (A > (B > $o))) @ P) @ Q) => (((P @ X2) @ Y2) => ((Q @ X2) @ Y2)))))).
% 0.31/1.81 thf(fact_138_rev__predicate2D, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),X2:A,Y2:B,Q:(A > (B > $o))]: ((((P @ X2) @ Y2) => ((((ord_less_eq @ (A > (B > $o))) @ P) @ Q) => ((Q @ X2) @ Y2)))))).
% 0.31/1.81 thf(fact_139_Composeo_Oinduct, axiom, (! [P:((option @ game) > ((option @ game) > $o)),A0:(option @ game),A1:(option @ game)]: (((! [Alpha:game,Beta:game]: (((P @ ((some @ game) @ Alpha)) @ ((some @ game) @ Beta)))) => ((! [Alpha:(option @ game)]: (((P @ Alpha) @ (none @ game)))) => ((! [V2:game]: (((P @ (none @ game)) @ ((some @ game) @ V2)))) => ((P @ A0) @ A1))))))).
% 0.31/1.81 thf(fact_140_undefg__equiv, axiom, (! [Alpha2:(option @ game)]: (((Alpha2 != (none @ game)) = (? [G2:game]: ((Alpha2 = ((some @ game) @ G2)))))))).
% 0.31/1.81 thf(fact_141_Loopo_Oinduct, axiom, (! [P:((option @ game) > $o),A0:(option @ game)]: (((! [Alpha:game]: ((P @ ((some @ game) @ Alpha)))) => ((P @ (none @ game)) => (P @ A0)))))).
% 0.31/1.81 thf(fact_142_Loopo_Ocases, axiom, (! [X2:(option @ game)]: (((! [Alpha:game]: ((X2 != ((some @ game) @ Alpha)))) => (X2 = (none @ game)))))).
% 0.31/1.81 thf(fact_143_option_Oexpand, axiom, (! [A:$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)))))).
% 0.31/1.81 thf(fact_144_option_Osel, axiom, (! [A:$tType,X23:A]: ((((the @ A) @ ((some @ A) @ X23)) = X23)))).
% 0.31/1.81 thf(fact_145_option_Oexhaust__sel, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) => (Option = ((some @ A) @ ((the @ A) @ Option))))))).
% 0.31/1.81 thf(fact_146_accp_Ocases, axiom, (! [A:$tType,R3:(A > (A > $o)),A4:A]: (((((accp @ A) @ R3) @ A4) => (! [Y5:A]: ((((R3 @ Y5) @ A4) => (((accp @ A) @ R3) @ Y5)))))))).
% 0.31/1.81 thf(fact_147_accp_Osimps, axiom, (! [A:$tType]: (((accp @ A) = (^ [R4:(A > (A > $o)),A5:A]: ((? [X3:A]: (((A5 = X3) & (! [Y3:A]: ((((R4 @ Y3) @ X3) => (((accp @ A) @ R4) @ Y3))))))))))))).
% 0.31/1.81 thf(fact_148_accp_Ointros, axiom, (! [A:$tType,R3:(A > (A > $o)),X2:A]: (((! [Y4:A]: ((((R3 @ Y4) @ X2) => (((accp @ A) @ R3) @ Y4)))) => (((accp @ A) @ R3) @ X2))))).
% 0.31/1.81 thf(fact_149_accp__induct, axiom, (! [A:$tType,R3:(A > (A > $o)),A4:A,P:(A > $o)]: (((((accp @ A) @ R3) @ A4) => ((! [X:A]: (((((accp @ A) @ R3) @ X) => ((! [Y5:A]: ((((R3 @ Y5) @ X) => (P @ Y5)))) => (P @ X))))) => (P @ A4)))))).
% 0.31/1.81 thf(fact_150_accp_Oinducts, axiom, (! [A:$tType,R3:(A > (A > $o)),X2:A,P:(A > $o)]: (((((accp @ A) @ R3) @ X2) => ((! [X:A]: (((! [Y5:A]: ((((R3 @ Y5) @ X) => (((accp @ A) @ R3) @ Y5)))) => ((! [Y5:A]: ((((R3 @ Y5) @ X) => (P @ Y5)))) => (P @ X))))) => (P @ X2)))))).
% 0.31/1.81 thf(fact_151_accp__downward, axiom, (! [A:$tType,R3:(A > (A > $o)),B4:A,A4:A]: (((((accp @ A) @ R3) @ B4) => (((R3 @ A4) @ B4) => (((accp @ A) @ R3) @ A4)))))).
% 0.31/1.81 thf(fact_152_not__accp__down, axiom, (! [A:$tType,R:(A > (A > $o)),X2:A]: (((~ ((((accp @ A) @ R) @ X2))) => (~ ((! [Z4:A]: ((((R @ Z4) @ X2) => (((accp @ A) @ R) @ Z4)))))))))).
% 0.31/1.81 thf(fact_153_accp__induct__rule, axiom, (! [A:$tType,R3:(A > (A > $o)),A4:A,P:(A > $o)]: (((((accp @ A) @ R3) @ A4) => ((! [X:A]: (((((accp @ A) @ R3) @ X) => ((! [Y5:A]: ((((R3 @ Y5) @ X) => (P @ Y5)))) => (P @ X))))) => (P @ A4)))))).
% 0.31/1.81 thf(fact_154_eq__subset, axiom, (! [A:$tType,P:(A > (A > $o))]: ((((ord_less_eq @ (A > (A > $o))) @ (^ [Y:A,Z:A]: ((Y = Z)))) @ (^ [A5:A,B5:A]: ((((P @ A5) @ B5) | (A5 = B5)))))))).
% 0.31/1.81 thf(fact_155_Geqo_Opelims, axiom, (! [X2:(option @ trm),Xa:(option @ trm),Y2:(option @ fml)]: (((((uSubst1556497037e_Geqo @ X2) @ Xa) = Y2) => ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst864323244qo_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ X2) @ Xa)) => ((! [Theta2:trm]: (((X2 = ((some @ trm) @ Theta2)) => (! [Eta2:trm]: (((Xa = ((some @ trm) @ Eta2)) => ((Y2 = ((some @ fml) @ ((geq @ Theta2) @ Eta2))) => (~ ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst864323244qo_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ ((some @ trm) @ Theta2)) @ ((some @ trm) @ Eta2)))))))))))) => (((X2 = (none @ trm)) => ((Y2 = (none @ fml)) => (~ ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst864323244qo_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ (none @ trm)) @ Xa)))))) => (~ ((! [V2:trm]: (((X2 = ((some @ trm) @ V2)) => ((Xa = (none @ trm)) => ((Y2 = (none @ fml)) => (~ ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst864323244qo_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ ((some @ trm) @ V2)) @ (none @ trm))))))))))))))))))).
% 0.31/1.81 thf(fact_156_Diamondo_Ocases, axiom, (! [X2:((product_prod @ (option @ game)) @ (option @ fml))]: (((! [Alpha:game,Phi2:fml]: ((X2 != ((((product_Pair @ (option @ game)) @ (option @ fml)) @ ((some @ game) @ Alpha)) @ ((some @ fml) @ Phi2))))) => ((! [Phi2:(option @ fml)]: ((X2 != ((((product_Pair @ (option @ game)) @ (option @ fml)) @ (none @ game)) @ Phi2)))) => (~ ((! [V2:game]: ((X2 != ((((product_Pair @ (option @ game)) @ (option @ fml)) @ ((some @ game) @ V2)) @ (none @ fml)))))))))))).
% 0.31/1.81 thf(fact_157_option_Osplit__sel, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F22:(A > B),Option:(option @ A)]: (((P @ (((((case_option @ B) @ A) @ F1) @ F22) @ Option)) = (((Option = (none @ A)) => (P @ F1)) & ((Option = ((some @ A) @ ((the @ A) @ Option))) => (P @ (F22 @ ((the @ A) @ Option))))))))).
% 0.31/1.81 thf(fact_158_subrelI, axiom, (! [B:$tType,A:$tType,R3:(set @ ((product_prod @ A) @ B)),S2:(set @ ((product_prod @ A) @ B))]: (((! [X:A,Y4:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y4)) @ R3) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y4)) @ S2)))) => (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R3) @ S2))))).
% 0.31/1.81 thf(fact_159_ssubst__Pair__rhs, axiom, (! [B:$tType,A:$tType,R3:A,S2:B,R:(set @ ((product_prod @ A) @ B)),S3:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R3) @ S2)) @ R) => ((S3 = S2) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R3) @ S3)) @ R)))))).
% 0.31/1.81 thf(fact_160_pred__equals__eq2, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: ((((^ [X3:A,Y3:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y3)) @ R))) = (^ [X3:A,Y3:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y3)) @ S)))) = (R = S))))).
% 0.31/1.81 thf(fact_161_option_Ocase__distrib, axiom, (! [C:$tType,B:$tType,A:$tType,H:(B > C),F1:B,F22:(A > B),Option:(option @ A)]: (((H @ (((((case_option @ B) @ A) @ F1) @ F22) @ Option)) = (((((case_option @ C) @ A) @ (H @ F1)) @ (^ [X3:A]: ((H @ (F22 @ X3))))) @ Option))))).
% 0.31/1.81 thf(fact_162_option_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F1:B,F22:(A > B)]: (((((((case_option @ B) @ A) @ F1) @ F22) @ (none @ A)) = F1)))).
% 0.31/1.81 thf(fact_163_pred__subset__eq2, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: (((((ord_less_eq @ (A > (B > $o))) @ (^ [X3:A,Y3:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y3)) @ R)))) @ (^ [X3:A,Y3:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y3)) @ S)))) = (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R) @ S))))).
% 0.31/1.81 thf(fact_164_option_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:B,F22:(A > B),X23:A]: (((((((case_option @ B) @ A) @ F1) @ F22) @ ((some @ A) @ X23)) = (F22 @ X23))))).
% 0.31/1.81 thf(fact_165_option_Odisc__eq__case_I1_J, axiom, (! [A:$tType,Option:(option @ A)]: (((Option = (none @ A)) = (((((case_option @ $o) @ A) @ $true) @ (^ [Uu:A]: ($false))) @ Option))))).
% 0.31/1.81 thf(fact_166_option_Odisc__eq__case_I2_J, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) = (((((case_option @ $o) @ A) @ $false) @ (^ [Uu:A]: ($true))) @ Option))))).
% 0.31/1.81 thf(fact_167_Timeso_Ocases, axiom, (! [X2:((product_prod @ (option @ trm)) @ (option @ trm))]: (((! [Theta2:trm,Eta2:trm]: ((X2 != ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ ((some @ trm) @ Theta2)) @ ((some @ trm) @ Eta2))))) => ((! [Eta2:(option @ trm)]: ((X2 != ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ (none @ trm)) @ Eta2)))) => (~ ((! [V2:trm]: ((X2 != ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ ((some @ trm) @ V2)) @ (none @ trm)))))))))))).
% 0.31/1.81 thf(fact_168_case__optionE, axiom, (! [A:$tType,P:$o,Q:(A > $o),X2:(option @ A)]: (((((((case_option @ $o) @ A) @ P) @ Q) @ X2) => (((X2 = (none @ A)) => (~ (P))) => (~ ((! [Y4:A]: (((X2 = ((some @ A) @ Y4)) => (~ ((Q @ Y4))))))))))))).
% 0.31/1.81 thf(fact_169_option_Ocase__eq__if, axiom, (! [A:$tType,B:$tType]: ((((case_option @ B) @ A) = (^ [F12:B,F23:(A > B),Option3:(option @ A)]: (((((if @ B) @ (Option3 = (none @ A))) @ F12) @ (F23 @ ((the @ A) @ Option3))))))))).
% 0.31/1.81 thf(fact_170_predicate2D__conj, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Q:(A > (B > $o)),R:$o,X2:A,Y2:B]: ((((((ord_less_eq @ (A > (B > $o))) @ P) @ Q) & R) => (R & (((P @ X2) @ Y2) => ((Q @ X2) @ Y2))))))).
% 0.31/1.81 thf(fact_171_option_Osplit__sel__asm, axiom, (! [B:$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))))))))))))).
% 0.31/1.81 thf(fact_172_Timeso_Opelims, axiom, (! [X2:(option @ trm),Xa:(option @ trm),Y2:(option @ trm)]: (((((uSubst277968634Timeso @ X2) @ Xa) = Y2) => ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst1377811071so_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ X2) @ Xa)) => ((! [Theta2:trm]: (((X2 = ((some @ trm) @ Theta2)) => (! [Eta2:trm]: (((Xa = ((some @ trm) @ Eta2)) => ((Y2 = ((some @ trm) @ ((times @ Theta2) @ Eta2))) => (~ ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst1377811071so_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ ((some @ trm) @ Theta2)) @ ((some @ trm) @ Eta2)))))))))))) => (((X2 = (none @ trm)) => ((Y2 = (none @ trm)) => (~ ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst1377811071so_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ (none @ trm)) @ Xa)))))) => (~ ((! [V2:trm]: (((X2 = ((some @ trm) @ V2)) => ((Xa = (none @ trm)) => ((Y2 = (none @ trm)) => (~ ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst1377811071so_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ ((some @ trm) @ V2)) @ (none @ trm))))))))))))))))))).
% 0.31/1.81 thf(fact_173_Pluso_Opelims, axiom, (! [X2:(option @ trm),Xa:(option @ trm),Y2:(option @ trm)]: (((((uSubst1112714340_Pluso @ X2) @ Xa) = Y2) => ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst270600597so_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ X2) @ Xa)) => ((! [Theta2:trm]: (((X2 = ((some @ trm) @ Theta2)) => (! [Eta2:trm]: (((Xa = ((some @ trm) @ Eta2)) => ((Y2 = ((some @ trm) @ ((plus @ Theta2) @ Eta2))) => (~ ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst270600597so_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ ((some @ trm) @ Theta2)) @ ((some @ trm) @ Eta2)))))))))))) => (((X2 = (none @ trm)) => ((Y2 = (none @ trm)) => (~ ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst270600597so_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ (none @ trm)) @ Xa)))))) => (~ ((! [V2:trm]: (((X2 = ((some @ trm) @ V2)) => ((Xa = (none @ trm)) => ((Y2 = (none @ trm)) => (~ ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst270600597so_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ ((some @ trm) @ V2)) @ (none @ trm))))))))))))))))))).
% 0.31/1.81 thf(fact_174_disjE__realizer2, axiom, (! [B:$tType,A:$tType,P:$o,Q:(A > $o),X2:(option @ A),R:(B > $o),F:B,G:(A > B)]: (((((((case_option @ $o) @ A) @ P) @ Q) @ X2) => ((P => (R @ F)) => ((! [Q2:A]: (((Q @ Q2) => (R @ (G @ Q2))))) => (R @ (((((case_option @ B) @ A) @ F) @ G) @ X2)))))))).
% 0.31/1.81 thf(fact_175_ODEo_Ocases, axiom, (! [X2:((product_prod @ char) @ (option @ trm))]: (((! [X:char,Theta2:trm]: ((X2 != ((((product_Pair @ char) @ (option @ trm)) @ X) @ ((some @ trm) @ Theta2))))) => (~ ((! [X:char]: ((X2 != ((((product_Pair @ char) @ (option @ trm)) @ X) @ (none @ trm))))))))))).
% 0.31/1.81 thf(fact_176_Assigno_Ocases, axiom, (! [X2:((product_prod @ variable) @ (option @ trm))]: (((! [X:variable,Theta2:trm]: ((X2 != ((((product_Pair @ variable) @ (option @ trm)) @ X) @ ((some @ trm) @ Theta2))))) => (~ ((! [X:variable]: ((X2 != ((((product_Pair @ variable) @ (option @ trm)) @ X) @ (none @ trm))))))))))).
% 0.31/1.81 thf(fact_177_Composeo_Ocases, axiom, (! [X2:((product_prod @ (option @ game)) @ (option @ game))]: (((! [Alpha:game,Beta:game]: ((X2 != ((((product_Pair @ (option @ game)) @ (option @ game)) @ ((some @ game) @ Alpha)) @ ((some @ game) @ Beta))))) => ((! [Alpha:(option @ game)]: ((X2 != ((((product_Pair @ (option @ game)) @ (option @ game)) @ Alpha) @ (none @ game))))) => (~ ((! [V2:game]: ((X2 != ((((product_Pair @ (option @ game)) @ (option @ game)) @ (none @ game)) @ ((some @ game) @ V2)))))))))))).
% 0.31/1.81 thf(fact_178_Existso_Ocases, axiom, (! [X2:((product_prod @ variable) @ (option @ fml))]: (((! [X:variable,Phi2:fml]: ((X2 != ((((product_Pair @ variable) @ (option @ fml)) @ X) @ ((some @ fml) @ Phi2))))) => (~ ((! [X:variable]: ((X2 != ((((product_Pair @ variable) @ (option @ fml)) @ X) @ (none @ fml))))))))))).
% 0.31/1.81 thf(fact_179_Ando_Ocases, axiom, (! [X2:((product_prod @ (option @ fml)) @ (option @ fml))]: (((! [Phi2:fml,Psi:fml]: ((X2 != ((((product_Pair @ (option @ fml)) @ (option @ fml)) @ ((some @ fml) @ Phi2)) @ ((some @ fml) @ Psi))))) => ((! [Psi:(option @ fml)]: ((X2 != ((((product_Pair @ (option @ fml)) @ (option @ fml)) @ (none @ fml)) @ Psi)))) => (~ ((! [V2:fml]: ((X2 != ((((product_Pair @ (option @ fml)) @ (option @ fml)) @ ((some @ fml) @ V2)) @ (none @ fml)))))))))))).
% 0.31/1.81 thf(fact_180_usubstappt_Opsimps_I7_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]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma) @ ((((product_Pair @ (set @ variable)) @ trm) @ U) @ (differential @ Theta)))) => ((((uSubst95898992stappt @ Sigma) @ U) @ (differential @ Theta)) = (uSubst259074819ntialo @ (((uSubst95898992stappt @ Sigma) @ ((collect @ variable) @ (^ [X3:variable]: ($true)))) @ Theta))))))).
% 0.31/1.81 thf(fact_181_usubstappt_Opsimps_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]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma) @ ((((product_Pair @ (set @ variable)) @ trm) @ U) @ ((times @ Theta) @ Eta)))) => ((((uSubst95898992stappt @ Sigma) @ U) @ ((times @ Theta) @ Eta)) = ((uSubst277968634Timeso @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta)) @ (((uSubst95898992stappt @ Sigma) @ U) @ Eta))))))).
% 0.31/1.81 thf(fact_182_usubstappt_Opsimps_I5_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]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma) @ ((((product_Pair @ (set @ variable)) @ trm) @ U) @ ((plus @ Theta) @ Eta)))) => ((((uSubst95898992stappt @ Sigma) @ U) @ ((plus @ Theta) @ Eta)) = ((uSubst1112714340_Pluso @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta)) @ (((uSubst95898992stappt @ Sigma) @ U) @ Eta))))))).
% 0.31/1.81 thf(fact_183_usubstappt_Opsimps_I1_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),X2:variable]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma) @ ((((product_Pair @ (set @ variable)) @ trm) @ U) @ (var @ X2)))) => ((((uSubst95898992stappt @ Sigma) @ U) @ (var @ X2)) = ((some @ trm) @ (var @ X2))))))).
% 0.31/1.81 thf(fact_184_usubstappt_Opsimps_I2_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),R3:real]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma) @ ((((product_Pair @ (set @ variable)) @ trm) @ U) @ (number @ R3)))) => ((((uSubst95898992stappt @ Sigma) @ U) @ (number @ R3)) = ((some @ trm) @ (number @ R3))))))).
% 0.31/1.81 thf(fact_185_in__lex__prod, axiom, (! [A:$tType,B:$tType,A4:A,B4:B,A7:A,B7:B,R3:(set @ ((product_prod @ A) @ A)),S2:(set @ ((product_prod @ B) @ B))]: (((((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A4) @ B4)) @ ((((product_Pair @ A) @ B) @ A7) @ B7))) @ ((((lex_prod @ A) @ B) @ R3) @ S2)) = ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A4) @ A7)) @ R3) | ((A4 = A7) & (((member @ ((product_prod @ B) @ B)) @ ((((product_Pair @ B) @ B) @ B4) @ B7)) @ S2))))))).
% 0.31/1.81 thf(fact_186_trm_Oinject_I2_J, axiom, (! [X23:real,Y23:real]: ((((number @ X23) = (number @ Y23)) = (X23 = Y23))))).
% 0.31/1.81 thf(fact_187_trm_Oinject_I1_J, axiom, (! [X1:variable,Y1:variable]: ((((var @ X1) = (var @ Y1)) = (X1 = Y1))))).
% 0.31/1.81 thf(fact_188_trm_Odistinct_I17_J, axiom, (! [X23:real,X51:trm,X52:trm]: (((number @ X23) != ((plus @ X51) @ X52))))).
% 0.31/1.81 thf(fact_189_trm_Odistinct_I19_J, axiom, (! [X23:real,X61:trm,X62:trm]: (((number @ X23) != ((times @ X61) @ X62))))).
% 0.31/1.81 thf(fact_190_trm_Odistinct_I21_J, axiom, (! [X23:real,X7:trm]: (((number @ X23) != (differential @ X7))))).
% 0.31/1.81 thf(fact_191_trm_Odistinct_I7_J, axiom, (! [X1:variable,X51:trm,X52:trm]: (((var @ X1) != ((plus @ X51) @ X52))))).
% 0.31/1.81 thf(fact_192_trm_Odistinct_I9_J, axiom, (! [X1:variable,X61:trm,X62:trm]: (((var @ X1) != ((times @ X61) @ X62))))).
% 0.31/1.81 thf(fact_193_trm_Odistinct_I11_J, axiom, (! [X1:variable,X7:trm]: (((var @ X1) != (differential @ X7))))).
% 0.31/1.81 thf(fact_194_trm_Odistinct_I1_J, axiom, (! [X1:variable,X23:real]: (((var @ X1) != (number @ X23))))).
% 0.31/1.81 thf(fact_195_usubstappt_Osimps_I2_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),R3:real]: (((((uSubst95898992stappt @ Sigma) @ U) @ (number @ R3)) = ((some @ trm) @ (number @ R3)))))).
% 0.31/1.81 thf(fact_196_usubstappt_Osimps_I1_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),X2:variable]: (((((uSubst95898992stappt @ Sigma) @ U) @ (var @ X2)) = ((some @ trm) @ (var @ X2)))))).
% 0.31/1.81 thf(fact_197_usubstappt_Ocases, axiom, (! [X2:((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))]: (((! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),X:variable]: ((X2 != ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma2) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (var @ X)))))) => ((! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),R5:real]: ((X2 != ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma2) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (number @ R5)))))) => ((! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),F3:char]: ((X2 != ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma2) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (const @ F3)))))) => ((! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),F3:char,Theta2:trm]: ((X2 != ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma2) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ ((func @ F3) @ Theta2)))))) => ((! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),Theta2:trm,Eta2:trm]: ((X2 != ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma2) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ ((plus @ Theta2) @ Eta2)))))) => ((! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),Theta2:trm,Eta2:trm]: ((X2 != ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma2) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ ((times @ Theta2) @ Eta2)))))) => (~ ((! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),Theta2:trm]: ((X2 != ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma2) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (differential @ Theta2))))))))))))))))).
% 0.31/1.81 thf(fact_198_Testo_Osimps_I2_J, axiom, ((uSubst190403692_Testo @ (none @ fml)) = (none @ game))).
% 0.31/1.81 thf(fact_199_Testo__undef, axiom, (! [Phi:(option @ fml)]: ((((uSubst190403692_Testo @ Phi) = (none @ game)) = (Phi = (none @ fml)))))).
% 0.31/1.81 thf(fact_200_trm_Oinject_I4_J, axiom, (! [X41:char,X42:trm,Y41:char,Y42:trm]: (((((func @ X41) @ X42) = ((func @ Y41) @ Y42)) = ((X41 = Y41) & (X42 = Y42)))))).
% 0.31/1.81 thf(fact_201_trm_Oinject_I3_J, axiom, (! [X32:char,Y32:char]: ((((const @ X32) = (const @ Y32)) = (X32 = Y32))))).
% 0.31/1.81 thf(fact_202_trm_Odistinct_I3_J, axiom, (! [X1:variable,X32:char]: (((var @ X1) != (const @ X32))))).
% 0.31/1.81 thf(fact_203_trm_Odistinct_I5_J, axiom, (! [X1:variable,X41:char,X42:trm]: (((var @ X1) != ((func @ X41) @ X42))))).
% 0.31/1.81 thf(fact_204_trm_Odistinct_I13_J, axiom, (! [X23:real,X32:char]: (((number @ X23) != (const @ X32))))).
% 0.31/1.81 thf(fact_205_trm_Odistinct_I15_J, axiom, (! [X23:real,X41:char,X42:trm]: (((number @ X23) != ((func @ X41) @ X42))))).
% 0.31/1.81 thf(fact_206_trm_Odistinct_I23_J, axiom, (! [X32:char,X41:char,X42:trm]: (((const @ X32) != ((func @ X41) @ X42))))).
% 0.31/1.81 thf(fact_207_trm_Odistinct_I29_J, axiom, (! [X32:char,X7:trm]: (((const @ X32) != (differential @ X7))))).
% 0.31/1.81 thf(fact_208_trm_Odistinct_I27_J, axiom, (! [X32:char,X61:trm,X62:trm]: (((const @ X32) != ((times @ X61) @ X62))))).
% 0.31/1.81 thf(fact_209_trm_Odistinct_I25_J, axiom, (! [X32:char,X51:trm,X52:trm]: (((const @ X32) != ((plus @ X51) @ X52))))).
% 0.31/1.81 thf(fact_210_trm_Odistinct_I35_J, axiom, (! [X41:char,X42:trm,X7:trm]: ((((func @ X41) @ X42) != (differential @ X7))))).
% 0.31/1.81 thf(fact_211_trm_Odistinct_I33_J, axiom, (! [X41:char,X42:trm,X61:trm,X62:trm]: ((((func @ X41) @ X42) != ((times @ X61) @ X62))))).
% 0.31/1.81 thf(fact_212_trm_Odistinct_I31_J, axiom, (! [X41:char,X42:trm,X51:trm,X52:trm]: ((((func @ X41) @ X42) != ((plus @ X51) @ X52))))).
% 0.31/1.81 thf(fact_213_trm_Oinduct, axiom, (! [P:(trm > $o),Trm:trm]: (((! [X:variable]: ((P @ (var @ X)))) => ((! [X:real]: ((P @ (number @ X)))) => ((! [X:char]: ((P @ (const @ X)))) => ((! [X1a:char,X2a:trm]: (((P @ X2a) => (P @ ((func @ X1a) @ X2a))))) => ((! [X1a:trm,X2a:trm]: (((P @ X1a) => ((P @ X2a) => (P @ ((plus @ X1a) @ X2a)))))) => ((! [X1a:trm,X2a:trm]: (((P @ X1a) => ((P @ X2a) => (P @ ((times @ X1a) @ X2a)))))) => ((! [X:trm]: (((P @ X) => (P @ (differential @ X))))) => (P @ Trm))))))))))).
% 0.31/1.81 thf(fact_214_trm_Oexhaust, axiom, (! [Y2:trm]: (((! [X12:variable]: ((Y2 != (var @ X12)))) => ((! [X24:real]: ((Y2 != (number @ X24)))) => ((! [X33:char]: ((Y2 != (const @ X33)))) => ((! [X412:char,X422:trm]: ((Y2 != ((func @ X412) @ X422)))) => ((! [X512:trm,X522:trm]: ((Y2 != ((plus @ X512) @ X522)))) => ((! [X612:trm,X622:trm]: ((Y2 != ((times @ X612) @ X622)))) => (~ ((! [X72:trm]: ((Y2 != (differential @ X72))))))))))))))).
% 0.31/1.81 thf(fact_215_term__sem_Ocases, axiom, (! [X2:((product_prod @ denotational_interp) @ trm)]: (((! [I2:denotational_interp,X:variable]: ((X2 != ((((product_Pair @ denotational_interp) @ trm) @ I2) @ (var @ X))))) => ((! [I2:denotational_interp,R5:real]: ((X2 != ((((product_Pair @ denotational_interp) @ trm) @ I2) @ (number @ R5))))) => ((! [I2:denotational_interp,F3:char]: ((X2 != ((((product_Pair @ denotational_interp) @ trm) @ I2) @ (const @ F3))))) => ((! [I2:denotational_interp,F3:char,Theta2:trm]: ((X2 != ((((product_Pair @ denotational_interp) @ trm) @ I2) @ ((func @ F3) @ Theta2))))) => ((! [I2:denotational_interp,Theta2:trm,Eta2:trm]: ((X2 != ((((product_Pair @ denotational_interp) @ trm) @ I2) @ ((plus @ Theta2) @ Eta2))))) => ((! [I2:denotational_interp,Theta2:trm,Eta2:trm]: ((X2 != ((((product_Pair @ denotational_interp) @ trm) @ I2) @ ((times @ Theta2) @ Eta2))))) => (~ ((! [I2:denotational_interp,Theta2:trm]: ((X2 != ((((product_Pair @ denotational_interp) @ trm) @ I2) @ (differential @ Theta2)))))))))))))))).
% 0.31/1.81 thf(fact_216_usubstappt_Opsimps_I3_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),F:char]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma) @ ((((product_Pair @ (set @ variable)) @ trm) @ U) @ (const @ F)))) => ((((uSubst95898992stappt @ Sigma) @ U) @ (const @ F)) = (((uSubst1138577137pconst @ Sigma) @ U) @ F)))))).
% 0.31/1.81 thf(fact_217_term__sem_Oinduct, axiom, (! [P:(denotational_interp > (trm > $o)),A0:denotational_interp,A1:trm]: (((! [I2:denotational_interp,X:variable]: (((P @ I2) @ (var @ X)))) => ((! [I2:denotational_interp,R5:real]: (((P @ I2) @ (number @ R5)))) => ((! [I2:denotational_interp,F3:char]: (((P @ I2) @ (const @ F3)))) => ((! [I2:denotational_interp,F3:char,Theta2:trm]: ((((P @ I2) @ Theta2) => ((P @ I2) @ ((func @ F3) @ Theta2))))) => ((! [I2:denotational_interp,Theta2:trm]: ((((P @ I2) @ Theta2) => (! [Eta2:trm]: ((((P @ I2) @ Eta2) => ((P @ I2) @ ((plus @ Theta2) @ Eta2)))))))) => ((! [I2:denotational_interp,Theta2:trm]: ((((P @ I2) @ Theta2) => (! [Eta2:trm]: ((((P @ I2) @ Eta2) => ((P @ I2) @ ((times @ Theta2) @ Eta2)))))))) => ((! [I2:denotational_interp,Theta2:trm]: ((((? [Xa2:char]: ((((member @ char) @ Xa2) @ ((collect @ char) @ (^ [Uu:char]: ($true)))))) => ((P @ I2) @ Theta2)) => ((P @ I2) @ (differential @ Theta2))))) => ((P @ A0) @ A1))))))))))).
% 0.31/1.81 thf(fact_218_usubstappt_Osimps_I3_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),F:char]: (((((uSubst95898992stappt @ Sigma) @ U) @ (const @ F)) = (((uSubst1138577137pconst @ Sigma) @ U) @ F))))).
% 0.31/1.81 thf(fact_219_image2__def, axiom, (! [A:$tType,B:$tType,C:$tType]: (((((bNF_Greatest_image2 @ C) @ A) @ B) = (^ [A3:(set @ C),F2:(C > A),G2:(C > B)]: (((collect @ ((product_prod @ A) @ B)) @ (^ [Uu:((product_prod @ A) @ B)]: ((? [A5:C]: (((Uu = ((((product_Pair @ A) @ B) @ (F2 @ A5)) @ (G2 @ A5))) & (((member @ C) @ A5) @ A3))))))))))))).
% 0.31/1.81 thf(fact_220_Testo_Oelims, axiom, (! [X2:(option @ fml),Y2:(option @ game)]: ((((uSubst190403692_Testo @ X2) = Y2) => ((! [Phi2:fml]: (((X2 = ((some @ fml) @ Phi2)) => (Y2 != ((some @ game) @ (test @ Phi2)))))) => (~ (((X2 = (none @ fml)) => (Y2 != (none @ game)))))))))).
% 0.31/1.81 thf(fact_221_game_Oinject_I3_J, axiom, (! [X32:fml,Y32:fml]: ((((test @ X32) = (test @ Y32)) = (X32 = Y32))))).
% 0.31/1.81 thf(fact_222_image2__eqI, axiom, (! [A:$tType,C:$tType,B:$tType,B4:A,F:(B > A),X2:B,C2:C,G:(B > C),A2:(set @ B)]: (((B4 = (F @ X2)) => ((C2 = (G @ X2)) => ((((member @ B) @ X2) @ A2) => (((member @ ((product_prod @ A) @ C)) @ ((((product_Pair @ A) @ C) @ B4) @ C2)) @ ((((((bNF_Greatest_image2 @ B) @ A) @ C) @ A2) @ F) @ G)))))))).
% 0.31/1.81 thf(fact_223_Testo_Osimps_I1_J, axiom, (! [Phi:fml]: (((uSubst190403692_Testo @ ((some @ fml) @ Phi)) = ((some @ game) @ (test @ Phi)))))).
% 0.31/1.81 thf(fact_224_Testo_Opelims, axiom, (! [X2:(option @ fml),Y2:(option @ game)]: ((((uSubst190403692_Testo @ X2) = Y2) => ((((accp @ (option @ fml)) @ uSubst533687181to_rel) @ X2) => ((! [Phi2:fml]: (((X2 = ((some @ fml) @ Phi2)) => ((Y2 = ((some @ game) @ (test @ Phi2))) => (~ ((((accp @ (option @ fml)) @ uSubst533687181to_rel) @ ((some @ fml) @ Phi2)))))))) => (~ (((X2 = (none @ fml)) => ((Y2 = (none @ game)) => (~ ((((accp @ (option @ fml)) @ uSubst533687181to_rel) @ (none @ fml)))))))))))))).
% 0.31/1.81 thf(fact_225_relImage__def, axiom, (! [A:$tType,B:$tType]: ((((bNF_Gr1317331620lImage @ B) @ A) = (^ [R6:(set @ ((product_prod @ B) @ B)),F2:(B > A)]: (((collect @ ((product_prod @ A) @ A)) @ (^ [Uu:((product_prod @ A) @ A)]: ((? [A12:B,A22:B]: (((Uu = ((((product_Pair @ A) @ A) @ (F2 @ A12)) @ (F2 @ A22))) & (((member @ ((product_prod @ B) @ B)) @ ((((product_Pair @ B) @ B) @ A12) @ A22)) @ R6))))))))))))).
% 0.31/1.81 thf(fact_226_relImage__mono, axiom, (! [B:$tType,A:$tType,R1:(set @ ((product_prod @ A) @ A)),R2:(set @ ((product_prod @ A) @ A)),F:(A > B)]: (((((ord_less_eq @ (set @ ((product_prod @ A) @ A))) @ R1) @ R2) => (((ord_less_eq @ (set @ ((product_prod @ B) @ B))) @ ((((bNF_Gr1317331620lImage @ A) @ B) @ R1) @ F)) @ ((((bNF_Gr1317331620lImage @ A) @ B) @ R2) @ F)))))).
% 0.31/1.81 thf(fact_227_relInvImage__def, axiom, (! [B:$tType,A:$tType]: ((((bNF_Gr2107612801vImage @ A) @ B) = (^ [A3:(set @ A),R6:(set @ ((product_prod @ B) @ B)),F2:(A > B)]: (((collect @ ((product_prod @ A) @ A)) @ (^ [Uu:((product_prod @ A) @ A)]: ((? [A12:A,A22:A]: (((Uu = ((((product_Pair @ A) @ A) @ A12) @ A22)) & ((((member @ A) @ A12) @ A3) & ((((member @ A) @ A22) @ A3) & (((member @ ((product_prod @ B) @ B)) @ ((((product_Pair @ B) @ B) @ (F2 @ A12)) @ (F2 @ A22))) @ R6))))))))))))))).
% 0.31/1.81 thf(fact_228_Assigno__undef, axiom, (! [X2:variable,Theta:(option @ trm)]: (((((uSubst1326326671ssigno @ X2) @ Theta) = (none @ game)) = (Theta = (none @ trm)))))).
% 0.31/1.81 thf(fact_229_relInvImage__mono, axiom, (! [A:$tType,B:$tType,R1:(set @ ((product_prod @ A) @ A)),R2:(set @ ((product_prod @ A) @ A)),A2:(set @ B),F:(B > A)]: (((((ord_less_eq @ (set @ ((product_prod @ A) @ A))) @ R1) @ R2) => (((ord_less_eq @ (set @ ((product_prod @ B) @ B))) @ (((((bNF_Gr2107612801vImage @ B) @ A) @ A2) @ R1) @ F)) @ (((((bNF_Gr2107612801vImage @ B) @ A) @ A2) @ R2) @ F)))))).
% 0.31/1.81 thf(fact_230_Assigno_Osimps_I2_J, axiom, (! [X2:variable]: ((((uSubst1326326671ssigno @ X2) @ (none @ trm)) = (none @ game))))).
% 0.31/1.81 thf(fact_231_Assigno_Oelims, axiom, (! [X2:variable,Xa:(option @ trm),Y2:(option @ game)]: (((((uSubst1326326671ssigno @ X2) @ Xa) = Y2) => ((! [Theta2:trm]: (((Xa = ((some @ trm) @ Theta2)) => (Y2 != ((some @ game) @ ((assign @ X2) @ Theta2)))))) => (~ (((Xa = (none @ trm)) => (Y2 != (none @ game)))))))))).
% 0.31/1.81 thf(fact_232_Assigno_Opelims, axiom, (! [X2:variable,Xa:(option @ trm),Y2:(option @ game)]: (((((uSubst1326326671ssigno @ X2) @ Xa) = Y2) => ((((accp @ ((product_prod @ variable) @ (option @ trm))) @ uSubst1741596714no_rel) @ ((((product_Pair @ variable) @ (option @ trm)) @ X2) @ Xa)) => ((! [Theta2:trm]: (((Xa = ((some @ trm) @ Theta2)) => ((Y2 = ((some @ game) @ ((assign @ X2) @ Theta2))) => (~ ((((accp @ ((product_prod @ variable) @ (option @ trm))) @ uSubst1741596714no_rel) @ ((((product_Pair @ variable) @ (option @ trm)) @ X2) @ ((some @ trm) @ Theta2))))))))) => (~ (((Xa = (none @ trm)) => ((Y2 = (none @ game)) => (~ ((((accp @ ((product_prod @ variable) @ (option @ trm))) @ uSubst1741596714no_rel) @ ((((product_Pair @ variable) @ (option @ trm)) @ X2) @ (none @ trm))))))))))))))).
% 0.31/1.81 thf(fact_233_game_Oinject_I2_J, axiom, (! [X21:variable,X22:trm,Y21:variable,Y22:trm]: (((((assign @ X21) @ X22) = ((assign @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 0.31/1.81 thf(fact_234_game_Odistinct_I15_J, axiom, (! [X21:variable,X22:trm,X32:fml]: ((((assign @ X21) @ X22) != (test @ X32))))).
% 0.31/1.81 thf(fact_235_Assigno_Osimps_I1_J, axiom, (! [X2:variable,Theta:trm]: ((((uSubst1326326671ssigno @ X2) @ ((some @ trm) @ Theta)) = ((some @ game) @ ((assign @ X2) @ Theta)))))).
% 0.31/1.81 thf(fact_236_relInvImage__UNIV__relImage, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ A)),F:(A > B)]: ((((ord_less_eq @ (set @ ((product_prod @ A) @ A))) @ R) @ (((((bNF_Gr2107612801vImage @ A) @ B) @ (top_top @ (set @ A))) @ ((((bNF_Gr1317331620lImage @ A) @ B) @ R) @ F)) @ F))))).
% 0.31/1.81 thf(fact_237_ODEo__undef, axiom, (! [X2:char,Theta:(option @ trm)]: (((((uSubst1083227664e_ODEo @ X2) @ Theta) = (none @ game)) = (Theta = (none @ trm)))))).
% 0.31/1.81 thf(fact_238_top__apply, axiom, (! [C:$tType,D2:$tType]: (((top @ C) => ((top_top @ (D2 > C)) = (^ [X3:D2]: ((top_top @ C)))))))).
% 0.31/1.81 thf(fact_239_UNIV__I, axiom, (! [A:$tType,X2:A]: ((((member @ A) @ X2) @ (top_top @ (set @ A)))))).
% 0.31/1.81 thf(fact_240_subset__UNIV, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ (top_top @ (set @ A)))))).
% 0.31/1.81 thf(fact_241_top__greatest, axiom, (! [A:$tType]: (((order_top @ A) => (! [A4:A]: ((((ord_less_eq @ A) @ A4) @ (top_top @ A)))))))).
% 0.31/1.81 thf(fact_242_top_Oextremum__unique, axiom, (! [A:$tType]: (((order_top @ A) => (! [A4:A]: (((((ord_less_eq @ A) @ (top_top @ A)) @ A4) = (A4 = (top_top @ A))))))))).
% 0.31/1.81 thf(fact_243_top_Oextremum__uniqueI, axiom, (! [A:$tType]: (((order_top @ A) => (! [A4:A]: (((((ord_less_eq @ A) @ (top_top @ A)) @ A4) => (A4 = (top_top @ A))))))))).
% 0.31/1.81 thf(fact_244_UNIV__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (^ [X3:A]: ($true))))))).
% 0.31/1.81 thf(fact_245_UNIV__eq__I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X:A]: ((((member @ A) @ X) @ A2))) => ((top_top @ (set @ A)) = A2))))).
% 0.31/1.81 thf(fact_246_UNIV__witness, axiom, (! [A:$tType]: ((? [X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A)))))))).
% 0.31/1.81 thf(fact_247_ODEo_Osimps_I2_J, axiom, (! [X2:char]: ((((uSubst1083227664e_ODEo @ X2) @ (none @ trm)) = (none @ game))))).
% 0.31/1.81 thf(fact_248_ODEo_Oelims, axiom, (! [X2:char,Xa:(option @ trm),Y2:(option @ game)]: (((((uSubst1083227664e_ODEo @ X2) @ Xa) = Y2) => ((! [Theta2:trm]: (((Xa = ((some @ trm) @ Theta2)) => (Y2 != ((some @ game) @ ((ode @ X2) @ Theta2)))))) => (~ (((Xa = (none @ trm)) => (Y2 != (none @ game)))))))))).
% 0.31/1.81 thf(fact_249_ODEo_Opelims, axiom, (! [X2:char,Xa:(option @ trm),Y2:(option @ game)]: (((((uSubst1083227664e_ODEo @ X2) @ Xa) = Y2) => ((((accp @ ((product_prod @ char) @ (option @ trm))) @ uSubst2007600873Eo_rel) @ ((((product_Pair @ char) @ (option @ trm)) @ X2) @ Xa)) => ((! [Theta2:trm]: (((Xa = ((some @ trm) @ Theta2)) => ((Y2 = ((some @ game) @ ((ode @ X2) @ Theta2))) => (~ ((((accp @ ((product_prod @ char) @ (option @ trm))) @ uSubst2007600873Eo_rel) @ ((((product_Pair @ char) @ (option @ trm)) @ X2) @ ((some @ trm) @ Theta2))))))))) => (~ (((Xa = (none @ trm)) => ((Y2 = (none @ game)) => (~ ((((accp @ ((product_prod @ char) @ (option @ trm))) @ uSubst2007600873Eo_rel) @ ((((product_Pair @ char) @ (option @ trm)) @ X2) @ (none @ trm))))))))))))))).
% 0.31/1.81 thf(fact_250_game_Oinject_I8_J, axiom, (! [X81:char,X82:trm,Y81:char,Y82:trm]: (((((ode @ X81) @ X82) = ((ode @ Y81) @ Y82)) = ((X81 = Y81) & (X82 = Y82)))))).
% 0.31/1.81 thf(fact_251_top__empty__eq2, axiom, (! [B:$tType,A:$tType]: (((top_top @ (A > (B > $o))) = (^ [X3:A,Y3:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y3)) @ (top_top @ (set @ ((product_prod @ A) @ B)))))))))).
% 0.31/1.81 thf(fact_252_top__empty__eq, axiom, (! [A:$tType]: (((top_top @ (A > $o)) = (^ [X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A))))))))).
% 0.31/1.81 thf(fact_253_top__set__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (top_top @ (A > $o))))))).
% 0.31/1.81 thf(fact_254_game_Odistinct_I35_J, axiom, (! [X32:fml,X81:char,X82:trm]: (((test @ X32) != ((ode @ X81) @ X82))))).
% 0.31/1.81 thf(tcon_fun___Orderings_Oorder__top, axiom, (! [A8:$tType,A9:$tType]: (((order_top @ A9) => (order_top @ (A8 > A9)))))).
% 0.31/1.81 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: (((preorder @ A9) => (preorder @ (A8 > A9)))))).
% 0.31/1.81 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: (((order @ A9) => (order @ (A8 > A9)))))).
% 0.31/1.81 thf(tcon_fun___Orderings_Otop, axiom, (! [A8:$tType,A9:$tType]: (((top @ A9) => (top @ (A8 > A9)))))).
% 0.31/1.81 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: (((ord @ A9) => (ord @ (A8 > A9)))))).
% 0.31/1.81 thf(tcon_Set_Oset___Orderings_Oorder__top_1, axiom, (! [A8:$tType]: ((order_top @ (set @ A8))))).
% 0.31/1.81 thf(tcon_Set_Oset___Orderings_Opreorder_2, axiom, (! [A8:$tType]: ((preorder @ (set @ A8))))).
% 0.31/1.81 thf(tcon_Set_Oset___Orderings_Oorder_3, axiom, (! [A8:$tType]: ((order @ (set @ A8))))).
% 0.31/1.81 thf(tcon_Set_Oset___Orderings_Otop_4, axiom, (! [A8:$tType]: ((top @ (set @ A8))))).
% 0.31/1.81 thf(tcon_Set_Oset___Orderings_Oord_5, axiom, (! [A8:$tType]: ((ord @ (set @ A8))))).
% 0.31/1.81 thf(tcon_HOL_Obool___Orderings_Oorder__top_6, axiom, (order_top @ $o)).
% 0.31/1.81 thf(tcon_HOL_Obool___Orderings_Opreorder_7, axiom, (preorder @ $o)).
% 0.31/1.81 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 0.31/1.81 thf(tcon_HOL_Obool___Orderings_Oorder_8, axiom, (order @ $o)).
% 0.31/1.81 thf(tcon_HOL_Obool___Orderings_Otop_9, axiom, (top @ $o)).
% 0.31/1.81 thf(tcon_HOL_Obool___Orderings_Oord_10, axiom, (ord @ $o)).
% 0.31/1.81 thf(tcon_Real_Oreal___Orderings_Opreorder_11, axiom, (preorder @ real)).
% 0.31/1.81 thf(tcon_Real_Oreal___Orderings_Olinorder_12, axiom, (linorder @ real)).
% 0.31/1.81 thf(tcon_Real_Oreal___Orderings_Oorder_13, axiom, (order @ real)).
% 0.31/1.81 thf(tcon_Real_Oreal___Orderings_Oord_14, axiom, (ord @ real)).
% 0.31/1.81 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 0.31/1.81 thf(help_If_2_1_T, axiom, (! [A:$tType,X2:A,Y2:A]: ((((((if @ A) @ $false) @ X2) @ Y2) = Y2)))).
% 0.31/1.81 thf(help_If_1_1_T, axiom, (! [A:$tType,X2:A,Y2:A]: ((((((if @ A) @ $true) @ X2) @ Y2) = X2)))).
% 0.31/1.81 thf(conj_0, conjecture, ((((uSubst95898992stappt @ sigma) @ ua) @ theta) != (none @ trm))).
% 0.31/1.81 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.LNgQuHokvE/DTF2DTF23487.p
% 0.31/1.81 ------------------------
% 0.31/1.87 ---- Cleaned THF ---
% 0.31/1.87 thf(ty_t_Denotational__Semantics_Ointerp,type,
% 0.31/1.87 denotational_interp: $tType ).
% 0.31/1.87
% 0.31/1.87 thf(ty_t_Product__Type_Oprod,type,
% 0.31/1.87 product_prod: $tType > $tType > $tType ).
% 0.31/1.87
% 0.31/1.87 thf(ty_t_Syntax_Ovariable,type,
% 0.31/1.87 variable: $tType ).
% 0.31/1.87
% 0.31/1.87 thf(ty_t_Option_Ooption,type,
% 0.31/1.87 option: $tType > $tType ).
% 0.31/1.87
% 0.31/1.87 thf(ty_t_Syntax_Ogame,type,
% 0.31/1.87 game: $tType ).
% 0.31/1.87
% 0.31/1.87 thf(ty_t_String_Ochar,type,
% 0.31/1.87 char: $tType ).
% 0.31/1.87
% 0.31/1.87 thf(ty_t_Syntax_Otrm,type,
% 0.31/1.87 trm: $tType ).
% 0.31/1.87
% 0.31/1.87 thf(ty_t_Syntax_Ofml,type,
% 0.31/1.87 fml: $tType ).
% 0.31/1.87
% 0.31/1.87 thf(ty_t_Real_Oreal,type,
% 0.31/1.87 real: $tType ).
% 0.31/1.87
% 0.31/1.87 thf(ty_t_Set_Oset,type,
% 0.31/1.87 set: $tType > $tType ).
% 0.31/1.87
% 0.31/1.87 thf(sy_cl_HOL_Otype,type,
% 0.31/1.87 type:
% 0.31/1.87 !>[A: $tType] : $o ).
% 0.31/1.87
% 0.31/1.87 thf(sy_cl_Orderings_Oord,type,
% 0.31/1.87 ord:
% 0.31/1.87 !>[A: $tType] : $o ).
% 0.31/1.87
% 0.31/1.87 thf(sy_cl_Orderings_Otop,type,
% 0.31/1.87 top:
% 0.31/1.87 !>[A: $tType] : $o ).
% 0.31/1.87
% 0.31/1.87 thf(sy_cl_Orderings_Oorder,type,
% 0.31/1.87 order:
% 0.31/1.87 !>[A: $tType] : $o ).
% 0.31/1.87
% 0.31/1.87 thf(sy_cl_Orderings_Olinorder,type,
% 0.31/1.87 linorder:
% 0.31/1.87 !>[A: $tType] : $o ).
% 0.31/1.87
% 0.31/1.87 thf(sy_cl_Orderings_Opreorder,type,
% 0.31/1.87 preorder:
% 0.31/1.87 !>[A: $tType] : $o ).
% 0.31/1.87
% 0.31/1.87 thf(sy_cl_Orderings_Oorder__top,type,
% 0.31/1.87 order_top:
% 0.31/1.87 !>[A: $tType] : $o ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2,type,
% 0.31/1.87 bNF_Greatest_image2:
% 0.31/1.87 !>[C: $tType,A: $tType,B: $tType] : ( ( set @ C ) > ( C > A ) > ( C > B ) > ( set @ ( product_prod @ A @ B ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_BNF__Greatest__Fixpoint_OrelImage,type,
% 0.31/1.87 bNF_Gr1317331620lImage:
% 0.31/1.87 !>[B: $tType,A: $tType] : ( ( set @ ( product_prod @ B @ B ) ) > ( B > A ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_BNF__Greatest__Fixpoint_OrelInvImage,type,
% 0.31/1.87 bNF_Gr2107612801vImage:
% 0.31/1.87 !>[A: $tType,B: $tType] : ( ( set @ A ) > ( set @ ( product_prod @ B @ B ) ) > ( A > B ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Denotational__Semantics_OUvariation,type,
% 0.31/1.87 denota1419872369iation: ( variable > real ) > ( variable > real ) > ( set @ variable ) > $o ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_If,type,
% 0.31/1.87 if:
% 0.31/1.87 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Option_Ooption_ONone,type,
% 0.31/1.87 none:
% 0.31/1.87 !>[A: $tType] : ( option @ A ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Option_Ooption_OSome,type,
% 0.31/1.87 some:
% 0.31/1.87 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Option_Ooption_Ocase__option,type,
% 0.31/1.87 case_option:
% 0.31/1.87 !>[B: $tType,A: $tType] : ( B > ( A > B ) > ( option @ A ) > B ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Option_Ooption_Othe,type,
% 0.31/1.87 the:
% 0.31/1.87 !>[A: $tType] : ( ( option @ A ) > A ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.31/1.87 ord_less_eq:
% 0.31/1.87 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Orderings_Oorder__class_OGreatest,type,
% 0.31/1.87 order_Greatest:
% 0.31/1.87 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.31/1.87 top_top:
% 0.31/1.87 !>[A: $tType] : A ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Product__Type_OPair,type,
% 0.31/1.87 product_Pair:
% 0.31/1.87 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Relation_OPowp,type,
% 0.31/1.87 powp:
% 0.31/1.87 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) > $o ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Set_OCollect,type,
% 0.31/1.87 collect:
% 0.31/1.87 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Syntax_Ofml_OGeq,type,
% 0.31/1.87 geq: trm > trm > fml ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Syntax_Ogame_OAssign,type,
% 0.31/1.87 assign: variable > trm > game ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Syntax_Ogame_OODE,type,
% 0.31/1.87 ode: char > trm > game ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Syntax_Ogame_OTest,type,
% 0.31/1.87 test: fml > game ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Syntax_Otrm_OConst,type,
% 0.31/1.87 const: char > trm ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Syntax_Otrm_ODifferential,type,
% 0.31/1.87 differential: trm > trm ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Syntax_Otrm_OFunc,type,
% 0.31/1.87 func: char > trm > trm ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Syntax_Otrm_ONumber,type,
% 0.31/1.87 number: real > trm ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Syntax_Otrm_OPlus,type,
% 0.31/1.87 plus: trm > trm > trm ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Syntax_Otrm_OTimes,type,
% 0.31/1.87 times: trm > trm > trm ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Syntax_Otrm_OVar,type,
% 0.31/1.87 var: variable > trm ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OAssigno,type,
% 0.31/1.87 uSubst1326326671ssigno: variable > ( option @ trm ) > ( option @ game ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OAssigno__rel,type,
% 0.31/1.87 uSubst1741596714no_rel: ( product_prod @ variable @ ( option @ trm ) ) > ( product_prod @ variable @ ( option @ trm ) ) > $o ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_USubst__Mirabelle__nnnzepxswx_ODifferentialo,type,
% 0.31/1.87 uSubst259074819ntialo: ( option @ trm ) > ( option @ trm ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_USubst__Mirabelle__nnnzepxswx_ODifferentialo__rel,type,
% 0.31/1.87 uSubst99643830lo_rel: ( option @ trm ) > ( option @ trm ) > $o ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OGeqo,type,
% 0.31/1.87 uSubst1556497037e_Geqo: ( option @ trm ) > ( option @ trm ) > ( option @ fml ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OGeqo__rel,type,
% 0.31/1.87 uSubst864323244qo_rel: ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > $o ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OODEo,type,
% 0.31/1.87 uSubst1083227664e_ODEo: char > ( option @ trm ) > ( option @ game ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OODEo__rel,type,
% 0.31/1.87 uSubst2007600873Eo_rel: ( product_prod @ char @ ( option @ trm ) ) > ( product_prod @ char @ ( option @ trm ) ) > $o ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OPluso,type,
% 0.31/1.87 uSubst1112714340_Pluso: ( option @ trm ) > ( option @ trm ) > ( option @ trm ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OPluso__rel,type,
% 0.31/1.87 uSubst270600597so_rel: ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > $o ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTesto,type,
% 0.31/1.87 uSubst190403692_Testo: ( option @ fml ) > ( option @ game ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTesto__rel,type,
% 0.31/1.87 uSubst533687181to_rel: ( option @ fml ) > ( option @ fml ) > $o ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTimeso,type,
% 0.31/1.87 uSubst277968634Timeso: ( option @ trm ) > ( option @ trm ) > ( option @ trm ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTimeso__rel,type,
% 0.31/1.87 uSubst1377811071so_rel: ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > $o ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousappconst,type,
% 0.31/1.87 uSubst1138577137pconst: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > char > ( option @ trm ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappf,type,
% 0.31/1.87 uSubst95898978stappf: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > fml > ( option @ fml ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappt,type,
% 0.31/1.87 uSubst95898992stappt: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > trm > ( option @ trm ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappt__rel,type,
% 0.31/1.87 uSubst2096773001pt_rel: ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) > ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) > $o ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Wellfounded_Oaccp,type,
% 0.31/1.87 accp:
% 0.31/1.87 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_Wellfounded_Olex__prod,type,
% 0.31/1.87 lex_prod:
% 0.31/1.87 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ B @ B ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_c_member,type,
% 0.31/1.87 member:
% 0.31/1.87 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_v_U,type,
% 0.31/1.87 u: set @ variable ).
% 0.31/1.87
% 0.31/1.87 thf(sy_v_Ua____,type,
% 0.31/1.87 ua: set @ variable ).
% 0.31/1.87
% 0.31/1.87 thf(sy_v__092_060eta_062____,type,
% 0.31/1.87 eta: trm ).
% 0.31/1.87
% 0.31/1.87 thf(sy_v__092_060nu_062,type,
% 0.31/1.87 nu: variable > real ).
% 0.31/1.87
% 0.31/1.87 thf(sy_v__092_060nu_062_H____,type,
% 0.31/1.87 nu2: variable > real ).
% 0.31/1.87
% 0.31/1.87 thf(sy_v__092_060omega_062,type,
% 0.31/1.87 omega: variable > real ).
% 0.31/1.87
% 0.31/1.87 thf(sy_v__092_060omega_062_H____,type,
% 0.31/1.87 omega2: variable > real ).
% 0.31/1.87
% 0.31/1.87 thf(sy_v__092_060sigma_062_H_H____,type,
% 0.31/1.87 sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(sy_v__092_060theta_062____,type,
% 0.31/1.87 theta: trm ).
% 0.31/1.87
% 0.31/1.87 thf(fact_0_vaouter,axiom,
% 0.31/1.87 denota1419872369iation @ nu @ omega @ u ).
% 0.31/1.87
% 0.31/1.87 thf(fact_1_usubstappf__geq__conv,axiom,
% 0.31/1.87 ! [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] :
% 0.31/1.87 ( ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.31/1.87 != ( none @ fml ) )
% 0.31/1.87 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.31/1.87 != ( none @ trm ) )
% 0.31/1.87 & ( ( uSubst95898992stappt @ Sigma @ U @ Eta )
% 0.31/1.87 != ( none @ trm ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_2_Geq_Oprems_I1_J,axiom,
% 0.31/1.87 ( ( uSubst95898978stappf @ sigma @ ua @ ( geq @ theta @ eta ) )
% 0.31/1.87 != ( none @ fml ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_3_undeft__None,axiom,
% 0.31/1.87 ( ( none @ trm )
% 0.31/1.87 = ( none @ trm ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_4_usubstappt__det,axiom,
% 0.31/1.87 ! [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] :
% 0.31/1.87 ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.31/1.87 != ( none @ trm ) )
% 0.31/1.87 => ( ( ( uSubst95898992stappt @ Sigma @ V @ Theta )
% 0.31/1.87 != ( none @ trm ) )
% 0.31/1.87 => ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.31/1.87 = ( uSubst95898992stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_5_Geq_Oprems_I2_J,axiom,
% 0.31/1.87 denota1419872369iation @ nu2 @ omega2 @ ua ).
% 0.31/1.87
% 0.31/1.87 thf(fact_6_usubstappt__plus__conv,axiom,
% 0.31/1.87 ! [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] :
% 0.31/1.87 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( plus @ Theta @ Eta ) )
% 0.31/1.87 != ( none @ trm ) )
% 0.31/1.87 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.31/1.87 != ( none @ trm ) )
% 0.31/1.87 & ( ( uSubst95898992stappt @ Sigma @ U @ Eta )
% 0.31/1.87 != ( none @ trm ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_7_usubstappt__times__conv,axiom,
% 0.31/1.87 ! [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] :
% 0.31/1.87 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 0.31/1.87 != ( none @ trm ) )
% 0.31/1.87 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.31/1.87 != ( none @ trm ) )
% 0.31/1.87 & ( ( uSubst95898992stappt @ Sigma @ U @ Eta )
% 0.31/1.87 != ( none @ trm ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_8_usubstappt__antimon,axiom,
% 0.31/1.87 ! [V: set @ variable,U: set @ variable,Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),Theta: trm] :
% 0.31/1.87 ( ( ord_less_eq @ ( set @ variable ) @ V @ U )
% 0.31/1.87 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.31/1.87 != ( none @ trm ) )
% 0.31/1.87 => ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.31/1.87 = ( uSubst95898992stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_9_Differentialo_Osimps_I2_J,axiom,
% 0.31/1.87 ( ( uSubst259074819ntialo @ ( none @ trm ) )
% 0.31/1.87 = ( none @ trm ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_10_Differentialo__undef,axiom,
% 0.31/1.87 ! [Theta: option @ trm] :
% 0.31/1.87 ( ( ( uSubst259074819ntialo @ Theta )
% 0.31/1.87 = ( none @ trm ) )
% 0.31/1.87 = ( Theta
% 0.31/1.87 = ( none @ trm ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_11_Pluso_Osimps_I2_J,axiom,
% 0.31/1.87 ! [Eta: option @ trm] :
% 0.31/1.87 ( ( uSubst1112714340_Pluso @ ( none @ trm ) @ Eta )
% 0.31/1.87 = ( none @ trm ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_12_Timeso_Osimps_I2_J,axiom,
% 0.31/1.87 ! [Eta: option @ trm] :
% 0.31/1.87 ( ( uSubst277968634Timeso @ ( none @ trm ) @ Eta )
% 0.31/1.87 = ( none @ trm ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_13_Pluso__undef,axiom,
% 0.31/1.87 ! [Theta: option @ trm,Eta: option @ trm] :
% 0.31/1.87 ( ( ( uSubst1112714340_Pluso @ Theta @ Eta )
% 0.31/1.87 = ( none @ trm ) )
% 0.31/1.87 = ( ( Theta
% 0.31/1.87 = ( none @ trm ) )
% 0.31/1.87 | ( Eta
% 0.31/1.87 = ( none @ trm ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_14_Timeso__undef,axiom,
% 0.31/1.87 ! [Theta: option @ trm,Eta: option @ trm] :
% 0.31/1.87 ( ( ( uSubst277968634Timeso @ Theta @ Eta )
% 0.31/1.87 = ( none @ trm ) )
% 0.31/1.87 = ( ( Theta
% 0.31/1.87 = ( none @ trm ) )
% 0.31/1.87 | ( Eta
% 0.31/1.87 = ( none @ trm ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_15_Geqo_Osimps_I2_J,axiom,
% 0.31/1.87 ! [Eta: option @ trm] :
% 0.31/1.87 ( ( uSubst1556497037e_Geqo @ ( none @ trm ) @ Eta )
% 0.31/1.87 = ( none @ fml ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_16_usubstappf__antimon,axiom,
% 0.31/1.87 ! [V: set @ variable,U: set @ variable,Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),Phi: fml] :
% 0.31/1.87 ( ( ord_less_eq @ ( set @ variable ) @ V @ U )
% 0.31/1.87 => ( ( ( uSubst95898978stappf @ Sigma @ U @ Phi )
% 0.31/1.87 != ( none @ fml ) )
% 0.31/1.87 => ( ( uSubst95898978stappf @ Sigma @ U @ Phi )
% 0.31/1.87 = ( uSubst95898978stappf @ Sigma @ V @ Phi ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_17_usubstappf__det,axiom,
% 0.31/1.87 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Phi: fml,V: set @ variable] :
% 0.31/1.87 ( ( ( uSubst95898978stappf @ Sigma @ U @ Phi )
% 0.31/1.87 != ( none @ fml ) )
% 0.31/1.87 => ( ( ( uSubst95898978stappf @ Sigma @ V @ Phi )
% 0.31/1.87 != ( none @ fml ) )
% 0.31/1.87 => ( ( uSubst95898978stappf @ Sigma @ U @ Phi )
% 0.31/1.87 = ( uSubst95898978stappf @ Sigma @ V @ Phi ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_18_usubstappt_Osimps_I5_J,axiom,
% 0.31/1.87 ! [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] :
% 0.31/1.87 ( ( uSubst95898992stappt @ Sigma @ U @ ( plus @ Theta @ Eta ) )
% 0.31/1.87 = ( uSubst1112714340_Pluso @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) @ ( uSubst95898992stappt @ Sigma @ U @ Eta ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_19_usubstappt_Osimps_I6_J,axiom,
% 0.31/1.87 ! [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] :
% 0.31/1.87 ( ( uSubst95898992stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 0.31/1.87 = ( uSubst277968634Timeso @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) @ ( uSubst95898992stappt @ Sigma @ U @ Eta ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_20_usubstappf_Osimps_I2_J,axiom,
% 0.31/1.87 ! [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] :
% 0.31/1.87 ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.31/1.87 = ( uSubst1556497037e_Geqo @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) @ ( uSubst95898992stappt @ Sigma @ U @ Eta ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_21_Geqo__undef,axiom,
% 0.31/1.87 ! [Theta: option @ trm,Eta: option @ trm] :
% 0.31/1.87 ( ( ( uSubst1556497037e_Geqo @ Theta @ Eta )
% 0.31/1.87 = ( none @ fml ) )
% 0.31/1.87 = ( ( Theta
% 0.31/1.87 = ( none @ trm ) )
% 0.31/1.87 | ( Eta
% 0.31/1.87 = ( none @ trm ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_22_trm_Oinject_I6_J,axiom,
% 0.31/1.87 ! [X61: trm,X62: trm,Y61: trm,Y62: trm] :
% 0.31/1.87 ( ( ( times @ X61 @ X62 )
% 0.31/1.87 = ( times @ Y61 @ Y62 ) )
% 0.31/1.87 = ( ( X61 = Y61 )
% 0.31/1.87 & ( X62 = Y62 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_23_trm_Oinject_I5_J,axiom,
% 0.31/1.87 ! [X51: trm,X52: trm,Y51: trm,Y52: trm] :
% 0.31/1.87 ( ( ( plus @ X51 @ X52 )
% 0.31/1.87 = ( plus @ Y51 @ Y52 ) )
% 0.31/1.87 = ( ( X51 = Y51 )
% 0.31/1.87 & ( X52 = Y52 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_24_fml_Oinject_I2_J,axiom,
% 0.31/1.87 ! [X21: trm,X22: trm,Y21: trm,Y22: trm] :
% 0.31/1.87 ( ( ( geq @ X21 @ X22 )
% 0.31/1.87 = ( geq @ Y21 @ Y22 ) )
% 0.31/1.87 = ( ( X21 = Y21 )
% 0.31/1.87 & ( X22 = Y22 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_25_Uvariation__mon,axiom,
% 0.31/1.87 ! [U: set @ variable,V: set @ variable,Omega: variable > real,Nu: variable > real] :
% 0.31/1.87 ( ( ord_less_eq @ ( set @ variable ) @ U @ V )
% 0.31/1.87 => ( ( denota1419872369iation @ Omega @ Nu @ U )
% 0.31/1.87 => ( denota1419872369iation @ Omega @ Nu @ V ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_26_subsetI,axiom,
% 0.31/1.87 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/1.87 ( ! [X: A] :
% 0.31/1.87 ( ( member @ A @ X @ A2 )
% 0.31/1.87 => ( member @ A @ X @ B2 ) )
% 0.31/1.87 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_27_subset__antisym,axiom,
% 0.31/1.87 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/1.87 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.31/1.87 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 0.31/1.87 => ( A2 = B2 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_28_trm_Odistinct_I37_J,axiom,
% 0.31/1.87 ! [X51: trm,X52: trm,X61: trm,X62: trm] :
% 0.31/1.87 ( ( plus @ X51 @ X52 )
% 0.31/1.87 != ( times @ X61 @ X62 ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_29_order__refl,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( preorder @ A )
% 0.31/1.87 => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_30_Uvariation__univ,axiom,
% 0.31/1.87 ! [Nu: variable > real,Nu2: variable > real] :
% 0.31/1.87 ( denota1419872369iation @ Nu @ Nu2
% 0.31/1.87 @ ( collect @ variable
% 0.31/1.87 @ ^ [X3: variable] : $true ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_31_Collect__subset,axiom,
% 0.31/1.87 ! [A: $tType,A2: set @ A,P: A > $o] :
% 0.31/1.87 ( ord_less_eq @ ( set @ A )
% 0.31/1.87 @ ( collect @ A
% 0.31/1.87 @ ^ [X3: A] :
% 0.31/1.87 ( ( member @ A @ X3 @ A2 )
% 0.31/1.87 & ( P @ X3 ) ) )
% 0.31/1.87 @ A2 ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_32_less__eq__set__def,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( ord_less_eq @ ( set @ A ) )
% 0.31/1.87 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.31/1.87 ( ord_less_eq @ ( A > $o )
% 0.31/1.87 @ ^ [X3: A] : ( member @ A @ X3 @ A3 )
% 0.31/1.87 @ ^ [X3: A] : ( member @ A @ X3 @ B3 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_33_dual__order_Oantisym,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( order @ A )
% 0.31/1.87 => ! [B4: A,A4: A] :
% 0.31/1.87 ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.31/1.87 => ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.87 => ( A4 = B4 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_34_dual__order_Oeq__iff,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( order @ A )
% 0.31/1.87 => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.31/1.87 = ( ^ [A5: A,B5: A] :
% 0.31/1.87 ( ( ord_less_eq @ A @ B5 @ A5 )
% 0.31/1.87 & ( ord_less_eq @ A @ A5 @ B5 ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_35_dual__order_Otrans,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( order @ A )
% 0.31/1.87 => ! [B4: A,A4: A,C2: A] :
% 0.31/1.87 ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.31/1.87 => ( ( ord_less_eq @ A @ C2 @ B4 )
% 0.31/1.87 => ( ord_less_eq @ A @ C2 @ A4 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_36_linorder__wlog,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( linorder @ A )
% 0.31/1.87 => ! [P: A > A > $o,A4: A,B4: A] :
% 0.31/1.87 ( ! [A6: A,B6: A] :
% 0.31/1.87 ( ( ord_less_eq @ A @ A6 @ B6 )
% 0.31/1.87 => ( P @ A6 @ B6 ) )
% 0.31/1.87 => ( ! [A6: A,B6: A] :
% 0.31/1.87 ( ( P @ B6 @ A6 )
% 0.31/1.87 => ( P @ A6 @ B6 ) )
% 0.31/1.87 => ( P @ A4 @ B4 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_37_dual__order_Orefl,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( order @ A )
% 0.31/1.87 => ! [A4: A] : ( ord_less_eq @ A @ A4 @ A4 ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_38_order__trans,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( preorder @ A )
% 0.31/1.87 => ! [X2: A,Y2: A,Z2: A] :
% 0.31/1.87 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.31/1.87 => ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 0.31/1.87 => ( ord_less_eq @ A @ X2 @ Z2 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_39_order__class_Oorder_Oantisym,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( order @ A )
% 0.31/1.87 => ! [A4: A,B4: A] :
% 0.31/1.87 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.87 => ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.31/1.87 => ( A4 = B4 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_40_ord__le__eq__trans,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( ord @ A )
% 0.31/1.87 => ! [A4: A,B4: A,C2: A] :
% 0.31/1.87 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.87 => ( ( B4 = C2 )
% 0.31/1.87 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_41_ord__eq__le__trans,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( ord @ A )
% 0.31/1.87 => ! [A4: A,B4: A,C2: A] :
% 0.31/1.87 ( ( A4 = B4 )
% 0.31/1.87 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 0.31/1.87 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_42_order__class_Oorder_Oeq__iff,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( order @ A )
% 0.31/1.87 => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.31/1.87 = ( ^ [A5: A,B5: A] :
% 0.31/1.87 ( ( ord_less_eq @ A @ A5 @ B5 )
% 0.31/1.87 & ( ord_less_eq @ A @ B5 @ A5 ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_43_antisym__conv,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( order @ A )
% 0.31/1.87 => ! [Y2: A,X2: A] :
% 0.31/1.87 ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.31/1.87 => ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.31/1.87 = ( X2 = Y2 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_44_mem__Collect__eq,axiom,
% 0.31/1.87 ! [A: $tType,A4: A,P: A > $o] :
% 0.31/1.87 ( ( member @ A @ A4 @ ( collect @ A @ P ) )
% 0.31/1.87 = ( P @ A4 ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_45_Collect__mem__eq,axiom,
% 0.31/1.87 ! [A: $tType,A2: set @ A] :
% 0.31/1.87 ( ( collect @ A
% 0.31/1.87 @ ^ [X3: A] : ( member @ A @ X3 @ A2 ) )
% 0.31/1.87 = A2 ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_46_Collect__cong,axiom,
% 0.31/1.87 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/1.87 ( ! [X: A] :
% 0.31/1.87 ( ( P @ X )
% 0.31/1.87 = ( Q @ X ) )
% 0.31/1.87 => ( ( collect @ A @ P )
% 0.31/1.87 = ( collect @ A @ Q ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_47_ext,axiom,
% 0.31/1.87 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.31/1.87 ( ! [X: A] :
% 0.31/1.87 ( ( F @ X )
% 0.31/1.87 = ( G @ X ) )
% 0.31/1.87 => ( F = G ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_48_le__cases3,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( linorder @ A )
% 0.31/1.87 => ! [X2: A,Y2: A,Z2: A] :
% 0.31/1.87 ( ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.31/1.87 => ~ ( ord_less_eq @ A @ Y2 @ Z2 ) )
% 0.31/1.87 => ( ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.31/1.87 => ~ ( ord_less_eq @ A @ X2 @ Z2 ) )
% 0.31/1.87 => ( ( ( ord_less_eq @ A @ X2 @ Z2 )
% 0.31/1.87 => ~ ( ord_less_eq @ A @ Z2 @ Y2 ) )
% 0.31/1.87 => ( ( ( ord_less_eq @ A @ Z2 @ Y2 )
% 0.31/1.87 => ~ ( ord_less_eq @ A @ Y2 @ X2 ) )
% 0.31/1.87 => ( ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 0.31/1.87 => ~ ( ord_less_eq @ A @ Z2 @ X2 ) )
% 0.31/1.87 => ~ ( ( ord_less_eq @ A @ Z2 @ X2 )
% 0.31/1.87 => ~ ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_49_order_Otrans,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( order @ A )
% 0.31/1.87 => ! [A4: A,B4: A,C2: A] :
% 0.31/1.87 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.87 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 0.31/1.87 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_50_le__cases,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( linorder @ A )
% 0.31/1.87 => ! [X2: A,Y2: A] :
% 0.31/1.87 ( ~ ( ord_less_eq @ A @ X2 @ Y2 )
% 0.31/1.87 => ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_51_eq__refl,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( preorder @ A )
% 0.31/1.87 => ! [X2: A,Y2: A] :
% 0.31/1.87 ( ( X2 = Y2 )
% 0.31/1.87 => ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_52_linear,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( linorder @ A )
% 0.31/1.87 => ! [X2: A,Y2: A] :
% 0.31/1.87 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.31/1.87 | ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_53_antisym,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( order @ A )
% 0.31/1.87 => ! [X2: A,Y2: A] :
% 0.31/1.87 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.31/1.87 => ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.31/1.87 => ( X2 = Y2 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_54_eq__iff,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( order @ A )
% 0.31/1.87 => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.31/1.87 = ( ^ [X3: A,Y3: A] :
% 0.31/1.87 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.31/1.87 & ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_55_ord__le__eq__subst,axiom,
% 0.31/1.87 ! [A: $tType,B: $tType] :
% 0.31/1.87 ( ( ( ord @ B )
% 0.31/1.87 & ( ord @ A ) )
% 0.31/1.87 => ! [A4: A,B4: A,F: A > B,C2: B] :
% 0.31/1.87 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.87 => ( ( ( F @ B4 )
% 0.31/1.87 = C2 )
% 0.31/1.87 => ( ! [X: A,Y4: A] :
% 0.31/1.87 ( ( ord_less_eq @ A @ X @ Y4 )
% 0.31/1.87 => ( ord_less_eq @ B @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/1.87 => ( ord_less_eq @ B @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_56_ord__eq__le__subst,axiom,
% 0.31/1.87 ! [A: $tType,B: $tType] :
% 0.31/1.87 ( ( ( ord @ B )
% 0.31/1.87 & ( ord @ A ) )
% 0.31/1.87 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 0.31/1.87 ( ( A4
% 0.31/1.87 = ( F @ B4 ) )
% 0.31/1.87 => ( ( ord_less_eq @ B @ B4 @ C2 )
% 0.31/1.87 => ( ! [X: B,Y4: B] :
% 0.31/1.87 ( ( ord_less_eq @ B @ X @ Y4 )
% 0.31/1.87 => ( ord_less_eq @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/1.87 => ( ord_less_eq @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_57_order__subst2,axiom,
% 0.31/1.87 ! [A: $tType,C: $tType] :
% 0.31/1.87 ( ( ( order @ C )
% 0.31/1.87 & ( order @ A ) )
% 0.31/1.87 => ! [A4: A,B4: A,F: A > C,C2: C] :
% 0.31/1.87 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.87 => ( ( ord_less_eq @ C @ ( F @ B4 ) @ C2 )
% 0.31/1.87 => ( ! [X: A,Y4: A] :
% 0.31/1.87 ( ( ord_less_eq @ A @ X @ Y4 )
% 0.31/1.87 => ( ord_less_eq @ C @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/1.87 => ( ord_less_eq @ C @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_58_order__subst1,axiom,
% 0.31/1.87 ! [A: $tType,B: $tType] :
% 0.31/1.87 ( ( ( order @ B )
% 0.31/1.87 & ( order @ A ) )
% 0.31/1.87 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 0.31/1.87 ( ( ord_less_eq @ A @ A4 @ ( F @ B4 ) )
% 0.31/1.87 => ( ( ord_less_eq @ B @ B4 @ C2 )
% 0.31/1.87 => ( ! [X: B,Y4: B] :
% 0.31/1.87 ( ( ord_less_eq @ B @ X @ Y4 )
% 0.31/1.87 => ( ord_less_eq @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/1.87 => ( ord_less_eq @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_59_le__fun__def,axiom,
% 0.31/1.87 ! [B: $tType,A: $tType] :
% 0.31/1.87 ( ( ord @ B )
% 0.31/1.87 => ( ( ord_less_eq @ ( A > B ) )
% 0.31/1.87 = ( ^ [F2: A > B,G2: A > B] :
% 0.31/1.87 ! [X3: A] : ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_60_le__funI,axiom,
% 0.31/1.87 ! [B: $tType,A: $tType] :
% 0.31/1.87 ( ( ord @ B )
% 0.31/1.87 => ! [F: A > B,G: A > B] :
% 0.31/1.87 ( ! [X: A] : ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) )
% 0.31/1.87 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_61_le__funE,axiom,
% 0.31/1.87 ! [B: $tType,A: $tType] :
% 0.31/1.87 ( ( ord @ B )
% 0.31/1.87 => ! [F: A > B,G: A > B,X2: A] :
% 0.31/1.87 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.31/1.87 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_62_le__funD,axiom,
% 0.31/1.87 ! [B: $tType,A: $tType] :
% 0.31/1.87 ( ( ord @ B )
% 0.31/1.87 => ! [F: A > B,G: A > B,X2: A] :
% 0.31/1.87 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.31/1.87 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_63_Collect__mono__iff,axiom,
% 0.31/1.87 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/1.87 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.31/1.87 = ( ! [X3: A] :
% 0.31/1.87 ( ( P @ X3 )
% 0.31/1.87 => ( Q @ X3 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_64_set__eq__subset,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( ^ [Y: set @ A,Z: set @ A] : ( Y = Z ) )
% 0.31/1.87 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.31/1.87 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.31/1.87 & ( ord_less_eq @ ( set @ A ) @ B3 @ A3 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_65_subset__trans,axiom,
% 0.31/1.87 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.31/1.87 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.31/1.87 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C3 )
% 0.31/1.87 => ( ord_less_eq @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_66_Collect__mono,axiom,
% 0.31/1.87 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/1.87 ( ! [X: A] :
% 0.31/1.87 ( ( P @ X )
% 0.31/1.87 => ( Q @ X ) )
% 0.31/1.87 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_67_subset__refl,axiom,
% 0.31/1.87 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_68_subset__iff,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( ord_less_eq @ ( set @ A ) )
% 0.31/1.87 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.31/1.87 ! [T: A] :
% 0.31/1.87 ( ( member @ A @ T @ A3 )
% 0.31/1.87 => ( member @ A @ T @ B3 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_69_equalityD2,axiom,
% 0.31/1.87 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/1.87 ( ( A2 = B2 )
% 0.31/1.87 => ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_70_equalityD1,axiom,
% 0.31/1.87 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/1.87 ( ( A2 = B2 )
% 0.31/1.87 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_71_subset__eq,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( ord_less_eq @ ( set @ A ) )
% 0.31/1.87 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.31/1.87 ! [X3: A] :
% 0.31/1.87 ( ( member @ A @ X3 @ A3 )
% 0.31/1.87 => ( member @ A @ X3 @ B3 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_72_equalityE,axiom,
% 0.31/1.87 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/1.87 ( ( A2 = B2 )
% 0.31/1.87 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.31/1.87 => ~ ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_73_subsetD,axiom,
% 0.31/1.87 ! [A: $tType,A2: set @ A,B2: set @ A,C2: A] :
% 0.31/1.87 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.31/1.87 => ( ( member @ A @ C2 @ A2 )
% 0.31/1.87 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_74_in__mono,axiom,
% 0.31/1.87 ! [A: $tType,A2: set @ A,B2: set @ A,X2: A] :
% 0.31/1.87 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.31/1.87 => ( ( member @ A @ X2 @ A2 )
% 0.31/1.87 => ( member @ A @ X2 @ B2 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_75_Uvariation__sym__rel,axiom,
% 0.31/1.87 ! [Omega: variable > real,Nu: variable > real,U: set @ variable] :
% 0.31/1.87 ( ( denota1419872369iation @ Omega @ Nu @ U )
% 0.31/1.87 => ( denota1419872369iation @ Nu @ Omega @ U ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_76_Uvariation__refl,axiom,
% 0.31/1.87 ! [Nu: variable > real,V: set @ variable] : ( denota1419872369iation @ Nu @ Nu @ V ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_77_Uvariation__sym,axiom,
% 0.31/1.87 ( denota1419872369iation
% 0.31/1.87 = ( ^ [Omega2: variable > real,Nu3: variable > real] : ( denota1419872369iation @ Nu3 @ Omega2 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_78_Uvariation__def,axiom,
% 0.31/1.87 ( denota1419872369iation
% 0.31/1.87 = ( ^ [Nu3: variable > real,Nu4: variable > real,U2: set @ variable] :
% 0.31/1.87 ! [I: variable] :
% 0.31/1.87 ( ~ ( member @ variable @ I @ U2 )
% 0.31/1.87 => ( ( Nu3 @ I )
% 0.31/1.87 = ( Nu4 @ I ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_79_pred__subset__eq,axiom,
% 0.31/1.87 ! [A: $tType,R: set @ A,S: set @ A] :
% 0.31/1.87 ( ( ord_less_eq @ ( A > $o )
% 0.31/1.87 @ ^ [X3: A] : ( member @ A @ X3 @ R )
% 0.31/1.87 @ ^ [X3: A] : ( member @ A @ X3 @ S ) )
% 0.31/1.87 = ( ord_less_eq @ ( set @ A ) @ R @ S ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_80_subset__Collect__iff,axiom,
% 0.31/1.87 ! [A: $tType,B2: set @ A,A2: set @ A,P: A > $o] :
% 0.31/1.87 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 0.31/1.87 => ( ( ord_less_eq @ ( set @ A ) @ B2
% 0.31/1.87 @ ( collect @ A
% 0.31/1.87 @ ^ [X3: A] :
% 0.31/1.87 ( ( member @ A @ X3 @ A2 )
% 0.31/1.87 & ( P @ X3 ) ) ) )
% 0.31/1.87 = ( ! [X3: A] :
% 0.31/1.87 ( ( member @ A @ X3 @ B2 )
% 0.31/1.87 => ( P @ X3 ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_81_subset__CollectI,axiom,
% 0.31/1.87 ! [A: $tType,B2: set @ A,A2: set @ A,Q: A > $o,P: A > $o] :
% 0.31/1.87 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 0.31/1.87 => ( ! [X: A] :
% 0.31/1.87 ( ( member @ A @ X @ B2 )
% 0.31/1.87 => ( ( Q @ X )
% 0.31/1.87 => ( P @ X ) ) )
% 0.31/1.87 => ( ord_less_eq @ ( set @ A )
% 0.31/1.87 @ ( collect @ A
% 0.31/1.87 @ ^ [X3: A] :
% 0.31/1.87 ( ( member @ A @ X3 @ B2 )
% 0.31/1.87 & ( Q @ X3 ) ) )
% 0.31/1.87 @ ( collect @ A
% 0.31/1.87 @ ^ [X3: A] :
% 0.31/1.87 ( ( member @ A @ X3 @ A2 )
% 0.31/1.87 & ( P @ X3 ) ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_82_Collect__restrict,axiom,
% 0.31/1.87 ! [A: $tType,X4: set @ A,P: A > $o] :
% 0.31/1.87 ( ord_less_eq @ ( set @ A )
% 0.31/1.87 @ ( collect @ A
% 0.31/1.87 @ ^ [X3: A] :
% 0.31/1.87 ( ( member @ A @ X3 @ X4 )
% 0.31/1.87 & ( P @ X3 ) ) )
% 0.31/1.87 @ X4 ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_83_prop__restrict,axiom,
% 0.31/1.87 ! [A: $tType,X2: A,Z3: set @ A,X4: set @ A,P: A > $o] :
% 0.31/1.87 ( ( member @ A @ X2 @ Z3 )
% 0.31/1.87 => ( ( ord_less_eq @ ( set @ A ) @ Z3
% 0.31/1.87 @ ( collect @ A
% 0.31/1.87 @ ^ [X3: A] :
% 0.31/1.87 ( ( member @ A @ X3 @ X4 )
% 0.31/1.87 & ( P @ X3 ) ) ) )
% 0.31/1.87 => ( P @ X2 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_84_conj__subset__def,axiom,
% 0.31/1.87 ! [A: $tType,A2: set @ A,P: A > $o,Q: A > $o] :
% 0.31/1.87 ( ( ord_less_eq @ ( set @ A ) @ A2
% 0.31/1.87 @ ( collect @ A
% 0.31/1.87 @ ^ [X3: A] :
% 0.31/1.87 ( ( P @ X3 )
% 0.31/1.87 & ( Q @ X3 ) ) ) )
% 0.31/1.87 = ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( collect @ A @ P ) )
% 0.31/1.87 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( collect @ A @ Q ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_85_Pluso_Oelims,axiom,
% 0.31/1.87 ! [X2: option @ trm,Xa: option @ trm,Y2: option @ trm] :
% 0.31/1.87 ( ( ( uSubst1112714340_Pluso @ X2 @ Xa )
% 0.31/1.87 = Y2 )
% 0.31/1.87 => ( ! [Theta2: trm] :
% 0.31/1.87 ( ( X2
% 0.31/1.87 = ( some @ trm @ Theta2 ) )
% 0.31/1.87 => ! [Eta2: trm] :
% 0.31/1.87 ( ( Xa
% 0.31/1.87 = ( some @ trm @ Eta2 ) )
% 0.31/1.87 => ( Y2
% 0.31/1.87 != ( some @ trm @ ( plus @ Theta2 @ Eta2 ) ) ) ) )
% 0.31/1.87 => ( ( ( X2
% 0.31/1.87 = ( none @ trm ) )
% 0.31/1.87 => ( Y2
% 0.31/1.87 != ( none @ trm ) ) )
% 0.31/1.87 => ~ ( ? [V2: trm] :
% 0.31/1.87 ( X2
% 0.31/1.87 = ( some @ trm @ V2 ) )
% 0.31/1.87 => ( ( Xa
% 0.31/1.87 = ( none @ trm ) )
% 0.31/1.87 => ( Y2
% 0.31/1.87 != ( none @ trm ) ) ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_86_Timeso_Oelims,axiom,
% 0.31/1.87 ! [X2: option @ trm,Xa: option @ trm,Y2: option @ trm] :
% 0.31/1.87 ( ( ( uSubst277968634Timeso @ X2 @ Xa )
% 0.31/1.87 = Y2 )
% 0.31/1.87 => ( ! [Theta2: trm] :
% 0.31/1.87 ( ( X2
% 0.31/1.87 = ( some @ trm @ Theta2 ) )
% 0.31/1.87 => ! [Eta2: trm] :
% 0.31/1.87 ( ( Xa
% 0.31/1.87 = ( some @ trm @ Eta2 ) )
% 0.31/1.87 => ( Y2
% 0.31/1.87 != ( some @ trm @ ( times @ Theta2 @ Eta2 ) ) ) ) )
% 0.31/1.87 => ( ( ( X2
% 0.31/1.87 = ( none @ trm ) )
% 0.31/1.87 => ( Y2
% 0.31/1.87 != ( none @ trm ) ) )
% 0.31/1.87 => ~ ( ? [V2: trm] :
% 0.31/1.87 ( X2
% 0.31/1.87 = ( some @ trm @ V2 ) )
% 0.31/1.87 => ( ( Xa
% 0.31/1.87 = ( none @ trm ) )
% 0.31/1.87 => ( Y2
% 0.31/1.87 != ( none @ trm ) ) ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_87_usubstappt_Osimps_I7_J,axiom,
% 0.31/1.87 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm] :
% 0.31/1.87 ( ( uSubst95898992stappt @ Sigma @ U @ ( differential @ Theta ) )
% 0.31/1.87 = ( uSubst259074819ntialo
% 0.31/1.87 @ ( uSubst95898992stappt @ Sigma
% 0.31/1.87 @ ( collect @ variable
% 0.31/1.87 @ ^ [X3: variable] : $true )
% 0.31/1.87 @ Theta ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_88_option_Oinject,axiom,
% 0.31/1.87 ! [A: $tType,X23: A,Y23: A] :
% 0.31/1.87 ( ( ( some @ A @ X23 )
% 0.31/1.87 = ( some @ A @ Y23 ) )
% 0.31/1.87 = ( X23 = Y23 ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_89_trm_Oinject_I7_J,axiom,
% 0.31/1.87 ! [X7: trm,Y7: trm] :
% 0.31/1.87 ( ( ( differential @ X7 )
% 0.31/1.87 = ( differential @ Y7 ) )
% 0.31/1.87 = ( X7 = Y7 ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_90_predicate1I,axiom,
% 0.31/1.87 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/1.87 ( ! [X: A] :
% 0.31/1.87 ( ( P @ X )
% 0.31/1.87 => ( Q @ X ) )
% 0.31/1.87 => ( ord_less_eq @ ( A > $o ) @ P @ Q ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_91_not__Some__eq,axiom,
% 0.31/1.87 ! [A: $tType,X2: option @ A] :
% 0.31/1.87 ( ( ! [Y3: A] :
% 0.31/1.87 ( X2
% 0.31/1.87 != ( some @ A @ Y3 ) ) )
% 0.31/1.87 = ( X2
% 0.31/1.87 = ( none @ A ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_92_not__None__eq,axiom,
% 0.31/1.87 ! [A: $tType,X2: option @ A] :
% 0.31/1.87 ( ( X2
% 0.31/1.87 != ( none @ A ) )
% 0.31/1.87 = ( ? [Y3: A] :
% 0.31/1.87 ( X2
% 0.31/1.87 = ( some @ A @ Y3 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_93_predicate1D,axiom,
% 0.31/1.87 ! [A: $tType,P: A > $o,Q: A > $o,X2: A] :
% 0.31/1.87 ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 0.31/1.87 => ( ( P @ X2 )
% 0.31/1.87 => ( Q @ X2 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_94_rev__predicate1D,axiom,
% 0.31/1.87 ! [A: $tType,P: A > $o,X2: A,Q: A > $o] :
% 0.31/1.87 ( ( P @ X2 )
% 0.31/1.87 => ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 0.31/1.87 => ( Q @ X2 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_95_Aterm__Some,axiom,
% 0.31/1.87 ( ( some @ trm )
% 0.31/1.87 = ( some @ trm ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_96_Differentialo_Osimps_I1_J,axiom,
% 0.31/1.87 ! [Theta: trm] :
% 0.31/1.87 ( ( uSubst259074819ntialo @ ( some @ trm @ Theta ) )
% 0.31/1.87 = ( some @ trm @ ( differential @ Theta ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_97_combine__options__cases,axiom,
% 0.31/1.87 ! [A: $tType,B: $tType,X2: option @ A,P: ( option @ A ) > ( option @ B ) > $o,Y2: option @ B] :
% 0.31/1.87 ( ( ( X2
% 0.31/1.87 = ( none @ A ) )
% 0.31/1.87 => ( P @ X2 @ Y2 ) )
% 0.31/1.87 => ( ( ( Y2
% 0.31/1.87 = ( none @ B ) )
% 0.31/1.87 => ( P @ X2 @ Y2 ) )
% 0.31/1.87 => ( ! [A6: A,B6: B] :
% 0.31/1.87 ( ( X2
% 0.31/1.87 = ( some @ A @ A6 ) )
% 0.31/1.87 => ( ( Y2
% 0.31/1.87 = ( some @ B @ B6 ) )
% 0.31/1.87 => ( P @ X2 @ Y2 ) ) )
% 0.31/1.87 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_98_split__option__all,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( ^ [P2: ( option @ A ) > $o] :
% 0.31/1.87 ! [X5: option @ A] : ( P2 @ X5 ) )
% 0.31/1.87 = ( ^ [P3: ( option @ A ) > $o] :
% 0.31/1.87 ( ( P3 @ ( none @ A ) )
% 0.31/1.87 & ! [X3: A] : ( P3 @ ( some @ A @ X3 ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_99_split__option__ex,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( ^ [P2: ( option @ A ) > $o] :
% 0.31/1.87 ? [X5: option @ A] : ( P2 @ X5 ) )
% 0.31/1.87 = ( ^ [P3: ( option @ A ) > $o] :
% 0.31/1.87 ( ( P3 @ ( none @ A ) )
% 0.31/1.87 | ? [X3: A] : ( P3 @ ( some @ A @ X3 ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_100_option_Oinducts,axiom,
% 0.31/1.87 ! [A: $tType,P: ( option @ A ) > $o,Option: option @ A] :
% 0.31/1.87 ( ( P @ ( none @ A ) )
% 0.31/1.87 => ( ! [X: A] : ( P @ ( some @ A @ X ) )
% 0.31/1.87 => ( P @ Option ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_101_option_Oexhaust,axiom,
% 0.31/1.87 ! [A: $tType,Y2: option @ A] :
% 0.31/1.87 ( ( Y2
% 0.31/1.87 != ( none @ A ) )
% 0.31/1.87 => ~ ! [X24: A] :
% 0.31/1.87 ( Y2
% 0.31/1.87 != ( some @ A @ X24 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_102_option_OdiscI,axiom,
% 0.31/1.87 ! [A: $tType,Option: option @ A,X23: A] :
% 0.31/1.87 ( ( Option
% 0.31/1.87 = ( some @ A @ X23 ) )
% 0.31/1.87 => ( Option
% 0.31/1.87 != ( none @ A ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_103_option_Odistinct_I1_J,axiom,
% 0.31/1.87 ! [A: $tType,X23: A] :
% 0.31/1.87 ( ( none @ A )
% 0.31/1.87 != ( some @ A @ X23 ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_104_Differentialo_Oinduct,axiom,
% 0.31/1.87 ! [P: ( option @ trm ) > $o,A0: option @ trm] :
% 0.31/1.87 ( ! [Theta2: trm] : ( P @ ( some @ trm @ Theta2 ) )
% 0.31/1.87 => ( ( P @ ( none @ trm ) )
% 0.31/1.87 => ( P @ A0 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_105_Differentialo_Ocases,axiom,
% 0.31/1.87 ! [X2: option @ trm] :
% 0.31/1.87 ( ! [Theta2: trm] :
% 0.31/1.87 ( X2
% 0.31/1.87 != ( some @ trm @ Theta2 ) )
% 0.31/1.87 => ( X2
% 0.31/1.87 = ( none @ trm ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_106_Assigno_Oinduct,axiom,
% 0.31/1.87 ! [P: variable > ( option @ trm ) > $o,A0: variable,A1: option @ trm] :
% 0.31/1.87 ( ! [X: variable,Theta2: trm] : ( P @ X @ ( some @ trm @ Theta2 ) )
% 0.31/1.87 => ( ! [X: variable] : ( P @ X @ ( none @ trm ) )
% 0.31/1.87 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_107_Timeso_Oinduct,axiom,
% 0.31/1.87 ! [P: ( option @ trm ) > ( option @ trm ) > $o,A0: option @ trm,A1: option @ trm] :
% 0.31/1.87 ( ! [Theta2: trm,Eta2: trm] : ( P @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta2 ) )
% 0.31/1.87 => ( ! [X_1: option @ trm] : ( P @ ( none @ trm ) @ X_1 )
% 0.31/1.87 => ( ! [V2: trm] : ( P @ ( some @ trm @ V2 ) @ ( none @ trm ) )
% 0.31/1.87 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_108_undeft__equiv,axiom,
% 0.31/1.87 ! [Theta: option @ trm] :
% 0.31/1.87 ( ( Theta
% 0.31/1.87 != ( none @ trm ) )
% 0.31/1.87 = ( ? [T: trm] :
% 0.31/1.87 ( Theta
% 0.31/1.87 = ( some @ trm @ T ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_109_ODEo_Oinduct,axiom,
% 0.31/1.87 ! [P: char > ( option @ trm ) > $o,A0: char,A1: option @ trm] :
% 0.31/1.87 ( ! [X: char,Theta2: trm] : ( P @ X @ ( some @ trm @ Theta2 ) )
% 0.31/1.87 => ( ! [X: char] : ( P @ X @ ( none @ trm ) )
% 0.31/1.87 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_110_Differentialo_Oelims,axiom,
% 0.31/1.87 ! [X2: option @ trm,Y2: option @ trm] :
% 0.31/1.87 ( ( ( uSubst259074819ntialo @ X2 )
% 0.31/1.87 = Y2 )
% 0.31/1.87 => ( ! [Theta2: trm] :
% 0.31/1.87 ( ( X2
% 0.31/1.87 = ( some @ trm @ Theta2 ) )
% 0.31/1.87 => ( Y2
% 0.31/1.87 != ( some @ trm @ ( differential @ Theta2 ) ) ) )
% 0.31/1.87 => ~ ( ( X2
% 0.31/1.87 = ( none @ trm ) )
% 0.31/1.87 => ( Y2
% 0.31/1.87 != ( none @ trm ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_111_trm_Odistinct_I41_J,axiom,
% 0.31/1.87 ! [X61: trm,X62: trm,X7: trm] :
% 0.31/1.87 ( ( times @ X61 @ X62 )
% 0.31/1.87 != ( differential @ X7 ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_112_trm_Odistinct_I39_J,axiom,
% 0.31/1.87 ! [X51: trm,X52: trm,X7: trm] :
% 0.31/1.87 ( ( plus @ X51 @ X52 )
% 0.31/1.87 != ( differential @ X7 ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_113_Timeso_Osimps_I3_J,axiom,
% 0.31/1.87 ! [V3: trm] :
% 0.31/1.87 ( ( uSubst277968634Timeso @ ( some @ trm @ V3 ) @ ( none @ trm ) )
% 0.31/1.87 = ( none @ trm ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_114_Pluso_Osimps_I3_J,axiom,
% 0.31/1.87 ! [V3: trm] :
% 0.31/1.87 ( ( uSubst1112714340_Pluso @ ( some @ trm @ V3 ) @ ( none @ trm ) )
% 0.31/1.87 = ( none @ trm ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_115_Pluso_Osimps_I1_J,axiom,
% 0.31/1.87 ! [Theta: trm,Eta: trm] :
% 0.31/1.87 ( ( uSubst1112714340_Pluso @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta ) )
% 0.31/1.87 = ( some @ trm @ ( plus @ Theta @ Eta ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_116_Timeso_Osimps_I1_J,axiom,
% 0.31/1.87 ! [Theta: trm,Eta: trm] :
% 0.31/1.87 ( ( uSubst277968634Timeso @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta ) )
% 0.31/1.87 = ( some @ trm @ ( times @ Theta @ Eta ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_117_usubstappt__differential__conv,axiom,
% 0.31/1.87 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm] :
% 0.31/1.87 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( differential @ Theta ) )
% 0.31/1.87 != ( none @ trm ) )
% 0.31/1.87 => ( ( uSubst95898992stappt @ Sigma
% 0.31/1.87 @ ( collect @ variable
% 0.31/1.87 @ ^ [X3: variable] : $true )
% 0.31/1.87 @ Theta )
% 0.31/1.87 != ( none @ trm ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_118_Geqo_Osimps_I3_J,axiom,
% 0.31/1.87 ! [V3: trm] :
% 0.31/1.87 ( ( uSubst1556497037e_Geqo @ ( some @ trm @ V3 ) @ ( none @ trm ) )
% 0.31/1.87 = ( none @ fml ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_119_Geqo_Oelims,axiom,
% 0.31/1.87 ! [X2: option @ trm,Xa: option @ trm,Y2: option @ fml] :
% 0.31/1.87 ( ( ( uSubst1556497037e_Geqo @ X2 @ Xa )
% 0.31/1.87 = Y2 )
% 0.31/1.87 => ( ! [Theta2: trm] :
% 0.31/1.87 ( ( X2
% 0.31/1.87 = ( some @ trm @ Theta2 ) )
% 0.31/1.87 => ! [Eta2: trm] :
% 0.31/1.87 ( ( Xa
% 0.31/1.87 = ( some @ trm @ Eta2 ) )
% 0.31/1.87 => ( Y2
% 0.31/1.87 != ( some @ fml @ ( geq @ Theta2 @ Eta2 ) ) ) ) )
% 0.31/1.87 => ( ( ( X2
% 0.31/1.87 = ( none @ trm ) )
% 0.31/1.87 => ( Y2
% 0.31/1.87 != ( none @ fml ) ) )
% 0.31/1.87 => ~ ( ? [V2: trm] :
% 0.31/1.87 ( X2
% 0.31/1.87 = ( some @ trm @ V2 ) )
% 0.31/1.87 => ( ( Xa
% 0.31/1.87 = ( none @ trm ) )
% 0.31/1.87 => ( Y2
% 0.31/1.87 != ( none @ fml ) ) ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_120_Differentialo_Opelims,axiom,
% 0.31/1.87 ! [X2: option @ trm,Y2: option @ trm] :
% 0.31/1.87 ( ( ( uSubst259074819ntialo @ X2 )
% 0.31/1.87 = Y2 )
% 0.31/1.87 => ( ( accp @ ( option @ trm ) @ uSubst99643830lo_rel @ X2 )
% 0.31/1.87 => ( ! [Theta2: trm] :
% 0.31/1.87 ( ( X2
% 0.31/1.87 = ( some @ trm @ Theta2 ) )
% 0.31/1.87 => ( ( Y2
% 0.31/1.87 = ( some @ trm @ ( differential @ Theta2 ) ) )
% 0.31/1.87 => ~ ( accp @ ( option @ trm ) @ uSubst99643830lo_rel @ ( some @ trm @ Theta2 ) ) ) )
% 0.31/1.87 => ~ ( ( X2
% 0.31/1.87 = ( none @ trm ) )
% 0.31/1.87 => ( ( Y2
% 0.31/1.87 = ( none @ trm ) )
% 0.31/1.87 => ~ ( accp @ ( option @ trm ) @ uSubst99643830lo_rel @ ( none @ trm ) ) ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_121_Powp__mono,axiom,
% 0.31/1.87 ! [A: $tType,A2: A > $o,B2: A > $o] :
% 0.31/1.87 ( ( ord_less_eq @ ( A > $o ) @ A2 @ B2 )
% 0.31/1.87 => ( ord_less_eq @ ( ( set @ A ) > $o ) @ ( powp @ A @ A2 ) @ ( powp @ A @ B2 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_122_Geqo_Osimps_I1_J,axiom,
% 0.31/1.87 ! [Theta: trm,Eta: trm] :
% 0.31/1.87 ( ( uSubst1556497037e_Geqo @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta ) )
% 0.31/1.87 = ( some @ fml @ ( geq @ Theta @ Eta ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_123_GreatestI2__order,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( order @ A )
% 0.31/1.87 => ! [P: A > $o,X2: A,Q: A > $o] :
% 0.31/1.87 ( ( P @ X2 )
% 0.31/1.87 => ( ! [Y4: A] :
% 0.31/1.87 ( ( P @ Y4 )
% 0.31/1.87 => ( ord_less_eq @ A @ Y4 @ X2 ) )
% 0.31/1.87 => ( ! [X: A] :
% 0.31/1.87 ( ( P @ X )
% 0.31/1.87 => ( ! [Y5: A] :
% 0.31/1.87 ( ( P @ Y5 )
% 0.31/1.87 => ( ord_less_eq @ A @ Y5 @ X ) )
% 0.31/1.87 => ( Q @ X ) ) )
% 0.31/1.87 => ( Q @ ( order_Greatest @ A @ P ) ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_124_Greatest__equality,axiom,
% 0.31/1.87 ! [A: $tType] :
% 0.31/1.87 ( ( order @ A )
% 0.31/1.87 => ! [P: A > $o,X2: A] :
% 0.31/1.87 ( ( P @ X2 )
% 0.31/1.87 => ( ! [Y4: A] :
% 0.31/1.87 ( ( P @ Y4 )
% 0.31/1.87 => ( ord_less_eq @ A @ Y4 @ X2 ) )
% 0.31/1.87 => ( ( order_Greatest @ A @ P )
% 0.31/1.87 = X2 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_125_Diamondo_Oinduct,axiom,
% 0.31/1.87 ! [P: ( option @ game ) > ( option @ fml ) > $o,A0: option @ game,A1: option @ fml] :
% 0.31/1.87 ( ! [Alpha: game,Phi2: fml] : ( P @ ( some @ game @ Alpha ) @ ( some @ fml @ Phi2 ) )
% 0.31/1.87 => ( ! [X_1: option @ fml] : ( P @ ( none @ game ) @ X_1 )
% 0.31/1.87 => ( ! [V2: game] : ( P @ ( some @ game @ V2 ) @ ( none @ fml ) )
% 0.31/1.87 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_126_Existso_Oinduct,axiom,
% 0.31/1.87 ! [P: variable > ( option @ fml ) > $o,A0: variable,A1: option @ fml] :
% 0.31/1.87 ( ! [X: variable,Phi2: fml] : ( P @ X @ ( some @ fml @ Phi2 ) )
% 0.31/1.87 => ( ! [X: variable] : ( P @ X @ ( none @ fml ) )
% 0.31/1.87 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_127_undeff__equiv,axiom,
% 0.31/1.87 ! [Phi: option @ fml] :
% 0.31/1.87 ( ( Phi
% 0.31/1.87 != ( none @ fml ) )
% 0.31/1.87 = ( ? [F2: fml] :
% 0.31/1.87 ( Phi
% 0.31/1.87 = ( some @ fml @ F2 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_128_Testo_Oinduct,axiom,
% 0.31/1.87 ! [P: ( option @ fml ) > $o,A0: option @ fml] :
% 0.31/1.87 ( ! [Phi2: fml] : ( P @ ( some @ fml @ Phi2 ) )
% 0.31/1.87 => ( ( P @ ( none @ fml ) )
% 0.31/1.87 => ( P @ A0 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_129_Testo_Ocases,axiom,
% 0.31/1.87 ! [X2: option @ fml] :
% 0.31/1.87 ( ! [Phi2: fml] :
% 0.31/1.87 ( X2
% 0.31/1.87 != ( some @ fml @ Phi2 ) )
% 0.31/1.87 => ( X2
% 0.31/1.87 = ( none @ fml ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_130_Ando_Oinduct,axiom,
% 0.31/1.87 ! [P: ( option @ fml ) > ( option @ fml ) > $o,A0: option @ fml,A1: option @ fml] :
% 0.31/1.87 ( ! [Phi2: fml,Psi: fml] : ( P @ ( some @ fml @ Phi2 ) @ ( some @ fml @ Psi ) )
% 0.31/1.87 => ( ! [X_1: option @ fml] : ( P @ ( none @ fml ) @ X_1 )
% 0.31/1.87 => ( ! [V2: fml] : ( P @ ( some @ fml @ V2 ) @ ( none @ fml ) )
% 0.31/1.87 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_131_accp__subset,axiom,
% 0.31/1.87 ! [A: $tType,R1: A > A > $o,R2: A > A > $o] :
% 0.31/1.87 ( ( ord_less_eq @ ( A > A > $o ) @ R1 @ R2 )
% 0.31/1.87 => ( ord_less_eq @ ( A > $o ) @ ( accp @ A @ R2 ) @ ( accp @ A @ R1 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_132_accp__subset__induct,axiom,
% 0.31/1.87 ! [A: $tType,D: A > $o,R: A > A > $o,X2: A,P: A > $o] :
% 0.31/1.87 ( ( ord_less_eq @ ( A > $o ) @ D @ ( accp @ A @ R ) )
% 0.31/1.87 => ( ! [X: A,Z4: A] :
% 0.31/1.87 ( ( D @ X )
% 0.31/1.87 => ( ( R @ Z4 @ X )
% 0.31/1.87 => ( D @ Z4 ) ) )
% 0.31/1.87 => ( ( D @ X2 )
% 0.31/1.87 => ( ! [X: A] :
% 0.31/1.87 ( ( D @ X )
% 0.31/1.87 => ( ! [Z5: A] :
% 0.31/1.87 ( ( R @ Z5 @ X )
% 0.31/1.87 => ( P @ Z5 ) )
% 0.31/1.87 => ( P @ X ) ) )
% 0.31/1.87 => ( P @ X2 ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_133_usubstappf__geqr,axiom,
% 0.31/1.87 ! [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] :
% 0.31/1.87 ( ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.31/1.87 != ( none @ fml ) )
% 0.31/1.87 => ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.31/1.87 = ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Eta ) ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_134_usubstappf__geq,axiom,
% 0.31/1.87 ! [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] :
% 0.31/1.87 ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.31/1.87 != ( none @ trm ) )
% 0.31/1.87 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Eta )
% 0.31/1.87 != ( none @ trm ) )
% 0.31/1.87 => ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.31/1.87 = ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Eta ) ) ) ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_135_predicate2I,axiom,
% 0.31/1.87 ! [B: $tType,A: $tType,P: A > B > $o,Q: A > B > $o] :
% 0.31/1.87 ( ! [X: A,Y4: B] :
% 0.31/1.87 ( ( P @ X @ Y4 )
% 0.31/1.87 => ( Q @ X @ Y4 ) )
% 0.31/1.87 => ( ord_less_eq @ ( A > B > $o ) @ P @ Q ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_136_option_Ocollapse,axiom,
% 0.31/1.87 ! [A: $tType,Option: option @ A] :
% 0.31/1.87 ( ( Option
% 0.31/1.87 != ( none @ A ) )
% 0.31/1.87 => ( ( some @ A @ ( the @ A @ Option ) )
% 0.31/1.87 = Option ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_137_predicate2D,axiom,
% 0.31/1.87 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,X2: A,Y2: B] :
% 0.31/1.87 ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 0.31/1.87 => ( ( P @ X2 @ Y2 )
% 0.31/1.87 => ( Q @ X2 @ Y2 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_138_rev__predicate2D,axiom,
% 0.31/1.87 ! [A: $tType,B: $tType,P: A > B > $o,X2: A,Y2: B,Q: A > B > $o] :
% 0.31/1.87 ( ( P @ X2 @ Y2 )
% 0.31/1.87 => ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 0.31/1.87 => ( Q @ X2 @ Y2 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_139_Composeo_Oinduct,axiom,
% 0.31/1.87 ! [P: ( option @ game ) > ( option @ game ) > $o,A0: option @ game,A1: option @ game] :
% 0.31/1.87 ( ! [Alpha: game,Beta: game] : ( P @ ( some @ game @ Alpha ) @ ( some @ game @ Beta ) )
% 0.31/1.87 => ( ! [Alpha: option @ game] : ( P @ Alpha @ ( none @ game ) )
% 0.31/1.87 => ( ! [V2: game] : ( P @ ( none @ game ) @ ( some @ game @ V2 ) )
% 0.31/1.87 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_140_undefg__equiv,axiom,
% 0.31/1.87 ! [Alpha2: option @ game] :
% 0.31/1.87 ( ( Alpha2
% 0.31/1.87 != ( none @ game ) )
% 0.31/1.87 = ( ? [G2: game] :
% 0.31/1.87 ( Alpha2
% 0.31/1.87 = ( some @ game @ G2 ) ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_141_Loopo_Oinduct,axiom,
% 0.31/1.87 ! [P: ( option @ game ) > $o,A0: option @ game] :
% 0.31/1.87 ( ! [Alpha: game] : ( P @ ( some @ game @ Alpha ) )
% 0.31/1.87 => ( ( P @ ( none @ game ) )
% 0.31/1.87 => ( P @ A0 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_142_Loopo_Ocases,axiom,
% 0.31/1.87 ! [X2: option @ game] :
% 0.31/1.87 ( ! [Alpha: game] :
% 0.31/1.87 ( X2
% 0.31/1.87 != ( some @ game @ Alpha ) )
% 0.31/1.87 => ( X2
% 0.31/1.87 = ( none @ game ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_143_option_Oexpand,axiom,
% 0.31/1.87 ! [A: $tType,Option: option @ A,Option2: option @ A] :
% 0.31/1.87 ( ( ( Option
% 0.31/1.87 = ( none @ A ) )
% 0.31/1.87 = ( Option2
% 0.31/1.87 = ( none @ A ) ) )
% 0.31/1.87 => ( ( ( Option
% 0.31/1.87 != ( none @ A ) )
% 0.31/1.87 => ( ( Option2
% 0.31/1.87 != ( none @ A ) )
% 0.31/1.87 => ( ( the @ A @ Option )
% 0.31/1.87 = ( the @ A @ Option2 ) ) ) )
% 0.31/1.87 => ( Option = Option2 ) ) ) ).
% 0.31/1.87
% 0.31/1.87 thf(fact_144_option_Osel,axiom,
% 0.31/1.88 ! [A: $tType,X23: A] :
% 0.31/1.88 ( ( the @ A @ ( some @ A @ X23 ) )
% 0.31/1.88 = X23 ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_145_option_Oexhaust__sel,axiom,
% 0.31/1.88 ! [A: $tType,Option: option @ A] :
% 0.31/1.88 ( ( Option
% 0.31/1.88 != ( none @ A ) )
% 0.31/1.88 => ( Option
% 0.31/1.88 = ( some @ A @ ( the @ A @ Option ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_146_accp_Ocases,axiom,
% 0.31/1.88 ! [A: $tType,R3: A > A > $o,A4: A] :
% 0.31/1.88 ( ( accp @ A @ R3 @ A4 )
% 0.31/1.88 => ! [Y5: A] :
% 0.31/1.88 ( ( R3 @ Y5 @ A4 )
% 0.31/1.88 => ( accp @ A @ R3 @ Y5 ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_147_accp_Osimps,axiom,
% 0.31/1.88 ! [A: $tType] :
% 0.31/1.88 ( ( accp @ A )
% 0.31/1.88 = ( ^ [R4: A > A > $o,A5: A] :
% 0.31/1.88 ? [X3: A] :
% 0.31/1.88 ( ( A5 = X3 )
% 0.31/1.88 & ! [Y3: A] :
% 0.31/1.88 ( ( R4 @ Y3 @ X3 )
% 0.31/1.88 => ( accp @ A @ R4 @ Y3 ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_148_accp_Ointros,axiom,
% 0.31/1.88 ! [A: $tType,R3: A > A > $o,X2: A] :
% 0.31/1.88 ( ! [Y4: A] :
% 0.31/1.88 ( ( R3 @ Y4 @ X2 )
% 0.31/1.88 => ( accp @ A @ R3 @ Y4 ) )
% 0.31/1.88 => ( accp @ A @ R3 @ X2 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_149_accp__induct,axiom,
% 0.31/1.88 ! [A: $tType,R3: A > A > $o,A4: A,P: A > $o] :
% 0.31/1.88 ( ( accp @ A @ R3 @ A4 )
% 0.31/1.88 => ( ! [X: A] :
% 0.31/1.88 ( ( accp @ A @ R3 @ X )
% 0.31/1.88 => ( ! [Y5: A] :
% 0.31/1.88 ( ( R3 @ Y5 @ X )
% 0.31/1.88 => ( P @ Y5 ) )
% 0.31/1.88 => ( P @ X ) ) )
% 0.31/1.88 => ( P @ A4 ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_150_accp_Oinducts,axiom,
% 0.31/1.88 ! [A: $tType,R3: A > A > $o,X2: A,P: A > $o] :
% 0.31/1.88 ( ( accp @ A @ R3 @ X2 )
% 0.31/1.88 => ( ! [X: A] :
% 0.31/1.88 ( ! [Y5: A] :
% 0.31/1.88 ( ( R3 @ Y5 @ X )
% 0.31/1.88 => ( accp @ A @ R3 @ Y5 ) )
% 0.31/1.88 => ( ! [Y5: A] :
% 0.31/1.88 ( ( R3 @ Y5 @ X )
% 0.31/1.88 => ( P @ Y5 ) )
% 0.31/1.88 => ( P @ X ) ) )
% 0.31/1.88 => ( P @ X2 ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_151_accp__downward,axiom,
% 0.31/1.88 ! [A: $tType,R3: A > A > $o,B4: A,A4: A] :
% 0.31/1.88 ( ( accp @ A @ R3 @ B4 )
% 0.31/1.88 => ( ( R3 @ A4 @ B4 )
% 0.31/1.88 => ( accp @ A @ R3 @ A4 ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_152_not__accp__down,axiom,
% 0.31/1.88 ! [A: $tType,R: A > A > $o,X2: A] :
% 0.31/1.88 ( ~ ( accp @ A @ R @ X2 )
% 0.31/1.88 => ~ ! [Z4: A] :
% 0.31/1.88 ( ( R @ Z4 @ X2 )
% 0.31/1.88 => ( accp @ A @ R @ Z4 ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_153_accp__induct__rule,axiom,
% 0.31/1.88 ! [A: $tType,R3: A > A > $o,A4: A,P: A > $o] :
% 0.31/1.88 ( ( accp @ A @ R3 @ A4 )
% 0.31/1.88 => ( ! [X: A] :
% 0.31/1.88 ( ( accp @ A @ R3 @ X )
% 0.31/1.88 => ( ! [Y5: A] :
% 0.31/1.88 ( ( R3 @ Y5 @ X )
% 0.31/1.88 => ( P @ Y5 ) )
% 0.31/1.88 => ( P @ X ) ) )
% 0.31/1.88 => ( P @ A4 ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_154_eq__subset,axiom,
% 0.31/1.88 ! [A: $tType,P: A > A > $o] :
% 0.31/1.88 ( ord_less_eq @ ( A > A > $o )
% 0.31/1.88 @ ^ [Y: A,Z: A] : ( Y = Z )
% 0.31/1.88 @ ^ [A5: A,B5: A] :
% 0.31/1.88 ( ( P @ A5 @ B5 )
% 0.31/1.88 | ( A5 = B5 ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_155_Geqo_Opelims,axiom,
% 0.31/1.88 ! [X2: option @ trm,Xa: option @ trm,Y2: option @ fml] :
% 0.31/1.88 ( ( ( uSubst1556497037e_Geqo @ X2 @ Xa )
% 0.31/1.88 = Y2 )
% 0.31/1.88 => ( ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst864323244qo_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ X2 @ Xa ) )
% 0.31/1.88 => ( ! [Theta2: trm] :
% 0.31/1.88 ( ( X2
% 0.31/1.88 = ( some @ trm @ Theta2 ) )
% 0.31/1.88 => ! [Eta2: trm] :
% 0.31/1.88 ( ( Xa
% 0.31/1.88 = ( some @ trm @ Eta2 ) )
% 0.31/1.88 => ( ( Y2
% 0.31/1.88 = ( some @ fml @ ( geq @ Theta2 @ Eta2 ) ) )
% 0.31/1.88 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst864323244qo_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta2 ) ) ) ) ) )
% 0.31/1.88 => ( ( ( X2
% 0.31/1.88 = ( none @ trm ) )
% 0.31/1.88 => ( ( Y2
% 0.31/1.88 = ( none @ fml ) )
% 0.31/1.88 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst864323244qo_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( none @ trm ) @ Xa ) ) ) )
% 0.31/1.88 => ~ ! [V2: trm] :
% 0.31/1.88 ( ( X2
% 0.31/1.88 = ( some @ trm @ V2 ) )
% 0.31/1.88 => ( ( Xa
% 0.31/1.88 = ( none @ trm ) )
% 0.31/1.88 => ( ( Y2
% 0.31/1.88 = ( none @ fml ) )
% 0.31/1.88 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst864323244qo_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ V2 ) @ ( none @ trm ) ) ) ) ) ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_156_Diamondo_Ocases,axiom,
% 0.31/1.88 ! [X2: product_prod @ ( option @ game ) @ ( option @ fml )] :
% 0.31/1.88 ( ! [Alpha: game,Phi2: fml] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ Alpha ) @ ( some @ fml @ Phi2 ) ) )
% 0.31/1.88 => ( ! [Phi2: option @ fml] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( none @ game ) @ Phi2 ) )
% 0.31/1.88 => ~ ! [V2: game] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ V2 ) @ ( none @ fml ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_157_option_Osplit__sel,axiom,
% 0.31/1.88 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 0.31/1.88 ( ( P @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 0.31/1.88 = ( ( ( Option
% 0.31/1.88 = ( none @ A ) )
% 0.31/1.88 => ( P @ F1 ) )
% 0.31/1.88 & ( ( Option
% 0.31/1.88 = ( some @ A @ ( the @ A @ Option ) ) )
% 0.31/1.88 => ( P @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_158_subrelI,axiom,
% 0.31/1.88 ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),S2: set @ ( product_prod @ A @ B )] :
% 0.31/1.88 ( ! [X: A,Y4: B] :
% 0.31/1.88 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y4 ) @ R3 )
% 0.31/1.88 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y4 ) @ S2 ) )
% 0.31/1.88 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R3 @ S2 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_159_ssubst__Pair__rhs,axiom,
% 0.31/1.88 ! [B: $tType,A: $tType,R3: A,S2: B,R: set @ ( product_prod @ A @ B ),S3: B] :
% 0.31/1.88 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S2 ) @ R )
% 0.31/1.88 => ( ( S3 = S2 )
% 0.31/1.88 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S3 ) @ R ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_160_pred__equals__eq2,axiom,
% 0.31/1.88 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.31/1.88 ( ( ( ^ [X3: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ R ) )
% 0.31/1.88 = ( ^ [X3: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ S ) ) )
% 0.31/1.88 = ( R = S ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_161_option_Ocase__distrib,axiom,
% 0.31/1.88 ! [C: $tType,B: $tType,A: $tType,H: B > C,F1: B,F22: A > B,Option: option @ A] :
% 0.31/1.88 ( ( H @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 0.31/1.88 = ( case_option @ C @ A @ ( H @ F1 )
% 0.31/1.88 @ ^ [X3: A] : ( H @ ( F22 @ X3 ) )
% 0.31/1.88 @ Option ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_162_option_Osimps_I4_J,axiom,
% 0.31/1.88 ! [A: $tType,B: $tType,F1: B,F22: A > B] :
% 0.31/1.88 ( ( case_option @ B @ A @ F1 @ F22 @ ( none @ A ) )
% 0.31/1.88 = F1 ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_163_pred__subset__eq2,axiom,
% 0.31/1.88 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.31/1.88 ( ( ord_less_eq @ ( A > B > $o )
% 0.31/1.88 @ ^ [X3: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ R )
% 0.31/1.88 @ ^ [X3: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ S ) )
% 0.31/1.88 = ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R @ S ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_164_option_Osimps_I5_J,axiom,
% 0.31/1.88 ! [B: $tType,A: $tType,F1: B,F22: A > B,X23: A] :
% 0.31/1.88 ( ( case_option @ B @ A @ F1 @ F22 @ ( some @ A @ X23 ) )
% 0.31/1.88 = ( F22 @ X23 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_165_option_Odisc__eq__case_I1_J,axiom,
% 0.31/1.88 ! [A: $tType,Option: option @ A] :
% 0.31/1.88 ( ( Option
% 0.31/1.88 = ( none @ A ) )
% 0.31/1.88 = ( case_option @ $o @ A @ $true
% 0.31/1.88 @ ^ [Uu: A] : $false
% 0.31/1.88 @ Option ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_166_option_Odisc__eq__case_I2_J,axiom,
% 0.31/1.88 ! [A: $tType,Option: option @ A] :
% 0.31/1.88 ( ( Option
% 0.31/1.88 != ( none @ A ) )
% 0.31/1.88 = ( case_option @ $o @ A @ $false
% 0.31/1.88 @ ^ [Uu: A] : $true
% 0.31/1.88 @ Option ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_167_Timeso_Ocases,axiom,
% 0.31/1.88 ! [X2: product_prod @ ( option @ trm ) @ ( option @ trm )] :
% 0.31/1.88 ( ! [Theta2: trm,Eta2: trm] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta2 ) ) )
% 0.31/1.88 => ( ! [Eta2: option @ trm] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( none @ trm ) @ Eta2 ) )
% 0.31/1.88 => ~ ! [V2: trm] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ V2 ) @ ( none @ trm ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_168_case__optionE,axiom,
% 0.31/1.88 ! [A: $tType,P: $o,Q: A > $o,X2: option @ A] :
% 0.31/1.88 ( ( case_option @ $o @ A @ P @ Q @ X2 )
% 0.31/1.88 => ( ( ( X2
% 0.31/1.88 = ( none @ A ) )
% 0.31/1.88 => ~ P )
% 0.31/1.88 => ~ ! [Y4: A] :
% 0.31/1.88 ( ( X2
% 0.31/1.88 = ( some @ A @ Y4 ) )
% 0.31/1.88 => ~ ( Q @ Y4 ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_169_option_Ocase__eq__if,axiom,
% 0.31/1.88 ! [A: $tType,B: $tType] :
% 0.31/1.88 ( ( case_option @ B @ A )
% 0.31/1.88 = ( ^ [F12: B,F23: A > B,Option3: option @ A] :
% 0.31/1.88 ( if @ B
% 0.31/1.88 @ ( Option3
% 0.31/1.88 = ( none @ A ) )
% 0.31/1.88 @ F12
% 0.31/1.88 @ ( F23 @ ( the @ A @ Option3 ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_170_predicate2D__conj,axiom,
% 0.31/1.88 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,R: $o,X2: A,Y2: B] :
% 0.31/1.88 ( ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 0.31/1.88 & R )
% 0.31/1.88 => ( R
% 0.31/1.88 & ( ( P @ X2 @ Y2 )
% 0.31/1.88 => ( Q @ X2 @ Y2 ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_171_option_Osplit__sel__asm,axiom,
% 0.31/1.88 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 0.31/1.88 ( ( P @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 0.31/1.88 = ( ~ ( ( ( Option
% 0.31/1.88 = ( none @ A ) )
% 0.31/1.88 & ~ ( P @ F1 ) )
% 0.31/1.88 | ( ( Option
% 0.31/1.88 = ( some @ A @ ( the @ A @ Option ) ) )
% 0.31/1.88 & ~ ( P @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_172_Timeso_Opelims,axiom,
% 0.31/1.88 ! [X2: option @ trm,Xa: option @ trm,Y2: option @ trm] :
% 0.31/1.88 ( ( ( uSubst277968634Timeso @ X2 @ Xa )
% 0.31/1.88 = Y2 )
% 0.31/1.88 => ( ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst1377811071so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ X2 @ Xa ) )
% 0.31/1.88 => ( ! [Theta2: trm] :
% 0.31/1.88 ( ( X2
% 0.31/1.88 = ( some @ trm @ Theta2 ) )
% 0.31/1.88 => ! [Eta2: trm] :
% 0.31/1.88 ( ( Xa
% 0.31/1.88 = ( some @ trm @ Eta2 ) )
% 0.31/1.88 => ( ( Y2
% 0.31/1.88 = ( some @ trm @ ( times @ Theta2 @ Eta2 ) ) )
% 0.31/1.88 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst1377811071so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta2 ) ) ) ) ) )
% 0.31/1.88 => ( ( ( X2
% 0.31/1.88 = ( none @ trm ) )
% 0.31/1.88 => ( ( Y2
% 0.31/1.88 = ( none @ trm ) )
% 0.31/1.88 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst1377811071so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( none @ trm ) @ Xa ) ) ) )
% 0.31/1.88 => ~ ! [V2: trm] :
% 0.31/1.88 ( ( X2
% 0.31/1.88 = ( some @ trm @ V2 ) )
% 0.31/1.88 => ( ( Xa
% 0.31/1.88 = ( none @ trm ) )
% 0.31/1.88 => ( ( Y2
% 0.31/1.88 = ( none @ trm ) )
% 0.31/1.88 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst1377811071so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ V2 ) @ ( none @ trm ) ) ) ) ) ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_173_Pluso_Opelims,axiom,
% 0.31/1.88 ! [X2: option @ trm,Xa: option @ trm,Y2: option @ trm] :
% 0.31/1.88 ( ( ( uSubst1112714340_Pluso @ X2 @ Xa )
% 0.31/1.88 = Y2 )
% 0.31/1.88 => ( ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst270600597so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ X2 @ Xa ) )
% 0.31/1.88 => ( ! [Theta2: trm] :
% 0.31/1.88 ( ( X2
% 0.31/1.88 = ( some @ trm @ Theta2 ) )
% 0.31/1.88 => ! [Eta2: trm] :
% 0.31/1.88 ( ( Xa
% 0.31/1.88 = ( some @ trm @ Eta2 ) )
% 0.31/1.88 => ( ( Y2
% 0.31/1.88 = ( some @ trm @ ( plus @ Theta2 @ Eta2 ) ) )
% 0.31/1.88 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst270600597so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta2 ) ) ) ) ) )
% 0.31/1.88 => ( ( ( X2
% 0.31/1.88 = ( none @ trm ) )
% 0.31/1.88 => ( ( Y2
% 0.31/1.88 = ( none @ trm ) )
% 0.31/1.88 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst270600597so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( none @ trm ) @ Xa ) ) ) )
% 0.31/1.88 => ~ ! [V2: trm] :
% 0.31/1.88 ( ( X2
% 0.31/1.88 = ( some @ trm @ V2 ) )
% 0.31/1.88 => ( ( Xa
% 0.31/1.88 = ( none @ trm ) )
% 0.31/1.88 => ( ( Y2
% 0.31/1.88 = ( none @ trm ) )
% 0.31/1.88 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst270600597so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ V2 ) @ ( none @ trm ) ) ) ) ) ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_174_disjE__realizer2,axiom,
% 0.31/1.88 ! [B: $tType,A: $tType,P: $o,Q: A > $o,X2: option @ A,R: B > $o,F: B,G: A > B] :
% 0.31/1.88 ( ( case_option @ $o @ A @ P @ Q @ X2 )
% 0.31/1.88 => ( ( P
% 0.31/1.88 => ( R @ F ) )
% 0.31/1.88 => ( ! [Q2: A] :
% 0.31/1.88 ( ( Q @ Q2 )
% 0.31/1.88 => ( R @ ( G @ Q2 ) ) )
% 0.31/1.88 => ( R @ ( case_option @ B @ A @ F @ G @ X2 ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_175_ODEo_Ocases,axiom,
% 0.31/1.88 ! [X2: product_prod @ char @ ( option @ trm )] :
% 0.31/1.88 ( ! [X: char,Theta2: trm] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ char @ ( option @ trm ) @ X @ ( some @ trm @ Theta2 ) ) )
% 0.31/1.88 => ~ ! [X: char] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ char @ ( option @ trm ) @ X @ ( none @ trm ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_176_Assigno_Ocases,axiom,
% 0.31/1.88 ! [X2: product_prod @ variable @ ( option @ trm )] :
% 0.31/1.88 ( ! [X: variable,Theta2: trm] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ variable @ ( option @ trm ) @ X @ ( some @ trm @ Theta2 ) ) )
% 0.31/1.88 => ~ ! [X: variable] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ variable @ ( option @ trm ) @ X @ ( none @ trm ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_177_Composeo_Ocases,axiom,
% 0.31/1.88 ! [X2: product_prod @ ( option @ game ) @ ( option @ game )] :
% 0.31/1.88 ( ! [Alpha: game,Beta: game] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ ( some @ game @ Alpha ) @ ( some @ game @ Beta ) ) )
% 0.31/1.88 => ( ! [Alpha: option @ game] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ Alpha @ ( none @ game ) ) )
% 0.31/1.88 => ~ ! [V2: game] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ ( none @ game ) @ ( some @ game @ V2 ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_178_Existso_Ocases,axiom,
% 0.31/1.88 ! [X2: product_prod @ variable @ ( option @ fml )] :
% 0.31/1.88 ( ! [X: variable,Phi2: fml] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ variable @ ( option @ fml ) @ X @ ( some @ fml @ Phi2 ) ) )
% 0.31/1.88 => ~ ! [X: variable] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ variable @ ( option @ fml ) @ X @ ( none @ fml ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_179_Ando_Ocases,axiom,
% 0.31/1.88 ! [X2: product_prod @ ( option @ fml ) @ ( option @ fml )] :
% 0.31/1.88 ( ! [Phi2: fml,Psi: fml] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ ( option @ fml ) @ ( option @ fml ) @ ( some @ fml @ Phi2 ) @ ( some @ fml @ Psi ) ) )
% 0.31/1.88 => ( ! [Psi: option @ fml] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ ( option @ fml ) @ ( option @ fml ) @ ( none @ fml ) @ Psi ) )
% 0.31/1.88 => ~ ! [V2: fml] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ ( option @ fml ) @ ( option @ fml ) @ ( some @ fml @ V2 ) @ ( none @ fml ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_180_usubstappt_Opsimps_I7_J,axiom,
% 0.31/1.88 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm] :
% 0.31/1.88 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( differential @ Theta ) ) ) )
% 0.31/1.88 => ( ( uSubst95898992stappt @ Sigma @ U @ ( differential @ Theta ) )
% 0.31/1.88 = ( uSubst259074819ntialo
% 0.31/1.88 @ ( uSubst95898992stappt @ Sigma
% 0.31/1.88 @ ( collect @ variable
% 0.31/1.88 @ ^ [X3: variable] : $true )
% 0.31/1.88 @ Theta ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_181_usubstappt_Opsimps_I6_J,axiom,
% 0.31/1.88 ! [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] :
% 0.31/1.88 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( times @ Theta @ Eta ) ) ) )
% 0.31/1.88 => ( ( uSubst95898992stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 0.31/1.88 = ( uSubst277968634Timeso @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) @ ( uSubst95898992stappt @ Sigma @ U @ Eta ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_182_usubstappt_Opsimps_I5_J,axiom,
% 0.31/1.88 ! [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] :
% 0.31/1.88 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( plus @ Theta @ Eta ) ) ) )
% 0.31/1.88 => ( ( uSubst95898992stappt @ Sigma @ U @ ( plus @ Theta @ Eta ) )
% 0.31/1.88 = ( uSubst1112714340_Pluso @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) @ ( uSubst95898992stappt @ Sigma @ U @ Eta ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_183_usubstappt_Opsimps_I1_J,axiom,
% 0.31/1.88 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,X2: variable] :
% 0.31/1.88 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( var @ X2 ) ) ) )
% 0.31/1.88 => ( ( uSubst95898992stappt @ Sigma @ U @ ( var @ X2 ) )
% 0.31/1.88 = ( some @ trm @ ( var @ X2 ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_184_usubstappt_Opsimps_I2_J,axiom,
% 0.31/1.88 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,R3: real] :
% 0.31/1.88 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( number @ R3 ) ) ) )
% 0.31/1.88 => ( ( uSubst95898992stappt @ Sigma @ U @ ( number @ R3 ) )
% 0.31/1.88 = ( some @ trm @ ( number @ R3 ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_185_in__lex__prod,axiom,
% 0.31/1.88 ! [A: $tType,B: $tType,A4: A,B4: B,A7: A,B7: B,R3: set @ ( product_prod @ A @ A ),S2: set @ ( product_prod @ B @ B )] :
% 0.31/1.88 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A4 @ B4 ) @ ( product_Pair @ A @ B @ A7 @ B7 ) ) @ ( lex_prod @ A @ B @ R3 @ S2 ) )
% 0.31/1.88 = ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A4 @ A7 ) @ R3 )
% 0.31/1.88 | ( ( A4 = A7 )
% 0.31/1.88 & ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ B4 @ B7 ) @ S2 ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_186_trm_Oinject_I2_J,axiom,
% 0.31/1.88 ! [X23: real,Y23: real] :
% 0.31/1.88 ( ( ( number @ X23 )
% 0.31/1.88 = ( number @ Y23 ) )
% 0.31/1.88 = ( X23 = Y23 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_187_trm_Oinject_I1_J,axiom,
% 0.31/1.88 ! [X1: variable,Y1: variable] :
% 0.31/1.88 ( ( ( var @ X1 )
% 0.31/1.88 = ( var @ Y1 ) )
% 0.31/1.88 = ( X1 = Y1 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_188_trm_Odistinct_I17_J,axiom,
% 0.31/1.88 ! [X23: real,X51: trm,X52: trm] :
% 0.31/1.88 ( ( number @ X23 )
% 0.31/1.88 != ( plus @ X51 @ X52 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_189_trm_Odistinct_I19_J,axiom,
% 0.31/1.88 ! [X23: real,X61: trm,X62: trm] :
% 0.31/1.88 ( ( number @ X23 )
% 0.31/1.88 != ( times @ X61 @ X62 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_190_trm_Odistinct_I21_J,axiom,
% 0.31/1.88 ! [X23: real,X7: trm] :
% 0.31/1.88 ( ( number @ X23 )
% 0.31/1.88 != ( differential @ X7 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_191_trm_Odistinct_I7_J,axiom,
% 0.31/1.88 ! [X1: variable,X51: trm,X52: trm] :
% 0.31/1.88 ( ( var @ X1 )
% 0.31/1.88 != ( plus @ X51 @ X52 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_192_trm_Odistinct_I9_J,axiom,
% 0.31/1.88 ! [X1: variable,X61: trm,X62: trm] :
% 0.31/1.88 ( ( var @ X1 )
% 0.31/1.88 != ( times @ X61 @ X62 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_193_trm_Odistinct_I11_J,axiom,
% 0.31/1.88 ! [X1: variable,X7: trm] :
% 0.31/1.88 ( ( var @ X1 )
% 0.31/1.88 != ( differential @ X7 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_194_trm_Odistinct_I1_J,axiom,
% 0.31/1.88 ! [X1: variable,X23: real] :
% 0.31/1.88 ( ( var @ X1 )
% 0.31/1.88 != ( number @ X23 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_195_usubstappt_Osimps_I2_J,axiom,
% 0.31/1.88 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,R3: real] :
% 0.31/1.88 ( ( uSubst95898992stappt @ Sigma @ U @ ( number @ R3 ) )
% 0.31/1.88 = ( some @ trm @ ( number @ R3 ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_196_usubstappt_Osimps_I1_J,axiom,
% 0.31/1.88 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,X2: variable] :
% 0.31/1.88 ( ( uSubst95898992stappt @ Sigma @ U @ ( var @ X2 ) )
% 0.31/1.88 = ( some @ trm @ ( var @ X2 ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_197_usubstappt_Ocases,axiom,
% 0.31/1.88 ! [X2: product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm )] :
% 0.31/1.88 ( ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,X: variable] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( var @ X ) ) ) )
% 0.31/1.88 => ( ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,R5: real] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( number @ R5 ) ) ) )
% 0.31/1.88 => ( ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F3: char] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( const @ F3 ) ) ) )
% 0.31/1.88 => ( ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F3: char,Theta2: trm] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( func @ F3 @ Theta2 ) ) ) )
% 0.31/1.88 => ( ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm,Eta2: trm] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( plus @ Theta2 @ Eta2 ) ) ) )
% 0.31/1.88 => ( ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm,Eta2: trm] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( times @ Theta2 @ Eta2 ) ) ) )
% 0.31/1.88 => ~ ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( differential @ Theta2 ) ) ) ) ) ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_198_Testo_Osimps_I2_J,axiom,
% 0.31/1.88 ( ( uSubst190403692_Testo @ ( none @ fml ) )
% 0.31/1.88 = ( none @ game ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_199_Testo__undef,axiom,
% 0.31/1.88 ! [Phi: option @ fml] :
% 0.31/1.88 ( ( ( uSubst190403692_Testo @ Phi )
% 0.31/1.88 = ( none @ game ) )
% 0.31/1.88 = ( Phi
% 0.31/1.88 = ( none @ fml ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_200_trm_Oinject_I4_J,axiom,
% 0.31/1.88 ! [X41: char,X42: trm,Y41: char,Y42: trm] :
% 0.31/1.88 ( ( ( func @ X41 @ X42 )
% 0.31/1.88 = ( func @ Y41 @ Y42 ) )
% 0.31/1.88 = ( ( X41 = Y41 )
% 0.31/1.88 & ( X42 = Y42 ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_201_trm_Oinject_I3_J,axiom,
% 0.31/1.88 ! [X32: char,Y32: char] :
% 0.31/1.88 ( ( ( const @ X32 )
% 0.31/1.88 = ( const @ Y32 ) )
% 0.31/1.88 = ( X32 = Y32 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_202_trm_Odistinct_I3_J,axiom,
% 0.31/1.88 ! [X1: variable,X32: char] :
% 0.31/1.88 ( ( var @ X1 )
% 0.31/1.88 != ( const @ X32 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_203_trm_Odistinct_I5_J,axiom,
% 0.31/1.88 ! [X1: variable,X41: char,X42: trm] :
% 0.31/1.88 ( ( var @ X1 )
% 0.31/1.88 != ( func @ X41 @ X42 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_204_trm_Odistinct_I13_J,axiom,
% 0.31/1.88 ! [X23: real,X32: char] :
% 0.31/1.88 ( ( number @ X23 )
% 0.31/1.88 != ( const @ X32 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_205_trm_Odistinct_I15_J,axiom,
% 0.31/1.88 ! [X23: real,X41: char,X42: trm] :
% 0.31/1.88 ( ( number @ X23 )
% 0.31/1.88 != ( func @ X41 @ X42 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_206_trm_Odistinct_I23_J,axiom,
% 0.31/1.88 ! [X32: char,X41: char,X42: trm] :
% 0.31/1.88 ( ( const @ X32 )
% 0.31/1.88 != ( func @ X41 @ X42 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_207_trm_Odistinct_I29_J,axiom,
% 0.31/1.88 ! [X32: char,X7: trm] :
% 0.31/1.88 ( ( const @ X32 )
% 0.31/1.88 != ( differential @ X7 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_208_trm_Odistinct_I27_J,axiom,
% 0.31/1.88 ! [X32: char,X61: trm,X62: trm] :
% 0.31/1.88 ( ( const @ X32 )
% 0.31/1.88 != ( times @ X61 @ X62 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_209_trm_Odistinct_I25_J,axiom,
% 0.31/1.88 ! [X32: char,X51: trm,X52: trm] :
% 0.31/1.88 ( ( const @ X32 )
% 0.31/1.88 != ( plus @ X51 @ X52 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_210_trm_Odistinct_I35_J,axiom,
% 0.31/1.88 ! [X41: char,X42: trm,X7: trm] :
% 0.31/1.88 ( ( func @ X41 @ X42 )
% 0.31/1.88 != ( differential @ X7 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_211_trm_Odistinct_I33_J,axiom,
% 0.31/1.88 ! [X41: char,X42: trm,X61: trm,X62: trm] :
% 0.31/1.88 ( ( func @ X41 @ X42 )
% 0.31/1.88 != ( times @ X61 @ X62 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_212_trm_Odistinct_I31_J,axiom,
% 0.31/1.88 ! [X41: char,X42: trm,X51: trm,X52: trm] :
% 0.31/1.88 ( ( func @ X41 @ X42 )
% 0.31/1.88 != ( plus @ X51 @ X52 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_213_trm_Oinduct,axiom,
% 0.31/1.88 ! [P: trm > $o,Trm: trm] :
% 0.31/1.88 ( ! [X: variable] : ( P @ ( var @ X ) )
% 0.31/1.88 => ( ! [X: real] : ( P @ ( number @ X ) )
% 0.31/1.88 => ( ! [X: char] : ( P @ ( const @ X ) )
% 0.31/1.88 => ( ! [X1a: char,X2a: trm] :
% 0.31/1.88 ( ( P @ X2a )
% 0.31/1.88 => ( P @ ( func @ X1a @ X2a ) ) )
% 0.31/1.88 => ( ! [X1a: trm,X2a: trm] :
% 0.31/1.88 ( ( P @ X1a )
% 0.31/1.88 => ( ( P @ X2a )
% 0.31/1.88 => ( P @ ( plus @ X1a @ X2a ) ) ) )
% 0.31/1.88 => ( ! [X1a: trm,X2a: trm] :
% 0.31/1.88 ( ( P @ X1a )
% 0.31/1.88 => ( ( P @ X2a )
% 0.31/1.88 => ( P @ ( times @ X1a @ X2a ) ) ) )
% 0.31/1.88 => ( ! [X: trm] :
% 0.31/1.88 ( ( P @ X )
% 0.31/1.88 => ( P @ ( differential @ X ) ) )
% 0.31/1.88 => ( P @ Trm ) ) ) ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_214_trm_Oexhaust,axiom,
% 0.31/1.88 ! [Y2: trm] :
% 0.31/1.88 ( ! [X12: variable] :
% 0.31/1.88 ( Y2
% 0.31/1.88 != ( var @ X12 ) )
% 0.31/1.88 => ( ! [X24: real] :
% 0.31/1.88 ( Y2
% 0.31/1.88 != ( number @ X24 ) )
% 0.31/1.88 => ( ! [X33: char] :
% 0.31/1.88 ( Y2
% 0.31/1.88 != ( const @ X33 ) )
% 0.31/1.88 => ( ! [X412: char,X422: trm] :
% 0.31/1.88 ( Y2
% 0.31/1.88 != ( func @ X412 @ X422 ) )
% 0.31/1.88 => ( ! [X512: trm,X522: trm] :
% 0.31/1.88 ( Y2
% 0.31/1.88 != ( plus @ X512 @ X522 ) )
% 0.31/1.88 => ( ! [X612: trm,X622: trm] :
% 0.31/1.88 ( Y2
% 0.31/1.88 != ( times @ X612 @ X622 ) )
% 0.31/1.88 => ~ ! [X72: trm] :
% 0.31/1.88 ( Y2
% 0.31/1.88 != ( differential @ X72 ) ) ) ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_215_term__sem_Ocases,axiom,
% 0.31/1.88 ! [X2: product_prod @ denotational_interp @ trm] :
% 0.31/1.88 ( ! [I2: denotational_interp,X: variable] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ denotational_interp @ trm @ I2 @ ( var @ X ) ) )
% 0.31/1.88 => ( ! [I2: denotational_interp,R5: real] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ denotational_interp @ trm @ I2 @ ( number @ R5 ) ) )
% 0.31/1.88 => ( ! [I2: denotational_interp,F3: char] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ denotational_interp @ trm @ I2 @ ( const @ F3 ) ) )
% 0.31/1.88 => ( ! [I2: denotational_interp,F3: char,Theta2: trm] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ denotational_interp @ trm @ I2 @ ( func @ F3 @ Theta2 ) ) )
% 0.31/1.88 => ( ! [I2: denotational_interp,Theta2: trm,Eta2: trm] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ denotational_interp @ trm @ I2 @ ( plus @ Theta2 @ Eta2 ) ) )
% 0.31/1.88 => ( ! [I2: denotational_interp,Theta2: trm,Eta2: trm] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ denotational_interp @ trm @ I2 @ ( times @ Theta2 @ Eta2 ) ) )
% 0.31/1.88 => ~ ! [I2: denotational_interp,Theta2: trm] :
% 0.31/1.88 ( X2
% 0.31/1.88 != ( product_Pair @ denotational_interp @ trm @ I2 @ ( differential @ Theta2 ) ) ) ) ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_216_usubstappt_Opsimps_I3_J,axiom,
% 0.31/1.88 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F: char] :
% 0.31/1.88 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( const @ F ) ) ) )
% 0.31/1.88 => ( ( uSubst95898992stappt @ Sigma @ U @ ( const @ F ) )
% 0.31/1.88 = ( uSubst1138577137pconst @ Sigma @ U @ F ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_217_term__sem_Oinduct,axiom,
% 0.31/1.88 ! [P: denotational_interp > trm > $o,A0: denotational_interp,A1: trm] :
% 0.31/1.88 ( ! [I2: denotational_interp,X: variable] : ( P @ I2 @ ( var @ X ) )
% 0.31/1.88 => ( ! [I2: denotational_interp,R5: real] : ( P @ I2 @ ( number @ R5 ) )
% 0.31/1.88 => ( ! [I2: denotational_interp,F3: char] : ( P @ I2 @ ( const @ F3 ) )
% 0.31/1.88 => ( ! [I2: denotational_interp,F3: char,Theta2: trm] :
% 0.31/1.88 ( ( P @ I2 @ Theta2 )
% 0.31/1.88 => ( P @ I2 @ ( func @ F3 @ Theta2 ) ) )
% 0.31/1.88 => ( ! [I2: denotational_interp,Theta2: trm] :
% 0.31/1.88 ( ( P @ I2 @ Theta2 )
% 0.31/1.88 => ! [Eta2: trm] :
% 0.31/1.88 ( ( P @ I2 @ Eta2 )
% 0.31/1.88 => ( P @ I2 @ ( plus @ Theta2 @ Eta2 ) ) ) )
% 0.31/1.88 => ( ! [I2: denotational_interp,Theta2: trm] :
% 0.31/1.88 ( ( P @ I2 @ Theta2 )
% 0.31/1.88 => ! [Eta2: trm] :
% 0.31/1.88 ( ( P @ I2 @ Eta2 )
% 0.31/1.88 => ( P @ I2 @ ( times @ Theta2 @ Eta2 ) ) ) )
% 0.31/1.88 => ( ! [I2: denotational_interp,Theta2: trm] :
% 0.31/1.88 ( ( ? [Xa2: char] :
% 0.31/1.88 ( member @ char @ Xa2
% 0.31/1.88 @ ( collect @ char
% 0.31/1.88 @ ^ [Uu: char] : $true ) )
% 0.31/1.88 => ( P @ I2 @ Theta2 ) )
% 0.31/1.88 => ( P @ I2 @ ( differential @ Theta2 ) ) )
% 0.31/1.88 => ( P @ A0 @ A1 ) ) ) ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_218_usubstappt_Osimps_I3_J,axiom,
% 0.31/1.88 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F: char] :
% 0.31/1.88 ( ( uSubst95898992stappt @ Sigma @ U @ ( const @ F ) )
% 0.31/1.88 = ( uSubst1138577137pconst @ Sigma @ U @ F ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_219_image2__def,axiom,
% 0.31/1.88 ! [A: $tType,B: $tType,C: $tType] :
% 0.31/1.88 ( ( bNF_Greatest_image2 @ C @ A @ B )
% 0.31/1.88 = ( ^ [A3: set @ C,F2: C > A,G2: C > B] :
% 0.31/1.88 ( collect @ ( product_prod @ A @ B )
% 0.31/1.88 @ ^ [Uu: product_prod @ A @ B] :
% 0.31/1.88 ? [A5: C] :
% 0.31/1.88 ( ( Uu
% 0.31/1.88 = ( product_Pair @ A @ B @ ( F2 @ A5 ) @ ( G2 @ A5 ) ) )
% 0.31/1.88 & ( member @ C @ A5 @ A3 ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_220_Testo_Oelims,axiom,
% 0.31/1.88 ! [X2: option @ fml,Y2: option @ game] :
% 0.31/1.88 ( ( ( uSubst190403692_Testo @ X2 )
% 0.31/1.88 = Y2 )
% 0.31/1.88 => ( ! [Phi2: fml] :
% 0.31/1.88 ( ( X2
% 0.31/1.88 = ( some @ fml @ Phi2 ) )
% 0.31/1.88 => ( Y2
% 0.31/1.88 != ( some @ game @ ( test @ Phi2 ) ) ) )
% 0.31/1.88 => ~ ( ( X2
% 0.31/1.88 = ( none @ fml ) )
% 0.31/1.88 => ( Y2
% 0.31/1.88 != ( none @ game ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_221_game_Oinject_I3_J,axiom,
% 0.31/1.88 ! [X32: fml,Y32: fml] :
% 0.31/1.88 ( ( ( test @ X32 )
% 0.31/1.88 = ( test @ Y32 ) )
% 0.31/1.88 = ( X32 = Y32 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_222_image2__eqI,axiom,
% 0.31/1.88 ! [A: $tType,C: $tType,B: $tType,B4: A,F: B > A,X2: B,C2: C,G: B > C,A2: set @ B] :
% 0.31/1.88 ( ( B4
% 0.31/1.88 = ( F @ X2 ) )
% 0.31/1.88 => ( ( C2
% 0.31/1.88 = ( G @ X2 ) )
% 0.31/1.88 => ( ( member @ B @ X2 @ A2 )
% 0.31/1.88 => ( member @ ( product_prod @ A @ C ) @ ( product_Pair @ A @ C @ B4 @ C2 ) @ ( bNF_Greatest_image2 @ B @ A @ C @ A2 @ F @ G ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_223_Testo_Osimps_I1_J,axiom,
% 0.31/1.88 ! [Phi: fml] :
% 0.31/1.88 ( ( uSubst190403692_Testo @ ( some @ fml @ Phi ) )
% 0.31/1.88 = ( some @ game @ ( test @ Phi ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_224_Testo_Opelims,axiom,
% 0.31/1.88 ! [X2: option @ fml,Y2: option @ game] :
% 0.31/1.88 ( ( ( uSubst190403692_Testo @ X2 )
% 0.31/1.88 = Y2 )
% 0.31/1.88 => ( ( accp @ ( option @ fml ) @ uSubst533687181to_rel @ X2 )
% 0.31/1.88 => ( ! [Phi2: fml] :
% 0.31/1.88 ( ( X2
% 0.31/1.88 = ( some @ fml @ Phi2 ) )
% 0.31/1.88 => ( ( Y2
% 0.31/1.88 = ( some @ game @ ( test @ Phi2 ) ) )
% 0.31/1.88 => ~ ( accp @ ( option @ fml ) @ uSubst533687181to_rel @ ( some @ fml @ Phi2 ) ) ) )
% 0.31/1.88 => ~ ( ( X2
% 0.31/1.88 = ( none @ fml ) )
% 0.31/1.88 => ( ( Y2
% 0.31/1.88 = ( none @ game ) )
% 0.31/1.88 => ~ ( accp @ ( option @ fml ) @ uSubst533687181to_rel @ ( none @ fml ) ) ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_225_relImage__def,axiom,
% 0.31/1.88 ! [A: $tType,B: $tType] :
% 0.31/1.88 ( ( bNF_Gr1317331620lImage @ B @ A )
% 0.31/1.88 = ( ^ [R6: set @ ( product_prod @ B @ B ),F2: B > A] :
% 0.31/1.88 ( collect @ ( product_prod @ A @ A )
% 0.31/1.88 @ ^ [Uu: product_prod @ A @ A] :
% 0.31/1.88 ? [A12: B,A22: B] :
% 0.31/1.88 ( ( Uu
% 0.31/1.88 = ( product_Pair @ A @ A @ ( F2 @ A12 ) @ ( F2 @ A22 ) ) )
% 0.31/1.88 & ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ A12 @ A22 ) @ R6 ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_226_relImage__mono,axiom,
% 0.31/1.88 ! [B: $tType,A: $tType,R1: set @ ( product_prod @ A @ A ),R2: set @ ( product_prod @ A @ A ),F: A > B] :
% 0.31/1.88 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ R1 @ R2 )
% 0.31/1.88 => ( ord_less_eq @ ( set @ ( product_prod @ B @ B ) ) @ ( bNF_Gr1317331620lImage @ A @ B @ R1 @ F ) @ ( bNF_Gr1317331620lImage @ A @ B @ R2 @ F ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_227_relInvImage__def,axiom,
% 0.31/1.88 ! [B: $tType,A: $tType] :
% 0.31/1.88 ( ( bNF_Gr2107612801vImage @ A @ B )
% 0.31/1.88 = ( ^ [A3: set @ A,R6: set @ ( product_prod @ B @ B ),F2: A > B] :
% 0.31/1.88 ( collect @ ( product_prod @ A @ A )
% 0.31/1.88 @ ^ [Uu: product_prod @ A @ A] :
% 0.31/1.88 ? [A12: A,A22: A] :
% 0.31/1.88 ( ( Uu
% 0.31/1.88 = ( product_Pair @ A @ A @ A12 @ A22 ) )
% 0.31/1.88 & ( member @ A @ A12 @ A3 )
% 0.31/1.88 & ( member @ A @ A22 @ A3 )
% 0.31/1.88 & ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ ( F2 @ A12 ) @ ( F2 @ A22 ) ) @ R6 ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_228_Assigno__undef,axiom,
% 0.31/1.88 ! [X2: variable,Theta: option @ trm] :
% 0.31/1.88 ( ( ( uSubst1326326671ssigno @ X2 @ Theta )
% 0.31/1.88 = ( none @ game ) )
% 0.31/1.88 = ( Theta
% 0.31/1.88 = ( none @ trm ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_229_relInvImage__mono,axiom,
% 0.31/1.88 ! [A: $tType,B: $tType,R1: set @ ( product_prod @ A @ A ),R2: set @ ( product_prod @ A @ A ),A2: set @ B,F: B > A] :
% 0.31/1.88 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ R1 @ R2 )
% 0.31/1.88 => ( ord_less_eq @ ( set @ ( product_prod @ B @ B ) ) @ ( bNF_Gr2107612801vImage @ B @ A @ A2 @ R1 @ F ) @ ( bNF_Gr2107612801vImage @ B @ A @ A2 @ R2 @ F ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_230_Assigno_Osimps_I2_J,axiom,
% 0.31/1.88 ! [X2: variable] :
% 0.31/1.88 ( ( uSubst1326326671ssigno @ X2 @ ( none @ trm ) )
% 0.31/1.88 = ( none @ game ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_231_Assigno_Oelims,axiom,
% 0.31/1.88 ! [X2: variable,Xa: option @ trm,Y2: option @ game] :
% 0.31/1.88 ( ( ( uSubst1326326671ssigno @ X2 @ Xa )
% 0.31/1.88 = Y2 )
% 0.31/1.88 => ( ! [Theta2: trm] :
% 0.31/1.88 ( ( Xa
% 0.31/1.88 = ( some @ trm @ Theta2 ) )
% 0.31/1.88 => ( Y2
% 0.31/1.88 != ( some @ game @ ( assign @ X2 @ Theta2 ) ) ) )
% 0.31/1.88 => ~ ( ( Xa
% 0.31/1.88 = ( none @ trm ) )
% 0.31/1.88 => ( Y2
% 0.31/1.88 != ( none @ game ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_232_Assigno_Opelims,axiom,
% 0.31/1.88 ! [X2: variable,Xa: option @ trm,Y2: option @ game] :
% 0.31/1.88 ( ( ( uSubst1326326671ssigno @ X2 @ Xa )
% 0.31/1.88 = Y2 )
% 0.31/1.88 => ( ( accp @ ( product_prod @ variable @ ( option @ trm ) ) @ uSubst1741596714no_rel @ ( product_Pair @ variable @ ( option @ trm ) @ X2 @ Xa ) )
% 0.31/1.88 => ( ! [Theta2: trm] :
% 0.31/1.88 ( ( Xa
% 0.31/1.88 = ( some @ trm @ Theta2 ) )
% 0.31/1.88 => ( ( Y2
% 0.31/1.88 = ( some @ game @ ( assign @ X2 @ Theta2 ) ) )
% 0.31/1.88 => ~ ( accp @ ( product_prod @ variable @ ( option @ trm ) ) @ uSubst1741596714no_rel @ ( product_Pair @ variable @ ( option @ trm ) @ X2 @ ( some @ trm @ Theta2 ) ) ) ) )
% 0.31/1.88 => ~ ( ( Xa
% 0.31/1.88 = ( none @ trm ) )
% 0.31/1.88 => ( ( Y2
% 0.31/1.88 = ( none @ game ) )
% 0.31/1.88 => ~ ( accp @ ( product_prod @ variable @ ( option @ trm ) ) @ uSubst1741596714no_rel @ ( product_Pair @ variable @ ( option @ trm ) @ X2 @ ( none @ trm ) ) ) ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_233_game_Oinject_I2_J,axiom,
% 0.31/1.88 ! [X21: variable,X22: trm,Y21: variable,Y22: trm] :
% 0.31/1.88 ( ( ( assign @ X21 @ X22 )
% 0.31/1.88 = ( assign @ Y21 @ Y22 ) )
% 0.31/1.88 = ( ( X21 = Y21 )
% 0.31/1.88 & ( X22 = Y22 ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_234_game_Odistinct_I15_J,axiom,
% 0.31/1.88 ! [X21: variable,X22: trm,X32: fml] :
% 0.31/1.88 ( ( assign @ X21 @ X22 )
% 0.31/1.88 != ( test @ X32 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_235_Assigno_Osimps_I1_J,axiom,
% 0.31/1.88 ! [X2: variable,Theta: trm] :
% 0.31/1.88 ( ( uSubst1326326671ssigno @ X2 @ ( some @ trm @ Theta ) )
% 0.31/1.88 = ( some @ game @ ( assign @ X2 @ Theta ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_236_relInvImage__UNIV__relImage,axiom,
% 0.31/1.88 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ A ),F: A > B] : ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ R @ ( bNF_Gr2107612801vImage @ A @ B @ ( top_top @ ( set @ A ) ) @ ( bNF_Gr1317331620lImage @ A @ B @ R @ F ) @ F ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_237_ODEo__undef,axiom,
% 0.31/1.88 ! [X2: char,Theta: option @ trm] :
% 0.31/1.88 ( ( ( uSubst1083227664e_ODEo @ X2 @ Theta )
% 0.31/1.88 = ( none @ game ) )
% 0.31/1.88 = ( Theta
% 0.31/1.88 = ( none @ trm ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_238_top__apply,axiom,
% 0.31/1.88 ! [C: $tType,D2: $tType] :
% 0.31/1.88 ( ( top @ C )
% 0.31/1.88 => ( ( top_top @ ( D2 > C ) )
% 0.31/1.88 = ( ^ [X3: D2] : ( top_top @ C ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_239_UNIV__I,axiom,
% 0.31/1.88 ! [A: $tType,X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_240_subset__UNIV,axiom,
% 0.31/1.88 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_241_top__greatest,axiom,
% 0.31/1.88 ! [A: $tType] :
% 0.31/1.88 ( ( order_top @ A )
% 0.31/1.88 => ! [A4: A] : ( ord_less_eq @ A @ A4 @ ( top_top @ A ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_242_top_Oextremum__unique,axiom,
% 0.31/1.88 ! [A: $tType] :
% 0.31/1.88 ( ( order_top @ A )
% 0.31/1.88 => ! [A4: A] :
% 0.31/1.88 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A4 )
% 0.31/1.88 = ( A4
% 0.31/1.88 = ( top_top @ A ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_243_top_Oextremum__uniqueI,axiom,
% 0.31/1.88 ! [A: $tType] :
% 0.31/1.88 ( ( order_top @ A )
% 0.31/1.88 => ! [A4: A] :
% 0.31/1.88 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A4 )
% 0.31/1.88 => ( A4
% 0.31/1.88 = ( top_top @ A ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_244_UNIV__def,axiom,
% 0.31/1.88 ! [A: $tType] :
% 0.31/1.88 ( ( top_top @ ( set @ A ) )
% 0.31/1.88 = ( collect @ A
% 0.31/1.88 @ ^ [X3: A] : $true ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_245_UNIV__eq__I,axiom,
% 0.31/1.88 ! [A: $tType,A2: set @ A] :
% 0.31/1.88 ( ! [X: A] : ( member @ A @ X @ A2 )
% 0.31/1.88 => ( ( top_top @ ( set @ A ) )
% 0.31/1.88 = A2 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_246_UNIV__witness,axiom,
% 0.31/1.88 ! [A: $tType] :
% 0.31/1.88 ? [X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_247_ODEo_Osimps_I2_J,axiom,
% 0.31/1.88 ! [X2: char] :
% 0.31/1.88 ( ( uSubst1083227664e_ODEo @ X2 @ ( none @ trm ) )
% 0.31/1.88 = ( none @ game ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_248_ODEo_Oelims,axiom,
% 0.31/1.88 ! [X2: char,Xa: option @ trm,Y2: option @ game] :
% 0.31/1.88 ( ( ( uSubst1083227664e_ODEo @ X2 @ Xa )
% 0.31/1.88 = Y2 )
% 0.31/1.88 => ( ! [Theta2: trm] :
% 0.31/1.88 ( ( Xa
% 0.31/1.88 = ( some @ trm @ Theta2 ) )
% 0.31/1.88 => ( Y2
% 0.31/1.88 != ( some @ game @ ( ode @ X2 @ Theta2 ) ) ) )
% 0.31/1.88 => ~ ( ( Xa
% 0.31/1.88 = ( none @ trm ) )
% 0.31/1.88 => ( Y2
% 0.31/1.88 != ( none @ game ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_249_ODEo_Opelims,axiom,
% 0.31/1.88 ! [X2: char,Xa: option @ trm,Y2: option @ game] :
% 0.31/1.88 ( ( ( uSubst1083227664e_ODEo @ X2 @ Xa )
% 0.31/1.88 = Y2 )
% 0.31/1.88 => ( ( accp @ ( product_prod @ char @ ( option @ trm ) ) @ uSubst2007600873Eo_rel @ ( product_Pair @ char @ ( option @ trm ) @ X2 @ Xa ) )
% 0.31/1.88 => ( ! [Theta2: trm] :
% 0.31/1.88 ( ( Xa
% 0.31/1.88 = ( some @ trm @ Theta2 ) )
% 0.31/1.88 => ( ( Y2
% 0.31/1.88 = ( some @ game @ ( ode @ X2 @ Theta2 ) ) )
% 0.31/1.88 => ~ ( accp @ ( product_prod @ char @ ( option @ trm ) ) @ uSubst2007600873Eo_rel @ ( product_Pair @ char @ ( option @ trm ) @ X2 @ ( some @ trm @ Theta2 ) ) ) ) )
% 0.31/1.88 => ~ ( ( Xa
% 0.31/1.88 = ( none @ trm ) )
% 0.31/1.88 => ( ( Y2
% 0.31/1.88 = ( none @ game ) )
% 0.31/1.88 => ~ ( accp @ ( product_prod @ char @ ( option @ trm ) ) @ uSubst2007600873Eo_rel @ ( product_Pair @ char @ ( option @ trm ) @ X2 @ ( none @ trm ) ) ) ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_250_game_Oinject_I8_J,axiom,
% 0.31/1.88 ! [X81: char,X82: trm,Y81: char,Y82: trm] :
% 0.31/1.88 ( ( ( ode @ X81 @ X82 )
% 0.31/1.88 = ( ode @ Y81 @ Y82 ) )
% 0.31/1.88 = ( ( X81 = Y81 )
% 0.31/1.88 & ( X82 = Y82 ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_251_top__empty__eq2,axiom,
% 0.31/1.88 ! [B: $tType,A: $tType] :
% 0.31/1.88 ( ( top_top @ ( A > B > $o ) )
% 0.31/1.88 = ( ^ [X3: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_252_top__empty__eq,axiom,
% 0.31/1.88 ! [A: $tType] :
% 0.31/1.88 ( ( top_top @ ( A > $o ) )
% 0.31/1.88 = ( ^ [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_253_top__set__def,axiom,
% 0.31/1.88 ! [A: $tType] :
% 0.31/1.88 ( ( top_top @ ( set @ A ) )
% 0.31/1.88 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(fact_254_game_Odistinct_I35_J,axiom,
% 0.31/1.88 ! [X32: fml,X81: char,X82: trm] :
% 0.31/1.88 ( ( test @ X32 )
% 0.31/1.88 != ( ode @ X81 @ X82 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 0.31/1.88 ! [A8: $tType,A9: $tType] :
% 0.31/1.88 ( ( order_top @ A9 )
% 0.31/1.88 => ( order_top @ ( A8 > A9 ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.31/1.88 ! [A8: $tType,A9: $tType] :
% 0.31/1.88 ( ( preorder @ A9 )
% 0.31/1.88 => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.31/1.88 ! [A8: $tType,A9: $tType] :
% 0.31/1.88 ( ( order @ A9 )
% 0.31/1.88 => ( order @ ( A8 > A9 ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_fun___Orderings_Otop,axiom,
% 0.31/1.88 ! [A8: $tType,A9: $tType] :
% 0.31/1.88 ( ( top @ A9 )
% 0.31/1.88 => ( top @ ( A8 > A9 ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_fun___Orderings_Oord,axiom,
% 0.31/1.88 ! [A8: $tType,A9: $tType] :
% 0.31/1.88 ( ( ord @ A9 )
% 0.31/1.88 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_Set_Oset___Orderings_Oorder__top_1,axiom,
% 0.31/1.88 ! [A8: $tType] : ( order_top @ ( set @ A8 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_Set_Oset___Orderings_Opreorder_2,axiom,
% 0.31/1.88 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_Set_Oset___Orderings_Oorder_3,axiom,
% 0.31/1.88 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_Set_Oset___Orderings_Otop_4,axiom,
% 0.31/1.88 ! [A8: $tType] : ( top @ ( set @ A8 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_Set_Oset___Orderings_Oord_5,axiom,
% 0.31/1.88 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_HOL_Obool___Orderings_Oorder__top_6,axiom,
% 0.31/1.88 order_top @ $o ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_HOL_Obool___Orderings_Opreorder_7,axiom,
% 0.31/1.88 preorder @ $o ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.31/1.88 linorder @ $o ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_HOL_Obool___Orderings_Oorder_8,axiom,
% 0.31/1.88 order @ $o ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_HOL_Obool___Orderings_Otop_9,axiom,
% 0.31/1.88 top @ $o ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_HOL_Obool___Orderings_Oord_10,axiom,
% 0.31/1.88 ord @ $o ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_Real_Oreal___Orderings_Opreorder_11,axiom,
% 0.31/1.88 preorder @ real ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_Real_Oreal___Orderings_Olinorder_12,axiom,
% 0.31/1.88 linorder @ real ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_Real_Oreal___Orderings_Oorder_13,axiom,
% 0.31/1.88 order @ real ).
% 0.31/1.88
% 0.31/1.88 thf(tcon_Real_Oreal___Orderings_Oord_14,axiom,
% 0.31/1.88 ord @ real ).
% 0.31/1.88
% 0.31/1.88 thf(help_If_3_1_T,axiom,
% 0.31/1.88 ! [P: $o] :
% 0.31/1.88 ( ( P = $true )
% 0.31/1.88 | ( P = $false ) ) ).
% 0.31/1.88
% 0.31/1.88 thf(help_If_2_1_T,axiom,
% 0.31/1.88 ! [A: $tType,X2: A,Y2: A] :
% 0.31/1.88 ( ( if @ A @ $false @ X2 @ Y2 )
% 0.31/1.88 = Y2 ) ).
% 0.31/1.88
% 0.31/1.88 thf(help_If_1_1_T,axiom,
% 0.31/1.88 ! [A: $tType,X2: A,Y2: A] :
% 0.31/1.88 ( ( if @ A @ $true @ X2 @ Y2 )
% 0.31/1.88 = X2 ) ).
% 0.31/1.88
% 0.31/1.88 thf(conj_0,conjecture,
% 0.31/1.88 ( ( uSubst95898992stappt @ sigma @ ua @ theta )
% 0.31/1.88 != ( none @ trm ) ) ).
% 0.31/1.88 ------------------------
% 3.99/1.92 % (23605)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23487 for (2999ds/18Mi)
% 3.99/1.92 % (23603)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_23487 for (2999ds/275Mi)
% 3.99/1.92 % (23601)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23487 for (2999ds/2Mi)
% 3.99/1.92 % (23602)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_23487 for (2999ds/2Mi)
% 3.99/1.92 % (23598)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23487 for (2999ds/183Mi)
% 3.99/1.92 % (23599)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_23487 for (2999ds/4Mi)
% 3.99/1.92 % (23600)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_23487 for (2999ds/27Mi)
% 3.99/1.92 % (23601)Instruction limit reached!
% 3.99/1.92 % (23601)------------------------------
% 3.99/1.92 % (23601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.99/1.92 % (23602)Instruction limit reached!
% 3.99/1.92 % (23602)------------------------------
% 3.99/1.92 % (23602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.99/1.92 % (23601)Termination reason: Unknown
% 3.99/1.92 % (23601)Termination phase: shuffling
% 3.99/1.92
% 3.99/1.92 % (23601)Memory used [KB]: 1407
% 3.99/1.92 % (23601)Time elapsed: 0.003 s
% 3.99/1.92 % (23601)Instructions burned: 2 (million)
% 3.99/1.92 % (23601)------------------------------
% 3.99/1.92 % (23601)------------------------------
% 3.99/1.92 % (23602)Termination reason: Unknown
% 3.99/1.92 % (23602)Termination phase: shuffling
% 3.99/1.92
% 3.99/1.92 % (23602)Memory used [KB]: 1407
% 3.99/1.92 % (23602)Time elapsed: 0.003 s
% 3.99/1.92 % (23602)Instructions burned: 2 (million)
% 3.99/1.92 % (23602)------------------------------
% 3.99/1.92 % (23602)------------------------------
% 3.99/1.92 % (23599)Instruction limit reached!
% 3.99/1.92 % (23599)------------------------------
% 3.99/1.92 % (23599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.99/1.92 % (23599)Termination reason: Unknown
% 3.99/1.92 % (23599)Termination phase: shuffling
% 3.99/1.92
% 3.99/1.92 % (23599)Memory used [KB]: 1407
% 3.99/1.92 % (23599)Time elapsed: 0.004 s
% 3.99/1.92 % (23599)Instructions burned: 4 (million)
% 3.99/1.92 % (23599)------------------------------
% 3.99/1.92 % (23599)------------------------------
% 3.99/1.93 % (23605)Instruction limit reached!
% 3.99/1.93 % (23605)------------------------------
% 3.99/1.93 % (23605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.99/1.93 % (23605)Termination reason: Unknown
% 3.99/1.93 % (23605)Termination phase: shuffling
% 3.99/1.93
% 3.99/1.93 % (23605)Memory used [KB]: 1791
% 3.99/1.93 % (23605)Time elapsed: 0.012 s
% 3.99/1.93 % (23605)Instructions burned: 18 (million)
% 3.99/1.93 % (23605)------------------------------
% 3.99/1.93 % (23605)------------------------------
% 3.99/1.94 % (23600)Instruction limit reached!
% 3.99/1.94 % (23600)------------------------------
% 3.99/1.94 % (23600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.99/1.94 % (23600)Termination reason: Unknown
% 3.99/1.94 % (23600)Termination phase: Property scanning
% 3.99/1.94
% 3.99/1.94 % (23600)Memory used [KB]: 1918
% 3.99/1.94 % (23600)Time elapsed: 0.017 s
% 3.99/1.94 % (23600)Instructions burned: 27 (million)
% 3.99/1.94 % (23600)------------------------------
% 3.99/1.94 % (23600)------------------------------
% 3.99/1.94 % (23606)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23487 for (2999ds/3Mi)
% 3.99/1.94 % (23607)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_23487 for (2999ds/37Mi)
% 3.99/1.94 % (23608)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_23487 for (2999ds/15Mi)
% 3.99/1.94 % (23606)Instruction limit reached!
% 3.99/1.94 % (23606)------------------------------
% 3.99/1.94 % (23606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.99/1.94 % (23606)Termination reason: Unknown
% 3.99/1.94 % (23606)Termination phase: shuffling
% 3.99/1.94
% 3.99/1.94 % (23606)Memory used [KB]: 1407
% 3.99/1.94 % (23606)Time elapsed: 0.004 s
% 3.99/1.94 % (23606)Instructions burned: 4 (million)
% 3.99/1.94 % (23606)------------------------------
% 3.99/1.94 % (23606)------------------------------
% 3.99/1.95 % (23608)Instruction limit reached!
% 3.99/1.95 % (23608)------------------------------
% 3.99/1.95 % (23608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.99/1.95 % (23608)Termination reason: Unknown
% 3.99/1.95 % (23608)Termination phase: shuffling
% 3.99/1.95
% 3.99/1.95 % (23608)Memory used [KB]: 1791
% 3.99/1.95 % (23608)Time elapsed: 0.010 s
% 3.99/1.95 % (23608)Instructions burned: 16 (million)
% 3.99/1.95 % (23608)------------------------------
% 3.99/1.95 % (23608)------------------------------
% 3.99/1.95 % (23609)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_23487 for (2999ds/3Mi)
% 3.99/1.95 % (23609)Instruction limit reached!
% 3.99/1.95 % (23609)------------------------------
% 3.99/1.95 % (23609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.99/1.95 % (23609)Termination reason: Unknown
% 3.99/1.95 % (23609)Termination phase: shuffling
% 3.99/1.95
% 3.99/1.95 % (23609)Memory used [KB]: 1407
% 3.99/1.95 % (23609)Time elapsed: 0.004 s
% 3.99/1.95 % (23609)Instructions burned: 3 (million)
% 3.99/1.95 % (23609)------------------------------
% 3.99/1.95 % (23609)------------------------------
% 3.99/1.95 % (23610)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_23487 for (2999ds/1041Mi)
% 3.99/1.96 % (23607)Instruction limit reached!
% 3.99/1.96 % (23607)------------------------------
% 3.99/1.96 % (23607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.99/1.96 % (23607)Termination reason: Unknown
% 3.99/1.96 % (23607)Termination phase: shuffling
% 3.99/1.96
% 3.99/1.96 % (23607)Memory used [KB]: 2174
% 3.99/1.96 % (23607)Time elapsed: 0.021 s
% 3.99/1.96 % (23607)Instructions burned: 37 (million)
% 3.99/1.96 % (23607)------------------------------
% 3.99/1.96 % (23607)------------------------------
% 3.99/1.96 % (23611)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_23487 for (2999ds/7Mi)
% 3.99/1.96 % (23611)Instruction limit reached!
% 3.99/1.96 % (23611)------------------------------
% 3.99/1.96 % (23611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.99/1.96 % (23611)Termination reason: Unknown
% 3.99/1.96 % (23611)Termination phase: shuffling
% 3.99/1.96
% 3.99/1.96 % (23611)Memory used [KB]: 1535
% 3.99/1.96 % (23611)Time elapsed: 0.006 s
% 3.99/1.96 % (23611)Instructions burned: 7 (million)
% 3.99/1.96 % (23611)------------------------------
% 3.99/1.96 % (23611)------------------------------
% 3.99/1.97 % (23612)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_23487 for (2999ds/16Mi)
% 3.99/1.97 % (23613)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_23487 for (2999ds/3Mi)
% 3.99/1.97 % (23613)Instruction limit reached!
% 3.99/1.97 % (23613)------------------------------
% 3.99/1.97 % (23613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.99/1.97 % (23613)Termination reason: Unknown
% 3.99/1.97 % (23613)Termination phase: shuffling
% 3.99/1.97
% 3.99/1.97 % (23613)Memory used [KB]: 1407
% 3.99/1.97 % (23613)Time elapsed: 0.004 s
% 3.99/1.97 % (23613)Instructions burned: 4 (million)
% 3.99/1.97 % (23613)------------------------------
% 3.99/1.97 % (23613)------------------------------
% 3.99/1.98 % (23612)Instruction limit reached!
% 3.99/1.98 % (23612)------------------------------
% 3.99/1.98 % (23612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.99/1.98 % (23612)Termination reason: Unknown
% 3.99/1.98 % (23612)Termination phase: shuffling
% 3.99/1.98
% 3.99/1.98 % (23612)Memory used [KB]: 1791
% 3.99/1.98 % (23612)Time elapsed: 0.011 s
% 3.99/1.98 % (23612)Instructions burned: 16 (million)
% 3.99/1.98 % (23612)------------------------------
% 3.99/1.98 % (23612)------------------------------
% 3.99/1.98 % (23614)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_23487 for (2999ds/3Mi)
% 3.99/1.98 % (23614)Instruction limit reached!
% 3.99/1.98 % (23614)------------------------------
% 3.99/1.98 % (23614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.99/1.98 % (23614)Termination reason: Unknown
% 3.99/1.98 % (23614)Termination phase: shuffling
% 3.99/1.98
% 3.99/1.98 % (23614)Memory used [KB]: 1407
% 3.99/1.98 % (23614)Time elapsed: 0.004 s
% 3.99/1.98 % (23614)Instructions burned: 3 (million)
% 3.99/1.98 % (23614)------------------------------
% 3.99/1.98 % (23614)------------------------------
% 3.99/1.98 % (23615)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_23487 for (2999ds/7Mi)
% 3.99/1.99 % (23615)Instruction limit reached!
% 3.99/1.99 % (23615)------------------------------
% 3.99/1.99 % (23615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.99/1.99 % (23615)Termination reason: Unknown
% 3.99/1.99 % (23615)Termination phase: shuffling
% 3.99/1.99
% 3.99/1.99 % (23615)Memory used [KB]: 1535
% 3.99/1.99 % (23615)Time elapsed: 0.005 s
% 3.99/1.99 % (23615)Instructions burned: 7 (million)
% 3.99/1.99 % (23615)------------------------------
% 3.99/1.99 % (23615)------------------------------
% 3.99/1.99 % (23616)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_23487 for (2999ds/3Mi)
% 3.99/1.99 % (23616)Instruction limit reached!
% 3.99/1.99 % (23616)------------------------------
% 3.99/1.99 % (23616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.99/1.99 % (23616)Termination reason: Unknown
% 3.99/1.99 % (23616)Termination phase: shuffling
% 3.99/1.99
% 3.99/1.99 % (23616)Memory used [KB]: 1407
% 3.99/1.99 % (23616)Time elapsed: 0.004 s
% 3.99/1.99 % (23616)Instructions burned: 3 (million)
% 3.99/1.99 % (23616)------------------------------
% 3.99/1.99 % (23616)------------------------------
% 3.99/1.99 % (23617)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_23487 for (2999ds/4Mi)
% 3.99/2.00 % (23617)Instruction limit reached!
% 3.99/2.00 % (23617)------------------------------
% 3.99/2.00 % (23617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.99/2.00 % (23617)Termination reason: Unknown
% 3.99/2.00 % (23617)Termination phase: shuffling
% 3.99/2.00
% 3.99/2.00 % (23617)Memory used [KB]: 1535
% 3.99/2.00 % (23617)Time elapsed: 0.005 s
% 3.99/2.00 % (23617)Instructions burned: 5 (million)
% 3.99/2.00 % (23617)------------------------------
% 3.99/2.00 % (23617)------------------------------
% 3.99/2.00 % (23618)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_23487 for (2999ds/18Mi)
% 3.99/2.01 % (23619)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_23487 for (2998ds/710Mi)
% 3.99/2.01 % (23618)Instruction limit reached!
% 3.99/2.01 % (23618)------------------------------
% 3.99/2.01 % (23618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.99/2.01 % (23618)Termination reason: Unknown
% 3.99/2.01 % (23618)Termination phase: shuffling
% 3.99/2.01
% 3.99/2.01 % (23618)Memory used [KB]: 1791
% 3.99/2.01 % (23618)Time elapsed: 0.012 s
% 3.99/2.01 % (23618)Instructions burned: 19 (million)
% 3.99/2.01 % (23618)------------------------------
% 3.99/2.01 % (23618)------------------------------
% 3.99/2.01 % (23620)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23487 for (2998ds/6Mi)
% 3.99/2.01 % (23620)Instruction limit reached!
% 3.99/2.01 % (23620)------------------------------
% 3.99/2.01 % (23620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.99/2.01 % (23620)Termination reason: Unknown
% 3.99/2.01 % (23620)Termination phase: shuffling
% 3.99/2.01
% 3.99/2.01 % (23620)Memory used [KB]: 1535
% 3.99/2.01 % (23620)Time elapsed: 0.005 s
% 3.99/2.01 % (23620)Instructions burned: 6 (million)
% 3.99/2.01 % (23620)------------------------------
% 3.99/2.01 % (23620)------------------------------
% 3.99/2.02 % (23621)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_23487 for (2998ds/902Mi)
% 3.99/2.02 % (23598)Instruction limit reached!
% 3.99/2.02 % (23598)------------------------------
% 3.99/2.02 % (23598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.99/2.02 % (23598)Termination reason: Unknown
% 3.99/2.02 % (23598)Termination phase: Saturation
% 3.99/2.02
% 3.99/2.02 % (23598)Memory used [KB]: 7419
% 3.99/2.02 % (23598)Time elapsed: 0.103 s
% 3.99/2.02 % (23598)Instructions burned: 183 (million)
% 3.99/2.02 % (23598)------------------------------
% 3.99/2.02 % (23598)------------------------------
% 3.99/2.03 % (23622)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_23487 for (2998ds/21Mi)
% 4.77/2.03 % (23623)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_23487 for (2998ds/5Mi)
% 4.77/2.04 % (23623)Instruction limit reached!
% 4.77/2.04 % (23623)------------------------------
% 4.77/2.04 % (23623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.04 % (23623)Termination reason: Unknown
% 4.77/2.04 % (23623)Termination phase: shuffling
% 4.77/2.04
% 4.77/2.04 % (23623)Memory used [KB]: 1535
% 4.77/2.04 % (23623)Time elapsed: 0.005 s
% 4.77/2.04 % (23623)Instructions burned: 5 (million)
% 4.77/2.04 % (23623)------------------------------
% 4.77/2.04 % (23623)------------------------------
% 4.77/2.04 % (23622)Instruction limit reached!
% 4.77/2.04 % (23622)------------------------------
% 4.77/2.04 % (23622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.04 % (23622)Termination reason: Unknown
% 4.77/2.04 % (23622)Termination phase: shuffling
% 4.77/2.04
% 4.77/2.04 % (23622)Memory used [KB]: 1791
% 4.77/2.04 % (23622)Time elapsed: 0.014 s
% 4.77/2.04 % (23622)Instructions burned: 21 (million)
% 4.77/2.04 % (23622)------------------------------
% 4.77/2.04 % (23622)------------------------------
% 4.77/2.04 % (23624)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_23487 for (2998ds/6Mi)
% 4.77/2.04 % (23624)Instruction limit reached!
% 4.77/2.04 % (23624)------------------------------
% 4.77/2.04 % (23624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.04 % (23624)Termination reason: Unknown
% 4.77/2.04 % (23624)Termination phase: shuffling
% 4.77/2.04
% 4.77/2.04 % (23624)Memory used [KB]: 1535
% 4.77/2.04 % (23624)Time elapsed: 0.005 s
% 4.77/2.04 % (23624)Instructions burned: 6 (million)
% 4.77/2.04 % (23624)------------------------------
% 4.77/2.04 % (23624)------------------------------
% 4.77/2.05 % (23603)Instruction limit reached!
% 4.77/2.05 % (23603)------------------------------
% 4.77/2.05 % (23603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.05 % (23603)Termination reason: Unknown
% 4.77/2.05 % (23603)Termination phase: Saturation
% 4.77/2.05
% 4.77/2.05 % (23603)Memory used [KB]: 6652
% 4.77/2.05 % (23603)Time elapsed: 0.133 s
% 4.77/2.05 % (23603)Instructions burned: 275 (million)
% 4.77/2.05 % (23603)------------------------------
% 4.77/2.05 % (23603)------------------------------
% 4.77/2.06 % (23625)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_23487 for (2998ds/377Mi)
% 4.77/2.06 % (23626)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_23487 for (2998ds/779Mi)
% 4.77/2.06 % (23627)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_23487 for (2998ds/19Mi)
% 4.77/2.07 % (23628)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_23487 for (2998ds/879Mi)
% 4.77/2.07 % (23627)Instruction limit reached!
% 4.77/2.07 % (23627)------------------------------
% 4.77/2.07 % (23627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.07 % (23627)Termination reason: Unknown
% 4.77/2.07 % (23627)Termination phase: shuffling
% 4.77/2.07
% 4.77/2.07 % (23627)Memory used [KB]: 1791
% 4.77/2.07 % (23627)Time elapsed: 0.012 s
% 4.77/2.07 % (23627)Instructions burned: 19 (million)
% 4.77/2.07 % (23627)------------------------------
% 4.77/2.07 % (23627)------------------------------
% 4.77/2.09 % (23629)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_23487 for (2998ds/17Mi)
% 4.77/2.10 % (23629)Instruction limit reached!
% 4.77/2.10 % (23629)------------------------------
% 4.77/2.10 % (23629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.10 % (23629)Termination reason: Unknown
% 4.77/2.10 % (23629)Termination phase: shuffling
% 4.77/2.10
% 4.77/2.10 % (23629)Memory used [KB]: 1791
% 4.77/2.10 % (23629)Time elapsed: 0.012 s
% 4.77/2.10 % (23629)Instructions burned: 17 (million)
% 4.77/2.10 % (23629)------------------------------
% 4.77/2.10 % (23629)------------------------------
% 4.77/2.12 % (23630)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_23487 for (2997ds/3Mi)
% 4.77/2.12 % (23630)Instruction limit reached!
% 4.77/2.12 % (23630)------------------------------
% 4.77/2.12 % (23630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.12 % (23630)Termination reason: Unknown
% 4.77/2.12 % (23630)Termination phase: shuffling
% 4.77/2.12
% 4.77/2.12 % (23630)Memory used [KB]: 1407
% 4.77/2.12 % (23630)Time elapsed: 0.004 s
% 4.77/2.12 % (23630)Instructions burned: 4 (million)
% 4.77/2.12 % (23630)------------------------------
% 4.77/2.12 % (23630)------------------------------
% 5.16/2.14 % (23631)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_23487 for (2997ds/30Mi)
% 5.16/2.15 % (23621)First to succeed.
% 5.16/2.15 % (23621)Refutation found. Thanks to Tanya!
% 5.16/2.15 % SZS status Theorem for DTF2THF_23487
% 5.16/2.15 % SZS output start Proof for DTF2THF_23487
% 5.16/2.15 thf(type_def_5, type, set: ($tType) > $tType).
% 5.16/2.15 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 5.16/2.15 thf(type_def_8, type, variable: $tType).
% 5.16/2.15 thf(type_def_9, type, real: $tType).
% 5.16/2.15 thf(type_def_10, type, option: ($tType) > $tType).
% 5.16/2.15 thf(type_def_11, type, trm: $tType).
% 5.16/2.15 thf(type_def_12, type, fml: $tType).
% 5.16/2.15 thf(type_def_13, type, game: $tType).
% 5.16/2.15 thf(type_def_14, type, char: $tType).
% 5.16/2.15 thf(type_def_15, type, denotational_interp: $tType).
% 5.16/2.15 thf(func_def_0, type, denotational_interp: $tType).
% 5.16/2.15 thf(func_def_1, type, product_prod: ($tType * $tType) > $tType).
% 5.16/2.15 thf(func_def_2, type, variable: $tType).
% 5.16/2.15 thf(func_def_3, type, option: ($tType) > $tType).
% 5.16/2.15 thf(func_def_4, type, game: $tType).
% 5.16/2.15 thf(func_def_5, type, char: $tType).
% 5.16/2.15 thf(func_def_6, type, trm: $tType).
% 5.16/2.15 thf(func_def_7, type, fml: $tType).
% 5.16/2.15 thf(func_def_8, type, real: $tType).
% 5.16/2.15 thf(func_def_9, type, set: ($tType) > $tType).
% 5.16/2.15 thf(func_def_10, type, type: !>[X0: $tType]:($o)).
% 5.16/2.15 thf(func_def_11, type, ord: !>[X0: $tType]:($o)).
% 5.16/2.15 thf(func_def_12, type, top: !>[X0: $tType]:($o)).
% 5.16/2.15 thf(func_def_13, type, order: !>[X0: $tType]:($o)).
% 5.16/2.15 thf(func_def_14, type, linorder: !>[X0: $tType]:($o)).
% 5.16/2.15 thf(func_def_15, type, preorder: !>[X0: $tType]:($o)).
% 5.16/2.15 thf(func_def_16, type, order_top: !>[X0: $tType]:($o)).
% 5.16/2.15 thf(func_def_17, type, bNF_Greatest_image2: !>[X0: $tType, X1: $tType, X2: $tType]:(set @ X0 > (X0 > X1) > (X0 > X2) > set @ product_prod @ X1 @ X2)).
% 5.16/2.15 thf(func_def_18, type, bNF_Gr1317331620lImage: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X0 > (X0 > X1) > set @ product_prod @ X1 @ X1)).
% 5.16/2.15 thf(func_def_19, type, bNF_Gr2107612801vImage: !>[X0: $tType, X1: $tType]:(set @ X0 > set @ product_prod @ X1 @ X1 > (X0 > X1) > set @ product_prod @ X0 @ X0)).
% 5.16/2.15 thf(func_def_20, type, denota1419872369iation: (variable > real) > (variable > real) > set @ variable > $o).
% 5.16/2.15 thf(func_def_21, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 5.16/2.15 thf(func_def_22, type, none: !>[X0: $tType]:(option @ X0)).
% 5.16/2.15 thf(func_def_23, type, some: !>[X0: $tType]:(X0 > option @ X0)).
% 5.16/2.15 thf(func_def_24, type, case_option: !>[X0: $tType, X1: $tType]:(X0 > (X1 > X0) > option @ X1 > X0)).
% 5.16/2.15 thf(func_def_25, type, the: !>[X0: $tType]:(option @ X0 > X0)).
% 5.16/2.15 thf(func_def_26, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 5.16/2.15 thf(func_def_27, type, order_Greatest: !>[X0: $tType]:((X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_28, type, top_top: !>[X0: $tType]:(X0)).
% 5.16/2.15 thf(func_def_29, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 5.16/2.15 thf(func_def_30, type, powp: !>[X0: $tType]:((X0 > $o) > set @ X0 > $o)).
% 5.16/2.15 thf(func_def_31, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 5.16/2.15 thf(func_def_32, type, geq: trm > trm > fml).
% 5.16/2.15 thf(func_def_33, type, assign: variable > trm > game).
% 5.16/2.15 thf(func_def_34, type, ode: char > trm > game).
% 5.16/2.15 thf(func_def_35, type, test: fml > game).
% 5.16/2.15 thf(func_def_36, type, const: char > trm).
% 5.16/2.15 thf(func_def_37, type, differential: trm > trm).
% 5.16/2.15 thf(func_def_38, type, func: char > trm > trm).
% 5.16/2.15 thf(func_def_39, type, number: real > trm).
% 5.16/2.15 thf(func_def_40, type, plus: trm > trm > trm).
% 5.16/2.15 thf(func_def_41, type, times: trm > trm > trm).
% 5.16/2.15 thf(func_def_42, type, var: variable > trm).
% 5.16/2.15 thf(func_def_43, type, uSubst1326326671ssigno: variable > option @ trm > option @ game).
% 5.16/2.15 thf(func_def_44, type, uSubst1741596714no_rel: product_prod @ variable @ option @ trm > product_prod @ variable @ option @ trm > $o).
% 5.16/2.15 thf(func_def_45, type, uSubst259074819ntialo: option @ trm > option @ trm).
% 5.16/2.15 thf(func_def_46, type, uSubst99643830lo_rel: option @ trm > option @ trm > $o).
% 5.16/2.15 thf(func_def_47, type, uSubst1556497037e_Geqo: option @ trm > option @ trm > option @ fml).
% 5.16/2.15 thf(func_def_48, type, uSubst864323244qo_rel: product_prod @ option @ trm @ option @ trm > product_prod @ option @ trm @ option @ trm > $o).
% 5.16/2.15 thf(func_def_49, type, uSubst1083227664e_ODEo: char > option @ trm > option @ game).
% 5.16/2.15 thf(func_def_50, type, uSubst2007600873Eo_rel: product_prod @ char @ option @ trm > product_prod @ char @ option @ trm > $o).
% 5.16/2.15 thf(func_def_51, type, uSubst1112714340_Pluso: option @ trm > option @ trm > option @ trm).
% 5.16/2.15 thf(func_def_52, type, uSubst270600597so_rel: product_prod @ option @ trm @ option @ trm > product_prod @ option @ trm @ option @ trm > $o).
% 5.16/2.15 thf(func_def_53, type, uSubst190403692_Testo: option @ fml > option @ game).
% 5.16/2.15 thf(func_def_54, type, uSubst533687181to_rel: option @ fml > option @ fml > $o).
% 5.16/2.15 thf(func_def_55, type, uSubst277968634Timeso: option @ trm > option @ trm > option @ trm).
% 5.16/2.15 thf(func_def_56, type, uSubst1377811071so_rel: product_prod @ option @ trm @ option @ trm > product_prod @ option @ trm @ option @ trm > $o).
% 5.16/2.15 thf(func_def_57, type, uSubst1138577137pconst: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > char > option @ trm).
% 5.16/2.15 thf(func_def_58, type, uSubst95898978stappf: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > fml > option @ fml).
% 5.16/2.15 thf(func_def_59, 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).
% 5.16/2.15 thf(func_def_60, type, uSubst2096773001pt_rel: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > $o).
% 5.16/2.15 thf(func_def_61, type, accp: !>[X0: $tType]:((X0 > X0 > $o) > X0 > $o)).
% 5.16/2.15 thf(func_def_62, type, lex_prod: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ X1 @ X1 > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1)).
% 5.16/2.15 thf(func_def_63, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 5.16/2.15 thf(func_def_64, type, u: set @ variable).
% 5.16/2.15 thf(func_def_65, type, ua: set @ variable).
% 5.16/2.15 thf(func_def_66, type, eta: trm).
% 5.16/2.15 thf(func_def_67, type, nu: variable > real).
% 5.16/2.15 thf(func_def_68, type, nu2: variable > real).
% 5.16/2.15 thf(func_def_69, type, omega: variable > real).
% 5.16/2.15 thf(func_def_70, type, omega2: variable > real).
% 5.16/2.15 thf(func_def_71, type, sigma: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 5.16/2.15 thf(func_def_72, type, theta: trm).
% 5.16/2.15 thf(func_def_90, type, sP0: (trm > $o) > $o).
% 5.16/2.15 thf(func_def_91, type, sP1: (trm > $o) > $o).
% 5.16/2.15 thf(func_def_92, type, sP2: (denotational_interp > trm > $o) > $o).
% 5.16/2.15 thf(func_def_93, type, sP3: (denotational_interp > trm > $o) > $o).
% 5.16/2.15 thf(func_def_94, type, sP4: option @ fml > option @ game > $o).
% 5.16/2.15 thf(func_def_95, type, sP5: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > (X0 > $o) > $o)).
% 5.16/2.15 thf(func_def_96, type, sP6: option @ trm > option @ trm > option @ trm > $o).
% 5.16/2.15 thf(func_def_97, type, sP7: option @ game > variable > option @ trm > $o).
% 5.16/2.15 thf(func_def_98, type, sP8: option @ trm > option @ trm > option @ trm > $o).
% 5.16/2.15 thf(func_def_99, type, sP9: option @ trm > option @ trm > option @ trm > $o).
% 5.16/2.15 thf(func_def_100, type, sP10: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 5.16/2.15 thf(func_def_101, type, sP11: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 5.16/2.15 thf(func_def_102, type, sP12: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 5.16/2.15 thf(func_def_103, type, sP13: option @ trm > char > option @ game > $o).
% 5.16/2.15 thf(func_def_104, type, sP14: option @ trm > option @ trm > $o).
% 5.16/2.15 thf(func_def_105, type, sP15: option @ trm > option @ trm > option @ trm > $o).
% 5.16/2.15 thf(func_def_106, type, sP16: option @ trm > option @ trm > option @ trm > $o).
% 5.16/2.15 thf(func_def_107, type, sP17: option @ trm > option @ trm > option @ trm > $o).
% 5.16/2.15 thf(func_def_108, type, sP18: !>[X0: $tType, X1: $tType]:((option @ X0 > option @ X1 > $o) > option @ X1 > option @ X0 > $o)).
% 5.16/2.15 thf(func_def_109, type, sP19: option @ trm > option @ fml > option @ trm > $o).
% 5.16/2.15 thf(func_def_110, type, sP20: option @ trm > option @ fml > option @ trm > $o).
% 5.16/2.15 thf(func_def_111, type, sP21: option @ trm > option @ fml > option @ trm > $o).
% 5.16/2.15 thf(func_def_112, type, sK22: option @ game > game).
% 5.16/2.15 thf(func_def_113, type, sK23: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > X1)).
% 5.16/2.15 thf(func_def_114, type, sK24: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_115, type, sK25: !>[X0: $tType]:(option @ X0 > X0)).
% 5.16/2.15 thf(func_def_116, type, sK26: (char > option @ trm > $o) > char).
% 5.16/2.15 thf(func_def_117, type, sK27: (char > option @ trm > $o) > trm).
% 5.16/2.15 thf(func_def_118, type, sK28: (char > option @ trm > $o) > char).
% 5.16/2.15 thf(func_def_119, type, sK29: (trm > $o) > trm).
% 5.16/2.15 thf(func_def_120, type, sK30: (trm > $o) > trm).
% 5.16/2.15 thf(func_def_121, type, sK31: (trm > $o) > trm).
% 5.16/2.15 thf(func_def_122, type, sK32: (trm > $o) > trm).
% 5.16/2.15 thf(func_def_123, type, sK33: (trm > $o) > char).
% 5.16/2.15 thf(func_def_124, type, sK34: (trm > $o) > trm).
% 5.16/2.15 thf(func_def_125, type, sK35: (trm > $o) > trm).
% 5.16/2.15 thf(func_def_126, type, sK36: (trm > $o) > real).
% 5.16/2.15 thf(func_def_127, type, sK37: (trm > $o) > char).
% 5.16/2.15 thf(func_def_128, type, sK38: (trm > $o) > variable).
% 5.16/2.15 thf(func_def_129, type, sK39: (denotational_interp > trm > $o) > denotational_interp).
% 5.16/2.15 thf(func_def_130, type, sK40: (denotational_interp > trm > $o) > trm).
% 5.16/2.15 thf(func_def_131, type, sK41: (denotational_interp > trm > $o) > trm).
% 5.16/2.15 thf(func_def_132, type, sK42: (denotational_interp > trm > $o) > denotational_interp).
% 5.16/2.15 thf(func_def_133, type, sK43: (denotational_interp > trm > $o) > trm).
% 5.16/2.15 thf(func_def_134, type, sK44: (denotational_interp > trm > $o) > trm).
% 5.16/2.15 thf(func_def_135, type, sK45: (denotational_interp > trm > $o) > denotational_interp).
% 5.16/2.15 thf(func_def_136, type, sK46: (denotational_interp > trm > $o) > char).
% 5.16/2.15 thf(func_def_137, type, sK47: (denotational_interp > trm > $o) > denotational_interp).
% 5.16/2.15 thf(func_def_138, type, sK48: (denotational_interp > trm > $o) > trm).
% 5.16/2.15 thf(func_def_139, type, sK49: (denotational_interp > trm > $o) > denotational_interp).
% 5.16/2.15 thf(func_def_140, type, sK50: (denotational_interp > trm > $o) > variable).
% 5.16/2.15 thf(func_def_141, type, sK51: (denotational_interp > trm > $o) > denotational_interp).
% 5.16/2.15 thf(func_def_142, type, sK52: (denotational_interp > trm > $o) > real).
% 5.16/2.15 thf(func_def_143, type, sK53: (denotational_interp > trm > $o) > denotational_interp).
% 5.16/2.15 thf(func_def_144, type, sK54: (denotational_interp > trm > $o) > char).
% 5.16/2.15 thf(func_def_145, type, sK55: (denotational_interp > trm > $o) > trm).
% 5.16/2.15 thf(func_def_146, type, sK56: option @ game > option @ fml > fml).
% 5.16/2.15 thf(func_def_147, type, sK57: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 5.16/2.15 thf(func_def_148, type, sK58: !>[X0: $tType]:(option @ X0 > (X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_149, type, sK59: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 5.16/2.15 thf(func_def_150, type, sK60: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 5.16/2.15 thf(func_def_151, type, sK61: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > (X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_152, type, sK62: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_153, type, sK63: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_154, type, sK64: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1)).
% 5.16/2.15 thf(func_def_155, type, sK65: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0)).
% 5.16/2.15 thf(func_def_156, type, sK66: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_157, type, sK67: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_158, type, sK68: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > set @ X0 > X0)).
% 5.16/2.15 thf(func_def_159, type, sK69: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 5.16/2.15 thf(func_def_160, type, sK70: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable).
% 5.16/2.15 thf(func_def_161, type, sK71: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > trm).
% 5.16/2.15 thf(func_def_162, type, sK72: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > trm).
% 5.16/2.15 thf(func_def_163, type, sK73: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 5.16/2.15 thf(func_def_164, type, sK74: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable).
% 5.16/2.15 thf(func_def_165, type, sK75: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > char).
% 5.16/2.15 thf(func_def_166, type, sK76: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > trm).
% 5.16/2.15 thf(func_def_167, type, sK77: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 5.16/2.15 thf(func_def_168, type, sK78: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable).
% 5.16/2.15 thf(func_def_169, type, sK79: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > variable).
% 5.16/2.15 thf(func_def_170, type, sK80: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 5.16/2.15 thf(func_def_171, type, sK81: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable).
% 5.16/2.15 thf(func_def_172, type, sK82: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > trm).
% 5.16/2.15 thf(func_def_173, type, sK83: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 5.16/2.15 thf(func_def_174, type, sK84: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable).
% 5.16/2.15 thf(func_def_175, type, sK85: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > real).
% 5.16/2.15 thf(func_def_176, type, sK86: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 5.16/2.15 thf(func_def_177, type, sK87: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable).
% 5.16/2.15 thf(func_def_178, type, sK88: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > char).
% 5.16/2.15 thf(func_def_179, type, sK89: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 5.16/2.15 thf(func_def_180, type, sK90: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable).
% 5.16/2.15 thf(func_def_181, type, sK91: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > trm).
% 5.16/2.15 thf(func_def_182, type, sK92: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > trm).
% 5.16/2.15 thf(func_def_183, type, sK93: option @ trm > trm).
% 5.16/2.15 thf(func_def_184, type, sK94: option @ trm > option @ trm > option @ trm > trm).
% 5.16/2.15 thf(func_def_185, type, sK95: option @ trm > option @ trm > option @ trm > trm).
% 5.16/2.15 thf(func_def_186, type, sK96: (variable > option @ trm > $o) > variable).
% 5.16/2.15 thf(func_def_187, type, sK97: (variable > option @ trm > $o) > variable).
% 5.16/2.15 thf(func_def_188, type, sK98: (variable > option @ trm > $o) > trm).
% 5.16/2.15 thf(func_def_189, type, sK99: (variable > option @ fml > $o) > variable).
% 5.16/2.15 thf(func_def_190, type, sK100: (variable > option @ fml > $o) > variable).
% 5.16/2.15 thf(func_def_191, type, sK101: (variable > option @ fml > $o) > fml).
% 5.16/2.15 thf(func_def_192, type, sK102: option @ game > option @ trm > variable > trm).
% 5.16/2.15 thf(func_def_193, type, sK103: option @ trm > option @ trm > option @ trm > trm).
% 5.16/2.15 thf(func_def_194, type, sK104: option @ trm > option @ trm > option @ trm > trm).
% 5.16/2.15 thf(func_def_195, type, sK105: option @ trm > option @ trm > option @ trm > trm).
% 5.16/2.15 thf(func_def_196, type, sK106: !>[X0: $tType]:(option @ X0 > X0)).
% 5.16/2.15 thf(func_def_197, type, sK107: product_prod @ char @ option @ trm > char).
% 5.16/2.15 thf(func_def_198, type, sK108: product_prod @ char @ option @ trm > trm).
% 5.16/2.15 thf(func_def_199, type, sK109: product_prod @ char @ option @ trm > char).
% 5.16/2.15 thf(func_def_200, type, sK110: product_prod @ option @ fml @ option @ fml > fml).
% 5.16/2.15 thf(func_def_201, type, sK111: product_prod @ option @ fml @ option @ fml > option @ fml).
% 5.16/2.15 thf(func_def_202, type, sK112: product_prod @ option @ fml @ option @ fml > fml).
% 5.16/2.15 thf(func_def_203, type, sK113: product_prod @ option @ fml @ option @ fml > fml).
% 5.16/2.15 thf(func_def_204, type, sK114: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_205, type, sK115: (option @ fml > $o) > fml).
% 5.16/2.15 thf(func_def_206, type, sK116: !>[X0: $tType]:((option @ X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_207, type, sK117: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_208, type, sK118: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_209, type, sK119: (option @ trm > option @ trm > $o) > trm).
% 5.16/2.15 thf(func_def_210, type, sK120: (option @ trm > option @ trm > $o) > option @ trm).
% 5.16/2.15 thf(func_def_211, type, sK121: (option @ trm > option @ trm > $o) > trm).
% 5.16/2.15 thf(func_def_212, type, sK122: (option @ trm > option @ trm > $o) > trm).
% 5.16/2.15 thf(func_def_213, type, sK123: (option @ game > option @ game > $o) > option @ game).
% 5.16/2.15 thf(func_def_214, type, sK124: (option @ game > option @ game > $o) > game).
% 5.16/2.15 thf(func_def_215, type, sK125: (option @ game > option @ game > $o) > game).
% 5.16/2.15 thf(func_def_216, type, sK126: (option @ game > option @ game > $o) > game).
% 5.16/2.15 thf(func_def_217, type, sK127: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 5.16/2.15 thf(func_def_218, type, sK128: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 5.16/2.15 thf(func_def_219, type, sK129: option @ fml > fml).
% 5.16/2.15 thf(func_def_220, type, sK130: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 5.16/2.15 thf(func_def_221, type, sK131: !>[X0: $tType]:(X0 > (X0 > X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_222, type, sK132: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 5.16/2.15 thf(func_def_223, type, sK133: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 5.16/2.15 thf(func_def_224, type, sK134: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 5.16/2.15 thf(func_def_225, type, sK135: option @ trm > char > option @ game > trm).
% 5.16/2.15 thf(func_def_226, type, sK136: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_227, type, sK137: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_228, type, sK138: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_229, type, sK139: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_230, type, sK140: !>[X0: $tType]:(option @ X0 > X0)).
% 5.16/2.15 thf(func_def_231, type, sK141: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X0 > $o) > (X1 > $o) > X1)).
% 5.16/2.15 thf(func_def_232, type, sK142: (option @ game > $o) > game).
% 5.16/2.15 thf(func_def_233, type, sK143: option @ trm > option @ trm > trm).
% 5.16/2.15 thf(func_def_234, type, sK144: option @ trm > option @ trm > trm).
% 5.16/2.15 thf(func_def_235, type, sK145: trm > real).
% 5.16/2.15 thf(func_def_236, type, sK146: trm > variable).
% 5.16/2.15 thf(func_def_237, type, sK147: trm > trm).
% 5.16/2.15 thf(func_def_238, type, sK148: trm > trm).
% 5.16/2.15 thf(func_def_239, type, sK149: trm > trm).
% 5.16/2.15 thf(func_def_240, type, sK150: trm > char).
% 5.16/2.15 thf(func_def_241, type, sK151: trm > trm).
% 5.16/2.15 thf(func_def_242, type, sK152: trm > char).
% 5.16/2.15 thf(func_def_243, type, sK153: trm > trm).
% 5.16/2.15 thf(func_def_244, type, sK154: trm > trm).
% 5.16/2.15 thf(func_def_245, type, sK155: (option @ trm > $o) > trm).
% 5.16/2.15 thf(func_def_246, type, sK156: option @ trm > option @ trm > option @ trm > trm).
% 5.16/2.15 thf(func_def_247, type, sK157: option @ trm > option @ trm > option @ trm > trm).
% 5.16/2.15 thf(func_def_248, type, sK158: option @ trm > option @ trm > option @ trm > trm).
% 5.16/2.15 thf(func_def_249, type, sK159: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 5.16/2.15 thf(func_def_250, type, sK160: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 5.16/2.15 thf(func_def_251, type, sK161: (option @ fml > option @ fml > $o) > option @ fml).
% 5.16/2.15 thf(func_def_252, type, sK162: (option @ fml > option @ fml > $o) > fml).
% 5.16/2.15 thf(func_def_253, type, sK163: (option @ fml > option @ fml > $o) > fml).
% 5.16/2.15 thf(func_def_254, type, sK164: (option @ fml > option @ fml > $o) > fml).
% 5.16/2.15 thf(func_def_255, type, sK165: product_prod @ variable @ option @ trm > variable).
% 5.16/2.15 thf(func_def_256, type, sK166: product_prod @ variable @ option @ trm > trm).
% 5.16/2.15 thf(func_def_257, type, sK167: product_prod @ variable @ option @ trm > variable).
% 5.16/2.15 thf(func_def_258, type, sK168: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_259, type, sK169: product_prod @ option @ game @ option @ fml > game).
% 5.16/2.15 thf(func_def_260, type, sK170: product_prod @ option @ game @ option @ fml > game).
% 5.16/2.15 thf(func_def_261, type, sK171: product_prod @ option @ game @ option @ fml > fml).
% 5.16/2.15 thf(func_def_262, type, sK172: product_prod @ option @ game @ option @ fml > option @ fml).
% 5.16/2.15 thf(func_def_263, type, sK173: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 5.16/2.15 thf(func_def_264, type, sK174: option @ game > game).
% 5.16/2.15 thf(func_def_265, type, sK175: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_266, type, sK176: !>[X0: $tType]:(set @ X0 > X0)).
% 5.16/2.15 thf(func_def_267, type, sK177: option @ trm > trm).
% 5.16/2.15 thf(func_def_268, type, sK178: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_269, type, sK179: option @ game > option @ fml > fml).
% 5.16/2.15 thf(func_def_270, type, sK180: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_271, type, sK181: option @ trm > trm).
% 5.16/2.15 thf(func_def_272, type, sK182: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_273, type, sK183: option @ game > option @ trm > variable > trm).
% 5.16/2.15 thf(func_def_274, type, sK184: option @ trm > trm).
% 5.16/2.15 thf(func_def_275, type, sK185: option @ trm > option @ trm > option @ trm > trm).
% 5.16/2.15 thf(func_def_276, type, sK186: option @ trm > option @ trm > option @ trm > trm).
% 5.16/2.15 thf(func_def_277, type, sK187: option @ fml > fml).
% 5.16/2.15 thf(func_def_278, type, sK188: product_prod @ variable @ option @ fml > variable).
% 5.16/2.15 thf(func_def_279, type, sK189: product_prod @ variable @ option @ fml > variable).
% 5.16/2.15 thf(func_def_280, type, sK190: product_prod @ variable @ option @ fml > fml).
% 5.16/2.15 thf(func_def_281, type, sK191: option @ game > option @ trm > char > trm).
% 5.16/2.15 thf(func_def_282, type, sK192: !>[X0: $tType]:(X0 > (X0 > X0 > $o) > X0)).
% 5.16/2.15 thf(func_def_283, type, sK193: product_prod @ option @ game @ option @ game > game).
% 5.16/2.15 thf(func_def_284, type, sK194: product_prod @ option @ game @ option @ game > game).
% 5.16/2.15 thf(func_def_285, type, sK195: product_prod @ option @ game @ option @ game > option @ game).
% 5.16/2.15 thf(func_def_286, type, sK196: product_prod @ option @ game @ option @ game > game).
% 5.16/2.15 thf(func_def_287, type, sK197: (option @ game > option @ fml > $o) > game).
% 5.16/2.15 thf(func_def_288, type, sK198: (option @ game > option @ fml > $o) > option @ fml).
% 5.16/2.15 thf(func_def_289, type, sK199: (option @ game > option @ fml > $o) > game).
% 5.16/2.15 thf(func_def_290, type, sK200: (option @ game > option @ fml > $o) > fml).
% 5.16/2.15 thf(func_def_291, type, sK201: !>[X0: $tType, X1: $tType]:((option @ X0 > option @ X1 > $o) > option @ X1 > option @ X0 > X0)).
% 5.16/2.15 thf(func_def_292, type, sK202: !>[X0: $tType, X1: $tType]:((option @ X0 > option @ X1 > $o) > option @ X1 > option @ X0 > X1)).
% 5.16/2.15 thf(func_def_293, type, sK203: product_prod @ option @ trm @ option @ trm > trm).
% 5.16/2.15 thf(func_def_294, type, sK204: product_prod @ option @ trm @ option @ trm > trm).
% 5.16/2.15 thf(func_def_295, type, sK205: product_prod @ option @ trm @ option @ trm > trm).
% 5.16/2.15 thf(func_def_296, type, sK206: product_prod @ option @ trm @ option @ trm > option @ trm).
% 5.16/2.15 thf(func_def_297, type, sK207: option @ trm > option @ fml > option @ trm > trm).
% 5.16/2.15 thf(func_def_298, type, sK208: option @ trm > option @ fml > option @ trm > trm).
% 5.16/2.15 thf(func_def_299, type, sK209: option @ trm > trm).
% 5.16/2.15 thf(func_def_300, type, sK210: product_prod @ denotational_interp @ trm > denotational_interp).
% 5.16/2.15 thf(func_def_301, type, sK211: product_prod @ denotational_interp @ trm > variable).
% 5.16/2.15 thf(func_def_302, type, sK212: product_prod @ denotational_interp @ trm > denotational_interp).
% 5.16/2.15 thf(func_def_303, type, sK213: product_prod @ denotational_interp @ trm > trm).
% 5.16/2.15 thf(func_def_304, type, sK214: product_prod @ denotational_interp @ trm > trm).
% 5.16/2.15 thf(func_def_305, type, sK215: product_prod @ denotational_interp @ trm > denotational_interp).
% 5.16/2.15 thf(func_def_306, type, sK216: product_prod @ denotational_interp @ trm > trm).
% 5.16/2.15 thf(func_def_307, type, sK217: product_prod @ denotational_interp @ trm > trm).
% 5.16/2.15 thf(func_def_308, type, sK218: product_prod @ denotational_interp @ trm > denotational_interp).
% 5.16/2.15 thf(func_def_309, type, sK219: product_prod @ denotational_interp @ trm > char).
% 5.16/2.15 thf(func_def_310, type, sK220: product_prod @ denotational_interp @ trm > denotational_interp).
% 5.16/2.15 thf(func_def_311, type, sK221: product_prod @ denotational_interp @ trm > char).
% 5.16/2.15 thf(func_def_312, type, sK222: product_prod @ denotational_interp @ trm > trm).
% 5.16/2.15 thf(func_def_313, type, sK223: product_prod @ denotational_interp @ trm > denotational_interp).
% 5.16/2.15 thf(func_def_314, type, sK224: product_prod @ denotational_interp @ trm > trm).
% 5.16/2.15 thf(func_def_315, type, sK225: product_prod @ denotational_interp @ trm > denotational_interp).
% 5.16/2.15 thf(func_def_316, type, sK226: product_prod @ denotational_interp @ trm > real).
% 5.16/2.15 thf(func_def_317, type, sK227: !>[X0: $tType]:(X0)).
% 5.16/2.15 thf(func_def_318, type, sK228: option @ trm > option @ fml > option @ trm > trm).
% 5.16/2.15 thf(func_def_319, type, sK229: option @ trm > option @ fml > option @ trm > trm).
% 5.16/2.15 thf(func_def_320, type, sK230: option @ trm > option @ fml > option @ trm > trm).
% 5.16/2.15 thf(func_def_322, type, ph232: !>[X0: $tType]:(X0)).
% 5.16/2.15 thf(f2349,plain,(
% 5.16/2.15 $false),
% 5.16/2.15 inference(trivial_inequality_removal,[status(thm)],[f2336])).
% 5.16/2.15 thf(f2336,plain,(
% 5.16/2.15 (none @ fml != none @ fml)),
% 5.16/2.15 inference(superposition,[status(thm)],[f1716,f2076])).
% 5.16/2.15 thf(f2076,plain,(
% 5.16/2.15 ( ! [X0 : trm] : ((none @ fml = (uSubst95898978stappf @ sigma @ ua @ (geq @ theta @ X0)))) )),
% 5.16/2.15 inference(forward_demodulation,[status(thm)],[f2032,f1922])).
% 5.16/2.15 thf(f1922,plain,(
% 5.16/2.15 ( ! [X1 : option @ trm] : ((none @ fml = (uSubst1556497037e_Geqo @ none @ trm @ X1))) )),
% 5.16/2.15 inference(equality_resolution,[status(thm)],[f1611])).
% 5.16/2.15 thf(f1611,plain,(
% 5.16/2.15 ( ! [X0 : option @ trm,X1 : option @ trm] : ((none @ fml = (uSubst1556497037e_Geqo @ X0 @ X1)) | (none @ trm != X0)) )),
% 5.16/2.15 inference(cnf_transformation,[status(thm)],[f1169])).
% 5.16/2.15 thf(f1169,plain,(
% 5.16/2.15 ! [X0 : option @ trm,X1 : option @ trm] : (((none @ fml = (uSubst1556497037e_Geqo @ X0 @ X1)) | ((none @ trm != X0) & (none @ trm != X1))) & ((none @ trm = X0) | (none @ trm = X1) | (none @ fml != (uSubst1556497037e_Geqo @ X0 @ X1))))),
% 5.16/2.15 inference(flattening,[status(thm)],[f1168])).
% 5.16/2.15 thf(f1168,plain,(
% 5.16/2.15 ! [X0 : option @ trm,X1 : option @ trm] : (((none @ fml = (uSubst1556497037e_Geqo @ X0 @ X1)) | ((none @ trm != X0) & (none @ trm != X1))) & (((none @ trm = X0) | (none @ trm = X1)) | (none @ fml != (uSubst1556497037e_Geqo @ X0 @ X1))))),
% 5.16/2.15 inference(nnf_transformation,[status(thm)],[f611])).
% 5.16/2.15 thf(f611,plain,(
% 5.16/2.15 ! [X0 : option @ trm,X1 : option @ trm] : ((none @ fml = (uSubst1556497037e_Geqo @ X0 @ X1)) <=> ((none @ trm = X0) | (none @ trm = X1)))),
% 5.16/2.15 inference(fool_elimination,[status(thm)],[f610])).
% 5.16/2.15 thf(f610,plain,(
% 5.16/2.15 ! [X0 : option @ trm,X1 : option @ trm] : ((none @ fml = (uSubst1556497037e_Geqo @ X0 @ X1)) = (none @ trm = X1) | (none @ trm = X0))),
% 5.16/2.15 inference(rectify,[status(thm)],[f22])).
% 5.16/2.15 thf(f22,axiom,(
% 5.16/2.15 ! [X5 : option @ trm,X6 : option @ trm] : ((none @ fml = (uSubst1556497037e_Geqo @ X5 @ X6)) = (none @ trm = X6) | (none @ trm = X5))),
% 5.16/2.15 file('/export/starexec/sandbox/tmp/tmp.LNgQuHokvE/DTF2THF_23487.p',fact_21_Geqo__undef)).
% 5.16/2.15 thf(f2032,plain,(
% 5.16/2.15 ( ! [X0 : trm] : (((uSubst95898978stappf @ sigma @ ua @ (geq @ theta @ X0)) = (uSubst1556497037e_Geqo @ none @ trm @ (uSubst95898992stappt @ sigma @ ua @ X0)))) )),
% 5.16/2.15 inference(superposition,[status(thm)],[f1834,f1382])).
% 5.16/2.15 thf(f1382,plain,(
% 5.16/2.15 (none @ trm = (uSubst95898992stappt @ sigma @ ua @ theta))),
% 5.16/2.15 inference(cnf_transformation,[status(thm)],[f733])).
% 5.16/2.15 thf(f733,plain,(
% 5.16/2.15 (none @ trm = (uSubst95898992stappt @ sigma @ ua @ theta))),
% 5.16/2.15 inference(flattening,[status(thm)],[f280])).
% 5.16/2.15 thf(f280,negated_conjecture,(
% 5.16/2.15 ~(none @ trm != (uSubst95898992stappt @ sigma @ ua @ theta))),
% 5.16/2.15 inference(negated_conjecture,[status(cth)],[f279])).
% 5.16/2.15 thf(f279,conjecture,(
% 5.16/2.15 (none @ trm != (uSubst95898992stappt @ sigma @ ua @ theta))),
% 5.16/2.15 file('/export/starexec/sandbox/tmp/tmp.LNgQuHokvE/DTF2THF_23487.p',conj_0)).
% 5.16/2.15 thf(f1834,plain,(
% 5.16/2.15 ( ! [X2 : trm,X3 : trm,X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X1 : set @ variable] : (((uSubst95898978stappf @ X0 @ X1 @ (geq @ X2 @ X3)) = (uSubst1556497037e_Geqo @ (uSubst95898992stappt @ X0 @ X1 @ X2) @ (uSubst95898992stappt @ X0 @ X1 @ X3)))) )),
% 5.16/2.16 inference(cnf_transformation,[status(thm)],[f719])).
% 5.16/2.16 thf(f719,plain,(
% 5.16/2.16 ! [X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X1 : set @ variable,X2 : trm,X3 : trm] : ((uSubst95898978stappf @ X0 @ X1 @ (geq @ X2 @ X3)) = (uSubst1556497037e_Geqo @ (uSubst95898992stappt @ X0 @ X1 @ X2) @ (uSubst95898992stappt @ X0 @ X1 @ X3)))),
% 5.16/2.16 inference(rectify,[status(thm)],[f21])).
% 5.16/2.16 thf(f21,axiom,(
% 5.16/2.16 ! [X3 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X4 : set @ variable,X5 : trm,X6 : trm] : ((uSubst95898978stappf @ X3 @ X4 @ (geq @ X5 @ X6)) = (uSubst1556497037e_Geqo @ (uSubst95898992stappt @ X3 @ X4 @ X5) @ (uSubst95898992stappt @ X3 @ X4 @ X6)))),
% 5.16/2.16 file('/export/starexec/sandbox/tmp/tmp.LNgQuHokvE/DTF2THF_23487.p',fact_20_usubstappf_Osimps_I2_J)).
% 5.16/2.16 thf(f1716,plain,(
% 5.16/2.16 (none @ fml != (uSubst95898978stappf @ sigma @ ua @ (geq @ theta @ eta)))),
% 5.16/2.16 inference(cnf_transformation,[status(thm)],[f3])).
% 5.16/2.16 thf(f3,axiom,(
% 5.16/2.16 (none @ fml != (uSubst95898978stappf @ sigma @ ua @ (geq @ theta @ eta)))),
% 5.16/2.16 file('/export/starexec/sandbox/tmp/tmp.LNgQuHokvE/DTF2THF_23487.p',fact_2_Geq_Oprems_I1_J)).
% 5.16/2.16 % SZS output end Proof for DTF2THF_23487
% 5.16/2.16 % (23621)------------------------------
% 5.16/2.16 % (23621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.16/2.16 % (23621)Termination reason: Refutation
% 5.16/2.16
% 5.16/2.16 % (23621)Memory used [KB]: 7931
% 5.16/2.16 % (23621)Time elapsed: 0.137 s
% 5.16/2.16 % (23621)Instructions burned: 237 (million)
% 5.16/2.16 % (23621)------------------------------
% 5.16/2.16 % (23621)------------------------------
% 5.16/2.16 % (23597)Success in time 0.26 s
%------------------------------------------------------------------------------