%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP202^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 08:56:23 AM UTC 2026
% Result : Theorem 3.08s 1.74s
% Output : Refutation 3.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP202^2 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n014.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:29:42 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : ITP202^2 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.46 % Domain : Interactive Theorem Proving
% 0.30/0.46 % Problem : Sledgehammer USubst problem prob_411__6333658_1
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Des21]
% 0.30/0.46 % Names : USubst/prob_411__6333658_1 [Des21]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v7.5.0
% 0.30/0.46 % Syntax : Number of formulae : 337 ( 149 unt; 61 typ; 0 def)
% 0.30/0.46 % Number of atoms : 695 ( 495 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 31 ( 2 avg)
% 0.30/0.46 % Number of connectives : 7368 ( 199 ~; 10 |; 25 &;6770 @)
% 0.30/0.46 % ( 0 <=>; 364 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 29 ( 7 avg)
% 0.30/0.46 % Number of types : 8 ( 7 usr)
% 0.30/0.46 % Number of type conns : 1260 (1260 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 57 ( 54 usr; 7 con; 0-8 aty)
% 0.30/0.46 % Number of variables : 1395 ( 225 ^;1126 !; 14 ?;1395 :)
% 0.30/0.46 % ( 30 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.46 % SPC : TH1_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:19:27.220
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % Could-be-implicit typings (10)
% 0.30/0.46 thf(ty_t_Denotational__Semantics_Ointerp,type,
% 0.30/0.46 denotational_interp: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Product__Type_Oprod,type,
% 0.30/0.46 product_prod: $tType > $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Syntax_Ovariable,type,
% 0.30/0.46 variable: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Option_Ooption,type,
% 0.30/0.46 option: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Syntax_Ogame,type,
% 0.30/0.46 game: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_String_Ochar,type,
% 0.30/0.46 char: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Syntax_Otrm,type,
% 0.30/0.46 trm: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Syntax_Ofml,type,
% 0.30/0.46 fml: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Real_Oreal,type,
% 0.30/0.46 real: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Set_Oset,type,
% 0.30/0.46 set: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 % Explicit typings (51)
% 0.30/0.46 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.30/0.46 bounded_lattice:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_HOL_Otype,type,
% 0.30/0.46 type:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Obot,type,
% 0.30/0.46 bot:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Lattices_Olattice,type,
% 0.30/0.46 lattice:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 0.30/0.46 semilattice_inf:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 0.30/0.46 bounded_lattice_bot:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_If,type,
% 0.30/0.46 if:
% 0.30/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.30/0.46 inf_inf:
% 0.30/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Option_Ocombine__options,type,
% 0.30/0.46 combine_options:
% 0.30/0.46 !>[A: $tType] : ( ( A > A > A ) > ( option @ A ) > ( option @ A ) > ( option @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Option_Ooption_ONone,type,
% 0.30/0.46 none:
% 0.30/0.46 !>[A: $tType] : ( option @ A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Option_Ooption_OSome,type,
% 0.30/0.46 some:
% 0.30/0.46 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Option_Ooption_Ocase__option,type,
% 0.30/0.46 case_option:
% 0.30/0.46 !>[B: $tType,A: $tType] : ( B > ( A > B ) > ( option @ A ) > B ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Option_Ooption_Othe,type,
% 0.30/0.46 the:
% 0.30/0.46 !>[A: $tType] : ( ( option @ A ) > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.30/0.46 bot_bot:
% 0.30/0.46 !>[A: $tType] : A ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair,type,
% 0.30/0.46 product_Pair:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.30/0.46 produc2004651681e_prod:
% 0.30/0.46 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.30/0.46 product_rec_prod:
% 0.30/0.46 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Oprod_Ocase__prod,type,
% 0.30/0.46 product_case_prod:
% 0.30/0.46 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect,type,
% 0.30/0.46 collect:
% 0.30/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Ois__empty,type,
% 0.30/0.46 is_empty:
% 0.30/0.46 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Static__Semantics_OFVF,type,
% 0.30/0.46 static_FVF: fml > ( set @ variable ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Static__Semantics_OFVT,type,
% 0.30/0.46 static_FVT: trm > ( set @ variable ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_String_Ochar_OChar,type,
% 0.30/0.46 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Ofml_OGeq,type,
% 0.30/0.46 geq: trm > trm > fml ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Ofml_OPred,type,
% 0.30/0.46 pred: char > trm > fml ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_OConst,type,
% 0.30/0.46 const: char > trm ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_ODifferential,type,
% 0.30/0.46 differential: trm > trm ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_OFunc,type,
% 0.30/0.46 func: char > trm > trm ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_ONumber,type,
% 0.30/0.46 number: real > trm ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_OPlus,type,
% 0.30/0.46 plus: trm > trm > trm ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_OTimes,type,
% 0.30/0.46 times: trm > trm > trm ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_OVar,type,
% 0.30/0.46 var: variable > trm ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_ODifferentialo,type,
% 0.30/0.46 uSubst259074819ntialo: ( option @ trm ) > ( option @ trm ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OGeqo,type,
% 0.30/0.46 uSubst1556497037e_Geqo: ( option @ trm ) > ( option @ trm ) > ( option @ fml ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OGeqo__rel,type,
% 0.30/0.46 uSubst864323244qo_rel: ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OPluso,type,
% 0.30/0.46 uSubst1112714340_Pluso: ( option @ trm ) > ( option @ trm ) > ( option @ trm ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OPluso__rel,type,
% 0.30/0.46 uSubst270600597so_rel: ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTimeso,type,
% 0.30/0.46 uSubst277968634Timeso: ( option @ trm ) > ( option @ trm ) > ( option @ trm ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTimeso__rel,type,
% 0.30/0.46 uSubst1377811071so_rel: ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Odot,type,
% 0.30/0.46 uSubst_Mirabelle_dot: trm ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Odotsubstt,type,
% 0.30/0.46 uSubst969145931substt: trm > ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousappconst,type,
% 0.30/0.46 uSubst1138577137pconst: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > char > ( option @ trm ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappf,type,
% 0.30/0.46 uSubst95898978stappf: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > fml > ( option @ fml ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappt,type,
% 0.30/0.46 uSubst95898992stappt: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > trm > ( option @ trm ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappt__rel,type,
% 0.30/0.46 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 ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Wellfounded_Oaccp,type,
% 0.30/0.46 accp:
% 0.30/0.46 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member,type,
% 0.30/0.46 member:
% 0.30/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_U,type,
% 0.30/0.46 u: set @ variable ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_V,type,
% 0.30/0.46 v: set @ variable ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v__092_060sigma_062,type,
% 0.30/0.46 sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_f____,type,
% 0.30/0.46 f: char ).
% 0.30/0.46
% 0.30/0.46 % Relevant facts (255)
% 0.30/0.46 thf(fact_0_f2,axiom,
% 0.30/0.46 ! [Z: option @ trm,F: trm > ( option @ trm ),Za: option @ trm] :
% 0.30/0.46 ( ( ( Za
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 => ( ( case_option @ ( option @ trm ) @ trm @ Z @ F @ Za )
% 0.30/0.46 = Z ) )
% 0.30/0.46 & ( ( Za
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( case_option @ ( option @ trm ) @ trm @ Z @ F @ Za )
% 0.30/0.46 = ( F @ ( the @ trm @ Za ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % f2
% 0.30/0.46 thf(fact_1_Const_Oprems_I1_J,axiom,
% 0.30/0.46 ( ( uSubst95898992stappt @ sigma @ u @ ( const @ f ) )
% 0.30/0.46 != ( none @ trm ) ) ).
% 0.30/0.46
% 0.30/0.46 % Const.prems(1)
% 0.30/0.46 thf(fact_2_Const_Oprems_I2_J,axiom,
% 0.30/0.46 ( ( uSubst95898992stappt @ sigma @ v @ ( const @ f ) )
% 0.30/0.46 != ( none @ trm ) ) ).
% 0.30/0.46
% 0.30/0.46 % Const.prems(2)
% 0.30/0.46 thf(fact_3_f3,axiom,
% 0.30/0.46 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ f )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( inf_inf @ ( set @ variable )
% 0.30/0.46 @ ( static_FVT
% 0.30/0.46 @ ( the @ trm
% 0.30/0.46 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ f ) ) )
% 0.30/0.46 @ u )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % f3
% 0.30/0.46 thf(fact_4__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062,axiom,
% 0.30/0.46 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ f )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( inf_inf @ ( set @ variable )
% 0.30/0.46 @ ( static_FVT
% 0.30/0.46 @ ( the @ trm
% 0.30/0.46 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ f ) ) )
% 0.30/0.46 @ v )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>SConst \<sigma> f \<noteq> undeft \<longrightarrow> FVT (the (SConst \<sigma> f)) \<inter> V = {}\<close>
% 0.30/0.46 thf(fact_5_usappconst__def,axiom,
% 0.30/0.46 ( uSubst1138577137pconst
% 0.30/0.46 = ( ^ [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F2: char] :
% 0.30/0.46 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( const @ F2 ) )
% 0.30/0.46 @ ^ [R: trm] :
% 0.30/0.46 ( if @ ( option @ trm )
% 0.30/0.46 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R ) @ U )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 @ ( some @ trm @ R )
% 0.30/0.46 @ ( none @ trm ) )
% 0.30/0.46 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ Sigma
% 0.30/0.46 @ F2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usappconst_def
% 0.30/0.46 thf(fact_6_f1,axiom,
% 0.30/0.46 ( ( uSubst95898992stappt @ sigma @ u @ ( const @ f ) )
% 0.30/0.46 = ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( const @ f ) )
% 0.30/0.46 @ ^ [T2: trm] :
% 0.30/0.46 ( if @ ( option @ trm )
% 0.30/0.46 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ T2 ) @ u )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 @ ( some @ trm @ T2 )
% 0.30/0.46 @ ( none @ trm ) )
% 0.30/0.46 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ f ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % f1
% 0.30/0.46 thf(fact_7_usubstappt_Osimps_I3_J,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,F3: char] :
% 0.30/0.46 ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( const @ F3 ) )
% 0.30/0.46 = ( uSubst1138577137pconst @ Sigma2 @ U2 @ F3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.simps(3)
% 0.30/0.46 thf(fact_8_undeft__None,axiom,
% 0.30/0.46 ( ( none @ trm )
% 0.30/0.46 = ( none @ trm ) ) ).
% 0.30/0.46
% 0.30/0.46 % undeft_None
% 0.30/0.46 thf(fact_9__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AV_Af_092_060close_062,axiom,
% 0.30/0.46 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ f )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( ( ( inf_inf @ ( set @ variable )
% 0.30/0.46 @ ( static_FVT
% 0.30/0.46 @ ( the @ trm
% 0.30/0.46 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ f ) ) )
% 0.30/0.46 @ v )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 => ( ( some @ trm
% 0.30/0.46 @ ( the @ trm
% 0.30/0.46 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ f ) ) )
% 0.30/0.46 = ( uSubst1138577137pconst @ sigma @ v @ f ) ) )
% 0.30/0.46 & ( ( ( inf_inf @ ( set @ variable )
% 0.30/0.46 @ ( static_FVT
% 0.30/0.46 @ ( the @ trm
% 0.30/0.46 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ f ) ) )
% 0.30/0.46 @ v )
% 0.30/0.46 != ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 => ( ( none @ trm )
% 0.30/0.46 = ( uSubst1138577137pconst @ sigma @ v @ f ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>SConst \<sigma> f \<noteq> undeft \<longrightarrow> (if FVT (the (SConst \<sigma> f)) \<inter> V = {} then Aterm (the (SConst \<sigma> f)) else undeft) = usappconst \<sigma> V f\<close>
% 0.30/0.46 thf(fact_10__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AU_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AU_Af_092_060close_062,axiom,
% 0.30/0.46 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ f )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( ( ( inf_inf @ ( set @ variable )
% 0.30/0.46 @ ( static_FVT
% 0.30/0.46 @ ( the @ trm
% 0.30/0.46 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ f ) ) )
% 0.30/0.46 @ u )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 => ( ( some @ trm
% 0.30/0.46 @ ( the @ trm
% 0.30/0.46 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ f ) ) )
% 0.30/0.46 = ( uSubst1138577137pconst @ sigma @ u @ f ) ) )
% 0.30/0.46 & ( ( ( inf_inf @ ( set @ variable )
% 0.30/0.46 @ ( static_FVT
% 0.30/0.46 @ ( the @ trm
% 0.30/0.46 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ f ) ) )
% 0.30/0.46 @ u )
% 0.30/0.46 != ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 => ( ( none @ trm )
% 0.30/0.46 = ( uSubst1138577137pconst @ sigma @ u @ f ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>SConst \<sigma> f \<noteq> undeft \<longrightarrow> (if FVT (the (SConst \<sigma> f)) \<inter> U = {} then Aterm (the (SConst \<sigma> f)) else undeft) = usappconst \<sigma> U f\<close>
% 0.30/0.46 thf(fact_11_trm_Oinject_I3_J,axiom,
% 0.30/0.46 ! [X3: char,Y3: char] :
% 0.30/0.46 ( ( ( const @ X3 )
% 0.30/0.46 = ( const @ Y3 ) )
% 0.30/0.46 = ( X3 = Y3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(3)
% 0.30/0.46 thf(fact_12_case__prod__app,axiom,
% 0.30/0.46 ! [A: $tType,D: $tType,C: $tType,B: $tType] :
% 0.30/0.46 ( ( product_case_prod @ B @ C @ ( D > A ) )
% 0.30/0.46 = ( ^ [F2: B > C > D > A,X: product_prod @ B @ C,Y: D] :
% 0.30/0.46 ( product_case_prod @ B @ C @ A
% 0.30/0.46 @ ^ [L: B,R: C] : ( F2 @ L @ R @ Y )
% 0.30/0.46 @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % case_prod_app
% 0.30/0.46 thf(fact_13_usubstappt__const,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F3: char,R2: trm,U2: set @ variable] :
% 0.30/0.46 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ Sigma2
% 0.30/0.46 @ F3 )
% 0.30/0.46 = ( some @ trm @ R2 ) )
% 0.30/0.46 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U2 )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( const @ F3 ) )
% 0.30/0.46 = ( some @ trm @ R2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt_const
% 0.30/0.46 thf(fact_14_usubstappt__const__conv,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,F3: char] :
% 0.30/0.46 ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( const @ F3 ) )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ Sigma2
% 0.30/0.46 @ F3 )
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 | ? [R3: trm] :
% 0.30/0.46 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ Sigma2
% 0.30/0.46 @ F3 )
% 0.30/0.46 = ( some @ trm @ R3 ) )
% 0.30/0.46 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R3 ) @ U2 )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt_const_conv
% 0.30/0.46 thf(fact_15_usappconst__simp,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F3: char,R2: trm,U2: set @ variable] :
% 0.30/0.46 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ Sigma2
% 0.30/0.46 @ F3 )
% 0.30/0.46 = ( some @ trm @ R2 ) )
% 0.30/0.46 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U2 )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 => ( ( uSubst1138577137pconst @ Sigma2 @ U2 @ F3 )
% 0.30/0.46 = ( some @ trm @ R2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usappconst_simp
% 0.30/0.46 thf(fact_16_usappconst__conv,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,F3: char] :
% 0.30/0.46 ( ( ( uSubst1138577137pconst @ Sigma2 @ U2 @ F3 )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ Sigma2
% 0.30/0.46 @ F3 )
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 | ? [R3: trm] :
% 0.30/0.46 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.46 @ Sigma2
% 0.30/0.46 @ F3 )
% 0.30/0.46 = ( some @ trm @ R3 ) )
% 0.30/0.46 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R3 ) @ U2 )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usappconst_conv
% 0.30/0.46 thf(fact_17_ODEo_Oinduct,axiom,
% 0.30/0.46 ! [P: char > ( option @ trm ) > $o,A0: char,A1: option @ trm] :
% 0.30/0.46 ( ! [X2: char,Theta: trm] : ( P @ X2 @ ( some @ trm @ Theta ) )
% 0.30/0.46 => ( ! [X2: char] : ( P @ X2 @ ( none @ trm ) )
% 0.30/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ODEo.induct
% 0.30/0.46 thf(fact_18_undeft__equiv,axiom,
% 0.30/0.46 ! [Theta2: option @ trm] :
% 0.30/0.46 ( ( Theta2
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 = ( ? [T2: trm] :
% 0.30/0.46 ( Theta2
% 0.30/0.46 = ( some @ trm @ T2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % undeft_equiv
% 0.30/0.46 thf(fact_19_Timeso_Oinduct,axiom,
% 0.30/0.46 ! [P: ( option @ trm ) > ( option @ trm ) > $o,A0: option @ trm,A1: option @ trm] :
% 0.30/0.46 ( ! [Theta: trm,Eta: trm] : ( P @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta ) )
% 0.30/0.46 => ( ! [X_1: option @ trm] : ( P @ ( none @ trm ) @ X_1 )
% 0.30/0.46 => ( ! [V: trm] : ( P @ ( some @ trm @ V ) @ ( none @ trm ) )
% 0.30/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Timeso.induct
% 0.30/0.46 thf(fact_20_Assigno_Oinduct,axiom,
% 0.30/0.46 ! [P: variable > ( option @ trm ) > $o,A0: variable,A1: option @ trm] :
% 0.30/0.46 ( ! [X2: variable,Theta: trm] : ( P @ X2 @ ( some @ trm @ Theta ) )
% 0.30/0.46 => ( ! [X2: variable] : ( P @ X2 @ ( none @ trm ) )
% 0.30/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Assigno.induct
% 0.30/0.46 thf(fact_21_Aterm__Some,axiom,
% 0.30/0.46 ( ( some @ trm )
% 0.30/0.46 = ( some @ trm ) ) ).
% 0.30/0.46
% 0.30/0.46 % Aterm_Some
% 0.30/0.46 thf(fact_22_Differentialo_Oinduct,axiom,
% 0.30/0.46 ! [P: ( option @ trm ) > $o,A0: option @ trm] :
% 0.30/0.46 ( ! [Theta: trm] : ( P @ ( some @ trm @ Theta ) )
% 0.30/0.46 => ( ( P @ ( none @ trm ) )
% 0.30/0.46 => ( P @ A0 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Differentialo.induct
% 0.30/0.46 thf(fact_23_Differentialo_Ocases,axiom,
% 0.30/0.46 ! [X4: option @ trm] :
% 0.30/0.46 ( ! [Theta: trm] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( some @ trm @ Theta ) )
% 0.30/0.46 => ( X4
% 0.30/0.46 = ( none @ trm ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Differentialo.cases
% 0.30/0.46 thf(fact_24_option_Ocollapse,axiom,
% 0.30/0.46 ! [A: $tType,Option: option @ A] :
% 0.30/0.46 ( ( Option
% 0.30/0.46 != ( none @ A ) )
% 0.30/0.46 => ( ( some @ A @ ( the @ A @ Option ) )
% 0.30/0.46 = Option ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.collapse
% 0.30/0.46 thf(fact_25_not__Some__eq,axiom,
% 0.30/0.46 ! [A: $tType,X4: option @ A] :
% 0.30/0.46 ( ( ! [Y: A] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( some @ A @ Y ) ) )
% 0.30/0.46 = ( X4
% 0.30/0.46 = ( none @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_Some_eq
% 0.30/0.46 thf(fact_26_not__None__eq,axiom,
% 0.30/0.46 ! [A: $tType,X4: option @ A] :
% 0.30/0.46 ( ( X4
% 0.30/0.46 != ( none @ A ) )
% 0.30/0.46 = ( ? [Y: A] :
% 0.30/0.46 ( X4
% 0.30/0.46 = ( some @ A @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_None_eq
% 0.30/0.46 thf(fact_27_inf__bot__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounded_lattice_bot @ A )
% 0.30/0.46 => ! [X4: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( bot_bot @ A ) @ X4 )
% 0.30/0.46 = ( bot_bot @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_bot_left
% 0.30/0.46 thf(fact_28_inf__bot__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounded_lattice_bot @ A )
% 0.30/0.46 => ! [X4: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X4 @ ( bot_bot @ A ) )
% 0.30/0.46 = ( bot_bot @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_bot_right
% 0.30/0.46 thf(fact_29_usubstappt__func2,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F3: char,R2: trm,U2: set @ variable,Theta2: trm] :
% 0.30/0.46 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F4: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 0.30/0.46 @ Sigma2
% 0.30/0.46 @ F3 )
% 0.30/0.46 = ( some @ trm @ R2 ) )
% 0.30/0.46 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U2 )
% 0.30/0.46 != ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 0.30/0.46 = ( none @ trm ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt_func2
% 0.30/0.46 thf(fact_30_option_Osplit__sel__asm,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 0.30/0.46 ( ( P @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 0.30/0.46 = ( ~ ( ( ( Option
% 0.30/0.46 = ( none @ A ) )
% 0.30/0.46 & ~ ( P @ F1 ) )
% 0.30/0.46 | ( ( Option
% 0.30/0.46 = ( some @ A @ ( the @ A @ Option ) ) )
% 0.30/0.46 & ~ ( P @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.split_sel_asm
% 0.30/0.46 thf(fact_31_option_Osplit__sel,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 0.30/0.46 ( ( P @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 0.30/0.46 = ( ( ( Option
% 0.30/0.46 = ( none @ A ) )
% 0.30/0.46 => ( P @ F1 ) )
% 0.30/0.46 & ( ( Option
% 0.30/0.46 = ( some @ A @ ( the @ A @ Option ) ) )
% 0.30/0.46 => ( P @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.split_sel
% 0.30/0.46 thf(fact_32_usubstappt__func__conv,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,F3: char,Theta2: trm] :
% 0.30/0.46 ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 & ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F4: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 0.30/0.46 @ Sigma2
% 0.30/0.46 @ F3 )
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 | ? [R3: trm] :
% 0.30/0.46 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F4: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 0.30/0.46 @ Sigma2
% 0.30/0.46 @ F3 )
% 0.30/0.46 = ( some @ trm @ R3 ) )
% 0.30/0.46 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R3 ) @ U2 )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt_func_conv
% 0.30/0.46 thf(fact_33_option_Ocase__eq__if,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( case_option @ B @ A )
% 0.30/0.46 = ( ^ [F12: B,F23: A > B,Option2: option @ A] :
% 0.30/0.46 ( if @ B
% 0.30/0.46 @ ( Option2
% 0.30/0.46 = ( none @ A ) )
% 0.30/0.46 @ F12
% 0.30/0.46 @ ( F23 @ ( the @ A @ Option2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.case_eq_if
% 0.30/0.46 thf(fact_34_inf__right__idem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X4: A,Y2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ X4 @ Y2 ) @ Y2 )
% 0.30/0.46 = ( inf_inf @ A @ X4 @ Y2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_right_idem
% 0.30/0.46 thf(fact_35_inf_Oright__idem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 )
% 0.30/0.46 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.right_idem
% 0.30/0.46 thf(fact_36_inf__left__idem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X4: A,Y2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X4 @ ( inf_inf @ A @ X4 @ Y2 ) )
% 0.30/0.46 = ( inf_inf @ A @ X4 @ Y2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_left_idem
% 0.30/0.46 thf(fact_37_inf_Oleft__idem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B2 ) )
% 0.30/0.46 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.left_idem
% 0.30/0.46 thf(fact_38_inf__idem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X4: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X4 @ X4 )
% 0.30/0.46 = X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_idem
% 0.30/0.46 thf(fact_39_inf_Oidem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ A2 @ A2 )
% 0.30/0.46 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.idem
% 0.30/0.46 thf(fact_40_inf__apply,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ B )
% 0.30/0.46 => ( ( inf_inf @ ( A > B ) )
% 0.30/0.46 = ( ^ [F2: A > B,G: A > B,X: A] : ( inf_inf @ B @ ( F2 @ X ) @ ( G @ X ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_apply
% 0.30/0.46 thf(fact_41_option_Oinject,axiom,
% 0.30/0.46 ! [A: $tType,X22: A,Y22: A] :
% 0.30/0.46 ( ( ( some @ A @ X22 )
% 0.30/0.46 = ( some @ A @ Y22 ) )
% 0.30/0.46 = ( X22 = Y22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.inject
% 0.30/0.46 thf(fact_42_trm_Oinject_I4_J,axiom,
% 0.30/0.46 ! [X41: char,X42: trm,Y41: char,Y42: trm] :
% 0.30/0.46 ( ( ( func @ X41 @ X42 )
% 0.30/0.46 = ( func @ Y41 @ Y42 ) )
% 0.30/0.46 = ( ( X41 = Y41 )
% 0.30/0.46 & ( X42 = Y42 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(4)
% 0.30/0.46 thf(fact_43_option_Odisc__eq__case_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,Option: option @ A] :
% 0.30/0.46 ( ( Option
% 0.30/0.46 != ( none @ A ) )
% 0.30/0.46 = ( case_option @ $o @ A @ $false
% 0.30/0.46 @ ^ [Uu: A] : $true
% 0.30/0.46 @ Option ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.disc_eq_case(2)
% 0.30/0.46 thf(fact_44_option_Odisc__eq__case_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,Option: option @ A] :
% 0.30/0.46 ( ( Option
% 0.30/0.46 = ( none @ A ) )
% 0.30/0.46 = ( case_option @ $o @ A @ $true
% 0.30/0.46 @ ^ [Uu: A] : $false
% 0.30/0.46 @ Option ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.disc_eq_case(1)
% 0.30/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,P: A > $o] :
% 0.30/0.46 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.30/0.46 = ( P @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A] :
% 0.30/0.46 ( ( collect @ A
% 0.30/0.46 @ ^ [X: A] : ( member @ A @ X @ A3 ) )
% 0.30/0.46 = A3 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_47_Collect__cong,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X2: A] :
% 0.30/0.46 ( ( P @ X2 )
% 0.30/0.46 = ( Q @ X2 ) )
% 0.30/0.46 => ( ( collect @ A @ P )
% 0.30/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_cong
% 0.30/0.46 thf(fact_48_ext,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F3: A > B,G2: A > B] :
% 0.30/0.46 ( ! [X2: A] :
% 0.30/0.46 ( ( F3 @ X2 )
% 0.30/0.46 = ( G2 @ X2 ) )
% 0.30/0.46 => ( F3 = G2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % ext
% 0.30/0.46 thf(fact_49_trm_Odistinct_I23_J,axiom,
% 0.30/0.46 ! [X3: char,X41: char,X42: trm] :
% 0.30/0.46 ( ( const @ X3 )
% 0.30/0.46 != ( func @ X41 @ X42 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(23)
% 0.30/0.46 thf(fact_50_case__optionE,axiom,
% 0.30/0.46 ! [A: $tType,P: $o,Q: A > $o,X4: option @ A] :
% 0.30/0.46 ( ( case_option @ $o @ A @ P @ Q @ X4 )
% 0.30/0.46 => ( ( ( X4
% 0.30/0.46 = ( none @ A ) )
% 0.30/0.46 => ~ P )
% 0.30/0.46 => ~ ! [Y4: A] :
% 0.30/0.46 ( ( X4
% 0.30/0.46 = ( some @ A @ Y4 ) )
% 0.30/0.46 => ~ ( Q @ Y4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % case_optionE
% 0.30/0.46 thf(fact_51_inf__left__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X4: A,Y2: A,Z2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X4 @ ( inf_inf @ A @ Y2 @ Z2 ) )
% 0.30/0.46 = ( inf_inf @ A @ Y2 @ ( inf_inf @ A @ X4 @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_left_commute
% 0.30/0.46 thf(fact_52_inf_Oleft__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ B2 @ ( inf_inf @ A @ A2 @ C2 ) )
% 0.30/0.46 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.left_commute
% 0.30/0.46 thf(fact_53_inf__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ( ( inf_inf @ A )
% 0.30/0.46 = ( ^ [X: A,Y: A] : ( inf_inf @ A @ Y @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_commute
% 0.30/0.46 thf(fact_54_inf_Ocommute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ( ( inf_inf @ A )
% 0.30/0.46 = ( ^ [A4: A,B3: A] : ( inf_inf @ A @ B3 @ A4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.commute
% 0.30/0.46 thf(fact_55_inf__assoc,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X4: A,Y2: A,Z2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ X4 @ Y2 ) @ Z2 )
% 0.30/0.46 = ( inf_inf @ A @ X4 @ ( inf_inf @ A @ Y2 @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_assoc
% 0.30/0.46 thf(fact_56_inf_Oassoc,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C2 )
% 0.30/0.46 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.assoc
% 0.30/0.46 thf(fact_57_boolean__algebra__cancel_Oinf2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [B4: A,K: A,B2: A,A2: A] :
% 0.30/0.46 ( ( B4
% 0.30/0.46 = ( inf_inf @ A @ K @ B2 ) )
% 0.30/0.46 => ( ( inf_inf @ A @ A2 @ B4 )
% 0.30/0.46 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % boolean_algebra_cancel.inf2
% 0.30/0.46 thf(fact_58_boolean__algebra__cancel_Oinf1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A3: A,K: A,A2: A,B2: A] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 = ( inf_inf @ A @ K @ A2 ) )
% 0.30/0.46 => ( ( inf_inf @ A @ A3 @ B2 )
% 0.30/0.46 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % boolean_algebra_cancel.inf1
% 0.30/0.46 thf(fact_59_inf__fun__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ B )
% 0.30/0.46 => ( ( inf_inf @ ( A > B ) )
% 0.30/0.46 = ( ^ [F2: A > B,G: A > B,X: A] : ( inf_inf @ B @ ( F2 @ X ) @ ( G @ X ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_fun_def
% 0.30/0.46 thf(fact_60_inf__sup__aci_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A )
% 0.30/0.46 => ( ( inf_inf @ A )
% 0.30/0.46 = ( ^ [X: A,Y: A] : ( inf_inf @ A @ Y @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_aci(1)
% 0.30/0.46 thf(fact_61_inf__sup__aci_I2_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A )
% 0.30/0.46 => ! [X4: A,Y2: A,Z2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ X4 @ Y2 ) @ Z2 )
% 0.30/0.46 = ( inf_inf @ A @ X4 @ ( inf_inf @ A @ Y2 @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_aci(2)
% 0.30/0.46 thf(fact_62_inf__sup__aci_I3_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A )
% 0.30/0.46 => ! [X4: A,Y2: A,Z2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X4 @ ( inf_inf @ A @ Y2 @ Z2 ) )
% 0.30/0.46 = ( inf_inf @ A @ Y2 @ ( inf_inf @ A @ X4 @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_aci(3)
% 0.30/0.46 thf(fact_63_inf__sup__aci_I4_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A )
% 0.30/0.46 => ! [X4: A,Y2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X4 @ ( inf_inf @ A @ X4 @ Y2 ) )
% 0.30/0.46 = ( inf_inf @ A @ X4 @ Y2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_aci(4)
% 0.30/0.46 thf(fact_64_option_Ocase__distrib,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType,H: B > C,F1: B,F22: A > B,Option: option @ A] :
% 0.30/0.46 ( ( H @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 0.30/0.46 = ( case_option @ C @ A @ ( H @ F1 )
% 0.30/0.46 @ ^ [X: A] : ( H @ ( F22 @ X ) )
% 0.30/0.46 @ Option ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.case_distrib
% 0.30/0.46 thf(fact_65_option_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,X22: A] :
% 0.30/0.46 ( ( none @ A )
% 0.30/0.46 != ( some @ A @ X22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.distinct(1)
% 0.30/0.46 thf(fact_66_option_OdiscI,axiom,
% 0.30/0.46 ! [A: $tType,Option: option @ A,X22: A] :
% 0.30/0.46 ( ( Option
% 0.30/0.46 = ( some @ A @ X22 ) )
% 0.30/0.46 => ( Option
% 0.30/0.46 != ( none @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.discI
% 0.30/0.46 thf(fact_67_option_Oexhaust,axiom,
% 0.30/0.46 ! [A: $tType,Y2: option @ A] :
% 0.30/0.46 ( ( Y2
% 0.30/0.46 != ( none @ A ) )
% 0.30/0.46 => ~ ! [X23: A] :
% 0.30/0.46 ( Y2
% 0.30/0.46 != ( some @ A @ X23 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.exhaust
% 0.30/0.46 thf(fact_68_option_Oinducts,axiom,
% 0.30/0.46 ! [A: $tType,P: ( option @ A ) > $o,Option: option @ A] :
% 0.30/0.46 ( ( P @ ( none @ A ) )
% 0.30/0.46 => ( ! [X2: A] : ( P @ ( some @ A @ X2 ) )
% 0.30/0.46 => ( P @ Option ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.inducts
% 0.30/0.46 thf(fact_69_split__option__ex,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ^ [P2: ( option @ A ) > $o] :
% 0.30/0.46 ? [X5: option @ A] : ( P2 @ X5 ) )
% 0.30/0.46 = ( ^ [P3: ( option @ A ) > $o] :
% 0.30/0.46 ( ( P3 @ ( none @ A ) )
% 0.30/0.46 | ? [X: A] : ( P3 @ ( some @ A @ X ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_option_ex
% 0.30/0.46 thf(fact_70_split__option__all,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ^ [P2: ( option @ A ) > $o] :
% 0.30/0.46 ! [X5: option @ A] : ( P2 @ X5 ) )
% 0.30/0.46 = ( ^ [P3: ( option @ A ) > $o] :
% 0.30/0.46 ( ( P3 @ ( none @ A ) )
% 0.30/0.46 & ! [X: A] : ( P3 @ ( some @ A @ X ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_option_all
% 0.30/0.46 thf(fact_71_combine__options__cases,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X4: option @ A,P: ( option @ A ) > ( option @ B ) > $o,Y2: option @ B] :
% 0.30/0.46 ( ( ( X4
% 0.30/0.46 = ( none @ A ) )
% 0.30/0.46 => ( P @ X4 @ Y2 ) )
% 0.30/0.46 => ( ( ( Y2
% 0.30/0.46 = ( none @ B ) )
% 0.30/0.46 => ( P @ X4 @ Y2 ) )
% 0.30/0.46 => ( ! [A5: A,B5: B] :
% 0.30/0.46 ( ( X4
% 0.30/0.46 = ( some @ A @ A5 ) )
% 0.30/0.46 => ( ( Y2
% 0.30/0.46 = ( some @ B @ B5 ) )
% 0.30/0.46 => ( P @ X4 @ Y2 ) ) )
% 0.30/0.46 => ( P @ X4 @ Y2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % combine_options_cases
% 0.30/0.46 thf(fact_72_option_Osimps_I4_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F1: B,F22: A > B] :
% 0.30/0.46 ( ( case_option @ B @ A @ F1 @ F22 @ ( none @ A ) )
% 0.30/0.46 = F1 ) ).
% 0.30/0.46
% 0.30/0.46 % option.simps(4)
% 0.30/0.46 thf(fact_73_option_Osimps_I5_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F1: B,F22: A > B,X22: A] :
% 0.30/0.46 ( ( case_option @ B @ A @ F1 @ F22 @ ( some @ A @ X22 ) )
% 0.30/0.46 = ( F22 @ X22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.simps(5)
% 0.30/0.46 thf(fact_74_option_Oexpand,axiom,
% 0.30/0.46 ! [A: $tType,Option: option @ A,Option3: option @ A] :
% 0.30/0.46 ( ( ( Option
% 0.30/0.46 = ( none @ A ) )
% 0.30/0.46 = ( Option3
% 0.30/0.46 = ( none @ A ) ) )
% 0.30/0.46 => ( ( ( Option
% 0.30/0.46 != ( none @ A ) )
% 0.30/0.46 => ( ( Option3
% 0.30/0.46 != ( none @ A ) )
% 0.30/0.46 => ( ( the @ A @ Option )
% 0.30/0.46 = ( the @ A @ Option3 ) ) ) )
% 0.30/0.46 => ( Option = Option3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.expand
% 0.30/0.46 thf(fact_75_option_Osel,axiom,
% 0.30/0.46 ! [A: $tType,X22: A] :
% 0.30/0.46 ( ( the @ A @ ( some @ A @ X22 ) )
% 0.30/0.46 = X22 ) ).
% 0.30/0.46
% 0.30/0.46 % option.sel
% 0.30/0.46 thf(fact_76_option_Oexhaust__sel,axiom,
% 0.30/0.46 ! [A: $tType,Option: option @ A] :
% 0.30/0.46 ( ( Option
% 0.30/0.46 != ( none @ A ) )
% 0.30/0.46 => ( Option
% 0.30/0.46 = ( some @ A @ ( the @ A @ Option ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.exhaust_sel
% 0.30/0.46 thf(fact_77_usubstappt__func,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F3: char,R2: trm,U2: set @ variable,Theta2: trm,Sigma_theta: trm] :
% 0.30/0.46 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F4: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 0.30/0.46 @ Sigma2
% 0.30/0.46 @ F3 )
% 0.30/0.46 = ( some @ trm @ R2 ) )
% 0.30/0.46 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U2 )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 => ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 )
% 0.30/0.46 = ( some @ trm @ Sigma_theta ) )
% 0.30/0.46 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 0.30/0.46 = ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta ) @ ( bot_bot @ ( set @ variable ) ) @ R2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt_func
% 0.30/0.46 thf(fact_78_usubstappt_Osimps_I4_J,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,F3: char,Theta2: trm] :
% 0.30/0.46 ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 0.30/0.46 = ( case_option @ ( option @ trm ) @ trm @ ( none @ trm )
% 0.30/0.46 @ ^ [Sigma_theta2: trm] :
% 0.30/0.46 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( func @ F3 @ Sigma_theta2 ) )
% 0.30/0.46 @ ^ [R: trm] :
% 0.30/0.46 ( if @ ( option @ trm )
% 0.30/0.46 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R ) @ U2 )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 @ ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta2 ) @ ( bot_bot @ ( set @ variable ) ) @ R )
% 0.30/0.46 @ ( none @ trm ) )
% 0.30/0.46 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F4: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 0.30/0.46 @ Sigma2
% 0.30/0.46 @ F3 ) )
% 0.30/0.46 @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.simps(4)
% 0.30/0.46 thf(fact_79_Int__iff,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.30/0.46 = ( ( member @ A @ C2 @ A3 )
% 0.30/0.46 & ( member @ A @ C2 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_iff
% 0.30/0.46 thf(fact_80_IntI,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ A3 )
% 0.30/0.46 => ( ( member @ A @ C2 @ B4 )
% 0.30/0.46 => ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % IntI
% 0.30/0.46 thf(fact_81_empty__Collect__eq,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o] :
% 0.30/0.46 ( ( ( bot_bot @ ( set @ A ) )
% 0.30/0.46 = ( collect @ A @ P ) )
% 0.30/0.46 = ( ! [X: A] :
% 0.30/0.46 ~ ( P @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % empty_Collect_eq
% 0.30/0.46 thf(fact_82_Collect__empty__eq,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o] :
% 0.30/0.46 ( ( ( collect @ A @ P )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( ! [X: A] :
% 0.30/0.46 ~ ( P @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_empty_eq
% 0.30/0.46 thf(fact_83_all__not__in__conv,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A] :
% 0.30/0.46 ( ( ! [X: A] :
% 0.30/0.46 ~ ( member @ A @ X @ A3 ) )
% 0.30/0.46 = ( A3
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % all_not_in_conv
% 0.30/0.46 thf(fact_84_empty__iff,axiom,
% 0.30/0.46 ! [A: $tType,C2: A] :
% 0.30/0.46 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % empty_iff
% 0.30/0.46 thf(fact_85_bot__apply,axiom,
% 0.30/0.46 ! [C: $tType,D: $tType] :
% 0.30/0.46 ( ( bot @ C )
% 0.30/0.46 => ( ( bot_bot @ ( D > C ) )
% 0.30/0.46 = ( ^ [X: D] : ( bot_bot @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_apply
% 0.30/0.46 thf(fact_86_bot__fun__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( bot @ B )
% 0.30/0.46 => ( ( bot_bot @ ( A > B ) )
% 0.30/0.46 = ( ^ [X: A] : ( bot_bot @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_fun_def
% 0.30/0.46 thf(fact_87_emptyE,axiom,
% 0.30/0.46 ! [A: $tType,A2: A] :
% 0.30/0.46 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % emptyE
% 0.30/0.46 thf(fact_88_equals0D,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,A2: A] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 => ~ ( member @ A @ A2 @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0D
% 0.30/0.46 thf(fact_89_equals0I,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A] :
% 0.30/0.46 ( ! [Y4: A] :
% 0.30/0.46 ~ ( member @ A @ Y4 @ A3 )
% 0.30/0.46 => ( A3
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0I
% 0.30/0.46 thf(fact_90_ex__in__conv,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A] :
% 0.30/0.46 ( ( ? [X: A] : ( member @ A @ X @ A3 ) )
% 0.30/0.46 = ( A3
% 0.30/0.46 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ex_in_conv
% 0.30/0.46 thf(fact_91_bot__set__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bot_bot @ ( set @ A ) )
% 0.30/0.46 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_set_def
% 0.30/0.46 thf(fact_92_IntE,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.30/0.46 => ~ ( ( member @ A @ C2 @ A3 )
% 0.30/0.46 => ~ ( member @ A @ C2 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % IntE
% 0.30/0.46 thf(fact_93_IntD1,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.30/0.46 => ( member @ A @ C2 @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % IntD1
% 0.30/0.46 thf(fact_94_IntD2,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.30/0.46 => ( member @ A @ C2 @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % IntD2
% 0.30/0.46 thf(fact_95_Int__assoc,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B4: set @ A,C3: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) @ C3 )
% 0.30/0.46 = ( inf_inf @ ( set @ A ) @ A3 @ ( inf_inf @ ( set @ A ) @ B4 @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_assoc
% 0.30/0.46 thf(fact_96_Int__absorb,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) @ A3 @ A3 )
% 0.30/0.46 = A3 ) ).
% 0.30/0.46
% 0.30/0.46 % Int_absorb
% 0.30/0.46 thf(fact_97_Int__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A6: set @ A,B6: set @ A] : ( inf_inf @ ( set @ A ) @ B6 @ A6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_commute
% 0.30/0.46 thf(fact_98_Int__left__absorb,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) @ A3 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.30/0.46 = ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_left_absorb
% 0.30/0.46 thf(fact_99_Int__left__commute,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B4: set @ A,C3: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) @ A3 @ ( inf_inf @ ( set @ A ) @ B4 @ C3 ) )
% 0.30/0.46 = ( inf_inf @ ( set @ A ) @ B4 @ ( inf_inf @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_left_commute
% 0.30/0.46 thf(fact_100_empty__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bot_bot @ ( set @ A ) )
% 0.30/0.46 = ( collect @ A
% 0.30/0.46 @ ^ [X: A] : $false ) ) ).
% 0.30/0.46
% 0.30/0.46 % empty_def
% 0.30/0.46 thf(fact_101_Collect__conj__eq,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ( collect @ A
% 0.30/0.46 @ ^ [X: A] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 & ( Q @ X ) ) )
% 0.30/0.46 = ( inf_inf @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_conj_eq
% 0.30/0.46 thf(fact_102_Int__Collect,axiom,
% 0.30/0.46 ! [A: $tType,X4: A,A3: set @ A,P: A > $o] :
% 0.30/0.46 ( ( member @ A @ X4 @ ( inf_inf @ ( set @ A ) @ A3 @ ( collect @ A @ P ) ) )
% 0.30/0.46 = ( ( member @ A @ X4 @ A3 )
% 0.30/0.46 & ( P @ X4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_Collect
% 0.30/0.46 thf(fact_103_Int__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.30/0.46 ( collect @ A
% 0.30/0.46 @ ^ [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ A6 )
% 0.30/0.46 & ( member @ A @ X @ B6 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_def
% 0.30/0.46 thf(fact_104_inf__set__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.30/0.46 ( collect @ A
% 0.30/0.46 @ ( inf_inf @ ( A > $o )
% 0.30/0.46 @ ^ [X: A] : ( member @ A @ X @ A6 )
% 0.30/0.46 @ ^ [X: A] : ( member @ A @ X @ B6 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_set_def
% 0.30/0.46 thf(fact_105_Int__emptyI,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.30/0.46 ( ! [X2: A] :
% 0.30/0.46 ( ( member @ A @ X2 @ A3 )
% 0.30/0.46 => ~ ( member @ A @ X2 @ B4 ) )
% 0.30/0.46 => ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_emptyI
% 0.30/0.46 thf(fact_106_disjoint__iff,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( ! [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ A3 )
% 0.30/0.46 => ~ ( member @ A @ X @ B4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % disjoint_iff
% 0.30/0.46 thf(fact_107_Int__empty__left,axiom,
% 0.30/0.46 ! [A: $tType,B4: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B4 )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_empty_left
% 0.30/0.46 thf(fact_108_Int__empty__right,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_empty_right
% 0.30/0.46 thf(fact_109_disjoint__iff__not__equal,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( ! [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ A3 )
% 0.30/0.46 => ! [Y: A] :
% 0.30/0.46 ( ( member @ A @ Y @ B4 )
% 0.30/0.46 => ( X != Y ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % disjoint_iff_not_equal
% 0.30/0.46 thf(fact_110_disjE__realizer2,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: $o,Q: A > $o,X4: option @ A,R4: B > $o,F3: B,G2: A > B] :
% 0.30/0.46 ( ( case_option @ $o @ A @ P @ Q @ X4 )
% 0.30/0.46 => ( ( P
% 0.30/0.46 => ( R4 @ F3 ) )
% 0.30/0.46 => ( ! [Q2: A] :
% 0.30/0.46 ( ( Q @ Q2 )
% 0.30/0.46 => ( R4 @ ( G2 @ Q2 ) ) )
% 0.30/0.46 => ( R4 @ ( case_option @ B @ A @ F3 @ G2 @ X4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % disjE_realizer2
% 0.30/0.46 thf(fact_111_Set_Ois__empty__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( is_empty @ A )
% 0.30/0.46 = ( ^ [A6: set @ A] :
% 0.30/0.46 ( A6
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Set.is_empty_def
% 0.30/0.46 thf(fact_112_prod_Ocase__distrib,axiom,
% 0.30/0.46 ! [C: $tType,D: $tType,B: $tType,A: $tType,H: C > D,F3: A > B > C,Prod: product_prod @ A @ B] :
% 0.30/0.46 ( ( H @ ( product_case_prod @ A @ B @ C @ F3 @ Prod ) )
% 0.30/0.46 = ( product_case_prod @ A @ B @ D
% 0.30/0.46 @ ^ [X1: A,X24: B] : ( H @ ( F3 @ X1 @ X24 ) )
% 0.30/0.46 @ Prod ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod.case_distrib
% 0.30/0.46 thf(fact_113_inf__Int__eq,axiom,
% 0.30/0.46 ! [A: $tType,R4: set @ A,S: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( A > $o )
% 0.30/0.46 @ ^ [X: A] : ( member @ A @ X @ R4 )
% 0.30/0.46 @ ^ [X: A] : ( member @ A @ X @ S ) )
% 0.30/0.46 = ( ^ [X: A] : ( member @ A @ X @ ( inf_inf @ ( set @ A ) @ R4 @ S ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_Int_eq
% 0.30/0.46 thf(fact_114_Timeso_Osimps_I3_J,axiom,
% 0.30/0.46 ! [V2: trm] :
% 0.30/0.46 ( ( uSubst277968634Timeso @ ( some @ trm @ V2 ) @ ( none @ trm ) )
% 0.30/0.46 = ( none @ trm ) ) ).
% 0.30/0.46
% 0.30/0.46 % Timeso.simps(3)
% 0.30/0.46 thf(fact_115_Pluso_Osimps_I3_J,axiom,
% 0.30/0.46 ! [V2: trm] :
% 0.30/0.46 ( ( uSubst1112714340_Pluso @ ( some @ trm @ V2 ) @ ( none @ trm ) )
% 0.30/0.46 = ( none @ trm ) ) ).
% 0.30/0.46
% 0.30/0.46 % Pluso.simps(3)
% 0.30/0.46 thf(fact_116_inf1I,axiom,
% 0.30/0.46 ! [A: $tType,A3: A > $o,X4: A,B4: A > $o] :
% 0.30/0.46 ( ( A3 @ X4 )
% 0.30/0.46 => ( ( B4 @ X4 )
% 0.30/0.46 => ( inf_inf @ ( A > $o ) @ A3 @ B4 @ X4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf1I
% 0.30/0.46 thf(fact_117_inf1E,axiom,
% 0.30/0.46 ! [A: $tType,A3: A > $o,B4: A > $o,X4: A] :
% 0.30/0.46 ( ( inf_inf @ ( A > $o ) @ A3 @ B4 @ X4 )
% 0.30/0.46 => ~ ( ( A3 @ X4 )
% 0.30/0.46 => ~ ( B4 @ X4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf1E
% 0.30/0.46 thf(fact_118_inf1D1,axiom,
% 0.30/0.46 ! [A: $tType,A3: A > $o,B4: A > $o,X4: A] :
% 0.30/0.46 ( ( inf_inf @ ( A > $o ) @ A3 @ B4 @ X4 )
% 0.30/0.46 => ( A3 @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf1D1
% 0.30/0.46 thf(fact_119_inf1D2,axiom,
% 0.30/0.46 ! [A: $tType,A3: A > $o,B4: A > $o,X4: A] :
% 0.30/0.46 ( ( inf_inf @ ( A > $o ) @ A3 @ B4 @ X4 )
% 0.30/0.46 => ( B4 @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf1D2
% 0.30/0.46 thf(fact_120_Pluso_Osimps_I2_J,axiom,
% 0.30/0.46 ! [Eta2: option @ trm] :
% 0.30/0.46 ( ( uSubst1112714340_Pluso @ ( none @ trm ) @ Eta2 )
% 0.30/0.46 = ( none @ trm ) ) ).
% 0.30/0.46
% 0.30/0.46 % Pluso.simps(2)
% 0.30/0.46 thf(fact_121_Timeso_Osimps_I2_J,axiom,
% 0.30/0.46 ! [Eta2: option @ trm] :
% 0.30/0.46 ( ( uSubst277968634Timeso @ ( none @ trm ) @ Eta2 )
% 0.30/0.46 = ( none @ trm ) ) ).
% 0.30/0.46
% 0.30/0.46 % Timeso.simps(2)
% 0.30/0.46 thf(fact_122_Pluso__undef,axiom,
% 0.30/0.46 ! [Theta2: option @ trm,Eta2: option @ trm] :
% 0.30/0.46 ( ( ( uSubst1112714340_Pluso @ Theta2 @ Eta2 )
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 = ( ( Theta2
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 | ( Eta2
% 0.30/0.46 = ( none @ trm ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Pluso_undef
% 0.30/0.46 thf(fact_123_Timeso__undef,axiom,
% 0.30/0.46 ! [Theta2: option @ trm,Eta2: option @ trm] :
% 0.30/0.46 ( ( ( uSubst277968634Timeso @ Theta2 @ Eta2 )
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 = ( ( Theta2
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 | ( Eta2
% 0.30/0.46 = ( none @ trm ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Timeso_undef
% 0.30/0.46 thf(fact_124_bot__empty__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bot_bot @ ( A > $o ) )
% 0.30/0.46 = ( ^ [X: A] : ( member @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_empty_eq
% 0.30/0.46 thf(fact_125_Collect__empty__eq__bot,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o] :
% 0.30/0.46 ( ( ( collect @ A @ P )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( P
% 0.30/0.46 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_empty_eq_bot
% 0.30/0.46 thf(fact_126_internal__case__prod__def,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( produc2004651681e_prod @ A @ B @ C )
% 0.30/0.46 = ( product_case_prod @ A @ B @ C ) ) ).
% 0.30/0.46
% 0.30/0.46 % internal_case_prod_def
% 0.30/0.46 thf(fact_127_Pluso_Oelims,axiom,
% 0.30/0.46 ! [X4: option @ trm,Xa: option @ trm,Y2: option @ trm] :
% 0.30/0.46 ( ( ( uSubst1112714340_Pluso @ X4 @ Xa )
% 0.30/0.46 = Y2 )
% 0.30/0.46 => ( ! [Theta: trm] :
% 0.30/0.46 ( ( X4
% 0.30/0.46 = ( some @ trm @ Theta ) )
% 0.30/0.46 => ! [Eta: trm] :
% 0.30/0.46 ( ( Xa
% 0.30/0.46 = ( some @ trm @ Eta ) )
% 0.30/0.46 => ( Y2
% 0.30/0.46 != ( some @ trm @ ( plus @ Theta @ Eta ) ) ) ) )
% 0.30/0.46 => ( ( ( X4
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 => ( Y2
% 0.30/0.46 != ( none @ trm ) ) )
% 0.30/0.46 => ~ ( ? [V: trm] :
% 0.30/0.46 ( X4
% 0.30/0.46 = ( some @ trm @ V ) )
% 0.30/0.46 => ( ( Xa
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 => ( Y2
% 0.30/0.46 != ( none @ trm ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Pluso.elims
% 0.30/0.46 thf(fact_128_Timeso_Oelims,axiom,
% 0.30/0.46 ! [X4: option @ trm,Xa: option @ trm,Y2: option @ trm] :
% 0.30/0.46 ( ( ( uSubst277968634Timeso @ X4 @ Xa )
% 0.30/0.46 = Y2 )
% 0.30/0.46 => ( ! [Theta: trm] :
% 0.30/0.46 ( ( X4
% 0.30/0.46 = ( some @ trm @ Theta ) )
% 0.30/0.46 => ! [Eta: trm] :
% 0.30/0.46 ( ( Xa
% 0.30/0.46 = ( some @ trm @ Eta ) )
% 0.30/0.46 => ( Y2
% 0.30/0.46 != ( some @ trm @ ( times @ Theta @ Eta ) ) ) ) )
% 0.30/0.46 => ( ( ( X4
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 => ( Y2
% 0.30/0.46 != ( none @ trm ) ) )
% 0.30/0.46 => ~ ( ? [V: trm] :
% 0.30/0.46 ( X4
% 0.30/0.46 = ( some @ trm @ V ) )
% 0.30/0.46 => ( ( Xa
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 => ( Y2
% 0.30/0.46 != ( none @ trm ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Timeso.elims
% 0.30/0.46 thf(fact_129_trm_Oinject_I5_J,axiom,
% 0.30/0.46 ! [X51: trm,X52: trm,Y51: trm,Y52: trm] :
% 0.30/0.46 ( ( ( plus @ X51 @ X52 )
% 0.30/0.46 = ( plus @ Y51 @ Y52 ) )
% 0.30/0.46 = ( ( X51 = Y51 )
% 0.30/0.46 & ( X52 = Y52 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(5)
% 0.30/0.46 thf(fact_130_trm_Oinject_I6_J,axiom,
% 0.30/0.46 ! [X61: trm,X62: trm,Y61: trm,Y62: trm] :
% 0.30/0.46 ( ( ( times @ X61 @ X62 )
% 0.30/0.46 = ( times @ Y61 @ Y62 ) )
% 0.30/0.46 = ( ( X61 = Y61 )
% 0.30/0.46 & ( X62 = Y62 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(6)
% 0.30/0.46 thf(fact_131_trm_Odistinct_I37_J,axiom,
% 0.30/0.46 ! [X51: trm,X52: trm,X61: trm,X62: trm] :
% 0.30/0.46 ( ( plus @ X51 @ X52 )
% 0.30/0.46 != ( times @ X61 @ X62 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(37)
% 0.30/0.46 thf(fact_132_trm_Odistinct_I25_J,axiom,
% 0.30/0.46 ! [X3: char,X51: trm,X52: trm] :
% 0.30/0.46 ( ( const @ X3 )
% 0.30/0.46 != ( plus @ X51 @ X52 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(25)
% 0.30/0.46 thf(fact_133_trm_Odistinct_I27_J,axiom,
% 0.30/0.46 ! [X3: char,X61: trm,X62: trm] :
% 0.30/0.46 ( ( const @ X3 )
% 0.30/0.46 != ( times @ X61 @ X62 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(27)
% 0.30/0.46 thf(fact_134_trm_Odistinct_I31_J,axiom,
% 0.30/0.46 ! [X41: char,X42: trm,X51: trm,X52: trm] :
% 0.30/0.46 ( ( func @ X41 @ X42 )
% 0.30/0.46 != ( plus @ X51 @ X52 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(31)
% 0.30/0.46 thf(fact_135_trm_Odistinct_I33_J,axiom,
% 0.30/0.46 ! [X41: char,X42: trm,X61: trm,X62: trm] :
% 0.30/0.46 ( ( func @ X41 @ X42 )
% 0.30/0.46 != ( times @ X61 @ X62 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(33)
% 0.30/0.46 thf(fact_136_usubstappt__times__conv,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 0.30/0.46 ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( times @ Theta2 @ Eta2 ) )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 & ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 )
% 0.30/0.46 != ( none @ trm ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt_times_conv
% 0.30/0.46 thf(fact_137_usubstappt__plus__conv,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 0.30/0.46 ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( plus @ Theta2 @ Eta2 ) )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 & ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 )
% 0.30/0.46 != ( none @ trm ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt_plus_conv
% 0.30/0.46 thf(fact_138_Timeso_Osimps_I1_J,axiom,
% 0.30/0.46 ! [Theta2: trm,Eta2: trm] :
% 0.30/0.46 ( ( uSubst277968634Timeso @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta2 ) )
% 0.30/0.46 = ( some @ trm @ ( times @ Theta2 @ Eta2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Timeso.simps(1)
% 0.30/0.46 thf(fact_139_Pluso_Osimps_I1_J,axiom,
% 0.30/0.46 ! [Theta2: trm,Eta2: trm] :
% 0.30/0.46 ( ( uSubst1112714340_Pluso @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta2 ) )
% 0.30/0.46 = ( some @ trm @ ( plus @ Theta2 @ Eta2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Pluso.simps(1)
% 0.30/0.46 thf(fact_140_usubstappt_Osimps_I6_J,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 0.30/0.46 ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( times @ Theta2 @ Eta2 ) )
% 0.30/0.46 = ( uSubst277968634Timeso @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.simps(6)
% 0.30/0.46 thf(fact_141_usubstappt_Osimps_I5_J,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 0.30/0.46 ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( plus @ Theta2 @ Eta2 ) )
% 0.30/0.46 = ( uSubst1112714340_Pluso @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.simps(5)
% 0.30/0.46 thf(fact_142_usubstappt_Oelims,axiom,
% 0.30/0.46 ! [X4: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),Xa: set @ variable,Xb: trm,Y2: option @ trm] :
% 0.30/0.46 ( ( ( uSubst95898992stappt @ X4 @ Xa @ Xb )
% 0.30/0.46 = Y2 )
% 0.30/0.46 => ( ! [X2: variable] :
% 0.30/0.46 ( ( Xb
% 0.30/0.46 = ( var @ X2 ) )
% 0.30/0.46 => ( Y2
% 0.30/0.46 != ( some @ trm @ ( var @ X2 ) ) ) )
% 0.30/0.46 => ( ! [R3: real] :
% 0.30/0.46 ( ( Xb
% 0.30/0.46 = ( number @ R3 ) )
% 0.30/0.46 => ( Y2
% 0.30/0.46 != ( some @ trm @ ( number @ R3 ) ) ) )
% 0.30/0.46 => ( ! [F5: char] :
% 0.30/0.46 ( ( Xb
% 0.30/0.46 = ( const @ F5 ) )
% 0.30/0.46 => ( Y2
% 0.30/0.46 != ( uSubst1138577137pconst @ X4 @ Xa @ F5 ) ) )
% 0.30/0.46 => ( ! [F5: char,Theta: trm] :
% 0.30/0.46 ( ( Xb
% 0.30/0.46 = ( func @ F5 @ Theta ) )
% 0.30/0.46 => ( Y2
% 0.30/0.46 != ( case_option @ ( option @ trm ) @ trm @ ( none @ trm )
% 0.30/0.46 @ ^ [Sigma_theta2: trm] :
% 0.30/0.46 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( func @ F5 @ Sigma_theta2 ) )
% 0.30/0.46 @ ^ [R: trm] :
% 0.30/0.46 ( if @ ( option @ trm )
% 0.30/0.46 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R ) @ Xa )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 @ ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta2 ) @ ( bot_bot @ ( set @ variable ) ) @ R )
% 0.30/0.46 @ ( none @ trm ) )
% 0.30/0.46 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F4: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 0.30/0.46 @ X4
% 0.30/0.46 @ F5 ) )
% 0.30/0.46 @ ( uSubst95898992stappt @ X4 @ Xa @ Theta ) ) ) )
% 0.30/0.46 => ( ! [Theta: trm,Eta: trm] :
% 0.30/0.46 ( ( Xb
% 0.30/0.46 = ( plus @ Theta @ Eta ) )
% 0.30/0.46 => ( Y2
% 0.30/0.46 != ( uSubst1112714340_Pluso @ ( uSubst95898992stappt @ X4 @ Xa @ Theta ) @ ( uSubst95898992stappt @ X4 @ Xa @ Eta ) ) ) )
% 0.30/0.46 => ( ! [Theta: trm,Eta: trm] :
% 0.30/0.46 ( ( Xb
% 0.30/0.46 = ( times @ Theta @ Eta ) )
% 0.30/0.46 => ( Y2
% 0.30/0.46 != ( uSubst277968634Timeso @ ( uSubst95898992stappt @ X4 @ Xa @ Theta ) @ ( uSubst95898992stappt @ X4 @ Xa @ Eta ) ) ) )
% 0.30/0.46 => ~ ! [Theta: trm] :
% 0.30/0.46 ( ( Xb
% 0.30/0.46 = ( differential @ Theta ) )
% 0.30/0.46 => ( Y2
% 0.30/0.46 != ( uSubst259074819ntialo
% 0.30/0.46 @ ( uSubst95898992stappt @ X4
% 0.30/0.46 @ ( collect @ variable
% 0.30/0.46 @ ^ [X: variable] : $true )
% 0.30/0.46 @ Theta ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.elims
% 0.30/0.46 thf(fact_143_usubstappt__induct,axiom,
% 0.30/0.46 ! [P: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > trm > $o,A0: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),A1: set @ variable,A22: trm] :
% 0.30/0.46 ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,X2: variable] : ( P @ Sigma3 @ U3 @ ( var @ X2 ) )
% 0.30/0.46 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,R3: real] : ( P @ Sigma3 @ U3 @ ( number @ R3 ) )
% 0.30/0.46 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F5: char] : ( P @ Sigma3 @ U3 @ ( const @ F5 ) )
% 0.30/0.46 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F5: char,Theta: trm] :
% 0.30/0.46 ( ( P @ Sigma3 @ U3 @ Theta )
% 0.30/0.46 => ( ! [X25: trm] :
% 0.30/0.46 ( ( ( uSubst95898992stappt @ Sigma3 @ U3 @ Theta )
% 0.30/0.46 = ( some @ trm @ X25 ) )
% 0.30/0.46 => ! [X2a: trm] :
% 0.30/0.46 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F4: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 0.30/0.46 @ Sigma3
% 0.30/0.46 @ F5 )
% 0.30/0.46 = ( some @ trm @ X2a ) )
% 0.30/0.46 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ X2a ) @ U3 )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 => ( P @ ( uSubst969145931substt @ X25 ) @ ( bot_bot @ ( set @ variable ) ) @ X2a ) ) ) )
% 0.30/0.46 => ( P @ Sigma3 @ U3 @ ( func @ F5 @ Theta ) ) ) )
% 0.30/0.46 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta: trm] :
% 0.30/0.46 ( ( P @ Sigma3 @ U3 @ Theta )
% 0.30/0.46 => ! [Eta: trm] :
% 0.30/0.46 ( ( P @ Sigma3 @ U3 @ Eta )
% 0.30/0.46 => ( P @ Sigma3 @ U3 @ ( plus @ Theta @ Eta ) ) ) )
% 0.30/0.46 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta: trm] :
% 0.30/0.46 ( ( P @ Sigma3 @ U3 @ Theta )
% 0.30/0.46 => ! [Eta: trm] :
% 0.30/0.46 ( ( P @ Sigma3 @ U3 @ Eta )
% 0.30/0.46 => ( P @ Sigma3 @ U3 @ ( times @ Theta @ Eta ) ) ) )
% 0.30/0.46 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta: trm] :
% 0.30/0.46 ( ( P @ Sigma3
% 0.30/0.46 @ ( collect @ variable
% 0.30/0.46 @ ^ [X: variable] : $true )
% 0.30/0.46 @ Theta )
% 0.30/0.46 => ( P @ Sigma3 @ U3 @ ( differential @ Theta ) ) )
% 0.30/0.46 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt_induct
% 0.30/0.46 thf(fact_144_Geqo_Osimps_I3_J,axiom,
% 0.30/0.46 ! [V2: trm] :
% 0.30/0.46 ( ( uSubst1556497037e_Geqo @ ( some @ trm @ V2 ) @ ( none @ trm ) )
% 0.30/0.46 = ( none @ fml ) ) ).
% 0.30/0.46
% 0.30/0.46 % Geqo.simps(3)
% 0.30/0.46 thf(fact_145_combine__options__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( combine_options @ A )
% 0.30/0.46 = ( ^ [F2: A > A > A,X: option @ A,Y: option @ A] :
% 0.30/0.46 ( case_option @ ( option @ A ) @ A @ Y
% 0.30/0.46 @ ^ [Z3: A] :
% 0.30/0.46 ( case_option @ ( option @ A ) @ A @ ( some @ A @ Z3 )
% 0.30/0.46 @ ^ [Aa: A] : ( some @ A @ ( F2 @ Z3 @ Aa ) )
% 0.30/0.46 @ Y )
% 0.30/0.46 @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % combine_options_def
% 0.30/0.46 thf(fact_146_trm_Oinject_I2_J,axiom,
% 0.30/0.46 ! [X22: real,Y22: real] :
% 0.30/0.46 ( ( ( number @ X22 )
% 0.30/0.46 = ( number @ Y22 ) )
% 0.30/0.46 = ( X22 = Y22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(2)
% 0.30/0.46 thf(fact_147_trm_Oinject_I1_J,axiom,
% 0.30/0.46 ! [X12: variable,Y1: variable] :
% 0.30/0.46 ( ( ( var @ X12 )
% 0.30/0.46 = ( var @ Y1 ) )
% 0.30/0.46 = ( X12 = Y1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(1)
% 0.30/0.46 thf(fact_148_trm_Oinject_I7_J,axiom,
% 0.30/0.46 ! [X7: trm,Y7: trm] :
% 0.30/0.46 ( ( ( differential @ X7 )
% 0.30/0.46 = ( differential @ Y7 ) )
% 0.30/0.46 = ( X7 = Y7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(7)
% 0.30/0.46 thf(fact_149_combine__options__simps_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,F3: A > A > A,X4: option @ A] :
% 0.30/0.46 ( ( combine_options @ A @ F3 @ X4 @ ( none @ A ) )
% 0.30/0.46 = X4 ) ).
% 0.30/0.46
% 0.30/0.46 % combine_options_simps(2)
% 0.30/0.46 thf(fact_150_combine__options__simps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,F3: A > A > A,Y2: option @ A] :
% 0.30/0.46 ( ( combine_options @ A @ F3 @ ( none @ A ) @ Y2 )
% 0.30/0.46 = Y2 ) ).
% 0.30/0.46
% 0.30/0.46 % combine_options_simps(1)
% 0.30/0.46 thf(fact_151_combine__options__simps_I3_J,axiom,
% 0.30/0.46 ! [A: $tType,F3: A > A > A,A2: A,B2: A] :
% 0.30/0.46 ( ( combine_options @ A @ F3 @ ( some @ A @ A2 ) @ ( some @ A @ B2 ) )
% 0.30/0.46 = ( some @ A @ ( F3 @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % combine_options_simps(3)
% 0.30/0.46 thf(fact_152_Differentialo_Osimps_I1_J,axiom,
% 0.30/0.46 ! [Theta2: trm] :
% 0.30/0.46 ( ( uSubst259074819ntialo @ ( some @ trm @ Theta2 ) )
% 0.30/0.46 = ( some @ trm @ ( differential @ Theta2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Differentialo.simps(1)
% 0.30/0.46 thf(fact_153_trm_Odistinct_I21_J,axiom,
% 0.30/0.46 ! [X22: real,X7: trm] :
% 0.30/0.46 ( ( number @ X22 )
% 0.30/0.46 != ( differential @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(21)
% 0.30/0.46 thf(fact_154_trm_Odistinct_I11_J,axiom,
% 0.30/0.46 ! [X12: variable,X7: trm] :
% 0.30/0.46 ( ( var @ X12 )
% 0.30/0.46 != ( differential @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(11)
% 0.30/0.46 thf(fact_155_trm_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [X12: variable,X22: real] :
% 0.30/0.46 ( ( var @ X12 )
% 0.30/0.46 != ( number @ X22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(1)
% 0.30/0.46 thf(fact_156_combine__options__assoc,axiom,
% 0.30/0.46 ! [A: $tType,F3: A > A > A,X4: option @ A,Y2: option @ A,Z2: option @ A] :
% 0.30/0.46 ( ! [X2: A,Y4: A,Z4: A] :
% 0.30/0.46 ( ( F3 @ ( F3 @ X2 @ Y4 ) @ Z4 )
% 0.30/0.46 = ( F3 @ X2 @ ( F3 @ Y4 @ Z4 ) ) )
% 0.30/0.46 => ( ( combine_options @ A @ F3 @ ( combine_options @ A @ F3 @ X4 @ Y2 ) @ Z2 )
% 0.30/0.46 = ( combine_options @ A @ F3 @ X4 @ ( combine_options @ A @ F3 @ Y2 @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % combine_options_assoc
% 0.30/0.46 thf(fact_157_combine__options__commute,axiom,
% 0.30/0.46 ! [A: $tType,F3: A > A > A,X4: option @ A,Y2: option @ A] :
% 0.30/0.46 ( ! [X2: A,Y4: A] :
% 0.30/0.46 ( ( F3 @ X2 @ Y4 )
% 0.30/0.46 = ( F3 @ Y4 @ X2 ) )
% 0.30/0.46 => ( ( combine_options @ A @ F3 @ X4 @ Y2 )
% 0.30/0.46 = ( combine_options @ A @ F3 @ Y2 @ X4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % combine_options_commute
% 0.30/0.46 thf(fact_158_combine__options__left__commute,axiom,
% 0.30/0.46 ! [A: $tType,F3: A > A > A,Y2: option @ A,X4: option @ A,Z2: option @ A] :
% 0.30/0.46 ( ! [X2: A,Y4: A] :
% 0.30/0.46 ( ( F3 @ X2 @ Y4 )
% 0.30/0.46 = ( F3 @ Y4 @ X2 ) )
% 0.30/0.46 => ( ! [X2: A,Y4: A,Z4: A] :
% 0.30/0.46 ( ( F3 @ ( F3 @ X2 @ Y4 ) @ Z4 )
% 0.30/0.46 = ( F3 @ X2 @ ( F3 @ Y4 @ Z4 ) ) )
% 0.30/0.46 => ( ( combine_options @ A @ F3 @ Y2 @ ( combine_options @ A @ F3 @ X4 @ Z2 ) )
% 0.30/0.46 = ( combine_options @ A @ F3 @ X4 @ ( combine_options @ A @ F3 @ Y2 @ Z2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % combine_options_left_commute
% 0.30/0.46 thf(fact_159_usubstappt_Osimps_I7_J,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm] :
% 0.30/0.46 ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( differential @ Theta2 ) )
% 0.30/0.46 = ( uSubst259074819ntialo
% 0.30/0.46 @ ( uSubst95898992stappt @ Sigma2
% 0.30/0.46 @ ( collect @ variable
% 0.30/0.46 @ ^ [X: variable] : $true )
% 0.30/0.46 @ Theta2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.simps(7)
% 0.30/0.46 thf(fact_160_trm_Odistinct_I13_J,axiom,
% 0.30/0.46 ! [X22: real,X3: char] :
% 0.30/0.46 ( ( number @ X22 )
% 0.30/0.46 != ( const @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(13)
% 0.30/0.46 thf(fact_161_trm_Odistinct_I15_J,axiom,
% 0.30/0.46 ! [X22: real,X41: char,X42: trm] :
% 0.30/0.46 ( ( number @ X22 )
% 0.30/0.46 != ( func @ X41 @ X42 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(15)
% 0.30/0.46 thf(fact_162_trm_Odistinct_I19_J,axiom,
% 0.30/0.46 ! [X22: real,X61: trm,X62: trm] :
% 0.30/0.46 ( ( number @ X22 )
% 0.30/0.46 != ( times @ X61 @ X62 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(19)
% 0.30/0.46 thf(fact_163_trm_Odistinct_I17_J,axiom,
% 0.30/0.46 ! [X22: real,X51: trm,X52: trm] :
% 0.30/0.46 ( ( number @ X22 )
% 0.30/0.46 != ( plus @ X51 @ X52 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(17)
% 0.30/0.46 thf(fact_164_Differentialo_Oelims,axiom,
% 0.30/0.46 ! [X4: option @ trm,Y2: option @ trm] :
% 0.30/0.46 ( ( ( uSubst259074819ntialo @ X4 )
% 0.30/0.46 = Y2 )
% 0.30/0.46 => ( ! [Theta: trm] :
% 0.30/0.46 ( ( X4
% 0.30/0.46 = ( some @ trm @ Theta ) )
% 0.30/0.46 => ( Y2
% 0.30/0.46 != ( some @ trm @ ( differential @ Theta ) ) ) )
% 0.30/0.46 => ~ ( ( X4
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 => ( Y2
% 0.30/0.46 != ( none @ trm ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Differentialo.elims
% 0.30/0.46 thf(fact_165_trm_Odistinct_I3_J,axiom,
% 0.30/0.46 ! [X12: variable,X3: char] :
% 0.30/0.46 ( ( var @ X12 )
% 0.30/0.46 != ( const @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(3)
% 0.30/0.46 thf(fact_166_trm_Odistinct_I5_J,axiom,
% 0.30/0.46 ! [X12: variable,X41: char,X42: trm] :
% 0.30/0.46 ( ( var @ X12 )
% 0.30/0.46 != ( func @ X41 @ X42 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(5)
% 0.30/0.46 thf(fact_167_trm_Odistinct_I9_J,axiom,
% 0.30/0.46 ! [X12: variable,X61: trm,X62: trm] :
% 0.30/0.46 ( ( var @ X12 )
% 0.30/0.46 != ( times @ X61 @ X62 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(9)
% 0.30/0.46 thf(fact_168_trm_Odistinct_I7_J,axiom,
% 0.30/0.46 ! [X12: variable,X51: trm,X52: trm] :
% 0.30/0.46 ( ( var @ X12 )
% 0.30/0.46 != ( plus @ X51 @ X52 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(7)
% 0.30/0.46 thf(fact_169_trm_Odistinct_I29_J,axiom,
% 0.30/0.46 ! [X3: char,X7: trm] :
% 0.30/0.46 ( ( const @ X3 )
% 0.30/0.46 != ( differential @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(29)
% 0.30/0.46 thf(fact_170_trm_Odistinct_I35_J,axiom,
% 0.30/0.46 ! [X41: char,X42: trm,X7: trm] :
% 0.30/0.46 ( ( func @ X41 @ X42 )
% 0.30/0.46 != ( differential @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(35)
% 0.30/0.46 thf(fact_171_trm_Odistinct_I41_J,axiom,
% 0.30/0.46 ! [X61: trm,X62: trm,X7: trm] :
% 0.30/0.46 ( ( times @ X61 @ X62 )
% 0.30/0.46 != ( differential @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(41)
% 0.30/0.46 thf(fact_172_trm_Odistinct_I39_J,axiom,
% 0.30/0.46 ! [X51: trm,X52: trm,X7: trm] :
% 0.30/0.46 ( ( plus @ X51 @ X52 )
% 0.30/0.46 != ( differential @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(39)
% 0.30/0.46 thf(fact_173_trm_Oexhaust,axiom,
% 0.30/0.46 ! [Y2: trm] :
% 0.30/0.46 ( ! [X13: variable] :
% 0.30/0.46 ( Y2
% 0.30/0.46 != ( var @ X13 ) )
% 0.30/0.46 => ( ! [X23: real] :
% 0.30/0.46 ( Y2
% 0.30/0.46 != ( number @ X23 ) )
% 0.30/0.46 => ( ! [X32: char] :
% 0.30/0.46 ( Y2
% 0.30/0.46 != ( const @ X32 ) )
% 0.30/0.46 => ( ! [X412: char,X422: trm] :
% 0.30/0.46 ( Y2
% 0.30/0.46 != ( func @ X412 @ X422 ) )
% 0.30/0.46 => ( ! [X512: trm,X522: trm] :
% 0.30/0.46 ( Y2
% 0.30/0.46 != ( plus @ X512 @ X522 ) )
% 0.30/0.46 => ( ! [X612: trm,X622: trm] :
% 0.30/0.46 ( Y2
% 0.30/0.46 != ( times @ X612 @ X622 ) )
% 0.30/0.46 => ~ ! [X72: trm] :
% 0.30/0.46 ( Y2
% 0.30/0.46 != ( differential @ X72 ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.exhaust
% 0.30/0.46 thf(fact_174_trm_Oinduct,axiom,
% 0.30/0.46 ! [P: trm > $o,Trm: trm] :
% 0.30/0.46 ( ! [X2: variable] : ( P @ ( var @ X2 ) )
% 0.30/0.46 => ( ! [X2: real] : ( P @ ( number @ X2 ) )
% 0.30/0.46 => ( ! [X2: char] : ( P @ ( const @ X2 ) )
% 0.30/0.46 => ( ! [X1a: char,X2a2: trm] :
% 0.30/0.46 ( ( P @ X2a2 )
% 0.30/0.46 => ( P @ ( func @ X1a @ X2a2 ) ) )
% 0.30/0.46 => ( ! [X1a: trm,X2a2: trm] :
% 0.30/0.46 ( ( P @ X1a )
% 0.30/0.46 => ( ( P @ X2a2 )
% 0.30/0.46 => ( P @ ( plus @ X1a @ X2a2 ) ) ) )
% 0.30/0.46 => ( ! [X1a: trm,X2a2: trm] :
% 0.30/0.46 ( ( P @ X1a )
% 0.30/0.46 => ( ( P @ X2a2 )
% 0.30/0.46 => ( P @ ( times @ X1a @ X2a2 ) ) ) )
% 0.30/0.46 => ( ! [X2: trm] :
% 0.30/0.46 ( ( P @ X2 )
% 0.30/0.46 => ( P @ ( differential @ X2 ) ) )
% 0.30/0.46 => ( P @ Trm ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.induct
% 0.30/0.46 thf(fact_175_Geqo_Osimps_I2_J,axiom,
% 0.30/0.46 ! [Eta2: option @ trm] :
% 0.30/0.46 ( ( uSubst1556497037e_Geqo @ ( none @ trm ) @ Eta2 )
% 0.30/0.46 = ( none @ fml ) ) ).
% 0.30/0.46
% 0.30/0.46 % Geqo.simps(2)
% 0.30/0.46 thf(fact_176_Geqo__undef,axiom,
% 0.30/0.46 ! [Theta2: option @ trm,Eta2: option @ trm] :
% 0.30/0.46 ( ( ( uSubst1556497037e_Geqo @ Theta2 @ Eta2 )
% 0.30/0.46 = ( none @ fml ) )
% 0.30/0.46 = ( ( Theta2
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 | ( Eta2
% 0.30/0.46 = ( none @ trm ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Geqo_undef
% 0.30/0.46 thf(fact_177_Differentialo_Osimps_I2_J,axiom,
% 0.30/0.46 ( ( uSubst259074819ntialo @ ( none @ trm ) )
% 0.30/0.46 = ( none @ trm ) ) ).
% 0.30/0.46
% 0.30/0.46 % Differentialo.simps(2)
% 0.30/0.46 thf(fact_178_Differentialo__undef,axiom,
% 0.30/0.46 ! [Theta2: option @ trm] :
% 0.30/0.46 ( ( ( uSubst259074819ntialo @ Theta2 )
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 = ( Theta2
% 0.30/0.46 = ( none @ trm ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Differentialo_undef
% 0.30/0.46 thf(fact_179_usubstappt_Osimps_I2_J,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,R2: real] :
% 0.30/0.46 ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( number @ R2 ) )
% 0.30/0.46 = ( some @ trm @ ( number @ R2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.simps(2)
% 0.30/0.46 thf(fact_180_usubstappt_Osimps_I1_J,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,X4: variable] :
% 0.30/0.46 ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( var @ X4 ) )
% 0.30/0.46 = ( some @ trm @ ( var @ X4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.simps(1)
% 0.30/0.46 thf(fact_181_usubstappt__differential__conv,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm] :
% 0.30/0.46 ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( differential @ Theta2 ) )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( uSubst95898992stappt @ Sigma2
% 0.30/0.46 @ ( collect @ variable
% 0.30/0.46 @ ^ [X: variable] : $true )
% 0.30/0.46 @ Theta2 )
% 0.30/0.46 != ( none @ trm ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt_differential_conv
% 0.30/0.46 thf(fact_182_usubstappt_Opelims,axiom,
% 0.30/0.46 ! [X4: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),Xa: set @ variable,Xb: trm,Y2: option @ trm] :
% 0.30/0.46 ( ( ( uSubst95898992stappt @ X4 @ Xa @ Xb )
% 0.30/0.46 = Y2 )
% 0.30/0.46 => ( ( 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 ) @ X4 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ Xb ) ) )
% 0.30/0.46 => ( ! [X2: variable] :
% 0.30/0.46 ( ( Xb
% 0.30/0.46 = ( var @ X2 ) )
% 0.30/0.46 => ( ( Y2
% 0.30/0.46 = ( some @ trm @ ( var @ X2 ) ) )
% 0.30/0.46 => ~ ( 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 ) @ X4 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( var @ X2 ) ) ) ) ) )
% 0.30/0.46 => ( ! [R3: real] :
% 0.30/0.46 ( ( Xb
% 0.30/0.46 = ( number @ R3 ) )
% 0.30/0.46 => ( ( Y2
% 0.30/0.46 = ( some @ trm @ ( number @ R3 ) ) )
% 0.30/0.46 => ~ ( 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 ) @ X4 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( number @ R3 ) ) ) ) ) )
% 0.30/0.46 => ( ! [F5: char] :
% 0.30/0.46 ( ( Xb
% 0.30/0.46 = ( const @ F5 ) )
% 0.30/0.46 => ( ( Y2
% 0.30/0.46 = ( uSubst1138577137pconst @ X4 @ Xa @ F5 ) )
% 0.30/0.46 => ~ ( 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 ) @ X4 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( const @ F5 ) ) ) ) ) )
% 0.30/0.46 => ( ! [F5: char,Theta: trm] :
% 0.30/0.46 ( ( Xb
% 0.30/0.46 = ( func @ F5 @ Theta ) )
% 0.30/0.46 => ( ( Y2
% 0.30/0.46 = ( case_option @ ( option @ trm ) @ trm @ ( none @ trm )
% 0.30/0.46 @ ^ [Sigma_theta2: trm] :
% 0.30/0.46 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( func @ F5 @ Sigma_theta2 ) )
% 0.30/0.46 @ ^ [R: trm] :
% 0.30/0.46 ( if @ ( option @ trm )
% 0.30/0.46 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R ) @ Xa )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 @ ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta2 ) @ ( bot_bot @ ( set @ variable ) ) @ R )
% 0.30/0.46 @ ( none @ trm ) )
% 0.30/0.46 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F4: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 0.30/0.46 @ X4
% 0.30/0.46 @ F5 ) )
% 0.30/0.46 @ ( uSubst95898992stappt @ X4 @ Xa @ Theta ) ) )
% 0.30/0.46 => ~ ( 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 ) @ X4 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( func @ F5 @ Theta ) ) ) ) ) )
% 0.30/0.46 => ( ! [Theta: trm,Eta: trm] :
% 0.30/0.46 ( ( Xb
% 0.30/0.46 = ( plus @ Theta @ Eta ) )
% 0.30/0.46 => ( ( Y2
% 0.30/0.46 = ( uSubst1112714340_Pluso @ ( uSubst95898992stappt @ X4 @ Xa @ Theta ) @ ( uSubst95898992stappt @ X4 @ Xa @ Eta ) ) )
% 0.30/0.46 => ~ ( 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 ) @ X4 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( plus @ Theta @ Eta ) ) ) ) ) )
% 0.30/0.46 => ( ! [Theta: trm,Eta: trm] :
% 0.30/0.46 ( ( Xb
% 0.30/0.46 = ( times @ Theta @ Eta ) )
% 0.30/0.46 => ( ( Y2
% 0.30/0.46 = ( uSubst277968634Timeso @ ( uSubst95898992stappt @ X4 @ Xa @ Theta ) @ ( uSubst95898992stappt @ X4 @ Xa @ Eta ) ) )
% 0.30/0.46 => ~ ( 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 ) @ X4 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( times @ Theta @ Eta ) ) ) ) ) )
% 0.30/0.46 => ~ ! [Theta: trm] :
% 0.30/0.46 ( ( Xb
% 0.30/0.46 = ( differential @ Theta ) )
% 0.30/0.46 => ( ( Y2
% 0.30/0.46 = ( uSubst259074819ntialo
% 0.30/0.46 @ ( uSubst95898992stappt @ X4
% 0.30/0.46 @ ( collect @ variable
% 0.30/0.46 @ ^ [X: variable] : $true )
% 0.30/0.46 @ Theta ) ) )
% 0.30/0.46 => ~ ( 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 ) @ X4 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( differential @ Theta ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.pelims
% 0.30/0.46 thf(fact_183_term__sem_Ocases,axiom,
% 0.30/0.46 ! [X4: product_prod @ denotational_interp @ trm] :
% 0.30/0.46 ( ! [I: denotational_interp,X2: variable] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ denotational_interp @ trm @ I @ ( var @ X2 ) ) )
% 0.30/0.46 => ( ! [I: denotational_interp,R3: real] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ denotational_interp @ trm @ I @ ( number @ R3 ) ) )
% 0.30/0.46 => ( ! [I: denotational_interp,F5: char] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ denotational_interp @ trm @ I @ ( const @ F5 ) ) )
% 0.30/0.46 => ( ! [I: denotational_interp,F5: char,Theta: trm] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ denotational_interp @ trm @ I @ ( func @ F5 @ Theta ) ) )
% 0.30/0.46 => ( ! [I: denotational_interp,Theta: trm,Eta: trm] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ denotational_interp @ trm @ I @ ( plus @ Theta @ Eta ) ) )
% 0.30/0.46 => ( ! [I: denotational_interp,Theta: trm,Eta: trm] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ denotational_interp @ trm @ I @ ( times @ Theta @ Eta ) ) )
% 0.30/0.46 => ~ ! [I: denotational_interp,Theta: trm] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ denotational_interp @ trm @ I @ ( differential @ Theta ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % term_sem.cases
% 0.30/0.46 thf(fact_184_term__sem_Oinduct,axiom,
% 0.30/0.46 ! [P: denotational_interp > trm > $o,A0: denotational_interp,A1: trm] :
% 0.30/0.46 ( ! [I: denotational_interp,X2: variable] : ( P @ I @ ( var @ X2 ) )
% 0.30/0.46 => ( ! [I: denotational_interp,R3: real] : ( P @ I @ ( number @ R3 ) )
% 0.30/0.46 => ( ! [I: denotational_interp,F5: char] : ( P @ I @ ( const @ F5 ) )
% 0.30/0.46 => ( ! [I: denotational_interp,F5: char,Theta: trm] :
% 0.30/0.46 ( ( P @ I @ Theta )
% 0.30/0.46 => ( P @ I @ ( func @ F5 @ Theta ) ) )
% 0.30/0.46 => ( ! [I: denotational_interp,Theta: trm] :
% 0.30/0.46 ( ( P @ I @ Theta )
% 0.30/0.46 => ! [Eta: trm] :
% 0.30/0.46 ( ( P @ I @ Eta )
% 0.30/0.46 => ( P @ I @ ( plus @ Theta @ Eta ) ) ) )
% 0.30/0.46 => ( ! [I: denotational_interp,Theta: trm] :
% 0.30/0.46 ( ( P @ I @ Theta )
% 0.30/0.46 => ! [Eta: trm] :
% 0.30/0.46 ( ( P @ I @ Eta )
% 0.30/0.46 => ( P @ I @ ( times @ Theta @ Eta ) ) ) )
% 0.30/0.46 => ( ! [I: denotational_interp,Theta: trm] :
% 0.30/0.46 ( ( ? [Xa2: char] :
% 0.30/0.46 ( member @ char @ Xa2
% 0.30/0.46 @ ( collect @ char
% 0.30/0.46 @ ^ [Uu: char] : $true ) )
% 0.30/0.46 => ( P @ I @ Theta ) )
% 0.30/0.46 => ( P @ I @ ( differential @ Theta ) ) )
% 0.30/0.46 => ( P @ A0 @ A1 ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % term_sem.induct
% 0.30/0.46 thf(fact_185_old_Oprod_Oinject,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,A2: A,B2: B,A7: A,B7: B] :
% 0.30/0.46 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.30/0.46 = ( product_Pair @ A @ B @ A7 @ B7 ) )
% 0.30/0.46 = ( ( A2 = A7 )
% 0.30/0.46 & ( B2 = B7 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inject
% 0.30/0.46 thf(fact_186_prod_Oinject,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X12: A,X22: B,Y1: A,Y22: B] :
% 0.30/0.46 ( ( ( product_Pair @ A @ B @ X12 @ X22 )
% 0.30/0.46 = ( product_Pair @ A @ B @ Y1 @ Y22 ) )
% 0.30/0.46 = ( ( X12 = Y1 )
% 0.30/0.46 & ( X22 = Y22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod.inject
% 0.30/0.46 thf(fact_187_case__prodI,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F3: A > B > $o,A2: A,B2: B] :
% 0.30/0.46 ( ( F3 @ A2 @ B2 )
% 0.30/0.46 => ( product_case_prod @ A @ B @ $o @ F3 @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % case_prodI
% 0.30/0.46 thf(fact_188_case__prodI2,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P4: product_prod @ A @ B,C2: A > B > $o] :
% 0.30/0.46 ( ! [A5: A,B5: B] :
% 0.30/0.46 ( ( P4
% 0.30/0.46 = ( product_Pair @ A @ B @ A5 @ B5 ) )
% 0.30/0.46 => ( C2 @ A5 @ B5 ) )
% 0.30/0.46 => ( product_case_prod @ A @ B @ $o @ C2 @ P4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % case_prodI2
% 0.30/0.46 thf(fact_189_case__prodI2_H,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,P4: product_prod @ A @ B,C2: A > B > C > $o,X4: C] :
% 0.30/0.46 ( ! [A5: A,B5: B] :
% 0.30/0.46 ( ( ( product_Pair @ A @ B @ A5 @ B5 )
% 0.30/0.46 = P4 )
% 0.30/0.46 => ( C2 @ A5 @ B5 @ X4 ) )
% 0.30/0.46 => ( product_case_prod @ A @ B @ ( C > $o ) @ C2 @ P4 @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % case_prodI2'
% 0.30/0.46 thf(fact_190_mem__case__prodI,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,Z2: A,C2: B > C > ( set @ A ),A2: B,B2: C] :
% 0.30/0.46 ( ( member @ A @ Z2 @ ( C2 @ A2 @ B2 ) )
% 0.30/0.46 => ( member @ A @ Z2 @ ( product_case_prod @ B @ C @ ( set @ A ) @ C2 @ ( product_Pair @ B @ C @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_case_prodI
% 0.30/0.46 thf(fact_191_mem__case__prodI2,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType,P4: product_prod @ A @ B,Z2: C,C2: A > B > ( set @ C )] :
% 0.30/0.46 ( ! [A5: A,B5: B] :
% 0.30/0.46 ( ( P4
% 0.30/0.46 = ( product_Pair @ A @ B @ A5 @ B5 ) )
% 0.30/0.46 => ( member @ C @ Z2 @ ( C2 @ A5 @ B5 ) ) )
% 0.30/0.46 => ( member @ C @ Z2 @ ( product_case_prod @ A @ B @ ( set @ C ) @ C2 @ P4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_case_prodI2
% 0.30/0.46 thf(fact_192_case__prod__conv,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,C: $tType,F3: B > C > A,A2: B,B2: C] :
% 0.30/0.46 ( ( product_case_prod @ B @ C @ A @ F3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.30/0.46 = ( F3 @ A2 @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % case_prod_conv
% 0.30/0.46 thf(fact_193_usubstappt_Opsimps_I7_J,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm] :
% 0.30/0.46 ( ( 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 ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U2 @ ( differential @ Theta2 ) ) ) )
% 0.30/0.46 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( differential @ Theta2 ) )
% 0.30/0.46 = ( uSubst259074819ntialo
% 0.30/0.46 @ ( uSubst95898992stappt @ Sigma2
% 0.30/0.46 @ ( collect @ variable
% 0.30/0.46 @ ^ [X: variable] : $true )
% 0.30/0.46 @ Theta2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.psimps(7)
% 0.30/0.46 thf(fact_194_usubstappt_Opsimps_I1_J,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,X4: variable] :
% 0.30/0.46 ( ( 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 ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U2 @ ( var @ X4 ) ) ) )
% 0.30/0.46 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( var @ X4 ) )
% 0.30/0.46 = ( some @ trm @ ( var @ X4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.psimps(1)
% 0.30/0.46 thf(fact_195_usubstappt_Opsimps_I2_J,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,R2: real] :
% 0.30/0.46 ( ( 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 ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U2 @ ( number @ R2 ) ) ) )
% 0.30/0.46 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( number @ R2 ) )
% 0.30/0.46 = ( some @ trm @ ( number @ R2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.psimps(2)
% 0.30/0.46 thf(fact_196_cond__case__prod__eta,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType,F3: A > B > C,G2: ( product_prod @ A @ B ) > C] :
% 0.30/0.46 ( ! [X2: A,Y4: B] :
% 0.30/0.46 ( ( F3 @ X2 @ Y4 )
% 0.30/0.46 = ( G2 @ ( product_Pair @ A @ B @ X2 @ Y4 ) ) )
% 0.30/0.46 => ( ( product_case_prod @ A @ B @ C @ F3 )
% 0.30/0.46 = G2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % cond_case_prod_eta
% 0.30/0.46 thf(fact_197_case__prod__eta,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType,F3: ( product_prod @ A @ B ) > C] :
% 0.30/0.46 ( ( product_case_prod @ A @ B @ C
% 0.30/0.46 @ ^ [X: A,Y: B] : ( F3 @ ( product_Pair @ A @ B @ X @ Y ) ) )
% 0.30/0.46 = F3 ) ).
% 0.30/0.46
% 0.30/0.46 % case_prod_eta
% 0.30/0.46 thf(fact_198_case__prodE2,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,C: $tType,Q: A > $o,P: B > C > A,Z2: product_prod @ B @ C] :
% 0.30/0.46 ( ( Q @ ( product_case_prod @ B @ C @ A @ P @ Z2 ) )
% 0.30/0.46 => ~ ! [X2: B,Y4: C] :
% 0.30/0.46 ( ( Z2
% 0.30/0.46 = ( product_Pair @ B @ C @ X2 @ Y4 ) )
% 0.30/0.46 => ~ ( Q @ ( P @ X2 @ Y4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % case_prodE2
% 0.30/0.46 thf(fact_199_inf__Int__eq2,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,R4: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( inf_inf @ ( A > B > $o )
% 0.30/0.46 @ ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ R4 )
% 0.30/0.46 @ ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ S ) )
% 0.30/0.46 = ( ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ ( inf_inf @ ( set @ ( product_prod @ A @ B ) ) @ R4 @ S ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_Int_eq2
% 0.30/0.46 thf(fact_200_bot__empty__eq2,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( bot_bot @ ( A > B > $o ) )
% 0.30/0.46 = ( ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ ( bot_bot @ ( set @ ( product_prod @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_empty_eq2
% 0.30/0.46 thf(fact_201_case__prodD,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F3: A > B > $o,A2: A,B2: B] :
% 0.30/0.46 ( ( product_case_prod @ A @ B @ $o @ F3 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.30/0.46 => ( F3 @ A2 @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % case_prodD
% 0.30/0.46 thf(fact_202_case__prodE,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C2: A > B > $o,P4: product_prod @ A @ B] :
% 0.30/0.46 ( ( product_case_prod @ A @ B @ $o @ C2 @ P4 )
% 0.30/0.46 => ~ ! [X2: A,Y4: B] :
% 0.30/0.46 ( ( P4
% 0.30/0.46 = ( product_Pair @ A @ B @ X2 @ Y4 ) )
% 0.30/0.46 => ~ ( C2 @ X2 @ Y4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % case_prodE
% 0.30/0.46 thf(fact_203_case__prodD_H,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,C: $tType,R4: A > B > C > $o,A2: A,B2: B,C2: C] :
% 0.30/0.46 ( ( product_case_prod @ A @ B @ ( C > $o ) @ R4 @ ( product_Pair @ A @ B @ A2 @ B2 ) @ C2 )
% 0.30/0.46 => ( R4 @ A2 @ B2 @ C2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % case_prodD'
% 0.30/0.46 thf(fact_204_case__prodE_H,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,C: $tType,C2: A > B > C > $o,P4: product_prod @ A @ B,Z2: C] :
% 0.30/0.46 ( ( product_case_prod @ A @ B @ ( C > $o ) @ C2 @ P4 @ Z2 )
% 0.30/0.46 => ~ ! [X2: A,Y4: B] :
% 0.30/0.46 ( ( P4
% 0.30/0.46 = ( product_Pair @ A @ B @ X2 @ Y4 ) )
% 0.30/0.46 => ~ ( C2 @ X2 @ Y4 @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % case_prodE'
% 0.30/0.46 thf(fact_205_pred__equals__eq2,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,R4: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( ( ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ R4 ) )
% 0.30/0.46 = ( ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ S ) ) )
% 0.30/0.46 = ( R4 = S ) ) ).
% 0.30/0.46
% 0.30/0.46 % pred_equals_eq2
% 0.30/0.46 thf(fact_206_mem__case__prodE,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,C: $tType,Z2: A,C2: B > C > ( set @ A ),P4: product_prod @ B @ C] :
% 0.30/0.46 ( ( member @ A @ Z2 @ ( product_case_prod @ B @ C @ ( set @ A ) @ C2 @ P4 ) )
% 0.30/0.46 => ~ ! [X2: B,Y4: C] :
% 0.30/0.46 ( ( P4
% 0.30/0.46 = ( product_Pair @ B @ C @ X2 @ Y4 ) )
% 0.30/0.46 => ~ ( member @ A @ Z2 @ ( C2 @ X2 @ Y4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_case_prodE
% 0.30/0.46 thf(fact_207_old_Oprod_Oinducts,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.30/0.46 ( ! [A5: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B5 ) )
% 0.30/0.46 => ( P @ Prod ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inducts
% 0.30/0.46 thf(fact_208_old_Oprod_Oexhaust,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Y2: product_prod @ A @ B] :
% 0.30/0.46 ~ ! [A5: A,B5: B] :
% 0.30/0.46 ( Y2
% 0.30/0.46 != ( product_Pair @ A @ B @ A5 @ B5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.exhaust
% 0.30/0.46 thf(fact_209_prod__induct7,axiom,
% 0.30/0.46 ! [G3: $tType,F6: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) ) ) ) ) > $o,X4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) ) ) )] :
% 0.30/0.46 ( ! [A5: A,B5: B,C4: C,D2: D,E2: E,F5: F6,G4: G3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F6 @ G3 ) @ E2 @ ( product_Pair @ F6 @ G3 @ F5 @ G4 ) ) ) ) ) ) )
% 0.30/0.46 => ( P @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct7
% 0.30/0.46 thf(fact_210_prod__induct6,axiom,
% 0.30/0.46 ! [F6: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F6 ) ) ) ) ) > $o,X4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F6 ) ) ) )] :
% 0.30/0.46 ( ! [A5: A,B5: B,C4: C,D2: D,E2: E,F5: F6] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F6 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F6 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F6 ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ F6 ) @ D2 @ ( product_Pair @ E @ F6 @ E2 @ F5 ) ) ) ) ) )
% 0.30/0.46 => ( P @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct6
% 0.30/0.46 thf(fact_211_prod__induct5,axiom,
% 0.30/0.46 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.30/0.46 ( ! [A5: A,B5: B,C4: C,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C4 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 0.30/0.46 => ( P @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct5
% 0.30/0.46 thf(fact_212_prod__induct4,axiom,
% 0.30/0.46 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.30/0.46 ( ! [A5: A,B5: B,C4: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C4 @ D2 ) ) ) )
% 0.30/0.46 => ( P @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct4
% 0.30/0.46 thf(fact_213_prod__induct3,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X4: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.30/0.46 ( ! [A5: A,B5: B,C4: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B5 @ C4 ) ) )
% 0.30/0.46 => ( P @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct3
% 0.30/0.46 thf(fact_214_prod__cases7,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F6: $tType,G3: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) ) ) )] :
% 0.30/0.46 ~ ! [A5: A,B5: B,C4: C,D2: D,E2: E,F5: F6,G4: G3] :
% 0.30/0.46 ( Y2
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F6 @ G3 ) @ E2 @ ( product_Pair @ F6 @ G3 @ F5 @ G4 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases7
% 0.30/0.46 thf(fact_215_prod__cases6,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F6: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F6 ) ) ) )] :
% 0.30/0.46 ~ ! [A5: A,B5: B,C4: C,D2: D,E2: E,F5: F6] :
% 0.30/0.46 ( Y2
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F6 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F6 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F6 ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ F6 ) @ D2 @ ( product_Pair @ E @ F6 @ E2 @ F5 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases6
% 0.30/0.46 thf(fact_216_prod__cases5,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.30/0.46 ~ ! [A5: A,B5: B,C4: C,D2: D,E2: E] :
% 0.30/0.46 ( Y2
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C4 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases5
% 0.30/0.46 thf(fact_217_prod__cases4,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.30/0.46 ~ ! [A5: A,B5: B,C4: C,D2: D] :
% 0.30/0.46 ( Y2
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C4 @ D2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases4
% 0.30/0.46 thf(fact_218_prod__cases3,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,Y2: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.30/0.46 ~ ! [A5: A,B5: B,C4: C] :
% 0.30/0.46 ( Y2
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B5 @ C4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases3
% 0.30/0.46 thf(fact_219_Pair__inject,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,A2: A,B2: B,A7: A,B7: B] :
% 0.30/0.46 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.30/0.46 = ( product_Pair @ A @ B @ A7 @ B7 ) )
% 0.30/0.46 => ~ ( ( A2 = A7 )
% 0.30/0.46 => ( B2 != B7 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Pair_inject
% 0.30/0.46 thf(fact_220_prod__cases,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P4: product_prod @ A @ B] :
% 0.30/0.46 ( ! [A5: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B5 ) )
% 0.30/0.46 => ( P @ P4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases
% 0.30/0.46 thf(fact_221_surj__pair,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,P4: product_prod @ A @ B] :
% 0.30/0.46 ? [X2: A,Y4: B] :
% 0.30/0.46 ( P4
% 0.30/0.46 = ( product_Pair @ A @ B @ X2 @ Y4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % surj_pair
% 0.30/0.46 thf(fact_222_old_Oprod_Ocase,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,B: $tType,F3: A > B > C,X12: A,X22: B] :
% 0.30/0.46 ( ( product_case_prod @ A @ B @ C @ F3 @ ( product_Pair @ A @ B @ X12 @ X22 ) )
% 0.30/0.46 = ( F3 @ X12 @ X22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.case
% 0.30/0.46 thf(fact_223_case__prod__Pair__iden,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P4: product_prod @ A @ B] :
% 0.30/0.46 ( ( product_case_prod @ A @ B @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B ) @ P4 )
% 0.30/0.46 = P4 ) ).
% 0.30/0.46
% 0.30/0.46 % case_prod_Pair_iden
% 0.30/0.46 thf(fact_224_usubstappt_Opsimps_I3_J,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,F3: char] :
% 0.30/0.46 ( ( 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 ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U2 @ ( const @ F3 ) ) ) )
% 0.30/0.46 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( const @ F3 ) )
% 0.30/0.46 = ( uSubst1138577137pconst @ Sigma2 @ U2 @ F3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.psimps(3)
% 0.30/0.46 thf(fact_225_usubstappt_Opsimps_I6_J,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 0.30/0.46 ( ( 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 ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U2 @ ( times @ Theta2 @ Eta2 ) ) ) )
% 0.30/0.46 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( times @ Theta2 @ Eta2 ) )
% 0.30/0.46 = ( uSubst277968634Timeso @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.psimps(6)
% 0.30/0.46 thf(fact_226_usubstappt_Opsimps_I5_J,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 0.30/0.46 ( ( 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 ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U2 @ ( plus @ Theta2 @ Eta2 ) ) ) )
% 0.30/0.46 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( plus @ Theta2 @ Eta2 ) )
% 0.30/0.46 = ( uSubst1112714340_Pluso @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.psimps(5)
% 0.30/0.46 thf(fact_227_internal__case__prod__conv,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,C: $tType,C2: B > C > A,A2: B,B2: C] :
% 0.30/0.46 ( ( produc2004651681e_prod @ B @ C @ A @ C2 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.30/0.46 = ( C2 @ A2 @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % internal_case_prod_conv
% 0.30/0.46 thf(fact_228_usubstappt_Opsimps_I4_J,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,F3: char,Theta2: trm] :
% 0.30/0.46 ( ( 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 ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U2 @ ( func @ F3 @ Theta2 ) ) ) )
% 0.30/0.46 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 0.30/0.46 = ( case_option @ ( option @ trm ) @ trm @ ( none @ trm )
% 0.30/0.46 @ ^ [Sigma_theta2: trm] :
% 0.30/0.46 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( func @ F3 @ Sigma_theta2 ) )
% 0.30/0.46 @ ^ [R: trm] :
% 0.30/0.46 ( if @ ( option @ trm )
% 0.30/0.46 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R ) @ U2 )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 @ ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta2 ) @ ( bot_bot @ ( set @ variable ) ) @ R )
% 0.30/0.46 @ ( none @ trm ) )
% 0.30/0.46 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F4: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 0.30/0.46 @ Sigma2
% 0.30/0.46 @ F3 ) )
% 0.30/0.46 @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.psimps(4)
% 0.30/0.46 thf(fact_229_usubstappt_Ocases,axiom,
% 0.30/0.46 ! [X4: 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 )] :
% 0.30/0.46 ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,X2: variable] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( var @ X2 ) ) ) )
% 0.30/0.46 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,R3: real] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( number @ R3 ) ) ) )
% 0.30/0.46 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F5: char] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( const @ F5 ) ) ) )
% 0.30/0.46 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F5: char,Theta: trm] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( func @ F5 @ Theta ) ) ) )
% 0.30/0.46 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta: trm,Eta: trm] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( plus @ Theta @ Eta ) ) ) )
% 0.30/0.46 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta: trm,Eta: trm] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( times @ Theta @ Eta ) ) ) )
% 0.30/0.46 => ~ ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta: trm] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( differential @ Theta ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.cases
% 0.30/0.46 thf(fact_230_usubstappt_Opinduct,axiom,
% 0.30/0.46 ! [A0: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),A1: set @ variable,A22: trm,P: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > trm > $o] :
% 0.30/0.46 ( ( 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 ) @ A0 @ ( product_Pair @ ( set @ variable ) @ trm @ A1 @ A22 ) ) )
% 0.30/0.46 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,X2: variable] :
% 0.30/0.46 ( ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( var @ X2 ) ) ) )
% 0.30/0.46 => ( P @ Sigma3 @ U3 @ ( var @ X2 ) ) )
% 0.30/0.46 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,R3: real] :
% 0.30/0.46 ( ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( number @ R3 ) ) ) )
% 0.30/0.46 => ( P @ Sigma3 @ U3 @ ( number @ R3 ) ) )
% 0.30/0.46 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F5: char] :
% 0.30/0.46 ( ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( const @ F5 ) ) ) )
% 0.30/0.46 => ( P @ Sigma3 @ U3 @ ( const @ F5 ) ) )
% 0.30/0.46 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F5: char,Theta: trm] :
% 0.30/0.46 ( ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( func @ F5 @ Theta ) ) ) )
% 0.30/0.46 => ( ( P @ Sigma3 @ U3 @ Theta )
% 0.30/0.46 => ( ! [X25: trm] :
% 0.30/0.46 ( ( ( uSubst95898992stappt @ Sigma3 @ U3 @ Theta )
% 0.30/0.46 = ( some @ trm @ X25 ) )
% 0.30/0.46 => ! [X2a: trm] :
% 0.30/0.46 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [F4: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 0.30/0.46 @ Sigma3
% 0.30/0.46 @ F5 )
% 0.30/0.46 = ( some @ trm @ X2a ) )
% 0.30/0.46 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ X2a ) @ U3 )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 => ( P @ ( uSubst969145931substt @ X25 ) @ ( bot_bot @ ( set @ variable ) ) @ X2a ) ) ) )
% 0.30/0.46 => ( P @ Sigma3 @ U3 @ ( func @ F5 @ Theta ) ) ) ) )
% 0.30/0.46 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta: trm,Eta: trm] :
% 0.30/0.46 ( ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( plus @ Theta @ Eta ) ) ) )
% 0.30/0.46 => ( ( P @ Sigma3 @ U3 @ Theta )
% 0.30/0.46 => ( ( P @ Sigma3 @ U3 @ Eta )
% 0.30/0.46 => ( P @ Sigma3 @ U3 @ ( plus @ Theta @ Eta ) ) ) ) )
% 0.30/0.46 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta: trm,Eta: trm] :
% 0.30/0.46 ( ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( times @ Theta @ Eta ) ) ) )
% 0.30/0.46 => ( ( P @ Sigma3 @ U3 @ Theta )
% 0.30/0.46 => ( ( P @ Sigma3 @ U3 @ Eta )
% 0.30/0.46 => ( P @ Sigma3 @ U3 @ ( times @ Theta @ Eta ) ) ) ) )
% 0.30/0.46 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta: trm] :
% 0.30/0.46 ( ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( differential @ Theta ) ) ) )
% 0.30/0.46 => ( ( P @ Sigma3
% 0.30/0.46 @ ( collect @ variable
% 0.30/0.46 @ ^ [X: variable] : $true )
% 0.30/0.46 @ Theta )
% 0.30/0.46 => ( P @ Sigma3 @ U3 @ ( differential @ Theta ) ) ) )
% 0.30/0.46 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.pinduct
% 0.30/0.46 thf(fact_231_old_Oprod_Orec,axiom,
% 0.30/0.46 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.30/0.46 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.30/0.46 = ( F1 @ A2 @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.rec
% 0.30/0.46 thf(fact_232_split__cong,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType,Q3: product_prod @ A @ B,F3: A > B > C,G2: A > B > C,P4: product_prod @ A @ B] :
% 0.30/0.46 ( ! [X2: A,Y4: B] :
% 0.30/0.46 ( ( ( product_Pair @ A @ B @ X2 @ Y4 )
% 0.30/0.46 = Q3 )
% 0.30/0.46 => ( ( F3 @ X2 @ Y4 )
% 0.30/0.46 = ( G2 @ X2 @ Y4 ) ) )
% 0.30/0.46 => ( ( P4 = Q3 )
% 0.30/0.46 => ( ( product_case_prod @ A @ B @ C @ F3 @ P4 )
% 0.30/0.46 = ( product_case_prod @ A @ B @ C @ G2 @ Q3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_cong
% 0.30/0.46 thf(fact_233_Geqo_Oelims,axiom,
% 0.30/0.46 ! [X4: option @ trm,Xa: option @ trm,Y2: option @ fml] :
% 0.30/0.46 ( ( ( uSubst1556497037e_Geqo @ X4 @ Xa )
% 0.30/0.46 = Y2 )
% 0.30/0.46 => ( ! [Theta: trm] :
% 0.30/0.46 ( ( X4
% 0.30/0.46 = ( some @ trm @ Theta ) )
% 0.30/0.46 => ! [Eta: trm] :
% 0.30/0.46 ( ( Xa
% 0.30/0.46 = ( some @ trm @ Eta ) )
% 0.30/0.46 => ( Y2
% 0.30/0.46 != ( some @ fml @ ( geq @ Theta @ Eta ) ) ) ) )
% 0.30/0.46 => ( ( ( X4
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 => ( Y2
% 0.30/0.46 != ( none @ fml ) ) )
% 0.30/0.46 => ~ ( ? [V: trm] :
% 0.30/0.46 ( X4
% 0.30/0.46 = ( some @ trm @ V ) )
% 0.30/0.46 => ( ( Xa
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 => ( Y2
% 0.30/0.46 != ( none @ fml ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Geqo.elims
% 0.30/0.46 thf(fact_234_fml_Oinject_I2_J,axiom,
% 0.30/0.46 ! [X21: trm,X222: trm,Y21: trm,Y222: trm] :
% 0.30/0.46 ( ( ( geq @ X21 @ X222 )
% 0.30/0.46 = ( geq @ Y21 @ Y222 ) )
% 0.30/0.46 = ( ( X21 = Y21 )
% 0.30/0.46 & ( X222 = Y222 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % fml.inject(2)
% 0.30/0.46 thf(fact_235_Diamondo_Ocases,axiom,
% 0.30/0.46 ! [X4: product_prod @ ( option @ game ) @ ( option @ fml )] :
% 0.30/0.46 ( ! [Alpha: game,Phi: fml] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ Alpha ) @ ( some @ fml @ Phi ) ) )
% 0.30/0.46 => ( ! [Phi: option @ fml] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( none @ game ) @ Phi ) )
% 0.30/0.46 => ~ ! [V: game] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ V ) @ ( none @ fml ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Diamondo.cases
% 0.30/0.46 thf(fact_236_Existso_Ocases,axiom,
% 0.30/0.46 ! [X4: product_prod @ variable @ ( option @ fml )] :
% 0.30/0.46 ( ! [X2: variable,Phi: fml] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ variable @ ( option @ fml ) @ X2 @ ( some @ fml @ Phi ) ) )
% 0.30/0.46 => ~ ! [X2: variable] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ variable @ ( option @ fml ) @ X2 @ ( none @ fml ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Existso.cases
% 0.30/0.46 thf(fact_237_Ando_Ocases,axiom,
% 0.30/0.46 ! [X4: product_prod @ ( option @ fml ) @ ( option @ fml )] :
% 0.30/0.46 ( ! [Phi: fml,Psi: fml] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ ( option @ fml ) @ ( option @ fml ) @ ( some @ fml @ Phi ) @ ( some @ fml @ Psi ) ) )
% 0.30/0.46 => ( ! [Psi: option @ fml] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ ( option @ fml ) @ ( option @ fml ) @ ( none @ fml ) @ Psi ) )
% 0.30/0.46 => ~ ! [V: fml] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ ( option @ fml ) @ ( option @ fml ) @ ( some @ fml @ V ) @ ( none @ fml ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Ando.cases
% 0.30/0.46 thf(fact_238_ODEo_Ocases,axiom,
% 0.30/0.46 ! [X4: product_prod @ char @ ( option @ trm )] :
% 0.30/0.46 ( ! [X2: char,Theta: trm] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ char @ ( option @ trm ) @ X2 @ ( some @ trm @ Theta ) ) )
% 0.30/0.46 => ~ ! [X2: char] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ char @ ( option @ trm ) @ X2 @ ( none @ trm ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ODEo.cases
% 0.30/0.46 thf(fact_239_Assigno_Ocases,axiom,
% 0.30/0.46 ! [X4: product_prod @ variable @ ( option @ trm )] :
% 0.30/0.46 ( ! [X2: variable,Theta: trm] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ variable @ ( option @ trm ) @ X2 @ ( some @ trm @ Theta ) ) )
% 0.30/0.46 => ~ ! [X2: variable] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ variable @ ( option @ trm ) @ X2 @ ( none @ trm ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Assigno.cases
% 0.30/0.46 thf(fact_240_Timeso_Ocases,axiom,
% 0.30/0.46 ! [X4: product_prod @ ( option @ trm ) @ ( option @ trm )] :
% 0.30/0.46 ( ! [Theta: trm,Eta: trm] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta ) ) )
% 0.30/0.46 => ( ! [Eta: option @ trm] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( none @ trm ) @ Eta ) )
% 0.30/0.46 => ~ ! [V: trm] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ V ) @ ( none @ trm ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Timeso.cases
% 0.30/0.46 thf(fact_241_Geqo_Osimps_I1_J,axiom,
% 0.30/0.46 ! [Theta2: trm,Eta2: trm] :
% 0.30/0.46 ( ( uSubst1556497037e_Geqo @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta2 ) )
% 0.30/0.46 = ( some @ fml @ ( geq @ Theta2 @ Eta2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Geqo.simps(1)
% 0.30/0.46 thf(fact_242_usubstappf__geqr,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 0.30/0.46 ( ( ( uSubst95898978stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 0.30/0.46 != ( none @ fml ) )
% 0.30/0.46 => ( ( uSubst95898978stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 0.30/0.46 = ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 ) ) @ ( the @ trm @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappf_geqr
% 0.30/0.46 thf(fact_243_usubstappf__geq,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 0.30/0.46 ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( uSubst95898978stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 0.30/0.46 = ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 ) ) @ ( the @ trm @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappf_geq
% 0.30/0.46 thf(fact_244_Composeo_Ocases,axiom,
% 0.30/0.46 ! [X4: product_prod @ ( option @ game ) @ ( option @ game )] :
% 0.30/0.46 ( ! [Alpha: game,Beta: game] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ ( some @ game @ Alpha ) @ ( some @ game @ Beta ) ) )
% 0.30/0.46 => ( ! [Alpha: option @ game] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ Alpha @ ( none @ game ) ) )
% 0.30/0.46 => ~ ! [V: game] :
% 0.30/0.46 ( X4
% 0.30/0.46 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ ( none @ game ) @ ( some @ game @ V ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Composeo.cases
% 0.30/0.46 thf(fact_245_usubstappf_Osimps_I2_J,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 0.30/0.46 ( ( uSubst95898978stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 0.30/0.46 = ( uSubst1556497037e_Geqo @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappf.simps(2)
% 0.30/0.46 thf(fact_246_usubstappf__geq__conv,axiom,
% 0.30/0.46 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 0.30/0.46 ( ( ( uSubst95898978stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 0.30/0.46 != ( none @ fml ) )
% 0.30/0.46 => ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 & ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 )
% 0.30/0.46 != ( none @ trm ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappf_geq_conv
% 0.30/0.46 thf(fact_247_dotsubstt__def,axiom,
% 0.30/0.46 ( uSubst969145931substt
% 0.30/0.46 = ( ^ [Theta3: trm] :
% 0.30/0.46 ( product_Pair @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) )
% 0.30/0.46 @ ^ [F2: char] :
% 0.30/0.46 ( if @ ( option @ trm )
% 0.30/0.46 @ ( F2
% 0.30/0.46 = ( char2 @ $false @ $true @ $true @ $true @ $false @ $true @ $false @ $false ) )
% 0.30/0.46 @ ( some @ trm @ Theta3 )
% 0.30/0.46 @ ( none @ trm ) )
% 0.30/0.46 @ ( product_Pair @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) )
% 0.30/0.46 @ ^ [Uu: char] : ( none @ trm )
% 0.30/0.46 @ ( product_Pair @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) )
% 0.30/0.46 @ ^ [Uu: char] : ( none @ fml )
% 0.30/0.46 @ ^ [Uu: char] : ( none @ game ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dotsubstt_def
% 0.30/0.46 thf(fact_248_Geqo_Opelims,axiom,
% 0.30/0.46 ! [X4: option @ trm,Xa: option @ trm,Y2: option @ fml] :
% 0.30/0.46 ( ( ( uSubst1556497037e_Geqo @ X4 @ Xa )
% 0.30/0.46 = Y2 )
% 0.30/0.46 => ( ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst864323244qo_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ X4 @ Xa ) )
% 0.30/0.46 => ( ! [Theta: trm] :
% 0.30/0.46 ( ( X4
% 0.30/0.46 = ( some @ trm @ Theta ) )
% 0.30/0.46 => ! [Eta: trm] :
% 0.30/0.46 ( ( Xa
% 0.30/0.46 = ( some @ trm @ Eta ) )
% 0.30/0.46 => ( ( Y2
% 0.30/0.46 = ( some @ fml @ ( geq @ Theta @ Eta ) ) )
% 0.30/0.46 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst864323244qo_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta ) ) ) ) ) )
% 0.30/0.46 => ( ( ( X4
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 => ( ( Y2
% 0.30/0.46 = ( none @ fml ) )
% 0.30/0.46 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst864323244qo_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( none @ trm ) @ Xa ) ) ) )
% 0.30/0.46 => ~ ! [V: trm] :
% 0.30/0.46 ( ( X4
% 0.30/0.46 = ( some @ trm @ V ) )
% 0.30/0.46 => ( ( Xa
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 => ( ( Y2
% 0.30/0.46 = ( none @ fml ) )
% 0.30/0.46 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst864323244qo_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ V ) @ ( none @ trm ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Geqo.pelims
% 0.30/0.46 thf(fact_249_Timeso_Opelims,axiom,
% 0.30/0.46 ! [X4: option @ trm,Xa: option @ trm,Y2: option @ trm] :
% 0.30/0.46 ( ( ( uSubst277968634Timeso @ X4 @ Xa )
% 0.30/0.46 = Y2 )
% 0.30/0.46 => ( ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst1377811071so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ X4 @ Xa ) )
% 0.30/0.46 => ( ! [Theta: trm] :
% 0.30/0.46 ( ( X4
% 0.30/0.46 = ( some @ trm @ Theta ) )
% 0.30/0.46 => ! [Eta: trm] :
% 0.30/0.46 ( ( Xa
% 0.30/0.46 = ( some @ trm @ Eta ) )
% 0.30/0.46 => ( ( Y2
% 0.30/0.46 = ( some @ trm @ ( times @ Theta @ Eta ) ) )
% 0.30/0.46 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst1377811071so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta ) ) ) ) ) )
% 0.30/0.46 => ( ( ( X4
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 => ( ( Y2
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst1377811071so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( none @ trm ) @ Xa ) ) ) )
% 0.30/0.46 => ~ ! [V: trm] :
% 0.30/0.46 ( ( X4
% 0.30/0.46 = ( some @ trm @ V ) )
% 0.30/0.46 => ( ( Xa
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 => ( ( Y2
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst1377811071so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ V ) @ ( none @ trm ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Timeso.pelims
% 0.30/0.46 thf(fact_250_Pluso_Opelims,axiom,
% 0.30/0.46 ! [X4: option @ trm,Xa: option @ trm,Y2: option @ trm] :
% 0.30/0.46 ( ( ( uSubst1112714340_Pluso @ X4 @ Xa )
% 0.30/0.46 = Y2 )
% 0.30/0.46 => ( ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst270600597so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ X4 @ Xa ) )
% 0.30/0.46 => ( ! [Theta: trm] :
% 0.30/0.46 ( ( X4
% 0.30/0.46 = ( some @ trm @ Theta ) )
% 0.30/0.46 => ! [Eta: trm] :
% 0.30/0.46 ( ( Xa
% 0.30/0.47 = ( some @ trm @ Eta ) )
% 0.30/0.47 => ( ( Y2
% 0.30/0.47 = ( some @ trm @ ( plus @ Theta @ Eta ) ) )
% 0.30/0.47 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst270600597so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta ) ) ) ) ) )
% 0.30/0.47 => ( ( ( X4
% 0.30/0.47 = ( none @ trm ) )
% 0.30/0.47 => ( ( Y2
% 0.30/0.47 = ( none @ trm ) )
% 0.30/0.47 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst270600597so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( none @ trm ) @ Xa ) ) ) )
% 0.30/0.47 => ~ ! [V: trm] :
% 0.30/0.47 ( ( X4
% 0.30/0.47 = ( some @ trm @ V ) )
% 0.30/0.47 => ( ( Xa
% 0.30/0.47 = ( none @ trm ) )
% 0.30/0.47 => ( ( Y2
% 0.30/0.47 = ( none @ trm ) )
% 0.30/0.47 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst270600597so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ V ) @ ( none @ trm ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Pluso.pelims
% 0.30/0.47 thf(fact_251_dot__def,axiom,
% 0.30/0.47 ( uSubst_Mirabelle_dot
% 0.30/0.47 = ( const @ ( char2 @ $false @ $true @ $true @ $true @ $false @ $true @ $false @ $false ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dot_def
% 0.30/0.47 thf(fact_252_usubstappf__pred,axiom,
% 0.30/0.47 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),P4: char,R2: fml,U2: set @ variable,Theta2: trm,Sigma_theta: trm] :
% 0.30/0.47 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.30/0.47 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.47 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.30/0.47 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.47 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.47 @ ^ [P3: char > ( option @ fml ),Uw: char > ( option @ game )] : P3 ) )
% 0.30/0.47 @ Sigma2
% 0.30/0.47 @ P4 )
% 0.30/0.47 = ( some @ fml @ R2 ) )
% 0.30/0.47 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R2 ) @ U2 )
% 0.30/0.47 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.47 => ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 )
% 0.30/0.47 = ( some @ trm @ Sigma_theta ) )
% 0.30/0.47 => ( ( uSubst95898978stappf @ Sigma2 @ U2 @ ( pred @ P4 @ Theta2 ) )
% 0.30/0.47 = ( uSubst95898978stappf @ ( uSubst969145931substt @ Sigma_theta ) @ ( bot_bot @ ( set @ variable ) ) @ R2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % usubstappf_pred
% 0.30/0.47 thf(fact_253_fml_Oinject_I1_J,axiom,
% 0.30/0.47 ! [X11: char,X122: trm,Y11: char,Y12: trm] :
% 0.30/0.47 ( ( ( pred @ X11 @ X122 )
% 0.30/0.47 = ( pred @ Y11 @ Y12 ) )
% 0.30/0.47 = ( ( X11 = Y11 )
% 0.30/0.47 & ( X122 = Y12 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % fml.inject(1)
% 0.30/0.47 thf(fact_254_usubstappf__pred2,axiom,
% 0.30/0.47 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),P4: char,R2: fml,U2: set @ variable,Theta2: trm] :
% 0.30/0.47 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.30/0.47 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.47 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.30/0.47 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.47 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.47 @ ^ [P3: char > ( option @ fml ),Uw: char > ( option @ game )] : P3 ) )
% 0.30/0.47 @ Sigma2
% 0.30/0.47 @ P4 )
% 0.30/0.47 = ( some @ fml @ R2 ) )
% 0.30/0.47 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R2 ) @ U2 )
% 0.30/0.47 != ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.47 => ( ( uSubst95898978stappf @ Sigma2 @ U2 @ ( pred @ P4 @ Theta2 ) )
% 0.30/0.47 = ( none @ fml ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % usubstappf_pred2
% 0.30/0.47
% 0.30/0.47 % Type constructors (17)
% 0.30/0.47 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.30/0.47 bounded_lattice @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.30/0.47 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( bounded_lattice @ A9 )
% 0.30/0.47 => ( bounded_lattice @ ( A8 > A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( bounded_lattice @ A9 )
% 0.30/0.47 => ( bounded_lattice_bot @ ( A8 > A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( semilattice_inf @ A9 )
% 0.30/0.47 => ( semilattice_inf @ ( A8 > A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( lattice @ A9 )
% 0.30/0.47 => ( lattice @ ( A8 > A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Orderings_Obot,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( bot @ A9 )
% 0.30/0.47 => ( bot @ ( A8 > A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_3,axiom,
% 0.30/0.47 ! [A8: $tType] : ( bounded_lattice_bot @ ( set @ A8 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_4,axiom,
% 0.30/0.47 ! [A8: $tType] : ( semilattice_inf @ ( set @ A8 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Lattices_Olattice_5,axiom,
% 0.30/0.47 ! [A8: $tType] : ( lattice @ ( set @ A8 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Orderings_Obot_6,axiom,
% 0.30/0.47 ! [A8: $tType] : ( bot @ ( set @ A8 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_7,axiom,
% 0.30/0.47 bounded_lattice_bot @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_8,axiom,
% 0.30/0.47 semilattice_inf @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Lattices_Olattice_9,axiom,
% 0.30/0.47 lattice @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Obot_10,axiom,
% 0.30/0.47 bot @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Real_Oreal___Lattices_Osemilattice__inf_11,axiom,
% 0.30/0.47 semilattice_inf @ real ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Real_Oreal___Lattices_Olattice_12,axiom,
% 0.30/0.47 lattice @ real ).
% 0.30/0.47
% 0.30/0.47 % Helper facts (3)
% 0.30/0.47 thf(help_If_3_1_T,axiom,
% 0.30/0.47 ! [P: $o] :
% 0.30/0.47 ( ( P = $true )
% 0.30/0.47 | ( P = $false ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(help_If_2_1_T,axiom,
% 0.30/0.47 ! [A: $tType,X4: A,Y2: A] :
% 0.30/0.47 ( ( if @ A @ $false @ X4 @ Y2 )
% 0.30/0.47 = Y2 ) ).
% 0.30/0.47
% 0.30/0.47 thf(help_If_1_1_T,axiom,
% 0.30/0.47 ! [A: $tType,X4: A,Y2: A] :
% 0.30/0.47 ( ( if @ A @ $true @ X4 @ Y2 )
% 0.30/0.47 = X4 ) ).
% 0.30/0.47
% 0.30/0.47 % Conjectures (1)
% 0.30/0.47 thf(conj_0,conjecture,
% 0.30/0.47 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.47 @ ^ [F0: char > ( option @ trm )] :
% 0.30/0.47 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.30/0.47 @ ^ [Uu: char > ( option @ trm )] :
% 0.30/0.47 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.30/0.47 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.30/0.47 @ sigma
% 0.30/0.47 @ f )
% 0.30/0.47 = ( none @ trm ) )
% 0.30/0.47 | ( ( uSubst95898992stappt @ sigma @ u @ ( const @ f ) )
% 0.30/0.47 = ( uSubst1138577137pconst @ sigma @ v @ f ) ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 2.96/1.53 ---- Embedded in THF ---
% 2.96/1.54 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.96/1.54 %%% Generated on Tue Feb 24 08:29:43 EST 2026
% 2.96/1.54 %%% using '$$dhol' embedding, version 1.3.0.
% 2.96/1.54 %%% Logic specification used:
% 2.96/1.54 %%% thf(spec, logic, $$dhol).
% 2.96/1.54
% 2.96/1.54 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.WzKSSIg5X4/DTF2DTF19715.p
% 2.96/1.54 thf(ty_t_Denotational__Semantics_Ointerp, type, denotational_interp: $tType).
% 2.96/1.54 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.96/1.54 thf(ty_t_Syntax_Ovariable, type, variable: $tType).
% 2.96/1.54 thf(ty_t_Option_Ooption, type, option: ($tType > $tType)).
% 2.96/1.54 thf(ty_t_Syntax_Ogame, type, game: $tType).
% 2.96/1.54 thf(ty_t_String_Ochar, type, char: $tType).
% 2.96/1.54 thf(ty_t_Syntax_Otrm, type, trm: $tType).
% 2.96/1.54 thf(ty_t_Syntax_Ofml, type, fml: $tType).
% 2.96/1.54 thf(ty_t_Real_Oreal, type, real: $tType).
% 2.96/1.54 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.96/1.54 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: ($o))).
% 2.96/1.54 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.96/1.54 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: ($o))).
% 2.96/1.54 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: ($o))).
% 2.96/1.54 thf(sy_cl_Lattices_Osemilattice__inf, type, semilattice_inf: (!> [A:$tType]: ($o))).
% 2.96/1.54 thf(sy_cl_Lattices_Obounded__lattice__bot, type, bounded_lattice_bot: (!> [A:$tType]: ($o))).
% 2.96/1.54 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.96/1.54 thf(sy_c_Lattices_Oinf__class_Oinf, type, inf_inf: (!> [A:$tType]: ((A > (A > A))))).
% 2.96/1.54 thf(sy_c_Option_Ocombine__options, type, combine_options: (!> [A:$tType]: (((A > (A > A)) > ((option @ A) > ((option @ A) > (option @ A))))))).
% 2.96/1.54 thf(sy_c_Option_Ooption_ONone, type, none: (!> [A:$tType]: ((option @ A)))).
% 2.96/1.54 thf(sy_c_Option_Ooption_OSome, type, some: (!> [A:$tType]: ((A > (option @ A))))).
% 2.96/1.54 thf(sy_c_Option_Ooption_Ocase__option, type, case_option: (!> [B:$tType,A:$tType]: ((B > ((A > B) > ((option @ A) > B)))))).
% 2.96/1.54 thf(sy_c_Option_Ooption_Othe, type, the: (!> [A:$tType]: (((option @ A) > A)))).
% 2.96/1.54 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.96/1.54 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.96/1.54 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 2.96/1.54 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 2.96/1.54 thf(sy_c_Product__Type_Oprod_Ocase__prod, type, product_case_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 2.96/1.54 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.96/1.54 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.96/1.54 thf(sy_c_Static__Semantics_OFVF, type, static_FVF: (fml > (set @ variable))).
% 2.96/1.54 thf(sy_c_Static__Semantics_OFVT, type, static_FVT: (trm > (set @ variable))).
% 2.96/1.54 thf(sy_c_String_Ochar_OChar, type, char2: ($o > ($o > ($o > ($o > ($o > ($o > ($o > ($o > char))))))))).
% 2.96/1.54 thf(sy_c_Syntax_Ofml_OGeq, type, geq: (trm > (trm > fml))).
% 2.96/1.54 thf(sy_c_Syntax_Ofml_OPred, type, pred: (char > (trm > fml))).
% 2.96/1.54 thf(sy_c_Syntax_Otrm_OConst, type, const: (char > trm)).
% 2.96/1.54 thf(sy_c_Syntax_Otrm_ODifferential, type, differential: (trm > trm)).
% 2.96/1.54 thf(sy_c_Syntax_Otrm_OFunc, type, func: (char > (trm > trm))).
% 2.96/1.54 thf(sy_c_Syntax_Otrm_ONumber, type, number: (real > trm)).
% 2.96/1.54 thf(sy_c_Syntax_Otrm_OPlus, type, plus: (trm > (trm > trm))).
% 2.96/1.54 thf(sy_c_Syntax_Otrm_OTimes, type, times: (trm > (trm > trm))).
% 2.96/1.54 thf(sy_c_Syntax_Otrm_OVar, type, var: (variable > trm)).
% 2.96/1.54 thf(sy_c_USubst__Mirabelle__nnnzepxswx_ODifferentialo, type, uSubst259074819ntialo: ((option @ trm) > (option @ trm))).
% 2.96/1.54 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OGeqo, type, uSubst1556497037e_Geqo: ((option @ trm) > ((option @ trm) > (option @ fml)))).
% 2.96/1.54 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OGeqo__rel, type, uSubst864323244qo_rel: (((product_prod @ (option @ trm)) @ (option @ trm)) > (((product_prod @ (option @ trm)) @ (option @ trm)) > $o))).
% 2.96/1.54 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OPluso, type, uSubst1112714340_Pluso: ((option @ trm) > ((option @ trm) > (option @ trm)))).
% 2.96/1.54 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OPluso__rel, type, uSubst270600597so_rel: (((product_prod @ (option @ trm)) @ (option @ trm)) > (((product_prod @ (option @ trm)) @ (option @ trm)) > $o))).
% 2.96/1.54 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTimeso, type, uSubst277968634Timeso: ((option @ trm) > ((option @ trm) > (option @ trm)))).
% 2.96/1.54 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTimeso__rel, type, uSubst1377811071so_rel: (((product_prod @ (option @ trm)) @ (option @ trm)) > (((product_prod @ (option @ trm)) @ (option @ trm)) > $o))).
% 2.96/1.54 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Odot, type, uSubst_Mirabelle_dot: trm).
% 2.96/1.54 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Odotsubstt, type, uSubst969145931substt: (trm > ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))))).
% 2.96/1.54 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))))).
% 2.96/1.54 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))))).
% 2.96/1.54 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))))).
% 2.96/1.54 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)) > $o))).
% 2.96/1.54 thf(sy_c_Wellfounded_Oaccp, type, accp: (!> [A:$tType]: (((A > (A > $o)) > (A > $o))))).
% 2.96/1.54 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.96/1.54 thf(sy_v_U, type, u: (set @ variable)).
% 2.96/1.54 thf(sy_v_V, type, v: (set @ variable)).
% 2.96/1.54 thf(sy_v__092_060sigma_062, type, sigma: ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))).
% 2.96/1.54 thf(sy_v_f____, type, f: char).
% 2.96/1.54 thf(fact_0_f2, axiom, (! [Z:(option @ trm),F:(trm > (option @ trm)),Za:(option @ trm)]: ((((Za = (none @ trm)) => ((((((case_option @ (option @ trm)) @ trm) @ Z) @ F) @ Za) = Z)) & ((Za != (none @ trm)) => ((((((case_option @ (option @ trm)) @ trm) @ Z) @ F) @ Za) = (F @ ((the @ trm) @ Za)))))))).
% 2.96/1.54 thf(fact_1_Const_Oprems_I1_J, axiom, ((((uSubst95898992stappt @ sigma) @ u) @ (const @ f)) != (none @ trm))).
% 2.96/1.54 thf(fact_2_Const_Oprems_I2_J, axiom, ((((uSubst95898992stappt @ sigma) @ v) @ (const @ f)) != (none @ trm))).
% 2.96/1.54 thf(fact_3_f3, axiom, ((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ sigma) @ f) != (none @ trm)) => ((((inf_inf @ (set @ variable)) @ (static_FVT @ ((the @ trm) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ sigma) @ f)))) @ u) = (bot_bot @ (set @ variable))))).
% 2.96/1.54 thf(fact_4__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062, axiom, ((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ sigma) @ f) != (none @ trm)) => ((((inf_inf @ (set @ variable)) @ (static_FVT @ ((the @ trm) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ sigma) @ f)))) @ v) = (bot_bot @ (set @ variable))))).
% 2.96/1.54 thf(fact_5_usappconst__def, axiom, (uSubst1138577137pconst = (^ [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),F2:char]: ((((((case_option @ (option @ trm)) @ trm) @ ((some @ trm) @ (const @ F2))) @ (^ [R:trm]: (((((if @ (option @ trm)) @ ((((inf_inf @ (set @ variable)) @ (static_FVT @ R)) @ U) = (bot_bot @ (set @ variable)))) @ ((some @ trm) @ R)) @ (none @ trm))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ Sigma) @ F2)))))).
% 2.96/1.54 thf(fact_6_f1, axiom, ((((uSubst95898992stappt @ sigma) @ u) @ (const @ f)) = (((((case_option @ (option @ trm)) @ trm) @ ((some @ trm) @ (const @ f))) @ (^ [T2:trm]: (((((if @ (option @ trm)) @ ((((inf_inf @ (set @ variable)) @ (static_FVT @ T2)) @ u) = (bot_bot @ (set @ variable)))) @ ((some @ trm) @ T2)) @ (none @ trm))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ sigma) @ f)))).
% 2.96/1.54 thf(fact_7_usubstappt_Osimps_I3_J, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),F3:char]: (((((uSubst95898992stappt @ Sigma2) @ U2) @ (const @ F3)) = (((uSubst1138577137pconst @ Sigma2) @ U2) @ F3))))).
% 2.96/1.54 thf(fact_8_undeft__None, axiom, ((none @ trm) = (none @ trm))).
% 2.96/1.54 thf(fact_9__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AV_Af_092_060close_062, axiom, ((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ sigma) @ f) != (none @ trm)) => ((((((inf_inf @ (set @ variable)) @ (static_FVT @ ((the @ trm) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ sigma) @ f)))) @ v) = (bot_bot @ (set @ variable))) => (((some @ trm) @ ((the @ trm) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ sigma) @ f))) = (((uSubst1138577137pconst @ sigma) @ v) @ f))) & (((((inf_inf @ (set @ variable)) @ (static_FVT @ ((the @ trm) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ sigma) @ f)))) @ v) != (bot_bot @ (set @ variable))) => ((none @ trm) = (((uSubst1138577137pconst @ sigma) @ v) @ f)))))).
% 2.96/1.54 thf(fact_10__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AU_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AU_Af_092_060close_062, axiom, ((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ sigma) @ f) != (none @ trm)) => ((((((inf_inf @ (set @ variable)) @ (static_FVT @ ((the @ trm) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ sigma) @ f)))) @ u) = (bot_bot @ (set @ variable))) => (((some @ trm) @ ((the @ trm) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ sigma) @ f))) = (((uSubst1138577137pconst @ sigma) @ u) @ f))) & (((((inf_inf @ (set @ variable)) @ (static_FVT @ ((the @ trm) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ sigma) @ f)))) @ u) != (bot_bot @ (set @ variable))) => ((none @ trm) = (((uSubst1138577137pconst @ sigma) @ u) @ f)))))).
% 2.96/1.54 thf(fact_11_trm_Oinject_I3_J, axiom, (! [X3:char,Y3:char]: ((((const @ X3) = (const @ Y3)) = (X3 = Y3))))).
% 2.96/1.54 thf(fact_12_case__prod__app, axiom, (! [A:$tType,D:$tType,C:$tType,B:$tType]: (((((product_case_prod @ B) @ C) @ (D > A)) = (^ [F2:(B > (C > (D > A))),X:((product_prod @ B) @ C),Y:D]: ((((((product_case_prod @ B) @ C) @ A) @ (^ [L:B,R:C]: ((((F2 @ L) @ R) @ Y)))) @ X))))))).
% 2.96/1.54 thf(fact_13_usubstappt__const, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),F3:char,R2:trm,U2:(set @ variable)]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ Sigma2) @ F3) = ((some @ trm) @ R2)) => (((((inf_inf @ (set @ variable)) @ (static_FVT @ R2)) @ U2) = (bot_bot @ (set @ variable))) => ((((uSubst95898992stappt @ Sigma2) @ U2) @ (const @ F3)) = ((some @ trm) @ R2))))))).
% 2.96/1.54 thf(fact_14_usubstappt__const__conv, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),F3:char]: ((((((uSubst95898992stappt @ Sigma2) @ U2) @ (const @ F3)) != (none @ trm)) => ((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ Sigma2) @ F3) = (none @ trm)) | (? [R3:trm]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ Sigma2) @ F3) = ((some @ trm) @ R3)) & ((((inf_inf @ (set @ variable)) @ (static_FVT @ R3)) @ U2) = (bot_bot @ (set @ variable))))))))))).
% 2.96/1.54 thf(fact_15_usappconst__simp, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),F3:char,R2:trm,U2:(set @ variable)]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ Sigma2) @ F3) = ((some @ trm) @ R2)) => (((((inf_inf @ (set @ variable)) @ (static_FVT @ R2)) @ U2) = (bot_bot @ (set @ variable))) => ((((uSubst1138577137pconst @ Sigma2) @ U2) @ F3) = ((some @ trm) @ R2))))))).
% 2.96/1.54 thf(fact_16_usappconst__conv, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),F3:char]: ((((((uSubst1138577137pconst @ Sigma2) @ U2) @ F3) != (none @ trm)) => ((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ Sigma2) @ F3) = (none @ trm)) | (? [R3:trm]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ Sigma2) @ F3) = ((some @ trm) @ R3)) & ((((inf_inf @ (set @ variable)) @ (static_FVT @ R3)) @ U2) = (bot_bot @ (set @ variable))))))))))).
% 2.96/1.54 thf(fact_17_ODEo_Oinduct, axiom, (! [P:(char > ((option @ trm) > $o)),A0:char,A1:(option @ trm)]: (((! [X2:char,Theta:trm]: (((P @ X2) @ ((some @ trm) @ Theta)))) => ((! [X2:char]: (((P @ X2) @ (none @ trm)))) => ((P @ A0) @ A1)))))).
% 2.96/1.54 thf(fact_18_undeft__equiv, axiom, (! [Theta2:(option @ trm)]: (((Theta2 != (none @ trm)) = (? [T2:trm]: ((Theta2 = ((some @ trm) @ T2)))))))).
% 2.96/1.54 thf(fact_19_Timeso_Oinduct, axiom, (! [P:((option @ trm) > ((option @ trm) > $o)),A0:(option @ trm),A1:(option @ trm)]: (((! [Theta:trm,Eta:trm]: (((P @ ((some @ trm) @ Theta)) @ ((some @ trm) @ Eta)))) => ((! [X_1:(option @ trm)]: (((P @ (none @ trm)) @ X_1))) => ((! [V:trm]: (((P @ ((some @ trm) @ V)) @ (none @ trm)))) => ((P @ A0) @ A1))))))).
% 2.96/1.54 thf(fact_20_Assigno_Oinduct, axiom, (! [P:(variable > ((option @ trm) > $o)),A0:variable,A1:(option @ trm)]: (((! [X2:variable,Theta:trm]: (((P @ X2) @ ((some @ trm) @ Theta)))) => ((! [X2:variable]: (((P @ X2) @ (none @ trm)))) => ((P @ A0) @ A1)))))).
% 2.96/1.54 thf(fact_21_Aterm__Some, axiom, ((some @ trm) = (some @ trm))).
% 2.96/1.54 thf(fact_22_Differentialo_Oinduct, axiom, (! [P:((option @ trm) > $o),A0:(option @ trm)]: (((! [Theta:trm]: ((P @ ((some @ trm) @ Theta)))) => ((P @ (none @ trm)) => (P @ A0)))))).
% 2.96/1.54 thf(fact_23_Differentialo_Ocases, axiom, (! [X4:(option @ trm)]: (((! [Theta:trm]: ((X4 != ((some @ trm) @ Theta)))) => (X4 = (none @ trm)))))).
% 2.96/1.54 thf(fact_24_option_Ocollapse, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) => (((some @ A) @ ((the @ A) @ Option)) = Option))))).
% 2.96/1.54 thf(fact_25_not__Some__eq, axiom, (! [A:$tType,X4:(option @ A)]: (((! [Y:A]: ((X4 != ((some @ A) @ Y)))) = (X4 = (none @ A)))))).
% 2.96/1.54 thf(fact_26_not__None__eq, axiom, (! [A:$tType,X4:(option @ A)]: (((X4 != (none @ A)) = (? [Y:A]: ((X4 = ((some @ A) @ Y)))))))).
% 2.96/1.54 thf(fact_27_inf__bot__left, axiom, (! [A:$tType]: (((bounded_lattice_bot @ A) => (! [X4:A]: (((((inf_inf @ A) @ (bot_bot @ A)) @ X4) = (bot_bot @ A)))))))).
% 2.96/1.54 thf(fact_28_inf__bot__right, axiom, (! [A:$tType]: (((bounded_lattice_bot @ A) => (! [X4:A]: (((((inf_inf @ A) @ X4) @ (bot_bot @ A)) = (bot_bot @ A)))))))).
% 2.96/1.54 thf(fact_29_usubstappt__func2, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),F3:char,R2:trm,U2:(set @ variable),Theta2:trm]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [F4:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F4))))))))) @ Sigma2) @ F3) = ((some @ trm) @ R2)) => (((((inf_inf @ (set @ variable)) @ (static_FVT @ R2)) @ U2) != (bot_bot @ (set @ variable))) => ((((uSubst95898992stappt @ Sigma2) @ U2) @ ((func @ F3) @ Theta2)) = (none @ trm))))))).
% 2.96/1.54 thf(fact_30_option_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F22:(A > B),Option:(option @ A)]: (((P @ (((((case_option @ B) @ A) @ F1) @ F22) @ Option)) = (~ ((((Option = (none @ A)) & (~ ((P @ F1)))) | ((Option = ((some @ A) @ ((the @ A) @ Option))) & (~ ((P @ (F22 @ ((the @ A) @ Option))))))))))))).
% 2.96/1.54 thf(fact_31_option_Osplit__sel, axiom, (! [B:$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))))))))).
% 2.96/1.54 thf(fact_32_usubstappt__func__conv, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),F3:char,Theta2:trm]: ((((((uSubst95898992stappt @ Sigma2) @ U2) @ ((func @ F3) @ Theta2)) != (none @ trm)) => (((((uSubst95898992stappt @ Sigma2) @ U2) @ Theta2) != (none @ trm)) & ((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [F4:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F4))))))))) @ Sigma2) @ F3) = (none @ trm)) | (? [R3:trm]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [F4:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F4))))))))) @ Sigma2) @ F3) = ((some @ trm) @ R3)) & ((((inf_inf @ (set @ variable)) @ (static_FVT @ R3)) @ U2) = (bot_bot @ (set @ variable)))))))))))).
% 2.96/1.54 thf(fact_33_option_Ocase__eq__if, axiom, (! [A:$tType,B:$tType]: ((((case_option @ B) @ A) = (^ [F12:B,F23:(A > B),Option2:(option @ A)]: (((((if @ B) @ (Option2 = (none @ A))) @ F12) @ (F23 @ ((the @ A) @ Option2))))))))).
% 2.96/1.54 thf(fact_34_inf__right__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X4:A,Y2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X4) @ Y2)) @ Y2) = (((inf_inf @ A) @ X4) @ Y2)))))))).
% 2.96/1.54 thf(fact_35_inf_Oright__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ B2) = (((inf_inf @ A) @ A2) @ B2)))))))).
% 2.96/1.54 thf(fact_36_inf__left__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X4:A,Y2:A]: (((((inf_inf @ A) @ X4) @ (((inf_inf @ A) @ X4) @ Y2)) = (((inf_inf @ A) @ X4) @ Y2)))))))).
% 2.96/1.54 thf(fact_37_inf_Oleft__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A]: (((((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ A2) @ B2)) = (((inf_inf @ A) @ A2) @ B2)))))))).
% 2.96/1.54 thf(fact_38_inf__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X4:A]: (((((inf_inf @ A) @ X4) @ X4) = X4))))))).
% 2.96/1.54 thf(fact_39_inf_Oidem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A]: (((((inf_inf @ A) @ A2) @ A2) = A2))))))).
% 2.96/1.54 thf(fact_40_inf__apply, axiom, (! [B:$tType,A:$tType]: (((semilattice_inf @ B) => ((inf_inf @ (A > B)) = (^ [F2:(A > B),G:(A > B),X:A]: ((((inf_inf @ B) @ (F2 @ X)) @ (G @ X))))))))).
% 2.96/1.54 thf(fact_41_option_Oinject, axiom, (! [A:$tType,X22:A,Y22:A]: (((((some @ A) @ X22) = ((some @ A) @ Y22)) = (X22 = Y22))))).
% 2.96/1.54 thf(fact_42_trm_Oinject_I4_J, axiom, (! [X41:char,X42:trm,Y41:char,Y42:trm]: (((((func @ X41) @ X42) = ((func @ Y41) @ Y42)) = ((X41 = Y41) & (X42 = Y42)))))).
% 2.96/1.54 thf(fact_43_option_Odisc__eq__case_I2_J, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) = (((((case_option @ $o) @ A) @ $false) @ (^ [Uu:A]: ($true))) @ Option))))).
% 2.96/1.54 thf(fact_44_option_Odisc__eq__case_I1_J, axiom, (! [A:$tType,Option:(option @ A)]: (((Option = (none @ A)) = (((((case_option @ $o) @ A) @ $true) @ (^ [Uu:A]: ($false))) @ Option))))).
% 2.96/1.54 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.96/1.54 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A3)))) = A3)))).
% 2.96/1.54 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) = (Q @ X2)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.96/1.54 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F3:(A > B),G2:(A > B)]: (((! [X2:A]: (((F3 @ X2) = (G2 @ X2)))) => (F3 = G2))))).
% 2.96/1.54 thf(fact_49_trm_Odistinct_I23_J, axiom, (! [X3:char,X41:char,X42:trm]: (((const @ X3) != ((func @ X41) @ X42))))).
% 2.96/1.54 thf(fact_50_case__optionE, axiom, (! [A:$tType,P:$o,Q:(A > $o),X4:(option @ A)]: (((((((case_option @ $o) @ A) @ P) @ Q) @ X4) => (((X4 = (none @ A)) => (~ (P))) => (~ ((! [Y4:A]: (((X4 = ((some @ A) @ Y4)) => (~ ((Q @ Y4))))))))))))).
% 2.96/1.54 thf(fact_51_inf__left__commute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X4:A,Y2:A,Z2:A]: (((((inf_inf @ A) @ X4) @ (((inf_inf @ A) @ Y2) @ Z2)) = (((inf_inf @ A) @ Y2) @ (((inf_inf @ A) @ X4) @ Z2))))))))).
% 2.96/1.54 thf(fact_52_inf_Oleft__commute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [B2:A,A2:A,C2:A]: (((((inf_inf @ A) @ B2) @ (((inf_inf @ A) @ A2) @ C2)) = (((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C2))))))))).
% 2.96/1.54 thf(fact_53_inf__commute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => ((inf_inf @ A) = (^ [X:A,Y:A]: ((((inf_inf @ A) @ Y) @ X)))))))).
% 2.96/1.54 thf(fact_54_inf_Ocommute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => ((inf_inf @ A) = (^ [A4:A,B3:A]: ((((inf_inf @ A) @ B3) @ A4)))))))).
% 2.96/1.54 thf(fact_55_inf__assoc, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X4:A,Y2:A,Z2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X4) @ Y2)) @ Z2) = (((inf_inf @ A) @ X4) @ (((inf_inf @ A) @ Y2) @ Z2))))))))).
% 2.96/1.54 thf(fact_56_inf_Oassoc, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A,C2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ C2) = (((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C2))))))))).
% 2.96/1.54 thf(fact_57_boolean__algebra__cancel_Oinf2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [B4:A,K:A,B2:A,A2:A]: (((B4 = (((inf_inf @ A) @ K) @ B2)) => ((((inf_inf @ A) @ A2) @ B4) = (((inf_inf @ A) @ K) @ (((inf_inf @ A) @ A2) @ B2)))))))))).
% 2.96/1.54 thf(fact_58_boolean__algebra__cancel_Oinf1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A3:A,K:A,A2:A,B2:A]: (((A3 = (((inf_inf @ A) @ K) @ A2)) => ((((inf_inf @ A) @ A3) @ B2) = (((inf_inf @ A) @ K) @ (((inf_inf @ A) @ A2) @ B2)))))))))).
% 2.96/1.54 thf(fact_59_inf__fun__def, axiom, (! [B:$tType,A:$tType]: (((semilattice_inf @ B) => ((inf_inf @ (A > B)) = (^ [F2:(A > B),G:(A > B),X:A]: ((((inf_inf @ B) @ (F2 @ X)) @ (G @ X))))))))).
% 2.96/1.54 thf(fact_60_inf__sup__aci_I1_J, axiom, (! [A:$tType]: (((lattice @ A) => ((inf_inf @ A) = (^ [X:A,Y:A]: ((((inf_inf @ A) @ Y) @ X)))))))).
% 2.96/1.54 thf(fact_61_inf__sup__aci_I2_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X4:A,Y2:A,Z2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X4) @ Y2)) @ Z2) = (((inf_inf @ A) @ X4) @ (((inf_inf @ A) @ Y2) @ Z2))))))))).
% 2.96/1.54 thf(fact_62_inf__sup__aci_I3_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X4:A,Y2:A,Z2:A]: (((((inf_inf @ A) @ X4) @ (((inf_inf @ A) @ Y2) @ Z2)) = (((inf_inf @ A) @ Y2) @ (((inf_inf @ A) @ X4) @ Z2))))))))).
% 2.96/1.54 thf(fact_63_inf__sup__aci_I4_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X4:A,Y2:A]: (((((inf_inf @ A) @ X4) @ (((inf_inf @ A) @ X4) @ Y2)) = (((inf_inf @ A) @ X4) @ Y2)))))))).
% 2.96/1.54 thf(fact_64_option_Ocase__distrib, axiom, (! [C:$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)) @ (^ [X:A]: ((H @ (F22 @ X))))) @ Option))))).
% 2.96/1.54 thf(fact_65_option_Odistinct_I1_J, axiom, (! [A:$tType,X22:A]: (((none @ A) != ((some @ A) @ X22))))).
% 2.96/1.54 thf(fact_66_option_OdiscI, axiom, (! [A:$tType,Option:(option @ A),X22:A]: (((Option = ((some @ A) @ X22)) => (Option != (none @ A)))))).
% 2.96/1.54 thf(fact_67_option_Oexhaust, axiom, (! [A:$tType,Y2:(option @ A)]: (((Y2 != (none @ A)) => (~ ((! [X23:A]: ((Y2 != ((some @ A) @ X23)))))))))).
% 2.96/1.54 thf(fact_68_option_Oinducts, axiom, (! [A:$tType,P:((option @ A) > $o),Option:(option @ A)]: (((P @ (none @ A)) => ((! [X2:A]: ((P @ ((some @ A) @ X2)))) => (P @ Option)))))).
% 2.96/1.54 thf(fact_69_split__option__ex, axiom, (! [A:$tType]: (((^ [P2:((option @ A) > $o)]: ((? [X5:(option @ A)]: ((P2 @ X5))))) = (^ [P3:((option @ A) > $o)]: (((P3 @ (none @ A)) | (? [X:A]: ((P3 @ ((some @ A) @ X))))))))))).
% 2.96/1.54 thf(fact_70_split__option__all, axiom, (! [A:$tType]: (((^ [P2:((option @ A) > $o)]: ((! [X5:(option @ A)]: ((P2 @ X5))))) = (^ [P3:((option @ A) > $o)]: (((P3 @ (none @ A)) & (! [X:A]: ((P3 @ ((some @ A) @ X))))))))))).
% 2.96/1.54 thf(fact_71_combine__options__cases, axiom, (! [A:$tType,B:$tType,X4:(option @ A),P:((option @ A) > ((option @ B) > $o)),Y2:(option @ B)]: ((((X4 = (none @ A)) => ((P @ X4) @ Y2)) => (((Y2 = (none @ B)) => ((P @ X4) @ Y2)) => ((! [A5:A,B5:B]: (((X4 = ((some @ A) @ A5)) => ((Y2 = ((some @ B) @ B5)) => ((P @ X4) @ Y2))))) => ((P @ X4) @ Y2))))))).
% 2.96/1.54 thf(fact_72_option_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F1:B,F22:(A > B)]: (((((((case_option @ B) @ A) @ F1) @ F22) @ (none @ A)) = F1)))).
% 2.96/1.54 thf(fact_73_option_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:B,F22:(A > B),X22:A]: (((((((case_option @ B) @ A) @ F1) @ F22) @ ((some @ A) @ X22)) = (F22 @ X22))))).
% 2.96/1.54 thf(fact_74_option_Oexpand, axiom, (! [A:$tType,Option:(option @ A),Option3:(option @ A)]: ((((Option = (none @ A)) = (Option3 = (none @ A))) => (((Option != (none @ A)) => ((Option3 != (none @ A)) => (((the @ A) @ Option) = ((the @ A) @ Option3)))) => (Option = Option3)))))).
% 2.96/1.54 thf(fact_75_option_Osel, axiom, (! [A:$tType,X22:A]: ((((the @ A) @ ((some @ A) @ X22)) = X22)))).
% 2.96/1.54 thf(fact_76_option_Oexhaust__sel, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) => (Option = ((some @ A) @ ((the @ A) @ Option))))))).
% 2.96/1.54 thf(fact_77_usubstappt__func, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),F3:char,R2:trm,U2:(set @ variable),Theta2:trm,Sigma_theta:trm]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [F4:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F4))))))))) @ Sigma2) @ F3) = ((some @ trm) @ R2)) => (((((inf_inf @ (set @ variable)) @ (static_FVT @ R2)) @ U2) = (bot_bot @ (set @ variable))) => (((((uSubst95898992stappt @ Sigma2) @ U2) @ Theta2) = ((some @ trm) @ Sigma_theta)) => ((((uSubst95898992stappt @ Sigma2) @ U2) @ ((func @ F3) @ Theta2)) = (((uSubst95898992stappt @ (uSubst969145931substt @ Sigma_theta)) @ (bot_bot @ (set @ variable))) @ R2)))))))).
% 2.96/1.54 thf(fact_78_usubstappt_Osimps_I4_J, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),F3:char,Theta2:trm]: (((((uSubst95898992stappt @ Sigma2) @ U2) @ ((func @ F3) @ Theta2)) = (((((case_option @ (option @ trm)) @ trm) @ (none @ trm)) @ (^ [Sigma_theta2:trm]: ((((((case_option @ (option @ trm)) @ trm) @ ((some @ trm) @ ((func @ F3) @ Sigma_theta2))) @ (^ [R:trm]: (((((if @ (option @ trm)) @ ((((inf_inf @ (set @ variable)) @ (static_FVT @ R)) @ U2) = (bot_bot @ (set @ variable)))) @ (((uSubst95898992stappt @ (uSubst969145931substt @ Sigma_theta2)) @ (bot_bot @ (set @ variable))) @ R)) @ (none @ trm))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [F4:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F4))))))))) @ Sigma2) @ F3))))) @ (((uSubst95898992stappt @ Sigma2) @ U2) @ Theta2)))))).
% 2.96/1.54 thf(fact_79_Int__iff, axiom, (! [A:$tType,C2:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) = ((((member @ A) @ C2) @ A3) & (((member @ A) @ C2) @ B4)))))).
% 2.96/1.54 thf(fact_80_IntI, axiom, (! [A:$tType,C2:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ A3) => ((((member @ A) @ C2) @ B4) => (((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A3) @ B4))))))).
% 2.96/1.54 thf(fact_81_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X:A]: ((~ ((P @ X))))))))).
% 2.96/1.54 thf(fact_82_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X:A]: ((~ ((P @ X))))))))).
% 2.96/1.54 thf(fact_83_all__not__in__conv, axiom, (! [A:$tType,A3:(set @ A)]: (((! [X:A]: ((~ ((((member @ A) @ X) @ A3))))) = (A3 = (bot_bot @ (set @ A))))))).
% 2.96/1.54 thf(fact_84_empty__iff, axiom, (! [A:$tType,C2:A]: ((~ ((((member @ A) @ C2) @ (bot_bot @ (set @ A)))))))).
% 2.96/1.54 thf(fact_85_bot__apply, axiom, (! [C:$tType,D:$tType]: (((bot @ C) => ((bot_bot @ (D > C)) = (^ [X:D]: ((bot_bot @ C)))))))).
% 2.96/1.54 thf(fact_86_bot__fun__def, axiom, (! [B:$tType,A:$tType]: (((bot @ B) => ((bot_bot @ (A > B)) = (^ [X:A]: ((bot_bot @ B)))))))).
% 2.96/1.54 thf(fact_87_emptyE, axiom, (! [A:$tType,A2:A]: ((~ ((((member @ A) @ A2) @ (bot_bot @ (set @ A)))))))).
% 2.96/1.54 thf(fact_88_equals0D, axiom, (! [A:$tType,A3:(set @ A),A2:A]: (((A3 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A2) @ A3))))))).
% 2.96/1.54 thf(fact_89_equals0I, axiom, (! [A:$tType,A3:(set @ A)]: (((! [Y4:A]: ((~ ((((member @ A) @ Y4) @ A3))))) => (A3 = (bot_bot @ (set @ A))))))).
% 2.96/1.54 thf(fact_90_ex__in__conv, axiom, (! [A:$tType,A3:(set @ A)]: (((? [X:A]: ((((member @ A) @ X) @ A3))) = (A3 != (bot_bot @ (set @ A))))))).
% 2.96/1.54 thf(fact_91_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 2.96/1.54 thf(fact_92_IntE, axiom, (! [A:$tType,C2:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) => (~ (((((member @ A) @ C2) @ A3) => (~ ((((member @ A) @ C2) @ B4)))))))))).
% 2.96/1.54 thf(fact_93_IntD1, axiom, (! [A:$tType,C2:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) => (((member @ A) @ C2) @ A3))))).
% 2.96/1.54 thf(fact_94_IntD2, axiom, (! [A:$tType,C2:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) => (((member @ A) @ C2) @ B4))))).
% 2.96/1.54 thf(fact_95_Int__assoc, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),C3:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) @ C3) = (((inf_inf @ (set @ A)) @ A3) @ (((inf_inf @ (set @ A)) @ B4) @ C3)))))).
% 2.96/1.54 thf(fact_96_Int__absorb, axiom, (! [A:$tType,A3:(set @ A)]: (((((inf_inf @ (set @ A)) @ A3) @ A3) = A3)))).
% 2.96/1.54 thf(fact_97_Int__commute, axiom, (! [A:$tType]: (((inf_inf @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((((inf_inf @ (set @ A)) @ B6) @ A6))))))).
% 2.96/1.54 thf(fact_98_Int__left__absorb, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((((inf_inf @ (set @ A)) @ A3) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) = (((inf_inf @ (set @ A)) @ A3) @ B4))))).
% 2.96/1.54 thf(fact_99_Int__left__commute, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),C3:(set @ A)]: (((((inf_inf @ (set @ A)) @ A3) @ (((inf_inf @ (set @ A)) @ B4) @ C3)) = (((inf_inf @ (set @ A)) @ B4) @ (((inf_inf @ (set @ A)) @ A3) @ C3)))))).
% 2.96/1.54 thf(fact_100_empty__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (^ [X:A]: ($false))))))).
% 2.96/1.54 thf(fact_101_Collect__conj__eq, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: ((((collect @ A) @ (^ [X:A]: (((P @ X) & (Q @ X))))) = (((inf_inf @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.96/1.54 thf(fact_102_Int__Collect, axiom, (! [A:$tType,X4:A,A3:(set @ A),P:(A > $o)]: (((((member @ A) @ X4) @ (((inf_inf @ (set @ A)) @ A3) @ ((collect @ A) @ P))) = ((((member @ A) @ X4) @ A3) & (P @ X4)))))).
% 2.96/1.54 thf(fact_103_Int__def, axiom, (! [A:$tType]: (((inf_inf @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: (((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ A6) & (((member @ A) @ X) @ B6))))))))))).
% 2.96/1.54 thf(fact_104_inf__set__def, axiom, (! [A:$tType]: (((inf_inf @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: (((collect @ A) @ (((inf_inf @ (A > $o)) @ (^ [X:A]: ((((member @ A) @ X) @ A6)))) @ (^ [X:A]: ((((member @ A) @ X) @ B6))))))))))).
% 2.96/1.54 thf(fact_105_Int__emptyI, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((! [X2:A]: (((((member @ A) @ X2) @ A3) => (~ ((((member @ A) @ X2) @ B4)))))) => ((((inf_inf @ (set @ A)) @ A3) @ B4) = (bot_bot @ (set @ A))))))).
% 2.96/1.54 thf(fact_106_disjoint__iff, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: ((((((inf_inf @ (set @ A)) @ A3) @ B4) = (bot_bot @ (set @ A))) = (! [X:A]: (((((member @ A) @ X) @ A3) => (~ ((((member @ A) @ X) @ B4)))))))))).
% 2.96/1.54 thf(fact_107_Int__empty__left, axiom, (! [A:$tType,B4:(set @ A)]: (((((inf_inf @ (set @ A)) @ (bot_bot @ (set @ A))) @ B4) = (bot_bot @ (set @ A)))))).
% 2.96/1.54 thf(fact_108_Int__empty__right, axiom, (! [A:$tType,A3:(set @ A)]: (((((inf_inf @ (set @ A)) @ A3) @ (bot_bot @ (set @ A))) = (bot_bot @ (set @ A)))))).
% 2.96/1.54 thf(fact_109_disjoint__iff__not__equal, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: ((((((inf_inf @ (set @ A)) @ A3) @ B4) = (bot_bot @ (set @ A))) = (! [X:A]: (((((member @ A) @ X) @ A3) => (! [Y:A]: (((((member @ A) @ Y) @ B4) => (X != Y))))))))))).
% 2.96/1.54 thf(fact_110_disjE__realizer2, axiom, (! [B:$tType,A:$tType,P:$o,Q:(A > $o),X4:(option @ A),R4:(B > $o),F3:B,G2:(A > B)]: (((((((case_option @ $o) @ A) @ P) @ Q) @ X4) => ((P => (R4 @ F3)) => ((! [Q2:A]: (((Q @ Q2) => (R4 @ (G2 @ Q2))))) => (R4 @ (((((case_option @ B) @ A) @ F3) @ G2) @ X4)))))))).
% 2.96/1.54 thf(fact_111_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A6:(set @ A)]: ((A6 = (bot_bot @ (set @ A))))))))).
% 2.96/1.54 thf(fact_112_prod_Ocase__distrib, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,H:(C > D),F3:(A > (B > C)),Prod:((product_prod @ A) @ B)]: (((H @ (((((product_case_prod @ A) @ B) @ C) @ F3) @ Prod)) = (((((product_case_prod @ A) @ B) @ D) @ (^ [X1:A,X24:B]: ((H @ ((F3 @ X1) @ X24))))) @ Prod))))).
% 2.96/1.54 thf(fact_113_inf__Int__eq, axiom, (! [A:$tType,R4:(set @ A),S:(set @ A)]: (((((inf_inf @ (A > $o)) @ (^ [X:A]: ((((member @ A) @ X) @ R4)))) @ (^ [X:A]: ((((member @ A) @ X) @ S)))) = (^ [X:A]: ((((member @ A) @ X) @ (((inf_inf @ (set @ A)) @ R4) @ S)))))))).
% 2.96/1.54 thf(fact_114_Timeso_Osimps_I3_J, axiom, (! [V2:trm]: ((((uSubst277968634Timeso @ ((some @ trm) @ V2)) @ (none @ trm)) = (none @ trm))))).
% 2.96/1.54 thf(fact_115_Pluso_Osimps_I3_J, axiom, (! [V2:trm]: ((((uSubst1112714340_Pluso @ ((some @ trm) @ V2)) @ (none @ trm)) = (none @ trm))))).
% 2.96/1.54 thf(fact_116_inf1I, axiom, (! [A:$tType,A3:(A > $o),X4:A,B4:(A > $o)]: (((A3 @ X4) => ((B4 @ X4) => ((((inf_inf @ (A > $o)) @ A3) @ B4) @ X4)))))).
% 2.96/1.54 thf(fact_117_inf1E, axiom, (! [A:$tType,A3:(A > $o),B4:(A > $o),X4:A]: ((((((inf_inf @ (A > $o)) @ A3) @ B4) @ X4) => (~ (((A3 @ X4) => (~ ((B4 @ X4)))))))))).
% 2.96/1.54 thf(fact_118_inf1D1, axiom, (! [A:$tType,A3:(A > $o),B4:(A > $o),X4:A]: ((((((inf_inf @ (A > $o)) @ A3) @ B4) @ X4) => (A3 @ X4))))).
% 2.96/1.54 thf(fact_119_inf1D2, axiom, (! [A:$tType,A3:(A > $o),B4:(A > $o),X4:A]: ((((((inf_inf @ (A > $o)) @ A3) @ B4) @ X4) => (B4 @ X4))))).
% 2.96/1.54 thf(fact_120_Pluso_Osimps_I2_J, axiom, (! [Eta2:(option @ trm)]: ((((uSubst1112714340_Pluso @ (none @ trm)) @ Eta2) = (none @ trm))))).
% 2.96/1.54 thf(fact_121_Timeso_Osimps_I2_J, axiom, (! [Eta2:(option @ trm)]: ((((uSubst277968634Timeso @ (none @ trm)) @ Eta2) = (none @ trm))))).
% 2.96/1.54 thf(fact_122_Pluso__undef, axiom, (! [Theta2:(option @ trm),Eta2:(option @ trm)]: (((((uSubst1112714340_Pluso @ Theta2) @ Eta2) = (none @ trm)) = ((Theta2 = (none @ trm)) | (Eta2 = (none @ trm))))))).
% 2.96/1.54 thf(fact_123_Timeso__undef, axiom, (! [Theta2:(option @ trm),Eta2:(option @ trm)]: (((((uSubst277968634Timeso @ Theta2) @ Eta2) = (none @ trm)) = ((Theta2 = (none @ trm)) | (Eta2 = (none @ trm))))))).
% 2.96/1.54 thf(fact_124_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X:A]: ((((member @ A) @ X) @ (bot_bot @ (set @ A))))))))).
% 2.96/1.54 thf(fact_125_Collect__empty__eq__bot, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (P = (bot_bot @ (A > $o))))))).
% 2.96/1.54 thf(fact_126_internal__case__prod__def, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((produc2004651681e_prod @ A) @ B) @ C) = (((product_case_prod @ A) @ B) @ C))))).
% 2.96/1.54 thf(fact_127_Pluso_Oelims, axiom, (! [X4:(option @ trm),Xa:(option @ trm),Y2:(option @ trm)]: (((((uSubst1112714340_Pluso @ X4) @ Xa) = Y2) => ((! [Theta:trm]: (((X4 = ((some @ trm) @ Theta)) => (! [Eta:trm]: (((Xa = ((some @ trm) @ Eta)) => (Y2 != ((some @ trm) @ ((plus @ Theta) @ Eta))))))))) => (((X4 = (none @ trm)) => (Y2 != (none @ trm))) => (~ (((? [V:trm]: ((X4 = ((some @ trm) @ V)))) => ((Xa = (none @ trm)) => (Y2 != (none @ trm)))))))))))).
% 2.96/1.54 thf(fact_128_Timeso_Oelims, axiom, (! [X4:(option @ trm),Xa:(option @ trm),Y2:(option @ trm)]: (((((uSubst277968634Timeso @ X4) @ Xa) = Y2) => ((! [Theta:trm]: (((X4 = ((some @ trm) @ Theta)) => (! [Eta:trm]: (((Xa = ((some @ trm) @ Eta)) => (Y2 != ((some @ trm) @ ((times @ Theta) @ Eta))))))))) => (((X4 = (none @ trm)) => (Y2 != (none @ trm))) => (~ (((? [V:trm]: ((X4 = ((some @ trm) @ V)))) => ((Xa = (none @ trm)) => (Y2 != (none @ trm)))))))))))).
% 2.96/1.54 thf(fact_129_trm_Oinject_I5_J, axiom, (! [X51:trm,X52:trm,Y51:trm,Y52:trm]: (((((plus @ X51) @ X52) = ((plus @ Y51) @ Y52)) = ((X51 = Y51) & (X52 = Y52)))))).
% 2.96/1.54 thf(fact_130_trm_Oinject_I6_J, axiom, (! [X61:trm,X62:trm,Y61:trm,Y62:trm]: (((((times @ X61) @ X62) = ((times @ Y61) @ Y62)) = ((X61 = Y61) & (X62 = Y62)))))).
% 2.96/1.54 thf(fact_131_trm_Odistinct_I37_J, axiom, (! [X51:trm,X52:trm,X61:trm,X62:trm]: ((((plus @ X51) @ X52) != ((times @ X61) @ X62))))).
% 2.96/1.54 thf(fact_132_trm_Odistinct_I25_J, axiom, (! [X3:char,X51:trm,X52:trm]: (((const @ X3) != ((plus @ X51) @ X52))))).
% 2.96/1.54 thf(fact_133_trm_Odistinct_I27_J, axiom, (! [X3:char,X61:trm,X62:trm]: (((const @ X3) != ((times @ X61) @ X62))))).
% 2.96/1.54 thf(fact_134_trm_Odistinct_I31_J, axiom, (! [X41:char,X42:trm,X51:trm,X52:trm]: ((((func @ X41) @ X42) != ((plus @ X51) @ X52))))).
% 2.96/1.54 thf(fact_135_trm_Odistinct_I33_J, axiom, (! [X41:char,X42:trm,X61:trm,X62:trm]: ((((func @ X41) @ X42) != ((times @ X61) @ X62))))).
% 2.96/1.54 thf(fact_136_usubstappt__times__conv, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),Theta2:trm,Eta2:trm]: ((((((uSubst95898992stappt @ Sigma2) @ U2) @ ((times @ Theta2) @ Eta2)) != (none @ trm)) => (((((uSubst95898992stappt @ Sigma2) @ U2) @ Theta2) != (none @ trm)) & ((((uSubst95898992stappt @ Sigma2) @ U2) @ Eta2) != (none @ trm))))))).
% 2.96/1.54 thf(fact_137_usubstappt__plus__conv, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),Theta2:trm,Eta2:trm]: ((((((uSubst95898992stappt @ Sigma2) @ U2) @ ((plus @ Theta2) @ Eta2)) != (none @ trm)) => (((((uSubst95898992stappt @ Sigma2) @ U2) @ Theta2) != (none @ trm)) & ((((uSubst95898992stappt @ Sigma2) @ U2) @ Eta2) != (none @ trm))))))).
% 2.96/1.54 thf(fact_138_Timeso_Osimps_I1_J, axiom, (! [Theta2:trm,Eta2:trm]: ((((uSubst277968634Timeso @ ((some @ trm) @ Theta2)) @ ((some @ trm) @ Eta2)) = ((some @ trm) @ ((times @ Theta2) @ Eta2)))))).
% 2.96/1.54 thf(fact_139_Pluso_Osimps_I1_J, axiom, (! [Theta2:trm,Eta2:trm]: ((((uSubst1112714340_Pluso @ ((some @ trm) @ Theta2)) @ ((some @ trm) @ Eta2)) = ((some @ trm) @ ((plus @ Theta2) @ Eta2)))))).
% 2.96/1.54 thf(fact_140_usubstappt_Osimps_I6_J, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),Theta2:trm,Eta2:trm]: (((((uSubst95898992stappt @ Sigma2) @ U2) @ ((times @ Theta2) @ Eta2)) = ((uSubst277968634Timeso @ (((uSubst95898992stappt @ Sigma2) @ U2) @ Theta2)) @ (((uSubst95898992stappt @ Sigma2) @ U2) @ Eta2)))))).
% 2.96/1.54 thf(fact_141_usubstappt_Osimps_I5_J, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),Theta2:trm,Eta2:trm]: (((((uSubst95898992stappt @ Sigma2) @ U2) @ ((plus @ Theta2) @ Eta2)) = ((uSubst1112714340_Pluso @ (((uSubst95898992stappt @ Sigma2) @ U2) @ Theta2)) @ (((uSubst95898992stappt @ Sigma2) @ U2) @ Eta2)))))).
% 2.96/1.54 thf(fact_142_usubstappt_Oelims, axiom, (! [X4:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),Xa:(set @ variable),Xb:trm,Y2:(option @ trm)]: ((((((uSubst95898992stappt @ X4) @ Xa) @ Xb) = Y2) => ((! [X2:variable]: (((Xb = (var @ X2)) => (Y2 != ((some @ trm) @ (var @ X2)))))) => ((! [R3:real]: (((Xb = (number @ R3)) => (Y2 != ((some @ trm) @ (number @ R3)))))) => ((! [F5:char]: (((Xb = (const @ F5)) => (Y2 != (((uSubst1138577137pconst @ X4) @ Xa) @ F5))))) => ((! [F5:char,Theta:trm]: (((Xb = ((func @ F5) @ Theta)) => (Y2 != (((((case_option @ (option @ trm)) @ trm) @ (none @ trm)) @ (^ [Sigma_theta2:trm]: ((((((case_option @ (option @ trm)) @ trm) @ ((some @ trm) @ ((func @ F5) @ Sigma_theta2))) @ (^ [R:trm]: (((((if @ (option @ trm)) @ ((((inf_inf @ (set @ variable)) @ (static_FVT @ R)) @ Xa) = (bot_bot @ (set @ variable)))) @ (((uSubst95898992stappt @ (uSubst969145931substt @ Sigma_theta2)) @ (bot_bot @ (set @ variable))) @ R)) @ (none @ trm))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [F4:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F4))))))))) @ X4) @ F5))))) @ (((uSubst95898992stappt @ X4) @ Xa) @ Theta)))))) => ((! [Theta:trm,Eta:trm]: (((Xb = ((plus @ Theta) @ Eta)) => (Y2 != ((uSubst1112714340_Pluso @ (((uSubst95898992stappt @ X4) @ Xa) @ Theta)) @ (((uSubst95898992stappt @ X4) @ Xa) @ Eta)))))) => ((! [Theta:trm,Eta:trm]: (((Xb = ((times @ Theta) @ Eta)) => (Y2 != ((uSubst277968634Timeso @ (((uSubst95898992stappt @ X4) @ Xa) @ Theta)) @ (((uSubst95898992stappt @ X4) @ Xa) @ Eta)))))) => (~ ((! [Theta:trm]: (((Xb = (differential @ Theta)) => (Y2 != (uSubst259074819ntialo @ (((uSubst95898992stappt @ X4) @ ((collect @ variable) @ (^ [X:variable]: ($true)))) @ Theta)))))))))))))))))).
% 2.96/1.54 thf(fact_143_usubstappt__induct, axiom, (! [P:(((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) > ((set @ variable) > (trm > $o))),A0:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),A1:(set @ variable),A22:trm]: (((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),X2:variable]: ((((P @ Sigma3) @ U3) @ (var @ X2)))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),R3:real]: ((((P @ Sigma3) @ U3) @ (number @ R3)))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),F5:char]: ((((P @ Sigma3) @ U3) @ (const @ F5)))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),F5:char,Theta:trm]: (((((P @ Sigma3) @ U3) @ Theta) => ((! [X25:trm]: ((((((uSubst95898992stappt @ Sigma3) @ U3) @ Theta) = ((some @ trm) @ X25)) => (! [X2a:trm]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [F4:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F4))))))))) @ Sigma3) @ F5) = ((some @ trm) @ X2a)) => (((((inf_inf @ (set @ variable)) @ (static_FVT @ X2a)) @ U3) = (bot_bot @ (set @ variable))) => (((P @ (uSubst969145931substt @ X25)) @ (bot_bot @ (set @ variable))) @ X2a)))))))) => (((P @ Sigma3) @ U3) @ ((func @ F5) @ Theta)))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),Theta:trm]: (((((P @ Sigma3) @ U3) @ Theta) => (! [Eta:trm]: (((((P @ Sigma3) @ U3) @ Eta) => (((P @ Sigma3) @ U3) @ ((plus @ Theta) @ Eta)))))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),Theta:trm]: (((((P @ Sigma3) @ U3) @ Theta) => (! [Eta:trm]: (((((P @ Sigma3) @ U3) @ Eta) => (((P @ Sigma3) @ U3) @ ((times @ Theta) @ Eta)))))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),Theta:trm]: (((((P @ Sigma3) @ ((collect @ variable) @ (^ [X:variable]: ($true)))) @ Theta) => (((P @ Sigma3) @ U3) @ (differential @ Theta))))) => (((P @ A0) @ A1) @ A22))))))))))).
% 2.96/1.54 thf(fact_144_Geqo_Osimps_I3_J, axiom, (! [V2:trm]: ((((uSubst1556497037e_Geqo @ ((some @ trm) @ V2)) @ (none @ trm)) = (none @ fml))))).
% 2.96/1.54 thf(fact_145_combine__options__def, axiom, (! [A:$tType]: (((combine_options @ A) = (^ [F2:(A > (A > A)),X:(option @ A),Y:(option @ A)]: ((((((case_option @ (option @ A)) @ A) @ Y) @ (^ [Z3:A]: ((((((case_option @ (option @ A)) @ A) @ ((some @ A) @ Z3)) @ (^ [Aa:A]: (((some @ A) @ ((F2 @ Z3) @ Aa))))) @ Y)))) @ X))))))).
% 2.96/1.54 thf(fact_146_trm_Oinject_I2_J, axiom, (! [X22:real,Y22:real]: ((((number @ X22) = (number @ Y22)) = (X22 = Y22))))).
% 2.96/1.54 thf(fact_147_trm_Oinject_I1_J, axiom, (! [X12:variable,Y1:variable]: ((((var @ X12) = (var @ Y1)) = (X12 = Y1))))).
% 2.96/1.54 thf(fact_148_trm_Oinject_I7_J, axiom, (! [X7:trm,Y7:trm]: ((((differential @ X7) = (differential @ Y7)) = (X7 = Y7))))).
% 2.96/1.54 thf(fact_149_combine__options__simps_I2_J, axiom, (! [A:$tType,F3:(A > (A > A)),X4:(option @ A)]: ((((((combine_options @ A) @ F3) @ X4) @ (none @ A)) = X4)))).
% 2.96/1.54 thf(fact_150_combine__options__simps_I1_J, axiom, (! [A:$tType,F3:(A > (A > A)),Y2:(option @ A)]: ((((((combine_options @ A) @ F3) @ (none @ A)) @ Y2) = Y2)))).
% 2.96/1.54 thf(fact_151_combine__options__simps_I3_J, axiom, (! [A:$tType,F3:(A > (A > A)),A2:A,B2:A]: ((((((combine_options @ A) @ F3) @ ((some @ A) @ A2)) @ ((some @ A) @ B2)) = ((some @ A) @ ((F3 @ A2) @ B2)))))).
% 2.96/1.54 thf(fact_152_Differentialo_Osimps_I1_J, axiom, (! [Theta2:trm]: (((uSubst259074819ntialo @ ((some @ trm) @ Theta2)) = ((some @ trm) @ (differential @ Theta2)))))).
% 2.96/1.54 thf(fact_153_trm_Odistinct_I21_J, axiom, (! [X22:real,X7:trm]: (((number @ X22) != (differential @ X7))))).
% 2.96/1.54 thf(fact_154_trm_Odistinct_I11_J, axiom, (! [X12:variable,X7:trm]: (((var @ X12) != (differential @ X7))))).
% 2.96/1.54 thf(fact_155_trm_Odistinct_I1_J, axiom, (! [X12:variable,X22:real]: (((var @ X12) != (number @ X22))))).
% 2.96/1.54 thf(fact_156_combine__options__assoc, axiom, (! [A:$tType,F3:(A > (A > A)),X4:(option @ A),Y2:(option @ A),Z2:(option @ A)]: (((! [X2:A,Y4:A,Z4:A]: ((((F3 @ ((F3 @ X2) @ Y4)) @ Z4) = ((F3 @ X2) @ ((F3 @ Y4) @ Z4))))) => (((((combine_options @ A) @ F3) @ ((((combine_options @ A) @ F3) @ X4) @ Y2)) @ Z2) = ((((combine_options @ A) @ F3) @ X4) @ ((((combine_options @ A) @ F3) @ Y2) @ Z2))))))).
% 2.96/1.54 thf(fact_157_combine__options__commute, axiom, (! [A:$tType,F3:(A > (A > A)),X4:(option @ A),Y2:(option @ A)]: (((! [X2:A,Y4:A]: ((((F3 @ X2) @ Y4) = ((F3 @ Y4) @ X2)))) => (((((combine_options @ A) @ F3) @ X4) @ Y2) = ((((combine_options @ A) @ F3) @ Y2) @ X4)))))).
% 2.96/1.54 thf(fact_158_combine__options__left__commute, axiom, (! [A:$tType,F3:(A > (A > A)),Y2:(option @ A),X4:(option @ A),Z2:(option @ A)]: (((! [X2:A,Y4:A]: ((((F3 @ X2) @ Y4) = ((F3 @ Y4) @ X2)))) => ((! [X2:A,Y4:A,Z4:A]: ((((F3 @ ((F3 @ X2) @ Y4)) @ Z4) = ((F3 @ X2) @ ((F3 @ Y4) @ Z4))))) => (((((combine_options @ A) @ F3) @ Y2) @ ((((combine_options @ A) @ F3) @ X4) @ Z2)) = ((((combine_options @ A) @ F3) @ X4) @ ((((combine_options @ A) @ F3) @ Y2) @ Z2)))))))).
% 2.96/1.54 thf(fact_159_usubstappt_Osimps_I7_J, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),Theta2:trm]: (((((uSubst95898992stappt @ Sigma2) @ U2) @ (differential @ Theta2)) = (uSubst259074819ntialo @ (((uSubst95898992stappt @ Sigma2) @ ((collect @ variable) @ (^ [X:variable]: ($true)))) @ Theta2)))))).
% 2.96/1.54 thf(fact_160_trm_Odistinct_I13_J, axiom, (! [X22:real,X3:char]: (((number @ X22) != (const @ X3))))).
% 2.96/1.54 thf(fact_161_trm_Odistinct_I15_J, axiom, (! [X22:real,X41:char,X42:trm]: (((number @ X22) != ((func @ X41) @ X42))))).
% 2.96/1.54 thf(fact_162_trm_Odistinct_I19_J, axiom, (! [X22:real,X61:trm,X62:trm]: (((number @ X22) != ((times @ X61) @ X62))))).
% 2.96/1.54 thf(fact_163_trm_Odistinct_I17_J, axiom, (! [X22:real,X51:trm,X52:trm]: (((number @ X22) != ((plus @ X51) @ X52))))).
% 2.96/1.54 thf(fact_164_Differentialo_Oelims, axiom, (! [X4:(option @ trm),Y2:(option @ trm)]: ((((uSubst259074819ntialo @ X4) = Y2) => ((! [Theta:trm]: (((X4 = ((some @ trm) @ Theta)) => (Y2 != ((some @ trm) @ (differential @ Theta)))))) => (~ (((X4 = (none @ trm)) => (Y2 != (none @ trm)))))))))).
% 2.96/1.54 thf(fact_165_trm_Odistinct_I3_J, axiom, (! [X12:variable,X3:char]: (((var @ X12) != (const @ X3))))).
% 2.96/1.54 thf(fact_166_trm_Odistinct_I5_J, axiom, (! [X12:variable,X41:char,X42:trm]: (((var @ X12) != ((func @ X41) @ X42))))).
% 2.96/1.54 thf(fact_167_trm_Odistinct_I9_J, axiom, (! [X12:variable,X61:trm,X62:trm]: (((var @ X12) != ((times @ X61) @ X62))))).
% 2.96/1.54 thf(fact_168_trm_Odistinct_I7_J, axiom, (! [X12:variable,X51:trm,X52:trm]: (((var @ X12) != ((plus @ X51) @ X52))))).
% 2.96/1.54 thf(fact_169_trm_Odistinct_I29_J, axiom, (! [X3:char,X7:trm]: (((const @ X3) != (differential @ X7))))).
% 2.96/1.54 thf(fact_170_trm_Odistinct_I35_J, axiom, (! [X41:char,X42:trm,X7:trm]: ((((func @ X41) @ X42) != (differential @ X7))))).
% 2.96/1.54 thf(fact_171_trm_Odistinct_I41_J, axiom, (! [X61:trm,X62:trm,X7:trm]: ((((times @ X61) @ X62) != (differential @ X7))))).
% 2.96/1.54 thf(fact_172_trm_Odistinct_I39_J, axiom, (! [X51:trm,X52:trm,X7:trm]: ((((plus @ X51) @ X52) != (differential @ X7))))).
% 2.96/1.54 thf(fact_173_trm_Oexhaust, axiom, (! [Y2:trm]: (((! [X13:variable]: ((Y2 != (var @ X13)))) => ((! [X23:real]: ((Y2 != (number @ X23)))) => ((! [X32:char]: ((Y2 != (const @ X32)))) => ((! [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))))))))))))))).
% 2.96/1.54 thf(fact_174_trm_Oinduct, axiom, (! [P:(trm > $o),Trm:trm]: (((! [X2:variable]: ((P @ (var @ X2)))) => ((! [X2:real]: ((P @ (number @ X2)))) => ((! [X2:char]: ((P @ (const @ X2)))) => ((! [X1a:char,X2a2:trm]: (((P @ X2a2) => (P @ ((func @ X1a) @ X2a2))))) => ((! [X1a:trm,X2a2:trm]: (((P @ X1a) => ((P @ X2a2) => (P @ ((plus @ X1a) @ X2a2)))))) => ((! [X1a:trm,X2a2:trm]: (((P @ X1a) => ((P @ X2a2) => (P @ ((times @ X1a) @ X2a2)))))) => ((! [X2:trm]: (((P @ X2) => (P @ (differential @ X2))))) => (P @ Trm))))))))))).
% 2.96/1.54 thf(fact_175_Geqo_Osimps_I2_J, axiom, (! [Eta2:(option @ trm)]: ((((uSubst1556497037e_Geqo @ (none @ trm)) @ Eta2) = (none @ fml))))).
% 2.96/1.54 thf(fact_176_Geqo__undef, axiom, (! [Theta2:(option @ trm),Eta2:(option @ trm)]: (((((uSubst1556497037e_Geqo @ Theta2) @ Eta2) = (none @ fml)) = ((Theta2 = (none @ trm)) | (Eta2 = (none @ trm))))))).
% 2.96/1.54 thf(fact_177_Differentialo_Osimps_I2_J, axiom, ((uSubst259074819ntialo @ (none @ trm)) = (none @ trm))).
% 2.96/1.54 thf(fact_178_Differentialo__undef, axiom, (! [Theta2:(option @ trm)]: ((((uSubst259074819ntialo @ Theta2) = (none @ trm)) = (Theta2 = (none @ trm)))))).
% 2.96/1.54 thf(fact_179_usubstappt_Osimps_I2_J, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),R2:real]: (((((uSubst95898992stappt @ Sigma2) @ U2) @ (number @ R2)) = ((some @ trm) @ (number @ R2)))))).
% 2.96/1.54 thf(fact_180_usubstappt_Osimps_I1_J, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),X4:variable]: (((((uSubst95898992stappt @ Sigma2) @ U2) @ (var @ X4)) = ((some @ trm) @ (var @ X4)))))).
% 2.96/1.54 thf(fact_181_usubstappt__differential__conv, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),Theta2:trm]: ((((((uSubst95898992stappt @ Sigma2) @ U2) @ (differential @ Theta2)) != (none @ trm)) => ((((uSubst95898992stappt @ Sigma2) @ ((collect @ variable) @ (^ [X:variable]: ($true)))) @ Theta2) != (none @ trm)))))).
% 2.96/1.54 thf(fact_182_usubstappt_Opelims, axiom, (! [X4:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),Xa:(set @ variable),Xb:trm,Y2:(option @ trm)]: ((((((uSubst95898992stappt @ X4) @ Xa) @ Xb) = Y2) => ((((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)) @ X4) @ ((((product_Pair @ (set @ variable)) @ trm) @ Xa) @ Xb))) => ((! [X2:variable]: (((Xb = (var @ X2)) => ((Y2 = ((some @ trm) @ (var @ X2))) => (~ ((((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)) @ X4) @ ((((product_Pair @ (set @ variable)) @ trm) @ Xa) @ (var @ X2)))))))))) => ((! [R3:real]: (((Xb = (number @ R3)) => ((Y2 = ((some @ trm) @ (number @ R3))) => (~ ((((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)) @ X4) @ ((((product_Pair @ (set @ variable)) @ trm) @ Xa) @ (number @ R3)))))))))) => ((! [F5:char]: (((Xb = (const @ F5)) => ((Y2 = (((uSubst1138577137pconst @ X4) @ Xa) @ F5)) => (~ ((((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)) @ X4) @ ((((product_Pair @ (set @ variable)) @ trm) @ Xa) @ (const @ F5)))))))))) => ((! [F5:char,Theta:trm]: (((Xb = ((func @ F5) @ Theta)) => ((Y2 = (((((case_option @ (option @ trm)) @ trm) @ (none @ trm)) @ (^ [Sigma_theta2:trm]: ((((((case_option @ (option @ trm)) @ trm) @ ((some @ trm) @ ((func @ F5) @ Sigma_theta2))) @ (^ [R:trm]: (((((if @ (option @ trm)) @ ((((inf_inf @ (set @ variable)) @ (static_FVT @ R)) @ Xa) = (bot_bot @ (set @ variable)))) @ (((uSubst95898992stappt @ (uSubst969145931substt @ Sigma_theta2)) @ (bot_bot @ (set @ variable))) @ R)) @ (none @ trm))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [F4:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F4))))))))) @ X4) @ F5))))) @ (((uSubst95898992stappt @ X4) @ Xa) @ Theta))) => (~ ((((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)) @ X4) @ ((((product_Pair @ (set @ variable)) @ trm) @ Xa) @ ((func @ F5) @ Theta)))))))))) => ((! [Theta:trm,Eta:trm]: (((Xb = ((plus @ Theta) @ Eta)) => ((Y2 = ((uSubst1112714340_Pluso @ (((uSubst95898992stappt @ X4) @ Xa) @ Theta)) @ (((uSubst95898992stappt @ X4) @ Xa) @ Eta))) => (~ ((((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)) @ X4) @ ((((product_Pair @ (set @ variable)) @ trm) @ Xa) @ ((plus @ Theta) @ Eta)))))))))) => ((! [Theta:trm,Eta:trm]: (((Xb = ((times @ Theta) @ Eta)) => ((Y2 = ((uSubst277968634Timeso @ (((uSubst95898992stappt @ X4) @ Xa) @ Theta)) @ (((uSubst95898992stappt @ X4) @ Xa) @ Eta))) => (~ ((((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)) @ X4) @ ((((product_Pair @ (set @ variable)) @ trm) @ Xa) @ ((times @ Theta) @ Eta)))))))))) => (~ ((! [Theta:trm]: (((Xb = (differential @ Theta)) => ((Y2 = (uSubst259074819ntialo @ (((uSubst95898992stappt @ X4) @ ((collect @ variable) @ (^ [X:variable]: ($true)))) @ Theta))) => (~ ((((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)) @ X4) @ ((((product_Pair @ (set @ variable)) @ trm) @ Xa) @ (differential @ Theta))))))))))))))))))))))).
% 2.96/1.54 thf(fact_183_term__sem_Ocases, axiom, (! [X4:((product_prod @ denotational_interp) @ trm)]: (((! [I:denotational_interp,X2:variable]: ((X4 != ((((product_Pair @ denotational_interp) @ trm) @ I) @ (var @ X2))))) => ((! [I:denotational_interp,R3:real]: ((X4 != ((((product_Pair @ denotational_interp) @ trm) @ I) @ (number @ R3))))) => ((! [I:denotational_interp,F5:char]: ((X4 != ((((product_Pair @ denotational_interp) @ trm) @ I) @ (const @ F5))))) => ((! [I:denotational_interp,F5:char,Theta:trm]: ((X4 != ((((product_Pair @ denotational_interp) @ trm) @ I) @ ((func @ F5) @ Theta))))) => ((! [I:denotational_interp,Theta:trm,Eta:trm]: ((X4 != ((((product_Pair @ denotational_interp) @ trm) @ I) @ ((plus @ Theta) @ Eta))))) => ((! [I:denotational_interp,Theta:trm,Eta:trm]: ((X4 != ((((product_Pair @ denotational_interp) @ trm) @ I) @ ((times @ Theta) @ Eta))))) => (~ ((! [I:denotational_interp,Theta:trm]: ((X4 != ((((product_Pair @ denotational_interp) @ trm) @ I) @ (differential @ Theta)))))))))))))))).
% 2.96/1.54 thf(fact_184_term__sem_Oinduct, axiom, (! [P:(denotational_interp > (trm > $o)),A0:denotational_interp,A1:trm]: (((! [I:denotational_interp,X2:variable]: (((P @ I) @ (var @ X2)))) => ((! [I:denotational_interp,R3:real]: (((P @ I) @ (number @ R3)))) => ((! [I:denotational_interp,F5:char]: (((P @ I) @ (const @ F5)))) => ((! [I:denotational_interp,F5:char,Theta:trm]: ((((P @ I) @ Theta) => ((P @ I) @ ((func @ F5) @ Theta))))) => ((! [I:denotational_interp,Theta:trm]: ((((P @ I) @ Theta) => (! [Eta:trm]: ((((P @ I) @ Eta) => ((P @ I) @ ((plus @ Theta) @ Eta)))))))) => ((! [I:denotational_interp,Theta:trm]: ((((P @ I) @ Theta) => (! [Eta:trm]: ((((P @ I) @ Eta) => ((P @ I) @ ((times @ Theta) @ Eta)))))))) => ((! [I:denotational_interp,Theta:trm]: ((((? [Xa2:char]: ((((member @ char) @ Xa2) @ ((collect @ char) @ (^ [Uu:char]: ($true)))))) => ((P @ I) @ Theta)) => ((P @ I) @ (differential @ Theta))))) => ((P @ A0) @ A1))))))))))).
% 2.96/1.54 thf(fact_185_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A7:A,B7:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A7) @ B7)) = ((A2 = A7) & (B2 = B7)))))).
% 2.96/1.54 thf(fact_186_prod_Oinject, axiom, (! [A:$tType,B:$tType,X12:A,X22:B,Y1:A,Y22:B]: (((((((product_Pair @ A) @ B) @ X12) @ X22) = ((((product_Pair @ A) @ B) @ Y1) @ Y22)) = ((X12 = Y1) & (X22 = Y22)))))).
% 2.96/1.54 thf(fact_187_case__prodI, axiom, (! [A:$tType,B:$tType,F3:(A > (B > $o)),A2:A,B2:B]: ((((F3 @ A2) @ B2) => (((((product_case_prod @ A) @ B) @ $o) @ F3) @ ((((product_Pair @ A) @ B) @ A2) @ B2)))))).
% 2.96/1.54 thf(fact_188_case__prodI2, axiom, (! [B:$tType,A:$tType,P4:((product_prod @ A) @ B),C2:(A > (B > $o))]: (((! [A5:A,B5:B]: (((P4 = ((((product_Pair @ A) @ B) @ A5) @ B5)) => ((C2 @ A5) @ B5)))) => (((((product_case_prod @ A) @ B) @ $o) @ C2) @ P4))))).
% 2.96/1.54 thf(fact_189_case__prodI2_H, axiom, (! [A:$tType,B:$tType,C:$tType,P4:((product_prod @ A) @ B),C2:(A > (B > (C > $o))),X4:C]: (((! [A5:A,B5:B]: (((((((product_Pair @ A) @ B) @ A5) @ B5) = P4) => (((C2 @ A5) @ B5) @ X4)))) => ((((((product_case_prod @ A) @ B) @ (C > $o)) @ C2) @ P4) @ X4))))).
% 2.96/1.54 thf(fact_190_mem__case__prodI, axiom, (! [A:$tType,B:$tType,C:$tType,Z2:A,C2:(B > (C > (set @ A))),A2:B,B2:C]: (((((member @ A) @ Z2) @ ((C2 @ A2) @ B2)) => (((member @ A) @ Z2) @ (((((product_case_prod @ B) @ C) @ (set @ A)) @ C2) @ ((((product_Pair @ B) @ C) @ A2) @ B2))))))).
% 2.96/1.54 thf(fact_191_mem__case__prodI2, axiom, (! [C:$tType,B:$tType,A:$tType,P4:((product_prod @ A) @ B),Z2:C,C2:(A > (B > (set @ C)))]: (((! [A5:A,B5:B]: (((P4 = ((((product_Pair @ A) @ B) @ A5) @ B5)) => (((member @ C) @ Z2) @ ((C2 @ A5) @ B5))))) => (((member @ C) @ Z2) @ (((((product_case_prod @ A) @ B) @ (set @ C)) @ C2) @ P4)))))).
% 2.96/1.54 thf(fact_192_case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,F3:(B > (C > A)),A2:B,B2:C]: (((((((product_case_prod @ B) @ C) @ A) @ F3) @ ((((product_Pair @ B) @ C) @ A2) @ B2)) = ((F3 @ A2) @ B2))))).
% 2.96/1.54 thf(fact_193_usubstappt_Opsimps_I7_J, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),Theta2: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)) @ Sigma2) @ ((((product_Pair @ (set @ variable)) @ trm) @ U2) @ (differential @ Theta2)))) => ((((uSubst95898992stappt @ Sigma2) @ U2) @ (differential @ Theta2)) = (uSubst259074819ntialo @ (((uSubst95898992stappt @ Sigma2) @ ((collect @ variable) @ (^ [X:variable]: ($true)))) @ Theta2))))))).
% 2.96/1.54 thf(fact_194_usubstappt_Opsimps_I1_J, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),X4:variable]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma2) @ ((((product_Pair @ (set @ variable)) @ trm) @ U2) @ (var @ X4)))) => ((((uSubst95898992stappt @ Sigma2) @ U2) @ (var @ X4)) = ((some @ trm) @ (var @ X4))))))).
% 2.96/1.54 thf(fact_195_usubstappt_Opsimps_I2_J, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),R2:real]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma2) @ ((((product_Pair @ (set @ variable)) @ trm) @ U2) @ (number @ R2)))) => ((((uSubst95898992stappt @ Sigma2) @ U2) @ (number @ R2)) = ((some @ trm) @ (number @ R2))))))).
% 2.96/1.54 thf(fact_196_cond__case__prod__eta, axiom, (! [C:$tType,B:$tType,A:$tType,F3:(A > (B > C)),G2:(((product_prod @ A) @ B) > C)]: (((! [X2:A,Y4:B]: ((((F3 @ X2) @ Y4) = (G2 @ ((((product_Pair @ A) @ B) @ X2) @ Y4))))) => (((((product_case_prod @ A) @ B) @ C) @ F3) = G2))))).
% 2.96/1.54 thf(fact_197_case__prod__eta, axiom, (! [C:$tType,B:$tType,A:$tType,F3:(((product_prod @ A) @ B) > C)]: ((((((product_case_prod @ A) @ B) @ C) @ (^ [X:A,Y:B]: ((F3 @ ((((product_Pair @ A) @ B) @ X) @ Y))))) = F3)))).
% 2.96/1.54 thf(fact_198_case__prodE2, axiom, (! [B:$tType,A:$tType,C:$tType,Q:(A > $o),P:(B > (C > A)),Z2:((product_prod @ B) @ C)]: (((Q @ (((((product_case_prod @ B) @ C) @ A) @ P) @ Z2)) => (~ ((! [X2:B,Y4:C]: (((Z2 = ((((product_Pair @ B) @ C) @ X2) @ Y4)) => (~ ((Q @ ((P @ X2) @ Y4))))))))))))).
% 2.96/1.54 thf(fact_199_inf__Int__eq2, axiom, (! [B:$tType,A:$tType,R4:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: (((((inf_inf @ (A > (B > $o))) @ (^ [X:A,Y:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y)) @ R4)))) @ (^ [X:A,Y:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y)) @ S)))) = (^ [X:A,Y:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y)) @ (((inf_inf @ (set @ ((product_prod @ A) @ B))) @ R4) @ S)))))))).
% 2.96/1.54 thf(fact_200_bot__empty__eq2, axiom, (! [B:$tType,A:$tType]: (((bot_bot @ (A > (B > $o))) = (^ [X:A,Y:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y)) @ (bot_bot @ (set @ ((product_prod @ A) @ B)))))))))).
% 2.96/1.54 thf(fact_201_case__prodD, axiom, (! [A:$tType,B:$tType,F3:(A > (B > $o)),A2:A,B2:B]: (((((((product_case_prod @ A) @ B) @ $o) @ F3) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) => ((F3 @ A2) @ B2))))).
% 2.96/1.54 thf(fact_202_case__prodE, axiom, (! [A:$tType,B:$tType,C2:(A > (B > $o)),P4:((product_prod @ A) @ B)]: (((((((product_case_prod @ A) @ B) @ $o) @ C2) @ P4) => (~ ((! [X2:A,Y4:B]: (((P4 = ((((product_Pair @ A) @ B) @ X2) @ Y4)) => (~ (((C2 @ X2) @ Y4)))))))))))).
% 2.96/1.54 thf(fact_203_case__prodD_H, axiom, (! [B:$tType,A:$tType,C:$tType,R4:(A > (B > (C > $o))),A2:A,B2:B,C2:C]: ((((((((product_case_prod @ A) @ B) @ (C > $o)) @ R4) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) @ C2) => (((R4 @ A2) @ B2) @ C2))))).
% 2.96/1.54 thf(fact_204_case__prodE_H, axiom, (! [B:$tType,A:$tType,C:$tType,C2:(A > (B > (C > $o))),P4:((product_prod @ A) @ B),Z2:C]: ((((((((product_case_prod @ A) @ B) @ (C > $o)) @ C2) @ P4) @ Z2) => (~ ((! [X2:A,Y4:B]: (((P4 = ((((product_Pair @ A) @ B) @ X2) @ Y4)) => (~ ((((C2 @ X2) @ Y4) @ Z2)))))))))))).
% 2.96/1.54 thf(fact_205_pred__equals__eq2, axiom, (! [B:$tType,A:$tType,R4:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: ((((^ [X:A,Y:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y)) @ R4))) = (^ [X:A,Y:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y)) @ S)))) = (R4 = S))))).
% 2.96/1.54 thf(fact_206_mem__case__prodE, axiom, (! [B:$tType,A:$tType,C:$tType,Z2:A,C2:(B > (C > (set @ A))),P4:((product_prod @ B) @ C)]: (((((member @ A) @ Z2) @ (((((product_case_prod @ B) @ C) @ (set @ A)) @ C2) @ P4)) => (~ ((! [X2:B,Y4:C]: (((P4 = ((((product_Pair @ B) @ C) @ X2) @ Y4)) => (~ ((((member @ A) @ Z2) @ ((C2 @ X2) @ Y4))))))))))))).
% 2.96/1.54 thf(fact_207_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A5:A,B5:B]: ((P @ ((((product_Pair @ A) @ B) @ A5) @ B5)))) => (P @ Prod))))).
% 2.96/1.54 thf(fact_208_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y2:((product_prod @ A) @ B)]: ((~ ((! [A5:A,B5:B]: ((Y2 != ((((product_Pair @ A) @ B) @ A5) @ B5))))))))).
% 2.96/1.54 thf(fact_209_prod__induct7, axiom, (! [G3:$tType,F6:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F6) @ G3)))))) > $o),X4:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F6) @ G3))))))]: (((! [A5:A,B5:B,C4:C,D2:D,E2:E,F5:F6,G4:G3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F6) @ G3)))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F6) @ G3))))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F6) @ G3)))) @ C4) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F6) @ G3))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F6) @ G3)) @ E2) @ ((((product_Pair @ F6) @ G3) @ F5) @ G4))))))))) => (P @ X4))))).
% 2.96/1.54 thf(fact_210_prod__induct6, axiom, (! [F6:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F6))))) > $o),X4:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F6)))))]: (((! [A5:A,B5:B,C4:C,D2:D,E2:E,F5:F6]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F6))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F6)))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F6))) @ C4) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F6)) @ D2) @ ((((product_Pair @ E) @ F6) @ E2) @ F5)))))))) => (P @ X4))))).
% 2.96/1.54 thf(fact_211_prod__induct5, axiom, (! [E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) > $o),X4:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: (((! [A5:A,B5:B,C4:C,D2:D,E2:E]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C4) @ ((((product_Pair @ D) @ E) @ D2) @ E2))))))) => (P @ X4))))).
% 2.96/1.54 thf(fact_212_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X4:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A5:A,B5:B,C4:C,D2:D]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B5) @ ((((product_Pair @ C) @ D) @ C4) @ D2)))))) => (P @ X4))))).
% 2.96/1.54 thf(fact_213_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X4:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A5:A,B5:B,C4:C]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A5) @ ((((product_Pair @ B) @ C) @ B5) @ C4))))) => (P @ X4))))).
% 2.96/1.54 thf(fact_214_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F6:$tType,G3:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F6) @ G3))))))]: ((~ ((! [A5:A,B5:B,C4:C,D2:D,E2:E,F5:F6,G4:G3]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F6) @ G3)))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F6) @ G3))))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F6) @ G3)))) @ C4) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F6) @ G3))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F6) @ G3)) @ E2) @ ((((product_Pair @ F6) @ G3) @ F5) @ G4)))))))))))))).
% 2.96/1.54 thf(fact_215_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F6:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F6)))))]: ((~ ((! [A5:A,B5:B,C4:C,D2:D,E2:E,F5:F6]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F6))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F6)))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F6))) @ C4) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F6)) @ D2) @ ((((product_Pair @ E) @ F6) @ E2) @ F5))))))))))))).
% 2.96/1.54 thf(fact_216_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: ((~ ((! [A5:A,B5:B,C4:C,D2:D,E2:E]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C4) @ ((((product_Pair @ D) @ E) @ D2) @ E2)))))))))))).
% 2.96/1.54 thf(fact_217_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A5:A,B5:B,C4:C,D2:D]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B5) @ ((((product_Pair @ C) @ D) @ C4) @ D2))))))))))).
% 2.96/1.54 thf(fact_218_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A5:A,B5:B,C4:C]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A5) @ ((((product_Pair @ B) @ C) @ B5) @ C4)))))))))).
% 2.96/1.54 thf(fact_219_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A7:A,B7:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A7) @ B7)) => (~ (((A2 = A7) => (B2 != B7)))))))).
% 2.96/1.54 thf(fact_220_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P4:((product_prod @ A) @ B)]: (((! [A5:A,B5:B]: ((P @ ((((product_Pair @ A) @ B) @ A5) @ B5)))) => (P @ P4))))).
% 2.96/1.54 thf(fact_221_surj__pair, axiom, (! [A:$tType,B:$tType,P4:((product_prod @ A) @ B)]: ((? [X2:A,Y4:B]: ((P4 = ((((product_Pair @ A) @ B) @ X2) @ Y4))))))).
% 2.96/1.54 thf(fact_222_old_Oprod_Ocase, axiom, (! [A:$tType,C:$tType,B:$tType,F3:(A > (B > C)),X12:A,X22:B]: (((((((product_case_prod @ A) @ B) @ C) @ F3) @ ((((product_Pair @ A) @ B) @ X12) @ X22)) = ((F3 @ X12) @ X22))))).
% 2.96/1.54 thf(fact_223_case__prod__Pair__iden, axiom, (! [B:$tType,A:$tType,P4:((product_prod @ A) @ B)]: (((((((product_case_prod @ A) @ B) @ ((product_prod @ A) @ B)) @ ((product_Pair @ A) @ B)) @ P4) = P4)))).
% 2.96/1.54 thf(fact_224_usubstappt_Opsimps_I3_J, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),F3: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)) @ Sigma2) @ ((((product_Pair @ (set @ variable)) @ trm) @ U2) @ (const @ F3)))) => ((((uSubst95898992stappt @ Sigma2) @ U2) @ (const @ F3)) = (((uSubst1138577137pconst @ Sigma2) @ U2) @ F3)))))).
% 2.96/1.54 thf(fact_225_usubstappt_Opsimps_I6_J, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),Theta2:trm,Eta2: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)) @ Sigma2) @ ((((product_Pair @ (set @ variable)) @ trm) @ U2) @ ((times @ Theta2) @ Eta2)))) => ((((uSubst95898992stappt @ Sigma2) @ U2) @ ((times @ Theta2) @ Eta2)) = ((uSubst277968634Timeso @ (((uSubst95898992stappt @ Sigma2) @ U2) @ Theta2)) @ (((uSubst95898992stappt @ Sigma2) @ U2) @ Eta2))))))).
% 2.96/1.54 thf(fact_226_usubstappt_Opsimps_I5_J, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),Theta2:trm,Eta2: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)) @ Sigma2) @ ((((product_Pair @ (set @ variable)) @ trm) @ U2) @ ((plus @ Theta2) @ Eta2)))) => ((((uSubst95898992stappt @ Sigma2) @ U2) @ ((plus @ Theta2) @ Eta2)) = ((uSubst1112714340_Pluso @ (((uSubst95898992stappt @ Sigma2) @ U2) @ Theta2)) @ (((uSubst95898992stappt @ Sigma2) @ U2) @ Eta2))))))).
% 2.96/1.54 thf(fact_227_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C2:(B > (C > A)),A2:B,B2:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C2) @ ((((product_Pair @ B) @ C) @ A2) @ B2)) = ((C2 @ A2) @ B2))))).
% 2.96/1.54 thf(fact_228_usubstappt_Opsimps_I4_J, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),F3:char,Theta2: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)) @ Sigma2) @ ((((product_Pair @ (set @ variable)) @ trm) @ U2) @ ((func @ F3) @ Theta2)))) => ((((uSubst95898992stappt @ Sigma2) @ U2) @ ((func @ F3) @ Theta2)) = (((((case_option @ (option @ trm)) @ trm) @ (none @ trm)) @ (^ [Sigma_theta2:trm]: ((((((case_option @ (option @ trm)) @ trm) @ ((some @ trm) @ ((func @ F3) @ Sigma_theta2))) @ (^ [R:trm]: (((((if @ (option @ trm)) @ ((((inf_inf @ (set @ variable)) @ (static_FVT @ R)) @ U2) = (bot_bot @ (set @ variable)))) @ (((uSubst95898992stappt @ (uSubst969145931substt @ Sigma_theta2)) @ (bot_bot @ (set @ variable))) @ R)) @ (none @ trm))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [F4:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F4))))))))) @ Sigma2) @ F3))))) @ (((uSubst95898992stappt @ Sigma2) @ U2) @ Theta2))))))).
% 2.96/1.54 thf(fact_229_usubstappt_Ocases, axiom, (! [X4:((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))]: (((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),X2:variable]: ((X4 != ((((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)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (var @ X2)))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),R3:real]: ((X4 != ((((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)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (number @ R3)))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),F5:char]: ((X4 != ((((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)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (const @ F5)))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),F5:char,Theta:trm]: ((X4 != ((((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)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ ((func @ F5) @ Theta)))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),Theta:trm,Eta:trm]: ((X4 != ((((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)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ ((plus @ Theta) @ Eta)))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),Theta:trm,Eta:trm]: ((X4 != ((((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)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ ((times @ Theta) @ Eta)))))) => (~ ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),Theta:trm]: ((X4 != ((((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)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (differential @ Theta))))))))))))))))).
% 2.96/1.54 thf(fact_230_usubstappt_Opinduct, axiom, (! [A0:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),A1:(set @ variable),A22:trm,P:(((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) > ((set @ variable) > (trm > $o)))]: (((((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)) @ A0) @ ((((product_Pair @ (set @ variable)) @ trm) @ A1) @ A22))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(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)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (var @ X2)))) => (((P @ Sigma3) @ U3) @ (var @ X2))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(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)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (number @ R3)))) => (((P @ Sigma3) @ U3) @ (number @ R3))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),F5: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)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (const @ F5)))) => (((P @ Sigma3) @ U3) @ (const @ F5))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),F5:char,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)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ ((func @ F5) @ Theta)))) => ((((P @ Sigma3) @ U3) @ Theta) => ((! [X25:trm]: ((((((uSubst95898992stappt @ Sigma3) @ U3) @ Theta) = ((some @ trm) @ X25)) => (! [X2a:trm]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [F4:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F4))))))))) @ Sigma3) @ F5) = ((some @ trm) @ X2a)) => (((((inf_inf @ (set @ variable)) @ (static_FVT @ X2a)) @ U3) = (bot_bot @ (set @ variable))) => (((P @ (uSubst969145931substt @ X25)) @ (bot_bot @ (set @ variable))) @ X2a)))))))) => (((P @ Sigma3) @ U3) @ ((func @ F5) @ Theta))))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(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)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ ((plus @ Theta) @ Eta)))) => ((((P @ Sigma3) @ U3) @ Theta) => ((((P @ Sigma3) @ U3) @ Eta) => (((P @ Sigma3) @ U3) @ ((plus @ Theta) @ Eta))))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(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)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ ((times @ Theta) @ Eta)))) => ((((P @ Sigma3) @ U3) @ Theta) => ((((P @ Sigma3) @ U3) @ Eta) => (((P @ Sigma3) @ U3) @ ((times @ Theta) @ Eta))))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(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)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (differential @ Theta)))) => ((((P @ Sigma3) @ ((collect @ variable) @ (^ [X:variable]: ($true)))) @ Theta) => (((P @ Sigma3) @ U3) @ (differential @ Theta)))))) => (((P @ A0) @ A1) @ A22)))))))))))).
% 2.96/1.54 thf(fact_231_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 2.96/1.54 thf(fact_232_split__cong, axiom, (! [C:$tType,B:$tType,A:$tType,Q3:((product_prod @ A) @ B),F3:(A > (B > C)),G2:(A > (B > C)),P4:((product_prod @ A) @ B)]: (((! [X2:A,Y4:B]: (((((((product_Pair @ A) @ B) @ X2) @ Y4) = Q3) => (((F3 @ X2) @ Y4) = ((G2 @ X2) @ Y4))))) => ((P4 = Q3) => ((((((product_case_prod @ A) @ B) @ C) @ F3) @ P4) = (((((product_case_prod @ A) @ B) @ C) @ G2) @ Q3))))))).
% 2.96/1.54 thf(fact_233_Geqo_Oelims, axiom, (! [X4:(option @ trm),Xa:(option @ trm),Y2:(option @ fml)]: (((((uSubst1556497037e_Geqo @ X4) @ Xa) = Y2) => ((! [Theta:trm]: (((X4 = ((some @ trm) @ Theta)) => (! [Eta:trm]: (((Xa = ((some @ trm) @ Eta)) => (Y2 != ((some @ fml) @ ((geq @ Theta) @ Eta))))))))) => (((X4 = (none @ trm)) => (Y2 != (none @ fml))) => (~ (((? [V:trm]: ((X4 = ((some @ trm) @ V)))) => ((Xa = (none @ trm)) => (Y2 != (none @ fml)))))))))))).
% 2.96/1.54 thf(fact_234_fml_Oinject_I2_J, axiom, (! [X21:trm,X222:trm,Y21:trm,Y222:trm]: (((((geq @ X21) @ X222) = ((geq @ Y21) @ Y222)) = ((X21 = Y21) & (X222 = Y222)))))).
% 2.96/1.54 thf(fact_235_Diamondo_Ocases, axiom, (! [X4:((product_prod @ (option @ game)) @ (option @ fml))]: (((! [Alpha:game,Phi:fml]: ((X4 != ((((product_Pair @ (option @ game)) @ (option @ fml)) @ ((some @ game) @ Alpha)) @ ((some @ fml) @ Phi))))) => ((! [Phi:(option @ fml)]: ((X4 != ((((product_Pair @ (option @ game)) @ (option @ fml)) @ (none @ game)) @ Phi)))) => (~ ((! [V:game]: ((X4 != ((((product_Pair @ (option @ game)) @ (option @ fml)) @ ((some @ game) @ V)) @ (none @ fml)))))))))))).
% 2.96/1.54 thf(fact_236_Existso_Ocases, axiom, (! [X4:((product_prod @ variable) @ (option @ fml))]: (((! [X2:variable,Phi:fml]: ((X4 != ((((product_Pair @ variable) @ (option @ fml)) @ X2) @ ((some @ fml) @ Phi))))) => (~ ((! [X2:variable]: ((X4 != ((((product_Pair @ variable) @ (option @ fml)) @ X2) @ (none @ fml))))))))))).
% 2.96/1.54 thf(fact_237_Ando_Ocases, axiom, (! [X4:((product_prod @ (option @ fml)) @ (option @ fml))]: (((! [Phi:fml,Psi:fml]: ((X4 != ((((product_Pair @ (option @ fml)) @ (option @ fml)) @ ((some @ fml) @ Phi)) @ ((some @ fml) @ Psi))))) => ((! [Psi:(option @ fml)]: ((X4 != ((((product_Pair @ (option @ fml)) @ (option @ fml)) @ (none @ fml)) @ Psi)))) => (~ ((! [V:fml]: ((X4 != ((((product_Pair @ (option @ fml)) @ (option @ fml)) @ ((some @ fml) @ V)) @ (none @ fml)))))))))))).
% 2.96/1.54 thf(fact_238_ODEo_Ocases, axiom, (! [X4:((product_prod @ char) @ (option @ trm))]: (((! [X2:char,Theta:trm]: ((X4 != ((((product_Pair @ char) @ (option @ trm)) @ X2) @ ((some @ trm) @ Theta))))) => (~ ((! [X2:char]: ((X4 != ((((product_Pair @ char) @ (option @ trm)) @ X2) @ (none @ trm))))))))))).
% 2.96/1.54 thf(fact_239_Assigno_Ocases, axiom, (! [X4:((product_prod @ variable) @ (option @ trm))]: (((! [X2:variable,Theta:trm]: ((X4 != ((((product_Pair @ variable) @ (option @ trm)) @ X2) @ ((some @ trm) @ Theta))))) => (~ ((! [X2:variable]: ((X4 != ((((product_Pair @ variable) @ (option @ trm)) @ X2) @ (none @ trm))))))))))).
% 2.96/1.54 thf(fact_240_Timeso_Ocases, axiom, (! [X4:((product_prod @ (option @ trm)) @ (option @ trm))]: (((! [Theta:trm,Eta:trm]: ((X4 != ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ ((some @ trm) @ Theta)) @ ((some @ trm) @ Eta))))) => ((! [Eta:(option @ trm)]: ((X4 != ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ (none @ trm)) @ Eta)))) => (~ ((! [V:trm]: ((X4 != ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ ((some @ trm) @ V)) @ (none @ trm)))))))))))).
% 2.96/1.54 thf(fact_241_Geqo_Osimps_I1_J, axiom, (! [Theta2:trm,Eta2:trm]: ((((uSubst1556497037e_Geqo @ ((some @ trm) @ Theta2)) @ ((some @ trm) @ Eta2)) = ((some @ fml) @ ((geq @ Theta2) @ Eta2)))))).
% 2.96/1.54 thf(fact_242_usubstappf__geqr, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),Theta2:trm,Eta2:trm]: ((((((uSubst95898978stappf @ Sigma2) @ U2) @ ((geq @ Theta2) @ Eta2)) != (none @ fml)) => ((((uSubst95898978stappf @ Sigma2) @ U2) @ ((geq @ Theta2) @ Eta2)) = ((some @ fml) @ ((geq @ ((the @ trm) @ (((uSubst95898992stappt @ Sigma2) @ U2) @ Theta2))) @ ((the @ trm) @ (((uSubst95898992stappt @ Sigma2) @ U2) @ Eta2))))))))).
% 2.96/1.54 thf(fact_243_usubstappf__geq, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),Theta2:trm,Eta2:trm]: ((((((uSubst95898992stappt @ Sigma2) @ U2) @ Theta2) != (none @ trm)) => (((((uSubst95898992stappt @ Sigma2) @ U2) @ Eta2) != (none @ trm)) => ((((uSubst95898978stappf @ Sigma2) @ U2) @ ((geq @ Theta2) @ Eta2)) = ((some @ fml) @ ((geq @ ((the @ trm) @ (((uSubst95898992stappt @ Sigma2) @ U2) @ Theta2))) @ ((the @ trm) @ (((uSubst95898992stappt @ Sigma2) @ U2) @ Eta2)))))))))).
% 2.96/1.54 thf(fact_244_Composeo_Ocases, axiom, (! [X4:((product_prod @ (option @ game)) @ (option @ game))]: (((! [Alpha:game,Beta:game]: ((X4 != ((((product_Pair @ (option @ game)) @ (option @ game)) @ ((some @ game) @ Alpha)) @ ((some @ game) @ Beta))))) => ((! [Alpha:(option @ game)]: ((X4 != ((((product_Pair @ (option @ game)) @ (option @ game)) @ Alpha) @ (none @ game))))) => (~ ((! [V:game]: ((X4 != ((((product_Pair @ (option @ game)) @ (option @ game)) @ (none @ game)) @ ((some @ game) @ V)))))))))))).
% 2.96/1.54 thf(fact_245_usubstappf_Osimps_I2_J, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),Theta2:trm,Eta2:trm]: (((((uSubst95898978stappf @ Sigma2) @ U2) @ ((geq @ Theta2) @ Eta2)) = ((uSubst1556497037e_Geqo @ (((uSubst95898992stappt @ Sigma2) @ U2) @ Theta2)) @ (((uSubst95898992stappt @ Sigma2) @ U2) @ Eta2)))))).
% 2.96/1.54 thf(fact_246_usubstappf__geq__conv, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),Theta2:trm,Eta2:trm]: ((((((uSubst95898978stappf @ Sigma2) @ U2) @ ((geq @ Theta2) @ Eta2)) != (none @ fml)) => (((((uSubst95898992stappt @ Sigma2) @ U2) @ Theta2) != (none @ trm)) & ((((uSubst95898992stappt @ Sigma2) @ U2) @ Eta2) != (none @ trm))))))).
% 2.96/1.54 thf(fact_247_dotsubstt__def, axiom, (uSubst969145931substt = (^ [Theta3:trm]: (((((product_Pair @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (^ [F2:char]: (((((if @ (option @ trm)) @ (F2 = ((((((((char2 @ $false) @ $true) @ $true) @ $true) @ $false) @ $true) @ $false) @ $false))) @ ((some @ trm) @ Theta3)) @ (none @ trm))))) @ ((((product_Pair @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (^ [Uu:char]: ((none @ trm)))) @ ((((product_Pair @ (char > (option @ fml))) @ (char > (option @ game))) @ (^ [Uu:char]: ((none @ fml)))) @ (^ [Uu:char]: ((none @ game)))))))))).
% 2.96/1.54 thf(fact_248_Geqo_Opelims, axiom, (! [X4:(option @ trm),Xa:(option @ trm),Y2:(option @ fml)]: (((((uSubst1556497037e_Geqo @ X4) @ Xa) = Y2) => ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst864323244qo_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ X4) @ Xa)) => ((! [Theta:trm]: (((X4 = ((some @ trm) @ Theta)) => (! [Eta:trm]: (((Xa = ((some @ trm) @ Eta)) => ((Y2 = ((some @ fml) @ ((geq @ Theta) @ Eta))) => (~ ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst864323244qo_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ ((some @ trm) @ Theta)) @ ((some @ trm) @ Eta)))))))))))) => (((X4 = (none @ trm)) => ((Y2 = (none @ fml)) => (~ ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst864323244qo_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ (none @ trm)) @ Xa)))))) => (~ ((! [V:trm]: (((X4 = ((some @ trm) @ V)) => ((Xa = (none @ trm)) => ((Y2 = (none @ fml)) => (~ ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst864323244qo_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ ((some @ trm) @ V)) @ (none @ trm))))))))))))))))))).
% 2.96/1.54 thf(fact_249_Timeso_Opelims, axiom, (! [X4:(option @ trm),Xa:(option @ trm),Y2:(option @ trm)]: (((((uSubst277968634Timeso @ X4) @ Xa) = Y2) => ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst1377811071so_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ X4) @ Xa)) => ((! [Theta:trm]: (((X4 = ((some @ trm) @ Theta)) => (! [Eta:trm]: (((Xa = ((some @ trm) @ Eta)) => ((Y2 = ((some @ trm) @ ((times @ Theta) @ Eta))) => (~ ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst1377811071so_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ ((some @ trm) @ Theta)) @ ((some @ trm) @ Eta)))))))))))) => (((X4 = (none @ trm)) => ((Y2 = (none @ trm)) => (~ ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst1377811071so_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ (none @ trm)) @ Xa)))))) => (~ ((! [V:trm]: (((X4 = ((some @ trm) @ V)) => ((Xa = (none @ trm)) => ((Y2 = (none @ trm)) => (~ ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst1377811071so_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ ((some @ trm) @ V)) @ (none @ trm))))))))))))))))))).
% 2.96/1.54 thf(fact_250_Pluso_Opelims, axiom, (! [X4:(option @ trm),Xa:(option @ trm),Y2:(option @ trm)]: (((((uSubst1112714340_Pluso @ X4) @ Xa) = Y2) => ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst270600597so_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ X4) @ Xa)) => ((! [Theta:trm]: (((X4 = ((some @ trm) @ Theta)) => (! [Eta:trm]: (((Xa = ((some @ trm) @ Eta)) => ((Y2 = ((some @ trm) @ ((plus @ Theta) @ Eta))) => (~ ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst270600597so_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ ((some @ trm) @ Theta)) @ ((some @ trm) @ Eta)))))))))))) => (((X4 = (none @ trm)) => ((Y2 = (none @ trm)) => (~ ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst270600597so_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ (none @ trm)) @ Xa)))))) => (~ ((! [V:trm]: (((X4 = ((some @ trm) @ V)) => ((Xa = (none @ trm)) => ((Y2 = (none @ trm)) => (~ ((((accp @ ((product_prod @ (option @ trm)) @ (option @ trm))) @ uSubst270600597so_rel) @ ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ ((some @ trm) @ V)) @ (none @ trm))))))))))))))))))).
% 2.96/1.54 thf(fact_251_dot__def, axiom, (uSubst_Mirabelle_dot = (const @ ((((((((char2 @ $false) @ $true) @ $true) @ $true) @ $false) @ $true) @ $false) @ $false)))).
% 2.96/1.54 thf(fact_252_usubstappf__pred, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),P4:char,R2:fml,U2:(set @ variable),Theta2:trm,Sigma_theta:trm]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P3:(char > (option @ fml)),Uw:(char > (option @ game))]: (P3))))))))) @ Sigma2) @ P4) = ((some @ fml) @ R2)) => (((((inf_inf @ (set @ variable)) @ (static_FVF @ R2)) @ U2) = (bot_bot @ (set @ variable))) => (((((uSubst95898992stappt @ Sigma2) @ U2) @ Theta2) = ((some @ trm) @ Sigma_theta)) => ((((uSubst95898978stappf @ Sigma2) @ U2) @ ((pred @ P4) @ Theta2)) = (((uSubst95898978stappf @ (uSubst969145931substt @ Sigma_theta)) @ (bot_bot @ (set @ variable))) @ R2)))))))).
% 2.96/1.54 thf(fact_253_fml_Oinject_I1_J, axiom, (! [X11:char,X122:trm,Y11:char,Y12:trm]: (((((pred @ X11) @ X122) = ((pred @ Y11) @ Y12)) = ((X11 = Y11) & (X122 = Y12)))))).
% 2.96/1.54 thf(fact_254_usubstappf__pred2, axiom, (! [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),P4:char,R2:fml,U2:(set @ variable),Theta2:trm]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P3:(char > (option @ fml)),Uw:(char > (option @ game))]: (P3))))))))) @ Sigma2) @ P4) = ((some @ fml) @ R2)) => (((((inf_inf @ (set @ variable)) @ (static_FVF @ R2)) @ U2) != (bot_bot @ (set @ variable))) => ((((uSubst95898978stappf @ Sigma2) @ U2) @ ((pred @ P4) @ Theta2)) = (none @ fml))))))).
% 2.96/1.54 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, (bounded_lattice @ $o)).
% 2.96/1.54 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A8:$tType]: ((bounded_lattice @ (set @ A8))))).
% 2.96/1.54 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounded_lattice @ (A8 > A9)))))).
% 2.96/1.54 thf(tcon_fun___Lattices_Obounded__lattice__bot, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounded_lattice_bot @ (A8 > A9)))))).
% 2.96/1.54 thf(tcon_fun___Lattices_Osemilattice__inf, axiom, (! [A8:$tType,A9:$tType]: (((semilattice_inf @ A9) => (semilattice_inf @ (A8 > A9)))))).
% 2.96/1.54 thf(tcon_fun___Lattices_Olattice, axiom, (! [A8:$tType,A9:$tType]: (((lattice @ A9) => (lattice @ (A8 > A9)))))).
% 2.96/1.54 thf(tcon_fun___Orderings_Obot, axiom, (! [A8:$tType,A9:$tType]: (((bot @ A9) => (bot @ (A8 > A9)))))).
% 2.96/1.54 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_3, axiom, (! [A8:$tType]: ((bounded_lattice_bot @ (set @ A8))))).
% 2.96/1.54 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_4, axiom, (! [A8:$tType]: ((semilattice_inf @ (set @ A8))))).
% 2.96/1.54 thf(tcon_Set_Oset___Lattices_Olattice_5, axiom, (! [A8:$tType]: ((lattice @ (set @ A8))))).
% 2.96/1.54 thf(tcon_Set_Oset___Orderings_Obot_6, axiom, (! [A8:$tType]: ((bot @ (set @ A8))))).
% 2.96/1.54 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_7, axiom, (bounded_lattice_bot @ $o)).
% 2.96/1.54 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_8, axiom, (semilattice_inf @ $o)).
% 2.96/1.54 thf(tcon_HOL_Obool___Lattices_Olattice_9, axiom, (lattice @ $o)).
% 2.96/1.54 thf(tcon_HOL_Obool___Orderings_Obot_10, axiom, (bot @ $o)).
% 2.96/1.54 thf(tcon_Real_Oreal___Lattices_Osemilattice__inf_11, axiom, (semilattice_inf @ real)).
% 2.96/1.54 thf(tcon_Real_Oreal___Lattices_Olattice_12, axiom, (lattice @ real)).
% 2.96/1.54 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.96/1.54 thf(help_If_2_1_T, axiom, (! [A:$tType,X4:A,Y2:A]: ((((((if @ A) @ $false) @ X4) @ Y2) = Y2)))).
% 2.96/1.54 thf(help_If_1_1_T, axiom, (! [A:$tType,X4:A,Y2:A]: ((((((if @ A) @ $true) @ X4) @ Y2) = X4)))).
% 2.96/1.54 thf(conj_0, conjecture, ((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ sigma) @ f) = (none @ trm)) | ((((uSubst95898992stappt @ sigma) @ u) @ (const @ f)) = (((uSubst1138577137pconst @ sigma) @ v) @ f)))).
% 2.96/1.54 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.WzKSSIg5X4/DTF2DTF19715.p
% 2.96/1.54 ------------------------
% 2.96/1.58 ---- Cleaned THF ---
% 2.96/1.58 thf(ty_t_Denotational__Semantics_Ointerp,type,
% 2.96/1.58 denotational_interp: $tType ).
% 2.96/1.58
% 2.96/1.58 thf(ty_t_Product__Type_Oprod,type,
% 2.96/1.58 product_prod: $tType > $tType > $tType ).
% 2.96/1.58
% 2.96/1.58 thf(ty_t_Syntax_Ovariable,type,
% 2.96/1.58 variable: $tType ).
% 2.96/1.58
% 2.96/1.58 thf(ty_t_Option_Ooption,type,
% 2.96/1.58 option: $tType > $tType ).
% 2.96/1.58
% 2.96/1.58 thf(ty_t_Syntax_Ogame,type,
% 2.96/1.58 game: $tType ).
% 2.96/1.58
% 2.96/1.58 thf(ty_t_String_Ochar,type,
% 2.96/1.58 char: $tType ).
% 2.96/1.58
% 2.96/1.58 thf(ty_t_Syntax_Otrm,type,
% 2.96/1.58 trm: $tType ).
% 2.96/1.58
% 2.96/1.58 thf(ty_t_Syntax_Ofml,type,
% 2.96/1.58 fml: $tType ).
% 2.96/1.58
% 2.96/1.58 thf(ty_t_Real_Oreal,type,
% 2.96/1.58 real: $tType ).
% 2.96/1.58
% 2.96/1.58 thf(ty_t_Set_Oset,type,
% 2.96/1.58 set: $tType > $tType ).
% 2.96/1.58
% 2.96/1.58 thf(sy_cl_Lattices_Obounded__lattice,type,
% 2.96/1.58 bounded_lattice:
% 2.96/1.58 !>[A: $tType] : $o ).
% 2.96/1.58
% 2.96/1.58 thf(sy_cl_HOL_Otype,type,
% 2.96/1.58 type:
% 2.96/1.58 !>[A: $tType] : $o ).
% 2.96/1.58
% 2.96/1.58 thf(sy_cl_Orderings_Obot,type,
% 2.96/1.58 bot:
% 2.96/1.58 !>[A: $tType] : $o ).
% 2.96/1.58
% 2.96/1.58 thf(sy_cl_Lattices_Olattice,type,
% 2.96/1.58 lattice:
% 2.96/1.58 !>[A: $tType] : $o ).
% 2.96/1.58
% 2.96/1.58 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 2.96/1.58 semilattice_inf:
% 2.96/1.58 !>[A: $tType] : $o ).
% 2.96/1.58
% 2.96/1.58 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 2.96/1.58 bounded_lattice_bot:
% 2.96/1.58 !>[A: $tType] : $o ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_If,type,
% 2.96/1.58 if:
% 2.96/1.58 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 2.96/1.58 inf_inf:
% 2.96/1.58 !>[A: $tType] : ( A > A > A ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Option_Ocombine__options,type,
% 2.96/1.58 combine_options:
% 2.96/1.58 !>[A: $tType] : ( ( A > A > A ) > ( option @ A ) > ( option @ A ) > ( option @ A ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Option_Ooption_ONone,type,
% 2.96/1.58 none:
% 2.96/1.58 !>[A: $tType] : ( option @ A ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Option_Ooption_OSome,type,
% 2.96/1.58 some:
% 2.96/1.58 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Option_Ooption_Ocase__option,type,
% 2.96/1.58 case_option:
% 2.96/1.58 !>[B: $tType,A: $tType] : ( B > ( A > B ) > ( option @ A ) > B ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Option_Ooption_Othe,type,
% 2.96/1.58 the:
% 2.96/1.58 !>[A: $tType] : ( ( option @ A ) > A ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.96/1.58 bot_bot:
% 2.96/1.58 !>[A: $tType] : A ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Product__Type_OPair,type,
% 2.96/1.58 product_Pair:
% 2.96/1.58 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 2.96/1.58 produc2004651681e_prod:
% 2.96/1.58 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 2.96/1.58 product_rec_prod:
% 2.96/1.58 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Product__Type_Oprod_Ocase__prod,type,
% 2.96/1.58 product_case_prod:
% 2.96/1.58 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Set_OCollect,type,
% 2.96/1.58 collect:
% 2.96/1.58 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Set_Ois__empty,type,
% 2.96/1.58 is_empty:
% 2.96/1.58 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Static__Semantics_OFVF,type,
% 2.96/1.58 static_FVF: fml > ( set @ variable ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Static__Semantics_OFVT,type,
% 2.96/1.58 static_FVT: trm > ( set @ variable ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_String_Ochar_OChar,type,
% 2.96/1.58 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Syntax_Ofml_OGeq,type,
% 2.96/1.58 geq: trm > trm > fml ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Syntax_Ofml_OPred,type,
% 2.96/1.58 pred: char > trm > fml ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Syntax_Otrm_OConst,type,
% 2.96/1.58 const: char > trm ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Syntax_Otrm_ODifferential,type,
% 2.96/1.58 differential: trm > trm ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Syntax_Otrm_OFunc,type,
% 2.96/1.58 func: char > trm > trm ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Syntax_Otrm_ONumber,type,
% 2.96/1.58 number: real > trm ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Syntax_Otrm_OPlus,type,
% 2.96/1.58 plus: trm > trm > trm ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Syntax_Otrm_OTimes,type,
% 2.96/1.58 times: trm > trm > trm ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Syntax_Otrm_OVar,type,
% 2.96/1.58 var: variable > trm ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_ODifferentialo,type,
% 2.96/1.58 uSubst259074819ntialo: ( option @ trm ) > ( option @ trm ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OGeqo,type,
% 2.96/1.58 uSubst1556497037e_Geqo: ( option @ trm ) > ( option @ trm ) > ( option @ fml ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OGeqo__rel,type,
% 2.96/1.58 uSubst864323244qo_rel: ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > $o ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OPluso,type,
% 2.96/1.58 uSubst1112714340_Pluso: ( option @ trm ) > ( option @ trm ) > ( option @ trm ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OPluso__rel,type,
% 2.96/1.58 uSubst270600597so_rel: ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > $o ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTimeso,type,
% 2.96/1.58 uSubst277968634Timeso: ( option @ trm ) > ( option @ trm ) > ( option @ trm ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTimeso__rel,type,
% 2.96/1.58 uSubst1377811071so_rel: ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) > $o ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Odot,type,
% 2.96/1.58 uSubst_Mirabelle_dot: trm ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Odotsubstt,type,
% 2.96/1.58 uSubst969145931substt: trm > ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousappconst,type,
% 2.96/1.58 uSubst1138577137pconst: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > char > ( option @ trm ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappf,type,
% 2.96/1.58 uSubst95898978stappf: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > fml > ( option @ fml ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappt,type,
% 2.96/1.58 uSubst95898992stappt: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > trm > ( option @ trm ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappt__rel,type,
% 2.96/1.58 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 ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_Wellfounded_Oaccp,type,
% 2.96/1.58 accp:
% 2.96/1.58 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_c_member,type,
% 2.96/1.58 member:
% 2.96/1.58 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_v_U,type,
% 2.96/1.58 u: set @ variable ).
% 2.96/1.58
% 2.96/1.58 thf(sy_v_V,type,
% 2.96/1.58 v: set @ variable ).
% 2.96/1.58
% 2.96/1.58 thf(sy_v__092_060sigma_062,type,
% 2.96/1.58 sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(sy_v_f____,type,
% 2.96/1.58 f: char ).
% 2.96/1.58
% 2.96/1.58 thf(fact_0_f2,axiom,
% 2.96/1.58 ! [Z: option @ trm,F: trm > ( option @ trm ),Za: option @ trm] :
% 2.96/1.58 ( ( ( Za
% 2.96/1.58 = ( none @ trm ) )
% 2.96/1.58 => ( ( case_option @ ( option @ trm ) @ trm @ Z @ F @ Za )
% 2.96/1.58 = Z ) )
% 2.96/1.58 & ( ( Za
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 => ( ( case_option @ ( option @ trm ) @ trm @ Z @ F @ Za )
% 2.96/1.58 = ( F @ ( the @ trm @ Za ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_1_Const_Oprems_I1_J,axiom,
% 2.96/1.58 ( ( uSubst95898992stappt @ sigma @ u @ ( const @ f ) )
% 2.96/1.58 != ( none @ trm ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_2_Const_Oprems_I2_J,axiom,
% 2.96/1.58 ( ( uSubst95898992stappt @ sigma @ v @ ( const @ f ) )
% 2.96/1.58 != ( none @ trm ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_3_f3,axiom,
% 2.96/1.58 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ f )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 => ( ( inf_inf @ ( set @ variable )
% 2.96/1.58 @ ( static_FVT
% 2.96/1.58 @ ( the @ trm
% 2.96/1.58 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ f ) ) )
% 2.96/1.58 @ u )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_4__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062,axiom,
% 2.96/1.58 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ f )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 => ( ( inf_inf @ ( set @ variable )
% 2.96/1.58 @ ( static_FVT
% 2.96/1.58 @ ( the @ trm
% 2.96/1.58 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ f ) ) )
% 2.96/1.58 @ v )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_5_usappconst__def,axiom,
% 2.96/1.58 ( uSubst1138577137pconst
% 2.96/1.58 = ( ^ [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F2: char] :
% 2.96/1.58 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( const @ F2 ) )
% 2.96/1.58 @ ^ [R: trm] :
% 2.96/1.58 ( if @ ( option @ trm )
% 2.96/1.58 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R ) @ U )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 @ ( some @ trm @ R )
% 2.96/1.58 @ ( none @ trm ) )
% 2.96/1.58 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ Sigma
% 2.96/1.58 @ F2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_6_f1,axiom,
% 2.96/1.58 ( ( uSubst95898992stappt @ sigma @ u @ ( const @ f ) )
% 2.96/1.58 = ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( const @ f ) )
% 2.96/1.58 @ ^ [T2: trm] :
% 2.96/1.58 ( if @ ( option @ trm )
% 2.96/1.58 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ T2 ) @ u )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 @ ( some @ trm @ T2 )
% 2.96/1.58 @ ( none @ trm ) )
% 2.96/1.58 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ f ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_7_usubstappt_Osimps_I3_J,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,F3: char] :
% 2.96/1.58 ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( const @ F3 ) )
% 2.96/1.58 = ( uSubst1138577137pconst @ Sigma2 @ U2 @ F3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_8_undeft__None,axiom,
% 2.96/1.58 ( ( none @ trm )
% 2.96/1.58 = ( none @ trm ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_9__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AV_Af_092_060close_062,axiom,
% 2.96/1.58 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ f )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 => ( ( ( ( inf_inf @ ( set @ variable )
% 2.96/1.58 @ ( static_FVT
% 2.96/1.58 @ ( the @ trm
% 2.96/1.58 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ f ) ) )
% 2.96/1.58 @ v )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 => ( ( some @ trm
% 2.96/1.58 @ ( the @ trm
% 2.96/1.58 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ f ) ) )
% 2.96/1.58 = ( uSubst1138577137pconst @ sigma @ v @ f ) ) )
% 2.96/1.58 & ( ( ( inf_inf @ ( set @ variable )
% 2.96/1.58 @ ( static_FVT
% 2.96/1.58 @ ( the @ trm
% 2.96/1.58 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ f ) ) )
% 2.96/1.58 @ v )
% 2.96/1.58 != ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 => ( ( none @ trm )
% 2.96/1.58 = ( uSubst1138577137pconst @ sigma @ v @ f ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_10__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AU_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AU_Af_092_060close_062,axiom,
% 2.96/1.58 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ f )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 => ( ( ( ( inf_inf @ ( set @ variable )
% 2.96/1.58 @ ( static_FVT
% 2.96/1.58 @ ( the @ trm
% 2.96/1.58 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ f ) ) )
% 2.96/1.58 @ u )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 => ( ( some @ trm
% 2.96/1.58 @ ( the @ trm
% 2.96/1.58 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ f ) ) )
% 2.96/1.58 = ( uSubst1138577137pconst @ sigma @ u @ f ) ) )
% 2.96/1.58 & ( ( ( inf_inf @ ( set @ variable )
% 2.96/1.58 @ ( static_FVT
% 2.96/1.58 @ ( the @ trm
% 2.96/1.58 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ f ) ) )
% 2.96/1.58 @ u )
% 2.96/1.58 != ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 => ( ( none @ trm )
% 2.96/1.58 = ( uSubst1138577137pconst @ sigma @ u @ f ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_11_trm_Oinject_I3_J,axiom,
% 2.96/1.58 ! [X3: char,Y3: char] :
% 2.96/1.58 ( ( ( const @ X3 )
% 2.96/1.58 = ( const @ Y3 ) )
% 2.96/1.58 = ( X3 = Y3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_12_case__prod__app,axiom,
% 2.96/1.58 ! [A: $tType,D: $tType,C: $tType,B: $tType] :
% 2.96/1.58 ( ( product_case_prod @ B @ C @ ( D > A ) )
% 2.96/1.58 = ( ^ [F2: B > C > D > A,X: product_prod @ B @ C,Y: D] :
% 2.96/1.58 ( product_case_prod @ B @ C @ A
% 2.96/1.58 @ ^ [L: B,R: C] : ( F2 @ L @ R @ Y )
% 2.96/1.58 @ X ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_13_usubstappt__const,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F3: char,R2: trm,U2: set @ variable] :
% 2.96/1.58 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ Sigma2
% 2.96/1.58 @ F3 )
% 2.96/1.58 = ( some @ trm @ R2 ) )
% 2.96/1.58 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U2 )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( const @ F3 ) )
% 2.96/1.58 = ( some @ trm @ R2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_14_usubstappt__const__conv,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,F3: char] :
% 2.96/1.58 ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( const @ F3 ) )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 => ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ Sigma2
% 2.96/1.58 @ F3 )
% 2.96/1.58 = ( none @ trm ) )
% 2.96/1.58 | ? [R3: trm] :
% 2.96/1.58 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ Sigma2
% 2.96/1.58 @ F3 )
% 2.96/1.58 = ( some @ trm @ R3 ) )
% 2.96/1.58 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R3 ) @ U2 )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_15_usappconst__simp,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F3: char,R2: trm,U2: set @ variable] :
% 2.96/1.58 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ Sigma2
% 2.96/1.58 @ F3 )
% 2.96/1.58 = ( some @ trm @ R2 ) )
% 2.96/1.58 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U2 )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 => ( ( uSubst1138577137pconst @ Sigma2 @ U2 @ F3 )
% 2.96/1.58 = ( some @ trm @ R2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_16_usappconst__conv,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,F3: char] :
% 2.96/1.58 ( ( ( uSubst1138577137pconst @ Sigma2 @ U2 @ F3 )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 => ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ Sigma2
% 2.96/1.58 @ F3 )
% 2.96/1.58 = ( none @ trm ) )
% 2.96/1.58 | ? [R3: trm] :
% 2.96/1.58 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.58 @ Sigma2
% 2.96/1.58 @ F3 )
% 2.96/1.58 = ( some @ trm @ R3 ) )
% 2.96/1.58 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R3 ) @ U2 )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_17_ODEo_Oinduct,axiom,
% 2.96/1.58 ! [P: char > ( option @ trm ) > $o,A0: char,A1: option @ trm] :
% 2.96/1.58 ( ! [X2: char,Theta: trm] : ( P @ X2 @ ( some @ trm @ Theta ) )
% 2.96/1.58 => ( ! [X2: char] : ( P @ X2 @ ( none @ trm ) )
% 2.96/1.58 => ( P @ A0 @ A1 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_18_undeft__equiv,axiom,
% 2.96/1.58 ! [Theta2: option @ trm] :
% 2.96/1.58 ( ( Theta2
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 = ( ? [T2: trm] :
% 2.96/1.58 ( Theta2
% 2.96/1.58 = ( some @ trm @ T2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_19_Timeso_Oinduct,axiom,
% 2.96/1.58 ! [P: ( option @ trm ) > ( option @ trm ) > $o,A0: option @ trm,A1: option @ trm] :
% 2.96/1.58 ( ! [Theta: trm,Eta: trm] : ( P @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta ) )
% 2.96/1.58 => ( ! [X_1: option @ trm] : ( P @ ( none @ trm ) @ X_1 )
% 2.96/1.58 => ( ! [V: trm] : ( P @ ( some @ trm @ V ) @ ( none @ trm ) )
% 2.96/1.58 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_20_Assigno_Oinduct,axiom,
% 2.96/1.58 ! [P: variable > ( option @ trm ) > $o,A0: variable,A1: option @ trm] :
% 2.96/1.58 ( ! [X2: variable,Theta: trm] : ( P @ X2 @ ( some @ trm @ Theta ) )
% 2.96/1.58 => ( ! [X2: variable] : ( P @ X2 @ ( none @ trm ) )
% 2.96/1.58 => ( P @ A0 @ A1 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_21_Aterm__Some,axiom,
% 2.96/1.58 ( ( some @ trm )
% 2.96/1.58 = ( some @ trm ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_22_Differentialo_Oinduct,axiom,
% 2.96/1.58 ! [P: ( option @ trm ) > $o,A0: option @ trm] :
% 2.96/1.58 ( ! [Theta: trm] : ( P @ ( some @ trm @ Theta ) )
% 2.96/1.58 => ( ( P @ ( none @ trm ) )
% 2.96/1.58 => ( P @ A0 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_23_Differentialo_Ocases,axiom,
% 2.96/1.58 ! [X4: option @ trm] :
% 2.96/1.58 ( ! [Theta: trm] :
% 2.96/1.58 ( X4
% 2.96/1.58 != ( some @ trm @ Theta ) )
% 2.96/1.58 => ( X4
% 2.96/1.58 = ( none @ trm ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_24_option_Ocollapse,axiom,
% 2.96/1.58 ! [A: $tType,Option: option @ A] :
% 2.96/1.58 ( ( Option
% 2.96/1.58 != ( none @ A ) )
% 2.96/1.58 => ( ( some @ A @ ( the @ A @ Option ) )
% 2.96/1.58 = Option ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_25_not__Some__eq,axiom,
% 2.96/1.58 ! [A: $tType,X4: option @ A] :
% 2.96/1.58 ( ( ! [Y: A] :
% 2.96/1.58 ( X4
% 2.96/1.58 != ( some @ A @ Y ) ) )
% 2.96/1.58 = ( X4
% 2.96/1.58 = ( none @ A ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_26_not__None__eq,axiom,
% 2.96/1.58 ! [A: $tType,X4: option @ A] :
% 2.96/1.58 ( ( X4
% 2.96/1.58 != ( none @ A ) )
% 2.96/1.58 = ( ? [Y: A] :
% 2.96/1.58 ( X4
% 2.96/1.58 = ( some @ A @ Y ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_27_inf__bot__left,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( bounded_lattice_bot @ A )
% 2.96/1.58 => ! [X4: A] :
% 2.96/1.58 ( ( inf_inf @ A @ ( bot_bot @ A ) @ X4 )
% 2.96/1.58 = ( bot_bot @ A ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_28_inf__bot__right,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( bounded_lattice_bot @ A )
% 2.96/1.58 => ! [X4: A] :
% 2.96/1.58 ( ( inf_inf @ A @ X4 @ ( bot_bot @ A ) )
% 2.96/1.58 = ( bot_bot @ A ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_29_usubstappt__func2,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F3: char,R2: trm,U2: set @ variable,Theta2: trm] :
% 2.96/1.58 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F4: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 2.96/1.58 @ Sigma2
% 2.96/1.58 @ F3 )
% 2.96/1.58 = ( some @ trm @ R2 ) )
% 2.96/1.58 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U2 )
% 2.96/1.58 != ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 2.96/1.58 = ( none @ trm ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_30_option_Osplit__sel__asm,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 2.96/1.58 ( ( P @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 2.96/1.58 = ( ~ ( ( ( Option
% 2.96/1.58 = ( none @ A ) )
% 2.96/1.58 & ~ ( P @ F1 ) )
% 2.96/1.58 | ( ( Option
% 2.96/1.58 = ( some @ A @ ( the @ A @ Option ) ) )
% 2.96/1.58 & ~ ( P @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_31_option_Osplit__sel,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 2.96/1.58 ( ( P @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 2.96/1.58 = ( ( ( Option
% 2.96/1.58 = ( none @ A ) )
% 2.96/1.58 => ( P @ F1 ) )
% 2.96/1.58 & ( ( Option
% 2.96/1.58 = ( some @ A @ ( the @ A @ Option ) ) )
% 2.96/1.58 => ( P @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_32_usubstappt__func__conv,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,F3: char,Theta2: trm] :
% 2.96/1.58 ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 => ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 & ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F4: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 2.96/1.58 @ Sigma2
% 2.96/1.58 @ F3 )
% 2.96/1.58 = ( none @ trm ) )
% 2.96/1.58 | ? [R3: trm] :
% 2.96/1.58 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F4: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 2.96/1.58 @ Sigma2
% 2.96/1.58 @ F3 )
% 2.96/1.58 = ( some @ trm @ R3 ) )
% 2.96/1.58 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R3 ) @ U2 )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_33_option_Ocase__eq__if,axiom,
% 2.96/1.58 ! [A: $tType,B: $tType] :
% 2.96/1.58 ( ( case_option @ B @ A )
% 2.96/1.58 = ( ^ [F12: B,F23: A > B,Option2: option @ A] :
% 2.96/1.58 ( if @ B
% 2.96/1.58 @ ( Option2
% 2.96/1.58 = ( none @ A ) )
% 2.96/1.58 @ F12
% 2.96/1.58 @ ( F23 @ ( the @ A @ Option2 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_34_inf__right__idem,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [X4: A,Y2: A] :
% 2.96/1.58 ( ( inf_inf @ A @ ( inf_inf @ A @ X4 @ Y2 ) @ Y2 )
% 2.96/1.58 = ( inf_inf @ A @ X4 @ Y2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_35_inf_Oright__idem,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A2: A,B2: A] :
% 2.96/1.58 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 )
% 2.96/1.58 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_36_inf__left__idem,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [X4: A,Y2: A] :
% 2.96/1.58 ( ( inf_inf @ A @ X4 @ ( inf_inf @ A @ X4 @ Y2 ) )
% 2.96/1.58 = ( inf_inf @ A @ X4 @ Y2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_37_inf_Oleft__idem,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A2: A,B2: A] :
% 2.96/1.58 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B2 ) )
% 2.96/1.58 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_38_inf__idem,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [X4: A] :
% 2.96/1.58 ( ( inf_inf @ A @ X4 @ X4 )
% 2.96/1.58 = X4 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_39_inf_Oidem,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A2: A] :
% 2.96/1.58 ( ( inf_inf @ A @ A2 @ A2 )
% 2.96/1.58 = A2 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_40_inf__apply,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ B )
% 2.96/1.58 => ( ( inf_inf @ ( A > B ) )
% 2.96/1.58 = ( ^ [F2: A > B,G: A > B,X: A] : ( inf_inf @ B @ ( F2 @ X ) @ ( G @ X ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_41_option_Oinject,axiom,
% 2.96/1.58 ! [A: $tType,X22: A,Y22: A] :
% 2.96/1.58 ( ( ( some @ A @ X22 )
% 2.96/1.58 = ( some @ A @ Y22 ) )
% 2.96/1.58 = ( X22 = Y22 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_42_trm_Oinject_I4_J,axiom,
% 2.96/1.58 ! [X41: char,X42: trm,Y41: char,Y42: trm] :
% 2.96/1.58 ( ( ( func @ X41 @ X42 )
% 2.96/1.58 = ( func @ Y41 @ Y42 ) )
% 2.96/1.58 = ( ( X41 = Y41 )
% 2.96/1.58 & ( X42 = Y42 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_43_option_Odisc__eq__case_I2_J,axiom,
% 2.96/1.58 ! [A: $tType,Option: option @ A] :
% 2.96/1.58 ( ( Option
% 2.96/1.58 != ( none @ A ) )
% 2.96/1.58 = ( case_option @ $o @ A @ $false
% 2.96/1.58 @ ^ [Uu: A] : $true
% 2.96/1.58 @ Option ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_44_option_Odisc__eq__case_I1_J,axiom,
% 2.96/1.58 ! [A: $tType,Option: option @ A] :
% 2.96/1.58 ( ( Option
% 2.96/1.58 = ( none @ A ) )
% 2.96/1.58 = ( case_option @ $o @ A @ $true
% 2.96/1.58 @ ^ [Uu: A] : $false
% 2.96/1.58 @ Option ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_45_mem__Collect__eq,axiom,
% 2.96/1.58 ! [A: $tType,A2: A,P: A > $o] :
% 2.96/1.58 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.96/1.58 = ( P @ A2 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_46_Collect__mem__eq,axiom,
% 2.96/1.58 ! [A: $tType,A3: set @ A] :
% 2.96/1.58 ( ( collect @ A
% 2.96/1.58 @ ^ [X: A] : ( member @ A @ X @ A3 ) )
% 2.96/1.58 = A3 ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_47_Collect__cong,axiom,
% 2.96/1.58 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.96/1.58 ( ! [X2: A] :
% 2.96/1.58 ( ( P @ X2 )
% 2.96/1.58 = ( Q @ X2 ) )
% 2.96/1.58 => ( ( collect @ A @ P )
% 2.96/1.58 = ( collect @ A @ Q ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_48_ext,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType,F3: A > B,G2: A > B] :
% 2.96/1.58 ( ! [X2: A] :
% 2.96/1.58 ( ( F3 @ X2 )
% 2.96/1.58 = ( G2 @ X2 ) )
% 2.96/1.58 => ( F3 = G2 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_49_trm_Odistinct_I23_J,axiom,
% 2.96/1.58 ! [X3: char,X41: char,X42: trm] :
% 2.96/1.58 ( ( const @ X3 )
% 2.96/1.58 != ( func @ X41 @ X42 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_50_case__optionE,axiom,
% 2.96/1.58 ! [A: $tType,P: $o,Q: A > $o,X4: option @ A] :
% 2.96/1.58 ( ( case_option @ $o @ A @ P @ Q @ X4 )
% 2.96/1.58 => ( ( ( X4
% 2.96/1.58 = ( none @ A ) )
% 2.96/1.58 => ~ P )
% 2.96/1.58 => ~ ! [Y4: A] :
% 2.96/1.58 ( ( X4
% 2.96/1.58 = ( some @ A @ Y4 ) )
% 2.96/1.58 => ~ ( Q @ Y4 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_51_inf__left__commute,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [X4: A,Y2: A,Z2: A] :
% 2.96/1.58 ( ( inf_inf @ A @ X4 @ ( inf_inf @ A @ Y2 @ Z2 ) )
% 2.96/1.58 = ( inf_inf @ A @ Y2 @ ( inf_inf @ A @ X4 @ Z2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_52_inf_Oleft__commute,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [B2: A,A2: A,C2: A] :
% 2.96/1.58 ( ( inf_inf @ A @ B2 @ ( inf_inf @ A @ A2 @ C2 ) )
% 2.96/1.58 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_53_inf__commute,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ( ( inf_inf @ A )
% 2.96/1.58 = ( ^ [X: A,Y: A] : ( inf_inf @ A @ Y @ X ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_54_inf_Ocommute,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ( ( inf_inf @ A )
% 2.96/1.58 = ( ^ [A4: A,B3: A] : ( inf_inf @ A @ B3 @ A4 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_55_inf__assoc,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [X4: A,Y2: A,Z2: A] :
% 2.96/1.58 ( ( inf_inf @ A @ ( inf_inf @ A @ X4 @ Y2 ) @ Z2 )
% 2.96/1.58 = ( inf_inf @ A @ X4 @ ( inf_inf @ A @ Y2 @ Z2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_56_inf_Oassoc,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A2: A,B2: A,C2: A] :
% 2.96/1.58 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C2 )
% 2.96/1.58 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_57_boolean__algebra__cancel_Oinf2,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [B4: A,K: A,B2: A,A2: A] :
% 2.96/1.58 ( ( B4
% 2.96/1.58 = ( inf_inf @ A @ K @ B2 ) )
% 2.96/1.58 => ( ( inf_inf @ A @ A2 @ B4 )
% 2.96/1.58 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_58_boolean__algebra__cancel_Oinf1,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A3: A,K: A,A2: A,B2: A] :
% 2.96/1.58 ( ( A3
% 2.96/1.58 = ( inf_inf @ A @ K @ A2 ) )
% 2.96/1.58 => ( ( inf_inf @ A @ A3 @ B2 )
% 2.96/1.58 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_59_inf__fun__def,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ B )
% 2.96/1.58 => ( ( inf_inf @ ( A > B ) )
% 2.96/1.58 = ( ^ [F2: A > B,G: A > B,X: A] : ( inf_inf @ B @ ( F2 @ X ) @ ( G @ X ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_60_inf__sup__aci_I1_J,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( lattice @ A )
% 2.96/1.58 => ( ( inf_inf @ A )
% 2.96/1.58 = ( ^ [X: A,Y: A] : ( inf_inf @ A @ Y @ X ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_61_inf__sup__aci_I2_J,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( lattice @ A )
% 2.96/1.58 => ! [X4: A,Y2: A,Z2: A] :
% 2.96/1.58 ( ( inf_inf @ A @ ( inf_inf @ A @ X4 @ Y2 ) @ Z2 )
% 2.96/1.58 = ( inf_inf @ A @ X4 @ ( inf_inf @ A @ Y2 @ Z2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_62_inf__sup__aci_I3_J,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( lattice @ A )
% 2.96/1.58 => ! [X4: A,Y2: A,Z2: A] :
% 2.96/1.58 ( ( inf_inf @ A @ X4 @ ( inf_inf @ A @ Y2 @ Z2 ) )
% 2.96/1.58 = ( inf_inf @ A @ Y2 @ ( inf_inf @ A @ X4 @ Z2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_63_inf__sup__aci_I4_J,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( lattice @ A )
% 2.96/1.58 => ! [X4: A,Y2: A] :
% 2.96/1.58 ( ( inf_inf @ A @ X4 @ ( inf_inf @ A @ X4 @ Y2 ) )
% 2.96/1.58 = ( inf_inf @ A @ X4 @ Y2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_64_option_Ocase__distrib,axiom,
% 2.96/1.58 ! [C: $tType,B: $tType,A: $tType,H: B > C,F1: B,F22: A > B,Option: option @ A] :
% 2.96/1.58 ( ( H @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 2.96/1.58 = ( case_option @ C @ A @ ( H @ F1 )
% 2.96/1.58 @ ^ [X: A] : ( H @ ( F22 @ X ) )
% 2.96/1.58 @ Option ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_65_option_Odistinct_I1_J,axiom,
% 2.96/1.58 ! [A: $tType,X22: A] :
% 2.96/1.58 ( ( none @ A )
% 2.96/1.58 != ( some @ A @ X22 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_66_option_OdiscI,axiom,
% 2.96/1.58 ! [A: $tType,Option: option @ A,X22: A] :
% 2.96/1.58 ( ( Option
% 2.96/1.58 = ( some @ A @ X22 ) )
% 2.96/1.58 => ( Option
% 2.96/1.58 != ( none @ A ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_67_option_Oexhaust,axiom,
% 2.96/1.58 ! [A: $tType,Y2: option @ A] :
% 2.96/1.58 ( ( Y2
% 2.96/1.58 != ( none @ A ) )
% 2.96/1.58 => ~ ! [X23: A] :
% 2.96/1.58 ( Y2
% 2.96/1.58 != ( some @ A @ X23 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_68_option_Oinducts,axiom,
% 2.96/1.58 ! [A: $tType,P: ( option @ A ) > $o,Option: option @ A] :
% 2.96/1.58 ( ( P @ ( none @ A ) )
% 2.96/1.58 => ( ! [X2: A] : ( P @ ( some @ A @ X2 ) )
% 2.96/1.58 => ( P @ Option ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_69_split__option__ex,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( ^ [P2: ( option @ A ) > $o] :
% 2.96/1.58 ? [X5: option @ A] : ( P2 @ X5 ) )
% 2.96/1.58 = ( ^ [P3: ( option @ A ) > $o] :
% 2.96/1.58 ( ( P3 @ ( none @ A ) )
% 2.96/1.58 | ? [X: A] : ( P3 @ ( some @ A @ X ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_70_split__option__all,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( ^ [P2: ( option @ A ) > $o] :
% 2.96/1.58 ! [X5: option @ A] : ( P2 @ X5 ) )
% 2.96/1.58 = ( ^ [P3: ( option @ A ) > $o] :
% 2.96/1.58 ( ( P3 @ ( none @ A ) )
% 2.96/1.58 & ! [X: A] : ( P3 @ ( some @ A @ X ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_71_combine__options__cases,axiom,
% 2.96/1.58 ! [A: $tType,B: $tType,X4: option @ A,P: ( option @ A ) > ( option @ B ) > $o,Y2: option @ B] :
% 2.96/1.58 ( ( ( X4
% 2.96/1.58 = ( none @ A ) )
% 2.96/1.58 => ( P @ X4 @ Y2 ) )
% 2.96/1.58 => ( ( ( Y2
% 2.96/1.58 = ( none @ B ) )
% 2.96/1.58 => ( P @ X4 @ Y2 ) )
% 2.96/1.58 => ( ! [A5: A,B5: B] :
% 2.96/1.58 ( ( X4
% 2.96/1.58 = ( some @ A @ A5 ) )
% 2.96/1.58 => ( ( Y2
% 2.96/1.58 = ( some @ B @ B5 ) )
% 2.96/1.58 => ( P @ X4 @ Y2 ) ) )
% 2.96/1.58 => ( P @ X4 @ Y2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_72_option_Osimps_I4_J,axiom,
% 2.96/1.58 ! [A: $tType,B: $tType,F1: B,F22: A > B] :
% 2.96/1.58 ( ( case_option @ B @ A @ F1 @ F22 @ ( none @ A ) )
% 2.96/1.58 = F1 ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_73_option_Osimps_I5_J,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType,F1: B,F22: A > B,X22: A] :
% 2.96/1.58 ( ( case_option @ B @ A @ F1 @ F22 @ ( some @ A @ X22 ) )
% 2.96/1.58 = ( F22 @ X22 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_74_option_Oexpand,axiom,
% 2.96/1.58 ! [A: $tType,Option: option @ A,Option3: option @ A] :
% 2.96/1.58 ( ( ( Option
% 2.96/1.58 = ( none @ A ) )
% 2.96/1.58 = ( Option3
% 2.96/1.58 = ( none @ A ) ) )
% 2.96/1.58 => ( ( ( Option
% 2.96/1.58 != ( none @ A ) )
% 2.96/1.58 => ( ( Option3
% 2.96/1.58 != ( none @ A ) )
% 2.96/1.58 => ( ( the @ A @ Option )
% 2.96/1.58 = ( the @ A @ Option3 ) ) ) )
% 2.96/1.58 => ( Option = Option3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_75_option_Osel,axiom,
% 2.96/1.58 ! [A: $tType,X22: A] :
% 2.96/1.58 ( ( the @ A @ ( some @ A @ X22 ) )
% 2.96/1.58 = X22 ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_76_option_Oexhaust__sel,axiom,
% 2.96/1.58 ! [A: $tType,Option: option @ A] :
% 2.96/1.58 ( ( Option
% 2.96/1.58 != ( none @ A ) )
% 2.96/1.58 => ( Option
% 2.96/1.58 = ( some @ A @ ( the @ A @ Option ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_77_usubstappt__func,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F3: char,R2: trm,U2: set @ variable,Theta2: trm,Sigma_theta: trm] :
% 2.96/1.58 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F4: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 2.96/1.58 @ Sigma2
% 2.96/1.58 @ F3 )
% 2.96/1.58 = ( some @ trm @ R2 ) )
% 2.96/1.58 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U2 )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 => ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 )
% 2.96/1.58 = ( some @ trm @ Sigma_theta ) )
% 2.96/1.58 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 2.96/1.58 = ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta ) @ ( bot_bot @ ( set @ variable ) ) @ R2 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_78_usubstappt_Osimps_I4_J,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,F3: char,Theta2: trm] :
% 2.96/1.58 ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 2.96/1.58 = ( case_option @ ( option @ trm ) @ trm @ ( none @ trm )
% 2.96/1.58 @ ^ [Sigma_theta2: trm] :
% 2.96/1.58 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( func @ F3 @ Sigma_theta2 ) )
% 2.96/1.58 @ ^ [R: trm] :
% 2.96/1.58 ( if @ ( option @ trm )
% 2.96/1.58 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R ) @ U2 )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 @ ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta2 ) @ ( bot_bot @ ( set @ variable ) ) @ R )
% 2.96/1.58 @ ( none @ trm ) )
% 2.96/1.58 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F4: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 2.96/1.58 @ Sigma2
% 2.96/1.58 @ F3 ) )
% 2.96/1.58 @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_79_Int__iff,axiom,
% 2.96/1.58 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 2.96/1.58 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 2.96/1.58 = ( ( member @ A @ C2 @ A3 )
% 2.96/1.58 & ( member @ A @ C2 @ B4 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_80_IntI,axiom,
% 2.96/1.58 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 2.96/1.58 ( ( member @ A @ C2 @ A3 )
% 2.96/1.58 => ( ( member @ A @ C2 @ B4 )
% 2.96/1.58 => ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_81_empty__Collect__eq,axiom,
% 2.96/1.58 ! [A: $tType,P: A > $o] :
% 2.96/1.58 ( ( ( bot_bot @ ( set @ A ) )
% 2.96/1.58 = ( collect @ A @ P ) )
% 2.96/1.58 = ( ! [X: A] :
% 2.96/1.58 ~ ( P @ X ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_82_Collect__empty__eq,axiom,
% 2.96/1.58 ! [A: $tType,P: A > $o] :
% 2.96/1.58 ( ( ( collect @ A @ P )
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) )
% 2.96/1.58 = ( ! [X: A] :
% 2.96/1.58 ~ ( P @ X ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_83_all__not__in__conv,axiom,
% 2.96/1.58 ! [A: $tType,A3: set @ A] :
% 2.96/1.58 ( ( ! [X: A] :
% 2.96/1.58 ~ ( member @ A @ X @ A3 ) )
% 2.96/1.58 = ( A3
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_84_empty__iff,axiom,
% 2.96/1.58 ! [A: $tType,C2: A] :
% 2.96/1.58 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_85_bot__apply,axiom,
% 2.96/1.58 ! [C: $tType,D: $tType] :
% 2.96/1.58 ( ( bot @ C )
% 2.96/1.58 => ( ( bot_bot @ ( D > C ) )
% 2.96/1.58 = ( ^ [X: D] : ( bot_bot @ C ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_86_bot__fun__def,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType] :
% 2.96/1.58 ( ( bot @ B )
% 2.96/1.58 => ( ( bot_bot @ ( A > B ) )
% 2.96/1.58 = ( ^ [X: A] : ( bot_bot @ B ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_87_emptyE,axiom,
% 2.96/1.58 ! [A: $tType,A2: A] :
% 2.96/1.58 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_88_equals0D,axiom,
% 2.96/1.58 ! [A: $tType,A3: set @ A,A2: A] :
% 2.96/1.58 ( ( A3
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) )
% 2.96/1.58 => ~ ( member @ A @ A2 @ A3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_89_equals0I,axiom,
% 2.96/1.58 ! [A: $tType,A3: set @ A] :
% 2.96/1.58 ( ! [Y4: A] :
% 2.96/1.58 ~ ( member @ A @ Y4 @ A3 )
% 2.96/1.58 => ( A3
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_90_ex__in__conv,axiom,
% 2.96/1.58 ! [A: $tType,A3: set @ A] :
% 2.96/1.58 ( ( ? [X: A] : ( member @ A @ X @ A3 ) )
% 2.96/1.58 = ( A3
% 2.96/1.58 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_91_bot__set__def,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( bot_bot @ ( set @ A ) )
% 2.96/1.58 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_92_IntE,axiom,
% 2.96/1.58 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 2.96/1.58 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 2.96/1.58 => ~ ( ( member @ A @ C2 @ A3 )
% 2.96/1.58 => ~ ( member @ A @ C2 @ B4 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_93_IntD1,axiom,
% 2.96/1.58 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 2.96/1.58 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 2.96/1.58 => ( member @ A @ C2 @ A3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_94_IntD2,axiom,
% 2.96/1.58 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 2.96/1.58 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 2.96/1.58 => ( member @ A @ C2 @ B4 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_95_Int__assoc,axiom,
% 2.96/1.58 ! [A: $tType,A3: set @ A,B4: set @ A,C3: set @ A] :
% 2.96/1.58 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) @ C3 )
% 2.96/1.58 = ( inf_inf @ ( set @ A ) @ A3 @ ( inf_inf @ ( set @ A ) @ B4 @ C3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_96_Int__absorb,axiom,
% 2.96/1.58 ! [A: $tType,A3: set @ A] :
% 2.96/1.58 ( ( inf_inf @ ( set @ A ) @ A3 @ A3 )
% 2.96/1.58 = A3 ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_97_Int__commute,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( inf_inf @ ( set @ A ) )
% 2.96/1.58 = ( ^ [A6: set @ A,B6: set @ A] : ( inf_inf @ ( set @ A ) @ B6 @ A6 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_98_Int__left__absorb,axiom,
% 2.96/1.58 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.96/1.58 ( ( inf_inf @ ( set @ A ) @ A3 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 2.96/1.58 = ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_99_Int__left__commute,axiom,
% 2.96/1.58 ! [A: $tType,A3: set @ A,B4: set @ A,C3: set @ A] :
% 2.96/1.58 ( ( inf_inf @ ( set @ A ) @ A3 @ ( inf_inf @ ( set @ A ) @ B4 @ C3 ) )
% 2.96/1.58 = ( inf_inf @ ( set @ A ) @ B4 @ ( inf_inf @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_100_empty__def,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( bot_bot @ ( set @ A ) )
% 2.96/1.58 = ( collect @ A
% 2.96/1.58 @ ^ [X: A] : $false ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_101_Collect__conj__eq,axiom,
% 2.96/1.58 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.96/1.58 ( ( collect @ A
% 2.96/1.58 @ ^ [X: A] :
% 2.96/1.58 ( ( P @ X )
% 2.96/1.58 & ( Q @ X ) ) )
% 2.96/1.58 = ( inf_inf @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_102_Int__Collect,axiom,
% 2.96/1.58 ! [A: $tType,X4: A,A3: set @ A,P: A > $o] :
% 2.96/1.58 ( ( member @ A @ X4 @ ( inf_inf @ ( set @ A ) @ A3 @ ( collect @ A @ P ) ) )
% 2.96/1.58 = ( ( member @ A @ X4 @ A3 )
% 2.96/1.58 & ( P @ X4 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_103_Int__def,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( inf_inf @ ( set @ A ) )
% 2.96/1.58 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.96/1.58 ( collect @ A
% 2.96/1.58 @ ^ [X: A] :
% 2.96/1.58 ( ( member @ A @ X @ A6 )
% 2.96/1.58 & ( member @ A @ X @ B6 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_104_inf__set__def,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( inf_inf @ ( set @ A ) )
% 2.96/1.58 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.96/1.58 ( collect @ A
% 2.96/1.58 @ ( inf_inf @ ( A > $o )
% 2.96/1.58 @ ^ [X: A] : ( member @ A @ X @ A6 )
% 2.96/1.58 @ ^ [X: A] : ( member @ A @ X @ B6 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_105_Int__emptyI,axiom,
% 2.96/1.58 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.96/1.58 ( ! [X2: A] :
% 2.96/1.58 ( ( member @ A @ X2 @ A3 )
% 2.96/1.58 => ~ ( member @ A @ X2 @ B4 ) )
% 2.96/1.58 => ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_106_disjoint__iff,axiom,
% 2.96/1.58 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.96/1.58 ( ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) )
% 2.96/1.58 = ( ! [X: A] :
% 2.96/1.58 ( ( member @ A @ X @ A3 )
% 2.96/1.58 => ~ ( member @ A @ X @ B4 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_107_Int__empty__left,axiom,
% 2.96/1.58 ! [A: $tType,B4: set @ A] :
% 2.96/1.58 ( ( inf_inf @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B4 )
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_108_Int__empty__right,axiom,
% 2.96/1.58 ! [A: $tType,A3: set @ A] :
% 2.96/1.58 ( ( inf_inf @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_109_disjoint__iff__not__equal,axiom,
% 2.96/1.58 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.96/1.58 ( ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) )
% 2.96/1.58 = ( ! [X: A] :
% 2.96/1.58 ( ( member @ A @ X @ A3 )
% 2.96/1.58 => ! [Y: A] :
% 2.96/1.58 ( ( member @ A @ Y @ B4 )
% 2.96/1.58 => ( X != Y ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_110_disjE__realizer2,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType,P: $o,Q: A > $o,X4: option @ A,R4: B > $o,F3: B,G2: A > B] :
% 2.96/1.58 ( ( case_option @ $o @ A @ P @ Q @ X4 )
% 2.96/1.58 => ( ( P
% 2.96/1.58 => ( R4 @ F3 ) )
% 2.96/1.58 => ( ! [Q2: A] :
% 2.96/1.58 ( ( Q @ Q2 )
% 2.96/1.58 => ( R4 @ ( G2 @ Q2 ) ) )
% 2.96/1.58 => ( R4 @ ( case_option @ B @ A @ F3 @ G2 @ X4 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_111_Set_Ois__empty__def,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( is_empty @ A )
% 2.96/1.58 = ( ^ [A6: set @ A] :
% 2.96/1.58 ( A6
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_112_prod_Ocase__distrib,axiom,
% 2.96/1.58 ! [C: $tType,D: $tType,B: $tType,A: $tType,H: C > D,F3: A > B > C,Prod: product_prod @ A @ B] :
% 2.96/1.58 ( ( H @ ( product_case_prod @ A @ B @ C @ F3 @ Prod ) )
% 2.96/1.58 = ( product_case_prod @ A @ B @ D
% 2.96/1.58 @ ^ [X1: A,X24: B] : ( H @ ( F3 @ X1 @ X24 ) )
% 2.96/1.58 @ Prod ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_113_inf__Int__eq,axiom,
% 2.96/1.58 ! [A: $tType,R4: set @ A,S: set @ A] :
% 2.96/1.58 ( ( inf_inf @ ( A > $o )
% 2.96/1.58 @ ^ [X: A] : ( member @ A @ X @ R4 )
% 2.96/1.58 @ ^ [X: A] : ( member @ A @ X @ S ) )
% 2.96/1.58 = ( ^ [X: A] : ( member @ A @ X @ ( inf_inf @ ( set @ A ) @ R4 @ S ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_114_Timeso_Osimps_I3_J,axiom,
% 2.96/1.58 ! [V2: trm] :
% 2.96/1.58 ( ( uSubst277968634Timeso @ ( some @ trm @ V2 ) @ ( none @ trm ) )
% 2.96/1.58 = ( none @ trm ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_115_Pluso_Osimps_I3_J,axiom,
% 2.96/1.58 ! [V2: trm] :
% 2.96/1.58 ( ( uSubst1112714340_Pluso @ ( some @ trm @ V2 ) @ ( none @ trm ) )
% 2.96/1.58 = ( none @ trm ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_116_inf1I,axiom,
% 2.96/1.58 ! [A: $tType,A3: A > $o,X4: A,B4: A > $o] :
% 2.96/1.58 ( ( A3 @ X4 )
% 2.96/1.58 => ( ( B4 @ X4 )
% 2.96/1.58 => ( inf_inf @ ( A > $o ) @ A3 @ B4 @ X4 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_117_inf1E,axiom,
% 2.96/1.58 ! [A: $tType,A3: A > $o,B4: A > $o,X4: A] :
% 2.96/1.58 ( ( inf_inf @ ( A > $o ) @ A3 @ B4 @ X4 )
% 2.96/1.58 => ~ ( ( A3 @ X4 )
% 2.96/1.58 => ~ ( B4 @ X4 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_118_inf1D1,axiom,
% 2.96/1.58 ! [A: $tType,A3: A > $o,B4: A > $o,X4: A] :
% 2.96/1.58 ( ( inf_inf @ ( A > $o ) @ A3 @ B4 @ X4 )
% 2.96/1.58 => ( A3 @ X4 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_119_inf1D2,axiom,
% 2.96/1.58 ! [A: $tType,A3: A > $o,B4: A > $o,X4: A] :
% 2.96/1.58 ( ( inf_inf @ ( A > $o ) @ A3 @ B4 @ X4 )
% 2.96/1.58 => ( B4 @ X4 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_120_Pluso_Osimps_I2_J,axiom,
% 2.96/1.58 ! [Eta2: option @ trm] :
% 2.96/1.58 ( ( uSubst1112714340_Pluso @ ( none @ trm ) @ Eta2 )
% 2.96/1.58 = ( none @ trm ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_121_Timeso_Osimps_I2_J,axiom,
% 2.96/1.58 ! [Eta2: option @ trm] :
% 2.96/1.58 ( ( uSubst277968634Timeso @ ( none @ trm ) @ Eta2 )
% 2.96/1.58 = ( none @ trm ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_122_Pluso__undef,axiom,
% 2.96/1.58 ! [Theta2: option @ trm,Eta2: option @ trm] :
% 2.96/1.58 ( ( ( uSubst1112714340_Pluso @ Theta2 @ Eta2 )
% 2.96/1.58 = ( none @ trm ) )
% 2.96/1.58 = ( ( Theta2
% 2.96/1.58 = ( none @ trm ) )
% 2.96/1.58 | ( Eta2
% 2.96/1.58 = ( none @ trm ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_123_Timeso__undef,axiom,
% 2.96/1.58 ! [Theta2: option @ trm,Eta2: option @ trm] :
% 2.96/1.58 ( ( ( uSubst277968634Timeso @ Theta2 @ Eta2 )
% 2.96/1.58 = ( none @ trm ) )
% 2.96/1.58 = ( ( Theta2
% 2.96/1.58 = ( none @ trm ) )
% 2.96/1.58 | ( Eta2
% 2.96/1.58 = ( none @ trm ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_124_bot__empty__eq,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( bot_bot @ ( A > $o ) )
% 2.96/1.58 = ( ^ [X: A] : ( member @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_125_Collect__empty__eq__bot,axiom,
% 2.96/1.58 ! [A: $tType,P: A > $o] :
% 2.96/1.58 ( ( ( collect @ A @ P )
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) )
% 2.96/1.58 = ( P
% 2.96/1.58 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_126_internal__case__prod__def,axiom,
% 2.96/1.58 ! [C: $tType,B: $tType,A: $tType] :
% 2.96/1.58 ( ( produc2004651681e_prod @ A @ B @ C )
% 2.96/1.58 = ( product_case_prod @ A @ B @ C ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_127_Pluso_Oelims,axiom,
% 2.96/1.58 ! [X4: option @ trm,Xa: option @ trm,Y2: option @ trm] :
% 2.96/1.58 ( ( ( uSubst1112714340_Pluso @ X4 @ Xa )
% 2.96/1.58 = Y2 )
% 2.96/1.58 => ( ! [Theta: trm] :
% 2.96/1.58 ( ( X4
% 2.96/1.58 = ( some @ trm @ Theta ) )
% 2.96/1.58 => ! [Eta: trm] :
% 2.96/1.58 ( ( Xa
% 2.96/1.58 = ( some @ trm @ Eta ) )
% 2.96/1.58 => ( Y2
% 2.96/1.58 != ( some @ trm @ ( plus @ Theta @ Eta ) ) ) ) )
% 2.96/1.58 => ( ( ( X4
% 2.96/1.58 = ( none @ trm ) )
% 2.96/1.58 => ( Y2
% 2.96/1.58 != ( none @ trm ) ) )
% 2.96/1.58 => ~ ( ? [V: trm] :
% 2.96/1.58 ( X4
% 2.96/1.58 = ( some @ trm @ V ) )
% 2.96/1.58 => ( ( Xa
% 2.96/1.58 = ( none @ trm ) )
% 2.96/1.58 => ( Y2
% 2.96/1.58 != ( none @ trm ) ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_128_Timeso_Oelims,axiom,
% 2.96/1.58 ! [X4: option @ trm,Xa: option @ trm,Y2: option @ trm] :
% 2.96/1.58 ( ( ( uSubst277968634Timeso @ X4 @ Xa )
% 2.96/1.58 = Y2 )
% 2.96/1.58 => ( ! [Theta: trm] :
% 2.96/1.58 ( ( X4
% 2.96/1.58 = ( some @ trm @ Theta ) )
% 2.96/1.58 => ! [Eta: trm] :
% 2.96/1.58 ( ( Xa
% 2.96/1.58 = ( some @ trm @ Eta ) )
% 2.96/1.58 => ( Y2
% 2.96/1.58 != ( some @ trm @ ( times @ Theta @ Eta ) ) ) ) )
% 2.96/1.58 => ( ( ( X4
% 2.96/1.58 = ( none @ trm ) )
% 2.96/1.58 => ( Y2
% 2.96/1.58 != ( none @ trm ) ) )
% 2.96/1.58 => ~ ( ? [V: trm] :
% 2.96/1.58 ( X4
% 2.96/1.58 = ( some @ trm @ V ) )
% 2.96/1.58 => ( ( Xa
% 2.96/1.58 = ( none @ trm ) )
% 2.96/1.58 => ( Y2
% 2.96/1.58 != ( none @ trm ) ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_129_trm_Oinject_I5_J,axiom,
% 2.96/1.58 ! [X51: trm,X52: trm,Y51: trm,Y52: trm] :
% 2.96/1.58 ( ( ( plus @ X51 @ X52 )
% 2.96/1.58 = ( plus @ Y51 @ Y52 ) )
% 2.96/1.58 = ( ( X51 = Y51 )
% 2.96/1.58 & ( X52 = Y52 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_130_trm_Oinject_I6_J,axiom,
% 2.96/1.58 ! [X61: trm,X62: trm,Y61: trm,Y62: trm] :
% 2.96/1.58 ( ( ( times @ X61 @ X62 )
% 2.96/1.58 = ( times @ Y61 @ Y62 ) )
% 2.96/1.58 = ( ( X61 = Y61 )
% 2.96/1.58 & ( X62 = Y62 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_131_trm_Odistinct_I37_J,axiom,
% 2.96/1.58 ! [X51: trm,X52: trm,X61: trm,X62: trm] :
% 2.96/1.58 ( ( plus @ X51 @ X52 )
% 2.96/1.58 != ( times @ X61 @ X62 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_132_trm_Odistinct_I25_J,axiom,
% 2.96/1.58 ! [X3: char,X51: trm,X52: trm] :
% 2.96/1.58 ( ( const @ X3 )
% 2.96/1.58 != ( plus @ X51 @ X52 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_133_trm_Odistinct_I27_J,axiom,
% 2.96/1.58 ! [X3: char,X61: trm,X62: trm] :
% 2.96/1.58 ( ( const @ X3 )
% 2.96/1.58 != ( times @ X61 @ X62 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_134_trm_Odistinct_I31_J,axiom,
% 2.96/1.58 ! [X41: char,X42: trm,X51: trm,X52: trm] :
% 2.96/1.58 ( ( func @ X41 @ X42 )
% 2.96/1.58 != ( plus @ X51 @ X52 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_135_trm_Odistinct_I33_J,axiom,
% 2.96/1.58 ! [X41: char,X42: trm,X61: trm,X62: trm] :
% 2.96/1.58 ( ( func @ X41 @ X42 )
% 2.96/1.58 != ( times @ X61 @ X62 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_136_usubstappt__times__conv,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 2.96/1.58 ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( times @ Theta2 @ Eta2 ) )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 => ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 & ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 )
% 2.96/1.58 != ( none @ trm ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_137_usubstappt__plus__conv,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 2.96/1.58 ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( plus @ Theta2 @ Eta2 ) )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 => ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 & ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 )
% 2.96/1.58 != ( none @ trm ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_138_Timeso_Osimps_I1_J,axiom,
% 2.96/1.58 ! [Theta2: trm,Eta2: trm] :
% 2.96/1.58 ( ( uSubst277968634Timeso @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta2 ) )
% 2.96/1.58 = ( some @ trm @ ( times @ Theta2 @ Eta2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_139_Pluso_Osimps_I1_J,axiom,
% 2.96/1.58 ! [Theta2: trm,Eta2: trm] :
% 2.96/1.58 ( ( uSubst1112714340_Pluso @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta2 ) )
% 2.96/1.58 = ( some @ trm @ ( plus @ Theta2 @ Eta2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_140_usubstappt_Osimps_I6_J,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 2.96/1.58 ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( times @ Theta2 @ Eta2 ) )
% 2.96/1.58 = ( uSubst277968634Timeso @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_141_usubstappt_Osimps_I5_J,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 2.96/1.58 ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( plus @ Theta2 @ Eta2 ) )
% 2.96/1.58 = ( uSubst1112714340_Pluso @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_142_usubstappt_Oelims,axiom,
% 2.96/1.58 ! [X4: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),Xa: set @ variable,Xb: trm,Y2: option @ trm] :
% 2.96/1.58 ( ( ( uSubst95898992stappt @ X4 @ Xa @ Xb )
% 2.96/1.58 = Y2 )
% 2.96/1.58 => ( ! [X2: variable] :
% 2.96/1.58 ( ( Xb
% 2.96/1.58 = ( var @ X2 ) )
% 2.96/1.58 => ( Y2
% 2.96/1.58 != ( some @ trm @ ( var @ X2 ) ) ) )
% 2.96/1.58 => ( ! [R3: real] :
% 2.96/1.58 ( ( Xb
% 2.96/1.58 = ( number @ R3 ) )
% 2.96/1.58 => ( Y2
% 2.96/1.58 != ( some @ trm @ ( number @ R3 ) ) ) )
% 2.96/1.58 => ( ! [F5: char] :
% 2.96/1.58 ( ( Xb
% 2.96/1.58 = ( const @ F5 ) )
% 2.96/1.58 => ( Y2
% 2.96/1.58 != ( uSubst1138577137pconst @ X4 @ Xa @ F5 ) ) )
% 2.96/1.58 => ( ! [F5: char,Theta: trm] :
% 2.96/1.58 ( ( Xb
% 2.96/1.58 = ( func @ F5 @ Theta ) )
% 2.96/1.58 => ( Y2
% 2.96/1.58 != ( case_option @ ( option @ trm ) @ trm @ ( none @ trm )
% 2.96/1.58 @ ^ [Sigma_theta2: trm] :
% 2.96/1.58 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( func @ F5 @ Sigma_theta2 ) )
% 2.96/1.58 @ ^ [R: trm] :
% 2.96/1.58 ( if @ ( option @ trm )
% 2.96/1.58 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R ) @ Xa )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 @ ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta2 ) @ ( bot_bot @ ( set @ variable ) ) @ R )
% 2.96/1.58 @ ( none @ trm ) )
% 2.96/1.58 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F4: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 2.96/1.58 @ X4
% 2.96/1.58 @ F5 ) )
% 2.96/1.58 @ ( uSubst95898992stappt @ X4 @ Xa @ Theta ) ) ) )
% 2.96/1.58 => ( ! [Theta: trm,Eta: trm] :
% 2.96/1.58 ( ( Xb
% 2.96/1.58 = ( plus @ Theta @ Eta ) )
% 2.96/1.58 => ( Y2
% 2.96/1.58 != ( uSubst1112714340_Pluso @ ( uSubst95898992stappt @ X4 @ Xa @ Theta ) @ ( uSubst95898992stappt @ X4 @ Xa @ Eta ) ) ) )
% 2.96/1.58 => ( ! [Theta: trm,Eta: trm] :
% 2.96/1.58 ( ( Xb
% 2.96/1.58 = ( times @ Theta @ Eta ) )
% 2.96/1.58 => ( Y2
% 2.96/1.58 != ( uSubst277968634Timeso @ ( uSubst95898992stappt @ X4 @ Xa @ Theta ) @ ( uSubst95898992stappt @ X4 @ Xa @ Eta ) ) ) )
% 2.96/1.58 => ~ ! [Theta: trm] :
% 2.96/1.58 ( ( Xb
% 2.96/1.58 = ( differential @ Theta ) )
% 2.96/1.58 => ( Y2
% 2.96/1.58 != ( uSubst259074819ntialo
% 2.96/1.58 @ ( uSubst95898992stappt @ X4
% 2.96/1.58 @ ( collect @ variable
% 2.96/1.58 @ ^ [X: variable] : $true )
% 2.96/1.58 @ Theta ) ) ) ) ) ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_143_usubstappt__induct,axiom,
% 2.96/1.58 ! [P: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > trm > $o,A0: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),A1: set @ variable,A22: trm] :
% 2.96/1.58 ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,X2: variable] : ( P @ Sigma3 @ U3 @ ( var @ X2 ) )
% 2.96/1.58 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,R3: real] : ( P @ Sigma3 @ U3 @ ( number @ R3 ) )
% 2.96/1.58 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F5: char] : ( P @ Sigma3 @ U3 @ ( const @ F5 ) )
% 2.96/1.58 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F5: char,Theta: trm] :
% 2.96/1.58 ( ( P @ Sigma3 @ U3 @ Theta )
% 2.96/1.58 => ( ! [X25: trm] :
% 2.96/1.58 ( ( ( uSubst95898992stappt @ Sigma3 @ U3 @ Theta )
% 2.96/1.58 = ( some @ trm @ X25 ) )
% 2.96/1.58 => ! [X2a: trm] :
% 2.96/1.58 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F4: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 2.96/1.58 @ Sigma3
% 2.96/1.58 @ F5 )
% 2.96/1.58 = ( some @ trm @ X2a ) )
% 2.96/1.58 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ X2a ) @ U3 )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 => ( P @ ( uSubst969145931substt @ X25 ) @ ( bot_bot @ ( set @ variable ) ) @ X2a ) ) ) )
% 2.96/1.58 => ( P @ Sigma3 @ U3 @ ( func @ F5 @ Theta ) ) ) )
% 2.96/1.58 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta: trm] :
% 2.96/1.58 ( ( P @ Sigma3 @ U3 @ Theta )
% 2.96/1.58 => ! [Eta: trm] :
% 2.96/1.58 ( ( P @ Sigma3 @ U3 @ Eta )
% 2.96/1.58 => ( P @ Sigma3 @ U3 @ ( plus @ Theta @ Eta ) ) ) )
% 2.96/1.58 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta: trm] :
% 2.96/1.58 ( ( P @ Sigma3 @ U3 @ Theta )
% 2.96/1.58 => ! [Eta: trm] :
% 2.96/1.58 ( ( P @ Sigma3 @ U3 @ Eta )
% 2.96/1.58 => ( P @ Sigma3 @ U3 @ ( times @ Theta @ Eta ) ) ) )
% 2.96/1.58 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta: trm] :
% 2.96/1.58 ( ( P @ Sigma3
% 2.96/1.58 @ ( collect @ variable
% 2.96/1.58 @ ^ [X: variable] : $true )
% 2.96/1.58 @ Theta )
% 2.96/1.58 => ( P @ Sigma3 @ U3 @ ( differential @ Theta ) ) )
% 2.96/1.58 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_144_Geqo_Osimps_I3_J,axiom,
% 2.96/1.58 ! [V2: trm] :
% 2.96/1.58 ( ( uSubst1556497037e_Geqo @ ( some @ trm @ V2 ) @ ( none @ trm ) )
% 2.96/1.58 = ( none @ fml ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_145_combine__options__def,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( combine_options @ A )
% 2.96/1.58 = ( ^ [F2: A > A > A,X: option @ A,Y: option @ A] :
% 2.96/1.58 ( case_option @ ( option @ A ) @ A @ Y
% 2.96/1.58 @ ^ [Z3: A] :
% 2.96/1.58 ( case_option @ ( option @ A ) @ A @ ( some @ A @ Z3 )
% 2.96/1.58 @ ^ [Aa: A] : ( some @ A @ ( F2 @ Z3 @ Aa ) )
% 2.96/1.58 @ Y )
% 2.96/1.58 @ X ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_146_trm_Oinject_I2_J,axiom,
% 2.96/1.58 ! [X22: real,Y22: real] :
% 2.96/1.58 ( ( ( number @ X22 )
% 2.96/1.58 = ( number @ Y22 ) )
% 2.96/1.58 = ( X22 = Y22 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_147_trm_Oinject_I1_J,axiom,
% 2.96/1.58 ! [X12: variable,Y1: variable] :
% 2.96/1.58 ( ( ( var @ X12 )
% 2.96/1.58 = ( var @ Y1 ) )
% 2.96/1.58 = ( X12 = Y1 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_148_trm_Oinject_I7_J,axiom,
% 2.96/1.58 ! [X7: trm,Y7: trm] :
% 2.96/1.58 ( ( ( differential @ X7 )
% 2.96/1.58 = ( differential @ Y7 ) )
% 2.96/1.58 = ( X7 = Y7 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_149_combine__options__simps_I2_J,axiom,
% 2.96/1.58 ! [A: $tType,F3: A > A > A,X4: option @ A] :
% 2.96/1.58 ( ( combine_options @ A @ F3 @ X4 @ ( none @ A ) )
% 2.96/1.58 = X4 ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_150_combine__options__simps_I1_J,axiom,
% 2.96/1.58 ! [A: $tType,F3: A > A > A,Y2: option @ A] :
% 2.96/1.58 ( ( combine_options @ A @ F3 @ ( none @ A ) @ Y2 )
% 2.96/1.58 = Y2 ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_151_combine__options__simps_I3_J,axiom,
% 2.96/1.58 ! [A: $tType,F3: A > A > A,A2: A,B2: A] :
% 2.96/1.58 ( ( combine_options @ A @ F3 @ ( some @ A @ A2 ) @ ( some @ A @ B2 ) )
% 2.96/1.58 = ( some @ A @ ( F3 @ A2 @ B2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_152_Differentialo_Osimps_I1_J,axiom,
% 2.96/1.58 ! [Theta2: trm] :
% 2.96/1.58 ( ( uSubst259074819ntialo @ ( some @ trm @ Theta2 ) )
% 2.96/1.58 = ( some @ trm @ ( differential @ Theta2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_153_trm_Odistinct_I21_J,axiom,
% 2.96/1.58 ! [X22: real,X7: trm] :
% 2.96/1.58 ( ( number @ X22 )
% 2.96/1.58 != ( differential @ X7 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_154_trm_Odistinct_I11_J,axiom,
% 2.96/1.58 ! [X12: variable,X7: trm] :
% 2.96/1.58 ( ( var @ X12 )
% 2.96/1.58 != ( differential @ X7 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_155_trm_Odistinct_I1_J,axiom,
% 2.96/1.58 ! [X12: variable,X22: real] :
% 2.96/1.58 ( ( var @ X12 )
% 2.96/1.58 != ( number @ X22 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_156_combine__options__assoc,axiom,
% 2.96/1.58 ! [A: $tType,F3: A > A > A,X4: option @ A,Y2: option @ A,Z2: option @ A] :
% 2.96/1.58 ( ! [X2: A,Y4: A,Z4: A] :
% 2.96/1.58 ( ( F3 @ ( F3 @ X2 @ Y4 ) @ Z4 )
% 2.96/1.58 = ( F3 @ X2 @ ( F3 @ Y4 @ Z4 ) ) )
% 2.96/1.58 => ( ( combine_options @ A @ F3 @ ( combine_options @ A @ F3 @ X4 @ Y2 ) @ Z2 )
% 2.96/1.58 = ( combine_options @ A @ F3 @ X4 @ ( combine_options @ A @ F3 @ Y2 @ Z2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_157_combine__options__commute,axiom,
% 2.96/1.58 ! [A: $tType,F3: A > A > A,X4: option @ A,Y2: option @ A] :
% 2.96/1.58 ( ! [X2: A,Y4: A] :
% 2.96/1.58 ( ( F3 @ X2 @ Y4 )
% 2.96/1.58 = ( F3 @ Y4 @ X2 ) )
% 2.96/1.58 => ( ( combine_options @ A @ F3 @ X4 @ Y2 )
% 2.96/1.58 = ( combine_options @ A @ F3 @ Y2 @ X4 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_158_combine__options__left__commute,axiom,
% 2.96/1.58 ! [A: $tType,F3: A > A > A,Y2: option @ A,X4: option @ A,Z2: option @ A] :
% 2.96/1.58 ( ! [X2: A,Y4: A] :
% 2.96/1.58 ( ( F3 @ X2 @ Y4 )
% 2.96/1.58 = ( F3 @ Y4 @ X2 ) )
% 2.96/1.58 => ( ! [X2: A,Y4: A,Z4: A] :
% 2.96/1.58 ( ( F3 @ ( F3 @ X2 @ Y4 ) @ Z4 )
% 2.96/1.58 = ( F3 @ X2 @ ( F3 @ Y4 @ Z4 ) ) )
% 2.96/1.58 => ( ( combine_options @ A @ F3 @ Y2 @ ( combine_options @ A @ F3 @ X4 @ Z2 ) )
% 2.96/1.58 = ( combine_options @ A @ F3 @ X4 @ ( combine_options @ A @ F3 @ Y2 @ Z2 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_159_usubstappt_Osimps_I7_J,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm] :
% 2.96/1.58 ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( differential @ Theta2 ) )
% 2.96/1.58 = ( uSubst259074819ntialo
% 2.96/1.58 @ ( uSubst95898992stappt @ Sigma2
% 2.96/1.58 @ ( collect @ variable
% 2.96/1.58 @ ^ [X: variable] : $true )
% 2.96/1.58 @ Theta2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_160_trm_Odistinct_I13_J,axiom,
% 2.96/1.58 ! [X22: real,X3: char] :
% 2.96/1.58 ( ( number @ X22 )
% 2.96/1.58 != ( const @ X3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_161_trm_Odistinct_I15_J,axiom,
% 2.96/1.58 ! [X22: real,X41: char,X42: trm] :
% 2.96/1.58 ( ( number @ X22 )
% 2.96/1.58 != ( func @ X41 @ X42 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_162_trm_Odistinct_I19_J,axiom,
% 2.96/1.58 ! [X22: real,X61: trm,X62: trm] :
% 2.96/1.58 ( ( number @ X22 )
% 2.96/1.58 != ( times @ X61 @ X62 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_163_trm_Odistinct_I17_J,axiom,
% 2.96/1.58 ! [X22: real,X51: trm,X52: trm] :
% 2.96/1.58 ( ( number @ X22 )
% 2.96/1.58 != ( plus @ X51 @ X52 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_164_Differentialo_Oelims,axiom,
% 2.96/1.58 ! [X4: option @ trm,Y2: option @ trm] :
% 2.96/1.58 ( ( ( uSubst259074819ntialo @ X4 )
% 2.96/1.58 = Y2 )
% 2.96/1.58 => ( ! [Theta: trm] :
% 2.96/1.58 ( ( X4
% 2.96/1.58 = ( some @ trm @ Theta ) )
% 2.96/1.58 => ( Y2
% 2.96/1.58 != ( some @ trm @ ( differential @ Theta ) ) ) )
% 2.96/1.58 => ~ ( ( X4
% 2.96/1.58 = ( none @ trm ) )
% 2.96/1.58 => ( Y2
% 2.96/1.58 != ( none @ trm ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_165_trm_Odistinct_I3_J,axiom,
% 2.96/1.58 ! [X12: variable,X3: char] :
% 2.96/1.58 ( ( var @ X12 )
% 2.96/1.58 != ( const @ X3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_166_trm_Odistinct_I5_J,axiom,
% 2.96/1.58 ! [X12: variable,X41: char,X42: trm] :
% 2.96/1.58 ( ( var @ X12 )
% 2.96/1.58 != ( func @ X41 @ X42 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_167_trm_Odistinct_I9_J,axiom,
% 2.96/1.58 ! [X12: variable,X61: trm,X62: trm] :
% 2.96/1.58 ( ( var @ X12 )
% 2.96/1.58 != ( times @ X61 @ X62 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_168_trm_Odistinct_I7_J,axiom,
% 2.96/1.58 ! [X12: variable,X51: trm,X52: trm] :
% 2.96/1.58 ( ( var @ X12 )
% 2.96/1.58 != ( plus @ X51 @ X52 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_169_trm_Odistinct_I29_J,axiom,
% 2.96/1.58 ! [X3: char,X7: trm] :
% 2.96/1.58 ( ( const @ X3 )
% 2.96/1.58 != ( differential @ X7 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_170_trm_Odistinct_I35_J,axiom,
% 2.96/1.58 ! [X41: char,X42: trm,X7: trm] :
% 2.96/1.58 ( ( func @ X41 @ X42 )
% 2.96/1.58 != ( differential @ X7 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_171_trm_Odistinct_I41_J,axiom,
% 2.96/1.58 ! [X61: trm,X62: trm,X7: trm] :
% 2.96/1.58 ( ( times @ X61 @ X62 )
% 2.96/1.58 != ( differential @ X7 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_172_trm_Odistinct_I39_J,axiom,
% 2.96/1.58 ! [X51: trm,X52: trm,X7: trm] :
% 2.96/1.58 ( ( plus @ X51 @ X52 )
% 2.96/1.58 != ( differential @ X7 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_173_trm_Oexhaust,axiom,
% 2.96/1.58 ! [Y2: trm] :
% 2.96/1.58 ( ! [X13: variable] :
% 2.96/1.58 ( Y2
% 2.96/1.58 != ( var @ X13 ) )
% 2.96/1.58 => ( ! [X23: real] :
% 2.96/1.58 ( Y2
% 2.96/1.58 != ( number @ X23 ) )
% 2.96/1.58 => ( ! [X32: char] :
% 2.96/1.58 ( Y2
% 2.96/1.58 != ( const @ X32 ) )
% 2.96/1.58 => ( ! [X412: char,X422: trm] :
% 2.96/1.58 ( Y2
% 2.96/1.58 != ( func @ X412 @ X422 ) )
% 2.96/1.58 => ( ! [X512: trm,X522: trm] :
% 2.96/1.58 ( Y2
% 2.96/1.58 != ( plus @ X512 @ X522 ) )
% 2.96/1.58 => ( ! [X612: trm,X622: trm] :
% 2.96/1.58 ( Y2
% 2.96/1.58 != ( times @ X612 @ X622 ) )
% 2.96/1.58 => ~ ! [X72: trm] :
% 2.96/1.58 ( Y2
% 2.96/1.58 != ( differential @ X72 ) ) ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_174_trm_Oinduct,axiom,
% 2.96/1.58 ! [P: trm > $o,Trm: trm] :
% 2.96/1.58 ( ! [X2: variable] : ( P @ ( var @ X2 ) )
% 2.96/1.58 => ( ! [X2: real] : ( P @ ( number @ X2 ) )
% 2.96/1.58 => ( ! [X2: char] : ( P @ ( const @ X2 ) )
% 2.96/1.58 => ( ! [X1a: char,X2a2: trm] :
% 2.96/1.58 ( ( P @ X2a2 )
% 2.96/1.58 => ( P @ ( func @ X1a @ X2a2 ) ) )
% 2.96/1.58 => ( ! [X1a: trm,X2a2: trm] :
% 2.96/1.58 ( ( P @ X1a )
% 2.96/1.58 => ( ( P @ X2a2 )
% 2.96/1.58 => ( P @ ( plus @ X1a @ X2a2 ) ) ) )
% 2.96/1.58 => ( ! [X1a: trm,X2a2: trm] :
% 2.96/1.58 ( ( P @ X1a )
% 2.96/1.58 => ( ( P @ X2a2 )
% 2.96/1.58 => ( P @ ( times @ X1a @ X2a2 ) ) ) )
% 2.96/1.58 => ( ! [X2: trm] :
% 2.96/1.58 ( ( P @ X2 )
% 2.96/1.58 => ( P @ ( differential @ X2 ) ) )
% 2.96/1.58 => ( P @ Trm ) ) ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_175_Geqo_Osimps_I2_J,axiom,
% 2.96/1.58 ! [Eta2: option @ trm] :
% 2.96/1.58 ( ( uSubst1556497037e_Geqo @ ( none @ trm ) @ Eta2 )
% 2.96/1.58 = ( none @ fml ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_176_Geqo__undef,axiom,
% 2.96/1.58 ! [Theta2: option @ trm,Eta2: option @ trm] :
% 2.96/1.58 ( ( ( uSubst1556497037e_Geqo @ Theta2 @ Eta2 )
% 2.96/1.58 = ( none @ fml ) )
% 2.96/1.58 = ( ( Theta2
% 2.96/1.58 = ( none @ trm ) )
% 2.96/1.58 | ( Eta2
% 2.96/1.58 = ( none @ trm ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_177_Differentialo_Osimps_I2_J,axiom,
% 2.96/1.58 ( ( uSubst259074819ntialo @ ( none @ trm ) )
% 2.96/1.58 = ( none @ trm ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_178_Differentialo__undef,axiom,
% 2.96/1.58 ! [Theta2: option @ trm] :
% 2.96/1.58 ( ( ( uSubst259074819ntialo @ Theta2 )
% 2.96/1.58 = ( none @ trm ) )
% 2.96/1.58 = ( Theta2
% 2.96/1.58 = ( none @ trm ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_179_usubstappt_Osimps_I2_J,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,R2: real] :
% 2.96/1.58 ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( number @ R2 ) )
% 2.96/1.58 = ( some @ trm @ ( number @ R2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_180_usubstappt_Osimps_I1_J,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,X4: variable] :
% 2.96/1.58 ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( var @ X4 ) )
% 2.96/1.58 = ( some @ trm @ ( var @ X4 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_181_usubstappt__differential__conv,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm] :
% 2.96/1.58 ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( differential @ Theta2 ) )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 => ( ( uSubst95898992stappt @ Sigma2
% 2.96/1.58 @ ( collect @ variable
% 2.96/1.58 @ ^ [X: variable] : $true )
% 2.96/1.58 @ Theta2 )
% 2.96/1.58 != ( none @ trm ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_182_usubstappt_Opelims,axiom,
% 2.96/1.58 ! [X4: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),Xa: set @ variable,Xb: trm,Y2: option @ trm] :
% 2.96/1.58 ( ( ( uSubst95898992stappt @ X4 @ Xa @ Xb )
% 2.96/1.58 = Y2 )
% 2.96/1.58 => ( ( 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 ) @ X4 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ Xb ) ) )
% 2.96/1.58 => ( ! [X2: variable] :
% 2.96/1.58 ( ( Xb
% 2.96/1.58 = ( var @ X2 ) )
% 2.96/1.58 => ( ( Y2
% 2.96/1.58 = ( some @ trm @ ( var @ X2 ) ) )
% 2.96/1.58 => ~ ( 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 ) @ X4 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( var @ X2 ) ) ) ) ) )
% 2.96/1.58 => ( ! [R3: real] :
% 2.96/1.58 ( ( Xb
% 2.96/1.58 = ( number @ R3 ) )
% 2.96/1.58 => ( ( Y2
% 2.96/1.58 = ( some @ trm @ ( number @ R3 ) ) )
% 2.96/1.58 => ~ ( 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 ) @ X4 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( number @ R3 ) ) ) ) ) )
% 2.96/1.58 => ( ! [F5: char] :
% 2.96/1.58 ( ( Xb
% 2.96/1.58 = ( const @ F5 ) )
% 2.96/1.58 => ( ( Y2
% 2.96/1.58 = ( uSubst1138577137pconst @ X4 @ Xa @ F5 ) )
% 2.96/1.58 => ~ ( 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 ) @ X4 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( const @ F5 ) ) ) ) ) )
% 2.96/1.58 => ( ! [F5: char,Theta: trm] :
% 2.96/1.58 ( ( Xb
% 2.96/1.58 = ( func @ F5 @ Theta ) )
% 2.96/1.58 => ( ( Y2
% 2.96/1.58 = ( case_option @ ( option @ trm ) @ trm @ ( none @ trm )
% 2.96/1.58 @ ^ [Sigma_theta2: trm] :
% 2.96/1.58 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( func @ F5 @ Sigma_theta2 ) )
% 2.96/1.58 @ ^ [R: trm] :
% 2.96/1.58 ( if @ ( option @ trm )
% 2.96/1.58 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R ) @ Xa )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 @ ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta2 ) @ ( bot_bot @ ( set @ variable ) ) @ R )
% 2.96/1.58 @ ( none @ trm ) )
% 2.96/1.58 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [F4: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 2.96/1.58 @ X4
% 2.96/1.58 @ F5 ) )
% 2.96/1.58 @ ( uSubst95898992stappt @ X4 @ Xa @ Theta ) ) )
% 2.96/1.58 => ~ ( 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 ) @ X4 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( func @ F5 @ Theta ) ) ) ) ) )
% 2.96/1.58 => ( ! [Theta: trm,Eta: trm] :
% 2.96/1.58 ( ( Xb
% 2.96/1.58 = ( plus @ Theta @ Eta ) )
% 2.96/1.58 => ( ( Y2
% 2.96/1.58 = ( uSubst1112714340_Pluso @ ( uSubst95898992stappt @ X4 @ Xa @ Theta ) @ ( uSubst95898992stappt @ X4 @ Xa @ Eta ) ) )
% 2.96/1.58 => ~ ( 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 ) @ X4 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( plus @ Theta @ Eta ) ) ) ) ) )
% 2.96/1.58 => ( ! [Theta: trm,Eta: trm] :
% 2.96/1.58 ( ( Xb
% 2.96/1.58 = ( times @ Theta @ Eta ) )
% 2.96/1.58 => ( ( Y2
% 2.96/1.58 = ( uSubst277968634Timeso @ ( uSubst95898992stappt @ X4 @ Xa @ Theta ) @ ( uSubst95898992stappt @ X4 @ Xa @ Eta ) ) )
% 2.96/1.58 => ~ ( 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 ) @ X4 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( times @ Theta @ Eta ) ) ) ) ) )
% 2.96/1.58 => ~ ! [Theta: trm] :
% 2.96/1.58 ( ( Xb
% 2.96/1.58 = ( differential @ Theta ) )
% 2.96/1.58 => ( ( Y2
% 2.96/1.58 = ( uSubst259074819ntialo
% 2.96/1.58 @ ( uSubst95898992stappt @ X4
% 2.96/1.58 @ ( collect @ variable
% 2.96/1.58 @ ^ [X: variable] : $true )
% 2.96/1.58 @ Theta ) ) )
% 2.96/1.58 => ~ ( 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 ) @ X4 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( differential @ Theta ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_183_term__sem_Ocases,axiom,
% 2.96/1.58 ! [X4: product_prod @ denotational_interp @ trm] :
% 2.96/1.58 ( ! [I: denotational_interp,X2: variable] :
% 2.96/1.58 ( X4
% 2.96/1.58 != ( product_Pair @ denotational_interp @ trm @ I @ ( var @ X2 ) ) )
% 2.96/1.58 => ( ! [I: denotational_interp,R3: real] :
% 2.96/1.58 ( X4
% 2.96/1.58 != ( product_Pair @ denotational_interp @ trm @ I @ ( number @ R3 ) ) )
% 2.96/1.58 => ( ! [I: denotational_interp,F5: char] :
% 2.96/1.58 ( X4
% 2.96/1.58 != ( product_Pair @ denotational_interp @ trm @ I @ ( const @ F5 ) ) )
% 2.96/1.58 => ( ! [I: denotational_interp,F5: char,Theta: trm] :
% 2.96/1.58 ( X4
% 2.96/1.58 != ( product_Pair @ denotational_interp @ trm @ I @ ( func @ F5 @ Theta ) ) )
% 2.96/1.58 => ( ! [I: denotational_interp,Theta: trm,Eta: trm] :
% 2.96/1.58 ( X4
% 2.96/1.58 != ( product_Pair @ denotational_interp @ trm @ I @ ( plus @ Theta @ Eta ) ) )
% 2.96/1.58 => ( ! [I: denotational_interp,Theta: trm,Eta: trm] :
% 2.96/1.58 ( X4
% 2.96/1.58 != ( product_Pair @ denotational_interp @ trm @ I @ ( times @ Theta @ Eta ) ) )
% 2.96/1.58 => ~ ! [I: denotational_interp,Theta: trm] :
% 2.96/1.58 ( X4
% 2.96/1.58 != ( product_Pair @ denotational_interp @ trm @ I @ ( differential @ Theta ) ) ) ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_184_term__sem_Oinduct,axiom,
% 2.96/1.58 ! [P: denotational_interp > trm > $o,A0: denotational_interp,A1: trm] :
% 2.96/1.58 ( ! [I: denotational_interp,X2: variable] : ( P @ I @ ( var @ X2 ) )
% 2.96/1.58 => ( ! [I: denotational_interp,R3: real] : ( P @ I @ ( number @ R3 ) )
% 2.96/1.58 => ( ! [I: denotational_interp,F5: char] : ( P @ I @ ( const @ F5 ) )
% 2.96/1.58 => ( ! [I: denotational_interp,F5: char,Theta: trm] :
% 2.96/1.58 ( ( P @ I @ Theta )
% 2.96/1.58 => ( P @ I @ ( func @ F5 @ Theta ) ) )
% 2.96/1.58 => ( ! [I: denotational_interp,Theta: trm] :
% 2.96/1.58 ( ( P @ I @ Theta )
% 2.96/1.58 => ! [Eta: trm] :
% 2.96/1.58 ( ( P @ I @ Eta )
% 2.96/1.58 => ( P @ I @ ( plus @ Theta @ Eta ) ) ) )
% 2.96/1.58 => ( ! [I: denotational_interp,Theta: trm] :
% 2.96/1.58 ( ( P @ I @ Theta )
% 2.96/1.58 => ! [Eta: trm] :
% 2.96/1.58 ( ( P @ I @ Eta )
% 2.96/1.58 => ( P @ I @ ( times @ Theta @ Eta ) ) ) )
% 2.96/1.58 => ( ! [I: denotational_interp,Theta: trm] :
% 2.96/1.58 ( ( ? [Xa2: char] :
% 2.96/1.58 ( member @ char @ Xa2
% 2.96/1.58 @ ( collect @ char
% 2.96/1.58 @ ^ [Uu: char] : $true ) )
% 2.96/1.58 => ( P @ I @ Theta ) )
% 2.96/1.58 => ( P @ I @ ( differential @ Theta ) ) )
% 2.96/1.58 => ( P @ A0 @ A1 ) ) ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_185_old_Oprod_Oinject,axiom,
% 2.96/1.58 ! [A: $tType,B: $tType,A2: A,B2: B,A7: A,B7: B] :
% 2.96/1.58 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.96/1.58 = ( product_Pair @ A @ B @ A7 @ B7 ) )
% 2.96/1.58 = ( ( A2 = A7 )
% 2.96/1.58 & ( B2 = B7 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_186_prod_Oinject,axiom,
% 2.96/1.58 ! [A: $tType,B: $tType,X12: A,X22: B,Y1: A,Y22: B] :
% 2.96/1.58 ( ( ( product_Pair @ A @ B @ X12 @ X22 )
% 2.96/1.58 = ( product_Pair @ A @ B @ Y1 @ Y22 ) )
% 2.96/1.58 = ( ( X12 = Y1 )
% 2.96/1.58 & ( X22 = Y22 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_187_case__prodI,axiom,
% 2.96/1.58 ! [A: $tType,B: $tType,F3: A > B > $o,A2: A,B2: B] :
% 2.96/1.58 ( ( F3 @ A2 @ B2 )
% 2.96/1.58 => ( product_case_prod @ A @ B @ $o @ F3 @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_188_case__prodI2,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType,P4: product_prod @ A @ B,C2: A > B > $o] :
% 2.96/1.58 ( ! [A5: A,B5: B] :
% 2.96/1.58 ( ( P4
% 2.96/1.58 = ( product_Pair @ A @ B @ A5 @ B5 ) )
% 2.96/1.58 => ( C2 @ A5 @ B5 ) )
% 2.96/1.58 => ( product_case_prod @ A @ B @ $o @ C2 @ P4 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_189_case__prodI2_H,axiom,
% 2.96/1.58 ! [A: $tType,B: $tType,C: $tType,P4: product_prod @ A @ B,C2: A > B > C > $o,X4: C] :
% 2.96/1.58 ( ! [A5: A,B5: B] :
% 2.96/1.58 ( ( ( product_Pair @ A @ B @ A5 @ B5 )
% 2.96/1.58 = P4 )
% 2.96/1.58 => ( C2 @ A5 @ B5 @ X4 ) )
% 2.96/1.58 => ( product_case_prod @ A @ B @ ( C > $o ) @ C2 @ P4 @ X4 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_190_mem__case__prodI,axiom,
% 2.96/1.58 ! [A: $tType,B: $tType,C: $tType,Z2: A,C2: B > C > ( set @ A ),A2: B,B2: C] :
% 2.96/1.58 ( ( member @ A @ Z2 @ ( C2 @ A2 @ B2 ) )
% 2.96/1.58 => ( member @ A @ Z2 @ ( product_case_prod @ B @ C @ ( set @ A ) @ C2 @ ( product_Pair @ B @ C @ A2 @ B2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_191_mem__case__prodI2,axiom,
% 2.96/1.58 ! [C: $tType,B: $tType,A: $tType,P4: product_prod @ A @ B,Z2: C,C2: A > B > ( set @ C )] :
% 2.96/1.58 ( ! [A5: A,B5: B] :
% 2.96/1.58 ( ( P4
% 2.96/1.58 = ( product_Pair @ A @ B @ A5 @ B5 ) )
% 2.96/1.58 => ( member @ C @ Z2 @ ( C2 @ A5 @ B5 ) ) )
% 2.96/1.58 => ( member @ C @ Z2 @ ( product_case_prod @ A @ B @ ( set @ C ) @ C2 @ P4 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_192_case__prod__conv,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType,C: $tType,F3: B > C > A,A2: B,B2: C] :
% 2.96/1.58 ( ( product_case_prod @ B @ C @ A @ F3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 2.96/1.58 = ( F3 @ A2 @ B2 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_193_usubstappt_Opsimps_I7_J,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm] :
% 2.96/1.58 ( ( 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 ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U2 @ ( differential @ Theta2 ) ) ) )
% 2.96/1.58 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( differential @ Theta2 ) )
% 2.96/1.58 = ( uSubst259074819ntialo
% 2.96/1.58 @ ( uSubst95898992stappt @ Sigma2
% 2.96/1.58 @ ( collect @ variable
% 2.96/1.58 @ ^ [X: variable] : $true )
% 2.96/1.58 @ Theta2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_194_usubstappt_Opsimps_I1_J,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,X4: variable] :
% 2.96/1.58 ( ( 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 ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U2 @ ( var @ X4 ) ) ) )
% 2.96/1.58 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( var @ X4 ) )
% 2.96/1.58 = ( some @ trm @ ( var @ X4 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_195_usubstappt_Opsimps_I2_J,axiom,
% 2.96/1.58 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,R2: real] :
% 2.96/1.58 ( ( 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 ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U2 @ ( number @ R2 ) ) ) )
% 2.96/1.58 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( number @ R2 ) )
% 2.96/1.58 = ( some @ trm @ ( number @ R2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_196_cond__case__prod__eta,axiom,
% 2.96/1.58 ! [C: $tType,B: $tType,A: $tType,F3: A > B > C,G2: ( product_prod @ A @ B ) > C] :
% 2.96/1.58 ( ! [X2: A,Y4: B] :
% 2.96/1.58 ( ( F3 @ X2 @ Y4 )
% 2.96/1.58 = ( G2 @ ( product_Pair @ A @ B @ X2 @ Y4 ) ) )
% 2.96/1.58 => ( ( product_case_prod @ A @ B @ C @ F3 )
% 2.96/1.58 = G2 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_197_case__prod__eta,axiom,
% 2.96/1.58 ! [C: $tType,B: $tType,A: $tType,F3: ( product_prod @ A @ B ) > C] :
% 2.96/1.58 ( ( product_case_prod @ A @ B @ C
% 2.96/1.58 @ ^ [X: A,Y: B] : ( F3 @ ( product_Pair @ A @ B @ X @ Y ) ) )
% 2.96/1.58 = F3 ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_198_case__prodE2,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType,C: $tType,Q: A > $o,P: B > C > A,Z2: product_prod @ B @ C] :
% 2.96/1.58 ( ( Q @ ( product_case_prod @ B @ C @ A @ P @ Z2 ) )
% 2.96/1.58 => ~ ! [X2: B,Y4: C] :
% 2.96/1.58 ( ( Z2
% 2.96/1.58 = ( product_Pair @ B @ C @ X2 @ Y4 ) )
% 2.96/1.58 => ~ ( Q @ ( P @ X2 @ Y4 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_199_inf__Int__eq2,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType,R4: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 2.96/1.58 ( ( inf_inf @ ( A > B > $o )
% 2.96/1.58 @ ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ R4 )
% 2.96/1.58 @ ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ S ) )
% 2.96/1.58 = ( ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ ( inf_inf @ ( set @ ( product_prod @ A @ B ) ) @ R4 @ S ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_200_bot__empty__eq2,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType] :
% 2.96/1.58 ( ( bot_bot @ ( A > B > $o ) )
% 2.96/1.58 = ( ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ ( bot_bot @ ( set @ ( product_prod @ A @ B ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_201_case__prodD,axiom,
% 2.96/1.58 ! [A: $tType,B: $tType,F3: A > B > $o,A2: A,B2: B] :
% 2.96/1.58 ( ( product_case_prod @ A @ B @ $o @ F3 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 2.96/1.58 => ( F3 @ A2 @ B2 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_202_case__prodE,axiom,
% 2.96/1.58 ! [A: $tType,B: $tType,C2: A > B > $o,P4: product_prod @ A @ B] :
% 2.96/1.58 ( ( product_case_prod @ A @ B @ $o @ C2 @ P4 )
% 2.96/1.58 => ~ ! [X2: A,Y4: B] :
% 2.96/1.58 ( ( P4
% 2.96/1.58 = ( product_Pair @ A @ B @ X2 @ Y4 ) )
% 2.96/1.58 => ~ ( C2 @ X2 @ Y4 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_203_case__prodD_H,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType,C: $tType,R4: A > B > C > $o,A2: A,B2: B,C2: C] :
% 2.96/1.58 ( ( product_case_prod @ A @ B @ ( C > $o ) @ R4 @ ( product_Pair @ A @ B @ A2 @ B2 ) @ C2 )
% 2.96/1.58 => ( R4 @ A2 @ B2 @ C2 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_204_case__prodE_H,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType,C: $tType,C2: A > B > C > $o,P4: product_prod @ A @ B,Z2: C] :
% 2.96/1.58 ( ( product_case_prod @ A @ B @ ( C > $o ) @ C2 @ P4 @ Z2 )
% 2.96/1.58 => ~ ! [X2: A,Y4: B] :
% 2.96/1.58 ( ( P4
% 2.96/1.58 = ( product_Pair @ A @ B @ X2 @ Y4 ) )
% 2.96/1.58 => ~ ( C2 @ X2 @ Y4 @ Z2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_205_pred__equals__eq2,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType,R4: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 2.96/1.58 ( ( ( ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ R4 ) )
% 2.96/1.58 = ( ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ S ) ) )
% 2.96/1.58 = ( R4 = S ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_206_mem__case__prodE,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType,C: $tType,Z2: A,C2: B > C > ( set @ A ),P4: product_prod @ B @ C] :
% 2.96/1.58 ( ( member @ A @ Z2 @ ( product_case_prod @ B @ C @ ( set @ A ) @ C2 @ P4 ) )
% 2.96/1.58 => ~ ! [X2: B,Y4: C] :
% 2.96/1.58 ( ( P4
% 2.96/1.58 = ( product_Pair @ B @ C @ X2 @ Y4 ) )
% 2.96/1.59 => ~ ( member @ A @ Z2 @ ( C2 @ X2 @ Y4 ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_207_old_Oprod_Oinducts,axiom,
% 2.96/1.59 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 2.96/1.59 ( ! [A5: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B5 ) )
% 2.96/1.59 => ( P @ Prod ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_208_old_Oprod_Oexhaust,axiom,
% 2.96/1.59 ! [A: $tType,B: $tType,Y2: product_prod @ A @ B] :
% 2.96/1.59 ~ ! [A5: A,B5: B] :
% 2.96/1.59 ( Y2
% 2.96/1.59 != ( product_Pair @ A @ B @ A5 @ B5 ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_209_prod__induct7,axiom,
% 2.96/1.59 ! [G3: $tType,F6: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) ) ) ) ) > $o,X4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) ) ) )] :
% 2.96/1.59 ( ! [A5: A,B5: B,C4: C,D2: D,E2: E,F5: F6,G4: G3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F6 @ G3 ) @ E2 @ ( product_Pair @ F6 @ G3 @ F5 @ G4 ) ) ) ) ) ) )
% 2.96/1.59 => ( P @ X4 ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_210_prod__induct6,axiom,
% 2.96/1.59 ! [F6: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F6 ) ) ) ) ) > $o,X4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F6 ) ) ) )] :
% 2.96/1.59 ( ! [A5: A,B5: B,C4: C,D2: D,E2: E,F5: F6] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F6 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F6 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F6 ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ F6 ) @ D2 @ ( product_Pair @ E @ F6 @ E2 @ F5 ) ) ) ) ) )
% 2.96/1.59 => ( P @ X4 ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_211_prod__induct5,axiom,
% 2.96/1.59 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 2.96/1.59 ( ! [A5: A,B5: B,C4: C,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C4 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 2.96/1.59 => ( P @ X4 ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_212_prod__induct4,axiom,
% 2.96/1.59 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.96/1.59 ( ! [A5: A,B5: B,C4: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C4 @ D2 ) ) ) )
% 2.96/1.59 => ( P @ X4 ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_213_prod__induct3,axiom,
% 2.96/1.59 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X4: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.96/1.59 ( ! [A5: A,B5: B,C4: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B5 @ C4 ) ) )
% 2.96/1.59 => ( P @ X4 ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_214_prod__cases7,axiom,
% 2.96/1.59 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F6: $tType,G3: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) ) ) )] :
% 2.96/1.59 ~ ! [A5: A,B5: B,C4: C,D2: D,E2: E,F5: F6,G4: G3] :
% 2.96/1.59 ( Y2
% 2.96/1.59 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F6 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F6 @ G3 ) @ E2 @ ( product_Pair @ F6 @ G3 @ F5 @ G4 ) ) ) ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_215_prod__cases6,axiom,
% 2.96/1.59 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F6: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F6 ) ) ) )] :
% 2.96/1.59 ~ ! [A5: A,B5: B,C4: C,D2: D,E2: E,F5: F6] :
% 2.96/1.59 ( Y2
% 2.96/1.59 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F6 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F6 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F6 ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ F6 ) @ D2 @ ( product_Pair @ E @ F6 @ E2 @ F5 ) ) ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_216_prod__cases5,axiom,
% 2.96/1.59 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 2.96/1.59 ~ ! [A5: A,B5: B,C4: C,D2: D,E2: E] :
% 2.96/1.59 ( Y2
% 2.96/1.59 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C4 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_217_prod__cases4,axiom,
% 2.96/1.59 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.96/1.59 ~ ! [A5: A,B5: B,C4: C,D2: D] :
% 2.96/1.59 ( Y2
% 2.96/1.59 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C4 @ D2 ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_218_prod__cases3,axiom,
% 2.96/1.59 ! [A: $tType,B: $tType,C: $tType,Y2: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.96/1.59 ~ ! [A5: A,B5: B,C4: C] :
% 2.96/1.59 ( Y2
% 2.96/1.59 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B5 @ C4 ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_219_Pair__inject,axiom,
% 2.96/1.59 ! [A: $tType,B: $tType,A2: A,B2: B,A7: A,B7: B] :
% 2.96/1.59 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.96/1.59 = ( product_Pair @ A @ B @ A7 @ B7 ) )
% 2.96/1.59 => ~ ( ( A2 = A7 )
% 2.96/1.59 => ( B2 != B7 ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_220_prod__cases,axiom,
% 2.96/1.59 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P4: product_prod @ A @ B] :
% 2.96/1.59 ( ! [A5: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B5 ) )
% 2.96/1.59 => ( P @ P4 ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_221_surj__pair,axiom,
% 2.96/1.59 ! [A: $tType,B: $tType,P4: product_prod @ A @ B] :
% 2.96/1.59 ? [X2: A,Y4: B] :
% 2.96/1.59 ( P4
% 2.96/1.59 = ( product_Pair @ A @ B @ X2 @ Y4 ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_222_old_Oprod_Ocase,axiom,
% 2.96/1.59 ! [A: $tType,C: $tType,B: $tType,F3: A > B > C,X12: A,X22: B] :
% 2.96/1.59 ( ( product_case_prod @ A @ B @ C @ F3 @ ( product_Pair @ A @ B @ X12 @ X22 ) )
% 2.96/1.59 = ( F3 @ X12 @ X22 ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_223_case__prod__Pair__iden,axiom,
% 2.96/1.59 ! [B: $tType,A: $tType,P4: product_prod @ A @ B] :
% 2.96/1.59 ( ( product_case_prod @ A @ B @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B ) @ P4 )
% 2.96/1.59 = P4 ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_224_usubstappt_Opsimps_I3_J,axiom,
% 2.96/1.59 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,F3: char] :
% 2.96/1.59 ( ( 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 ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U2 @ ( const @ F3 ) ) ) )
% 2.96/1.59 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( const @ F3 ) )
% 2.96/1.59 = ( uSubst1138577137pconst @ Sigma2 @ U2 @ F3 ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_225_usubstappt_Opsimps_I6_J,axiom,
% 2.96/1.59 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 2.96/1.59 ( ( 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 ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U2 @ ( times @ Theta2 @ Eta2 ) ) ) )
% 2.96/1.59 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( times @ Theta2 @ Eta2 ) )
% 2.96/1.59 = ( uSubst277968634Timeso @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_226_usubstappt_Opsimps_I5_J,axiom,
% 2.96/1.59 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 2.96/1.59 ( ( 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 ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U2 @ ( plus @ Theta2 @ Eta2 ) ) ) )
% 2.96/1.59 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( plus @ Theta2 @ Eta2 ) )
% 2.96/1.59 = ( uSubst1112714340_Pluso @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_227_internal__case__prod__conv,axiom,
% 2.96/1.59 ! [B: $tType,A: $tType,C: $tType,C2: B > C > A,A2: B,B2: C] :
% 2.96/1.59 ( ( produc2004651681e_prod @ B @ C @ A @ C2 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 2.96/1.59 = ( C2 @ A2 @ B2 ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_228_usubstappt_Opsimps_I4_J,axiom,
% 2.96/1.59 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,F3: char,Theta2: trm] :
% 2.96/1.59 ( ( 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 ) @ Sigma2 @ ( product_Pair @ ( set @ variable ) @ trm @ U2 @ ( func @ F3 @ Theta2 ) ) ) )
% 2.96/1.59 => ( ( uSubst95898992stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 2.96/1.59 = ( case_option @ ( option @ trm ) @ trm @ ( none @ trm )
% 2.96/1.59 @ ^ [Sigma_theta2: trm] :
% 2.96/1.59 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( func @ F3 @ Sigma_theta2 ) )
% 2.96/1.59 @ ^ [R: trm] :
% 2.96/1.59 ( if @ ( option @ trm )
% 2.96/1.59 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R ) @ U2 )
% 2.96/1.59 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.59 @ ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta2 ) @ ( bot_bot @ ( set @ variable ) ) @ R )
% 2.96/1.59 @ ( none @ trm ) )
% 2.96/1.59 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.59 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.59 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.59 @ ^ [F4: char > ( option @ trm )] :
% 2.96/1.59 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.59 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 2.96/1.59 @ Sigma2
% 2.96/1.59 @ F3 ) )
% 2.96/1.59 @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_229_usubstappt_Ocases,axiom,
% 2.96/1.59 ! [X4: 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 )] :
% 2.96/1.59 ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,X2: variable] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( var @ X2 ) ) ) )
% 2.96/1.59 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,R3: real] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( number @ R3 ) ) ) )
% 2.96/1.59 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F5: char] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( const @ F5 ) ) ) )
% 2.96/1.59 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F5: char,Theta: trm] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( func @ F5 @ Theta ) ) ) )
% 2.96/1.59 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta: trm,Eta: trm] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( plus @ Theta @ Eta ) ) ) )
% 2.96/1.59 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta: trm,Eta: trm] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( times @ Theta @ Eta ) ) ) )
% 2.96/1.59 => ~ ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta: trm] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( differential @ Theta ) ) ) ) ) ) ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_230_usubstappt_Opinduct,axiom,
% 2.96/1.59 ! [A0: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),A1: set @ variable,A22: trm,P: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > trm > $o] :
% 2.96/1.59 ( ( 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 ) @ A0 @ ( product_Pair @ ( set @ variable ) @ trm @ A1 @ A22 ) ) )
% 2.96/1.59 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,X2: variable] :
% 2.96/1.59 ( ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( var @ X2 ) ) ) )
% 2.96/1.59 => ( P @ Sigma3 @ U3 @ ( var @ X2 ) ) )
% 2.96/1.59 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,R3: real] :
% 2.96/1.59 ( ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( number @ R3 ) ) ) )
% 2.96/1.59 => ( P @ Sigma3 @ U3 @ ( number @ R3 ) ) )
% 2.96/1.59 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F5: char] :
% 2.96/1.59 ( ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( const @ F5 ) ) ) )
% 2.96/1.59 => ( P @ Sigma3 @ U3 @ ( const @ F5 ) ) )
% 2.96/1.59 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F5: char,Theta: trm] :
% 2.96/1.59 ( ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( func @ F5 @ Theta ) ) ) )
% 2.96/1.59 => ( ( P @ Sigma3 @ U3 @ Theta )
% 2.96/1.59 => ( ! [X25: trm] :
% 2.96/1.59 ( ( ( uSubst95898992stappt @ Sigma3 @ U3 @ Theta )
% 2.96/1.59 = ( some @ trm @ X25 ) )
% 2.96/1.59 => ! [X2a: trm] :
% 2.96/1.59 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.59 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.59 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.59 @ ^ [F4: char > ( option @ trm )] :
% 2.96/1.59 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.59 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 2.96/1.59 @ Sigma3
% 2.96/1.59 @ F5 )
% 2.96/1.59 = ( some @ trm @ X2a ) )
% 2.96/1.59 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ X2a ) @ U3 )
% 2.96/1.59 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.59 => ( P @ ( uSubst969145931substt @ X25 ) @ ( bot_bot @ ( set @ variable ) ) @ X2a ) ) ) )
% 2.96/1.59 => ( P @ Sigma3 @ U3 @ ( func @ F5 @ Theta ) ) ) ) )
% 2.96/1.59 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta: trm,Eta: trm] :
% 2.96/1.59 ( ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( plus @ Theta @ Eta ) ) ) )
% 2.96/1.59 => ( ( P @ Sigma3 @ U3 @ Theta )
% 2.96/1.59 => ( ( P @ Sigma3 @ U3 @ Eta )
% 2.96/1.59 => ( P @ Sigma3 @ U3 @ ( plus @ Theta @ Eta ) ) ) ) )
% 2.96/1.59 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta: trm,Eta: trm] :
% 2.96/1.59 ( ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( times @ Theta @ Eta ) ) ) )
% 2.96/1.59 => ( ( P @ Sigma3 @ U3 @ Theta )
% 2.96/1.59 => ( ( P @ Sigma3 @ U3 @ Eta )
% 2.96/1.59 => ( P @ Sigma3 @ U3 @ ( times @ Theta @ Eta ) ) ) ) )
% 2.96/1.59 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta: trm] :
% 2.96/1.59 ( ( 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 ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( differential @ Theta ) ) ) )
% 2.96/1.59 => ( ( P @ Sigma3
% 2.96/1.59 @ ( collect @ variable
% 2.96/1.59 @ ^ [X: variable] : $true )
% 2.96/1.59 @ Theta )
% 2.96/1.59 => ( P @ Sigma3 @ U3 @ ( differential @ Theta ) ) ) )
% 2.96/1.59 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_231_old_Oprod_Orec,axiom,
% 2.96/1.59 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 2.96/1.59 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 2.96/1.59 = ( F1 @ A2 @ B2 ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_232_split__cong,axiom,
% 2.96/1.59 ! [C: $tType,B: $tType,A: $tType,Q3: product_prod @ A @ B,F3: A > B > C,G2: A > B > C,P4: product_prod @ A @ B] :
% 2.96/1.59 ( ! [X2: A,Y4: B] :
% 2.96/1.59 ( ( ( product_Pair @ A @ B @ X2 @ Y4 )
% 2.96/1.59 = Q3 )
% 2.96/1.59 => ( ( F3 @ X2 @ Y4 )
% 2.96/1.59 = ( G2 @ X2 @ Y4 ) ) )
% 2.96/1.59 => ( ( P4 = Q3 )
% 2.96/1.59 => ( ( product_case_prod @ A @ B @ C @ F3 @ P4 )
% 2.96/1.59 = ( product_case_prod @ A @ B @ C @ G2 @ Q3 ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_233_Geqo_Oelims,axiom,
% 2.96/1.59 ! [X4: option @ trm,Xa: option @ trm,Y2: option @ fml] :
% 2.96/1.59 ( ( ( uSubst1556497037e_Geqo @ X4 @ Xa )
% 2.96/1.59 = Y2 )
% 2.96/1.59 => ( ! [Theta: trm] :
% 2.96/1.59 ( ( X4
% 2.96/1.59 = ( some @ trm @ Theta ) )
% 2.96/1.59 => ! [Eta: trm] :
% 2.96/1.59 ( ( Xa
% 2.96/1.59 = ( some @ trm @ Eta ) )
% 2.96/1.59 => ( Y2
% 2.96/1.59 != ( some @ fml @ ( geq @ Theta @ Eta ) ) ) ) )
% 2.96/1.59 => ( ( ( X4
% 2.96/1.59 = ( none @ trm ) )
% 2.96/1.59 => ( Y2
% 2.96/1.59 != ( none @ fml ) ) )
% 2.96/1.59 => ~ ( ? [V: trm] :
% 2.96/1.59 ( X4
% 2.96/1.59 = ( some @ trm @ V ) )
% 2.96/1.59 => ( ( Xa
% 2.96/1.59 = ( none @ trm ) )
% 2.96/1.59 => ( Y2
% 2.96/1.59 != ( none @ fml ) ) ) ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_234_fml_Oinject_I2_J,axiom,
% 2.96/1.59 ! [X21: trm,X222: trm,Y21: trm,Y222: trm] :
% 2.96/1.59 ( ( ( geq @ X21 @ X222 )
% 2.96/1.59 = ( geq @ Y21 @ Y222 ) )
% 2.96/1.59 = ( ( X21 = Y21 )
% 2.96/1.59 & ( X222 = Y222 ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_235_Diamondo_Ocases,axiom,
% 2.96/1.59 ! [X4: product_prod @ ( option @ game ) @ ( option @ fml )] :
% 2.96/1.59 ( ! [Alpha: game,Phi: fml] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ Alpha ) @ ( some @ fml @ Phi ) ) )
% 2.96/1.59 => ( ! [Phi: option @ fml] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( none @ game ) @ Phi ) )
% 2.96/1.59 => ~ ! [V: game] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ V ) @ ( none @ fml ) ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_236_Existso_Ocases,axiom,
% 2.96/1.59 ! [X4: product_prod @ variable @ ( option @ fml )] :
% 2.96/1.59 ( ! [X2: variable,Phi: fml] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( product_Pair @ variable @ ( option @ fml ) @ X2 @ ( some @ fml @ Phi ) ) )
% 2.96/1.59 => ~ ! [X2: variable] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( product_Pair @ variable @ ( option @ fml ) @ X2 @ ( none @ fml ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_237_Ando_Ocases,axiom,
% 2.96/1.59 ! [X4: product_prod @ ( option @ fml ) @ ( option @ fml )] :
% 2.96/1.59 ( ! [Phi: fml,Psi: fml] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( product_Pair @ ( option @ fml ) @ ( option @ fml ) @ ( some @ fml @ Phi ) @ ( some @ fml @ Psi ) ) )
% 2.96/1.59 => ( ! [Psi: option @ fml] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( product_Pair @ ( option @ fml ) @ ( option @ fml ) @ ( none @ fml ) @ Psi ) )
% 2.96/1.59 => ~ ! [V: fml] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( product_Pair @ ( option @ fml ) @ ( option @ fml ) @ ( some @ fml @ V ) @ ( none @ fml ) ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_238_ODEo_Ocases,axiom,
% 2.96/1.59 ! [X4: product_prod @ char @ ( option @ trm )] :
% 2.96/1.59 ( ! [X2: char,Theta: trm] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( product_Pair @ char @ ( option @ trm ) @ X2 @ ( some @ trm @ Theta ) ) )
% 2.96/1.59 => ~ ! [X2: char] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( product_Pair @ char @ ( option @ trm ) @ X2 @ ( none @ trm ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_239_Assigno_Ocases,axiom,
% 2.96/1.59 ! [X4: product_prod @ variable @ ( option @ trm )] :
% 2.96/1.59 ( ! [X2: variable,Theta: trm] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( product_Pair @ variable @ ( option @ trm ) @ X2 @ ( some @ trm @ Theta ) ) )
% 2.96/1.59 => ~ ! [X2: variable] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( product_Pair @ variable @ ( option @ trm ) @ X2 @ ( none @ trm ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_240_Timeso_Ocases,axiom,
% 2.96/1.59 ! [X4: product_prod @ ( option @ trm ) @ ( option @ trm )] :
% 2.96/1.59 ( ! [Theta: trm,Eta: trm] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta ) ) )
% 2.96/1.59 => ( ! [Eta: option @ trm] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( none @ trm ) @ Eta ) )
% 2.96/1.59 => ~ ! [V: trm] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ V ) @ ( none @ trm ) ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_241_Geqo_Osimps_I1_J,axiom,
% 2.96/1.59 ! [Theta2: trm,Eta2: trm] :
% 2.96/1.59 ( ( uSubst1556497037e_Geqo @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta2 ) )
% 2.96/1.59 = ( some @ fml @ ( geq @ Theta2 @ Eta2 ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_242_usubstappf__geqr,axiom,
% 2.96/1.59 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 2.96/1.59 ( ( ( uSubst95898978stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 2.96/1.59 != ( none @ fml ) )
% 2.96/1.59 => ( ( uSubst95898978stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 2.96/1.59 = ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 ) ) @ ( the @ trm @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_243_usubstappf__geq,axiom,
% 2.96/1.59 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 2.96/1.59 ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 )
% 2.96/1.59 != ( none @ trm ) )
% 2.96/1.59 => ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 )
% 2.96/1.59 != ( none @ trm ) )
% 2.96/1.59 => ( ( uSubst95898978stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 2.96/1.59 = ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 ) ) @ ( the @ trm @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_244_Composeo_Ocases,axiom,
% 2.96/1.59 ! [X4: product_prod @ ( option @ game ) @ ( option @ game )] :
% 2.96/1.59 ( ! [Alpha: game,Beta: game] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ ( some @ game @ Alpha ) @ ( some @ game @ Beta ) ) )
% 2.96/1.59 => ( ! [Alpha: option @ game] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ Alpha @ ( none @ game ) ) )
% 2.96/1.59 => ~ ! [V: game] :
% 2.96/1.59 ( X4
% 2.96/1.59 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ ( none @ game ) @ ( some @ game @ V ) ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_245_usubstappf_Osimps_I2_J,axiom,
% 2.96/1.59 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 2.96/1.59 ( ( uSubst95898978stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 2.96/1.59 = ( uSubst1556497037e_Geqo @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_246_usubstappf__geq__conv,axiom,
% 2.96/1.59 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,Theta2: trm,Eta2: trm] :
% 2.96/1.59 ( ( ( uSubst95898978stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 2.96/1.59 != ( none @ fml ) )
% 2.96/1.59 => ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 )
% 2.96/1.59 != ( none @ trm ) )
% 2.96/1.59 & ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Eta2 )
% 2.96/1.59 != ( none @ trm ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_247_dotsubstt__def,axiom,
% 2.96/1.59 ( uSubst969145931substt
% 2.96/1.59 = ( ^ [Theta3: trm] :
% 2.96/1.59 ( product_Pair @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) )
% 2.96/1.59 @ ^ [F2: char] :
% 2.96/1.59 ( if @ ( option @ trm )
% 2.96/1.59 @ ( F2
% 2.96/1.59 = ( char2 @ $false @ $true @ $true @ $true @ $false @ $true @ $false @ $false ) )
% 2.96/1.59 @ ( some @ trm @ Theta3 )
% 2.96/1.59 @ ( none @ trm ) )
% 2.96/1.59 @ ( product_Pair @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) )
% 2.96/1.59 @ ^ [Uu: char] : ( none @ trm )
% 2.96/1.59 @ ( product_Pair @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) )
% 2.96/1.59 @ ^ [Uu: char] : ( none @ fml )
% 2.96/1.59 @ ^ [Uu: char] : ( none @ game ) ) ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_248_Geqo_Opelims,axiom,
% 2.96/1.59 ! [X4: option @ trm,Xa: option @ trm,Y2: option @ fml] :
% 2.96/1.59 ( ( ( uSubst1556497037e_Geqo @ X4 @ Xa )
% 2.96/1.59 = Y2 )
% 2.96/1.59 => ( ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst864323244qo_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ X4 @ Xa ) )
% 2.96/1.59 => ( ! [Theta: trm] :
% 2.96/1.59 ( ( X4
% 2.96/1.59 = ( some @ trm @ Theta ) )
% 2.96/1.59 => ! [Eta: trm] :
% 2.96/1.59 ( ( Xa
% 2.96/1.59 = ( some @ trm @ Eta ) )
% 2.96/1.59 => ( ( Y2
% 2.96/1.59 = ( some @ fml @ ( geq @ Theta @ Eta ) ) )
% 2.96/1.59 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst864323244qo_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta ) ) ) ) ) )
% 2.96/1.59 => ( ( ( X4
% 2.96/1.59 = ( none @ trm ) )
% 2.96/1.59 => ( ( Y2
% 2.96/1.59 = ( none @ fml ) )
% 2.96/1.59 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst864323244qo_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( none @ trm ) @ Xa ) ) ) )
% 2.96/1.59 => ~ ! [V: trm] :
% 2.96/1.59 ( ( X4
% 2.96/1.59 = ( some @ trm @ V ) )
% 2.96/1.59 => ( ( Xa
% 2.96/1.59 = ( none @ trm ) )
% 2.96/1.59 => ( ( Y2
% 2.96/1.59 = ( none @ fml ) )
% 2.96/1.59 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst864323244qo_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ V ) @ ( none @ trm ) ) ) ) ) ) ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_249_Timeso_Opelims,axiom,
% 2.96/1.59 ! [X4: option @ trm,Xa: option @ trm,Y2: option @ trm] :
% 2.96/1.59 ( ( ( uSubst277968634Timeso @ X4 @ Xa )
% 2.96/1.59 = Y2 )
% 2.96/1.59 => ( ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst1377811071so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ X4 @ Xa ) )
% 2.96/1.59 => ( ! [Theta: trm] :
% 2.96/1.59 ( ( X4
% 2.96/1.59 = ( some @ trm @ Theta ) )
% 2.96/1.59 => ! [Eta: trm] :
% 2.96/1.59 ( ( Xa
% 2.96/1.59 = ( some @ trm @ Eta ) )
% 2.96/1.59 => ( ( Y2
% 2.96/1.59 = ( some @ trm @ ( times @ Theta @ Eta ) ) )
% 2.96/1.59 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst1377811071so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta ) ) ) ) ) )
% 2.96/1.59 => ( ( ( X4
% 2.96/1.59 = ( none @ trm ) )
% 2.96/1.59 => ( ( Y2
% 2.96/1.59 = ( none @ trm ) )
% 2.96/1.59 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst1377811071so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( none @ trm ) @ Xa ) ) ) )
% 2.96/1.59 => ~ ! [V: trm] :
% 2.96/1.59 ( ( X4
% 2.96/1.59 = ( some @ trm @ V ) )
% 2.96/1.59 => ( ( Xa
% 2.96/1.59 = ( none @ trm ) )
% 2.96/1.59 => ( ( Y2
% 2.96/1.59 = ( none @ trm ) )
% 2.96/1.59 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst1377811071so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ V ) @ ( none @ trm ) ) ) ) ) ) ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_250_Pluso_Opelims,axiom,
% 2.96/1.59 ! [X4: option @ trm,Xa: option @ trm,Y2: option @ trm] :
% 2.96/1.59 ( ( ( uSubst1112714340_Pluso @ X4 @ Xa )
% 2.96/1.59 = Y2 )
% 2.96/1.59 => ( ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst270600597so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ X4 @ Xa ) )
% 2.96/1.59 => ( ! [Theta: trm] :
% 2.96/1.59 ( ( X4
% 2.96/1.59 = ( some @ trm @ Theta ) )
% 2.96/1.59 => ! [Eta: trm] :
% 2.96/1.59 ( ( Xa
% 2.96/1.59 = ( some @ trm @ Eta ) )
% 2.96/1.59 => ( ( Y2
% 2.96/1.59 = ( some @ trm @ ( plus @ Theta @ Eta ) ) )
% 2.96/1.59 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst270600597so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta ) ) ) ) ) )
% 2.96/1.59 => ( ( ( X4
% 2.96/1.59 = ( none @ trm ) )
% 2.96/1.59 => ( ( Y2
% 2.96/1.59 = ( none @ trm ) )
% 2.96/1.59 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst270600597so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( none @ trm ) @ Xa ) ) ) )
% 2.96/1.59 => ~ ! [V: trm] :
% 2.96/1.59 ( ( X4
% 2.96/1.59 = ( some @ trm @ V ) )
% 2.96/1.59 => ( ( Xa
% 2.96/1.59 = ( none @ trm ) )
% 2.96/1.59 => ( ( Y2
% 2.96/1.59 = ( none @ trm ) )
% 2.96/1.59 => ~ ( accp @ ( product_prod @ ( option @ trm ) @ ( option @ trm ) ) @ uSubst270600597so_rel @ ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ V ) @ ( none @ trm ) ) ) ) ) ) ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_251_dot__def,axiom,
% 2.96/1.59 ( uSubst_Mirabelle_dot
% 2.96/1.59 = ( const @ ( char2 @ $false @ $true @ $true @ $true @ $false @ $true @ $false @ $false ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_252_usubstappf__pred,axiom,
% 2.96/1.59 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),P4: char,R2: fml,U2: set @ variable,Theta2: trm,Sigma_theta: trm] :
% 2.96/1.59 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 2.96/1.59 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.59 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 2.96/1.59 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.59 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.59 @ ^ [P3: char > ( option @ fml ),Uw: char > ( option @ game )] : P3 ) )
% 2.96/1.59 @ Sigma2
% 2.96/1.59 @ P4 )
% 2.96/1.59 = ( some @ fml @ R2 ) )
% 2.96/1.59 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R2 ) @ U2 )
% 2.96/1.59 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.59 => ( ( ( uSubst95898992stappt @ Sigma2 @ U2 @ Theta2 )
% 2.96/1.59 = ( some @ trm @ Sigma_theta ) )
% 2.96/1.59 => ( ( uSubst95898978stappf @ Sigma2 @ U2 @ ( pred @ P4 @ Theta2 ) )
% 2.96/1.59 = ( uSubst95898978stappf @ ( uSubst969145931substt @ Sigma_theta ) @ ( bot_bot @ ( set @ variable ) ) @ R2 ) ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_253_fml_Oinject_I1_J,axiom,
% 2.96/1.59 ! [X11: char,X122: trm,Y11: char,Y12: trm] :
% 2.96/1.59 ( ( ( pred @ X11 @ X122 )
% 2.96/1.59 = ( pred @ Y11 @ Y12 ) )
% 2.96/1.59 = ( ( X11 = Y11 )
% 2.96/1.59 & ( X122 = Y12 ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(fact_254_usubstappf__pred2,axiom,
% 2.96/1.59 ! [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),P4: char,R2: fml,U2: set @ variable,Theta2: trm] :
% 2.96/1.59 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 2.96/1.59 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.59 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 2.96/1.59 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.59 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.59 @ ^ [P3: char > ( option @ fml ),Uw: char > ( option @ game )] : P3 ) )
% 2.96/1.59 @ Sigma2
% 2.96/1.59 @ P4 )
% 2.96/1.59 = ( some @ fml @ R2 ) )
% 2.96/1.59 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R2 ) @ U2 )
% 2.96/1.59 != ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.59 => ( ( uSubst95898978stappf @ Sigma2 @ U2 @ ( pred @ P4 @ Theta2 ) )
% 2.96/1.59 = ( none @ fml ) ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 2.96/1.59 bounded_lattice @ $o ).
% 2.96/1.59
% 2.96/1.59 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 2.96/1.59 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 2.96/1.59 ! [A8: $tType,A9: $tType] :
% 2.96/1.59 ( ( bounded_lattice @ A9 )
% 2.96/1.59 => ( bounded_lattice @ ( A8 > A9 ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 2.96/1.59 ! [A8: $tType,A9: $tType] :
% 2.96/1.59 ( ( bounded_lattice @ A9 )
% 2.96/1.59 => ( bounded_lattice_bot @ ( A8 > A9 ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 2.96/1.59 ! [A8: $tType,A9: $tType] :
% 2.96/1.59 ( ( semilattice_inf @ A9 )
% 2.96/1.59 => ( semilattice_inf @ ( A8 > A9 ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(tcon_fun___Lattices_Olattice,axiom,
% 2.96/1.59 ! [A8: $tType,A9: $tType] :
% 2.96/1.59 ( ( lattice @ A9 )
% 2.96/1.59 => ( lattice @ ( A8 > A9 ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(tcon_fun___Orderings_Obot,axiom,
% 2.96/1.59 ! [A8: $tType,A9: $tType] :
% 2.96/1.59 ( ( bot @ A9 )
% 2.96/1.59 => ( bot @ ( A8 > A9 ) ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_3,axiom,
% 2.96/1.59 ! [A8: $tType] : ( bounded_lattice_bot @ ( set @ A8 ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_4,axiom,
% 2.96/1.59 ! [A8: $tType] : ( semilattice_inf @ ( set @ A8 ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(tcon_Set_Oset___Lattices_Olattice_5,axiom,
% 2.96/1.59 ! [A8: $tType] : ( lattice @ ( set @ A8 ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(tcon_Set_Oset___Orderings_Obot_6,axiom,
% 2.96/1.59 ! [A8: $tType] : ( bot @ ( set @ A8 ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_7,axiom,
% 2.96/1.59 bounded_lattice_bot @ $o ).
% 2.96/1.59
% 2.96/1.59 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_8,axiom,
% 2.96/1.59 semilattice_inf @ $o ).
% 2.96/1.59
% 2.96/1.59 thf(tcon_HOL_Obool___Lattices_Olattice_9,axiom,
% 2.96/1.59 lattice @ $o ).
% 2.96/1.59
% 2.96/1.59 thf(tcon_HOL_Obool___Orderings_Obot_10,axiom,
% 2.96/1.59 bot @ $o ).
% 2.96/1.59
% 2.96/1.59 thf(tcon_Real_Oreal___Lattices_Osemilattice__inf_11,axiom,
% 2.96/1.59 semilattice_inf @ real ).
% 2.96/1.59
% 2.96/1.59 thf(tcon_Real_Oreal___Lattices_Olattice_12,axiom,
% 2.96/1.59 lattice @ real ).
% 2.96/1.59
% 2.96/1.59 thf(help_If_3_1_T,axiom,
% 2.96/1.59 ! [P: $o] :
% 2.96/1.59 ( ( P = $true )
% 2.96/1.59 | ( P = $false ) ) ).
% 2.96/1.59
% 2.96/1.59 thf(help_If_2_1_T,axiom,
% 2.96/1.59 ! [A: $tType,X4: A,Y2: A] :
% 2.96/1.59 ( ( if @ A @ $false @ X4 @ Y2 )
% 2.96/1.59 = Y2 ) ).
% 2.96/1.59
% 2.96/1.59 thf(help_If_1_1_T,axiom,
% 2.96/1.59 ! [A: $tType,X4: A,Y2: A] :
% 2.96/1.59 ( ( if @ A @ $true @ X4 @ Y2 )
% 2.96/1.59 = X4 ) ).
% 2.96/1.59
% 2.96/1.59 thf(conj_0,conjecture,
% 2.96/1.59 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.59 @ ^ [F0: char > ( option @ trm )] :
% 2.96/1.59 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 2.96/1.59 @ ^ [Uu: char > ( option @ trm )] :
% 2.96/1.59 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 2.96/1.59 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 2.96/1.59 @ sigma
% 2.96/1.59 @ f )
% 2.96/1.59 = ( none @ trm ) )
% 2.96/1.59 | ( ( uSubst95898992stappt @ sigma @ u @ ( const @ f ) )
% 2.96/1.59 = ( uSubst1138577137pconst @ sigma @ v @ f ) ) ) ).
% 2.96/1.59 ------------------------
% 3.08/1.63 % (19935)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_19715 for (2999ds/4Mi)
% 3.08/1.63 % (19936)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_19715 for (2999ds/27Mi)
% 3.08/1.63 % (19935)Instruction limit reached!
% 3.08/1.63 % (19935)------------------------------
% 3.08/1.63 % (19935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.63 % (19935)Termination reason: Unknown
% 3.08/1.63 % (19935)Termination phase: shuffling
% 3.08/1.63
% 3.08/1.63 % (19935)Memory used [KB]: 1535
% 3.08/1.63 % (19935)Time elapsed: 0.003 s
% 3.08/1.63 % (19935)Instructions burned: 6 (million)
% 3.08/1.63 % (19935)------------------------------
% 3.08/1.63 % (19935)------------------------------
% 3.08/1.64 % (19934)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19715 for (2999ds/183Mi)
% 3.08/1.64 % (19937)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19715 for (2999ds/2Mi)
% 3.08/1.64 % (19938)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_19715 for (2999ds/2Mi)
% 3.08/1.64 % (19939)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_19715 for (2999ds/275Mi)
% 3.08/1.64 % (19940)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19715 for (2999ds/18Mi)
% 3.08/1.64 % (19937)Instruction limit reached!
% 3.08/1.64 % (19937)------------------------------
% 3.08/1.64 % (19937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.64 % (19937)Termination reason: Unknown
% 3.08/1.64 % (19937)Termination phase: shuffling
% 3.08/1.64
% 3.08/1.64 % (19937)Memory used [KB]: 1407
% 3.08/1.64 % (19937)Time elapsed: 0.004 s
% 3.08/1.64 % (19937)Instructions burned: 3 (million)
% 3.08/1.64 % (19937)------------------------------
% 3.08/1.64 % (19937)------------------------------
% 3.08/1.64 % (19938)Instruction limit reached!
% 3.08/1.64 % (19938)------------------------------
% 3.08/1.64 % (19938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.64 % (19938)Termination reason: Unknown
% 3.08/1.64 % (19938)Termination phase: shuffling
% 3.08/1.64
% 3.08/1.64 % (19938)Memory used [KB]: 1407
% 3.08/1.64 % (19938)Time elapsed: 0.004 s
% 3.08/1.64 % (19938)Instructions burned: 3 (million)
% 3.08/1.64 % (19938)------------------------------
% 3.08/1.64 % (19938)------------------------------
% 3.08/1.64 % (19941)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19715 for (2999ds/3Mi)
% 3.08/1.64 % (19941)Instruction limit reached!
% 3.08/1.64 % (19941)------------------------------
% 3.08/1.64 % (19941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.64 % (19941)Termination reason: Unknown
% 3.08/1.64 % (19941)Termination phase: shuffling
% 3.08/1.64
% 3.08/1.64 % (19941)Memory used [KB]: 1407
% 3.08/1.64 % (19941)Time elapsed: 0.002 s
% 3.08/1.64 % (19941)Instructions burned: 3 (million)
% 3.08/1.64 % (19941)------------------------------
% 3.08/1.64 % (19941)------------------------------
% 3.08/1.64 % (19936)Instruction limit reached!
% 3.08/1.64 % (19936)------------------------------
% 3.08/1.64 % (19936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.64 % (19936)Termination reason: Unknown
% 3.08/1.64 % (19936)Termination phase: shuffling
% 3.08/1.64
% 3.08/1.64 % (19936)Memory used [KB]: 1791
% 3.08/1.64 % (19936)Time elapsed: 0.014 s
% 3.08/1.64 % (19936)Instructions burned: 29 (million)
% 3.08/1.64 % (19936)------------------------------
% 3.08/1.64 % (19936)------------------------------
% 3.08/1.65 % (19940)Instruction limit reached!
% 3.08/1.65 % (19940)------------------------------
% 3.08/1.65 % (19940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.65 % (19940)Termination reason: Unknown
% 3.08/1.65 % (19940)Termination phase: shuffling
% 3.08/1.65
% 3.08/1.65 % (19940)Memory used [KB]: 1663
% 3.08/1.65 % (19940)Time elapsed: 0.013 s
% 3.08/1.65 % (19940)Instructions burned: 18 (million)
% 3.08/1.65 % (19940)------------------------------
% 3.08/1.65 % (19940)------------------------------
% 3.08/1.65 % (19944)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_19715 for (2999ds/3Mi)
% 3.08/1.65 % (19944)Instruction limit reached!
% 3.08/1.65 % (19944)------------------------------
% 3.08/1.65 % (19944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.65 % (19944)Termination reason: Unknown
% 3.08/1.65 % (19944)Termination phase: shuffling
% 3.08/1.65
% 3.08/1.65 % (19944)Memory used [KB]: 1407
% 3.08/1.65 % (19944)Time elapsed: 0.002 s
% 3.08/1.65 % (19944)Instructions burned: 3 (million)
% 3.08/1.65 % (19944)------------------------------
% 3.08/1.65 % (19944)------------------------------
% 3.08/1.66 % (19945)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_19715 for (2999ds/1041Mi)
% 3.08/1.66 % (19943)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_19715 for (2999ds/15Mi)
% 3.08/1.66 % (19942)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_19715 for (2999ds/37Mi)
% 3.08/1.66 % (19947)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_19715 for (2999ds/16Mi)
% 3.08/1.67 % (19943)Instruction limit reached!
% 3.08/1.67 % (19943)------------------------------
% 3.08/1.67 % (19943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.67 % (19943)Termination reason: Unknown
% 3.08/1.67 % (19943)Termination phase: shuffling
% 3.08/1.67
% 3.08/1.67 % (19943)Memory used [KB]: 1535
% 3.08/1.67 % (19943)Time elapsed: 0.010 s
% 3.08/1.67 % (19943)Instructions burned: 16 (million)
% 3.08/1.67 % (19943)------------------------------
% 3.08/1.67 % (19943)------------------------------
% 3.08/1.67 % (19946)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19715 for (2999ds/7Mi)
% 3.08/1.67 % (19947)Instruction limit reached!
% 3.08/1.67 % (19947)------------------------------
% 3.08/1.67 % (19947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.67 % (19947)Termination reason: Unknown
% 3.08/1.67 % (19947)Termination phase: shuffling
% 3.08/1.67
% 3.08/1.67 % (19947)Memory used [KB]: 1663
% 3.08/1.67 % (19947)Time elapsed: 0.007 s
% 3.08/1.67 % (19947)Instructions burned: 18 (million)
% 3.08/1.67 % (19947)------------------------------
% 3.08/1.67 % (19947)------------------------------
% 3.08/1.67 % (19946)Instruction limit reached!
% 3.08/1.67 % (19946)------------------------------
% 3.08/1.67 % (19946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.67 % (19946)Termination reason: Unknown
% 3.08/1.67 % (19946)Termination phase: shuffling
% 3.08/1.67
% 3.08/1.67 % (19946)Memory used [KB]: 1535
% 3.08/1.67 % (19946)Time elapsed: 0.007 s
% 3.08/1.67 % (19946)Instructions burned: 8 (million)
% 3.08/1.67 % (19946)------------------------------
% 3.08/1.67 % (19946)------------------------------
% 3.08/1.68 % (19942)Instruction limit reached!
% 3.08/1.68 % (19942)------------------------------
% 3.08/1.68 % (19942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.68 % (19942)Termination reason: Unknown
% 3.08/1.68 % (19942)Termination phase: shuffling
% 3.08/1.68
% 3.08/1.68 % (19942)Memory used [KB]: 2174
% 3.08/1.68 % (19942)Time elapsed: 0.019 s
% 3.08/1.68 % (19942)Instructions burned: 37 (million)
% 3.08/1.68 % (19942)------------------------------
% 3.08/1.68 % (19942)------------------------------
% 3.08/1.68 % (19949)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_19715 for (2999ds/3Mi)
% 3.08/1.68 % (19948)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_19715 for (2999ds/3Mi)
% 3.08/1.68 % (19949)Instruction limit reached!
% 3.08/1.68 % (19949)------------------------------
% 3.08/1.68 % (19949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.68 % (19949)Termination reason: Unknown
% 3.08/1.68 % (19949)Termination phase: shuffling
% 3.08/1.68
% 3.08/1.68 % (19949)Memory used [KB]: 1407
% 3.08/1.68 % (19949)Time elapsed: 0.002 s
% 3.08/1.68 % (19949)Instructions burned: 3 (million)
% 3.08/1.68 % (19949)------------------------------
% 3.08/1.68 % (19949)------------------------------
% 3.08/1.68 % (19948)Instruction limit reached!
% 3.08/1.68 % (19948)------------------------------
% 3.08/1.68 % (19948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.68 % (19948)Termination reason: Unknown
% 3.08/1.68 % (19948)Termination phase: shuffling
% 3.08/1.68
% 3.08/1.68 % (19948)Memory used [KB]: 1407
% 3.08/1.68 % (19948)Time elapsed: 0.002 s
% 3.08/1.68 % (19948)Instructions burned: 3 (million)
% 3.08/1.68 % (19948)------------------------------
% 3.08/1.68 % (19948)------------------------------
% 3.08/1.69 % (19951)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_19715 for (2999ds/3Mi)
% 3.08/1.69 % (19952)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_19715 for (2999ds/4Mi)
% 3.08/1.69 % (19951)Instruction limit reached!
% 3.08/1.69 % (19951)------------------------------
% 3.08/1.69 % (19951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.69 % (19951)Termination reason: Unknown
% 3.08/1.69 % (19951)Termination phase: shuffling
% 3.08/1.69
% 3.08/1.69 % (19951)Memory used [KB]: 1407
% 3.08/1.69 % (19951)Time elapsed: 0.003 s
% 3.08/1.69 % (19951)Instructions burned: 3 (million)
% 3.08/1.69 % (19951)------------------------------
% 3.08/1.69 % (19951)------------------------------
% 3.08/1.69 % (19953)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_19715 for (2999ds/18Mi)
% 3.08/1.69 % (19952)Instruction limit reached!
% 3.08/1.69 % (19952)------------------------------
% 3.08/1.69 % (19952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.69 % (19952)Termination reason: Unknown
% 3.08/1.69 % (19952)Termination phase: shuffling
% 3.08/1.69
% 3.08/1.69 % (19952)Memory used [KB]: 1407
% 3.08/1.69 % (19950)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_19715 for (2999ds/7Mi)
% 3.08/1.69 % (19952)Time elapsed: 0.003 s
% 3.08/1.69 % (19952)Instructions burned: 6 (million)
% 3.08/1.69 % (19952)------------------------------
% 3.08/1.69 % (19952)------------------------------
% 3.08/1.69 % (19950)Instruction limit reached!
% 3.08/1.69 % (19950)------------------------------
% 3.08/1.69 % (19950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.69 % (19950)Termination reason: Unknown
% 3.08/1.69 % (19950)Termination phase: shuffling
% 3.08/1.69
% 3.08/1.69 % (19950)Memory used [KB]: 1535
% 3.08/1.69 % (19950)Time elapsed: 0.006 s
% 3.08/1.69 % (19950)Instructions burned: 7 (million)
% 3.08/1.69 % (19950)------------------------------
% 3.08/1.69 % (19950)------------------------------
% 3.08/1.70 % (19953)Instruction limit reached!
% 3.08/1.70 % (19953)------------------------------
% 3.08/1.70 % (19953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.70 % (19953)Termination reason: Unknown
% 3.08/1.70 % (19953)Termination phase: shuffling
% 3.08/1.70
% 3.08/1.70 % (19953)Memory used [KB]: 1663
% 3.08/1.70 % (19953)Time elapsed: 0.008 s
% 3.08/1.70 % (19953)Instructions burned: 18 (million)
% 3.08/1.70 % (19953)------------------------------
% 3.08/1.70 % (19953)------------------------------
% 3.08/1.70 % (19954)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_19715 for (2999ds/710Mi)
% 3.08/1.70 % (19955)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19715 for (2999ds/6Mi)
% 3.08/1.70 % (19955)Instruction limit reached!
% 3.08/1.70 % (19955)------------------------------
% 3.08/1.70 % (19955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.70 % (19955)Termination reason: Unknown
% 3.08/1.70 % (19955)Termination phase: shuffling
% 3.08/1.70
% 3.08/1.70 % (19955)Memory used [KB]: 1535
% 3.08/1.70 % (19955)Time elapsed: 0.003 s
% 3.08/1.70 % (19955)Instructions burned: 6 (million)
% 3.08/1.70 % (19955)------------------------------
% 3.08/1.70 % (19955)------------------------------
% 3.08/1.71 % (19957)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_19715 for (2999ds/21Mi)
% 3.08/1.71 % (19958)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_19715 for (2998ds/5Mi)
% 3.08/1.71 % (19956)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_19715 for (2999ds/902Mi)
% 3.08/1.71 % (19934)Instruction limit reached!
% 3.08/1.71 % (19934)------------------------------
% 3.08/1.71 % (19934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.71 % (19934)Termination reason: Unknown
% 3.08/1.71 % (19934)Termination phase: Saturation
% 3.08/1.71
% 3.08/1.71 % (19934)Memory used [KB]: 7291
% 3.08/1.71 % (19934)Time elapsed: 0.076 s
% 3.08/1.71 % (19934)Instructions burned: 183 (million)
% 3.08/1.71 % (19934)------------------------------
% 3.08/1.71 % (19934)------------------------------
% 3.08/1.71 % (19958)Instruction limit reached!
% 3.08/1.71 % (19958)------------------------------
% 3.08/1.71 % (19958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.71 % (19958)Termination reason: Unknown
% 3.08/1.71 % (19958)Termination phase: shuffling
% 3.08/1.71
% 3.08/1.71 % (19958)Memory used [KB]: 1535
% 3.08/1.71 % (19958)Time elapsed: 0.003 s
% 3.08/1.71 % (19958)Instructions burned: 7 (million)
% 3.08/1.71 % (19958)------------------------------
% 3.08/1.71 % (19958)------------------------------
% 3.08/1.71 % (19957)Instruction limit reached!
% 3.08/1.71 % (19957)------------------------------
% 3.08/1.71 % (19957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.71 % (19957)Termination reason: Unknown
% 3.08/1.71 % (19957)Termination phase: shuffling
% 3.08/1.71
% 3.08/1.71 % (19957)Memory used [KB]: 1791
% 3.08/1.71 % (19957)Time elapsed: 0.009 s
% 3.08/1.71 % (19957)Instructions burned: 21 (million)
% 3.08/1.71 % (19957)------------------------------
% 3.08/1.71 % (19957)------------------------------
% 3.08/1.72 % (19960)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_19715 for (2998ds/377Mi)
% 3.08/1.72 % (19959)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_19715 for (2998ds/6Mi)
% 3.08/1.72 % (19961)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_19715 for (2998ds/779Mi)
% 3.08/1.72 % (19959)Instruction limit reached!
% 3.08/1.72 % (19959)------------------------------
% 3.08/1.72 % (19959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.72 % (19959)Termination reason: Unknown
% 3.08/1.72 % (19959)Termination phase: shuffling
% 3.08/1.72
% 3.08/1.72 % (19959)Memory used [KB]: 1535
% 3.08/1.72 % (19959)Time elapsed: 0.003 s
% 3.08/1.72 % (19959)Instructions burned: 7 (million)
% 3.08/1.72 % (19959)------------------------------
% 3.08/1.72 % (19959)------------------------------
% 3.08/1.73 % (19954)First to succeed.
% 3.08/1.74 % (19962)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_19715 for (2998ds/19Mi)
% 3.08/1.74 % (19954)Refutation found. Thanks to Tanya!
% 3.08/1.74 % SZS status Theorem for DTF2THF_19715
% 3.08/1.74 % SZS output start Proof for DTF2THF_19715
% 3.08/1.74 thf(type_def_6, type, option: ($tType) > $tType).
% 3.08/1.74 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 3.08/1.74 thf(type_def_8, type, set: ($tType) > $tType).
% 3.08/1.74 thf(type_def_9, type, fml: $tType).
% 3.08/1.74 thf(type_def_10, type, variable: $tType).
% 3.08/1.74 thf(type_def_11, type, trm: $tType).
% 3.08/1.74 thf(type_def_12, type, char: $tType).
% 3.08/1.74 thf(type_def_13, type, real: $tType).
% 3.08/1.74 thf(type_def_14, type, game: $tType).
% 3.08/1.74 thf(type_def_15, type, denotational_interp: $tType).
% 3.08/1.74 thf(func_def_0, type, denotational_interp: $tType).
% 3.08/1.74 thf(func_def_1, type, product_prod: ($tType * $tType) > $tType).
% 3.08/1.74 thf(func_def_2, type, variable: $tType).
% 3.08/1.74 thf(func_def_3, type, option: ($tType) > $tType).
% 3.08/1.74 thf(func_def_4, type, game: $tType).
% 3.08/1.74 thf(func_def_5, type, char: $tType).
% 3.08/1.74 thf(func_def_6, type, trm: $tType).
% 3.08/1.74 thf(func_def_7, type, fml: $tType).
% 3.08/1.74 thf(func_def_8, type, real: $tType).
% 3.08/1.74 thf(func_def_9, type, set: ($tType) > $tType).
% 3.08/1.74 thf(func_def_10, type, bounded_lattice: !>[X0: $tType]:($o)).
% 3.08/1.74 thf(func_def_11, type, type: !>[X0: $tType]:($o)).
% 3.08/1.74 thf(func_def_12, type, bot: !>[X0: $tType]:($o)).
% 3.08/1.74 thf(func_def_13, type, lattice: !>[X0: $tType]:($o)).
% 3.08/1.74 thf(func_def_14, type, semilattice_inf: !>[X0: $tType]:($o)).
% 3.08/1.74 thf(func_def_15, type, bounded_lattice_bot: !>[X0: $tType]:($o)).
% 3.08/1.74 thf(func_def_16, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 3.08/1.74 thf(func_def_17, type, inf_inf: !>[X0: $tType]:(X0 > X0 > X0)).
% 3.08/1.74 thf(func_def_18, type, combine_options: !>[X0: $tType]:((X0 > X0 > X0) > option @ X0 > option @ X0 > option @ X0)).
% 3.08/1.74 thf(func_def_19, type, none: !>[X0: $tType]:(option @ X0)).
% 3.08/1.74 thf(func_def_20, type, some: !>[X0: $tType]:(X0 > option @ X0)).
% 3.08/1.74 thf(func_def_21, type, case_option: !>[X0: $tType, X1: $tType]:(X0 > (X1 > X0) > option @ X1 > X0)).
% 3.08/1.74 thf(func_def_22, type, the: !>[X0: $tType]:(option @ X0 > X0)).
% 3.08/1.74 thf(func_def_23, type, bot_bot: !>[X0: $tType]:(X0)).
% 3.08/1.74 thf(func_def_24, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 3.08/1.74 thf(func_def_25, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 3.08/1.74 thf(func_def_26, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 3.08/1.74 thf(func_def_27, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 3.08/1.74 thf(func_def_28, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 3.08/1.74 thf(func_def_29, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 3.08/1.74 thf(func_def_30, type, static_FVF: fml > set @ variable).
% 3.08/1.74 thf(func_def_31, type, static_FVT: trm > set @ variable).
% 3.08/1.74 thf(func_def_32, type, char2: $o > $o > $o > $o > $o > $o > $o > $o > char).
% 3.08/1.74 thf(func_def_33, type, geq: trm > trm > fml).
% 3.08/1.74 thf(func_def_34, type, pred: char > trm > fml).
% 3.08/1.74 thf(func_def_35, type, const: char > trm).
% 3.08/1.74 thf(func_def_36, type, differential: trm > trm).
% 3.08/1.74 thf(func_def_37, type, func: char > trm > trm).
% 3.08/1.74 thf(func_def_38, type, number: real > trm).
% 3.08/1.74 thf(func_def_39, type, plus: trm > trm > trm).
% 3.08/1.74 thf(func_def_40, type, times: trm > trm > trm).
% 3.08/1.74 thf(func_def_41, type, var: variable > trm).
% 3.08/1.74 thf(func_def_42, type, uSubst259074819ntialo: option @ trm > option @ trm).
% 3.08/1.74 thf(func_def_43, type, uSubst1556497037e_Geqo: option @ trm > option @ trm > option @ fml).
% 3.08/1.74 thf(func_def_44, type, uSubst864323244qo_rel: product_prod @ option @ trm @ option @ trm > product_prod @ option @ trm @ option @ trm > $o).
% 3.08/1.74 thf(func_def_45, type, uSubst1112714340_Pluso: option @ trm > option @ trm > option @ trm).
% 3.08/1.74 thf(func_def_46, type, uSubst270600597so_rel: product_prod @ option @ trm @ option @ trm > product_prod @ option @ trm @ option @ trm > $o).
% 3.08/1.74 thf(func_def_47, type, uSubst277968634Timeso: option @ trm > option @ trm > option @ trm).
% 3.08/1.74 thf(func_def_48, type, uSubst1377811071so_rel: product_prod @ option @ trm @ option @ trm > product_prod @ option @ trm @ option @ trm > $o).
% 3.08/1.74 thf(func_def_49, type, uSubst_Mirabelle_dot: trm).
% 3.08/1.74 thf(func_def_50, type, uSubst969145931substt: trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 3.08/1.74 thf(func_def_51, 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).
% 3.08/1.74 thf(func_def_52, 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).
% 3.08/1.74 thf(func_def_53, type, uSubst95898992stappt: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > option @ trm).
% 3.08/1.74 thf(func_def_54, 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).
% 3.08/1.74 thf(func_def_55, type, accp: !>[X0: $tType]:((X0 > X0 > $o) > X0 > $o)).
% 3.08/1.74 thf(func_def_56, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 3.08/1.74 thf(func_def_57, type, u: set @ variable).
% 3.08/1.74 thf(func_def_58, type, v: set @ variable).
% 3.08/1.74 thf(func_def_59, type, sigma: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 3.08/1.74 thf(func_def_60, type, f: char).
% 3.08/1.74 thf(func_def_75, type, sK0: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 3.08/1.74 thf(func_def_76, type, sK1: char > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > trm).
% 3.08/1.74 thf(func_def_77, type, sK2: product_prod @ option @ fml @ option @ fml > fml).
% 3.08/1.74 thf(func_def_78, type, sK3: product_prod @ option @ fml @ option @ fml > fml).
% 3.08/1.74 thf(func_def_79, type, sK4: product_prod @ option @ fml @ option @ fml > option @ fml).
% 3.08/1.74 thf(func_def_80, type, sK5: product_prod @ option @ fml @ option @ fml > fml).
% 3.08/1.74 thf(func_def_81, type, sK6: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > product_prod @ X1 @ X0 > X1)).
% 3.08/1.74 thf(func_def_82, type, sK7: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > product_prod @ X1 @ X0 > X0)).
% 3.08/1.74 thf(func_def_83, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > product_prod @ X1 @ X0 > (X1 > X0 > X2 > $o) > X1)).
% 3.08/1.74 thf(func_def_84, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > product_prod @ X1 @ X0 > (X1 > X0 > X2 > $o) > X0)).
% 3.08/1.74 thf(func_def_85, type, sK10: (char > option @ trm > $o) > char).
% 3.08/1.74 thf(func_def_86, type, sK11: (char > option @ trm > $o) > char).
% 3.08/1.74 thf(func_def_87, type, sK12: (char > option @ trm > $o) > trm).
% 3.08/1.74 thf(func_def_88, type, sK13: product_prod @ option @ game @ option @ game > game).
% 3.08/1.74 thf(func_def_89, type, sK14: product_prod @ option @ game @ option @ game > game).
% 3.08/1.74 thf(func_def_90, type, sK15: product_prod @ option @ game @ option @ game > option @ game).
% 3.08/1.74 thf(func_def_91, type, sK16: product_prod @ option @ game @ option @ game > game).
% 3.08/1.74 thf(func_def_92, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X1 > $o) > X0)).
% 3.08/1.74 thf(func_def_93, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X1 > $o) > X2)).
% 3.08/1.74 thf(func_def_94, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X2)).
% 3.08/1.74 thf(func_def_95, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X1)).
% 3.08/1.74 thf(func_def_96, type, sK21: product_prod @ variable @ option @ trm > variable).
% 3.08/1.74 thf(func_def_97, type, sK22: product_prod @ variable @ option @ trm > trm).
% 3.08/1.74 thf(func_def_98, type, sK23: product_prod @ variable @ option @ trm > variable).
% 3.08/1.74 thf(func_def_99, type, sK24: product_prod @ variable @ option @ fml > variable).
% 3.08/1.74 thf(func_def_100, type, sK25: product_prod @ variable @ option @ fml > variable).
% 3.08/1.74 thf(func_def_101, type, sK26: product_prod @ variable @ option @ fml > fml).
% 3.08/1.74 thf(func_def_102, type, sK27: product_prod @ option @ game @ option @ fml > option @ fml).
% 3.08/1.74 thf(func_def_103, type, sK28: product_prod @ option @ game @ option @ fml > game).
% 3.08/1.74 thf(func_def_104, type, sK29: product_prod @ option @ game @ option @ fml > game).
% 3.08/1.74 thf(func_def_105, type, sK30: product_prod @ option @ game @ option @ fml > fml).
% 3.08/1.74 thf(func_def_106, type, sK31: (variable > option @ trm > $o) > variable).
% 3.08/1.74 thf(func_def_107, type, sK32: (variable > option @ trm > $o) > trm).
% 3.08/1.74 thf(func_def_108, type, sK33: (variable > option @ trm > $o) > variable).
% 3.08/1.74 thf(func_def_109, type, sK34: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > (X0 > X1 > $o) > X0)).
% 3.08/1.74 thf(func_def_110, type, sK35: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > (X0 > X1 > $o) > X1)).
% 3.08/1.74 thf(func_def_111, type, sK36: char > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > trm).
% 3.08/1.74 thf(func_def_112, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > (X0 > X1 > X2 > $o) > product_prod @ X0 @ X1 > X0)).
% 3.08/1.74 thf(func_def_113, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > (X0 > X1 > X2 > $o) > product_prod @ X0 @ X1 > X1)).
% 3.08/1.74 thf(func_def_114, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ X1 > X0) > (X2 > X1 > X0) > X2)).
% 3.08/1.74 thf(func_def_115, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ X1 > X0) > (X2 > X1 > X0) > X1)).
% 3.08/1.74 thf(f818,plain,(
% 3.08/1.74 $false),
% 3.08/1.74 inference(avatar_sat_refutation,[status(thm)],[f788,f802,f808,f813,f814,f817])).
% 3.08/1.74 thf(f817,plain,(
% 3.08/1.74 ~spl41_2 | ~spl41_6),
% 3.08/1.74 inference(avatar_contradiction_clause,[status(thm)],[f816])).
% 3.08/1.74 thf(f816,plain,(
% 3.08/1.74 $false | (~spl41_2 | ~spl41_6)),
% 3.08/1.74 inference(subsumption_resolution,[status(thm)],[f815,f811])).
% 3.08/1.74 thf(f811,plain,(
% 3.08/1.74 ((uSubst1138577137pconst @ sigma @ v @ f) != (uSubst1138577137pconst @ sigma @ u @ f))),
% 3.08/1.74 inference(backward_demodulation,[status(thm)],[f732,f737])).
% 3.08/1.74 thf(f737,plain,(
% 3.08/1.74 ( ! [X2 : char,X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X1 : set @ variable] : (((uSubst95898992stappt @ X0 @ X1 @ (const @ X2)) = (uSubst1138577137pconst @ X0 @ X1 @ X2))) )),
% 3.08/1.74 inference(cnf_transformation,[status(thm)],[f637])).
% 3.08/1.74 thf(f637,plain,(
% 3.08/1.74 ! [X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X1 : set @ variable,X2 : char] : ((uSubst95898992stappt @ X0 @ X1 @ (const @ X2)) = (uSubst1138577137pconst @ X0 @ X1 @ X2))),
% 3.08/1.74 inference(rectify,[status(thm)],[f8])).
% 3.08/1.74 thf(f8,axiom,(
% 3.08/1.74 ! [X16 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X17 : set @ variable,X18 : char] : ((uSubst95898992stappt @ X16 @ X17 @ (const @ X18)) = (uSubst1138577137pconst @ X16 @ X17 @ X18))),
% 3.08/1.74 file('/export/starexec/sandbox2/tmp/tmp.WzKSSIg5X4/DTF2THF_19715.p',fact_7_usubstappt_Osimps_I3_J)).
% 3.08/1.74 thf(f732,plain,(
% 3.08/1.74 ((uSubst95898992stappt @ sigma @ u @ (const @ f)) != (uSubst1138577137pconst @ sigma @ v @ f))),
% 3.08/1.74 inference(cnf_transformation,[status(thm)],[f670])).
% 3.08/1.74 thf(f670,plain,(
% 3.08/1.74 ((uSubst95898992stappt @ sigma @ u @ (const @ f)) != (uSubst1138577137pconst @ sigma @ v @ f)) & (none @ trm != (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))),
% 3.08/1.74 inference(ennf_transformation,[status(thm)],[f585])).
% 3.08/1.74 thf(f585,plain,(
% 3.08/1.74 ~(((uSubst95898992stappt @ sigma @ u @ (const @ f)) = (uSubst1138577137pconst @ sigma @ v @ f)) | (none @ trm = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)))),
% 3.08/1.74 inference(fool_elimination,[status(thm)],[f584])).
% 3.08/1.74 thf(f584,plain,(
% 3.08/1.74 ~(((uSubst95898992stappt @ sigma @ u @ (const @ f)) = (uSubst1138577137pconst @ sigma @ v @ f)) | ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X0 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X1 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X2 : char > option @ fml, X3 : char > option @ game] : (X0)))))) @ sigma @ f) = none @ trm))),
% 3.08/1.74 inference(rectify,[status(thm)],[f277])).
% 3.08/1.74 thf(f277,negated_conjecture,(
% 3.08/1.74 ~(((uSubst95898992stappt @ sigma @ u @ (const @ f)) = (uSubst1138577137pconst @ sigma @ v @ f)) | ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X7)))))) @ sigma @ f) = none @ trm))),
% 3.08/1.74 inference(negated_conjecture,[status(cth)],[f276])).
% 3.08/1.74 thf(f276,conjecture,(
% 3.08/1.74 ((uSubst95898992stappt @ sigma @ u @ (const @ f)) = (uSubst1138577137pconst @ sigma @ v @ f)) | ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X7)))))) @ sigma @ f) = none @ trm)),
% 3.08/1.74 file('/export/starexec/sandbox2/tmp/tmp.WzKSSIg5X4/DTF2THF_19715.p',conj_0)).
% 3.08/1.74 thf(f815,plain,(
% 3.08/1.74 ((uSubst1138577137pconst @ sigma @ v @ f) = (uSubst1138577137pconst @ sigma @ u @ f)) | (~spl41_2 | ~spl41_6)),
% 3.08/1.74 inference(forward_demodulation,[status(thm)],[f801,f783])).
% 3.08/1.74 thf(f783,plain,(
% 3.08/1.74 ((uSubst1138577137pconst @ sigma @ u @ f) = (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)))) | ~spl41_2),
% 3.08/1.74 inference(avatar_component_clause,[status(thm)],[f781])).
% 3.08/1.74 thf(f781,definition,(
% 3.08/1.74 spl41_2 <=> ((uSubst1138577137pconst @ sigma @ u @ f) = (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))))),
% 3.08/1.74 introduced(definition,[new_symbols(naming,[spl41_2])],[avatar_definition])).
% 3.08/1.74 thf(f801,plain,(
% 3.08/1.74 ((uSubst1138577137pconst @ sigma @ v @ f) = (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)))) | ~spl41_6),
% 3.08/1.74 inference(avatar_component_clause,[status(thm)],[f799])).
% 3.08/1.74 thf(f799,definition,(
% 3.08/1.74 spl41_6 <=> ((uSubst1138577137pconst @ sigma @ v @ f) = (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))))),
% 3.08/1.74 introduced(definition,[new_symbols(naming,[spl41_6])],[avatar_definition])).
% 3.08/1.74 thf(f814,plain,(
% 3.08/1.74 spl41_3 | spl41_1),
% 3.08/1.74 inference(avatar_split_clause,[status(thm)],[f728,f777,f785])).
% 3.08/1.74 thf(f785,definition,(
% 3.08/1.74 spl41_3 <=> (none @ trm = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))),
% 3.08/1.74 introduced(definition,[new_symbols(naming,[spl41_3])],[avatar_definition])).
% 3.08/1.74 thf(f777,definition,(
% 3.08/1.74 spl41_1 <=> (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ u))),
% 3.08/1.74 introduced(definition,[new_symbols(naming,[spl41_1])],[avatar_definition])).
% 3.08/1.74 thf(f728,plain,(
% 3.08/1.74 (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ u)) | (none @ trm = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))),
% 3.08/1.74 inference(cnf_transformation,[status(thm)],[f667])).
% 3.08/1.74 thf(f667,plain,(
% 3.08/1.74 (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ u)) | (none @ trm = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))),
% 3.08/1.74 inference(ennf_transformation,[status(thm)],[f477])).
% 3.08/1.74 thf(f477,plain,(
% 3.08/1.74 (none @ trm != (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)) => (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ u))),
% 3.08/1.74 inference(fool_elimination,[status(thm)],[f476])).
% 3.08/1.74 thf(f476,plain,(
% 3.08/1.74 (none @ trm != (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X0 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X1 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X2 : char > option @ fml, X3 : char > option @ game] : (X0)))))) @ sigma @ f)) => ((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X4 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X5 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X6 : char > option @ fml, X7 : char > option @ game] : (X4)))))) @ sigma @ f))) @ u) = bot_bot @ set @ variable)),
% 3.08/1.74 inference(rectify,[status(thm)],[f4])).
% 3.08/1.74 thf(f4,axiom,(
% 3.08/1.74 (none @ trm != (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X7)))))) @ sigma @ f)) => ((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X7)))))) @ sigma @ f))) @ u) = bot_bot @ set @ variable)),
% 3.08/1.74 file('/export/starexec/sandbox2/tmp/tmp.WzKSSIg5X4/DTF2THF_19715.p',fact_3_f3)).
% 3.08/1.74 thf(f813,plain,(
% 3.08/1.74 spl41_3 | spl41_5),
% 3.08/1.74 inference(avatar_split_clause,[status(thm)],[f747,f794,f785])).
% 3.08/1.74 thf(f794,definition,(
% 3.08/1.74 spl41_5 <=> (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ v))),
% 3.08/1.74 introduced(definition,[new_symbols(naming,[spl41_5])],[avatar_definition])).
% 3.08/1.74 thf(f747,plain,(
% 3.08/1.74 (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ v)) | (none @ trm = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))),
% 3.08/1.74 inference(cnf_transformation,[status(thm)],[f645])).
% 3.08/1.74 thf(f645,plain,(
% 3.08/1.74 (none @ trm = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)) | (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ v))),
% 3.08/1.74 inference(ennf_transformation,[status(thm)],[f338])).
% 3.08/1.74 thf(f338,plain,(
% 3.08/1.74 (none @ trm != (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)) => (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ v))),
% 3.08/1.74 inference(fool_elimination,[status(thm)],[f337])).
% 3.08/1.74 thf(f337,plain,(
% 3.08/1.74 (none @ trm != (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X0 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X1 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X2 : char > option @ fml, X3 : char > option @ game] : (X0)))))) @ sigma @ f)) => (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X4 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X5 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X6 : char > option @ fml, X7 : char > option @ game] : (X4)))))) @ sigma @ f))) @ v))),
% 3.08/1.74 inference(rectify,[status(thm)],[f5])).
% 3.08/1.74 thf(f5,axiom,(
% 3.08/1.74 (none @ trm != (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X7)))))) @ sigma @ f)) => (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X7)))))) @ sigma @ f))) @ v))),
% 3.08/1.74 file('/export/starexec/sandbox2/tmp/tmp.WzKSSIg5X4/DTF2THF_19715.p',fact_4__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062)).
% 3.08/1.74 thf(f808,plain,(
% 3.08/1.74 ~spl41_3),
% 3.08/1.74 inference(avatar_split_clause,[status(thm)],[f731,f785])).
% 3.08/1.74 thf(f731,plain,(
% 3.08/1.74 (none @ trm != (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))),
% 3.08/1.74 inference(cnf_transformation,[status(thm)],[f670])).
% 3.08/1.74 thf(f802,plain,(
% 3.08/1.74 ~spl41_5 | spl41_3 | spl41_6),
% 3.08/1.74 inference(avatar_split_clause,[status(thm)],[f770,f799,f785,f794])).
% 3.08/1.74 thf(f770,plain,(
% 3.08/1.74 ((uSubst1138577137pconst @ sigma @ v @ f) = (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)))) | (bot_bot @ set @ variable != (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ v)) | (none @ trm = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))),
% 3.08/1.74 inference(cnf_transformation,[status(thm)],[f666])).
% 3.08/1.74 thf(f666,plain,(
% 3.08/1.74 (((none @ trm = (uSubst1138577137pconst @ sigma @ v @ f)) | (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ v))) & ((bot_bot @ set @ variable != (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ v)) | ((uSubst1138577137pconst @ sigma @ v @ f) = (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)))))) | (none @ trm = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))),
% 3.08/1.74 inference(ennf_transformation,[status(thm)],[f607])).
% 3.08/1.74 thf(f607,plain,(
% 3.08/1.74 (none @ trm != (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)) => (((bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ v)) => ((uSubst1138577137pconst @ sigma @ v @ f) = (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))))) & ((bot_bot @ set @ variable != (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ v)) => (none @ trm = (uSubst1138577137pconst @ sigma @ v @ f))))),
% 3.08/1.74 inference(fool_elimination,[status(thm)],[f606])).
% 3.08/1.74 thf(f606,plain,(
% 3.08/1.74 ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X0 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X1 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X2 : char > option @ fml, X3 : char > option @ game] : (X0)))))) @ sigma @ f) != none @ trm) => ((((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X4 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X5 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X6 : char > option @ fml, X7 : char > option @ game] : (X4)))))) @ sigma @ f))) @ v) = bot_bot @ set @ variable) => ((uSubst1138577137pconst @ sigma @ v @ f) = (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X9 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X10 : char > option @ fml, X11 : char > option @ game] : (X8)))))) @ sigma @ f))))) & ((bot_bot @ set @ variable != (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X12 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X13 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X14 : char > option @ fml, X15 : char > option @ game] : (X12)))))) @ sigma @ f))) @ v)) => (none @ trm = (uSubst1138577137pconst @ sigma @ v @ f))))),
% 3.08/1.74 inference(rectify,[status(thm)],[f10])).
% 3.08/1.74 thf(f10,axiom,(
% 3.08/1.74 ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X7)))))) @ sigma @ f) != none @ trm) => ((((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X7)))))) @ sigma @ f))) @ v) = bot_bot @ set @ variable) => ((uSubst1138577137pconst @ sigma @ v @ f) = (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X7)))))) @ sigma @ f))))) & ((bot_bot @ set @ variable != (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X7)))))) @ sigma @ f))) @ v)) => (none @ trm = (uSubst1138577137pconst @ sigma @ v @ f))))),
% 3.08/1.74 file('/export/starexec/sandbox2/tmp/tmp.WzKSSIg5X4/DTF2THF_19715.p',fact_9__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AV_Af_092_060close_062)).
% 3.08/1.74 thf(f788,plain,(
% 3.08/1.74 ~spl41_1 | spl41_2 | spl41_3),
% 3.08/1.74 inference(avatar_split_clause,[status(thm)],[f744,f785,f781,f777])).
% 3.08/1.74 thf(f744,plain,(
% 3.08/1.74 ((uSubst1138577137pconst @ sigma @ u @ f) = (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)))) | (bot_bot @ set @ variable != (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ u)) | (none @ trm = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))),
% 3.08/1.74 inference(cnf_transformation,[status(thm)],[f660])).
% 3.08/1.74 thf(f660,plain,(
% 3.08/1.74 (none @ trm = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)) | (((bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ u)) | (none @ trm = (uSubst1138577137pconst @ sigma @ u @ f))) & (((uSubst1138577137pconst @ sigma @ u @ f) = (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)))) | (bot_bot @ set @ variable != (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ u))))),
% 3.08/1.74 inference(ennf_transformation,[status(thm)],[f346])).
% 3.08/1.74 thf(f346,plain,(
% 3.08/1.74 (none @ trm != (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)) => (((bot_bot @ set @ variable != (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ u)) => (none @ trm = (uSubst1138577137pconst @ sigma @ u @ f))) & ((bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ u)) => ((uSubst1138577137pconst @ sigma @ u @ f) = (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))))))),
% 3.08/1.74 inference(fool_elimination,[status(thm)],[f345])).
% 3.08/1.74 thf(f345,plain,(
% 3.08/1.74 (none @ trm != (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X0 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X1 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X2 : char > option @ fml, X3 : char > option @ game] : (X0)))))) @ sigma @ f)) => ((((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X4 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X5 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X6 : char > option @ fml, X7 : char > option @ game] : (X4)))))) @ sigma @ f))) @ u) != bot_bot @ set @ variable) => (none @ trm = (uSubst1138577137pconst @ sigma @ u @ f))) & ((bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X9 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X10 : char > option @ fml, X11 : char > option @ game] : (X8)))))) @ sigma @ f))) @ u)) => ((uSubst1138577137pconst @ sigma @ u @ f) = (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X12 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X13 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X14 : char > option @ fml, X15 : char > option @ game] : (X12)))))) @ sigma @ f))))))),
% 3.08/1.74 inference(rectify,[status(thm)],[f11])).
% 3.08/1.74 thf(f11,axiom,(
% 3.08/1.74 (none @ trm != (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X7)))))) @ sigma @ f)) => ((((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X7)))))) @ sigma @ f))) @ u) != bot_bot @ set @ variable) => (none @ trm = (uSubst1138577137pconst @ sigma @ u @ f))) & ((bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X7)))))) @ sigma @ f))) @ u)) => ((uSubst1138577137pconst @ sigma @ u @ f) = (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X7)))))) @ sigma @ f))))))),
% 3.08/1.74 file('/export/starexec/sandbox2/tmp/tmp.WzKSSIg5X4/DTF2THF_19715.p',fact_10__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AU_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AU_Af_092_060close_062)).
% 3.08/1.74 % SZS output end Proof for DTF2THF_19715
% 3.08/1.74 % (19954)------------------------------
% 3.08/1.74 % (19954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.74 % (19954)Termination reason: Refutation
% 3.08/1.74
% 3.08/1.74 % (19954)Memory used [KB]: 6908
% 3.08/1.74 % (19954)Time elapsed: 0.037 s
% 3.08/1.74 % (19954)Instructions burned: 102 (million)
% 3.08/1.74 % (19954)------------------------------
% 3.08/1.74 % (19954)------------------------------
% 3.08/1.74 % (19933)Success in time 0.135 s
%------------------------------------------------------------------------------