%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP204^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 08:56:24 AM UTC 2026
% Result : Theorem 3.07s 1.81s
% Output : Refutation 3.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP204^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n005.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:29:45 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : ITP204^2 : 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_793__6341386_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_793__6341386_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 : 338 ( 111 unt; 51 typ; 0 def)
% 0.30/0.46 % Number of atoms : 739 ( 338 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 13 ( 2 avg)
% 0.30/0.46 % Number of connectives : 5346 ( 110 ~; 25 |; 53 &;4816 @)
% 0.30/0.46 % ( 0 <=>; 342 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 22 ( 7 avg)
% 0.30/0.46 % Number of types : 6 ( 5 usr)
% 0.30/0.46 % Number of type conns : 955 ( 955 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 49 ( 46 usr; 7 con; 0-5 aty)
% 0.30/0.46 % Number of variables : 1181 ( 268 ^; 867 !; 15 ?;1181 :)
% 0.30/0.46 % ( 31 !>; 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 16:20:54.337
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % Could-be-implicit typings (8)
% 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_Set_Oset,type,
% 0.30/0.46 set: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 % Explicit typings (43)
% 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_Orderings_Oord,type,
% 0.30/0.46 ord:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.30/0.46 order:
% 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_Orderings_Olinorder,type,
% 0.30/0.46 linorder:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Opreorder,type,
% 0.30/0.46 preorder:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Oorder__bot,type,
% 0.30/0.46 order_bot:
% 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_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_Orderings_Oord__class_Oless__eq,type,
% 0.30/0.46 ord_less_eq:
% 0.30/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 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_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_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_OFunc,type,
% 0.30/0.46 func: char > trm > 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_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_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_Ua____,type,
% 0.30/0.46 ua: set @ variable ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_Va____,type,
% 0.30/0.46 va: 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__092_060theta_062____,type,
% 0.30/0.46 theta: trm ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_p____,type,
% 0.30/0.46 p: char ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_vv____,type,
% 0.30/0.46 vv: ( set @ variable ) > ( set @ variable ) > variable ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_vva____,type,
% 0.30/0.46 vva: ( set @ variable ) > ( set @ variable ) > variable ).
% 0.30/0.46
% 0.30/0.46 % Relevant facts (255)
% 0.30/0.46 thf(fact_0__092_060open_062_092_060forall_062x0_Ax1_O_A_I_092_060exists_062v2_O_Av2_A_092_060in_062_Ax1_A_092_060and_062_A_I_092_060exists_062v3_O_Av3_A_092_060in_062_Ax0_A_092_060and_062_Av2_A_061_Av3_J_J_A_061_A_Ivv_Ax0_Ax1_A_092_060in_062_Ax1_A_092_060and_062_A_I_092_060exists_062v3_O_Av3_A_092_060in_062_Ax0_A_092_060and_062_Avv_Ax0_Ax1_A_061_Av3_J_J_092_060close_062,axiom,
% 0.30/0.46 ! [X0: set @ variable,X1: set @ variable] :
% 0.30/0.46 ( ( ? [V2: variable] :
% 0.30/0.46 ( ( member @ variable @ V2 @ X1 )
% 0.30/0.46 & ? [V3: variable] :
% 0.30/0.46 ( ( member @ variable @ V3 @ X0 )
% 0.30/0.46 & ( V2 = V3 ) ) ) )
% 0.30/0.46 = ( ( member @ variable @ ( vv @ X0 @ X1 ) @ X1 )
% 0.30/0.46 & ? [V3: variable] :
% 0.30/0.46 ( ( member @ variable @ V3 @ X0 )
% 0.30/0.46 & ( ( vv @ X0 @ X1 )
% 0.30/0.46 = V3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>\<forall>x0 x1. (\<exists>v2. v2 \<in> x1 \<and> (\<exists>v3. v3 \<in> x0 \<and> v2 = v3)) = (vv x0 x1 \<in> x1 \<and> (\<exists>v3. v3 \<in> x0 \<and> vv x0 x1 = v3))\<close>
% 0.30/0.46 thf(fact_1_Pred_Oprems_I2_J,axiom,
% 0.30/0.46 ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.30/0.46 != ( none @ fml ) ) ).
% 0.30/0.46
% 0.30/0.46 % Pred.prems(2)
% 0.30/0.46 thf(fact_2__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Aundeff_092_060close_062,axiom,
% 0.30/0.46 ~ ( ( ( inf_inf @ ( set @ variable )
% 0.30/0.46 @ ( static_FVF
% 0.30/0.46 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) ) )
% 0.30/0.46 @ va )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 => ( ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) )
% 0.30/0.46 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) ) )
% 0.30/0.46 = ( none @ fml ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>(if FVF (the (SPreds \<sigma> p)) \<inter> V = {} then usubstappf (dotsubstt (the (usubstappt \<sigma> V \<theta>))) {} (the (SPreds \<sigma> p)) else undeff) \<noteq> undeff\<close>
% 0.30/0.46 thf(fact_3__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_A_092_060Longrightarrow_062_ASPreds_A_092_060sigma_062_Ap_A_061_Aundeff_092_060close_062,axiom,
% 0.30/0.46 ( ~ ( ( ( ( inf_inf @ ( set @ variable )
% 0.30/0.46 @ ( static_FVF
% 0.30/0.46 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) ) )
% 0.30/0.46 @ va )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 => ( ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) )
% 0.30/0.46 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) ) )
% 0.30/0.46 = ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) )
% 0.30/0.46 & ( ( ( inf_inf @ ( set @ variable )
% 0.30/0.46 @ ( static_FVF
% 0.30/0.46 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) ) )
% 0.30/0.46 @ va )
% 0.30/0.46 != ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 => ( ( none @ fml )
% 0.30/0.46 = ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) )
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p )
% 0.30/0.46 = ( none @ fml ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>(if FVF (the (SPreds \<sigma> p)) \<inter> V = {} then usubstappf (dotsubstt (the (usubstappt \<sigma> V \<theta>))) {} (the (SPreds \<sigma> p)) else undeff) \<noteq> usubstappf \<sigma> V (Pred p \<theta>) \<Longrightarrow> SPreds \<sigma> p = undeff\<close>
% 0.30/0.46 thf(fact_4_usubstappf__det,axiom,
% 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,Phi: fml,V: set @ variable] :
% 0.30/0.46 ( ( ( uSubst95898978stappf @ Sigma @ U @ Phi )
% 0.30/0.46 != ( none @ fml ) )
% 0.30/0.46 => ( ( ( uSubst95898978stappf @ Sigma @ V @ Phi )
% 0.30/0.46 != ( none @ fml ) )
% 0.30/0.46 => ( ( uSubst95898978stappf @ Sigma @ U @ Phi )
% 0.30/0.46 = ( uSubst95898978stappf @ Sigma @ V @ Phi ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappf_det
% 0.30/0.46 thf(fact_5_f8,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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p )
% 0.30/0.46 = ( none @ fml ) )
% 0.30/0.46 => ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.30/0.46 = ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % f8
% 0.30/0.46 thf(fact_6__092_060open_062vv_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060notin_062_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060or_062_Avva_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060notin_062_AV_A_092_060or_062_Avv_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060noteq_062_Avva_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_092_060close_062,axiom,
% 0.30/0.46 ( ~ ( member @ variable
% 0.30/0.46 @ ( vv @ va
% 0.30/0.46 @ ( static_FVF
% 0.30/0.46 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) ) ) )
% 0.30/0.46 @ ( static_FVF
% 0.30/0.46 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) ) ) )
% 0.30/0.46 | ~ ( member @ variable
% 0.30/0.46 @ ( vva @ va
% 0.30/0.46 @ ( static_FVF
% 0.30/0.46 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) ) ) )
% 0.30/0.46 @ va )
% 0.30/0.46 | ( ( vv @ va
% 0.30/0.46 @ ( static_FVF
% 0.30/0.46 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) ) ) )
% 0.30/0.46 != ( vva @ va
% 0.30/0.46 @ ( static_FVF
% 0.30/0.46 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>vv V (FVF (the (SPreds \<sigma> p))) \<notin> FVF (the (SPreds \<sigma> p)) \<or> vva V (FVF (the (SPreds \<sigma> p))) \<notin> V \<or> vv V (FVF (the (SPreds \<sigma> p))) \<noteq> vva V (FVF (the (SPreds \<sigma> p)))\<close>
% 0.30/0.46 thf(fact_7_fml_Oinject_I1_J,axiom,
% 0.30/0.46 ! [X11: char,X12: trm,Y11: char,Y12: trm] :
% 0.30/0.46 ( ( ( pred @ X11 @ X12 )
% 0.30/0.46 = ( pred @ Y11 @ Y12 ) )
% 0.30/0.46 = ( ( X11 = Y11 )
% 0.30/0.46 & ( X12 = Y12 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % fml.inject(1)
% 0.30/0.46 thf(fact_8_f7,axiom,
% 0.30/0.46 ( ( uSubst95898992stappt @ sigma @ ua @ theta )
% 0.30/0.46 = ( uSubst95898992stappt @ sigma @ va @ theta ) ) ).
% 0.30/0.46
% 0.30/0.46 % f7
% 0.30/0.46 thf(fact_9_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 = ( ^ [F: 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] : ( F @ 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_10_f1,axiom,
% 0.30/0.46 ! [V4: variable] :
% 0.30/0.46 ( ~ ( member @ variable @ V4 @ va )
% 0.30/0.46 | ( member @ variable @ V4 @ ua ) ) ).
% 0.30/0.46
% 0.30/0.46 % f1
% 0.30/0.46 thf(fact_11_f10,axiom,
% 0.30/0.46 ( ( ( ( inf_inf @ ( set @ variable )
% 0.30/0.46 @ ( static_FVF
% 0.30/0.46 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) ) )
% 0.30/0.46 @ va )
% 0.30/0.46 != ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 | ! [V4: variable] :
% 0.30/0.46 ( ~ ( member @ variable @ V4
% 0.30/0.46 @ ( static_FVF
% 0.30/0.46 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) ) ) )
% 0.30/0.46 | ! [Va: variable] :
% 0.30/0.46 ( ~ ( member @ variable @ Va @ va )
% 0.30/0.46 | ( V4 != Va ) ) ) )
% 0.30/0.46 & ( ( ( inf_inf @ ( set @ variable )
% 0.30/0.46 @ ( static_FVF
% 0.30/0.46 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) ) )
% 0.30/0.46 @ va )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 | ( ( member @ variable
% 0.30/0.46 @ ( vv @ va
% 0.30/0.46 @ ( static_FVF
% 0.30/0.46 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) ) ) )
% 0.30/0.46 @ ( static_FVF
% 0.30/0.46 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) ) ) )
% 0.30/0.46 & ( member @ variable
% 0.30/0.46 @ ( vva @ va
% 0.30/0.46 @ ( static_FVF
% 0.30/0.46 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) ) ) )
% 0.30/0.46 @ va )
% 0.30/0.46 & ( ( vv @ va
% 0.30/0.46 @ ( static_FVF
% 0.30/0.46 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) ) ) )
% 0.30/0.46 = ( vva @ va
% 0.30/0.46 @ ( static_FVF
% 0.30/0.46 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % f10
% 0.30/0.46 thf(fact_12_prod_Ocase__distrib,axiom,
% 0.30/0.46 ! [C: $tType,D: $tType,B: $tType,A: $tType,H: C > D,F2: A > B > C,Prod: product_prod @ A @ B] :
% 0.30/0.46 ( ( H @ ( product_case_prod @ A @ B @ C @ F2 @ Prod ) )
% 0.30/0.46 = ( product_case_prod @ A @ B @ D
% 0.30/0.46 @ ^ [X13: A,X2: B] : ( H @ ( F2 @ X13 @ X2 ) )
% 0.30/0.46 @ Prod ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod.case_distrib
% 0.30/0.46 thf(fact_13_usubstappf__pred2,axiom,
% 0.30/0.46 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),P2: char,R2: fml,U: set @ variable,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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ Sigma
% 0.30/0.46 @ P2 )
% 0.30/0.46 = ( some @ fml @ R2 ) )
% 0.30/0.46 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R2 ) @ U )
% 0.30/0.46 != ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 => ( ( uSubst95898978stappf @ Sigma @ U @ ( pred @ P2 @ Theta ) )
% 0.30/0.46 = ( none @ fml ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappf_pred2
% 0.30/0.46 thf(fact_14_f2,axiom,
% 0.30/0.46 ! [Z: option @ fml,F3: fml > ( option @ fml ),Za: option @ fml] :
% 0.30/0.46 ( ( ( Za
% 0.30/0.46 = ( none @ fml ) )
% 0.30/0.46 => ( ( case_option @ ( option @ fml ) @ fml @ Z @ F3 @ Za )
% 0.30/0.46 = Z ) )
% 0.30/0.46 & ( ( Za
% 0.30/0.46 != ( none @ fml ) )
% 0.30/0.46 => ( ( case_option @ ( option @ fml ) @ fml @ Z @ F3 @ Za )
% 0.30/0.46 = ( F3 @ ( the @ fml @ Za ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % f2
% 0.30/0.46 thf(fact_15_Pred_Oprems_I1_J,axiom,
% 0.30/0.46 ord_less_eq @ ( set @ variable ) @ va @ ua ).
% 0.30/0.46
% 0.30/0.46 % Pred.prems(1)
% 0.30/0.46 thf(fact_16_f9,axiom,
% 0.30/0.46 ! [V5: set @ variable,Va2: set @ variable] :
% 0.30/0.46 ( ( ( ( inf_inf @ ( set @ variable ) @ V5 @ Va2 )
% 0.30/0.46 != ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 | ! [V4: variable] :
% 0.30/0.46 ( ~ ( member @ variable @ V4 @ V5 )
% 0.30/0.46 | ! [Va: variable] :
% 0.30/0.46 ( ~ ( member @ variable @ Va @ Va2 )
% 0.30/0.46 | ( V4 != Va ) ) ) )
% 0.30/0.46 & ( ( ( inf_inf @ ( set @ variable ) @ V5 @ Va2 )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 | ( ( member @ variable @ ( vv @ Va2 @ V5 ) @ V5 )
% 0.30/0.46 & ( member @ variable @ ( vva @ Va2 @ V5 ) @ Va2 )
% 0.30/0.46 & ( ( vv @ Va2 @ V5 )
% 0.30/0.46 = ( vva @ Va2 @ V5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % f9
% 0.30/0.46 thf(fact_17__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062vva_O_A_092_060forall_062V_AVa_O_A_IV_A_092_060inter_062_AVa_A_092_060noteq_062_A_123_125_A_092_060or_062_A_I_092_060forall_062v_O_Av_A_092_060notin_062_AV_A_092_060or_062_A_I_092_060forall_062va_O_Ava_A_092_060notin_062_AVa_A_092_060or_062_Av_A_092_060noteq_062_Ava_J_J_J_A_092_060and_062_A_IV_A_092_060inter_062_AVa_A_061_A_123_125_A_092_060or_062_Avv_AVa_AV_A_092_060in_062_AV_A_092_060and_062_Avva_AVa_AV_A_092_060in_062_AVa_A_092_060and_062_Avv_AVa_AV_A_061_Avva_AVa_AV_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.30/0.46 ~ ! [Vva: ( set @ variable ) > ( set @ variable ) > variable] :
% 0.30/0.46 ~ ! [V5: set @ variable,Va2: set @ variable] :
% 0.30/0.46 ( ( ( ( inf_inf @ ( set @ variable ) @ V5 @ Va2 )
% 0.30/0.46 != ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 | ! [V4: variable] :
% 0.30/0.46 ( ~ ( member @ variable @ V4 @ V5 )
% 0.30/0.46 | ! [Va: variable] :
% 0.30/0.46 ( ~ ( member @ variable @ Va @ Va2 )
% 0.30/0.46 | ( V4 != Va ) ) ) )
% 0.30/0.46 & ( ( ( inf_inf @ ( set @ variable ) @ V5 @ Va2 )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 | ( ( member @ variable @ ( vv @ Va2 @ V5 ) @ V5 )
% 0.30/0.46 & ( member @ variable @ ( Vva @ Va2 @ V5 ) @ Va2 )
% 0.30/0.46 & ( ( vv @ Va2 @ V5 )
% 0.30/0.46 = ( Vva @ Va2 @ V5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>\<And>thesis. (\<And>vva. \<forall>V Va. (V \<inter> Va \<noteq> {} \<or> (\<forall>v. v \<notin> V \<or> (\<forall>va. va \<notin> Va \<or> v \<noteq> va))) \<and> (V \<inter> Va = {} \<or> vv Va V \<in> V \<and> vva Va V \<in> Va \<and> vv Va V = vva Va V) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.30/0.46 thf(fact_18_option_Oinject,axiom,
% 0.30/0.46 ! [A: $tType,X22: A,Y2: A] :
% 0.30/0.46 ( ( ( some @ A @ X22 )
% 0.30/0.46 = ( some @ A @ Y2 ) )
% 0.30/0.46 = ( X22 = Y2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.inject
% 0.30/0.46 thf(fact_19_f5,axiom,
% 0.30/0.46 ( ( uSubst95898992stappt @ sigma @ ua @ theta )
% 0.30/0.46 != ( none @ trm ) ) ).
% 0.30/0.46
% 0.30/0.46 % f5
% 0.30/0.46 thf(fact_20_not__Some__eq,axiom,
% 0.30/0.46 ! [A: $tType,X3: option @ A] :
% 0.30/0.46 ( ( ! [Y: A] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( some @ A @ Y ) ) )
% 0.30/0.46 = ( X3
% 0.30/0.46 = ( none @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_Some_eq
% 0.30/0.46 thf(fact_21_not__None__eq,axiom,
% 0.30/0.46 ! [A: $tType,X3: option @ A] :
% 0.30/0.46 ( ( X3
% 0.30/0.46 != ( none @ A ) )
% 0.30/0.46 = ( ? [Y: A] :
% 0.30/0.46 ( X3
% 0.30/0.46 = ( some @ A @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_None_eq
% 0.30/0.46 thf(fact_22_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_23_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_24_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_25_option_Osplit__sel,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P3: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 0.30/0.46 ( ( P3 @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 0.30/0.46 = ( ( ( Option
% 0.30/0.46 = ( none @ A ) )
% 0.30/0.46 => ( P3 @ F1 ) )
% 0.30/0.46 & ( ( Option
% 0.30/0.46 = ( some @ A @ ( the @ A @ Option ) ) )
% 0.30/0.46 => ( P3 @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.split_sel
% 0.30/0.46 thf(fact_26_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_27_option_Osplit__sel__asm,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P3: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 0.30/0.46 ( ( P3 @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 0.30/0.46 = ( ~ ( ( ( Option
% 0.30/0.46 = ( none @ A ) )
% 0.30/0.46 & ~ ( P3 @ F1 ) )
% 0.30/0.46 | ( ( Option
% 0.30/0.46 = ( some @ A @ ( the @ A @ Option ) ) )
% 0.30/0.46 & ~ ( P3 @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.split_sel_asm
% 0.30/0.46 thf(fact_28_usubstappt__det,axiom,
% 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,Theta: trm,V: set @ variable] :
% 0.30/0.46 ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( ( uSubst95898992stappt @ Sigma @ V @ Theta )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.30/0.46 = ( uSubst95898992stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt_det
% 0.30/0.46 thf(fact_29_usubstappt__antimon,axiom,
% 0.30/0.46 ! [V: set @ variable,U: set @ variable,Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),Theta: trm] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ variable ) @ V @ U )
% 0.30/0.46 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.30/0.46 = ( uSubst95898992stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt_antimon
% 0.30/0.46 thf(fact_30_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_31_combine__options__cases,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X3: option @ A,P3: ( option @ A ) > ( option @ B ) > $o,Y3: option @ B] :
% 0.30/0.46 ( ( ( X3
% 0.30/0.46 = ( none @ A ) )
% 0.30/0.46 => ( P3 @ X3 @ Y3 ) )
% 0.30/0.46 => ( ( ( Y3
% 0.30/0.46 = ( none @ B ) )
% 0.30/0.46 => ( P3 @ X3 @ Y3 ) )
% 0.30/0.46 => ( ! [A2: A,B2: B] :
% 0.30/0.46 ( ( X3
% 0.30/0.46 = ( some @ A @ A2 ) )
% 0.30/0.46 => ( ( Y3
% 0.30/0.46 = ( some @ B @ B2 ) )
% 0.30/0.46 => ( P3 @ X3 @ Y3 ) ) )
% 0.30/0.46 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % combine_options_cases
% 0.30/0.46 thf(fact_32_split__option__all,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ^ [P4: ( option @ A ) > $o] :
% 0.30/0.46 ! [X4: option @ A] : ( P4 @ X4 ) )
% 0.30/0.46 = ( ^ [P: ( option @ A ) > $o] :
% 0.30/0.46 ( ( P @ ( none @ A ) )
% 0.30/0.46 & ! [X: A] : ( P @ ( some @ A @ X ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_option_all
% 0.30/0.46 thf(fact_33_split__option__ex,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ^ [P4: ( option @ A ) > $o] :
% 0.30/0.46 ? [X4: option @ A] : ( P4 @ X4 ) )
% 0.30/0.46 = ( ^ [P: ( option @ A ) > $o] :
% 0.30/0.46 ( ( P @ ( none @ A ) )
% 0.30/0.46 | ? [X: A] : ( P @ ( some @ A @ X ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_option_ex
% 0.30/0.46 thf(fact_34_option_Oinducts,axiom,
% 0.30/0.46 ! [A: $tType,P3: ( option @ A ) > $o,Option: option @ A] :
% 0.30/0.46 ( ( P3 @ ( none @ A ) )
% 0.30/0.46 => ( ! [X5: A] : ( P3 @ ( some @ A @ X5 ) )
% 0.30/0.46 => ( P3 @ Option ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.inducts
% 0.30/0.46 thf(fact_35_option_Oexhaust,axiom,
% 0.30/0.46 ! [A: $tType,Y3: option @ A] :
% 0.30/0.46 ( ( Y3
% 0.30/0.46 != ( none @ A ) )
% 0.30/0.46 => ~ ! [X23: A] :
% 0.30/0.46 ( Y3
% 0.30/0.46 != ( some @ A @ X23 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % option.exhaust
% 0.30/0.46 thf(fact_36_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_37_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_38_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_39_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_40_Existso_Oinduct,axiom,
% 0.30/0.46 ! [P3: variable > ( option @ fml ) > $o,A0: variable,A1: option @ fml] :
% 0.30/0.46 ( ! [X5: variable,Phi2: fml] : ( P3 @ X5 @ ( some @ fml @ Phi2 ) )
% 0.30/0.46 => ( ! [X5: variable] : ( P3 @ X5 @ ( none @ fml ) )
% 0.30/0.46 => ( P3 @ A0 @ A1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Existso.induct
% 0.30/0.46 thf(fact_41_undeff__equiv,axiom,
% 0.30/0.46 ! [Phi: option @ fml] :
% 0.30/0.46 ( ( Phi
% 0.30/0.46 != ( none @ fml ) )
% 0.30/0.46 = ( ? [F: fml] :
% 0.30/0.46 ( Phi
% 0.30/0.46 = ( some @ fml @ F ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % undeff_equiv
% 0.30/0.46 thf(fact_42_Testo_Oinduct,axiom,
% 0.30/0.46 ! [P3: ( option @ fml ) > $o,A0: option @ fml] :
% 0.30/0.46 ( ! [Phi2: fml] : ( P3 @ ( some @ fml @ Phi2 ) )
% 0.30/0.46 => ( ( P3 @ ( none @ fml ) )
% 0.30/0.46 => ( P3 @ A0 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Testo.induct
% 0.30/0.46 thf(fact_43_Testo_Ocases,axiom,
% 0.30/0.46 ! [X3: option @ fml] :
% 0.30/0.46 ( ! [Phi2: fml] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( some @ fml @ Phi2 ) )
% 0.30/0.46 => ( X3
% 0.30/0.46 = ( none @ fml ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Testo.cases
% 0.30/0.46 thf(fact_44_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: $tType,A3: A,P3: A > $o] :
% 0.30/0.46 ( ( member @ A @ A3 @ ( collect @ A @ P3 ) )
% 0.30/0.46 = ( P3 @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_45_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ( collect @ A
% 0.30/0.46 @ ^ [X: A] : ( member @ A @ X @ A4 ) )
% 0.30/0.46 = A4 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_46_Collect__cong,axiom,
% 0.30/0.46 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X5: A] :
% 0.30/0.46 ( ( P3 @ X5 )
% 0.30/0.46 = ( Q @ X5 ) )
% 0.30/0.46 => ( ( collect @ A @ P3 )
% 0.30/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_cong
% 0.30/0.46 thf(fact_47_ext,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F2: A > B,G: A > B] :
% 0.30/0.46 ( ! [X5: A] :
% 0.30/0.46 ( ( F2 @ X5 )
% 0.30/0.46 = ( G @ X5 ) )
% 0.30/0.46 => ( F2 = G ) ) ).
% 0.30/0.46
% 0.30/0.46 % ext
% 0.30/0.46 thf(fact_48_Ando_Oinduct,axiom,
% 0.30/0.46 ! [P3: ( option @ fml ) > ( option @ fml ) > $o,A0: option @ fml,A1: option @ fml] :
% 0.30/0.46 ( ! [Phi2: fml,Psi: fml] : ( P3 @ ( some @ fml @ Phi2 ) @ ( some @ fml @ Psi ) )
% 0.30/0.46 => ( ! [X_1: option @ fml] : ( P3 @ ( none @ fml ) @ X_1 )
% 0.30/0.46 => ( ! [V6: fml] : ( P3 @ ( some @ fml @ V6 ) @ ( none @ fml ) )
% 0.30/0.46 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Ando.induct
% 0.30/0.46 thf(fact_49_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_50_usubstappf__pred__conv,axiom,
% 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,P2: char,Theta: trm] :
% 0.30/0.46 ( ( ( uSubst95898978stappf @ Sigma @ U @ ( pred @ P2 @ Theta ) )
% 0.30/0.46 != ( none @ fml ) )
% 0.30/0.46 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ Sigma
% 0.30/0.46 @ P2 )
% 0.30/0.46 = ( none @ fml ) )
% 0.30/0.46 | ? [R3: fml] :
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ Sigma
% 0.30/0.46 @ P2 )
% 0.30/0.46 = ( some @ fml @ R3 ) )
% 0.30/0.46 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R3 ) @ U )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappf_pred_conv
% 0.30/0.46 thf(fact_51_f6,axiom,
% 0.30/0.46 ( ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
% 0.30/0.46 @ ^ [T: trm] :
% 0.30/0.46 ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ T ) )
% 0.30/0.46 @ ^ [F: fml] :
% 0.30/0.46 ( if @ ( option @ fml )
% 0.30/0.46 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F ) @ ua )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ T ) @ ( bot_bot @ ( set @ variable ) ) @ F )
% 0.30/0.46 @ ( none @ fml ) )
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) )
% 0.30/0.46 @ ( uSubst95898992stappt @ sigma @ ua @ theta ) )
% 0.30/0.46 = ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ua @ theta ) ) ) )
% 0.30/0.46 @ ^ [F: fml] :
% 0.30/0.46 ( if @ ( option @ fml )
% 0.30/0.46 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F ) @ ua )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ua @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) ) @ F )
% 0.30/0.46 @ ( none @ fml ) )
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % f6
% 0.30/0.46 thf(fact_52_f3,axiom,
% 0.30/0.46 ( ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
% 0.30/0.46 @ ^ [T: trm] :
% 0.30/0.46 ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ T ) )
% 0.30/0.46 @ ^ [F: fml] :
% 0.30/0.46 ( if @ ( option @ fml )
% 0.30/0.46 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F ) @ ua )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ T ) @ ( bot_bot @ ( set @ variable ) ) @ F )
% 0.30/0.46 @ ( none @ fml ) )
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p ) )
% 0.30/0.46 @ ( uSubst95898992stappt @ sigma @ ua @ theta ) )
% 0.30/0.46 != ( none @ fml ) ) ).
% 0.30/0.46
% 0.30/0.46 % f3
% 0.30/0.46 thf(fact_53_usubstappf_Osimps_I1_J,axiom,
% 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,P2: char,Theta: trm] :
% 0.30/0.46 ( ( uSubst95898978stappf @ Sigma @ U @ ( pred @ P2 @ Theta ) )
% 0.30/0.46 = ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
% 0.30/0.46 @ ^ [Sigma_theta: trm] :
% 0.30/0.46 ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ P2 @ Sigma_theta ) )
% 0.30/0.46 @ ^ [R: fml] :
% 0.30/0.46 ( if @ ( option @ fml )
% 0.30/0.46 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R ) @ U )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ Sigma_theta ) @ ( bot_bot @ ( set @ variable ) ) @ R )
% 0.30/0.46 @ ( none @ fml ) )
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ Sigma
% 0.30/0.46 @ P2 ) )
% 0.30/0.46 @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappf.simps(1)
% 0.30/0.46 thf(fact_54_Int__subset__iff,axiom,
% 0.30/0.46 ! [A: $tType,C2: set @ A,A4: set @ A,B3: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 0.30/0.46 = ( ( ord_less_eq @ ( set @ A ) @ C2 @ A4 )
% 0.30/0.46 & ( ord_less_eq @ ( set @ A ) @ C2 @ B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_subset_iff
% 0.30/0.46 thf(fact_55_inf__bot__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounded_lattice_bot @ A )
% 0.30/0.46 => ! [X3: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( bot_bot @ A ) @ X3 )
% 0.30/0.46 = ( bot_bot @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_bot_left
% 0.30/0.46 thf(fact_56_inf__bot__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounded_lattice_bot @ A )
% 0.30/0.46 => ! [X3: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X3 @ ( 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_57_subset__empty,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( A4
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_empty
% 0.30/0.46 thf(fact_58_empty__subsetI,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 ) ).
% 0.30/0.46
% 0.30/0.46 % empty_subsetI
% 0.30/0.46 thf(fact_59_le__inf__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X3: A,Y3: A,Z2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ ( inf_inf @ A @ Y3 @ Z2 ) )
% 0.30/0.46 = ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.30/0.46 & ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_inf_iff
% 0.30/0.46 thf(fact_60_inf_Obounded__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A3: A,B4: A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ ( inf_inf @ A @ B4 @ C3 ) )
% 0.30/0.46 = ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/0.46 & ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.bounded_iff
% 0.30/0.46 thf(fact_61_f4,axiom,
% 0.30/0.46 ! [Z: option @ fml,F3: trm > ( option @ fml ),Za: option @ trm] :
% 0.30/0.46 ( ( ( Za
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 => ( ( case_option @ ( option @ fml ) @ trm @ Z @ F3 @ Za )
% 0.30/0.46 = Z ) )
% 0.30/0.46 & ( ( Za
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( case_option @ ( option @ fml ) @ trm @ Z @ F3 @ Za )
% 0.30/0.46 = ( F3 @ ( the @ trm @ Za ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % f4
% 0.30/0.46 thf(fact_62_empty__Collect__eq,axiom,
% 0.30/0.46 ! [A: $tType,P3: A > $o] :
% 0.30/0.46 ( ( ( bot_bot @ ( set @ A ) )
% 0.30/0.46 = ( collect @ A @ P3 ) )
% 0.30/0.46 = ( ! [X: A] :
% 0.30/0.46 ~ ( P3 @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % empty_Collect_eq
% 0.30/0.46 thf(fact_63_Collect__empty__eq,axiom,
% 0.30/0.46 ! [A: $tType,P3: A > $o] :
% 0.30/0.46 ( ( ( collect @ A @ P3 )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( ! [X: A] :
% 0.30/0.46 ~ ( P3 @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_empty_eq
% 0.30/0.46 thf(fact_64_all__not__in__conv,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ( ! [X: A] :
% 0.30/0.46 ~ ( member @ A @ X @ A4 ) )
% 0.30/0.46 = ( A4
% 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_65_empty__iff,axiom,
% 0.30/0.46 ! [A: $tType,C3: A] :
% 0.30/0.46 ~ ( member @ A @ C3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % empty_iff
% 0.30/0.46 thf(fact_66_subset__antisym,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B3 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ A4 )
% 0.30/0.46 => ( A4 = B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_antisym
% 0.30/0.46 thf(fact_67_subsetI,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 0.30/0.46 ( ! [X5: A] :
% 0.30/0.46 ( ( member @ A @ X5 @ A4 )
% 0.30/0.46 => ( member @ A @ X5 @ B3 ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A4 @ B3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % subsetI
% 0.30/0.46 thf(fact_68_inf__right__idem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ X3 @ Y3 ) @ Y3 )
% 0.30/0.46 = ( inf_inf @ A @ X3 @ Y3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_right_idem
% 0.30/0.46 thf(fact_69_inf_Oright__idem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A3: A,B4: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ A3 @ B4 ) @ B4 )
% 0.30/0.46 = ( inf_inf @ A @ A3 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.right_idem
% 0.30/0.46 thf(fact_70_inf__left__idem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X3 @ ( inf_inf @ A @ X3 @ Y3 ) )
% 0.30/0.46 = ( inf_inf @ A @ X3 @ Y3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_left_idem
% 0.30/0.46 thf(fact_71_inf_Oleft__idem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A3: A,B4: A] :
% 0.30/0.46 ( ( inf_inf @ A @ A3 @ ( inf_inf @ A @ A3 @ B4 ) )
% 0.30/0.46 = ( inf_inf @ A @ A3 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.left_idem
% 0.30/0.46 thf(fact_72_inf__idem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X3: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X3 @ X3 )
% 0.30/0.46 = X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_idem
% 0.30/0.46 thf(fact_73_inf_Oidem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A3: A] :
% 0.30/0.46 ( ( inf_inf @ A @ A3 @ A3 )
% 0.30/0.46 = A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.idem
% 0.30/0.46 thf(fact_74_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 = ( ^ [F: A > B,G2: A > B,X: A] : ( inf_inf @ B @ ( F @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_apply
% 0.30/0.46 thf(fact_75_Int__iff,axiom,
% 0.30/0.46 ! [A: $tType,C3: A,A4: set @ A,B3: set @ A] :
% 0.30/0.46 ( ( member @ A @ C3 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 0.30/0.46 = ( ( member @ A @ C3 @ A4 )
% 0.30/0.46 & ( member @ A @ C3 @ B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_iff
% 0.30/0.46 thf(fact_76_IntI,axiom,
% 0.30/0.46 ! [A: $tType,C3: A,A4: set @ A,B3: set @ A] :
% 0.30/0.46 ( ( member @ A @ C3 @ A4 )
% 0.30/0.46 => ( ( member @ A @ C3 @ B3 )
% 0.30/0.46 => ( member @ A @ C3 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % IntI
% 0.30/0.46 thf(fact_77_usubstappf__pred,axiom,
% 0.30/0.46 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),P2: char,R2: fml,U: set @ variable,Theta: trm,Sigma_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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ Sigma
% 0.30/0.46 @ P2 )
% 0.30/0.46 = ( some @ fml @ R2 ) )
% 0.30/0.46 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R2 ) @ U )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.30/0.46 = ( some @ trm @ Sigma_theta2 ) )
% 0.30/0.46 => ( ( uSubst95898978stappf @ Sigma @ U @ ( pred @ P2 @ Theta ) )
% 0.30/0.46 = ( uSubst95898978stappf @ ( uSubst969145931substt @ Sigma_theta2 ) @ ( bot_bot @ ( set @ variable ) ) @ R2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappf_pred
% 0.30/0.46 thf(fact_78_ODEo_Oinduct,axiom,
% 0.30/0.46 ! [P3: char > ( option @ trm ) > $o,A0: char,A1: option @ trm] :
% 0.30/0.46 ( ! [X5: char,Theta2: trm] : ( P3 @ X5 @ ( some @ trm @ Theta2 ) )
% 0.30/0.46 => ( ! [X5: char] : ( P3 @ X5 @ ( none @ trm ) )
% 0.30/0.46 => ( P3 @ A0 @ A1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ODEo.induct
% 0.30/0.46 thf(fact_79_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_80_undeft__equiv,axiom,
% 0.30/0.46 ! [Theta: option @ trm] :
% 0.30/0.46 ( ( Theta
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 = ( ? [T: trm] :
% 0.30/0.46 ( Theta
% 0.30/0.46 = ( some @ trm @ T ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % undeft_equiv
% 0.30/0.46 thf(fact_81_Timeso_Oinduct,axiom,
% 0.30/0.46 ! [P3: ( option @ trm ) > ( option @ trm ) > $o,A0: option @ trm,A1: option @ trm] :
% 0.30/0.46 ( ! [Theta2: trm,Eta: trm] : ( P3 @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta ) )
% 0.30/0.46 => ( ! [X_1: option @ trm] : ( P3 @ ( none @ trm ) @ X_1 )
% 0.30/0.46 => ( ! [V6: trm] : ( P3 @ ( some @ trm @ V6 ) @ ( none @ trm ) )
% 0.30/0.46 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Timeso.induct
% 0.30/0.46 thf(fact_82_Assigno_Oinduct,axiom,
% 0.30/0.46 ! [P3: variable > ( option @ trm ) > $o,A0: variable,A1: option @ trm] :
% 0.30/0.46 ( ! [X5: variable,Theta2: trm] : ( P3 @ X5 @ ( some @ trm @ Theta2 ) )
% 0.30/0.46 => ( ! [X5: variable] : ( P3 @ X5 @ ( none @ trm ) )
% 0.30/0.46 => ( P3 @ A0 @ A1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Assigno.induct
% 0.30/0.46 thf(fact_83_Differentialo_Ocases,axiom,
% 0.30/0.46 ! [X3: option @ trm] :
% 0.30/0.46 ( ! [Theta2: trm] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( some @ trm @ Theta2 ) )
% 0.30/0.46 => ( X3
% 0.30/0.46 = ( none @ trm ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Differentialo.cases
% 0.30/0.46 thf(fact_84_Differentialo_Oinduct,axiom,
% 0.30/0.46 ! [P3: ( option @ trm ) > $o,A0: option @ trm] :
% 0.30/0.46 ( ! [Theta2: trm] : ( P3 @ ( some @ trm @ Theta2 ) )
% 0.30/0.46 => ( ( P3 @ ( none @ trm ) )
% 0.30/0.46 => ( P3 @ A0 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Differentialo.induct
% 0.30/0.46 thf(fact_85_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_86_inf__set__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A5: set @ A,B5: 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 @ A5 )
% 0.30/0.46 @ ^ [X: A] : ( member @ A @ X @ B5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_set_def
% 0.30/0.46 thf(fact_87_less__eq__set__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ord_less_eq @ ( A > $o )
% 0.30/0.46 @ ^ [X: A] : ( member @ A @ X @ A5 )
% 0.30/0.46 @ ^ [X: A] : ( member @ A @ X @ B5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_eq_set_def
% 0.30/0.46 thf(fact_88_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_89_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_90_Diamondo_Oinduct,axiom,
% 0.30/0.46 ! [P3: ( option @ game ) > ( option @ fml ) > $o,A0: option @ game,A1: option @ fml] :
% 0.30/0.46 ( ! [Alpha: game,Phi2: fml] : ( P3 @ ( some @ game @ Alpha ) @ ( some @ fml @ Phi2 ) )
% 0.30/0.46 => ( ! [X_1: option @ fml] : ( P3 @ ( none @ game ) @ X_1 )
% 0.30/0.46 => ( ! [V6: game] : ( P3 @ ( some @ game @ V6 ) @ ( none @ fml ) )
% 0.30/0.46 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Diamondo.induct
% 0.30/0.46 thf(fact_91_case__optionE,axiom,
% 0.30/0.46 ! [A: $tType,P3: $o,Q: A > $o,X3: option @ A] :
% 0.30/0.46 ( ( case_option @ $o @ A @ P3 @ Q @ X3 )
% 0.30/0.46 => ( ( ( X3
% 0.30/0.46 = ( none @ A ) )
% 0.30/0.46 => ~ P3 )
% 0.30/0.46 => ~ ! [Y4: A] :
% 0.30/0.46 ( ( X3
% 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_92_ex__in__conv,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ( ? [X: A] : ( member @ A @ X @ A4 ) )
% 0.30/0.46 = ( A4
% 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_93_equals0I,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ! [Y4: A] :
% 0.30/0.46 ~ ( member @ A @ Y4 @ A4 )
% 0.30/0.46 => ( A4
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0I
% 0.30/0.46 thf(fact_94_equals0D,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,A3: A] :
% 0.30/0.46 ( ( A4
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 => ~ ( member @ A @ A3 @ A4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0D
% 0.30/0.46 thf(fact_95_emptyE,axiom,
% 0.30/0.46 ! [A: $tType,A3: A] :
% 0.30/0.46 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % emptyE
% 0.30/0.46 thf(fact_96_Collect__mono__iff,axiom,
% 0.30/0.46 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P3 ) @ ( collect @ A @ Q ) )
% 0.30/0.46 = ( ! [X: A] :
% 0.30/0.46 ( ( P3 @ X )
% 0.30/0.46 => ( Q @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mono_iff
% 0.30/0.46 thf(fact_97_set__eq__subset,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ^ [Y5: set @ A,Z3: set @ A] : ( Y5 = Z3 ) )
% 0.30/0.46 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.30/0.46 & ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % set_eq_subset
% 0.30/0.46 thf(fact_98_subset__trans,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B3: set @ A,C2: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B3 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ C2 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A4 @ C2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_trans
% 0.30/0.46 thf(fact_99_Collect__mono,axiom,
% 0.30/0.46 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X5: A] :
% 0.30/0.46 ( ( P3 @ X5 )
% 0.30/0.46 => ( Q @ X5 ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P3 ) @ ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mono
% 0.30/0.46 thf(fact_100_subset__refl,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 0.30/0.46
% 0.30/0.46 % subset_refl
% 0.30/0.46 thf(fact_101_subset__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.30/0.46 ! [T: A] :
% 0.30/0.46 ( ( member @ A @ T @ A5 )
% 0.30/0.46 => ( member @ A @ T @ B5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_iff
% 0.30/0.46 thf(fact_102_equalityD2,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 0.30/0.46 ( ( A4 = B3 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ B3 @ A4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityD2
% 0.30/0.46 thf(fact_103_equalityD1,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 0.30/0.46 ( ( A4 = B3 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A4 @ B3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityD1
% 0.30/0.46 thf(fact_104_subset__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.30/0.46 ! [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ A5 )
% 0.30/0.46 => ( member @ A @ X @ B5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_eq
% 0.30/0.46 thf(fact_105_equalityE,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 0.30/0.46 ( ( A4 = B3 )
% 0.30/0.46 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B3 )
% 0.30/0.46 => ~ ( ord_less_eq @ ( set @ A ) @ B3 @ A4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityE
% 0.30/0.46 thf(fact_106_subsetD,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B3: set @ A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B3 )
% 0.30/0.46 => ( ( member @ A @ C3 @ A4 )
% 0.30/0.46 => ( member @ A @ C3 @ B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subsetD
% 0.30/0.46 thf(fact_107_in__mono,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B3: set @ A,X3: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B3 )
% 0.30/0.46 => ( ( member @ A @ X3 @ A4 )
% 0.30/0.46 => ( member @ A @ X3 @ B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_mono
% 0.30/0.46 thf(fact_108_inf__left__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X3: A,Y3: A,Z2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X3 @ ( inf_inf @ A @ Y3 @ Z2 ) )
% 0.30/0.46 = ( inf_inf @ A @ Y3 @ ( inf_inf @ A @ X3 @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_left_commute
% 0.30/0.46 thf(fact_109_inf_Oleft__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [B4: A,A3: A,C3: A] :
% 0.30/0.46 ( ( inf_inf @ A @ B4 @ ( inf_inf @ A @ A3 @ C3 ) )
% 0.30/0.46 = ( inf_inf @ A @ A3 @ ( inf_inf @ A @ B4 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.left_commute
% 0.30/0.46 thf(fact_110_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_111_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 = ( ^ [A6: A,B6: A] : ( inf_inf @ A @ B6 @ A6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.commute
% 0.30/0.46 thf(fact_112_inf__assoc,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X3: A,Y3: A,Z2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ X3 @ Y3 ) @ Z2 )
% 0.30/0.46 = ( inf_inf @ A @ X3 @ ( inf_inf @ A @ Y3 @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_assoc
% 0.30/0.46 thf(fact_113_inf_Oassoc,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A3: A,B4: A,C3: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ A3 @ B4 ) @ C3 )
% 0.30/0.46 = ( inf_inf @ A @ A3 @ ( inf_inf @ A @ B4 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.assoc
% 0.30/0.46 thf(fact_114_boolean__algebra__cancel_Oinf2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [B3: A,K: A,B4: A,A3: A] :
% 0.30/0.46 ( ( B3
% 0.30/0.46 = ( inf_inf @ A @ K @ B4 ) )
% 0.30/0.46 => ( ( inf_inf @ A @ A3 @ B3 )
% 0.30/0.46 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A3 @ B4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % boolean_algebra_cancel.inf2
% 0.30/0.46 thf(fact_115_boolean__algebra__cancel_Oinf1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A4: A,K: A,A3: A,B4: A] :
% 0.30/0.46 ( ( A4
% 0.30/0.46 = ( inf_inf @ A @ K @ A3 ) )
% 0.30/0.46 => ( ( inf_inf @ A @ A4 @ B4 )
% 0.30/0.46 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A3 @ B4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % boolean_algebra_cancel.inf1
% 0.30/0.46 thf(fact_116_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 = ( ^ [F: A > B,G2: A > B,X: A] : ( inf_inf @ B @ ( F @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_fun_def
% 0.30/0.46 thf(fact_117_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_118_inf__sup__aci_I2_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A )
% 0.30/0.46 => ! [X3: A,Y3: A,Z2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ X3 @ Y3 ) @ Z2 )
% 0.30/0.46 = ( inf_inf @ A @ X3 @ ( inf_inf @ A @ Y3 @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_aci(2)
% 0.30/0.46 thf(fact_119_inf__sup__aci_I3_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A )
% 0.30/0.46 => ! [X3: A,Y3: A,Z2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X3 @ ( inf_inf @ A @ Y3 @ Z2 ) )
% 0.30/0.46 = ( inf_inf @ A @ Y3 @ ( inf_inf @ A @ X3 @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_aci(3)
% 0.30/0.46 thf(fact_120_inf__sup__aci_I4_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X3 @ ( inf_inf @ A @ X3 @ Y3 ) )
% 0.30/0.46 = ( inf_inf @ A @ X3 @ Y3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_aci(4)
% 0.30/0.46 thf(fact_121_Int__left__commute,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B3: set @ A,C2: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) @ A4 @ ( inf_inf @ ( set @ A ) @ B3 @ C2 ) )
% 0.30/0.46 = ( inf_inf @ ( set @ A ) @ B3 @ ( inf_inf @ ( set @ A ) @ A4 @ C2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_left_commute
% 0.30/0.46 thf(fact_122_Int__left__absorb,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) @ A4 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 0.30/0.46 = ( inf_inf @ ( set @ A ) @ A4 @ B3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_left_absorb
% 0.30/0.46 thf(fact_123_Int__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A5: set @ A,B5: set @ A] : ( inf_inf @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_commute
% 0.30/0.46 thf(fact_124_Int__absorb,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) @ A4 @ A4 )
% 0.30/0.46 = A4 ) ).
% 0.30/0.46
% 0.30/0.46 % Int_absorb
% 0.30/0.46 thf(fact_125_Int__assoc,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B3: set @ A,C2: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) @ C2 )
% 0.30/0.46 = ( inf_inf @ ( set @ A ) @ A4 @ ( inf_inf @ ( set @ A ) @ B3 @ C2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_assoc
% 0.30/0.46 thf(fact_126_IntD2,axiom,
% 0.30/0.46 ! [A: $tType,C3: A,A4: set @ A,B3: set @ A] :
% 0.30/0.46 ( ( member @ A @ C3 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 0.30/0.46 => ( member @ A @ C3 @ B3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % IntD2
% 0.30/0.46 thf(fact_127_IntD1,axiom,
% 0.30/0.46 ! [A: $tType,C3: A,A4: set @ A,B3: set @ A] :
% 0.30/0.46 ( ( member @ A @ C3 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 0.30/0.46 => ( member @ A @ C3 @ A4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % IntD1
% 0.30/0.46 thf(fact_128_IntE,axiom,
% 0.30/0.46 ! [A: $tType,C3: A,A4: set @ A,B3: set @ A] :
% 0.30/0.46 ( ( member @ A @ C3 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 0.30/0.46 => ~ ( ( member @ A @ C3 @ A4 )
% 0.30/0.46 => ~ ( member @ A @ C3 @ B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % IntE
% 0.30/0.46 thf(fact_129_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_130_Collect__subset,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,P3: A > $o] :
% 0.30/0.46 ( ord_less_eq @ ( set @ A )
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ A4 )
% 0.30/0.46 & ( P3 @ X ) ) )
% 0.30/0.46 @ A4 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_subset
% 0.30/0.46 thf(fact_131_Int__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( collect @ A
% 0.30/0.46 @ ^ [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ A5 )
% 0.30/0.46 & ( member @ A @ X @ B5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_def
% 0.30/0.46 thf(fact_132_Int__Collect,axiom,
% 0.30/0.46 ! [A: $tType,X3: A,A4: set @ A,P3: A > $o] :
% 0.30/0.46 ( ( member @ A @ X3 @ ( inf_inf @ ( set @ A ) @ A4 @ ( collect @ A @ P3 ) ) )
% 0.30/0.46 = ( ( member @ A @ X3 @ A4 )
% 0.30/0.46 & ( P3 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_Collect
% 0.30/0.46 thf(fact_133_Collect__conj__eq,axiom,
% 0.30/0.46 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 0.30/0.46 ( ( collect @ A
% 0.30/0.46 @ ^ [X: A] :
% 0.30/0.46 ( ( P3 @ X )
% 0.30/0.46 & ( Q @ X ) ) )
% 0.30/0.46 = ( inf_inf @ ( set @ A ) @ ( collect @ A @ P3 ) @ ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_conj_eq
% 0.30/0.46 thf(fact_134_inf_OcoboundedI2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [B4: A,C3: A,A3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B4 @ C3 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( inf_inf @ A @ A3 @ B4 ) @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.coboundedI2
% 0.30/0.46 thf(fact_135_inf_OcoboundedI1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A3: A,C3: A,B4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ C3 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( inf_inf @ A @ A3 @ B4 ) @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.coboundedI1
% 0.30/0.46 thf(fact_136_inf_Oabsorb__iff2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ( ( ord_less_eq @ A )
% 0.30/0.46 = ( ^ [B6: A,A6: A] :
% 0.30/0.46 ( ( inf_inf @ A @ A6 @ B6 )
% 0.30/0.46 = B6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.absorb_iff2
% 0.30/0.46 thf(fact_137_inf_Oabsorb__iff1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ( ( ord_less_eq @ A )
% 0.30/0.46 = ( ^ [A6: A,B6: A] :
% 0.30/0.46 ( ( inf_inf @ A @ A6 @ B6 )
% 0.30/0.46 = A6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.absorb_iff1
% 0.30/0.46 thf(fact_138_inf_Ocobounded2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A3: A,B4: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ A3 @ B4 ) @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.cobounded2
% 0.30/0.46 thf(fact_139_inf_Ocobounded1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A3: A,B4: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ A3 @ B4 ) @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.cobounded1
% 0.30/0.46 thf(fact_140_inf_Oorder__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ( ( ord_less_eq @ A )
% 0.30/0.46 = ( ^ [A6: A,B6: A] :
% 0.30/0.46 ( A6
% 0.30/0.46 = ( inf_inf @ A @ A6 @ B6 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.order_iff
% 0.30/0.46 thf(fact_141_inf__greatest,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X3: A,Y3: A,Z2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ X3 @ Z2 )
% 0.30/0.46 => ( ord_less_eq @ A @ X3 @ ( inf_inf @ A @ Y3 @ Z2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_greatest
% 0.30/0.46 thf(fact_142_inf_OboundedI,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A3: A,B4: A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ A3 @ C3 )
% 0.30/0.46 => ( ord_less_eq @ A @ A3 @ ( inf_inf @ A @ B4 @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.boundedI
% 0.30/0.46 thf(fact_143_inf_OboundedE,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A3: A,B4: A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ ( inf_inf @ A @ B4 @ C3 ) )
% 0.30/0.46 => ~ ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.boundedE
% 0.30/0.46 thf(fact_144_inf__absorb2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [Y3: A,X3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.30/0.46 => ( ( inf_inf @ A @ X3 @ Y3 )
% 0.30/0.46 = Y3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_absorb2
% 0.30/0.46 thf(fact_145_inf__absorb1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.30/0.46 => ( ( inf_inf @ A @ X3 @ Y3 )
% 0.30/0.46 = X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_absorb1
% 0.30/0.46 thf(fact_146_inf_Oabsorb2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [B4: A,A3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B4 @ A3 )
% 0.30/0.46 => ( ( inf_inf @ A @ A3 @ B4 )
% 0.30/0.46 = B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.absorb2
% 0.30/0.46 thf(fact_147_inf_Oabsorb1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A3: A,B4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/0.46 => ( ( inf_inf @ A @ A3 @ B4 )
% 0.30/0.46 = A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.absorb1
% 0.30/0.46 thf(fact_148_le__iff__inf,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ( ( ord_less_eq @ A )
% 0.30/0.46 = ( ^ [X: A,Y: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X @ Y )
% 0.30/0.46 = X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_iff_inf
% 0.30/0.46 thf(fact_149_inf__unique,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [F2: A > A > A,X3: A,Y3: A] :
% 0.30/0.46 ( ! [X5: A,Y4: A] : ( ord_less_eq @ A @ ( F2 @ X5 @ Y4 ) @ X5 )
% 0.30/0.46 => ( ! [X5: A,Y4: A] : ( ord_less_eq @ A @ ( F2 @ X5 @ Y4 ) @ Y4 )
% 0.30/0.46 => ( ! [X5: A,Y4: A,Z4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X5 @ Y4 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ X5 @ Z4 )
% 0.30/0.46 => ( ord_less_eq @ A @ X5 @ ( F2 @ Y4 @ Z4 ) ) ) )
% 0.30/0.46 => ( ( inf_inf @ A @ X3 @ Y3 )
% 0.30/0.46 = ( F2 @ X3 @ Y3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_unique
% 0.30/0.46 thf(fact_150_inf_OorderI,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A3: A,B4: A] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 = ( inf_inf @ A @ A3 @ B4 ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A3 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.orderI
% 0.30/0.46 thf(fact_151_inf_OorderE,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A3: A,B4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/0.46 => ( A3
% 0.30/0.46 = ( inf_inf @ A @ A3 @ B4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.orderE
% 0.30/0.46 thf(fact_152_le__infI2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [B4: A,X3: A,A3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B4 @ X3 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( inf_inf @ A @ A3 @ B4 ) @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_infI2
% 0.30/0.46 thf(fact_153_le__infI1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A3: A,X3: A,B4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ X3 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( inf_inf @ A @ A3 @ B4 ) @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_infI1
% 0.30/0.46 thf(fact_154_inf__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A3: A,C3: A,B4: A,D2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ C3 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B4 @ D2 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( inf_inf @ A @ A3 @ B4 ) @ ( inf_inf @ A @ C3 @ D2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_mono
% 0.30/0.46 thf(fact_155_le__infI,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X3: A,A3: A,B4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ A3 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ X3 @ B4 )
% 0.30/0.46 => ( ord_less_eq @ A @ X3 @ ( inf_inf @ A @ A3 @ B4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_infI
% 0.30/0.46 thf(fact_156_le__infE,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X3: A,A3: A,B4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ ( inf_inf @ A @ A3 @ B4 ) )
% 0.30/0.46 => ~ ( ( ord_less_eq @ A @ X3 @ A3 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ X3 @ B4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_infE
% 0.30/0.46 thf(fact_157_inf__le2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X3 @ Y3 ) @ Y3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_le2
% 0.30/0.46 thf(fact_158_inf__le1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X3 @ Y3 ) @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_le1
% 0.30/0.46 thf(fact_159_inf__sup__ord_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X3 @ Y3 ) @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_ord(1)
% 0.30/0.46 thf(fact_160_inf__sup__ord_I2_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X3 @ Y3 ) @ Y3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_ord(2)
% 0.30/0.46 thf(fact_161_disjoint__iff__not__equal,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 0.30/0.46 ( ( ( inf_inf @ ( set @ A ) @ A4 @ B3 )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( ! [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ A4 )
% 0.30/0.46 => ! [Y: A] :
% 0.30/0.46 ( ( member @ A @ Y @ B3 )
% 0.30/0.46 => ( X != Y ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % disjoint_iff_not_equal
% 0.30/0.46 thf(fact_162_Int__empty__right,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) @ A4 @ ( 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_163_Int__empty__left,axiom,
% 0.30/0.46 ! [A: $tType,B3: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B3 )
% 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_164_disjoint__iff,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 0.30/0.46 ( ( ( inf_inf @ ( set @ A ) @ A4 @ B3 )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( ! [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ A4 )
% 0.30/0.46 => ~ ( member @ A @ X @ B3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % disjoint_iff
% 0.30/0.46 thf(fact_165_Int__emptyI,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 0.30/0.46 ( ! [X5: A] :
% 0.30/0.46 ( ( member @ A @ X5 @ A4 )
% 0.30/0.46 => ~ ( member @ A @ X5 @ B3 ) )
% 0.30/0.46 => ( ( inf_inf @ ( set @ A ) @ A4 @ B3 )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_emptyI
% 0.30/0.46 thf(fact_166_Int__Collect__mono,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B3: set @ A,P3: A > $o,Q: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B3 )
% 0.30/0.46 => ( ! [X5: A] :
% 0.30/0.46 ( ( member @ A @ X5 @ A4 )
% 0.30/0.46 => ( ( P3 @ X5 )
% 0.30/0.46 => ( Q @ X5 ) ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ ( collect @ A @ P3 ) ) @ ( inf_inf @ ( set @ A ) @ B3 @ ( collect @ A @ Q ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_Collect_mono
% 0.30/0.46 thf(fact_167_Int__greatest,axiom,
% 0.30/0.46 ! [A: $tType,C2: set @ A,A4: set @ A,B3: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ C2 @ A4 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ C2 @ B3 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_greatest
% 0.30/0.46 thf(fact_168_Int__absorb2,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B3 )
% 0.30/0.46 => ( ( inf_inf @ ( set @ A ) @ A4 @ B3 )
% 0.30/0.46 = A4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_absorb2
% 0.30/0.46 thf(fact_169_Int__absorb1,axiom,
% 0.30/0.46 ! [A: $tType,B3: set @ A,A4: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ B3 @ A4 )
% 0.30/0.46 => ( ( inf_inf @ ( set @ A ) @ A4 @ B3 )
% 0.30/0.46 = B3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_absorb1
% 0.30/0.46 thf(fact_170_Int__lower2,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) @ B3 ) ).
% 0.30/0.46
% 0.30/0.46 % Int_lower2
% 0.30/0.46 thf(fact_171_Int__lower1,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) @ A4 ) ).
% 0.30/0.46
% 0.30/0.46 % Int_lower1
% 0.30/0.46 thf(fact_172_Int__mono,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,C2: set @ A,B3: set @ A,D3: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ C2 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ D3 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) @ ( inf_inf @ ( set @ A ) @ C2 @ D3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_mono
% 0.30/0.46 thf(fact_173_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_174_order__refl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_refl
% 0.30/0.46 thf(fact_175_subset__emptyI,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ! [X5: A] :
% 0.30/0.46 ~ ( member @ A @ X5 @ A4 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_emptyI
% 0.30/0.46 thf(fact_176_bot_Oextremum__uniqueI,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order_bot @ A )
% 0.30/0.46 => ! [A3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ ( bot_bot @ A ) )
% 0.30/0.46 => ( A3
% 0.30/0.46 = ( bot_bot @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot.extremum_uniqueI
% 0.30/0.46 thf(fact_177_bot_Oextremum__unique,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order_bot @ A )
% 0.30/0.46 => ! [A3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ ( bot_bot @ A ) )
% 0.30/0.46 = ( A3
% 0.30/0.46 = ( bot_bot @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot.extremum_unique
% 0.30/0.46 thf(fact_178_bot_Oextremum,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order_bot @ A )
% 0.30/0.46 => ! [A3: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot.extremum
% 0.30/0.46 thf(fact_179_usubstappf__geqr,axiom,
% 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,Theta: trm,Eta2: trm] :
% 0.30/0.46 ( ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.30/0.46 != ( none @ fml ) )
% 0.30/0.46 => ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.30/0.46 = ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Eta2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappf_geqr
% 0.30/0.46 thf(fact_180_fml_Oinject_I2_J,axiom,
% 0.30/0.46 ! [X21: trm,X222: trm,Y21: trm,Y22: trm] :
% 0.30/0.46 ( ( ( geq @ X21 @ X222 )
% 0.30/0.46 = ( geq @ Y21 @ Y22 ) )
% 0.30/0.46 = ( ( X21 = Y21 )
% 0.30/0.46 & ( X222 = Y22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % fml.inject(2)
% 0.30/0.46 thf(fact_181_predicate1I,axiom,
% 0.30/0.46 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X5: A] :
% 0.30/0.46 ( ( P3 @ X5 )
% 0.30/0.46 => ( Q @ X5 ) )
% 0.30/0.46 => ( ord_less_eq @ ( A > $o ) @ P3 @ Q ) ) ).
% 0.30/0.46
% 0.30/0.46 % predicate1I
% 0.30/0.46 thf(fact_182_inf1I,axiom,
% 0.30/0.46 ! [A: $tType,A4: A > $o,X3: A,B3: A > $o] :
% 0.30/0.46 ( ( A4 @ X3 )
% 0.30/0.46 => ( ( B3 @ X3 )
% 0.30/0.46 => ( inf_inf @ ( A > $o ) @ A4 @ B3 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf1I
% 0.30/0.46 thf(fact_183_inf1E,axiom,
% 0.30/0.46 ! [A: $tType,A4: A > $o,B3: A > $o,X3: A] :
% 0.30/0.46 ( ( inf_inf @ ( A > $o ) @ A4 @ B3 @ X3 )
% 0.30/0.46 => ~ ( ( A4 @ X3 )
% 0.30/0.46 => ~ ( B3 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf1E
% 0.30/0.46 thf(fact_184_inf1D1,axiom,
% 0.30/0.46 ! [A: $tType,A4: A > $o,B3: A > $o,X3: A] :
% 0.30/0.46 ( ( inf_inf @ ( A > $o ) @ A4 @ B3 @ X3 )
% 0.30/0.46 => ( A4 @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf1D1
% 0.30/0.46 thf(fact_185_inf1D2,axiom,
% 0.30/0.46 ! [A: $tType,A4: A > $o,B3: A > $o,X3: A] :
% 0.30/0.46 ( ( inf_inf @ ( A > $o ) @ A4 @ B3 @ X3 )
% 0.30/0.46 => ( B3 @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf1D2
% 0.30/0.46 thf(fact_186_predicate1D,axiom,
% 0.30/0.46 ! [A: $tType,P3: A > $o,Q: A > $o,X3: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > $o ) @ P3 @ Q )
% 0.30/0.46 => ( ( P3 @ X3 )
% 0.30/0.46 => ( Q @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % predicate1D
% 0.30/0.46 thf(fact_187_rev__predicate1D,axiom,
% 0.30/0.46 ! [A: $tType,P3: A > $o,X3: A,Q: A > $o] :
% 0.30/0.46 ( ( P3 @ X3 )
% 0.30/0.46 => ( ( ord_less_eq @ ( A > $o ) @ P3 @ Q )
% 0.30/0.46 => ( Q @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev_predicate1D
% 0.30/0.46 thf(fact_188_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_189_Loopo_Ocases,axiom,
% 0.30/0.46 ! [X3: option @ game] :
% 0.30/0.46 ( ! [Alpha: game] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( some @ game @ Alpha ) )
% 0.30/0.46 => ( X3
% 0.30/0.46 = ( none @ game ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Loopo.cases
% 0.30/0.46 thf(fact_190_Loopo_Oinduct,axiom,
% 0.30/0.46 ! [P3: ( option @ game ) > $o,A0: option @ game] :
% 0.30/0.46 ( ! [Alpha: game] : ( P3 @ ( some @ game @ Alpha ) )
% 0.30/0.46 => ( ( P3 @ ( none @ game ) )
% 0.30/0.46 => ( P3 @ A0 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Loopo.induct
% 0.30/0.46 thf(fact_191_undefg__equiv,axiom,
% 0.30/0.46 ! [Alpha2: option @ game] :
% 0.30/0.46 ( ( Alpha2
% 0.30/0.46 != ( none @ game ) )
% 0.30/0.46 = ( ? [G2: game] :
% 0.30/0.46 ( Alpha2
% 0.30/0.46 = ( some @ game @ G2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % undefg_equiv
% 0.30/0.46 thf(fact_192_Composeo_Oinduct,axiom,
% 0.30/0.46 ! [P3: ( option @ game ) > ( option @ game ) > $o,A0: option @ game,A1: option @ game] :
% 0.30/0.46 ( ! [Alpha: game,Beta: game] : ( P3 @ ( some @ game @ Alpha ) @ ( some @ game @ Beta ) )
% 0.30/0.46 => ( ! [Alpha: option @ game] : ( P3 @ Alpha @ ( none @ game ) )
% 0.30/0.46 => ( ! [V6: game] : ( P3 @ ( none @ game ) @ ( some @ game @ V6 ) )
% 0.30/0.46 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Composeo.induct
% 0.30/0.46 thf(fact_193_fml_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [X11: char,X12: trm,X21: trm,X222: trm] :
% 0.30/0.46 ( ( pred @ X11 @ X12 )
% 0.30/0.46 != ( geq @ X21 @ X222 ) ) ).
% 0.30/0.46
% 0.30/0.46 % fml.distinct(1)
% 0.30/0.46 thf(fact_194_le__funD,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F2: A > B,G: A > B,X3: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B ) @ F2 @ G )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funD
% 0.30/0.46 thf(fact_195_le__funE,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F2: A > B,G: A > B,X3: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B ) @ F2 @ G )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funE
% 0.30/0.46 thf(fact_196_le__funI,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F2: A > B,G: A > B] :
% 0.30/0.46 ( ! [X5: A] : ( ord_less_eq @ B @ ( F2 @ X5 ) @ ( G @ X5 ) )
% 0.30/0.46 => ( ord_less_eq @ ( A > B ) @ F2 @ G ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funI
% 0.30/0.46 thf(fact_197_le__fun__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ( ( ord_less_eq @ ( A > B ) )
% 0.30/0.46 = ( ^ [F: A > B,G2: A > B] :
% 0.30/0.46 ! [X: A] : ( ord_less_eq @ B @ ( F @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_fun_def
% 0.30/0.46 thf(fact_198_order__subst1,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( order @ B )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A3: A,F2: B > A,B4: B,C3: B] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ ( F2 @ B4 ) )
% 0.30/0.46 => ( ( ord_less_eq @ B @ B4 @ C3 )
% 0.30/0.46 => ( ! [X5: B,Y4: B] :
% 0.30/0.46 ( ( ord_less_eq @ B @ X5 @ Y4 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A3 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst1
% 0.30/0.46 thf(fact_199_order__subst2,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType] :
% 0.30/0.46 ( ( ( order @ C )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A3: A,B4: A,F2: A > C,C3: C] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/0.46 => ( ( ord_less_eq @ C @ ( F2 @ B4 ) @ C3 )
% 0.30/0.46 => ( ! [X5: A,Y4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X5 @ Y4 )
% 0.30/0.46 => ( ord_less_eq @ C @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
% 0.30/0.46 => ( ord_less_eq @ C @ ( F2 @ A3 ) @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst2
% 0.30/0.46 thf(fact_200_ord__eq__le__subst,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( ord @ B )
% 0.30/0.46 & ( ord @ A ) )
% 0.30/0.46 => ! [A3: A,F2: B > A,B4: B,C3: B] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 = ( F2 @ B4 ) )
% 0.30/0.46 => ( ( ord_less_eq @ B @ B4 @ C3 )
% 0.30/0.46 => ( ! [X5: B,Y4: B] :
% 0.30/0.46 ( ( ord_less_eq @ B @ X5 @ Y4 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A3 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_subst
% 0.30/0.46 thf(fact_201_ord__le__eq__subst,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( ord @ B )
% 0.30/0.46 & ( ord @ A ) )
% 0.30/0.46 => ! [A3: A,B4: A,F2: A > B,C3: B] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/0.46 => ( ( ( F2 @ B4 )
% 0.30/0.46 = C3 )
% 0.30/0.46 => ( ! [X5: A,Y4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X5 @ Y4 )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F2 @ A3 ) @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_subst
% 0.30/0.46 thf(fact_202_eq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y5: A,Z3: A] : ( Y5 = Z3 ) )
% 0.30/0.46 = ( ^ [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 & ( ord_less_eq @ A @ Y @ X ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_iff
% 0.30/0.46 thf(fact_203_antisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.30/0.46 => ( X3 = Y3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym
% 0.30/0.46 thf(fact_204_linear,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.30/0.46 | ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linear
% 0.30/0.46 thf(fact_205_eq__refl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( X3 = Y3 )
% 0.30/0.46 => ( ord_less_eq @ A @ X3 @ Y3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_refl
% 0.30/0.46 thf(fact_206_le__cases,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] :
% 0.30/0.46 ( ~ ( ord_less_eq @ A @ X3 @ Y3 )
% 0.30/0.46 => ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_cases
% 0.30/0.46 thf(fact_207_order_Otrans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A3: A,B4: A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B4 @ C3 )
% 0.30/0.46 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.trans
% 0.30/0.46 thf(fact_208_le__cases3,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X3: A,Y3: A,Z2: A] :
% 0.30/0.46 ( ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Y3 @ Z2 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Z2 @ Y3 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Z2 @ Y3 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Y3 @ X3 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 0.30/0.46 => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ X3 @ Y3 ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_cases3
% 0.30/0.46 thf(fact_209_antisym__conv,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [Y3: A,X3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.30/0.46 = ( X3 = Y3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym_conv
% 0.30/0.46 thf(fact_210_order__class_Oorder_Oeq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y5: A,Z3: A] : ( Y5 = Z3 ) )
% 0.30/0.46 = ( ^ [A6: A,B6: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A6 @ B6 )
% 0.30/0.46 & ( ord_less_eq @ A @ B6 @ A6 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.eq_iff
% 0.30/0.46 thf(fact_211_ord__eq__le__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [A3: A,B4: A,C3: A] :
% 0.30/0.46 ( ( A3 = B4 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B4 @ C3 )
% 0.30/0.46 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_trans
% 0.30/0.46 thf(fact_212_ord__le__eq__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [A3: A,B4: A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/0.46 => ( ( B4 = C3 )
% 0.30/0.46 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_trans
% 0.30/0.46 thf(fact_213_order__class_Oorder_Oantisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A3: A,B4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B4 @ A3 )
% 0.30/0.46 => ( A3 = B4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.antisym
% 0.30/0.46 thf(fact_214_order__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X3: A,Y3: A,Z2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 0.30/0.46 => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_trans
% 0.30/0.46 thf(fact_215_dual__order_Orefl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.refl
% 0.30/0.46 thf(fact_216_linorder__wlog,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [P3: A > A > $o,A3: A,B4: A] :
% 0.30/0.46 ( ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( P3 @ A2 @ B2 ) )
% 0.30/0.46 => ( ! [A2: A,B2: A] :
% 0.30/0.46 ( ( P3 @ B2 @ A2 )
% 0.30/0.46 => ( P3 @ A2 @ B2 ) )
% 0.30/0.46 => ( P3 @ A3 @ B4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linorder_wlog
% 0.30/0.46 thf(fact_217_dual__order_Otrans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B4: A,A3: A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B4 @ A3 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ C3 @ B4 )
% 0.30/0.46 => ( ord_less_eq @ A @ C3 @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.trans
% 0.30/0.46 thf(fact_218_dual__order_Oeq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y5: A,Z3: A] : ( Y5 = Z3 ) )
% 0.30/0.46 = ( ^ [A6: A,B6: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B6 @ A6 )
% 0.30/0.46 & ( ord_less_eq @ A @ A6 @ B6 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.eq_iff
% 0.30/0.46 thf(fact_219_dual__order_Oantisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B4: A,A3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B4 @ A3 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/0.46 => ( A3 = B4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.antisym
% 0.30/0.46 thf(fact_220_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_221_prop__restrict,axiom,
% 0.30/0.46 ! [A: $tType,X3: A,Z5: set @ A,X6: set @ A,P3: A > $o] :
% 0.30/0.46 ( ( member @ A @ X3 @ Z5 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ Z5
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ X6 )
% 0.30/0.46 & ( P3 @ X ) ) ) )
% 0.30/0.46 => ( P3 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prop_restrict
% 0.30/0.46 thf(fact_222_Collect__restrict,axiom,
% 0.30/0.46 ! [A: $tType,X6: set @ A,P3: A > $o] :
% 0.30/0.46 ( ord_less_eq @ ( set @ A )
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ X6 )
% 0.30/0.46 & ( P3 @ X ) ) )
% 0.30/0.46 @ X6 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_restrict
% 0.30/0.46 thf(fact_223_usubstappf__geq__conv,axiom,
% 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,Theta: trm,Eta2: trm] :
% 0.30/0.46 ( ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.30/0.46 != ( none @ fml ) )
% 0.30/0.46 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 & ( ( uSubst95898992stappt @ Sigma @ U @ Eta2 )
% 0.30/0.46 != ( none @ trm ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappf_geq_conv
% 0.30/0.46 thf(fact_224_usubstappf__geq,axiom,
% 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,Theta: trm,Eta2: trm] :
% 0.30/0.46 ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Eta2 )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.30/0.46 = ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Eta2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappf_geq
% 0.30/0.46 thf(fact_225_disjE__realizer2,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P3: $o,Q: A > $o,X3: option @ A,R4: B > $o,F2: B,G: A > B] :
% 0.30/0.46 ( ( case_option @ $o @ A @ P3 @ Q @ X3 )
% 0.30/0.46 => ( ( P3
% 0.30/0.46 => ( R4 @ F2 ) )
% 0.30/0.46 => ( ! [Q2: A] :
% 0.30/0.46 ( ( Q @ Q2 )
% 0.30/0.46 => ( R4 @ ( G @ Q2 ) ) )
% 0.30/0.46 => ( R4 @ ( case_option @ B @ A @ F2 @ G @ X3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % disjE_realizer2
% 0.30/0.46 thf(fact_226_Geqo_Oelims,axiom,
% 0.30/0.46 ! [X3: option @ trm,Xa: option @ trm,Y3: option @ fml] :
% 0.30/0.46 ( ( ( uSubst1556497037e_Geqo @ X3 @ Xa )
% 0.30/0.46 = Y3 )
% 0.30/0.46 => ( ! [Theta2: trm] :
% 0.30/0.46 ( ( X3
% 0.30/0.46 = ( some @ trm @ Theta2 ) )
% 0.30/0.46 => ! [Eta: trm] :
% 0.30/0.46 ( ( Xa
% 0.30/0.46 = ( some @ trm @ Eta ) )
% 0.30/0.46 => ( Y3
% 0.30/0.46 != ( some @ fml @ ( geq @ Theta2 @ Eta ) ) ) ) )
% 0.30/0.46 => ( ( ( X3
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 => ( Y3
% 0.30/0.46 != ( none @ fml ) ) )
% 0.30/0.46 => ~ ( ? [V6: trm] :
% 0.30/0.46 ( X3
% 0.30/0.46 = ( some @ trm @ V6 ) )
% 0.30/0.46 => ( ( Xa
% 0.30/0.46 = ( none @ trm ) )
% 0.30/0.46 => ( Y3
% 0.30/0.46 != ( none @ fml ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Geqo.elims
% 0.30/0.46 thf(fact_227_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_228_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_229_Geqo__undef,axiom,
% 0.30/0.46 ! [Theta: option @ trm,Eta2: option @ trm] :
% 0.30/0.46 ( ( ( uSubst1556497037e_Geqo @ Theta @ Eta2 )
% 0.30/0.46 = ( none @ fml ) )
% 0.30/0.46 = ( ( Theta
% 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_230_Geqo_Osimps_I3_J,axiom,
% 0.30/0.46 ! [V7: trm] :
% 0.30/0.46 ( ( uSubst1556497037e_Geqo @ ( some @ trm @ V7 ) @ ( 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_231_Geqo_Osimps_I1_J,axiom,
% 0.30/0.46 ! [Theta: trm,Eta2: trm] :
% 0.30/0.46 ( ( uSubst1556497037e_Geqo @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta2 ) )
% 0.30/0.46 = ( some @ fml @ ( geq @ Theta @ Eta2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Geqo.simps(1)
% 0.30/0.46 thf(fact_232_usubstappf_Osimps_I2_J,axiom,
% 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,Theta: trm,Eta2: trm] :
% 0.30/0.46 ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.30/0.46 = ( uSubst1556497037e_Geqo @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) @ ( uSubst95898992stappt @ Sigma @ U @ Eta2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappf.simps(2)
% 0.30/0.46 thf(fact_233_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_234_pred__subset__eq,axiom,
% 0.30/0.46 ! [A: $tType,R4: set @ A,S: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( 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 = ( ord_less_eq @ ( set @ A ) @ R4 @ S ) ) ).
% 0.30/0.46
% 0.30/0.46 % pred_subset_eq
% 0.30/0.46 thf(fact_235_Collect__empty__eq__bot,axiom,
% 0.30/0.46 ! [A: $tType,P3: A > $o] :
% 0.30/0.46 ( ( ( collect @ A @ P3 )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( P3
% 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_236_Set_Ois__empty__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( is_empty @ A )
% 0.30/0.46 = ( ^ [A5: set @ A] :
% 0.30/0.46 ( A5
% 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_237_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_238_usubstappt_Osimps_I4_J,axiom,
% 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,Theta: trm] :
% 0.30/0.46 ( ( uSubst95898992stappt @ Sigma @ U @ ( func @ F2 @ Theta ) )
% 0.30/0.46 = ( case_option @ ( option @ trm ) @ trm @ ( none @ trm )
% 0.30/0.46 @ ^ [Sigma_theta: trm] :
% 0.30/0.46 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( func @ F2 @ Sigma_theta ) )
% 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 @ ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta ) @ ( 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 @ Sigma
% 0.30/0.46 @ F2 ) )
% 0.30/0.46 @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.simps(4)
% 0.30/0.46 thf(fact_239_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_240_usubstappt__func2,axiom,
% 0.30/0.46 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F2: char,R2: trm,U: set @ variable,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 @ Sigma
% 0.30/0.46 @ F2 )
% 0.30/0.46 = ( some @ trm @ R2 ) )
% 0.30/0.46 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U )
% 0.30/0.46 != ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 => ( ( uSubst95898992stappt @ Sigma @ U @ ( func @ F2 @ Theta ) )
% 0.30/0.46 = ( none @ trm ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt_func2
% 0.30/0.46 thf(fact_241_usubstappt__func,axiom,
% 0.30/0.46 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F2: char,R2: trm,U: set @ variable,Theta: trm,Sigma_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 @ Sigma
% 0.30/0.46 @ F2 )
% 0.30/0.46 = ( some @ trm @ R2 ) )
% 0.30/0.46 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.30/0.46 = ( some @ trm @ Sigma_theta2 ) )
% 0.30/0.46 => ( ( uSubst95898992stappt @ Sigma @ U @ ( func @ F2 @ Theta ) )
% 0.30/0.46 = ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta2 ) @ ( bot_bot @ ( set @ variable ) ) @ R2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt_func
% 0.30/0.46 thf(fact_242_usubstappt__func__conv,axiom,
% 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,Theta: trm] :
% 0.30/0.46 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( func @ F2 @ Theta ) )
% 0.30/0.46 != ( none @ trm ) )
% 0.30/0.46 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 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 @ Sigma
% 0.30/0.46 @ F2 )
% 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 @ Sigma
% 0.30/0.46 @ F2 )
% 0.30/0.46 = ( some @ trm @ R3 ) )
% 0.30/0.46 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R3 ) @ U )
% 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_243_usappconst__simp,axiom,
% 0.30/0.46 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F2: char,R2: trm,U: 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 @ Sigma
% 0.30/0.46 @ F2 )
% 0.30/0.46 = ( some @ trm @ R2 ) )
% 0.30/0.46 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 => ( ( uSubst1138577137pconst @ Sigma @ U @ F2 )
% 0.30/0.46 = ( some @ trm @ R2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usappconst_simp
% 0.30/0.46 thf(fact_244_usappconst__conv,axiom,
% 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 ( ( ( uSubst1138577137pconst @ Sigma @ U @ F2 )
% 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 = ( 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 @ Sigma
% 0.30/0.46 @ F2 )
% 0.30/0.46 = ( some @ trm @ R3 ) )
% 0.30/0.46 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R3 ) @ U )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usappconst_conv
% 0.30/0.46 thf(fact_245_usappconst__def,axiom,
% 0.30/0.46 ( uSubst1138577137pconst
% 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,F: char] :
% 0.30/0.46 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( const @ F ) )
% 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 @ ( 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 @ Sigma2
% 0.30/0.46 @ F ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usappconst_def
% 0.30/0.46 thf(fact_246_usubstappt__const,axiom,
% 0.30/0.46 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F2: char,R2: trm,U: 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 @ Sigma
% 0.30/0.46 @ F2 )
% 0.30/0.46 = ( some @ trm @ R2 ) )
% 0.30/0.46 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U )
% 0.30/0.46 = ( bot_bot @ ( set @ variable ) ) )
% 0.30/0.46 => ( ( uSubst95898992stappt @ Sigma @ U @ ( const @ F2 ) )
% 0.30/0.46 = ( some @ trm @ R2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt_const
% 0.30/0.46 thf(fact_247_trm_Oinject_I3_J,axiom,
% 0.30/0.46 ! [X32: char,Y32: char] :
% 0.30/0.46 ( ( ( const @ X32 )
% 0.30/0.46 = ( const @ Y32 ) )
% 0.30/0.46 = ( X32 = Y32 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(3)
% 0.30/0.46 thf(fact_248_usubstappt_Osimps_I3_J,axiom,
% 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 ( ( uSubst95898992stappt @ Sigma @ U @ ( const @ F2 ) )
% 0.30/0.46 = ( uSubst1138577137pconst @ Sigma @ U @ F2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappt.simps(3)
% 0.30/0.46 thf(fact_249_trm_Odistinct_I23_J,axiom,
% 0.30/0.46 ! [X32: char,X41: char,X42: trm] :
% 0.30/0.46 ( ( const @ X32 )
% 0.30/0.46 != ( func @ X41 @ X42 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(23)
% 0.30/0.46 thf(fact_250_usubstappt__const__conv,axiom,
% 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 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( const @ F2 ) )
% 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 = ( 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 @ Sigma
% 0.30/0.46 @ F2 )
% 0.30/0.46 = ( some @ trm @ R3 ) )
% 0.30/0.46 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R3 ) @ U )
% 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_251_subset__Collect__iff,axiom,
% 0.30/0.46 ! [A: $tType,B3: set @ A,A4: set @ A,P3: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ B3 @ A4 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B3
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ A4 )
% 0.30/0.46 & ( P3 @ X ) ) ) )
% 0.30/0.46 = ( ! [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ B3 )
% 0.30/0.46 => ( P3 @ X ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_Collect_iff
% 0.30/0.46 thf(fact_252_subset__CollectI,axiom,
% 0.30/0.46 ! [A: $tType,B3: set @ A,A4: set @ A,Q: A > $o,P3: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ B3 @ A4 )
% 0.30/0.46 => ( ! [X5: A] :
% 0.30/0.46 ( ( member @ A @ X5 @ B3 )
% 0.30/0.46 => ( ( Q @ X5 )
% 0.30/0.46 => ( P3 @ X5 ) ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A )
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ B3 )
% 0.30/0.46 & ( Q @ X ) ) )
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ A4 )
% 0.30/0.46 & ( P3 @ X ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_CollectI
% 0.30/0.46 thf(fact_253_conj__subset__def,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,P3: A > $o,Q: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X: A] :
% 0.30/0.46 ( ( P3 @ X )
% 0.30/0.46 & ( Q @ X ) ) ) )
% 0.30/0.46 = ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( collect @ A @ P3 ) )
% 0.30/0.46 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( collect @ A @ Q ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % conj_subset_def
% 0.30/0.46 thf(fact_254_Diamondo_Ocases,axiom,
% 0.30/0.46 ! [X3: product_prod @ ( option @ game ) @ ( option @ fml )] :
% 0.30/0.46 ( ! [Alpha: game,Phi2: fml] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ Alpha ) @ ( some @ fml @ Phi2 ) ) )
% 0.30/0.46 => ( ! [Phi2: option @ fml] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( none @ game ) @ Phi2 ) )
% 0.30/0.46 => ~ ! [V6: game] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ V6 ) @ ( none @ fml ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Diamondo.cases
% 0.30/0.46
% 0.30/0.46 % Type constructors (28)
% 0.30/0.46 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.30/0.46 bounded_lattice @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.30/0.46 ! [A7: $tType] : ( bounded_lattice @ ( set @ A7 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( bounded_lattice @ A8 )
% 0.30/0.46 => ( bounded_lattice @ ( A7 > A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( bounded_lattice @ A8 )
% 0.30/0.46 => ( bounded_lattice_bot @ ( A7 > A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A8 )
% 0.30/0.46 => ( semilattice_inf @ ( A7 > A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( order_bot @ A8 )
% 0.30/0.46 => ( order_bot @ ( A7 > A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( preorder @ A8 )
% 0.30/0.46 => ( preorder @ ( A7 > A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( lattice @ A8 )
% 0.30/0.46 => ( lattice @ ( A7 > A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( order @ A8 )
% 0.30/0.46 => ( order @ ( A7 > A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Oord,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( ord @ A8 )
% 0.30/0.46 => ( ord @ ( A7 > A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Obot,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( bot @ A8 )
% 0.30/0.46 => ( bot @ ( A7 > A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_3,axiom,
% 0.30/0.46 ! [A7: $tType] : ( bounded_lattice_bot @ ( set @ A7 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_4,axiom,
% 0.30/0.46 ! [A7: $tType] : ( semilattice_inf @ ( set @ A7 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Oorder__bot_5,axiom,
% 0.30/0.46 ! [A7: $tType] : ( order_bot @ ( set @ A7 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Opreorder_6,axiom,
% 0.30/0.46 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Lattices_Olattice_7,axiom,
% 0.30/0.46 ! [A7: $tType] : ( lattice @ ( set @ A7 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Oorder_8,axiom,
% 0.30/0.46 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Oord_9,axiom,
% 0.30/0.46 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Obot_10,axiom,
% 0.30/0.46 ! [A7: $tType] : ( bot @ ( set @ A7 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_11,axiom,
% 0.30/0.46 bounded_lattice_bot @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_12,axiom,
% 0.30/0.46 semilattice_inf @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Oorder__bot_13,axiom,
% 0.30/0.46 order_bot @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Opreorder_14,axiom,
% 0.30/0.46 preorder @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.30/0.46 linorder @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Lattices_Olattice_15,axiom,
% 0.30/0.46 lattice @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Oorder_16,axiom,
% 0.30/0.46 order @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Oord_17,axiom,
% 0.30/0.46 ord @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Obot_18,axiom,
% 0.30/0.46 bot @ $o ).
% 0.30/0.46
% 0.30/0.46 % Helper facts (3)
% 0.30/0.46 thf(help_If_3_1_T,axiom,
% 0.30/0.46 ! [P3: $o] :
% 0.30/0.46 ( ( P3 = $true )
% 0.30/0.46 | ( P3 = $false ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(help_If_2_1_T,axiom,
% 0.30/0.46 ! [A: $tType,X3: A,Y3: A] :
% 0.30/0.46 ( ( if @ A @ $false @ X3 @ Y3 )
% 0.30/0.46 = Y3 ) ).
% 0.30/0.46
% 0.30/0.46 thf(help_If_1_1_T,axiom,
% 0.30/0.46 ! [A: $tType,X3: A,Y3: A] :
% 0.30/0.46 ( ( if @ A @ $true @ X3 @ Y3 )
% 0.30/0.46 = X3 ) ).
% 0.30/0.46
% 0.30/0.46 % Conjectures (1)
% 0.30/0.46 thf(conj_0,conjecture,
% 0.30/0.46 ( ( ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) )
% 0.30/0.46 != ( none @ fml ) )
% 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 @ fml ) )
% 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 @ fml ) )
% 0.30/0.46 @ ^ [Uv: char > ( option @ trm )] :
% 0.30/0.46 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.30/0.46 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.30/0.46 @ sigma
% 0.30/0.46 @ p )
% 0.30/0.46 = ( none @ fml ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 2.96/1.53 ---- Embedded in THF ---
% 2.96/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.96/1.53 %%% Generated on Tue Feb 24 08:29:46 EST 2026
% 2.96/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.96/1.53 %%% Logic specification used:
% 2.96/1.53 %%% thf(spec, logic, $$dhol).
% 2.96/1.53
% 2.96/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.JL8G97Ngch/DTF2DTF22545.p
% 2.96/1.53 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.96/1.53 thf(ty_t_Syntax_Ovariable, type, variable: $tType).
% 2.96/1.53 thf(ty_t_Option_Ooption, type, option: ($tType > $tType)).
% 2.96/1.53 thf(ty_t_Syntax_Ogame, type, game: $tType).
% 2.96/1.53 thf(ty_t_String_Ochar, type, char: $tType).
% 2.96/1.53 thf(ty_t_Syntax_Otrm, type, trm: $tType).
% 2.96/1.53 thf(ty_t_Syntax_Ofml, type, fml: $tType).
% 2.96/1.53 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.96/1.53 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: ($o))).
% 2.96/1.53 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.96/1.53 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: ($o))).
% 2.96/1.53 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.96/1.53 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.96/1.53 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: ($o))).
% 2.96/1.53 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.96/1.53 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.96/1.53 thf(sy_cl_Orderings_Oorder__bot, type, order_bot: (!> [A:$tType]: ($o))).
% 2.96/1.53 thf(sy_cl_Lattices_Osemilattice__inf, type, semilattice_inf: (!> [A:$tType]: ($o))).
% 2.96/1.53 thf(sy_cl_Lattices_Obounded__lattice__bot, type, bounded_lattice_bot: (!> [A:$tType]: ($o))).
% 2.96/1.53 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.96/1.53 thf(sy_c_Lattices_Oinf__class_Oinf, type, inf_inf: (!> [A:$tType]: ((A > (A > A))))).
% 2.96/1.53 thf(sy_c_Option_Ooption_ONone, type, none: (!> [A:$tType]: ((option @ A)))).
% 2.96/1.53 thf(sy_c_Option_Ooption_OSome, type, some: (!> [A:$tType]: ((A > (option @ A))))).
% 2.96/1.53 thf(sy_c_Option_Ooption_Ocase__option, type, case_option: (!> [B:$tType,A:$tType]: ((B > ((A > B) > ((option @ A) > B)))))).
% 2.96/1.53 thf(sy_c_Option_Ooption_Othe, type, the: (!> [A:$tType]: (((option @ A) > A)))).
% 2.96/1.53 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.96/1.53 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.96/1.53 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.96/1.53 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 2.96/1.53 thf(sy_c_Product__Type_Oprod_Ocase__prod, type, product_case_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 2.96/1.53 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.96/1.53 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.96/1.53 thf(sy_c_Static__Semantics_OFVF, type, static_FVF: (fml > (set @ variable))).
% 2.96/1.53 thf(sy_c_Static__Semantics_OFVT, type, static_FVT: (trm > (set @ variable))).
% 2.96/1.53 thf(sy_c_Syntax_Ofml_OGeq, type, geq: (trm > (trm > fml))).
% 2.96/1.53 thf(sy_c_Syntax_Ofml_OPred, type, pred: (char > (trm > fml))).
% 2.96/1.53 thf(sy_c_Syntax_Otrm_OConst, type, const: (char > trm)).
% 2.96/1.53 thf(sy_c_Syntax_Otrm_OFunc, type, func: (char > (trm > trm))).
% 2.96/1.53 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OGeqo, type, uSubst1556497037e_Geqo: ((option @ trm) > ((option @ trm) > (option @ fml)))).
% 2.96/1.53 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Odotsubstt, type, uSubst969145931substt: (trm > ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))))).
% 2.96/1.53 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousappconst, type, uSubst1138577137pconst: (((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) > ((set @ variable) > (char > (option @ trm))))).
% 2.96/1.53 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappf, type, uSubst95898978stappf: (((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) > ((set @ variable) > (fml > (option @ fml))))).
% 2.96/1.53 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappt, type, uSubst95898992stappt: (((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) > ((set @ variable) > (trm > (option @ trm))))).
% 2.96/1.53 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.96/1.53 thf(sy_v_Ua____, type, ua: (set @ variable)).
% 2.96/1.53 thf(sy_v_Va____, type, va: (set @ variable)).
% 2.96/1.53 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)))))).
% 2.96/1.53 thf(sy_v__092_060theta_062____, type, theta: trm).
% 2.96/1.53 thf(sy_v_p____, type, p: char).
% 2.96/1.53 thf(sy_v_vv____, type, vv: ((set @ variable) > ((set @ variable) > variable))).
% 2.96/1.53 thf(sy_v_vva____, type, vva: ((set @ variable) > ((set @ variable) > variable))).
% 2.96/1.53 thf(fact_0__092_060open_062_092_060forall_062x0_Ax1_O_A_I_092_060exists_062v2_O_Av2_A_092_060in_062_Ax1_A_092_060and_062_A_I_092_060exists_062v3_O_Av3_A_092_060in_062_Ax0_A_092_060and_062_Av2_A_061_Av3_J_J_A_061_A_Ivv_Ax0_Ax1_A_092_060in_062_Ax1_A_092_060and_062_A_I_092_060exists_062v3_O_Av3_A_092_060in_062_Ax0_A_092_060and_062_Avv_Ax0_Ax1_A_061_Av3_J_J_092_060close_062, axiom, (! [X0:(set @ variable),X1:(set @ variable)]: (((? [V2:variable]: (((((member @ variable) @ V2) @ X1) & (? [V3:variable]: (((((member @ variable) @ V3) @ X0) & (V2 = V3))))))) = ((((member @ variable) @ ((vv @ X0) @ X1)) @ X1) & (? [V3:variable]: (((((member @ variable) @ V3) @ X0) & (((vv @ X0) @ X1) = V3))))))))).
% 2.96/1.53 thf(fact_1_Pred_Oprems_I2_J, axiom, ((((uSubst95898978stappf @ sigma) @ ua) @ ((pred @ p) @ theta)) != (none @ fml))).
% 2.96/1.53 thf(fact_2__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Aundeff_092_060close_062, axiom, (~ ((((((inf_inf @ (set @ variable)) @ (static_FVF @ ((the @ fml) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))) @ va) = (bot_bot @ (set @ variable))) => ((((uSubst95898978stappf @ (uSubst969145931substt @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ va) @ theta)))) @ (bot_bot @ (set @ variable))) @ ((the @ fml) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p))) = (none @ fml)))))).
% 2.96/1.53 thf(fact_3__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_A_092_060Longrightarrow_062_ASPreds_A_092_060sigma_062_Ap_A_061_Aundeff_092_060close_062, axiom, ((~ (((((((inf_inf @ (set @ variable)) @ (static_FVF @ ((the @ fml) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))) @ va) = (bot_bot @ (set @ variable))) => ((((uSubst95898978stappf @ (uSubst969145931substt @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ va) @ theta)))) @ (bot_bot @ (set @ variable))) @ ((the @ fml) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p))) = (((uSubst95898978stappf @ sigma) @ va) @ ((pred @ p) @ theta)))) & (((((inf_inf @ (set @ variable)) @ (static_FVF @ ((the @ fml) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))) @ va) != (bot_bot @ (set @ variable))) => ((none @ fml) = (((uSubst95898978stappf @ sigma) @ va) @ ((pred @ p) @ theta))))))) => (((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p) = (none @ fml)))).
% 2.96/1.53 thf(fact_4_usubstappf__det, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Phi:fml,V:(set @ variable)]: ((((((uSubst95898978stappf @ Sigma) @ U) @ Phi) != (none @ fml)) => (((((uSubst95898978stappf @ Sigma) @ V) @ Phi) != (none @ fml)) => ((((uSubst95898978stappf @ Sigma) @ U) @ Phi) = (((uSubst95898978stappf @ Sigma) @ V) @ Phi))))))).
% 2.96/1.53 thf(fact_5_f8, axiom, ((((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p) = (none @ fml)) => ((((uSubst95898978stappf @ sigma) @ ua) @ ((pred @ p) @ theta)) = (((uSubst95898978stappf @ sigma) @ va) @ ((pred @ p) @ theta))))).
% 2.96/1.53 thf(fact_6__092_060open_062vv_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060notin_062_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060or_062_Avva_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060notin_062_AV_A_092_060or_062_Avv_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060noteq_062_Avva_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_092_060close_062, axiom, ((~ ((((member @ variable) @ ((vv @ va) @ (static_FVF @ ((the @ fml) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p))))) @ (static_FVF @ ((the @ fml) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))))) | ((~ ((((member @ variable) @ ((vva @ va) @ (static_FVF @ ((the @ fml) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p))))) @ va))) | (((vv @ va) @ (static_FVF @ ((the @ fml) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))) != ((vva @ va) @ (static_FVF @ ((the @ fml) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))))))).
% 2.96/1.53 thf(fact_7_fml_Oinject_I1_J, axiom, (! [X11:char,X12:trm,Y11:char,Y12:trm]: (((((pred @ X11) @ X12) = ((pred @ Y11) @ Y12)) = ((X11 = Y11) & (X12 = Y12)))))).
% 2.96/1.53 thf(fact_8_f7, axiom, ((((uSubst95898992stappt @ sigma) @ ua) @ theta) = (((uSubst95898992stappt @ sigma) @ va) @ theta))).
% 2.96/1.53 thf(fact_9_case__prod__app, axiom, (! [A:$tType,D:$tType,C:$tType,B:$tType]: (((((product_case_prod @ B) @ C) @ (D > A)) = (^ [F:(B > (C > (D > A))),X:((product_prod @ B) @ C),Y:D]: ((((((product_case_prod @ B) @ C) @ A) @ (^ [L:B,R:C]: ((((F @ L) @ R) @ Y)))) @ X))))))).
% 2.96/1.53 thf(fact_10_f1, axiom, (! [V4:variable]: (((~ ((((member @ variable) @ V4) @ va))) | (((member @ variable) @ V4) @ ua))))).
% 2.96/1.53 thf(fact_11_f10, axiom, ((((((inf_inf @ (set @ variable)) @ (static_FVF @ ((the @ fml) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))) @ va) != (bot_bot @ (set @ variable))) | (! [V4:variable]: (((~ ((((member @ variable) @ V4) @ (static_FVF @ ((the @ fml) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))))) | (! [Va:variable]: (((~ ((((member @ variable) @ Va) @ va))) | (V4 != Va)))))))) & (((((inf_inf @ (set @ variable)) @ (static_FVF @ ((the @ fml) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))) @ va) = (bot_bot @ (set @ variable))) | ((((member @ variable) @ ((vv @ va) @ (static_FVF @ ((the @ fml) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p))))) @ (static_FVF @ ((the @ fml) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))) & ((((member @ variable) @ ((vva @ va) @ (static_FVF @ ((the @ fml) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p))))) @ va) & (((vv @ va) @ (static_FVF @ ((the @ fml) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))) = ((vva @ va) @ (static_FVF @ ((the @ fml) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))))))))).
% 2.96/1.53 thf(fact_12_prod_Ocase__distrib, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,H:(C > D),F2:(A > (B > C)),Prod:((product_prod @ A) @ B)]: (((H @ (((((product_case_prod @ A) @ B) @ C) @ F2) @ Prod)) = (((((product_case_prod @ A) @ B) @ D) @ (^ [X13:A,X2:B]: ((H @ ((F2 @ X13) @ X2))))) @ Prod))))).
% 2.96/1.53 thf(fact_13_usubstappf__pred2, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),P2:char,R2:fml,U:(set @ variable),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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ Sigma) @ P2) = ((some @ fml) @ R2)) => (((((inf_inf @ (set @ variable)) @ (static_FVF @ R2)) @ U) != (bot_bot @ (set @ variable))) => ((((uSubst95898978stappf @ Sigma) @ U) @ ((pred @ P2) @ Theta)) = (none @ fml))))))).
% 2.96/1.53 thf(fact_14_f2, axiom, (! [Z:(option @ fml),F3:(fml > (option @ fml)),Za:(option @ fml)]: ((((Za = (none @ fml)) => ((((((case_option @ (option @ fml)) @ fml) @ Z) @ F3) @ Za) = Z)) & ((Za != (none @ fml)) => ((((((case_option @ (option @ fml)) @ fml) @ Z) @ F3) @ Za) = (F3 @ ((the @ fml) @ Za)))))))).
% 2.96/1.53 thf(fact_15_Pred_Oprems_I1_J, axiom, (((ord_less_eq @ (set @ variable)) @ va) @ ua)).
% 2.96/1.53 thf(fact_16_f9, axiom, (! [V5:(set @ variable),Va2:(set @ variable)]: (((((((inf_inf @ (set @ variable)) @ V5) @ Va2) != (bot_bot @ (set @ variable))) | (! [V4:variable]: (((~ ((((member @ variable) @ V4) @ V5))) | (! [Va:variable]: (((~ ((((member @ variable) @ Va) @ Va2))) | (V4 != Va)))))))) & (((((inf_inf @ (set @ variable)) @ V5) @ Va2) = (bot_bot @ (set @ variable))) | ((((member @ variable) @ ((vv @ Va2) @ V5)) @ V5) & ((((member @ variable) @ ((vva @ Va2) @ V5)) @ Va2) & (((vv @ Va2) @ V5) = ((vva @ Va2) @ V5))))))))).
% 2.96/1.53 thf(fact_17__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062vva_O_A_092_060forall_062V_AVa_O_A_IV_A_092_060inter_062_AVa_A_092_060noteq_062_A_123_125_A_092_060or_062_A_I_092_060forall_062v_O_Av_A_092_060notin_062_AV_A_092_060or_062_A_I_092_060forall_062va_O_Ava_A_092_060notin_062_AVa_A_092_060or_062_Av_A_092_060noteq_062_Ava_J_J_J_A_092_060and_062_A_IV_A_092_060inter_062_AVa_A_061_A_123_125_A_092_060or_062_Avv_AVa_AV_A_092_060in_062_AV_A_092_060and_062_Avva_AVa_AV_A_092_060in_062_AVa_A_092_060and_062_Avv_AVa_AV_A_061_Avva_AVa_AV_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [Vva:((set @ variable) > ((set @ variable) > variable))]: ((~ ((! [V5:(set @ variable),Va2:(set @ variable)]: (((((((inf_inf @ (set @ variable)) @ V5) @ Va2) != (bot_bot @ (set @ variable))) | (! [V4:variable]: (((~ ((((member @ variable) @ V4) @ V5))) | (! [Va:variable]: (((~ ((((member @ variable) @ Va) @ Va2))) | (V4 != Va)))))))) & (((((inf_inf @ (set @ variable)) @ V5) @ Va2) = (bot_bot @ (set @ variable))) | ((((member @ variable) @ ((vv @ Va2) @ V5)) @ V5) & ((((member @ variable) @ ((Vva @ Va2) @ V5)) @ Va2) & (((vv @ Va2) @ V5) = ((Vva @ Va2) @ V5))))))))))))))).
% 2.96/1.53 thf(fact_18_option_Oinject, axiom, (! [A:$tType,X22:A,Y2:A]: (((((some @ A) @ X22) = ((some @ A) @ Y2)) = (X22 = Y2))))).
% 2.96/1.53 thf(fact_19_f5, axiom, ((((uSubst95898992stappt @ sigma) @ ua) @ theta) != (none @ trm))).
% 2.96/1.53 thf(fact_20_not__Some__eq, axiom, (! [A:$tType,X3:(option @ A)]: (((! [Y:A]: ((X3 != ((some @ A) @ Y)))) = (X3 = (none @ A)))))).
% 2.96/1.53 thf(fact_21_not__None__eq, axiom, (! [A:$tType,X3:(option @ A)]: (((X3 != (none @ A)) = (? [Y:A]: ((X3 = ((some @ A) @ Y)))))))).
% 2.96/1.53 thf(fact_22_option_Ocollapse, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) => (((some @ A) @ ((the @ A) @ Option)) = Option))))).
% 2.96/1.53 thf(fact_23_option_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:B,F22:(A > B),X22:A]: (((((((case_option @ B) @ A) @ F1) @ F22) @ ((some @ A) @ X22)) = (F22 @ X22))))).
% 2.96/1.53 thf(fact_24_option_Osel, axiom, (! [A:$tType,X22:A]: ((((the @ A) @ ((some @ A) @ X22)) = X22)))).
% 2.96/1.53 thf(fact_25_option_Osplit__sel, axiom, (! [B:$tType,A:$tType,P3:(B > $o),F1:B,F22:(A > B),Option:(option @ A)]: (((P3 @ (((((case_option @ B) @ A) @ F1) @ F22) @ Option)) = (((Option = (none @ A)) => (P3 @ F1)) & ((Option = ((some @ A) @ ((the @ A) @ Option))) => (P3 @ (F22 @ ((the @ A) @ Option))))))))).
% 2.96/1.53 thf(fact_26_option_Ocase__distrib, axiom, (! [C:$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))))).
% 2.96/1.53 thf(fact_27_option_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P3:(B > $o),F1:B,F22:(A > B),Option:(option @ A)]: (((P3 @ (((((case_option @ B) @ A) @ F1) @ F22) @ Option)) = (~ ((((Option = (none @ A)) & (~ ((P3 @ F1)))) | ((Option = ((some @ A) @ ((the @ A) @ Option))) & (~ ((P3 @ (F22 @ ((the @ A) @ Option))))))))))))).
% 2.96/1.53 thf(fact_28_usubstappt__det, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm,V:(set @ variable)]: ((((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (none @ trm)) => (((((uSubst95898992stappt @ Sigma) @ V) @ Theta) != (none @ trm)) => ((((uSubst95898992stappt @ Sigma) @ U) @ Theta) = (((uSubst95898992stappt @ Sigma) @ V) @ Theta))))))).
% 2.96/1.53 thf(fact_29_usubstappt__antimon, axiom, (! [V:(set @ variable),U:(set @ variable),Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),Theta:trm]: (((((ord_less_eq @ (set @ variable)) @ V) @ U) => (((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (none @ trm)) => ((((uSubst95898992stappt @ Sigma) @ U) @ Theta) = (((uSubst95898992stappt @ Sigma) @ V) @ Theta))))))).
% 2.96/1.53 thf(fact_30_option_Oexhaust__sel, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) => (Option = ((some @ A) @ ((the @ A) @ Option))))))).
% 2.96/1.53 thf(fact_31_combine__options__cases, axiom, (! [A:$tType,B:$tType,X3:(option @ A),P3:((option @ A) > ((option @ B) > $o)),Y3:(option @ B)]: ((((X3 = (none @ A)) => ((P3 @ X3) @ Y3)) => (((Y3 = (none @ B)) => ((P3 @ X3) @ Y3)) => ((! [A2:A,B2:B]: (((X3 = ((some @ A) @ A2)) => ((Y3 = ((some @ B) @ B2)) => ((P3 @ X3) @ Y3))))) => ((P3 @ X3) @ Y3))))))).
% 2.96/1.53 thf(fact_32_split__option__all, axiom, (! [A:$tType]: (((^ [P4:((option @ A) > $o)]: ((! [X4:(option @ A)]: ((P4 @ X4))))) = (^ [P:((option @ A) > $o)]: (((P @ (none @ A)) & (! [X:A]: ((P @ ((some @ A) @ X))))))))))).
% 2.96/1.53 thf(fact_33_split__option__ex, axiom, (! [A:$tType]: (((^ [P4:((option @ A) > $o)]: ((? [X4:(option @ A)]: ((P4 @ X4))))) = (^ [P:((option @ A) > $o)]: (((P @ (none @ A)) | (? [X:A]: ((P @ ((some @ A) @ X))))))))))).
% 2.96/1.53 thf(fact_34_option_Oinducts, axiom, (! [A:$tType,P3:((option @ A) > $o),Option:(option @ A)]: (((P3 @ (none @ A)) => ((! [X5:A]: ((P3 @ ((some @ A) @ X5)))) => (P3 @ Option)))))).
% 2.96/1.53 thf(fact_35_option_Oexhaust, axiom, (! [A:$tType,Y3:(option @ A)]: (((Y3 != (none @ A)) => (~ ((! [X23:A]: ((Y3 != ((some @ A) @ X23)))))))))).
% 2.96/1.53 thf(fact_36_option_OdiscI, axiom, (! [A:$tType,Option:(option @ A),X22:A]: (((Option = ((some @ A) @ X22)) => (Option != (none @ A)))))).
% 2.96/1.53 thf(fact_37_option_Odistinct_I1_J, axiom, (! [A:$tType,X22:A]: (((none @ A) != ((some @ A) @ X22))))).
% 2.96/1.53 thf(fact_38_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))))))))).
% 2.96/1.53 thf(fact_39_option_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F1:B,F22:(A > B)]: (((((((case_option @ B) @ A) @ F1) @ F22) @ (none @ A)) = F1)))).
% 2.96/1.53 thf(fact_40_Existso_Oinduct, axiom, (! [P3:(variable > ((option @ fml) > $o)),A0:variable,A1:(option @ fml)]: (((! [X5:variable,Phi2:fml]: (((P3 @ X5) @ ((some @ fml) @ Phi2)))) => ((! [X5:variable]: (((P3 @ X5) @ (none @ fml)))) => ((P3 @ A0) @ A1)))))).
% 2.96/1.53 thf(fact_41_undeff__equiv, axiom, (! [Phi:(option @ fml)]: (((Phi != (none @ fml)) = (? [F:fml]: ((Phi = ((some @ fml) @ F)))))))).
% 2.96/1.53 thf(fact_42_Testo_Oinduct, axiom, (! [P3:((option @ fml) > $o),A0:(option @ fml)]: (((! [Phi2:fml]: ((P3 @ ((some @ fml) @ Phi2)))) => ((P3 @ (none @ fml)) => (P3 @ A0)))))).
% 2.96/1.53 thf(fact_43_Testo_Ocases, axiom, (! [X3:(option @ fml)]: (((! [Phi2:fml]: ((X3 != ((some @ fml) @ Phi2)))) => (X3 = (none @ fml)))))).
% 2.96/1.53 thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P3:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P3)) = (P3 @ A3))))).
% 2.96/1.53 thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A4)))) = A4)))).
% 2.96/1.53 thf(fact_46_Collect__cong, axiom, (! [A:$tType,P3:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P3 @ X5) = (Q @ X5)))) => (((collect @ A) @ P3) = ((collect @ A) @ Q)))))).
% 2.96/1.53 thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F2:(A > B),G:(A > B)]: (((! [X5:A]: (((F2 @ X5) = (G @ X5)))) => (F2 = G))))).
% 2.96/1.53 thf(fact_48_Ando_Oinduct, axiom, (! [P3:((option @ fml) > ((option @ fml) > $o)),A0:(option @ fml),A1:(option @ fml)]: (((! [Phi2:fml,Psi:fml]: (((P3 @ ((some @ fml) @ Phi2)) @ ((some @ fml) @ Psi)))) => ((! [X_1:(option @ fml)]: (((P3 @ (none @ fml)) @ X_1))) => ((! [V6:fml]: (((P3 @ ((some @ fml) @ V6)) @ (none @ fml)))) => ((P3 @ A0) @ A1))))))).
% 2.96/1.53 thf(fact_49_option_Oexpand, axiom, (! [A:$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)))))).
% 2.96/1.53 thf(fact_50_usubstappf__pred__conv, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),P2:char,Theta:trm]: ((((((uSubst95898978stappf @ Sigma) @ U) @ ((pred @ P2) @ Theta)) != (none @ fml)) => (((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (none @ 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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ Sigma) @ P2) = (none @ fml)) | (? [R3:fml]: (((((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ Sigma) @ P2) = ((some @ fml) @ R3)) & ((((inf_inf @ (set @ variable)) @ (static_FVF @ R3)) @ U) = (bot_bot @ (set @ variable)))))))))))).
% 2.96/1.53 thf(fact_51_f6, axiom, ((((((case_option @ (option @ fml)) @ trm) @ (none @ fml)) @ (^ [T:trm]: ((((((case_option @ (option @ fml)) @ fml) @ ((some @ fml) @ ((pred @ p) @ T))) @ (^ [F:fml]: (((((if @ (option @ fml)) @ ((((inf_inf @ (set @ variable)) @ (static_FVF @ F)) @ ua) = (bot_bot @ (set @ variable)))) @ (((uSubst95898978stappf @ (uSubst969145931substt @ T)) @ (bot_bot @ (set @ variable))) @ F)) @ (none @ fml))))) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p))))) @ (((uSubst95898992stappt @ sigma) @ ua) @ theta)) = (((((case_option @ (option @ fml)) @ fml) @ ((some @ fml) @ ((pred @ p) @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ ua) @ theta))))) @ (^ [F:fml]: (((((if @ (option @ fml)) @ ((((inf_inf @ (set @ variable)) @ (static_FVF @ F)) @ ua) = (bot_bot @ (set @ variable)))) @ (((uSubst95898978stappf @ (uSubst969145931substt @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ ua) @ theta)))) @ (bot_bot @ (set @ variable))) @ F)) @ (none @ fml))))) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))).
% 2.96/1.53 thf(fact_52_f3, axiom, ((((((case_option @ (option @ fml)) @ trm) @ (none @ fml)) @ (^ [T:trm]: ((((((case_option @ (option @ fml)) @ fml) @ ((some @ fml) @ ((pred @ p) @ T))) @ (^ [F:fml]: (((((if @ (option @ fml)) @ ((((inf_inf @ (set @ variable)) @ (static_FVF @ F)) @ ua) = (bot_bot @ (set @ variable)))) @ (((uSubst95898978stappf @ (uSubst969145931substt @ T)) @ (bot_bot @ (set @ variable))) @ F)) @ (none @ fml))))) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p))))) @ (((uSubst95898992stappt @ sigma) @ ua) @ theta)) != (none @ fml))).
% 2.96/1.53 thf(fact_53_usubstappf_Osimps_I1_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),P2:char,Theta:trm]: (((((uSubst95898978stappf @ Sigma) @ U) @ ((pred @ P2) @ Theta)) = (((((case_option @ (option @ fml)) @ trm) @ (none @ fml)) @ (^ [Sigma_theta:trm]: ((((((case_option @ (option @ fml)) @ fml) @ ((some @ fml) @ ((pred @ P2) @ Sigma_theta))) @ (^ [R:fml]: (((((if @ (option @ fml)) @ ((((inf_inf @ (set @ variable)) @ (static_FVF @ R)) @ U) = (bot_bot @ (set @ variable)))) @ (((uSubst95898978stappf @ (uSubst969145931substt @ Sigma_theta)) @ (bot_bot @ (set @ variable))) @ R)) @ (none @ fml))))) @ ((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ Sigma) @ P2))))) @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta)))))).
% 2.96/1.53 thf(fact_54_Int__subset__iff, axiom, (! [A:$tType,C2:(set @ A),A4:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C2) @ (((inf_inf @ (set @ A)) @ A4) @ B3)) = ((((ord_less_eq @ (set @ A)) @ C2) @ A4) & (((ord_less_eq @ (set @ A)) @ C2) @ B3)))))).
% 2.96/1.53 thf(fact_55_inf__bot__left, axiom, (! [A:$tType]: (((bounded_lattice_bot @ A) => (! [X3:A]: (((((inf_inf @ A) @ (bot_bot @ A)) @ X3) = (bot_bot @ A)))))))).
% 2.96/1.53 thf(fact_56_inf__bot__right, axiom, (! [A:$tType]: (((bounded_lattice_bot @ A) => (! [X3:A]: (((((inf_inf @ A) @ X3) @ (bot_bot @ A)) = (bot_bot @ A)))))))).
% 2.96/1.53 thf(fact_57_subset__empty, axiom, (! [A:$tType,A4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ (bot_bot @ (set @ A))) = (A4 = (bot_bot @ (set @ A))))))).
% 2.96/1.53 thf(fact_58_empty__subsetI, axiom, (! [A:$tType,A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A4)))).
% 2.96/1.53 thf(fact_59_le__inf__iff, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X3:A,Y3:A,Z2:A]: (((((ord_less_eq @ A) @ X3) @ (((inf_inf @ A) @ Y3) @ Z2)) = ((((ord_less_eq @ A) @ X3) @ Y3) & (((ord_less_eq @ A) @ X3) @ Z2))))))))).
% 2.96/1.53 thf(fact_60_inf_Obounded__iff, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A3:A,B4:A,C3:A]: (((((ord_less_eq @ A) @ A3) @ (((inf_inf @ A) @ B4) @ C3)) = ((((ord_less_eq @ A) @ A3) @ B4) & (((ord_less_eq @ A) @ A3) @ C3))))))))).
% 2.96/1.53 thf(fact_61_f4, axiom, (! [Z:(option @ fml),F3:(trm > (option @ fml)),Za:(option @ trm)]: ((((Za = (none @ trm)) => ((((((case_option @ (option @ fml)) @ trm) @ Z) @ F3) @ Za) = Z)) & ((Za != (none @ trm)) => ((((((case_option @ (option @ fml)) @ trm) @ Z) @ F3) @ Za) = (F3 @ ((the @ trm) @ Za)))))))).
% 2.96/1.53 thf(fact_62_empty__Collect__eq, axiom, (! [A:$tType,P3:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P3)) = (! [X:A]: ((~ ((P3 @ X))))))))).
% 2.96/1.53 thf(fact_63_Collect__empty__eq, axiom, (! [A:$tType,P3:(A > $o)]: (((((collect @ A) @ P3) = (bot_bot @ (set @ A))) = (! [X:A]: ((~ ((P3 @ X))))))))).
% 2.96/1.53 thf(fact_64_all__not__in__conv, axiom, (! [A:$tType,A4:(set @ A)]: (((! [X:A]: ((~ ((((member @ A) @ X) @ A4))))) = (A4 = (bot_bot @ (set @ A))))))).
% 2.96/1.53 thf(fact_65_empty__iff, axiom, (! [A:$tType,C3:A]: ((~ ((((member @ A) @ C3) @ (bot_bot @ (set @ A)))))))).
% 2.96/1.53 thf(fact_66_subset__antisym, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B3) => ((((ord_less_eq @ (set @ A)) @ B3) @ A4) => (A4 = B3)))))).
% 2.96/1.53 thf(fact_67_subsetI, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A)]: (((! [X5:A]: (((((member @ A) @ X5) @ A4) => (((member @ A) @ X5) @ B3)))) => (((ord_less_eq @ (set @ A)) @ A4) @ B3))))).
% 2.96/1.53 thf(fact_68_inf__right__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X3:A,Y3:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X3) @ Y3)) @ Y3) = (((inf_inf @ A) @ X3) @ Y3)))))))).
% 2.96/1.53 thf(fact_69_inf_Oright__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A3:A,B4:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A3) @ B4)) @ B4) = (((inf_inf @ A) @ A3) @ B4)))))))).
% 2.96/1.53 thf(fact_70_inf__left__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X3:A,Y3:A]: (((((inf_inf @ A) @ X3) @ (((inf_inf @ A) @ X3) @ Y3)) = (((inf_inf @ A) @ X3) @ Y3)))))))).
% 2.96/1.53 thf(fact_71_inf_Oleft__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A3:A,B4:A]: (((((inf_inf @ A) @ A3) @ (((inf_inf @ A) @ A3) @ B4)) = (((inf_inf @ A) @ A3) @ B4)))))))).
% 2.96/1.53 thf(fact_72_inf__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X3:A]: (((((inf_inf @ A) @ X3) @ X3) = X3))))))).
% 2.96/1.53 thf(fact_73_inf_Oidem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A3:A]: (((((inf_inf @ A) @ A3) @ A3) = A3))))))).
% 2.96/1.53 thf(fact_74_inf__apply, axiom, (! [B:$tType,A:$tType]: (((semilattice_inf @ B) => ((inf_inf @ (A > B)) = (^ [F:(A > B),G2:(A > B),X:A]: ((((inf_inf @ B) @ (F @ X)) @ (G2 @ X))))))))).
% 2.96/1.53 thf(fact_75_Int__iff, axiom, (! [A:$tType,C3:A,A4:(set @ A),B3:(set @ A)]: (((((member @ A) @ C3) @ (((inf_inf @ (set @ A)) @ A4) @ B3)) = ((((member @ A) @ C3) @ A4) & (((member @ A) @ C3) @ B3)))))).
% 2.96/1.53 thf(fact_76_IntI, axiom, (! [A:$tType,C3:A,A4:(set @ A),B3:(set @ A)]: (((((member @ A) @ C3) @ A4) => ((((member @ A) @ C3) @ B3) => (((member @ A) @ C3) @ (((inf_inf @ (set @ A)) @ A4) @ B3))))))).
% 2.96/1.53 thf(fact_77_usubstappf__pred, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),P2:char,R2:fml,U:(set @ variable),Theta:trm,Sigma_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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ Sigma) @ P2) = ((some @ fml) @ R2)) => (((((inf_inf @ (set @ variable)) @ (static_FVF @ R2)) @ U) = (bot_bot @ (set @ variable))) => (((((uSubst95898992stappt @ Sigma) @ U) @ Theta) = ((some @ trm) @ Sigma_theta2)) => ((((uSubst95898978stappf @ Sigma) @ U) @ ((pred @ P2) @ Theta)) = (((uSubst95898978stappf @ (uSubst969145931substt @ Sigma_theta2)) @ (bot_bot @ (set @ variable))) @ R2)))))))).
% 2.96/1.53 thf(fact_78_ODEo_Oinduct, axiom, (! [P3:(char > ((option @ trm) > $o)),A0:char,A1:(option @ trm)]: (((! [X5:char,Theta2:trm]: (((P3 @ X5) @ ((some @ trm) @ Theta2)))) => ((! [X5:char]: (((P3 @ X5) @ (none @ trm)))) => ((P3 @ A0) @ A1)))))).
% 2.96/1.53 thf(fact_79_undeft__None, axiom, ((none @ trm) = (none @ trm))).
% 2.96/1.53 thf(fact_80_undeft__equiv, axiom, (! [Theta:(option @ trm)]: (((Theta != (none @ trm)) = (? [T:trm]: ((Theta = ((some @ trm) @ T)))))))).
% 2.96/1.53 thf(fact_81_Timeso_Oinduct, axiom, (! [P3:((option @ trm) > ((option @ trm) > $o)),A0:(option @ trm),A1:(option @ trm)]: (((! [Theta2:trm,Eta:trm]: (((P3 @ ((some @ trm) @ Theta2)) @ ((some @ trm) @ Eta)))) => ((! [X_1:(option @ trm)]: (((P3 @ (none @ trm)) @ X_1))) => ((! [V6:trm]: (((P3 @ ((some @ trm) @ V6)) @ (none @ trm)))) => ((P3 @ A0) @ A1))))))).
% 2.96/1.53 thf(fact_82_Assigno_Oinduct, axiom, (! [P3:(variable > ((option @ trm) > $o)),A0:variable,A1:(option @ trm)]: (((! [X5:variable,Theta2:trm]: (((P3 @ X5) @ ((some @ trm) @ Theta2)))) => ((! [X5:variable]: (((P3 @ X5) @ (none @ trm)))) => ((P3 @ A0) @ A1)))))).
% 2.96/1.53 thf(fact_83_Differentialo_Ocases, axiom, (! [X3:(option @ trm)]: (((! [Theta2:trm]: ((X3 != ((some @ trm) @ Theta2)))) => (X3 = (none @ trm)))))).
% 2.96/1.53 thf(fact_84_Differentialo_Oinduct, axiom, (! [P3:((option @ trm) > $o),A0:(option @ trm)]: (((! [Theta2:trm]: ((P3 @ ((some @ trm) @ Theta2)))) => ((P3 @ (none @ trm)) => (P3 @ A0)))))).
% 2.96/1.53 thf(fact_85_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 2.96/1.53 thf(fact_86_inf__set__def, axiom, (! [A:$tType]: (((inf_inf @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: (((collect @ A) @ (((inf_inf @ (A > $o)) @ (^ [X:A]: ((((member @ A) @ X) @ A5)))) @ (^ [X:A]: ((((member @ A) @ X) @ B5))))))))))).
% 2.96/1.53 thf(fact_87_less__eq__set__def, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: ((((ord_less_eq @ (A > $o)) @ (^ [X:A]: ((((member @ A) @ X) @ A5)))) @ (^ [X:A]: ((((member @ A) @ X) @ B5)))))))))).
% 2.96/1.53 thf(fact_88_option_Odisc__eq__case_I2_J, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) = (((((case_option @ $o) @ A) @ $false) @ (^ [Uu:A]: ($true))) @ Option))))).
% 2.96/1.53 thf(fact_89_option_Odisc__eq__case_I1_J, axiom, (! [A:$tType,Option:(option @ A)]: (((Option = (none @ A)) = (((((case_option @ $o) @ A) @ $true) @ (^ [Uu:A]: ($false))) @ Option))))).
% 2.96/1.53 thf(fact_90_Diamondo_Oinduct, axiom, (! [P3:((option @ game) > ((option @ fml) > $o)),A0:(option @ game),A1:(option @ fml)]: (((! [Alpha:game,Phi2:fml]: (((P3 @ ((some @ game) @ Alpha)) @ ((some @ fml) @ Phi2)))) => ((! [X_1:(option @ fml)]: (((P3 @ (none @ game)) @ X_1))) => ((! [V6:game]: (((P3 @ ((some @ game) @ V6)) @ (none @ fml)))) => ((P3 @ A0) @ A1))))))).
% 2.96/1.53 thf(fact_91_case__optionE, axiom, (! [A:$tType,P3:$o,Q:(A > $o),X3:(option @ A)]: (((((((case_option @ $o) @ A) @ P3) @ Q) @ X3) => (((X3 = (none @ A)) => (~ (P3))) => (~ ((! [Y4:A]: (((X3 = ((some @ A) @ Y4)) => (~ ((Q @ Y4))))))))))))).
% 2.96/1.53 thf(fact_92_ex__in__conv, axiom, (! [A:$tType,A4:(set @ A)]: (((? [X:A]: ((((member @ A) @ X) @ A4))) = (A4 != (bot_bot @ (set @ A))))))).
% 2.96/1.53 thf(fact_93_equals0I, axiom, (! [A:$tType,A4:(set @ A)]: (((! [Y4:A]: ((~ ((((member @ A) @ Y4) @ A4))))) => (A4 = (bot_bot @ (set @ A))))))).
% 2.96/1.53 thf(fact_94_equals0D, axiom, (! [A:$tType,A4:(set @ A),A3:A]: (((A4 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A3) @ A4))))))).
% 2.96/1.53 thf(fact_95_emptyE, axiom, (! [A:$tType,A3:A]: ((~ ((((member @ A) @ A3) @ (bot_bot @ (set @ A)))))))).
% 2.96/1.53 thf(fact_96_Collect__mono__iff, axiom, (! [A:$tType,P3:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P3)) @ ((collect @ A) @ Q)) = (! [X:A]: (((P3 @ X) => (Q @ X)))))))).
% 2.96/1.53 thf(fact_97_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y5:(set @ A),Z3:(set @ A)]: ((Y5 = Z3))) = (^ [A5:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) & (((ord_less_eq @ (set @ A)) @ B5) @ A5)))))))).
% 2.96/1.53 thf(fact_98_subset__trans, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A),C2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B3) => ((((ord_less_eq @ (set @ A)) @ B3) @ C2) => (((ord_less_eq @ (set @ A)) @ A4) @ C2)))))).
% 2.96/1.53 thf(fact_99_Collect__mono, axiom, (! [A:$tType,P3:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P3 @ X5) => (Q @ X5)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P3)) @ ((collect @ A) @ Q)))))).
% 2.96/1.53 thf(fact_100_subset__refl, axiom, (! [A:$tType,A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A4) @ A4)))).
% 2.96/1.53 thf(fact_101_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: ((! [T:A]: (((((member @ A) @ T) @ A5) => (((member @ A) @ T) @ B5)))))))))).
% 2.96/1.53 thf(fact_102_equalityD2, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A)]: (((A4 = B3) => (((ord_less_eq @ (set @ A)) @ B3) @ A4))))).
% 2.96/1.53 thf(fact_103_equalityD1, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A)]: (((A4 = B3) => (((ord_less_eq @ (set @ A)) @ A4) @ B3))))).
% 2.96/1.53 thf(fact_104_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: ((! [X:A]: (((((member @ A) @ X) @ A5) => (((member @ A) @ X) @ B5)))))))))).
% 2.96/1.53 thf(fact_105_equalityE, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A)]: (((A4 = B3) => (~ (((((ord_less_eq @ (set @ A)) @ A4) @ B3) => (~ ((((ord_less_eq @ (set @ A)) @ B3) @ A4)))))))))).
% 2.96/1.53 thf(fact_106_subsetD, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A),C3:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B3) => ((((member @ A) @ C3) @ A4) => (((member @ A) @ C3) @ B3)))))).
% 2.96/1.53 thf(fact_107_in__mono, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A),X3:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B3) => ((((member @ A) @ X3) @ A4) => (((member @ A) @ X3) @ B3)))))).
% 2.96/1.53 thf(fact_108_inf__left__commute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X3:A,Y3:A,Z2:A]: (((((inf_inf @ A) @ X3) @ (((inf_inf @ A) @ Y3) @ Z2)) = (((inf_inf @ A) @ Y3) @ (((inf_inf @ A) @ X3) @ Z2))))))))).
% 2.96/1.53 thf(fact_109_inf_Oleft__commute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [B4:A,A3:A,C3:A]: (((((inf_inf @ A) @ B4) @ (((inf_inf @ A) @ A3) @ C3)) = (((inf_inf @ A) @ A3) @ (((inf_inf @ A) @ B4) @ C3))))))))).
% 2.96/1.53 thf(fact_110_inf__commute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => ((inf_inf @ A) = (^ [X:A,Y:A]: ((((inf_inf @ A) @ Y) @ X)))))))).
% 2.96/1.53 thf(fact_111_inf_Ocommute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => ((inf_inf @ A) = (^ [A6:A,B6:A]: ((((inf_inf @ A) @ B6) @ A6)))))))).
% 2.96/1.53 thf(fact_112_inf__assoc, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X3:A,Y3:A,Z2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X3) @ Y3)) @ Z2) = (((inf_inf @ A) @ X3) @ (((inf_inf @ A) @ Y3) @ Z2))))))))).
% 2.96/1.53 thf(fact_113_inf_Oassoc, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A3:A,B4:A,C3:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A3) @ B4)) @ C3) = (((inf_inf @ A) @ A3) @ (((inf_inf @ A) @ B4) @ C3))))))))).
% 2.96/1.53 thf(fact_114_boolean__algebra__cancel_Oinf2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [B3:A,K:A,B4:A,A3:A]: (((B3 = (((inf_inf @ A) @ K) @ B4)) => ((((inf_inf @ A) @ A3) @ B3) = (((inf_inf @ A) @ K) @ (((inf_inf @ A) @ A3) @ B4)))))))))).
% 2.96/1.53 thf(fact_115_boolean__algebra__cancel_Oinf1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A4:A,K:A,A3:A,B4:A]: (((A4 = (((inf_inf @ A) @ K) @ A3)) => ((((inf_inf @ A) @ A4) @ B4) = (((inf_inf @ A) @ K) @ (((inf_inf @ A) @ A3) @ B4)))))))))).
% 2.96/1.53 thf(fact_116_inf__fun__def, axiom, (! [B:$tType,A:$tType]: (((semilattice_inf @ B) => ((inf_inf @ (A > B)) = (^ [F:(A > B),G2:(A > B),X:A]: ((((inf_inf @ B) @ (F @ X)) @ (G2 @ X))))))))).
% 2.96/1.53 thf(fact_117_inf__sup__aci_I1_J, axiom, (! [A:$tType]: (((lattice @ A) => ((inf_inf @ A) = (^ [X:A,Y:A]: ((((inf_inf @ A) @ Y) @ X)))))))).
% 2.96/1.53 thf(fact_118_inf__sup__aci_I2_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X3:A,Y3:A,Z2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X3) @ Y3)) @ Z2) = (((inf_inf @ A) @ X3) @ (((inf_inf @ A) @ Y3) @ Z2))))))))).
% 2.96/1.53 thf(fact_119_inf__sup__aci_I3_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X3:A,Y3:A,Z2:A]: (((((inf_inf @ A) @ X3) @ (((inf_inf @ A) @ Y3) @ Z2)) = (((inf_inf @ A) @ Y3) @ (((inf_inf @ A) @ X3) @ Z2))))))))).
% 2.96/1.53 thf(fact_120_inf__sup__aci_I4_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X3:A,Y3:A]: (((((inf_inf @ A) @ X3) @ (((inf_inf @ A) @ X3) @ Y3)) = (((inf_inf @ A) @ X3) @ Y3)))))))).
% 2.96/1.53 thf(fact_121_Int__left__commute, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A),C2:(set @ A)]: (((((inf_inf @ (set @ A)) @ A4) @ (((inf_inf @ (set @ A)) @ B3) @ C2)) = (((inf_inf @ (set @ A)) @ B3) @ (((inf_inf @ (set @ A)) @ A4) @ C2)))))).
% 2.96/1.53 thf(fact_122_Int__left__absorb, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A)]: (((((inf_inf @ (set @ A)) @ A4) @ (((inf_inf @ (set @ A)) @ A4) @ B3)) = (((inf_inf @ (set @ A)) @ A4) @ B3))))).
% 2.96/1.53 thf(fact_123_Int__commute, axiom, (! [A:$tType]: (((inf_inf @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: ((((inf_inf @ (set @ A)) @ B5) @ A5))))))).
% 2.96/1.53 thf(fact_124_Int__absorb, axiom, (! [A:$tType,A4:(set @ A)]: (((((inf_inf @ (set @ A)) @ A4) @ A4) = A4)))).
% 2.96/1.53 thf(fact_125_Int__assoc, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A),C2:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A4) @ B3)) @ C2) = (((inf_inf @ (set @ A)) @ A4) @ (((inf_inf @ (set @ A)) @ B3) @ C2)))))).
% 2.96/1.53 thf(fact_126_IntD2, axiom, (! [A:$tType,C3:A,A4:(set @ A),B3:(set @ A)]: (((((member @ A) @ C3) @ (((inf_inf @ (set @ A)) @ A4) @ B3)) => (((member @ A) @ C3) @ B3))))).
% 2.96/1.53 thf(fact_127_IntD1, axiom, (! [A:$tType,C3:A,A4:(set @ A),B3:(set @ A)]: (((((member @ A) @ C3) @ (((inf_inf @ (set @ A)) @ A4) @ B3)) => (((member @ A) @ C3) @ A4))))).
% 2.96/1.53 thf(fact_128_IntE, axiom, (! [A:$tType,C3:A,A4:(set @ A),B3:(set @ A)]: (((((member @ A) @ C3) @ (((inf_inf @ (set @ A)) @ A4) @ B3)) => (~ (((((member @ A) @ C3) @ A4) => (~ ((((member @ A) @ C3) @ B3)))))))))).
% 2.96/1.53 thf(fact_129_empty__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (^ [X:A]: ($false))))))).
% 2.96/1.53 thf(fact_130_Collect__subset, axiom, (! [A:$tType,A4:(set @ A),P3:(A > $o)]: ((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ A4) & (P3 @ X)))))) @ A4)))).
% 2.96/1.53 thf(fact_131_Int__def, axiom, (! [A:$tType]: (((inf_inf @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: (((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ A5) & (((member @ A) @ X) @ B5))))))))))).
% 2.96/1.53 thf(fact_132_Int__Collect, axiom, (! [A:$tType,X3:A,A4:(set @ A),P3:(A > $o)]: (((((member @ A) @ X3) @ (((inf_inf @ (set @ A)) @ A4) @ ((collect @ A) @ P3))) = ((((member @ A) @ X3) @ A4) & (P3 @ X3)))))).
% 2.96/1.53 thf(fact_133_Collect__conj__eq, axiom, (! [A:$tType,P3:(A > $o),Q:(A > $o)]: ((((collect @ A) @ (^ [X:A]: (((P3 @ X) & (Q @ X))))) = (((inf_inf @ (set @ A)) @ ((collect @ A) @ P3)) @ ((collect @ A) @ Q)))))).
% 2.96/1.53 thf(fact_134_inf_OcoboundedI2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [B4:A,C3:A,A3:A]: (((((ord_less_eq @ A) @ B4) @ C3) => (((ord_less_eq @ A) @ (((inf_inf @ A) @ A3) @ B4)) @ C3)))))))).
% 2.96/1.53 thf(fact_135_inf_OcoboundedI1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A3:A,C3:A,B4:A]: (((((ord_less_eq @ A) @ A3) @ C3) => (((ord_less_eq @ A) @ (((inf_inf @ A) @ A3) @ B4)) @ C3)))))))).
% 2.96/1.53 thf(fact_136_inf_Oabsorb__iff2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => ((ord_less_eq @ A) = (^ [B6:A,A6:A]: (((((inf_inf @ A) @ A6) @ B6) = B6)))))))).
% 2.96/1.53 thf(fact_137_inf_Oabsorb__iff1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => ((ord_less_eq @ A) = (^ [A6:A,B6:A]: (((((inf_inf @ A) @ A6) @ B6) = A6)))))))).
% 2.96/1.53 thf(fact_138_inf_Ocobounded2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A3:A,B4:A]: ((((ord_less_eq @ A) @ (((inf_inf @ A) @ A3) @ B4)) @ B4))))))).
% 2.96/1.53 thf(fact_139_inf_Ocobounded1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A3:A,B4:A]: ((((ord_less_eq @ A) @ (((inf_inf @ A) @ A3) @ B4)) @ A3))))))).
% 2.96/1.53 thf(fact_140_inf_Oorder__iff, axiom, (! [A:$tType]: (((semilattice_inf @ A) => ((ord_less_eq @ A) = (^ [A6:A,B6:A]: ((A6 = (((inf_inf @ A) @ A6) @ B6))))))))).
% 2.96/1.53 thf(fact_141_inf__greatest, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X3:A,Y3:A,Z2:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => ((((ord_less_eq @ A) @ X3) @ Z2) => (((ord_less_eq @ A) @ X3) @ (((inf_inf @ A) @ Y3) @ Z2)))))))))).
% 2.96/1.53 thf(fact_142_inf_OboundedI, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A3:A,B4:A,C3:A]: (((((ord_less_eq @ A) @ A3) @ B4) => ((((ord_less_eq @ A) @ A3) @ C3) => (((ord_less_eq @ A) @ A3) @ (((inf_inf @ A) @ B4) @ C3)))))))))).
% 2.96/1.53 thf(fact_143_inf_OboundedE, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A3:A,B4:A,C3:A]: (((((ord_less_eq @ A) @ A3) @ (((inf_inf @ A) @ B4) @ C3)) => (~ (((((ord_less_eq @ A) @ A3) @ B4) => (~ ((((ord_less_eq @ A) @ A3) @ C3))))))))))))).
% 2.96/1.53 thf(fact_144_inf__absorb2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [Y3:A,X3:A]: (((((ord_less_eq @ A) @ Y3) @ X3) => ((((inf_inf @ A) @ X3) @ Y3) = Y3)))))))).
% 2.96/1.53 thf(fact_145_inf__absorb1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => ((((inf_inf @ A) @ X3) @ Y3) = X3)))))))).
% 2.96/1.53 thf(fact_146_inf_Oabsorb2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [B4:A,A3:A]: (((((ord_less_eq @ A) @ B4) @ A3) => ((((inf_inf @ A) @ A3) @ B4) = B4)))))))).
% 2.96/1.53 thf(fact_147_inf_Oabsorb1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A3:A,B4:A]: (((((ord_less_eq @ A) @ A3) @ B4) => ((((inf_inf @ A) @ A3) @ B4) = A3)))))))).
% 2.96/1.53 thf(fact_148_le__iff__inf, axiom, (! [A:$tType]: (((semilattice_inf @ A) => ((ord_less_eq @ A) = (^ [X:A,Y:A]: (((((inf_inf @ A) @ X) @ Y) = X)))))))).
% 2.96/1.53 thf(fact_149_inf__unique, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [F2:(A > (A > A)),X3:A,Y3:A]: (((! [X5:A,Y4:A]: ((((ord_less_eq @ A) @ ((F2 @ X5) @ Y4)) @ X5))) => ((! [X5:A,Y4:A]: ((((ord_less_eq @ A) @ ((F2 @ X5) @ Y4)) @ Y4))) => ((! [X5:A,Y4:A,Z4:A]: (((((ord_less_eq @ A) @ X5) @ Y4) => ((((ord_less_eq @ A) @ X5) @ Z4) => (((ord_less_eq @ A) @ X5) @ ((F2 @ Y4) @ Z4)))))) => ((((inf_inf @ A) @ X3) @ Y3) = ((F2 @ X3) @ Y3))))))))))).
% 2.96/1.53 thf(fact_150_inf_OorderI, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A3:A,B4:A]: (((A3 = (((inf_inf @ A) @ A3) @ B4)) => (((ord_less_eq @ A) @ A3) @ B4)))))))).
% 2.96/1.53 thf(fact_151_inf_OorderE, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A3:A,B4:A]: (((((ord_less_eq @ A) @ A3) @ B4) => (A3 = (((inf_inf @ A) @ A3) @ B4))))))))).
% 2.96/1.53 thf(fact_152_le__infI2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [B4:A,X3:A,A3:A]: (((((ord_less_eq @ A) @ B4) @ X3) => (((ord_less_eq @ A) @ (((inf_inf @ A) @ A3) @ B4)) @ X3)))))))).
% 2.96/1.53 thf(fact_153_le__infI1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A3:A,X3:A,B4:A]: (((((ord_less_eq @ A) @ A3) @ X3) => (((ord_less_eq @ A) @ (((inf_inf @ A) @ A3) @ B4)) @ X3)))))))).
% 2.96/1.53 thf(fact_154_inf__mono, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A3:A,C3:A,B4:A,D2:A]: (((((ord_less_eq @ A) @ A3) @ C3) => ((((ord_less_eq @ A) @ B4) @ D2) => (((ord_less_eq @ A) @ (((inf_inf @ A) @ A3) @ B4)) @ (((inf_inf @ A) @ C3) @ D2)))))))))).
% 2.96/1.53 thf(fact_155_le__infI, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X3:A,A3:A,B4:A]: (((((ord_less_eq @ A) @ X3) @ A3) => ((((ord_less_eq @ A) @ X3) @ B4) => (((ord_less_eq @ A) @ X3) @ (((inf_inf @ A) @ A3) @ B4)))))))))).
% 2.96/1.53 thf(fact_156_le__infE, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X3:A,A3:A,B4:A]: (((((ord_less_eq @ A) @ X3) @ (((inf_inf @ A) @ A3) @ B4)) => (~ (((((ord_less_eq @ A) @ X3) @ A3) => (~ ((((ord_less_eq @ A) @ X3) @ B4))))))))))))).
% 2.96/1.53 thf(fact_157_inf__le2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X3:A,Y3:A]: ((((ord_less_eq @ A) @ (((inf_inf @ A) @ X3) @ Y3)) @ Y3))))))).
% 2.96/1.53 thf(fact_158_inf__le1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X3:A,Y3:A]: ((((ord_less_eq @ A) @ (((inf_inf @ A) @ X3) @ Y3)) @ X3))))))).
% 2.96/1.53 thf(fact_159_inf__sup__ord_I1_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X3:A,Y3:A]: ((((ord_less_eq @ A) @ (((inf_inf @ A) @ X3) @ Y3)) @ X3))))))).
% 2.96/1.53 thf(fact_160_inf__sup__ord_I2_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X3:A,Y3:A]: ((((ord_less_eq @ A) @ (((inf_inf @ A) @ X3) @ Y3)) @ Y3))))))).
% 2.96/1.53 thf(fact_161_disjoint__iff__not__equal, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A)]: ((((((inf_inf @ (set @ A)) @ A4) @ B3) = (bot_bot @ (set @ A))) = (! [X:A]: (((((member @ A) @ X) @ A4) => (! [Y:A]: (((((member @ A) @ Y) @ B3) => (X != Y))))))))))).
% 2.96/1.53 thf(fact_162_Int__empty__right, axiom, (! [A:$tType,A4:(set @ A)]: (((((inf_inf @ (set @ A)) @ A4) @ (bot_bot @ (set @ A))) = (bot_bot @ (set @ A)))))).
% 2.96/1.53 thf(fact_163_Int__empty__left, axiom, (! [A:$tType,B3:(set @ A)]: (((((inf_inf @ (set @ A)) @ (bot_bot @ (set @ A))) @ B3) = (bot_bot @ (set @ A)))))).
% 2.96/1.53 thf(fact_164_disjoint__iff, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A)]: ((((((inf_inf @ (set @ A)) @ A4) @ B3) = (bot_bot @ (set @ A))) = (! [X:A]: (((((member @ A) @ X) @ A4) => (~ ((((member @ A) @ X) @ B3)))))))))).
% 2.96/1.53 thf(fact_165_Int__emptyI, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A)]: (((! [X5:A]: (((((member @ A) @ X5) @ A4) => (~ ((((member @ A) @ X5) @ B3)))))) => ((((inf_inf @ (set @ A)) @ A4) @ B3) = (bot_bot @ (set @ A))))))).
% 2.96/1.53 thf(fact_166_Int__Collect__mono, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A),P3:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B3) => ((! [X5:A]: (((((member @ A) @ X5) @ A4) => ((P3 @ X5) => (Q @ X5))))) => (((ord_less_eq @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A4) @ ((collect @ A) @ P3))) @ (((inf_inf @ (set @ A)) @ B3) @ ((collect @ A) @ Q)))))))).
% 2.96/1.53 thf(fact_167_Int__greatest, axiom, (! [A:$tType,C2:(set @ A),A4:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C2) @ A4) => ((((ord_less_eq @ (set @ A)) @ C2) @ B3) => (((ord_less_eq @ (set @ A)) @ C2) @ (((inf_inf @ (set @ A)) @ A4) @ B3))))))).
% 2.96/1.53 thf(fact_168_Int__absorb2, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B3) => ((((inf_inf @ (set @ A)) @ A4) @ B3) = A4))))).
% 2.96/1.53 thf(fact_169_Int__absorb1, axiom, (! [A:$tType,B3:(set @ A),A4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B3) @ A4) => ((((inf_inf @ (set @ A)) @ A4) @ B3) = B3))))).
% 2.96/1.53 thf(fact_170_Int__lower2, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A4) @ B3)) @ B3)))).
% 2.96/1.53 thf(fact_171_Int__lower1, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A4) @ B3)) @ A4)))).
% 2.96/1.53 thf(fact_172_Int__mono, axiom, (! [A:$tType,A4:(set @ A),C2:(set @ A),B3:(set @ A),D3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ C2) => ((((ord_less_eq @ (set @ A)) @ B3) @ D3) => (((ord_less_eq @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A4) @ B3)) @ (((inf_inf @ (set @ A)) @ C2) @ D3))))))).
% 2.96/1.53 thf(fact_173_bot__apply, axiom, (! [C:$tType,D:$tType]: (((bot @ C) => ((bot_bot @ (D > C)) = (^ [X:D]: ((bot_bot @ C)))))))).
% 2.96/1.53 thf(fact_174_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A]: ((((ord_less_eq @ A) @ X3) @ X3))))))).
% 2.96/1.53 thf(fact_175_subset__emptyI, axiom, (! [A:$tType,A4:(set @ A)]: (((! [X5:A]: ((~ ((((member @ A) @ X5) @ A4))))) => (((ord_less_eq @ (set @ A)) @ A4) @ (bot_bot @ (set @ A))))))).
% 2.96/1.53 thf(fact_176_bot_Oextremum__uniqueI, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A3:A]: (((((ord_less_eq @ A) @ A3) @ (bot_bot @ A)) => (A3 = (bot_bot @ A))))))))).
% 2.96/1.53 thf(fact_177_bot_Oextremum__unique, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A3:A]: (((((ord_less_eq @ A) @ A3) @ (bot_bot @ A)) = (A3 = (bot_bot @ A))))))))).
% 2.96/1.53 thf(fact_178_bot_Oextremum, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A3:A]: ((((ord_less_eq @ A) @ (bot_bot @ A)) @ A3))))))).
% 2.96/1.53 thf(fact_179_usubstappf__geqr, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm,Eta2:trm]: ((((((uSubst95898978stappf @ Sigma) @ U) @ ((geq @ Theta) @ Eta2)) != (none @ fml)) => ((((uSubst95898978stappf @ Sigma) @ U) @ ((geq @ Theta) @ Eta2)) = ((some @ fml) @ ((geq @ ((the @ trm) @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta))) @ ((the @ trm) @ (((uSubst95898992stappt @ Sigma) @ U) @ Eta2))))))))).
% 2.96/1.53 thf(fact_180_fml_Oinject_I2_J, axiom, (! [X21:trm,X222:trm,Y21:trm,Y22:trm]: (((((geq @ X21) @ X222) = ((geq @ Y21) @ Y22)) = ((X21 = Y21) & (X222 = Y22)))))).
% 2.96/1.53 thf(fact_181_predicate1I, axiom, (! [A:$tType,P3:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P3 @ X5) => (Q @ X5)))) => (((ord_less_eq @ (A > $o)) @ P3) @ Q))))).
% 2.96/1.53 thf(fact_182_inf1I, axiom, (! [A:$tType,A4:(A > $o),X3:A,B3:(A > $o)]: (((A4 @ X3) => ((B3 @ X3) => ((((inf_inf @ (A > $o)) @ A4) @ B3) @ X3)))))).
% 2.96/1.53 thf(fact_183_inf1E, axiom, (! [A:$tType,A4:(A > $o),B3:(A > $o),X3:A]: ((((((inf_inf @ (A > $o)) @ A4) @ B3) @ X3) => (~ (((A4 @ X3) => (~ ((B3 @ X3)))))))))).
% 2.96/1.53 thf(fact_184_inf1D1, axiom, (! [A:$tType,A4:(A > $o),B3:(A > $o),X3:A]: ((((((inf_inf @ (A > $o)) @ A4) @ B3) @ X3) => (A4 @ X3))))).
% 2.96/1.53 thf(fact_185_inf1D2, axiom, (! [A:$tType,A4:(A > $o),B3:(A > $o),X3:A]: ((((((inf_inf @ (A > $o)) @ A4) @ B3) @ X3) => (B3 @ X3))))).
% 2.96/1.53 thf(fact_186_predicate1D, axiom, (! [A:$tType,P3:(A > $o),Q:(A > $o),X3:A]: (((((ord_less_eq @ (A > $o)) @ P3) @ Q) => ((P3 @ X3) => (Q @ X3)))))).
% 2.96/1.53 thf(fact_187_rev__predicate1D, axiom, (! [A:$tType,P3:(A > $o),X3:A,Q:(A > $o)]: (((P3 @ X3) => ((((ord_less_eq @ (A > $o)) @ P3) @ Q) => (Q @ X3)))))).
% 2.96/1.53 thf(fact_188_Aterm__Some, axiom, ((some @ trm) = (some @ trm))).
% 2.96/1.53 thf(fact_189_Loopo_Ocases, axiom, (! [X3:(option @ game)]: (((! [Alpha:game]: ((X3 != ((some @ game) @ Alpha)))) => (X3 = (none @ game)))))).
% 2.96/1.53 thf(fact_190_Loopo_Oinduct, axiom, (! [P3:((option @ game) > $o),A0:(option @ game)]: (((! [Alpha:game]: ((P3 @ ((some @ game) @ Alpha)))) => ((P3 @ (none @ game)) => (P3 @ A0)))))).
% 2.96/1.53 thf(fact_191_undefg__equiv, axiom, (! [Alpha2:(option @ game)]: (((Alpha2 != (none @ game)) = (? [G2:game]: ((Alpha2 = ((some @ game) @ G2)))))))).
% 2.96/1.53 thf(fact_192_Composeo_Oinduct, axiom, (! [P3:((option @ game) > ((option @ game) > $o)),A0:(option @ game),A1:(option @ game)]: (((! [Alpha:game,Beta:game]: (((P3 @ ((some @ game) @ Alpha)) @ ((some @ game) @ Beta)))) => ((! [Alpha:(option @ game)]: (((P3 @ Alpha) @ (none @ game)))) => ((! [V6:game]: (((P3 @ (none @ game)) @ ((some @ game) @ V6)))) => ((P3 @ A0) @ A1))))))).
% 2.96/1.53 thf(fact_193_fml_Odistinct_I1_J, axiom, (! [X11:char,X12:trm,X21:trm,X222:trm]: ((((pred @ X11) @ X12) != ((geq @ X21) @ X222))))).
% 2.96/1.53 thf(fact_194_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F2:(A > B),G:(A > B),X3:A]: (((((ord_less_eq @ (A > B)) @ F2) @ G) => (((ord_less_eq @ B) @ (F2 @ X3)) @ (G @ X3))))))))).
% 2.96/1.53 thf(fact_195_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F2:(A > B),G:(A > B),X3:A]: (((((ord_less_eq @ (A > B)) @ F2) @ G) => (((ord_less_eq @ B) @ (F2 @ X3)) @ (G @ X3))))))))).
% 2.96/1.53 thf(fact_196_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F2:(A > B),G:(A > B)]: (((! [X5:A]: ((((ord_less_eq @ B) @ (F2 @ X5)) @ (G @ X5)))) => (((ord_less_eq @ (A > B)) @ F2) @ G)))))))).
% 2.96/1.53 thf(fact_197_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F:(A > B),G2:(A > B)]: ((! [X:A]: ((((ord_less_eq @ B) @ (F @ X)) @ (G2 @ X))))))))))).
% 2.96/1.53 thf(fact_198_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A3:A,F2:(B > A),B4:B,C3:B]: (((((ord_less_eq @ A) @ A3) @ (F2 @ B4)) => ((((ord_less_eq @ B) @ B4) @ C3) => ((! [X5:B,Y4:B]: (((((ord_less_eq @ B) @ X5) @ Y4) => (((ord_less_eq @ A) @ (F2 @ X5)) @ (F2 @ Y4))))) => (((ord_less_eq @ A) @ A3) @ (F2 @ C3))))))))))).
% 2.96/1.53 thf(fact_199_order__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A3:A,B4:A,F2:(A > C),C3:C]: (((((ord_less_eq @ A) @ A3) @ B4) => ((((ord_less_eq @ C) @ (F2 @ B4)) @ C3) => ((! [X5:A,Y4:A]: (((((ord_less_eq @ A) @ X5) @ Y4) => (((ord_less_eq @ C) @ (F2 @ X5)) @ (F2 @ Y4))))) => (((ord_less_eq @ C) @ (F2 @ A3)) @ C3)))))))))).
% 2.96/1.53 thf(fact_200_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A3:A,F2:(B > A),B4:B,C3:B]: (((A3 = (F2 @ B4)) => ((((ord_less_eq @ B) @ B4) @ C3) => ((! [X5:B,Y4:B]: (((((ord_less_eq @ B) @ X5) @ Y4) => (((ord_less_eq @ A) @ (F2 @ X5)) @ (F2 @ Y4))))) => (((ord_less_eq @ A) @ A3) @ (F2 @ C3))))))))))).
% 2.96/1.53 thf(fact_201_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A3:A,B4:A,F2:(A > B),C3:B]: (((((ord_less_eq @ A) @ A3) @ B4) => (((F2 @ B4) = C3) => ((! [X5:A,Y4:A]: (((((ord_less_eq @ A) @ X5) @ Y4) => (((ord_less_eq @ B) @ (F2 @ X5)) @ (F2 @ Y4))))) => (((ord_less_eq @ B) @ (F2 @ A3)) @ C3)))))))))).
% 2.96/1.53 thf(fact_202_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y5:A,Z3:A]: ((Y5 = Z3))) = (^ [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) & (((ord_less_eq @ A) @ Y) @ X))))))))).
% 2.96/1.53 thf(fact_203_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => ((((ord_less_eq @ A) @ Y3) @ X3) => (X3 = Y3))))))))).
% 2.96/1.53 thf(fact_204_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) | (((ord_less_eq @ A) @ Y3) @ X3)))))))).
% 2.96/1.53 thf(fact_205_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y3:A]: (((X3 = Y3) => (((ord_less_eq @ A) @ X3) @ Y3)))))))).
% 2.96/1.53 thf(fact_206_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y3:A]: (((~ ((((ord_less_eq @ A) @ X3) @ Y3))) => (((ord_less_eq @ A) @ Y3) @ X3)))))))).
% 2.96/1.53 thf(fact_207_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B4:A,C3:A]: (((((ord_less_eq @ A) @ A3) @ B4) => ((((ord_less_eq @ A) @ B4) @ C3) => (((ord_less_eq @ A) @ A3) @ C3))))))))).
% 2.96/1.53 thf(fact_208_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y3:A,Z2:A]: ((((((ord_less_eq @ A) @ X3) @ Y3) => (~ ((((ord_less_eq @ A) @ Y3) @ Z2)))) => (((((ord_less_eq @ A) @ Y3) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Z2)))) => (((((ord_less_eq @ A) @ X3) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y3)))) => (((((ord_less_eq @ A) @ Z2) @ Y3) => (~ ((((ord_less_eq @ A) @ Y3) @ X3)))) => (((((ord_less_eq @ A) @ Y3) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X3)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Y3))))))))))))))))).
% 2.96/1.53 thf(fact_209_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y3:A,X3:A]: (((((ord_less_eq @ A) @ Y3) @ X3) => ((((ord_less_eq @ A) @ X3) @ Y3) = (X3 = Y3))))))))).
% 2.96/1.53 thf(fact_210_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y5:A,Z3:A]: ((Y5 = Z3))) = (^ [A6:A,B6:A]: (((((ord_less_eq @ A) @ A6) @ B6) & (((ord_less_eq @ A) @ B6) @ A6))))))))).
% 2.96/1.53 thf(fact_211_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B4:A,C3:A]: (((A3 = B4) => ((((ord_less_eq @ A) @ B4) @ C3) => (((ord_less_eq @ A) @ A3) @ C3))))))))).
% 2.96/1.53 thf(fact_212_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B4:A,C3:A]: (((((ord_less_eq @ A) @ A3) @ B4) => ((B4 = C3) => (((ord_less_eq @ A) @ A3) @ C3))))))))).
% 2.96/1.53 thf(fact_213_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B4:A]: (((((ord_less_eq @ A) @ A3) @ B4) => ((((ord_less_eq @ A) @ B4) @ A3) => (A3 = B4))))))))).
% 2.96/1.53 thf(fact_214_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y3:A,Z2:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => ((((ord_less_eq @ A) @ Y3) @ Z2) => (((ord_less_eq @ A) @ X3) @ Z2))))))))).
% 2.96/1.53 thf(fact_215_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A]: ((((ord_less_eq @ A) @ A3) @ A3))))))).
% 2.96/1.53 thf(fact_216_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P3:(A > (A > $o)),A3:A,B4:A]: (((! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((P3 @ A2) @ B2)))) => ((! [A2:A,B2:A]: ((((P3 @ B2) @ A2) => ((P3 @ A2) @ B2)))) => ((P3 @ A3) @ B4))))))))).
% 2.96/1.53 thf(fact_217_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A3:A,C3:A]: (((((ord_less_eq @ A) @ B4) @ A3) => ((((ord_less_eq @ A) @ C3) @ B4) => (((ord_less_eq @ A) @ C3) @ A3))))))))).
% 2.96/1.53 thf(fact_218_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y5:A,Z3:A]: ((Y5 = Z3))) = (^ [A6:A,B6:A]: (((((ord_less_eq @ A) @ B6) @ A6) & (((ord_less_eq @ A) @ A6) @ B6))))))))).
% 2.96/1.53 thf(fact_219_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A3:A]: (((((ord_less_eq @ A) @ B4) @ A3) => ((((ord_less_eq @ A) @ A3) @ B4) => (A3 = B4))))))))).
% 2.96/1.53 thf(fact_220_bot__fun__def, axiom, (! [B:$tType,A:$tType]: (((bot @ B) => ((bot_bot @ (A > B)) = (^ [X:A]: ((bot_bot @ B)))))))).
% 2.96/1.53 thf(fact_221_prop__restrict, axiom, (! [A:$tType,X3:A,Z5:(set @ A),X6:(set @ A),P3:(A > $o)]: (((((member @ A) @ X3) @ Z5) => ((((ord_less_eq @ (set @ A)) @ Z5) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ X6) & (P3 @ X)))))) => (P3 @ X3)))))).
% 2.96/1.53 thf(fact_222_Collect__restrict, axiom, (! [A:$tType,X6:(set @ A),P3:(A > $o)]: ((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ X6) & (P3 @ X)))))) @ X6)))).
% 2.96/1.53 thf(fact_223_usubstappf__geq__conv, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm,Eta2:trm]: ((((((uSubst95898978stappf @ Sigma) @ U) @ ((geq @ Theta) @ Eta2)) != (none @ fml)) => (((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (none @ trm)) & ((((uSubst95898992stappt @ Sigma) @ U) @ Eta2) != (none @ trm))))))).
% 2.96/1.53 thf(fact_224_usubstappf__geq, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm,Eta2:trm]: ((((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (none @ trm)) => (((((uSubst95898992stappt @ Sigma) @ U) @ Eta2) != (none @ trm)) => ((((uSubst95898978stappf @ Sigma) @ U) @ ((geq @ Theta) @ Eta2)) = ((some @ fml) @ ((geq @ ((the @ trm) @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta))) @ ((the @ trm) @ (((uSubst95898992stappt @ Sigma) @ U) @ Eta2)))))))))).
% 2.96/1.53 thf(fact_225_disjE__realizer2, axiom, (! [B:$tType,A:$tType,P3:$o,Q:(A > $o),X3:(option @ A),R4:(B > $o),F2:B,G:(A > B)]: (((((((case_option @ $o) @ A) @ P3) @ Q) @ X3) => ((P3 => (R4 @ F2)) => ((! [Q2:A]: (((Q @ Q2) => (R4 @ (G @ Q2))))) => (R4 @ (((((case_option @ B) @ A) @ F2) @ G) @ X3)))))))).
% 2.96/1.53 thf(fact_226_Geqo_Oelims, axiom, (! [X3:(option @ trm),Xa:(option @ trm),Y3:(option @ fml)]: (((((uSubst1556497037e_Geqo @ X3) @ Xa) = Y3) => ((! [Theta2:trm]: (((X3 = ((some @ trm) @ Theta2)) => (! [Eta:trm]: (((Xa = ((some @ trm) @ Eta)) => (Y3 != ((some @ fml) @ ((geq @ Theta2) @ Eta))))))))) => (((X3 = (none @ trm)) => (Y3 != (none @ fml))) => (~ (((? [V6:trm]: ((X3 = ((some @ trm) @ V6)))) => ((Xa = (none @ trm)) => (Y3 != (none @ fml)))))))))))).
% 2.96/1.53 thf(fact_227_inf__Int__eq, axiom, (! [A:$tType,R4:(set @ A),S:(set @ A)]: (((((inf_inf @ (A > $o)) @ (^ [X:A]: ((((member @ A) @ X) @ R4)))) @ (^ [X:A]: ((((member @ A) @ X) @ S)))) = (^ [X:A]: ((((member @ A) @ X) @ (((inf_inf @ (set @ A)) @ R4) @ S)))))))).
% 2.96/1.53 thf(fact_228_Geqo_Osimps_I2_J, axiom, (! [Eta2:(option @ trm)]: ((((uSubst1556497037e_Geqo @ (none @ trm)) @ Eta2) = (none @ fml))))).
% 2.96/1.53 thf(fact_229_Geqo__undef, axiom, (! [Theta:(option @ trm),Eta2:(option @ trm)]: (((((uSubst1556497037e_Geqo @ Theta) @ Eta2) = (none @ fml)) = ((Theta = (none @ trm)) | (Eta2 = (none @ trm))))))).
% 2.96/1.53 thf(fact_230_Geqo_Osimps_I3_J, axiom, (! [V7:trm]: ((((uSubst1556497037e_Geqo @ ((some @ trm) @ V7)) @ (none @ trm)) = (none @ fml))))).
% 2.96/1.53 thf(fact_231_Geqo_Osimps_I1_J, axiom, (! [Theta:trm,Eta2:trm]: ((((uSubst1556497037e_Geqo @ ((some @ trm) @ Theta)) @ ((some @ trm) @ Eta2)) = ((some @ fml) @ ((geq @ Theta) @ Eta2)))))).
% 2.96/1.53 thf(fact_232_usubstappf_Osimps_I2_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm,Eta2:trm]: (((((uSubst95898978stappf @ Sigma) @ U) @ ((geq @ Theta) @ Eta2)) = ((uSubst1556497037e_Geqo @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta)) @ (((uSubst95898992stappt @ Sigma) @ U) @ Eta2)))))).
% 2.96/1.53 thf(fact_233_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X:A]: ((((member @ A) @ X) @ (bot_bot @ (set @ A))))))))).
% 2.96/1.53 thf(fact_234_pred__subset__eq, axiom, (! [A:$tType,R4:(set @ A),S:(set @ A)]: (((((ord_less_eq @ (A > $o)) @ (^ [X:A]: ((((member @ A) @ X) @ R4)))) @ (^ [X:A]: ((((member @ A) @ X) @ S)))) = (((ord_less_eq @ (set @ A)) @ R4) @ S))))).
% 2.96/1.53 thf(fact_235_Collect__empty__eq__bot, axiom, (! [A:$tType,P3:(A > $o)]: (((((collect @ A) @ P3) = (bot_bot @ (set @ A))) = (P3 = (bot_bot @ (A > $o))))))).
% 2.96/1.53 thf(fact_236_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A5:(set @ A)]: ((A5 = (bot_bot @ (set @ A))))))))).
% 2.96/1.53 thf(fact_237_internal__case__prod__def, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((produc2004651681e_prod @ A) @ B) @ C) = (((product_case_prod @ A) @ B) @ C))))).
% 2.96/1.53 thf(fact_238_usubstappt_Osimps_I4_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),F2:char,Theta:trm]: (((((uSubst95898992stappt @ Sigma) @ U) @ ((func @ F2) @ Theta)) = (((((case_option @ (option @ trm)) @ trm) @ (none @ trm)) @ (^ [Sigma_theta:trm]: ((((((case_option @ (option @ trm)) @ trm) @ ((some @ trm) @ ((func @ F2) @ Sigma_theta))) @ (^ [R:trm]: (((((if @ (option @ trm)) @ ((((inf_inf @ (set @ variable)) @ (static_FVT @ R)) @ U) = (bot_bot @ (set @ variable)))) @ (((uSubst95898992stappt @ (uSubst969145931substt @ Sigma_theta)) @ (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))))))))) @ Sigma) @ F2))))) @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta)))))).
% 2.96/1.53 thf(fact_239_trm_Oinject_I4_J, axiom, (! [X41:char,X42:trm,Y41:char,Y42:trm]: (((((func @ X41) @ X42) = ((func @ Y41) @ Y42)) = ((X41 = Y41) & (X42 = Y42)))))).
% 2.96/1.53 thf(fact_240_usubstappt__func2, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),F2:char,R2:trm,U:(set @ variable),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))))))))) @ Sigma) @ F2) = ((some @ trm) @ R2)) => (((((inf_inf @ (set @ variable)) @ (static_FVT @ R2)) @ U) != (bot_bot @ (set @ variable))) => ((((uSubst95898992stappt @ Sigma) @ U) @ ((func @ F2) @ Theta)) = (none @ trm))))))).
% 2.96/1.53 thf(fact_241_usubstappt__func, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),F2:char,R2:trm,U:(set @ variable),Theta:trm,Sigma_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))))))))) @ Sigma) @ F2) = ((some @ trm) @ R2)) => (((((inf_inf @ (set @ variable)) @ (static_FVT @ R2)) @ U) = (bot_bot @ (set @ variable))) => (((((uSubst95898992stappt @ Sigma) @ U) @ Theta) = ((some @ trm) @ Sigma_theta2)) => ((((uSubst95898992stappt @ Sigma) @ U) @ ((func @ F2) @ Theta)) = (((uSubst95898992stappt @ (uSubst969145931substt @ Sigma_theta2)) @ (bot_bot @ (set @ variable))) @ R2)))))))).
% 2.96/1.53 thf(fact_242_usubstappt__func__conv, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),F2:char,Theta:trm]: ((((((uSubst95898992stappt @ Sigma) @ U) @ ((func @ F2) @ Theta)) != (none @ trm)) => (((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (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))))))))) @ Sigma) @ F2) = (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))))))))) @ Sigma) @ F2) = ((some @ trm) @ R3)) & ((((inf_inf @ (set @ variable)) @ (static_FVT @ R3)) @ U) = (bot_bot @ (set @ variable)))))))))))).
% 2.96/1.53 thf(fact_243_usappconst__simp, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),F2:char,R2:trm,U:(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))))))))) @ Sigma) @ F2) = ((some @ trm) @ R2)) => (((((inf_inf @ (set @ variable)) @ (static_FVT @ R2)) @ U) = (bot_bot @ (set @ variable))) => ((((uSubst1138577137pconst @ Sigma) @ U) @ F2) = ((some @ trm) @ R2))))))).
% 2.96/1.53 thf(fact_244_usappconst__conv, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),F2:char]: ((((((uSubst1138577137pconst @ Sigma) @ U) @ F2) != (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) = (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))))))))) @ Sigma) @ F2) = ((some @ trm) @ R3)) & ((((inf_inf @ (set @ variable)) @ (static_FVT @ R3)) @ U) = (bot_bot @ (set @ variable))))))))))).
% 2.96/1.53 thf(fact_245_usappconst__def, axiom, (uSubst1138577137pconst = (^ [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),F:char]: ((((((case_option @ (option @ trm)) @ trm) @ ((some @ trm) @ (const @ F))) @ (^ [R:trm]: (((((if @ (option @ trm)) @ ((((inf_inf @ (set @ variable)) @ (static_FVT @ R)) @ U2) = (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))))))))) @ Sigma2) @ F)))))).
% 2.96/1.53 thf(fact_246_usubstappt__const, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),F2:char,R2:trm,U:(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))))))))) @ Sigma) @ F2) = ((some @ trm) @ R2)) => (((((inf_inf @ (set @ variable)) @ (static_FVT @ R2)) @ U) = (bot_bot @ (set @ variable))) => ((((uSubst95898992stappt @ Sigma) @ U) @ (const @ F2)) = ((some @ trm) @ R2))))))).
% 2.96/1.53 thf(fact_247_trm_Oinject_I3_J, axiom, (! [X32:char,Y32:char]: ((((const @ X32) = (const @ Y32)) = (X32 = Y32))))).
% 2.96/1.53 thf(fact_248_usubstappt_Osimps_I3_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),F2:char]: (((((uSubst95898992stappt @ Sigma) @ U) @ (const @ F2)) = (((uSubst1138577137pconst @ Sigma) @ U) @ F2))))).
% 2.96/1.53 thf(fact_249_trm_Odistinct_I23_J, axiom, (! [X32:char,X41:char,X42:trm]: (((const @ X32) != ((func @ X41) @ X42))))).
% 2.96/1.53 thf(fact_250_usubstappt__const__conv, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),F2:char]: ((((((uSubst95898992stappt @ Sigma) @ U) @ (const @ F2)) != (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) = (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))))))))) @ Sigma) @ F2) = ((some @ trm) @ R3)) & ((((inf_inf @ (set @ variable)) @ (static_FVT @ R3)) @ U) = (bot_bot @ (set @ variable))))))))))).
% 2.96/1.53 thf(fact_251_subset__Collect__iff, axiom, (! [A:$tType,B3:(set @ A),A4:(set @ A),P3:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ B3) @ A4) => ((((ord_less_eq @ (set @ A)) @ B3) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ A4) & (P3 @ X)))))) = (! [X:A]: (((((member @ A) @ X) @ B3) => (P3 @ X))))))))).
% 2.96/1.53 thf(fact_252_subset__CollectI, axiom, (! [A:$tType,B3:(set @ A),A4:(set @ A),Q:(A > $o),P3:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ B3) @ A4) => ((! [X5:A]: (((((member @ A) @ X5) @ B3) => ((Q @ X5) => (P3 @ X5))))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ B3) & (Q @ X)))))) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ A4) & (P3 @ X))))))))))).
% 2.96/1.53 thf(fact_253_conj__subset__def, axiom, (! [A:$tType,A4:(set @ A),P3:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ A4) @ ((collect @ A) @ (^ [X:A]: (((P3 @ X) & (Q @ X)))))) = ((((ord_less_eq @ (set @ A)) @ A4) @ ((collect @ A) @ P3)) & (((ord_less_eq @ (set @ A)) @ A4) @ ((collect @ A) @ Q))))))).
% 2.96/1.53 thf(fact_254_Diamondo_Ocases, axiom, (! [X3:((product_prod @ (option @ game)) @ (option @ fml))]: (((! [Alpha:game,Phi2:fml]: ((X3 != ((((product_Pair @ (option @ game)) @ (option @ fml)) @ ((some @ game) @ Alpha)) @ ((some @ fml) @ Phi2))))) => ((! [Phi2:(option @ fml)]: ((X3 != ((((product_Pair @ (option @ game)) @ (option @ fml)) @ (none @ game)) @ Phi2)))) => (~ ((! [V6:game]: ((X3 != ((((product_Pair @ (option @ game)) @ (option @ fml)) @ ((some @ game) @ V6)) @ (none @ fml)))))))))))).
% 2.96/1.53 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, (bounded_lattice @ $o)).
% 2.96/1.53 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A7:$tType]: ((bounded_lattice @ (set @ A7))))).
% 2.96/1.53 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A7:$tType,A8:$tType]: (((bounded_lattice @ A8) => (bounded_lattice @ (A7 > A8)))))).
% 2.96/1.53 thf(tcon_fun___Lattices_Obounded__lattice__bot, axiom, (! [A7:$tType,A8:$tType]: (((bounded_lattice @ A8) => (bounded_lattice_bot @ (A7 > A8)))))).
% 2.96/1.53 thf(tcon_fun___Lattices_Osemilattice__inf, axiom, (! [A7:$tType,A8:$tType]: (((semilattice_inf @ A8) => (semilattice_inf @ (A7 > A8)))))).
% 2.96/1.53 thf(tcon_fun___Orderings_Oorder__bot, axiom, (! [A7:$tType,A8:$tType]: (((order_bot @ A8) => (order_bot @ (A7 > A8)))))).
% 2.96/1.53 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A8:$tType]: (((preorder @ A8) => (preorder @ (A7 > A8)))))).
% 2.96/1.53 thf(tcon_fun___Lattices_Olattice, axiom, (! [A7:$tType,A8:$tType]: (((lattice @ A8) => (lattice @ (A7 > A8)))))).
% 2.96/1.53 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: (((order @ A8) => (order @ (A7 > A8)))))).
% 2.96/1.53 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: (((ord @ A8) => (ord @ (A7 > A8)))))).
% 2.96/1.53 thf(tcon_fun___Orderings_Obot, axiom, (! [A7:$tType,A8:$tType]: (((bot @ A8) => (bot @ (A7 > A8)))))).
% 2.96/1.53 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_3, axiom, (! [A7:$tType]: ((bounded_lattice_bot @ (set @ A7))))).
% 2.96/1.53 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_4, axiom, (! [A7:$tType]: ((semilattice_inf @ (set @ A7))))).
% 2.96/1.53 thf(tcon_Set_Oset___Orderings_Oorder__bot_5, axiom, (! [A7:$tType]: ((order_bot @ (set @ A7))))).
% 2.96/1.53 thf(tcon_Set_Oset___Orderings_Opreorder_6, axiom, (! [A7:$tType]: ((preorder @ (set @ A7))))).
% 2.96/1.53 thf(tcon_Set_Oset___Lattices_Olattice_7, axiom, (! [A7:$tType]: ((lattice @ (set @ A7))))).
% 2.96/1.53 thf(tcon_Set_Oset___Orderings_Oorder_8, axiom, (! [A7:$tType]: ((order @ (set @ A7))))).
% 2.96/1.53 thf(tcon_Set_Oset___Orderings_Oord_9, axiom, (! [A7:$tType]: ((ord @ (set @ A7))))).
% 2.96/1.53 thf(tcon_Set_Oset___Orderings_Obot_10, axiom, (! [A7:$tType]: ((bot @ (set @ A7))))).
% 2.96/1.53 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_11, axiom, (bounded_lattice_bot @ $o)).
% 2.96/1.53 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_12, axiom, (semilattice_inf @ $o)).
% 2.96/1.53 thf(tcon_HOL_Obool___Orderings_Oorder__bot_13, axiom, (order_bot @ $o)).
% 2.96/1.53 thf(tcon_HOL_Obool___Orderings_Opreorder_14, axiom, (preorder @ $o)).
% 2.96/1.53 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 2.96/1.53 thf(tcon_HOL_Obool___Lattices_Olattice_15, axiom, (lattice @ $o)).
% 2.96/1.53 thf(tcon_HOL_Obool___Orderings_Oorder_16, axiom, (order @ $o)).
% 2.96/1.53 thf(tcon_HOL_Obool___Orderings_Oord_17, axiom, (ord @ $o)).
% 2.96/1.53 thf(tcon_HOL_Obool___Orderings_Obot_18, axiom, (bot @ $o)).
% 2.96/1.53 thf(help_If_3_1_T, axiom, (! [P3:$o]: (((P3 = $true) | (P3 = $false))))).
% 2.96/1.53 thf(help_If_2_1_T, axiom, (! [A:$tType,X3:A,Y3:A]: ((((((if @ A) @ $false) @ X3) @ Y3) = Y3)))).
% 2.96/1.53 thf(help_If_1_1_T, axiom, (! [A:$tType,X3:A,Y3:A]: ((((((if @ A) @ $true) @ X3) @ Y3) = X3)))).
% 2.96/1.53 thf(conj_0, conjecture, (((((uSubst95898978stappf @ sigma) @ va) @ ((pred @ p) @ theta)) != (none @ fml)) | (((((((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))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p) = (none @ fml)))).
% 2.96/1.53 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.JL8G97Ngch/DTF2DTF22545.p
% 2.96/1.53 ------------------------
% 2.96/1.57 ---- Cleaned THF ---
% 2.96/1.57 thf(ty_t_Product__Type_Oprod,type,
% 2.96/1.57 product_prod: $tType > $tType > $tType ).
% 2.96/1.57
% 2.96/1.57 thf(ty_t_Syntax_Ovariable,type,
% 2.96/1.57 variable: $tType ).
% 2.96/1.57
% 2.96/1.57 thf(ty_t_Option_Ooption,type,
% 2.96/1.57 option: $tType > $tType ).
% 2.96/1.57
% 2.96/1.57 thf(ty_t_Syntax_Ogame,type,
% 2.96/1.57 game: $tType ).
% 2.96/1.57
% 2.96/1.57 thf(ty_t_String_Ochar,type,
% 2.96/1.57 char: $tType ).
% 2.96/1.57
% 2.96/1.57 thf(ty_t_Syntax_Otrm,type,
% 2.96/1.57 trm: $tType ).
% 2.96/1.57
% 2.96/1.57 thf(ty_t_Syntax_Ofml,type,
% 2.96/1.57 fml: $tType ).
% 2.96/1.57
% 2.96/1.57 thf(ty_t_Set_Oset,type,
% 2.96/1.57 set: $tType > $tType ).
% 2.96/1.57
% 2.96/1.57 thf(sy_cl_Lattices_Obounded__lattice,type,
% 2.96/1.57 bounded_lattice:
% 2.96/1.57 !>[A: $tType] : $o ).
% 2.96/1.57
% 2.96/1.57 thf(sy_cl_HOL_Otype,type,
% 2.96/1.57 type:
% 2.96/1.57 !>[A: $tType] : $o ).
% 2.96/1.57
% 2.96/1.57 thf(sy_cl_Orderings_Obot,type,
% 2.96/1.57 bot:
% 2.96/1.57 !>[A: $tType] : $o ).
% 2.96/1.57
% 2.96/1.57 thf(sy_cl_Orderings_Oord,type,
% 2.96/1.57 ord:
% 2.96/1.57 !>[A: $tType] : $o ).
% 2.96/1.57
% 2.96/1.57 thf(sy_cl_Orderings_Oorder,type,
% 2.96/1.57 order:
% 2.96/1.57 !>[A: $tType] : $o ).
% 2.96/1.57
% 2.96/1.57 thf(sy_cl_Lattices_Olattice,type,
% 2.96/1.57 lattice:
% 2.96/1.57 !>[A: $tType] : $o ).
% 2.96/1.57
% 2.96/1.57 thf(sy_cl_Orderings_Olinorder,type,
% 2.96/1.57 linorder:
% 2.96/1.57 !>[A: $tType] : $o ).
% 2.96/1.57
% 2.96/1.57 thf(sy_cl_Orderings_Opreorder,type,
% 2.96/1.57 preorder:
% 2.96/1.57 !>[A: $tType] : $o ).
% 2.96/1.57
% 2.96/1.57 thf(sy_cl_Orderings_Oorder__bot,type,
% 2.96/1.57 order_bot:
% 2.96/1.57 !>[A: $tType] : $o ).
% 2.96/1.57
% 2.96/1.57 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 2.96/1.57 semilattice_inf:
% 2.96/1.57 !>[A: $tType] : $o ).
% 2.96/1.57
% 2.96/1.57 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 2.96/1.57 bounded_lattice_bot:
% 2.96/1.57 !>[A: $tType] : $o ).
% 2.96/1.57
% 2.96/1.57 thf(sy_c_If,type,
% 2.96/1.57 if:
% 2.96/1.57 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.96/1.57
% 2.96/1.57 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 2.96/1.57 inf_inf:
% 2.96/1.57 !>[A: $tType] : ( A > A > A ) ).
% 2.96/1.57
% 2.96/1.57 thf(sy_c_Option_Ooption_ONone,type,
% 2.96/1.57 none:
% 2.96/1.57 !>[A: $tType] : ( option @ A ) ).
% 2.96/1.57
% 2.96/1.57 thf(sy_c_Option_Ooption_OSome,type,
% 2.96/1.57 some:
% 2.96/1.57 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 2.96/1.57
% 2.96/1.57 thf(sy_c_Option_Ooption_Ocase__option,type,
% 2.96/1.57 case_option:
% 2.96/1.57 !>[B: $tType,A: $tType] : ( B > ( A > B ) > ( option @ A ) > B ) ).
% 2.96/1.57
% 2.96/1.57 thf(sy_c_Option_Ooption_Othe,type,
% 2.96/1.57 the:
% 2.96/1.57 !>[A: $tType] : ( ( option @ A ) > A ) ).
% 2.96/1.57
% 2.96/1.57 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.96/1.57 bot_bot:
% 2.96/1.57 !>[A: $tType] : A ).
% 2.96/1.57
% 2.96/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.96/1.57 ord_less_eq:
% 2.96/1.57 !>[A: $tType] : ( A > A > $o ) ).
% 2.96/1.57
% 2.96/1.57 thf(sy_c_Product__Type_OPair,type,
% 2.96/1.57 product_Pair:
% 2.96/1.57 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.96/1.57
% 2.96/1.57 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 2.96/1.57 produc2004651681e_prod:
% 2.96/1.57 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 2.96/1.57
% 2.96/1.57 thf(sy_c_Product__Type_Oprod_Ocase__prod,type,
% 2.96/1.57 product_case_prod:
% 2.96/1.57 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 2.96/1.57
% 2.96/1.57 thf(sy_c_Set_OCollect,type,
% 2.96/1.57 collect:
% 2.96/1.57 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.96/1.57
% 2.96/1.57 thf(sy_c_Set_Ois__empty,type,
% 2.96/1.57 is_empty:
% 2.96/1.57 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.96/1.57
% 2.96/1.57 thf(sy_c_Static__Semantics_OFVF,type,
% 2.96/1.57 static_FVF: fml > ( set @ variable ) ).
% 2.96/1.57
% 2.96/1.57 thf(sy_c_Static__Semantics_OFVT,type,
% 2.96/1.57 static_FVT: trm > ( set @ variable ) ).
% 2.96/1.57
% 2.96/1.57 thf(sy_c_Syntax_Ofml_OGeq,type,
% 2.96/1.57 geq: trm > trm > fml ).
% 2.96/1.57
% 2.96/1.57 thf(sy_c_Syntax_Ofml_OPred,type,
% 2.96/1.57 pred: char > trm > fml ).
% 2.96/1.57
% 2.96/1.57 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_OFunc,type,
% 2.96/1.58 func: char > trm > 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_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_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_Ua____,type,
% 2.96/1.58 ua: set @ variable ).
% 2.96/1.58
% 2.96/1.58 thf(sy_v_Va____,type,
% 2.96/1.58 va: 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__092_060theta_062____,type,
% 2.96/1.58 theta: trm ).
% 2.96/1.58
% 2.96/1.58 thf(sy_v_p____,type,
% 2.96/1.58 p: char ).
% 2.96/1.58
% 2.96/1.58 thf(sy_v_vv____,type,
% 2.96/1.58 vv: ( set @ variable ) > ( set @ variable ) > variable ).
% 2.96/1.58
% 2.96/1.58 thf(sy_v_vva____,type,
% 2.96/1.58 vva: ( set @ variable ) > ( set @ variable ) > variable ).
% 2.96/1.58
% 2.96/1.58 thf(fact_0__092_060open_062_092_060forall_062x0_Ax1_O_A_I_092_060exists_062v2_O_Av2_A_092_060in_062_Ax1_A_092_060and_062_A_I_092_060exists_062v3_O_Av3_A_092_060in_062_Ax0_A_092_060and_062_Av2_A_061_Av3_J_J_A_061_A_Ivv_Ax0_Ax1_A_092_060in_062_Ax1_A_092_060and_062_A_I_092_060exists_062v3_O_Av3_A_092_060in_062_Ax0_A_092_060and_062_Avv_Ax0_Ax1_A_061_Av3_J_J_092_060close_062,axiom,
% 2.96/1.58 ! [X0: set @ variable,X1: set @ variable] :
% 2.96/1.58 ( ( ? [V2: variable] :
% 2.96/1.58 ( ( member @ variable @ V2 @ X1 )
% 2.96/1.58 & ? [V3: variable] :
% 2.96/1.58 ( ( member @ variable @ V3 @ X0 )
% 2.96/1.58 & ( V2 = V3 ) ) ) )
% 2.96/1.58 = ( ( member @ variable @ ( vv @ X0 @ X1 ) @ X1 )
% 2.96/1.58 & ? [V3: variable] :
% 2.96/1.58 ( ( member @ variable @ V3 @ X0 )
% 2.96/1.58 & ( ( vv @ X0 @ X1 )
% 2.96/1.58 = V3 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_1_Pred_Oprems_I2_J,axiom,
% 2.96/1.58 ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 2.96/1.58 != ( none @ fml ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_2__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Aundeff_092_060close_062,axiom,
% 2.96/1.58 ~ ( ( ( inf_inf @ ( set @ variable )
% 2.96/1.58 @ ( static_FVF
% 2.96/1.58 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) ) )
% 2.96/1.58 @ va )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 => ( ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) )
% 2.96/1.58 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) ) )
% 2.96/1.58 = ( none @ fml ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_3__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_A_092_060Longrightarrow_062_ASPreds_A_092_060sigma_062_Ap_A_061_Aundeff_092_060close_062,axiom,
% 2.96/1.58 ( ~ ( ( ( ( inf_inf @ ( set @ variable )
% 2.96/1.58 @ ( static_FVF
% 2.96/1.58 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) ) )
% 2.96/1.58 @ va )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 => ( ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) )
% 2.96/1.58 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) ) )
% 2.96/1.58 = ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) )
% 2.96/1.58 & ( ( ( inf_inf @ ( set @ variable )
% 2.96/1.58 @ ( static_FVF
% 2.96/1.58 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) ) )
% 2.96/1.58 @ va )
% 2.96/1.58 != ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 => ( ( none @ fml )
% 2.96/1.58 = ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) )
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p )
% 2.96/1.58 = ( none @ fml ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_4_usubstappf__det,axiom,
% 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,Phi: fml,V: set @ variable] :
% 2.96/1.58 ( ( ( uSubst95898978stappf @ Sigma @ U @ Phi )
% 2.96/1.58 != ( none @ fml ) )
% 2.96/1.58 => ( ( ( uSubst95898978stappf @ Sigma @ V @ Phi )
% 2.96/1.58 != ( none @ fml ) )
% 2.96/1.58 => ( ( uSubst95898978stappf @ Sigma @ U @ Phi )
% 2.96/1.58 = ( uSubst95898978stappf @ Sigma @ V @ Phi ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_5_f8,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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p )
% 2.96/1.58 = ( none @ fml ) )
% 2.96/1.58 => ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 2.96/1.58 = ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_6__092_060open_062vv_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060notin_062_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060or_062_Avva_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060notin_062_AV_A_092_060or_062_Avv_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060noteq_062_Avva_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_092_060close_062,axiom,
% 2.96/1.58 ( ~ ( member @ variable
% 2.96/1.58 @ ( vv @ va
% 2.96/1.58 @ ( static_FVF
% 2.96/1.58 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) ) ) )
% 2.96/1.58 @ ( static_FVF
% 2.96/1.58 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) ) ) )
% 2.96/1.58 | ~ ( member @ variable
% 2.96/1.58 @ ( vva @ va
% 2.96/1.58 @ ( static_FVF
% 2.96/1.58 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) ) ) )
% 2.96/1.58 @ va )
% 2.96/1.58 | ( ( vv @ va
% 2.96/1.58 @ ( static_FVF
% 2.96/1.58 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) ) ) )
% 2.96/1.58 != ( vva @ va
% 2.96/1.58 @ ( static_FVF
% 2.96/1.58 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_7_fml_Oinject_I1_J,axiom,
% 2.96/1.58 ! [X11: char,X12: trm,Y11: char,Y12: trm] :
% 2.96/1.58 ( ( ( pred @ X11 @ X12 )
% 2.96/1.58 = ( pred @ Y11 @ Y12 ) )
% 2.96/1.58 = ( ( X11 = Y11 )
% 2.96/1.58 & ( X12 = Y12 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_8_f7,axiom,
% 2.96/1.58 ( ( uSubst95898992stappt @ sigma @ ua @ theta )
% 2.96/1.58 = ( uSubst95898992stappt @ sigma @ va @ theta ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_9_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 = ( ^ [F: 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] : ( F @ L @ R @ Y )
% 2.96/1.58 @ X ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_10_f1,axiom,
% 2.96/1.58 ! [V4: variable] :
% 2.96/1.58 ( ~ ( member @ variable @ V4 @ va )
% 2.96/1.58 | ( member @ variable @ V4 @ ua ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_11_f10,axiom,
% 2.96/1.58 ( ( ( ( inf_inf @ ( set @ variable )
% 2.96/1.58 @ ( static_FVF
% 2.96/1.58 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) ) )
% 2.96/1.58 @ va )
% 2.96/1.58 != ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 | ! [V4: variable] :
% 2.96/1.58 ( ~ ( member @ variable @ V4
% 2.96/1.58 @ ( static_FVF
% 2.96/1.58 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) ) ) )
% 2.96/1.58 | ! [Va: variable] :
% 2.96/1.58 ( ~ ( member @ variable @ Va @ va )
% 2.96/1.58 | ( V4 != Va ) ) ) )
% 2.96/1.58 & ( ( ( inf_inf @ ( set @ variable )
% 2.96/1.58 @ ( static_FVF
% 2.96/1.58 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) ) )
% 2.96/1.58 @ va )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 | ( ( member @ variable
% 2.96/1.58 @ ( vv @ va
% 2.96/1.58 @ ( static_FVF
% 2.96/1.58 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) ) ) )
% 2.96/1.58 @ ( static_FVF
% 2.96/1.58 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) ) ) )
% 2.96/1.58 & ( member @ variable
% 2.96/1.58 @ ( vva @ va
% 2.96/1.58 @ ( static_FVF
% 2.96/1.58 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) ) ) )
% 2.96/1.58 @ va )
% 2.96/1.58 & ( ( vv @ va
% 2.96/1.58 @ ( static_FVF
% 2.96/1.58 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) ) ) )
% 2.96/1.58 = ( vva @ va
% 2.96/1.58 @ ( static_FVF
% 2.96/1.58 @ ( the @ fml
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) ) ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_12_prod_Ocase__distrib,axiom,
% 2.96/1.58 ! [C: $tType,D: $tType,B: $tType,A: $tType,H: C > D,F2: A > B > C,Prod: product_prod @ A @ B] :
% 2.96/1.58 ( ( H @ ( product_case_prod @ A @ B @ C @ F2 @ Prod ) )
% 2.96/1.58 = ( product_case_prod @ A @ B @ D
% 2.96/1.58 @ ^ [X13: A,X2: B] : ( H @ ( F2 @ X13 @ X2 ) )
% 2.96/1.58 @ Prod ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_13_usubstappf__pred2,axiom,
% 2.96/1.58 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),P2: char,R2: fml,U: set @ variable,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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ Sigma
% 2.96/1.58 @ P2 )
% 2.96/1.58 = ( some @ fml @ R2 ) )
% 2.96/1.58 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R2 ) @ U )
% 2.96/1.58 != ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 => ( ( uSubst95898978stappf @ Sigma @ U @ ( pred @ P2 @ Theta ) )
% 2.96/1.58 = ( none @ fml ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_14_f2,axiom,
% 2.96/1.58 ! [Z: option @ fml,F3: fml > ( option @ fml ),Za: option @ fml] :
% 2.96/1.58 ( ( ( Za
% 2.96/1.58 = ( none @ fml ) )
% 2.96/1.58 => ( ( case_option @ ( option @ fml ) @ fml @ Z @ F3 @ Za )
% 2.96/1.58 = Z ) )
% 2.96/1.58 & ( ( Za
% 2.96/1.58 != ( none @ fml ) )
% 2.96/1.58 => ( ( case_option @ ( option @ fml ) @ fml @ Z @ F3 @ Za )
% 2.96/1.58 = ( F3 @ ( the @ fml @ Za ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_15_Pred_Oprems_I1_J,axiom,
% 2.96/1.58 ord_less_eq @ ( set @ variable ) @ va @ ua ).
% 2.96/1.58
% 2.96/1.58 thf(fact_16_f9,axiom,
% 2.96/1.58 ! [V5: set @ variable,Va2: set @ variable] :
% 2.96/1.58 ( ( ( ( inf_inf @ ( set @ variable ) @ V5 @ Va2 )
% 2.96/1.58 != ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 | ! [V4: variable] :
% 2.96/1.58 ( ~ ( member @ variable @ V4 @ V5 )
% 2.96/1.58 | ! [Va: variable] :
% 2.96/1.58 ( ~ ( member @ variable @ Va @ Va2 )
% 2.96/1.58 | ( V4 != Va ) ) ) )
% 2.96/1.58 & ( ( ( inf_inf @ ( set @ variable ) @ V5 @ Va2 )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 | ( ( member @ variable @ ( vv @ Va2 @ V5 ) @ V5 )
% 2.96/1.58 & ( member @ variable @ ( vva @ Va2 @ V5 ) @ Va2 )
% 2.96/1.58 & ( ( vv @ Va2 @ V5 )
% 2.96/1.58 = ( vva @ Va2 @ V5 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_17__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062vva_O_A_092_060forall_062V_AVa_O_A_IV_A_092_060inter_062_AVa_A_092_060noteq_062_A_123_125_A_092_060or_062_A_I_092_060forall_062v_O_Av_A_092_060notin_062_AV_A_092_060or_062_A_I_092_060forall_062va_O_Ava_A_092_060notin_062_AVa_A_092_060or_062_Av_A_092_060noteq_062_Ava_J_J_J_A_092_060and_062_A_IV_A_092_060inter_062_AVa_A_061_A_123_125_A_092_060or_062_Avv_AVa_AV_A_092_060in_062_AV_A_092_060and_062_Avva_AVa_AV_A_092_060in_062_AVa_A_092_060and_062_Avv_AVa_AV_A_061_Avva_AVa_AV_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.96/1.58 ~ ! [Vva: ( set @ variable ) > ( set @ variable ) > variable] :
% 2.96/1.58 ~ ! [V5: set @ variable,Va2: set @ variable] :
% 2.96/1.58 ( ( ( ( inf_inf @ ( set @ variable ) @ V5 @ Va2 )
% 2.96/1.58 != ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 | ! [V4: variable] :
% 2.96/1.58 ( ~ ( member @ variable @ V4 @ V5 )
% 2.96/1.58 | ! [Va: variable] :
% 2.96/1.58 ( ~ ( member @ variable @ Va @ Va2 )
% 2.96/1.58 | ( V4 != Va ) ) ) )
% 2.96/1.58 & ( ( ( inf_inf @ ( set @ variable ) @ V5 @ Va2 )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 | ( ( member @ variable @ ( vv @ Va2 @ V5 ) @ V5 )
% 2.96/1.58 & ( member @ variable @ ( Vva @ Va2 @ V5 ) @ Va2 )
% 2.96/1.58 & ( ( vv @ Va2 @ V5 )
% 2.96/1.58 = ( Vva @ Va2 @ V5 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_18_option_Oinject,axiom,
% 2.96/1.58 ! [A: $tType,X22: A,Y2: A] :
% 2.96/1.58 ( ( ( some @ A @ X22 )
% 2.96/1.58 = ( some @ A @ Y2 ) )
% 2.96/1.58 = ( X22 = Y2 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_19_f5,axiom,
% 2.96/1.58 ( ( uSubst95898992stappt @ sigma @ ua @ theta )
% 2.96/1.58 != ( none @ trm ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_20_not__Some__eq,axiom,
% 2.96/1.58 ! [A: $tType,X3: option @ A] :
% 2.96/1.58 ( ( ! [Y: A] :
% 2.96/1.58 ( X3
% 2.96/1.58 != ( some @ A @ Y ) ) )
% 2.96/1.58 = ( X3
% 2.96/1.58 = ( none @ A ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_21_not__None__eq,axiom,
% 2.96/1.58 ! [A: $tType,X3: option @ A] :
% 2.96/1.58 ( ( X3
% 2.96/1.58 != ( none @ A ) )
% 2.96/1.58 = ( ? [Y: A] :
% 2.96/1.58 ( X3
% 2.96/1.58 = ( some @ A @ Y ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_22_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_23_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_24_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_25_option_Osplit__sel,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType,P3: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 2.96/1.58 ( ( P3 @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 2.96/1.58 = ( ( ( Option
% 2.96/1.58 = ( none @ A ) )
% 2.96/1.58 => ( P3 @ F1 ) )
% 2.96/1.58 & ( ( Option
% 2.96/1.58 = ( some @ A @ ( the @ A @ Option ) ) )
% 2.96/1.58 => ( P3 @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_26_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_27_option_Osplit__sel__asm,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType,P3: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 2.96/1.58 ( ( P3 @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 2.96/1.58 = ( ~ ( ( ( Option
% 2.96/1.58 = ( none @ A ) )
% 2.96/1.58 & ~ ( P3 @ F1 ) )
% 2.96/1.58 | ( ( Option
% 2.96/1.58 = ( some @ A @ ( the @ A @ Option ) ) )
% 2.96/1.58 & ~ ( P3 @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_28_usubstappt__det,axiom,
% 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,Theta: trm,V: set @ variable] :
% 2.96/1.58 ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 => ( ( ( uSubst95898992stappt @ Sigma @ V @ Theta )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 => ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 2.96/1.58 = ( uSubst95898992stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_29_usubstappt__antimon,axiom,
% 2.96/1.58 ! [V: set @ variable,U: set @ variable,Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),Theta: trm] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ variable ) @ V @ U )
% 2.96/1.58 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 => ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 2.96/1.58 = ( uSubst95898992stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_30_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_31_combine__options__cases,axiom,
% 2.96/1.58 ! [A: $tType,B: $tType,X3: option @ A,P3: ( option @ A ) > ( option @ B ) > $o,Y3: option @ B] :
% 2.96/1.58 ( ( ( X3
% 2.96/1.58 = ( none @ A ) )
% 2.96/1.58 => ( P3 @ X3 @ Y3 ) )
% 2.96/1.58 => ( ( ( Y3
% 2.96/1.58 = ( none @ B ) )
% 2.96/1.58 => ( P3 @ X3 @ Y3 ) )
% 2.96/1.58 => ( ! [A2: A,B2: B] :
% 2.96/1.58 ( ( X3
% 2.96/1.58 = ( some @ A @ A2 ) )
% 2.96/1.58 => ( ( Y3
% 2.96/1.58 = ( some @ B @ B2 ) )
% 2.96/1.58 => ( P3 @ X3 @ Y3 ) ) )
% 2.96/1.58 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_32_split__option__all,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( ^ [P4: ( option @ A ) > $o] :
% 2.96/1.58 ! [X4: option @ A] : ( P4 @ X4 ) )
% 2.96/1.58 = ( ^ [P: ( option @ A ) > $o] :
% 2.96/1.58 ( ( P @ ( none @ A ) )
% 2.96/1.58 & ! [X: A] : ( P @ ( some @ A @ X ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_33_split__option__ex,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( ^ [P4: ( option @ A ) > $o] :
% 2.96/1.58 ? [X4: option @ A] : ( P4 @ X4 ) )
% 2.96/1.58 = ( ^ [P: ( option @ A ) > $o] :
% 2.96/1.58 ( ( P @ ( none @ A ) )
% 2.96/1.58 | ? [X: A] : ( P @ ( some @ A @ X ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_34_option_Oinducts,axiom,
% 2.96/1.58 ! [A: $tType,P3: ( option @ A ) > $o,Option: option @ A] :
% 2.96/1.58 ( ( P3 @ ( none @ A ) )
% 2.96/1.58 => ( ! [X5: A] : ( P3 @ ( some @ A @ X5 ) )
% 2.96/1.58 => ( P3 @ Option ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_35_option_Oexhaust,axiom,
% 2.96/1.58 ! [A: $tType,Y3: option @ A] :
% 2.96/1.58 ( ( Y3
% 2.96/1.58 != ( none @ A ) )
% 2.96/1.58 => ~ ! [X23: A] :
% 2.96/1.58 ( Y3
% 2.96/1.58 != ( some @ A @ X23 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_36_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_37_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_38_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_39_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_40_Existso_Oinduct,axiom,
% 2.96/1.58 ! [P3: variable > ( option @ fml ) > $o,A0: variable,A1: option @ fml] :
% 2.96/1.58 ( ! [X5: variable,Phi2: fml] : ( P3 @ X5 @ ( some @ fml @ Phi2 ) )
% 2.96/1.58 => ( ! [X5: variable] : ( P3 @ X5 @ ( none @ fml ) )
% 2.96/1.58 => ( P3 @ A0 @ A1 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_41_undeff__equiv,axiom,
% 2.96/1.58 ! [Phi: option @ fml] :
% 2.96/1.58 ( ( Phi
% 2.96/1.58 != ( none @ fml ) )
% 2.96/1.58 = ( ? [F: fml] :
% 2.96/1.58 ( Phi
% 2.96/1.58 = ( some @ fml @ F ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_42_Testo_Oinduct,axiom,
% 2.96/1.58 ! [P3: ( option @ fml ) > $o,A0: option @ fml] :
% 2.96/1.58 ( ! [Phi2: fml] : ( P3 @ ( some @ fml @ Phi2 ) )
% 2.96/1.58 => ( ( P3 @ ( none @ fml ) )
% 2.96/1.58 => ( P3 @ A0 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_43_Testo_Ocases,axiom,
% 2.96/1.58 ! [X3: option @ fml] :
% 2.96/1.58 ( ! [Phi2: fml] :
% 2.96/1.58 ( X3
% 2.96/1.58 != ( some @ fml @ Phi2 ) )
% 2.96/1.58 => ( X3
% 2.96/1.58 = ( none @ fml ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_44_mem__Collect__eq,axiom,
% 2.96/1.58 ! [A: $tType,A3: A,P3: A > $o] :
% 2.96/1.58 ( ( member @ A @ A3 @ ( collect @ A @ P3 ) )
% 2.96/1.58 = ( P3 @ A3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_45_Collect__mem__eq,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A] :
% 2.96/1.58 ( ( collect @ A
% 2.96/1.58 @ ^ [X: A] : ( member @ A @ X @ A4 ) )
% 2.96/1.58 = A4 ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_46_Collect__cong,axiom,
% 2.96/1.58 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 2.96/1.58 ( ! [X5: A] :
% 2.96/1.58 ( ( P3 @ X5 )
% 2.96/1.58 = ( Q @ X5 ) )
% 2.96/1.58 => ( ( collect @ A @ P3 )
% 2.96/1.58 = ( collect @ A @ Q ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_47_ext,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType,F2: A > B,G: A > B] :
% 2.96/1.58 ( ! [X5: A] :
% 2.96/1.58 ( ( F2 @ X5 )
% 2.96/1.58 = ( G @ X5 ) )
% 2.96/1.58 => ( F2 = G ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_48_Ando_Oinduct,axiom,
% 2.96/1.58 ! [P3: ( option @ fml ) > ( option @ fml ) > $o,A0: option @ fml,A1: option @ fml] :
% 2.96/1.58 ( ! [Phi2: fml,Psi: fml] : ( P3 @ ( some @ fml @ Phi2 ) @ ( some @ fml @ Psi ) )
% 2.96/1.58 => ( ! [X_1: option @ fml] : ( P3 @ ( none @ fml ) @ X_1 )
% 2.96/1.58 => ( ! [V6: fml] : ( P3 @ ( some @ fml @ V6 ) @ ( none @ fml ) )
% 2.96/1.58 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_49_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_50_usubstappf__pred__conv,axiom,
% 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,P2: char,Theta: trm] :
% 2.96/1.58 ( ( ( uSubst95898978stappf @ Sigma @ U @ ( pred @ P2 @ Theta ) )
% 2.96/1.58 != ( none @ fml ) )
% 2.96/1.58 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ Sigma
% 2.96/1.58 @ P2 )
% 2.96/1.58 = ( none @ fml ) )
% 2.96/1.58 | ? [R3: fml] :
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ Sigma
% 2.96/1.58 @ P2 )
% 2.96/1.58 = ( some @ fml @ R3 ) )
% 2.96/1.58 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R3 ) @ U )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_51_f6,axiom,
% 2.96/1.58 ( ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
% 2.96/1.58 @ ^ [T: trm] :
% 2.96/1.58 ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ T ) )
% 2.96/1.58 @ ^ [F: fml] :
% 2.96/1.58 ( if @ ( option @ fml )
% 2.96/1.58 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F ) @ ua )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ T ) @ ( bot_bot @ ( set @ variable ) ) @ F )
% 2.96/1.58 @ ( none @ fml ) )
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) )
% 2.96/1.58 @ ( uSubst95898992stappt @ sigma @ ua @ theta ) )
% 2.96/1.58 = ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ua @ theta ) ) ) )
% 2.96/1.58 @ ^ [F: fml] :
% 2.96/1.58 ( if @ ( option @ fml )
% 2.96/1.58 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F ) @ ua )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ua @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) ) @ F )
% 2.96/1.58 @ ( none @ fml ) )
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_52_f3,axiom,
% 2.96/1.58 ( ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
% 2.96/1.58 @ ^ [T: trm] :
% 2.96/1.58 ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ T ) )
% 2.96/1.58 @ ^ [F: fml] :
% 2.96/1.58 ( if @ ( option @ fml )
% 2.96/1.58 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F ) @ ua )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ T ) @ ( bot_bot @ ( set @ variable ) ) @ F )
% 2.96/1.58 @ ( none @ fml ) )
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p ) )
% 2.96/1.58 @ ( uSubst95898992stappt @ sigma @ ua @ theta ) )
% 2.96/1.58 != ( none @ fml ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_53_usubstappf_Osimps_I1_J,axiom,
% 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,P2: char,Theta: trm] :
% 2.96/1.58 ( ( uSubst95898978stappf @ Sigma @ U @ ( pred @ P2 @ Theta ) )
% 2.96/1.58 = ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
% 2.96/1.58 @ ^ [Sigma_theta: trm] :
% 2.96/1.58 ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ P2 @ Sigma_theta ) )
% 2.96/1.58 @ ^ [R: fml] :
% 2.96/1.58 ( if @ ( option @ fml )
% 2.96/1.58 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R ) @ U )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ Sigma_theta ) @ ( bot_bot @ ( set @ variable ) ) @ R )
% 2.96/1.58 @ ( none @ fml ) )
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ Sigma
% 2.96/1.58 @ P2 ) )
% 2.96/1.58 @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_54_Int__subset__iff,axiom,
% 2.96/1.58 ! [A: $tType,C2: set @ A,A4: set @ A,B3: set @ A] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ A ) @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 2.96/1.58 = ( ( ord_less_eq @ ( set @ A ) @ C2 @ A4 )
% 2.96/1.58 & ( ord_less_eq @ ( set @ A ) @ C2 @ B3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_55_inf__bot__left,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( bounded_lattice_bot @ A )
% 2.96/1.58 => ! [X3: A] :
% 2.96/1.58 ( ( inf_inf @ A @ ( bot_bot @ A ) @ X3 )
% 2.96/1.58 = ( bot_bot @ A ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_56_inf__bot__right,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( bounded_lattice_bot @ A )
% 2.96/1.58 => ! [X3: A] :
% 2.96/1.58 ( ( inf_inf @ A @ X3 @ ( bot_bot @ A ) )
% 2.96/1.58 = ( bot_bot @ A ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_57_subset__empty,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 2.96/1.58 = ( A4
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_58_empty__subsetI,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_59_le__inf__iff,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [X3: A,Y3: A,Z2: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ X3 @ ( inf_inf @ A @ Y3 @ Z2 ) )
% 2.96/1.58 = ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.96/1.58 & ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_60_inf_Obounded__iff,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A3: A,B4: A,C3: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ A3 @ ( inf_inf @ A @ B4 @ C3 ) )
% 2.96/1.58 = ( ( ord_less_eq @ A @ A3 @ B4 )
% 2.96/1.58 & ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_61_f4,axiom,
% 2.96/1.58 ! [Z: option @ fml,F3: trm > ( option @ fml ),Za: option @ trm] :
% 2.96/1.58 ( ( ( Za
% 2.96/1.58 = ( none @ trm ) )
% 2.96/1.58 => ( ( case_option @ ( option @ fml ) @ trm @ Z @ F3 @ Za )
% 2.96/1.58 = Z ) )
% 2.96/1.58 & ( ( Za
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 => ( ( case_option @ ( option @ fml ) @ trm @ Z @ F3 @ Za )
% 2.96/1.58 = ( F3 @ ( the @ trm @ Za ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_62_empty__Collect__eq,axiom,
% 2.96/1.58 ! [A: $tType,P3: A > $o] :
% 2.96/1.58 ( ( ( bot_bot @ ( set @ A ) )
% 2.96/1.58 = ( collect @ A @ P3 ) )
% 2.96/1.58 = ( ! [X: A] :
% 2.96/1.58 ~ ( P3 @ X ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_63_Collect__empty__eq,axiom,
% 2.96/1.58 ! [A: $tType,P3: A > $o] :
% 2.96/1.58 ( ( ( collect @ A @ P3 )
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) )
% 2.96/1.58 = ( ! [X: A] :
% 2.96/1.58 ~ ( P3 @ X ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_64_all__not__in__conv,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A] :
% 2.96/1.58 ( ( ! [X: A] :
% 2.96/1.58 ~ ( member @ A @ X @ A4 ) )
% 2.96/1.58 = ( A4
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_65_empty__iff,axiom,
% 2.96/1.58 ! [A: $tType,C3: A] :
% 2.96/1.58 ~ ( member @ A @ C3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_66_subset__antisym,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B3 )
% 2.96/1.58 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ A4 )
% 2.96/1.58 => ( A4 = B3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_67_subsetI,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 2.96/1.58 ( ! [X5: A] :
% 2.96/1.58 ( ( member @ A @ X5 @ A4 )
% 2.96/1.58 => ( member @ A @ X5 @ B3 ) )
% 2.96/1.58 => ( ord_less_eq @ ( set @ A ) @ A4 @ B3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_68_inf__right__idem,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [X3: A,Y3: A] :
% 2.96/1.58 ( ( inf_inf @ A @ ( inf_inf @ A @ X3 @ Y3 ) @ Y3 )
% 2.96/1.58 = ( inf_inf @ A @ X3 @ Y3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_69_inf_Oright__idem,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A3: A,B4: A] :
% 2.96/1.58 ( ( inf_inf @ A @ ( inf_inf @ A @ A3 @ B4 ) @ B4 )
% 2.96/1.58 = ( inf_inf @ A @ A3 @ B4 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_70_inf__left__idem,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [X3: A,Y3: A] :
% 2.96/1.58 ( ( inf_inf @ A @ X3 @ ( inf_inf @ A @ X3 @ Y3 ) )
% 2.96/1.58 = ( inf_inf @ A @ X3 @ Y3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_71_inf_Oleft__idem,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A3: A,B4: A] :
% 2.96/1.58 ( ( inf_inf @ A @ A3 @ ( inf_inf @ A @ A3 @ B4 ) )
% 2.96/1.58 = ( inf_inf @ A @ A3 @ B4 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_72_inf__idem,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [X3: A] :
% 2.96/1.58 ( ( inf_inf @ A @ X3 @ X3 )
% 2.96/1.58 = X3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_73_inf_Oidem,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A3: A] :
% 2.96/1.58 ( ( inf_inf @ A @ A3 @ A3 )
% 2.96/1.58 = A3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_74_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 = ( ^ [F: A > B,G2: A > B,X: A] : ( inf_inf @ B @ ( F @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_75_Int__iff,axiom,
% 2.96/1.58 ! [A: $tType,C3: A,A4: set @ A,B3: set @ A] :
% 2.96/1.58 ( ( member @ A @ C3 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 2.96/1.58 = ( ( member @ A @ C3 @ A4 )
% 2.96/1.58 & ( member @ A @ C3 @ B3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_76_IntI,axiom,
% 2.96/1.58 ! [A: $tType,C3: A,A4: set @ A,B3: set @ A] :
% 2.96/1.58 ( ( member @ A @ C3 @ A4 )
% 2.96/1.58 => ( ( member @ A @ C3 @ B3 )
% 2.96/1.58 => ( member @ A @ C3 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_77_usubstappf__pred,axiom,
% 2.96/1.58 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),P2: char,R2: fml,U: set @ variable,Theta: trm,Sigma_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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ Sigma
% 2.96/1.58 @ P2 )
% 2.96/1.58 = ( some @ fml @ R2 ) )
% 2.96/1.58 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R2 ) @ U )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 2.96/1.58 = ( some @ trm @ Sigma_theta2 ) )
% 2.96/1.58 => ( ( uSubst95898978stappf @ Sigma @ U @ ( pred @ P2 @ Theta ) )
% 2.96/1.58 = ( uSubst95898978stappf @ ( uSubst969145931substt @ Sigma_theta2 ) @ ( bot_bot @ ( set @ variable ) ) @ R2 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_78_ODEo_Oinduct,axiom,
% 2.96/1.58 ! [P3: char > ( option @ trm ) > $o,A0: char,A1: option @ trm] :
% 2.96/1.58 ( ! [X5: char,Theta2: trm] : ( P3 @ X5 @ ( some @ trm @ Theta2 ) )
% 2.96/1.58 => ( ! [X5: char] : ( P3 @ X5 @ ( none @ trm ) )
% 2.96/1.58 => ( P3 @ A0 @ A1 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_79_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_80_undeft__equiv,axiom,
% 2.96/1.58 ! [Theta: option @ trm] :
% 2.96/1.58 ( ( Theta
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 = ( ? [T: trm] :
% 2.96/1.58 ( Theta
% 2.96/1.58 = ( some @ trm @ T ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_81_Timeso_Oinduct,axiom,
% 2.96/1.58 ! [P3: ( option @ trm ) > ( option @ trm ) > $o,A0: option @ trm,A1: option @ trm] :
% 2.96/1.58 ( ! [Theta2: trm,Eta: trm] : ( P3 @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta ) )
% 2.96/1.58 => ( ! [X_1: option @ trm] : ( P3 @ ( none @ trm ) @ X_1 )
% 2.96/1.58 => ( ! [V6: trm] : ( P3 @ ( some @ trm @ V6 ) @ ( none @ trm ) )
% 2.96/1.58 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_82_Assigno_Oinduct,axiom,
% 2.96/1.58 ! [P3: variable > ( option @ trm ) > $o,A0: variable,A1: option @ trm] :
% 2.96/1.58 ( ! [X5: variable,Theta2: trm] : ( P3 @ X5 @ ( some @ trm @ Theta2 ) )
% 2.96/1.58 => ( ! [X5: variable] : ( P3 @ X5 @ ( none @ trm ) )
% 2.96/1.58 => ( P3 @ A0 @ A1 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_83_Differentialo_Ocases,axiom,
% 2.96/1.58 ! [X3: option @ trm] :
% 2.96/1.58 ( ! [Theta2: trm] :
% 2.96/1.58 ( X3
% 2.96/1.58 != ( some @ trm @ Theta2 ) )
% 2.96/1.58 => ( X3
% 2.96/1.58 = ( none @ trm ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_84_Differentialo_Oinduct,axiom,
% 2.96/1.58 ! [P3: ( option @ trm ) > $o,A0: option @ trm] :
% 2.96/1.58 ( ! [Theta2: trm] : ( P3 @ ( some @ trm @ Theta2 ) )
% 2.96/1.58 => ( ( P3 @ ( none @ trm ) )
% 2.96/1.58 => ( P3 @ A0 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_85_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_86_inf__set__def,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( inf_inf @ ( set @ A ) )
% 2.96/1.58 = ( ^ [A5: set @ A,B5: 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 @ A5 )
% 2.96/1.58 @ ^ [X: A] : ( member @ A @ X @ B5 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_87_less__eq__set__def,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ A ) )
% 2.96/1.58 = ( ^ [A5: set @ A,B5: set @ A] :
% 2.96/1.58 ( ord_less_eq @ ( A > $o )
% 2.96/1.58 @ ^ [X: A] : ( member @ A @ X @ A5 )
% 2.96/1.58 @ ^ [X: A] : ( member @ A @ X @ B5 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_88_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_89_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_90_Diamondo_Oinduct,axiom,
% 2.96/1.58 ! [P3: ( option @ game ) > ( option @ fml ) > $o,A0: option @ game,A1: option @ fml] :
% 2.96/1.58 ( ! [Alpha: game,Phi2: fml] : ( P3 @ ( some @ game @ Alpha ) @ ( some @ fml @ Phi2 ) )
% 2.96/1.58 => ( ! [X_1: option @ fml] : ( P3 @ ( none @ game ) @ X_1 )
% 2.96/1.58 => ( ! [V6: game] : ( P3 @ ( some @ game @ V6 ) @ ( none @ fml ) )
% 2.96/1.58 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_91_case__optionE,axiom,
% 2.96/1.58 ! [A: $tType,P3: $o,Q: A > $o,X3: option @ A] :
% 2.96/1.58 ( ( case_option @ $o @ A @ P3 @ Q @ X3 )
% 2.96/1.58 => ( ( ( X3
% 2.96/1.58 = ( none @ A ) )
% 2.96/1.58 => ~ P3 )
% 2.96/1.58 => ~ ! [Y4: A] :
% 2.96/1.58 ( ( X3
% 2.96/1.58 = ( some @ A @ Y4 ) )
% 2.96/1.58 => ~ ( Q @ Y4 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_92_ex__in__conv,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A] :
% 2.96/1.58 ( ( ? [X: A] : ( member @ A @ X @ A4 ) )
% 2.96/1.58 = ( A4
% 2.96/1.58 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_93_equals0I,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A] :
% 2.96/1.58 ( ! [Y4: A] :
% 2.96/1.58 ~ ( member @ A @ Y4 @ A4 )
% 2.96/1.58 => ( A4
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_94_equals0D,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,A3: A] :
% 2.96/1.58 ( ( A4
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) )
% 2.96/1.58 => ~ ( member @ A @ A3 @ A4 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_95_emptyE,axiom,
% 2.96/1.58 ! [A: $tType,A3: A] :
% 2.96/1.58 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_96_Collect__mono__iff,axiom,
% 2.96/1.58 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P3 ) @ ( collect @ A @ Q ) )
% 2.96/1.58 = ( ! [X: A] :
% 2.96/1.58 ( ( P3 @ X )
% 2.96/1.58 => ( Q @ X ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_97_set__eq__subset,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( ^ [Y5: set @ A,Z3: set @ A] : ( Y5 = Z3 ) )
% 2.96/1.58 = ( ^ [A5: set @ A,B5: set @ A] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 2.96/1.58 & ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_98_subset__trans,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,B3: set @ A,C2: set @ A] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B3 )
% 2.96/1.58 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ C2 )
% 2.96/1.58 => ( ord_less_eq @ ( set @ A ) @ A4 @ C2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_99_Collect__mono,axiom,
% 2.96/1.58 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 2.96/1.58 ( ! [X5: A] :
% 2.96/1.58 ( ( P3 @ X5 )
% 2.96/1.58 => ( Q @ X5 ) )
% 2.96/1.58 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P3 ) @ ( collect @ A @ Q ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_100_subset__refl,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_101_subset__iff,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ A ) )
% 2.96/1.58 = ( ^ [A5: set @ A,B5: set @ A] :
% 2.96/1.58 ! [T: A] :
% 2.96/1.58 ( ( member @ A @ T @ A5 )
% 2.96/1.58 => ( member @ A @ T @ B5 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_102_equalityD2,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 2.96/1.58 ( ( A4 = B3 )
% 2.96/1.58 => ( ord_less_eq @ ( set @ A ) @ B3 @ A4 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_103_equalityD1,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 2.96/1.58 ( ( A4 = B3 )
% 2.96/1.58 => ( ord_less_eq @ ( set @ A ) @ A4 @ B3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_104_subset__eq,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ A ) )
% 2.96/1.58 = ( ^ [A5: set @ A,B5: set @ A] :
% 2.96/1.58 ! [X: A] :
% 2.96/1.58 ( ( member @ A @ X @ A5 )
% 2.96/1.58 => ( member @ A @ X @ B5 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_105_equalityE,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 2.96/1.58 ( ( A4 = B3 )
% 2.96/1.58 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B3 )
% 2.96/1.58 => ~ ( ord_less_eq @ ( set @ A ) @ B3 @ A4 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_106_subsetD,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,B3: set @ A,C3: A] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B3 )
% 2.96/1.58 => ( ( member @ A @ C3 @ A4 )
% 2.96/1.58 => ( member @ A @ C3 @ B3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_107_in__mono,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,B3: set @ A,X3: A] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B3 )
% 2.96/1.58 => ( ( member @ A @ X3 @ A4 )
% 2.96/1.58 => ( member @ A @ X3 @ B3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_108_inf__left__commute,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [X3: A,Y3: A,Z2: A] :
% 2.96/1.58 ( ( inf_inf @ A @ X3 @ ( inf_inf @ A @ Y3 @ Z2 ) )
% 2.96/1.58 = ( inf_inf @ A @ Y3 @ ( inf_inf @ A @ X3 @ Z2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_109_inf_Oleft__commute,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [B4: A,A3: A,C3: A] :
% 2.96/1.58 ( ( inf_inf @ A @ B4 @ ( inf_inf @ A @ A3 @ C3 ) )
% 2.96/1.58 = ( inf_inf @ A @ A3 @ ( inf_inf @ A @ B4 @ C3 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_110_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_111_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 = ( ^ [A6: A,B6: A] : ( inf_inf @ A @ B6 @ A6 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_112_inf__assoc,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [X3: A,Y3: A,Z2: A] :
% 2.96/1.58 ( ( inf_inf @ A @ ( inf_inf @ A @ X3 @ Y3 ) @ Z2 )
% 2.96/1.58 = ( inf_inf @ A @ X3 @ ( inf_inf @ A @ Y3 @ Z2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_113_inf_Oassoc,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A3: A,B4: A,C3: A] :
% 2.96/1.58 ( ( inf_inf @ A @ ( inf_inf @ A @ A3 @ B4 ) @ C3 )
% 2.96/1.58 = ( inf_inf @ A @ A3 @ ( inf_inf @ A @ B4 @ C3 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_114_boolean__algebra__cancel_Oinf2,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [B3: A,K: A,B4: A,A3: A] :
% 2.96/1.58 ( ( B3
% 2.96/1.58 = ( inf_inf @ A @ K @ B4 ) )
% 2.96/1.58 => ( ( inf_inf @ A @ A3 @ B3 )
% 2.96/1.58 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A3 @ B4 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_115_boolean__algebra__cancel_Oinf1,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A4: A,K: A,A3: A,B4: A] :
% 2.96/1.58 ( ( A4
% 2.96/1.58 = ( inf_inf @ A @ K @ A3 ) )
% 2.96/1.58 => ( ( inf_inf @ A @ A4 @ B4 )
% 2.96/1.58 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A3 @ B4 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_116_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 = ( ^ [F: A > B,G2: A > B,X: A] : ( inf_inf @ B @ ( F @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_117_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_118_inf__sup__aci_I2_J,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( lattice @ A )
% 2.96/1.58 => ! [X3: A,Y3: A,Z2: A] :
% 2.96/1.58 ( ( inf_inf @ A @ ( inf_inf @ A @ X3 @ Y3 ) @ Z2 )
% 2.96/1.58 = ( inf_inf @ A @ X3 @ ( inf_inf @ A @ Y3 @ Z2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_119_inf__sup__aci_I3_J,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( lattice @ A )
% 2.96/1.58 => ! [X3: A,Y3: A,Z2: A] :
% 2.96/1.58 ( ( inf_inf @ A @ X3 @ ( inf_inf @ A @ Y3 @ Z2 ) )
% 2.96/1.58 = ( inf_inf @ A @ Y3 @ ( inf_inf @ A @ X3 @ Z2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_120_inf__sup__aci_I4_J,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( lattice @ A )
% 2.96/1.58 => ! [X3: A,Y3: A] :
% 2.96/1.58 ( ( inf_inf @ A @ X3 @ ( inf_inf @ A @ X3 @ Y3 ) )
% 2.96/1.58 = ( inf_inf @ A @ X3 @ Y3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_121_Int__left__commute,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,B3: set @ A,C2: set @ A] :
% 2.96/1.58 ( ( inf_inf @ ( set @ A ) @ A4 @ ( inf_inf @ ( set @ A ) @ B3 @ C2 ) )
% 2.96/1.58 = ( inf_inf @ ( set @ A ) @ B3 @ ( inf_inf @ ( set @ A ) @ A4 @ C2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_122_Int__left__absorb,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 2.96/1.58 ( ( inf_inf @ ( set @ A ) @ A4 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 2.96/1.58 = ( inf_inf @ ( set @ A ) @ A4 @ B3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_123_Int__commute,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( inf_inf @ ( set @ A ) )
% 2.96/1.58 = ( ^ [A5: set @ A,B5: set @ A] : ( inf_inf @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_124_Int__absorb,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A] :
% 2.96/1.58 ( ( inf_inf @ ( set @ A ) @ A4 @ A4 )
% 2.96/1.58 = A4 ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_125_Int__assoc,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,B3: set @ A,C2: set @ A] :
% 2.96/1.58 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) @ C2 )
% 2.96/1.58 = ( inf_inf @ ( set @ A ) @ A4 @ ( inf_inf @ ( set @ A ) @ B3 @ C2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_126_IntD2,axiom,
% 2.96/1.58 ! [A: $tType,C3: A,A4: set @ A,B3: set @ A] :
% 2.96/1.58 ( ( member @ A @ C3 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 2.96/1.58 => ( member @ A @ C3 @ B3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_127_IntD1,axiom,
% 2.96/1.58 ! [A: $tType,C3: A,A4: set @ A,B3: set @ A] :
% 2.96/1.58 ( ( member @ A @ C3 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 2.96/1.58 => ( member @ A @ C3 @ A4 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_128_IntE,axiom,
% 2.96/1.58 ! [A: $tType,C3: A,A4: set @ A,B3: set @ A] :
% 2.96/1.58 ( ( member @ A @ C3 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 2.96/1.58 => ~ ( ( member @ A @ C3 @ A4 )
% 2.96/1.58 => ~ ( member @ A @ C3 @ B3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_129_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_130_Collect__subset,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,P3: A > $o] :
% 2.96/1.58 ( ord_less_eq @ ( set @ A )
% 2.96/1.58 @ ( collect @ A
% 2.96/1.58 @ ^ [X: A] :
% 2.96/1.58 ( ( member @ A @ X @ A4 )
% 2.96/1.58 & ( P3 @ X ) ) )
% 2.96/1.58 @ A4 ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_131_Int__def,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( inf_inf @ ( set @ A ) )
% 2.96/1.58 = ( ^ [A5: set @ A,B5: set @ A] :
% 2.96/1.58 ( collect @ A
% 2.96/1.58 @ ^ [X: A] :
% 2.96/1.58 ( ( member @ A @ X @ A5 )
% 2.96/1.58 & ( member @ A @ X @ B5 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_132_Int__Collect,axiom,
% 2.96/1.58 ! [A: $tType,X3: A,A4: set @ A,P3: A > $o] :
% 2.96/1.58 ( ( member @ A @ X3 @ ( inf_inf @ ( set @ A ) @ A4 @ ( collect @ A @ P3 ) ) )
% 2.96/1.58 = ( ( member @ A @ X3 @ A4 )
% 2.96/1.58 & ( P3 @ X3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_133_Collect__conj__eq,axiom,
% 2.96/1.58 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 2.96/1.58 ( ( collect @ A
% 2.96/1.58 @ ^ [X: A] :
% 2.96/1.58 ( ( P3 @ X )
% 2.96/1.58 & ( Q @ X ) ) )
% 2.96/1.58 = ( inf_inf @ ( set @ A ) @ ( collect @ A @ P3 ) @ ( collect @ A @ Q ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_134_inf_OcoboundedI2,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [B4: A,C3: A,A3: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ B4 @ C3 )
% 2.96/1.58 => ( ord_less_eq @ A @ ( inf_inf @ A @ A3 @ B4 ) @ C3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_135_inf_OcoboundedI1,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A3: A,C3: A,B4: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ A3 @ C3 )
% 2.96/1.58 => ( ord_less_eq @ A @ ( inf_inf @ A @ A3 @ B4 ) @ C3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_136_inf_Oabsorb__iff2,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ( ( ord_less_eq @ A )
% 2.96/1.58 = ( ^ [B6: A,A6: A] :
% 2.96/1.58 ( ( inf_inf @ A @ A6 @ B6 )
% 2.96/1.58 = B6 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_137_inf_Oabsorb__iff1,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ( ( ord_less_eq @ A )
% 2.96/1.58 = ( ^ [A6: A,B6: A] :
% 2.96/1.58 ( ( inf_inf @ A @ A6 @ B6 )
% 2.96/1.58 = A6 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_138_inf_Ocobounded2,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A3: A,B4: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ A3 @ B4 ) @ B4 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_139_inf_Ocobounded1,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A3: A,B4: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ A3 @ B4 ) @ A3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_140_inf_Oorder__iff,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ( ( ord_less_eq @ A )
% 2.96/1.58 = ( ^ [A6: A,B6: A] :
% 2.96/1.58 ( A6
% 2.96/1.58 = ( inf_inf @ A @ A6 @ B6 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_141_inf__greatest,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [X3: A,Y3: A,Z2: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.96/1.58 => ( ( ord_less_eq @ A @ X3 @ Z2 )
% 2.96/1.58 => ( ord_less_eq @ A @ X3 @ ( inf_inf @ A @ Y3 @ Z2 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_142_inf_OboundedI,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A3: A,B4: A,C3: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ A3 @ B4 )
% 2.96/1.58 => ( ( ord_less_eq @ A @ A3 @ C3 )
% 2.96/1.58 => ( ord_less_eq @ A @ A3 @ ( inf_inf @ A @ B4 @ C3 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_143_inf_OboundedE,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A3: A,B4: A,C3: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ A3 @ ( inf_inf @ A @ B4 @ C3 ) )
% 2.96/1.58 => ~ ( ( ord_less_eq @ A @ A3 @ B4 )
% 2.96/1.58 => ~ ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_144_inf__absorb2,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [Y3: A,X3: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ Y3 @ X3 )
% 2.96/1.58 => ( ( inf_inf @ A @ X3 @ Y3 )
% 2.96/1.58 = Y3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_145_inf__absorb1,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [X3: A,Y3: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.96/1.58 => ( ( inf_inf @ A @ X3 @ Y3 )
% 2.96/1.58 = X3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_146_inf_Oabsorb2,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [B4: A,A3: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ B4 @ A3 )
% 2.96/1.58 => ( ( inf_inf @ A @ A3 @ B4 )
% 2.96/1.58 = B4 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_147_inf_Oabsorb1,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A3: A,B4: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ A3 @ B4 )
% 2.96/1.58 => ( ( inf_inf @ A @ A3 @ B4 )
% 2.96/1.58 = A3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_148_le__iff__inf,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ( ( ord_less_eq @ A )
% 2.96/1.58 = ( ^ [X: A,Y: A] :
% 2.96/1.58 ( ( inf_inf @ A @ X @ Y )
% 2.96/1.58 = X ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_149_inf__unique,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [F2: A > A > A,X3: A,Y3: A] :
% 2.96/1.58 ( ! [X5: A,Y4: A] : ( ord_less_eq @ A @ ( F2 @ X5 @ Y4 ) @ X5 )
% 2.96/1.58 => ( ! [X5: A,Y4: A] : ( ord_less_eq @ A @ ( F2 @ X5 @ Y4 ) @ Y4 )
% 2.96/1.58 => ( ! [X5: A,Y4: A,Z4: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ X5 @ Y4 )
% 2.96/1.58 => ( ( ord_less_eq @ A @ X5 @ Z4 )
% 2.96/1.58 => ( ord_less_eq @ A @ X5 @ ( F2 @ Y4 @ Z4 ) ) ) )
% 2.96/1.58 => ( ( inf_inf @ A @ X3 @ Y3 )
% 2.96/1.58 = ( F2 @ X3 @ Y3 ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_150_inf_OorderI,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A3: A,B4: A] :
% 2.96/1.58 ( ( A3
% 2.96/1.58 = ( inf_inf @ A @ A3 @ B4 ) )
% 2.96/1.58 => ( ord_less_eq @ A @ A3 @ B4 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_151_inf_OorderE,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A3: A,B4: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ A3 @ B4 )
% 2.96/1.58 => ( A3
% 2.96/1.58 = ( inf_inf @ A @ A3 @ B4 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_152_le__infI2,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [B4: A,X3: A,A3: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ B4 @ X3 )
% 2.96/1.58 => ( ord_less_eq @ A @ ( inf_inf @ A @ A3 @ B4 ) @ X3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_153_le__infI1,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A3: A,X3: A,B4: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ A3 @ X3 )
% 2.96/1.58 => ( ord_less_eq @ A @ ( inf_inf @ A @ A3 @ B4 ) @ X3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_154_inf__mono,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [A3: A,C3: A,B4: A,D2: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ A3 @ C3 )
% 2.96/1.58 => ( ( ord_less_eq @ A @ B4 @ D2 )
% 2.96/1.58 => ( ord_less_eq @ A @ ( inf_inf @ A @ A3 @ B4 ) @ ( inf_inf @ A @ C3 @ D2 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_155_le__infI,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [X3: A,A3: A,B4: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ X3 @ A3 )
% 2.96/1.58 => ( ( ord_less_eq @ A @ X3 @ B4 )
% 2.96/1.58 => ( ord_less_eq @ A @ X3 @ ( inf_inf @ A @ A3 @ B4 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_156_le__infE,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [X3: A,A3: A,B4: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ X3 @ ( inf_inf @ A @ A3 @ B4 ) )
% 2.96/1.58 => ~ ( ( ord_less_eq @ A @ X3 @ A3 )
% 2.96/1.58 => ~ ( ord_less_eq @ A @ X3 @ B4 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_157_inf__le2,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [X3: A,Y3: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X3 @ Y3 ) @ Y3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_158_inf__le1,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A )
% 2.96/1.58 => ! [X3: A,Y3: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X3 @ Y3 ) @ X3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_159_inf__sup__ord_I1_J,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( lattice @ A )
% 2.96/1.58 => ! [X3: A,Y3: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X3 @ Y3 ) @ X3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_160_inf__sup__ord_I2_J,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( lattice @ A )
% 2.96/1.58 => ! [X3: A,Y3: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X3 @ Y3 ) @ Y3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_161_disjoint__iff__not__equal,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 2.96/1.58 ( ( ( inf_inf @ ( set @ A ) @ A4 @ B3 )
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) )
% 2.96/1.58 = ( ! [X: A] :
% 2.96/1.58 ( ( member @ A @ X @ A4 )
% 2.96/1.58 => ! [Y: A] :
% 2.96/1.58 ( ( member @ A @ Y @ B3 )
% 2.96/1.58 => ( X != Y ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_162_Int__empty__right,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A] :
% 2.96/1.58 ( ( inf_inf @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_163_Int__empty__left,axiom,
% 2.96/1.58 ! [A: $tType,B3: set @ A] :
% 2.96/1.58 ( ( inf_inf @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B3 )
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_164_disjoint__iff,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 2.96/1.58 ( ( ( inf_inf @ ( set @ A ) @ A4 @ B3 )
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) )
% 2.96/1.58 = ( ! [X: A] :
% 2.96/1.58 ( ( member @ A @ X @ A4 )
% 2.96/1.58 => ~ ( member @ A @ X @ B3 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_165_Int__emptyI,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 2.96/1.58 ( ! [X5: A] :
% 2.96/1.58 ( ( member @ A @ X5 @ A4 )
% 2.96/1.58 => ~ ( member @ A @ X5 @ B3 ) )
% 2.96/1.58 => ( ( inf_inf @ ( set @ A ) @ A4 @ B3 )
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_166_Int__Collect__mono,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,B3: set @ A,P3: A > $o,Q: A > $o] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B3 )
% 2.96/1.58 => ( ! [X5: A] :
% 2.96/1.58 ( ( member @ A @ X5 @ A4 )
% 2.96/1.58 => ( ( P3 @ X5 )
% 2.96/1.58 => ( Q @ X5 ) ) )
% 2.96/1.58 => ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ ( collect @ A @ P3 ) ) @ ( inf_inf @ ( set @ A ) @ B3 @ ( collect @ A @ Q ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_167_Int__greatest,axiom,
% 2.96/1.58 ! [A: $tType,C2: set @ A,A4: set @ A,B3: set @ A] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ A ) @ C2 @ A4 )
% 2.96/1.58 => ( ( ord_less_eq @ ( set @ A ) @ C2 @ B3 )
% 2.96/1.58 => ( ord_less_eq @ ( set @ A ) @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_168_Int__absorb2,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B3 )
% 2.96/1.58 => ( ( inf_inf @ ( set @ A ) @ A4 @ B3 )
% 2.96/1.58 = A4 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_169_Int__absorb1,axiom,
% 2.96/1.58 ! [A: $tType,B3: set @ A,A4: set @ A] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ A ) @ B3 @ A4 )
% 2.96/1.58 => ( ( inf_inf @ ( set @ A ) @ A4 @ B3 )
% 2.96/1.58 = B3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_170_Int__lower2,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,B3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) @ B3 ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_171_Int__lower1,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,B3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) @ A4 ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_172_Int__mono,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,C2: set @ A,B3: set @ A,D3: set @ A] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ A ) @ A4 @ C2 )
% 2.96/1.58 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ D3 )
% 2.96/1.58 => ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) @ ( inf_inf @ ( set @ A ) @ C2 @ D3 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_173_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_174_order__refl,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( preorder @ A )
% 2.96/1.58 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_175_subset__emptyI,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A] :
% 2.96/1.58 ( ! [X5: A] :
% 2.96/1.58 ~ ( member @ A @ X5 @ A4 )
% 2.96/1.58 => ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_176_bot_Oextremum__uniqueI,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( order_bot @ A )
% 2.96/1.58 => ! [A3: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ A3 @ ( bot_bot @ A ) )
% 2.96/1.58 => ( A3
% 2.96/1.58 = ( bot_bot @ A ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_177_bot_Oextremum__unique,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( order_bot @ A )
% 2.96/1.58 => ! [A3: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ A3 @ ( bot_bot @ A ) )
% 2.96/1.58 = ( A3
% 2.96/1.58 = ( bot_bot @ A ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_178_bot_Oextremum,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( order_bot @ A )
% 2.96/1.58 => ! [A3: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_179_usubstappf__geqr,axiom,
% 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,Theta: trm,Eta2: trm] :
% 2.96/1.58 ( ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 2.96/1.58 != ( none @ fml ) )
% 2.96/1.58 => ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 2.96/1.58 = ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Eta2 ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_180_fml_Oinject_I2_J,axiom,
% 2.96/1.58 ! [X21: trm,X222: trm,Y21: trm,Y22: trm] :
% 2.96/1.58 ( ( ( geq @ X21 @ X222 )
% 2.96/1.58 = ( geq @ Y21 @ Y22 ) )
% 2.96/1.58 = ( ( X21 = Y21 )
% 2.96/1.58 & ( X222 = Y22 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_181_predicate1I,axiom,
% 2.96/1.58 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 2.96/1.58 ( ! [X5: A] :
% 2.96/1.58 ( ( P3 @ X5 )
% 2.96/1.58 => ( Q @ X5 ) )
% 2.96/1.58 => ( ord_less_eq @ ( A > $o ) @ P3 @ Q ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_182_inf1I,axiom,
% 2.96/1.58 ! [A: $tType,A4: A > $o,X3: A,B3: A > $o] :
% 2.96/1.58 ( ( A4 @ X3 )
% 2.96/1.58 => ( ( B3 @ X3 )
% 2.96/1.58 => ( inf_inf @ ( A > $o ) @ A4 @ B3 @ X3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_183_inf1E,axiom,
% 2.96/1.58 ! [A: $tType,A4: A > $o,B3: A > $o,X3: A] :
% 2.96/1.58 ( ( inf_inf @ ( A > $o ) @ A4 @ B3 @ X3 )
% 2.96/1.58 => ~ ( ( A4 @ X3 )
% 2.96/1.58 => ~ ( B3 @ X3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_184_inf1D1,axiom,
% 2.96/1.58 ! [A: $tType,A4: A > $o,B3: A > $o,X3: A] :
% 2.96/1.58 ( ( inf_inf @ ( A > $o ) @ A4 @ B3 @ X3 )
% 2.96/1.58 => ( A4 @ X3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_185_inf1D2,axiom,
% 2.96/1.58 ! [A: $tType,A4: A > $o,B3: A > $o,X3: A] :
% 2.96/1.58 ( ( inf_inf @ ( A > $o ) @ A4 @ B3 @ X3 )
% 2.96/1.58 => ( B3 @ X3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_186_predicate1D,axiom,
% 2.96/1.58 ! [A: $tType,P3: A > $o,Q: A > $o,X3: A] :
% 2.96/1.58 ( ( ord_less_eq @ ( A > $o ) @ P3 @ Q )
% 2.96/1.58 => ( ( P3 @ X3 )
% 2.96/1.58 => ( Q @ X3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_187_rev__predicate1D,axiom,
% 2.96/1.58 ! [A: $tType,P3: A > $o,X3: A,Q: A > $o] :
% 2.96/1.58 ( ( P3 @ X3 )
% 2.96/1.58 => ( ( ord_less_eq @ ( A > $o ) @ P3 @ Q )
% 2.96/1.58 => ( Q @ X3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_188_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_189_Loopo_Ocases,axiom,
% 2.96/1.58 ! [X3: option @ game] :
% 2.96/1.58 ( ! [Alpha: game] :
% 2.96/1.58 ( X3
% 2.96/1.58 != ( some @ game @ Alpha ) )
% 2.96/1.58 => ( X3
% 2.96/1.58 = ( none @ game ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_190_Loopo_Oinduct,axiom,
% 2.96/1.58 ! [P3: ( option @ game ) > $o,A0: option @ game] :
% 2.96/1.58 ( ! [Alpha: game] : ( P3 @ ( some @ game @ Alpha ) )
% 2.96/1.58 => ( ( P3 @ ( none @ game ) )
% 2.96/1.58 => ( P3 @ A0 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_191_undefg__equiv,axiom,
% 2.96/1.58 ! [Alpha2: option @ game] :
% 2.96/1.58 ( ( Alpha2
% 2.96/1.58 != ( none @ game ) )
% 2.96/1.58 = ( ? [G2: game] :
% 2.96/1.58 ( Alpha2
% 2.96/1.58 = ( some @ game @ G2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_192_Composeo_Oinduct,axiom,
% 2.96/1.58 ! [P3: ( option @ game ) > ( option @ game ) > $o,A0: option @ game,A1: option @ game] :
% 2.96/1.58 ( ! [Alpha: game,Beta: game] : ( P3 @ ( some @ game @ Alpha ) @ ( some @ game @ Beta ) )
% 2.96/1.58 => ( ! [Alpha: option @ game] : ( P3 @ Alpha @ ( none @ game ) )
% 2.96/1.58 => ( ! [V6: game] : ( P3 @ ( none @ game ) @ ( some @ game @ V6 ) )
% 2.96/1.58 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_193_fml_Odistinct_I1_J,axiom,
% 2.96/1.58 ! [X11: char,X12: trm,X21: trm,X222: trm] :
% 2.96/1.58 ( ( pred @ X11 @ X12 )
% 2.96/1.58 != ( geq @ X21 @ X222 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_194_le__funD,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType] :
% 2.96/1.58 ( ( ord @ B )
% 2.96/1.58 => ! [F2: A > B,G: A > B,X3: A] :
% 2.96/1.58 ( ( ord_less_eq @ ( A > B ) @ F2 @ G )
% 2.96/1.58 => ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_195_le__funE,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType] :
% 2.96/1.58 ( ( ord @ B )
% 2.96/1.58 => ! [F2: A > B,G: A > B,X3: A] :
% 2.96/1.58 ( ( ord_less_eq @ ( A > B ) @ F2 @ G )
% 2.96/1.58 => ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_196_le__funI,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType] :
% 2.96/1.58 ( ( ord @ B )
% 2.96/1.58 => ! [F2: A > B,G: A > B] :
% 2.96/1.58 ( ! [X5: A] : ( ord_less_eq @ B @ ( F2 @ X5 ) @ ( G @ X5 ) )
% 2.96/1.58 => ( ord_less_eq @ ( A > B ) @ F2 @ G ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_197_le__fun__def,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType] :
% 2.96/1.58 ( ( ord @ B )
% 2.96/1.58 => ( ( ord_less_eq @ ( A > B ) )
% 2.96/1.58 = ( ^ [F: A > B,G2: A > B] :
% 2.96/1.58 ! [X: A] : ( ord_less_eq @ B @ ( F @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_198_order__subst1,axiom,
% 2.96/1.58 ! [A: $tType,B: $tType] :
% 2.96/1.58 ( ( ( order @ B )
% 2.96/1.58 & ( order @ A ) )
% 2.96/1.58 => ! [A3: A,F2: B > A,B4: B,C3: B] :
% 2.96/1.58 ( ( ord_less_eq @ A @ A3 @ ( F2 @ B4 ) )
% 2.96/1.58 => ( ( ord_less_eq @ B @ B4 @ C3 )
% 2.96/1.58 => ( ! [X5: B,Y4: B] :
% 2.96/1.58 ( ( ord_less_eq @ B @ X5 @ Y4 )
% 2.96/1.58 => ( ord_less_eq @ A @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
% 2.96/1.58 => ( ord_less_eq @ A @ A3 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_199_order__subst2,axiom,
% 2.96/1.58 ! [A: $tType,C: $tType] :
% 2.96/1.58 ( ( ( order @ C )
% 2.96/1.58 & ( order @ A ) )
% 2.96/1.58 => ! [A3: A,B4: A,F2: A > C,C3: C] :
% 2.96/1.58 ( ( ord_less_eq @ A @ A3 @ B4 )
% 2.96/1.58 => ( ( ord_less_eq @ C @ ( F2 @ B4 ) @ C3 )
% 2.96/1.58 => ( ! [X5: A,Y4: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ X5 @ Y4 )
% 2.96/1.58 => ( ord_less_eq @ C @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
% 2.96/1.58 => ( ord_less_eq @ C @ ( F2 @ A3 ) @ C3 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_200_ord__eq__le__subst,axiom,
% 2.96/1.58 ! [A: $tType,B: $tType] :
% 2.96/1.58 ( ( ( ord @ B )
% 2.96/1.58 & ( ord @ A ) )
% 2.96/1.58 => ! [A3: A,F2: B > A,B4: B,C3: B] :
% 2.96/1.58 ( ( A3
% 2.96/1.58 = ( F2 @ B4 ) )
% 2.96/1.58 => ( ( ord_less_eq @ B @ B4 @ C3 )
% 2.96/1.58 => ( ! [X5: B,Y4: B] :
% 2.96/1.58 ( ( ord_less_eq @ B @ X5 @ Y4 )
% 2.96/1.58 => ( ord_less_eq @ A @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
% 2.96/1.58 => ( ord_less_eq @ A @ A3 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_201_ord__le__eq__subst,axiom,
% 2.96/1.58 ! [A: $tType,B: $tType] :
% 2.96/1.58 ( ( ( ord @ B )
% 2.96/1.58 & ( ord @ A ) )
% 2.96/1.58 => ! [A3: A,B4: A,F2: A > B,C3: B] :
% 2.96/1.58 ( ( ord_less_eq @ A @ A3 @ B4 )
% 2.96/1.58 => ( ( ( F2 @ B4 )
% 2.96/1.58 = C3 )
% 2.96/1.58 => ( ! [X5: A,Y4: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ X5 @ Y4 )
% 2.96/1.58 => ( ord_less_eq @ B @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
% 2.96/1.58 => ( ord_less_eq @ B @ ( F2 @ A3 ) @ C3 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_202_eq__iff,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( order @ A )
% 2.96/1.58 => ( ( ^ [Y5: A,Z3: A] : ( Y5 = Z3 ) )
% 2.96/1.58 = ( ^ [X: A,Y: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ X @ Y )
% 2.96/1.58 & ( ord_less_eq @ A @ Y @ X ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_203_antisym,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( order @ A )
% 2.96/1.58 => ! [X3: A,Y3: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.96/1.58 => ( ( ord_less_eq @ A @ Y3 @ X3 )
% 2.96/1.58 => ( X3 = Y3 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_204_linear,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( linorder @ A )
% 2.96/1.58 => ! [X3: A,Y3: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.96/1.58 | ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_205_eq__refl,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( preorder @ A )
% 2.96/1.58 => ! [X3: A,Y3: A] :
% 2.96/1.58 ( ( X3 = Y3 )
% 2.96/1.58 => ( ord_less_eq @ A @ X3 @ Y3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_206_le__cases,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( linorder @ A )
% 2.96/1.58 => ! [X3: A,Y3: A] :
% 2.96/1.58 ( ~ ( ord_less_eq @ A @ X3 @ Y3 )
% 2.96/1.58 => ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_207_order_Otrans,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( order @ A )
% 2.96/1.58 => ! [A3: A,B4: A,C3: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ A3 @ B4 )
% 2.96/1.58 => ( ( ord_less_eq @ A @ B4 @ C3 )
% 2.96/1.58 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_208_le__cases3,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( linorder @ A )
% 2.96/1.58 => ! [X3: A,Y3: A,Z2: A] :
% 2.96/1.58 ( ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.96/1.58 => ~ ( ord_less_eq @ A @ Y3 @ Z2 ) )
% 2.96/1.58 => ( ( ( ord_less_eq @ A @ Y3 @ X3 )
% 2.96/1.58 => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 2.96/1.58 => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 2.96/1.58 => ~ ( ord_less_eq @ A @ Z2 @ Y3 ) )
% 2.96/1.58 => ( ( ( ord_less_eq @ A @ Z2 @ Y3 )
% 2.96/1.58 => ~ ( ord_less_eq @ A @ Y3 @ X3 ) )
% 2.96/1.58 => ( ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 2.96/1.58 => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 2.96/1.58 => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 2.96/1.58 => ~ ( ord_less_eq @ A @ X3 @ Y3 ) ) ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_209_antisym__conv,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( order @ A )
% 2.96/1.58 => ! [Y3: A,X3: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ Y3 @ X3 )
% 2.96/1.58 => ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.96/1.58 = ( X3 = Y3 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_210_order__class_Oorder_Oeq__iff,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( order @ A )
% 2.96/1.58 => ( ( ^ [Y5: A,Z3: A] : ( Y5 = Z3 ) )
% 2.96/1.58 = ( ^ [A6: A,B6: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ A6 @ B6 )
% 2.96/1.58 & ( ord_less_eq @ A @ B6 @ A6 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_211_ord__eq__le__trans,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( ord @ A )
% 2.96/1.58 => ! [A3: A,B4: A,C3: A] :
% 2.96/1.58 ( ( A3 = B4 )
% 2.96/1.58 => ( ( ord_less_eq @ A @ B4 @ C3 )
% 2.96/1.58 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_212_ord__le__eq__trans,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( ord @ A )
% 2.96/1.58 => ! [A3: A,B4: A,C3: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ A3 @ B4 )
% 2.96/1.58 => ( ( B4 = C3 )
% 2.96/1.58 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_213_order__class_Oorder_Oantisym,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( order @ A )
% 2.96/1.58 => ! [A3: A,B4: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ A3 @ B4 )
% 2.96/1.58 => ( ( ord_less_eq @ A @ B4 @ A3 )
% 2.96/1.58 => ( A3 = B4 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_214_order__trans,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( preorder @ A )
% 2.96/1.58 => ! [X3: A,Y3: A,Z2: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.96/1.58 => ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 2.96/1.58 => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_215_dual__order_Orefl,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( order @ A )
% 2.96/1.58 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_216_linorder__wlog,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( linorder @ A )
% 2.96/1.58 => ! [P3: A > A > $o,A3: A,B4: A] :
% 2.96/1.58 ( ! [A2: A,B2: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.96/1.58 => ( P3 @ A2 @ B2 ) )
% 2.96/1.58 => ( ! [A2: A,B2: A] :
% 2.96/1.58 ( ( P3 @ B2 @ A2 )
% 2.96/1.58 => ( P3 @ A2 @ B2 ) )
% 2.96/1.58 => ( P3 @ A3 @ B4 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_217_dual__order_Otrans,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( order @ A )
% 2.96/1.58 => ! [B4: A,A3: A,C3: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ B4 @ A3 )
% 2.96/1.58 => ( ( ord_less_eq @ A @ C3 @ B4 )
% 2.96/1.58 => ( ord_less_eq @ A @ C3 @ A3 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_218_dual__order_Oeq__iff,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( order @ A )
% 2.96/1.58 => ( ( ^ [Y5: A,Z3: A] : ( Y5 = Z3 ) )
% 2.96/1.58 = ( ^ [A6: A,B6: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ B6 @ A6 )
% 2.96/1.58 & ( ord_less_eq @ A @ A6 @ B6 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_219_dual__order_Oantisym,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( order @ A )
% 2.96/1.58 => ! [B4: A,A3: A] :
% 2.96/1.58 ( ( ord_less_eq @ A @ B4 @ A3 )
% 2.96/1.58 => ( ( ord_less_eq @ A @ A3 @ B4 )
% 2.96/1.58 => ( A3 = B4 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_220_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_221_prop__restrict,axiom,
% 2.96/1.58 ! [A: $tType,X3: A,Z5: set @ A,X6: set @ A,P3: A > $o] :
% 2.96/1.58 ( ( member @ A @ X3 @ Z5 )
% 2.96/1.58 => ( ( ord_less_eq @ ( set @ A ) @ Z5
% 2.96/1.58 @ ( collect @ A
% 2.96/1.58 @ ^ [X: A] :
% 2.96/1.58 ( ( member @ A @ X @ X6 )
% 2.96/1.58 & ( P3 @ X ) ) ) )
% 2.96/1.58 => ( P3 @ X3 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_222_Collect__restrict,axiom,
% 2.96/1.58 ! [A: $tType,X6: set @ A,P3: A > $o] :
% 2.96/1.58 ( ord_less_eq @ ( set @ A )
% 2.96/1.58 @ ( collect @ A
% 2.96/1.58 @ ^ [X: A] :
% 2.96/1.58 ( ( member @ A @ X @ X6 )
% 2.96/1.58 & ( P3 @ X ) ) )
% 2.96/1.58 @ X6 ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_223_usubstappf__geq__conv,axiom,
% 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,Theta: trm,Eta2: trm] :
% 2.96/1.58 ( ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 2.96/1.58 != ( none @ fml ) )
% 2.96/1.58 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 & ( ( uSubst95898992stappt @ Sigma @ U @ Eta2 )
% 2.96/1.58 != ( none @ trm ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_224_usubstappf__geq,axiom,
% 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,Theta: trm,Eta2: trm] :
% 2.96/1.58 ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Eta2 )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 => ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 2.96/1.58 = ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Eta2 ) ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_225_disjE__realizer2,axiom,
% 2.96/1.58 ! [B: $tType,A: $tType,P3: $o,Q: A > $o,X3: option @ A,R4: B > $o,F2: B,G: A > B] :
% 2.96/1.58 ( ( case_option @ $o @ A @ P3 @ Q @ X3 )
% 2.96/1.58 => ( ( P3
% 2.96/1.58 => ( R4 @ F2 ) )
% 2.96/1.58 => ( ! [Q2: A] :
% 2.96/1.58 ( ( Q @ Q2 )
% 2.96/1.58 => ( R4 @ ( G @ Q2 ) ) )
% 2.96/1.58 => ( R4 @ ( case_option @ B @ A @ F2 @ G @ X3 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_226_Geqo_Oelims,axiom,
% 2.96/1.58 ! [X3: option @ trm,Xa: option @ trm,Y3: option @ fml] :
% 2.96/1.58 ( ( ( uSubst1556497037e_Geqo @ X3 @ Xa )
% 2.96/1.58 = Y3 )
% 2.96/1.58 => ( ! [Theta2: trm] :
% 2.96/1.58 ( ( X3
% 2.96/1.58 = ( some @ trm @ Theta2 ) )
% 2.96/1.58 => ! [Eta: trm] :
% 2.96/1.58 ( ( Xa
% 2.96/1.58 = ( some @ trm @ Eta ) )
% 2.96/1.58 => ( Y3
% 2.96/1.58 != ( some @ fml @ ( geq @ Theta2 @ Eta ) ) ) ) )
% 2.96/1.58 => ( ( ( X3
% 2.96/1.58 = ( none @ trm ) )
% 2.96/1.58 => ( Y3
% 2.96/1.58 != ( none @ fml ) ) )
% 2.96/1.58 => ~ ( ? [V6: trm] :
% 2.96/1.58 ( X3
% 2.96/1.58 = ( some @ trm @ V6 ) )
% 2.96/1.58 => ( ( Xa
% 2.96/1.58 = ( none @ trm ) )
% 2.96/1.58 => ( Y3
% 2.96/1.58 != ( none @ fml ) ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_227_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_228_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_229_Geqo__undef,axiom,
% 2.96/1.58 ! [Theta: option @ trm,Eta2: option @ trm] :
% 2.96/1.58 ( ( ( uSubst1556497037e_Geqo @ Theta @ Eta2 )
% 2.96/1.58 = ( none @ fml ) )
% 2.96/1.58 = ( ( Theta
% 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_230_Geqo_Osimps_I3_J,axiom,
% 2.96/1.58 ! [V7: trm] :
% 2.96/1.58 ( ( uSubst1556497037e_Geqo @ ( some @ trm @ V7 ) @ ( none @ trm ) )
% 2.96/1.58 = ( none @ fml ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_231_Geqo_Osimps_I1_J,axiom,
% 2.96/1.58 ! [Theta: trm,Eta2: trm] :
% 2.96/1.58 ( ( uSubst1556497037e_Geqo @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta2 ) )
% 2.96/1.58 = ( some @ fml @ ( geq @ Theta @ Eta2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_232_usubstappf_Osimps_I2_J,axiom,
% 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,Theta: trm,Eta2: trm] :
% 2.96/1.58 ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 2.96/1.58 = ( uSubst1556497037e_Geqo @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) @ ( uSubst95898992stappt @ Sigma @ U @ Eta2 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_233_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_234_pred__subset__eq,axiom,
% 2.96/1.58 ! [A: $tType,R4: set @ A,S: set @ A] :
% 2.96/1.58 ( ( ord_less_eq @ ( 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 = ( ord_less_eq @ ( set @ A ) @ R4 @ S ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_235_Collect__empty__eq__bot,axiom,
% 2.96/1.58 ! [A: $tType,P3: A > $o] :
% 2.96/1.58 ( ( ( collect @ A @ P3 )
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) )
% 2.96/1.58 = ( P3
% 2.96/1.58 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_236_Set_Ois__empty__def,axiom,
% 2.96/1.58 ! [A: $tType] :
% 2.96/1.58 ( ( is_empty @ A )
% 2.96/1.58 = ( ^ [A5: set @ A] :
% 2.96/1.58 ( A5
% 2.96/1.58 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_237_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_238_usubstappt_Osimps_I4_J,axiom,
% 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,Theta: trm] :
% 2.96/1.58 ( ( uSubst95898992stappt @ Sigma @ U @ ( func @ F2 @ Theta ) )
% 2.96/1.58 = ( case_option @ ( option @ trm ) @ trm @ ( none @ trm )
% 2.96/1.58 @ ^ [Sigma_theta: trm] :
% 2.96/1.58 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( func @ F2 @ Sigma_theta ) )
% 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 @ ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta ) @ ( 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 @ Sigma
% 2.96/1.58 @ F2 ) )
% 2.96/1.58 @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_239_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_240_usubstappt__func2,axiom,
% 2.96/1.58 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F2: char,R2: trm,U: set @ variable,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 @ Sigma
% 2.96/1.58 @ F2 )
% 2.96/1.58 = ( some @ trm @ R2 ) )
% 2.96/1.58 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U )
% 2.96/1.58 != ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 => ( ( uSubst95898992stappt @ Sigma @ U @ ( func @ F2 @ Theta ) )
% 2.96/1.58 = ( none @ trm ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_241_usubstappt__func,axiom,
% 2.96/1.58 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F2: char,R2: trm,U: set @ variable,Theta: trm,Sigma_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 @ Sigma
% 2.96/1.58 @ F2 )
% 2.96/1.58 = ( some @ trm @ R2 ) )
% 2.96/1.58 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 2.96/1.58 = ( some @ trm @ Sigma_theta2 ) )
% 2.96/1.58 => ( ( uSubst95898992stappt @ Sigma @ U @ ( func @ F2 @ Theta ) )
% 2.96/1.58 = ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta2 ) @ ( bot_bot @ ( set @ variable ) ) @ R2 ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_242_usubstappt__func__conv,axiom,
% 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,Theta: trm] :
% 2.96/1.58 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( func @ F2 @ Theta ) )
% 2.96/1.58 != ( none @ trm ) )
% 2.96/1.58 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 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 @ Sigma
% 2.96/1.58 @ F2 )
% 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 @ Sigma
% 2.96/1.58 @ F2 )
% 2.96/1.58 = ( some @ trm @ R3 ) )
% 2.96/1.58 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R3 ) @ U )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_243_usappconst__simp,axiom,
% 2.96/1.58 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F2: char,R2: trm,U: 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 @ Sigma
% 2.96/1.58 @ F2 )
% 2.96/1.58 = ( some @ trm @ R2 ) )
% 2.96/1.58 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 => ( ( uSubst1138577137pconst @ Sigma @ U @ F2 )
% 2.96/1.58 = ( some @ trm @ R2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_244_usappconst__conv,axiom,
% 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 ( ( ( uSubst1138577137pconst @ Sigma @ U @ F2 )
% 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 = ( 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 @ Sigma
% 2.96/1.58 @ F2 )
% 2.96/1.58 = ( some @ trm @ R3 ) )
% 2.96/1.58 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R3 ) @ U )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_245_usappconst__def,axiom,
% 2.96/1.58 ( uSubst1138577137pconst
% 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,F: char] :
% 2.96/1.58 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( const @ F ) )
% 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 @ ( 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 @ Sigma2
% 2.96/1.58 @ F ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_246_usubstappt__const,axiom,
% 2.96/1.58 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F2: char,R2: trm,U: 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 @ Sigma
% 2.96/1.58 @ F2 )
% 2.96/1.58 = ( some @ trm @ R2 ) )
% 2.96/1.58 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) )
% 2.96/1.58 => ( ( uSubst95898992stappt @ Sigma @ U @ ( const @ F2 ) )
% 2.96/1.58 = ( some @ trm @ R2 ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_247_trm_Oinject_I3_J,axiom,
% 2.96/1.58 ! [X32: char,Y32: char] :
% 2.96/1.58 ( ( ( const @ X32 )
% 2.96/1.58 = ( const @ Y32 ) )
% 2.96/1.58 = ( X32 = Y32 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_248_usubstappt_Osimps_I3_J,axiom,
% 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 ( ( uSubst95898992stappt @ Sigma @ U @ ( const @ F2 ) )
% 2.96/1.58 = ( uSubst1138577137pconst @ Sigma @ U @ F2 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_249_trm_Odistinct_I23_J,axiom,
% 2.96/1.58 ! [X32: char,X41: char,X42: trm] :
% 2.96/1.58 ( ( const @ X32 )
% 2.96/1.58 != ( func @ X41 @ X42 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_250_usubstappt__const__conv,axiom,
% 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 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( const @ F2 ) )
% 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 = ( 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 @ Sigma
% 2.96/1.58 @ F2 )
% 2.96/1.58 = ( some @ trm @ R3 ) )
% 2.96/1.58 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R3 ) @ U )
% 2.96/1.58 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_251_subset__Collect__iff,axiom,
% 2.96/1.58 ! [A: $tType,B3: set @ A,A4: set @ A,P3: A > $o] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ A ) @ B3 @ A4 )
% 2.96/1.58 => ( ( ord_less_eq @ ( set @ A ) @ B3
% 2.96/1.58 @ ( collect @ A
% 2.96/1.58 @ ^ [X: A] :
% 2.96/1.58 ( ( member @ A @ X @ A4 )
% 2.96/1.58 & ( P3 @ X ) ) ) )
% 2.96/1.58 = ( ! [X: A] :
% 2.96/1.58 ( ( member @ A @ X @ B3 )
% 2.96/1.58 => ( P3 @ X ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_252_subset__CollectI,axiom,
% 2.96/1.58 ! [A: $tType,B3: set @ A,A4: set @ A,Q: A > $o,P3: A > $o] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ A ) @ B3 @ A4 )
% 2.96/1.58 => ( ! [X5: A] :
% 2.96/1.58 ( ( member @ A @ X5 @ B3 )
% 2.96/1.58 => ( ( Q @ X5 )
% 2.96/1.58 => ( P3 @ X5 ) ) )
% 2.96/1.58 => ( ord_less_eq @ ( set @ A )
% 2.96/1.58 @ ( collect @ A
% 2.96/1.58 @ ^ [X: A] :
% 2.96/1.58 ( ( member @ A @ X @ B3 )
% 2.96/1.58 & ( Q @ X ) ) )
% 2.96/1.58 @ ( collect @ A
% 2.96/1.58 @ ^ [X: A] :
% 2.96/1.58 ( ( member @ A @ X @ A4 )
% 2.96/1.58 & ( P3 @ X ) ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_253_conj__subset__def,axiom,
% 2.96/1.58 ! [A: $tType,A4: set @ A,P3: A > $o,Q: A > $o] :
% 2.96/1.58 ( ( ord_less_eq @ ( set @ A ) @ A4
% 2.96/1.58 @ ( collect @ A
% 2.96/1.58 @ ^ [X: A] :
% 2.96/1.58 ( ( P3 @ X )
% 2.96/1.58 & ( Q @ X ) ) ) )
% 2.96/1.58 = ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( collect @ A @ P3 ) )
% 2.96/1.58 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( collect @ A @ Q ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(fact_254_Diamondo_Ocases,axiom,
% 2.96/1.58 ! [X3: product_prod @ ( option @ game ) @ ( option @ fml )] :
% 2.96/1.58 ( ! [Alpha: game,Phi2: fml] :
% 2.96/1.58 ( X3
% 2.96/1.58 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ Alpha ) @ ( some @ fml @ Phi2 ) ) )
% 2.96/1.58 => ( ! [Phi2: option @ fml] :
% 2.96/1.58 ( X3
% 2.96/1.58 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( none @ game ) @ Phi2 ) )
% 2.96/1.58 => ~ ! [V6: game] :
% 2.96/1.58 ( X3
% 2.96/1.58 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ V6 ) @ ( none @ fml ) ) ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 2.96/1.58 bounded_lattice @ $o ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 2.96/1.58 ! [A7: $tType] : ( bounded_lattice @ ( set @ A7 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 2.96/1.58 ! [A7: $tType,A8: $tType] :
% 2.96/1.58 ( ( bounded_lattice @ A8 )
% 2.96/1.58 => ( bounded_lattice @ ( A7 > A8 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 2.96/1.58 ! [A7: $tType,A8: $tType] :
% 2.96/1.58 ( ( bounded_lattice @ A8 )
% 2.96/1.58 => ( bounded_lattice_bot @ ( A7 > A8 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 2.96/1.58 ! [A7: $tType,A8: $tType] :
% 2.96/1.58 ( ( semilattice_inf @ A8 )
% 2.96/1.58 => ( semilattice_inf @ ( A7 > A8 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 2.96/1.58 ! [A7: $tType,A8: $tType] :
% 2.96/1.58 ( ( order_bot @ A8 )
% 2.96/1.58 => ( order_bot @ ( A7 > A8 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.96/1.58 ! [A7: $tType,A8: $tType] :
% 2.96/1.58 ( ( preorder @ A8 )
% 2.96/1.58 => ( preorder @ ( A7 > A8 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_fun___Lattices_Olattice,axiom,
% 2.96/1.58 ! [A7: $tType,A8: $tType] :
% 2.96/1.58 ( ( lattice @ A8 )
% 2.96/1.58 => ( lattice @ ( A7 > A8 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.96/1.58 ! [A7: $tType,A8: $tType] :
% 2.96/1.58 ( ( order @ A8 )
% 2.96/1.58 => ( order @ ( A7 > A8 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_fun___Orderings_Oord,axiom,
% 2.96/1.58 ! [A7: $tType,A8: $tType] :
% 2.96/1.58 ( ( ord @ A8 )
% 2.96/1.58 => ( ord @ ( A7 > A8 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_fun___Orderings_Obot,axiom,
% 2.96/1.58 ! [A7: $tType,A8: $tType] :
% 2.96/1.58 ( ( bot @ A8 )
% 2.96/1.58 => ( bot @ ( A7 > A8 ) ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_3,axiom,
% 2.96/1.58 ! [A7: $tType] : ( bounded_lattice_bot @ ( set @ A7 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_4,axiom,
% 2.96/1.58 ! [A7: $tType] : ( semilattice_inf @ ( set @ A7 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_Set_Oset___Orderings_Oorder__bot_5,axiom,
% 2.96/1.58 ! [A7: $tType] : ( order_bot @ ( set @ A7 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_Set_Oset___Orderings_Opreorder_6,axiom,
% 2.96/1.58 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_Set_Oset___Lattices_Olattice_7,axiom,
% 2.96/1.58 ! [A7: $tType] : ( lattice @ ( set @ A7 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_Set_Oset___Orderings_Oorder_8,axiom,
% 2.96/1.58 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_Set_Oset___Orderings_Oord_9,axiom,
% 2.96/1.58 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_Set_Oset___Orderings_Obot_10,axiom,
% 2.96/1.58 ! [A7: $tType] : ( bot @ ( set @ A7 ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_11,axiom,
% 2.96/1.58 bounded_lattice_bot @ $o ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_12,axiom,
% 2.96/1.58 semilattice_inf @ $o ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_HOL_Obool___Orderings_Oorder__bot_13,axiom,
% 2.96/1.58 order_bot @ $o ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_HOL_Obool___Orderings_Opreorder_14,axiom,
% 2.96/1.58 preorder @ $o ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.96/1.58 linorder @ $o ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_HOL_Obool___Lattices_Olattice_15,axiom,
% 2.96/1.58 lattice @ $o ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_HOL_Obool___Orderings_Oorder_16,axiom,
% 2.96/1.58 order @ $o ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_HOL_Obool___Orderings_Oord_17,axiom,
% 2.96/1.58 ord @ $o ).
% 2.96/1.58
% 2.96/1.58 thf(tcon_HOL_Obool___Orderings_Obot_18,axiom,
% 2.96/1.58 bot @ $o ).
% 2.96/1.58
% 2.96/1.58 thf(help_If_3_1_T,axiom,
% 2.96/1.58 ! [P3: $o] :
% 2.96/1.58 ( ( P3 = $true )
% 2.96/1.58 | ( P3 = $false ) ) ).
% 2.96/1.58
% 2.96/1.58 thf(help_If_2_1_T,axiom,
% 2.96/1.58 ! [A: $tType,X3: A,Y3: A] :
% 2.96/1.58 ( ( if @ A @ $false @ X3 @ Y3 )
% 2.96/1.58 = Y3 ) ).
% 2.96/1.58
% 2.96/1.58 thf(help_If_1_1_T,axiom,
% 2.96/1.58 ! [A: $tType,X3: A,Y3: A] :
% 2.96/1.58 ( ( if @ A @ $true @ X3 @ Y3 )
% 2.96/1.58 = X3 ) ).
% 2.96/1.58
% 2.96/1.58 thf(conj_0,conjecture,
% 2.96/1.58 ( ( ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) )
% 2.96/1.58 != ( none @ fml ) )
% 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 @ fml ) )
% 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 @ fml ) )
% 2.96/1.58 @ ^ [Uv: char > ( option @ trm )] :
% 2.96/1.58 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 2.96/1.58 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 2.96/1.58 @ sigma
% 2.96/1.58 @ p )
% 2.96/1.58 = ( none @ fml ) ) ) ).
% 2.96/1.58 ------------------------
% 3.07/1.62 % (22858)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_22545 for (2999ds/4Mi)
% 3.07/1.62 % (22857)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22545 for (2999ds/183Mi)
% 3.07/1.62 % (22859)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_22545 for (2999ds/27Mi)
% 3.07/1.62 % (22860)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22545 for (2999ds/2Mi)
% 3.07/1.62 % (22860)Instruction limit reached!
% 3.07/1.62 % (22860)------------------------------
% 3.07/1.62 % (22860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.62 % (22860)Termination reason: Unknown
% 3.07/1.62 % (22860)Termination phase: shuffling
% 3.07/1.62
% 3.07/1.62 % (22860)Memory used [KB]: 1407
% 3.07/1.62 % (22860)Time elapsed: 0.002 s
% 3.07/1.62 % (22860)Instructions burned: 2 (million)
% 3.07/1.62 % (22860)------------------------------
% 3.07/1.62 % (22860)------------------------------
% 3.07/1.62 % (22858)Instruction limit reached!
% 3.07/1.62 % (22858)------------------------------
% 3.07/1.62 % (22858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.62 % (22858)Termination reason: Unknown
% 3.07/1.62 % (22858)Termination phase: shuffling
% 3.07/1.62
% 3.07/1.62 % (22858)Memory used [KB]: 1535
% 3.07/1.62 % (22858)Time elapsed: 0.003 s
% 3.07/1.62 % (22858)Instructions burned: 7 (million)
% 3.07/1.62 % (22858)------------------------------
% 3.07/1.62 % (22858)------------------------------
% 3.07/1.62 % (22861)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_22545 for (2999ds/2Mi)
% 3.07/1.62 % (22862)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_22545 for (2999ds/275Mi)
% 3.07/1.62 % (22863)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22545 for (2999ds/18Mi)
% 3.07/1.63 % (22861)Instruction limit reached!
% 3.07/1.63 % (22861)------------------------------
% 3.07/1.63 % (22861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.63 % (22861)Termination reason: Unknown
% 3.07/1.63 % (22861)Termination phase: shuffling
% 3.07/1.63
% 3.07/1.63 % (22861)Memory used [KB]: 1407
% 3.07/1.63 % (22861)Time elapsed: 0.004 s
% 3.07/1.63 % (22861)Instructions burned: 3 (million)
% 3.07/1.63 % (22861)------------------------------
% 3.07/1.63 % (22861)------------------------------
% 3.07/1.63 % (22859)Instruction limit reached!
% 3.07/1.63 % (22859)------------------------------
% 3.07/1.63 % (22859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.63 % (22859)Termination reason: Unknown
% 3.07/1.63 % (22859)Termination phase: shuffling
% 3.07/1.63
% 3.07/1.63 % (22859)Memory used [KB]: 1918
% 3.07/1.63 % (22859)Time elapsed: 0.011 s
% 3.07/1.63 % (22859)Instructions burned: 29 (million)
% 3.07/1.63 % (22859)------------------------------
% 3.07/1.63 % (22859)------------------------------
% 3.07/1.63 % (22864)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22545 for (2999ds/3Mi)
% 3.07/1.63 % (22865)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_22545 for (2999ds/37Mi)
% 3.07/1.63 % (22864)Instruction limit reached!
% 3.07/1.63 % (22864)------------------------------
% 3.07/1.63 % (22864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.63 % (22864)Termination reason: Unknown
% 3.07/1.63 % (22864)Termination phase: shuffling
% 3.07/1.63
% 3.07/1.63 % (22864)Memory used [KB]: 1407
% 3.07/1.63 % (22864)Time elapsed: 0.003 s
% 3.07/1.63 % (22864)Instructions burned: 3 (million)
% 3.07/1.63 % (22864)------------------------------
% 3.07/1.63 % (22864)------------------------------
% 3.07/1.64 % (22863)Instruction limit reached!
% 3.07/1.64 % (22863)------------------------------
% 3.07/1.64 % (22863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.64 % (22863)Termination reason: Unknown
% 3.07/1.64 % (22863)Termination phase: shuffling
% 3.07/1.64
% 3.07/1.64 % (22863)Memory used [KB]: 1663
% 3.07/1.64 % (22863)Time elapsed: 0.013 s
% 3.07/1.64 % (22863)Instructions burned: 18 (million)
% 3.07/1.64 % (22863)------------------------------
% 3.07/1.64 % (22863)------------------------------
% 3.07/1.64 % (22867)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_22545 for (2999ds/3Mi)
% 3.07/1.64 % (22867)Instruction limit reached!
% 3.07/1.64 % (22867)------------------------------
% 3.07/1.64 % (22867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.64 % (22867)Termination reason: Unknown
% 3.07/1.64 % (22867)Termination phase: shuffling
% 3.07/1.64
% 3.07/1.64 % (22867)Memory used [KB]: 1407
% 3.07/1.64 % (22867)Time elapsed: 0.003 s
% 3.07/1.64 % (22867)Instructions burned: 3 (million)
% 3.07/1.64 % (22867)------------------------------
% 3.07/1.64 % (22867)------------------------------
% 3.07/1.64 % (22865)Instruction limit reached!
% 3.07/1.64 % (22865)------------------------------
% 3.07/1.64 % (22865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.64 % (22865)Termination reason: Unknown
% 3.07/1.64 % (22865)Termination phase: shuffling
% 3.07/1.64
% 3.07/1.64 % (22865)Memory used [KB]: 2302
% 3.07/1.64 % (22865)Time elapsed: 0.012 s
% 3.07/1.64 % (22865)Instructions burned: 38 (million)
% 3.07/1.64 % (22865)------------------------------
% 3.07/1.64 % (22865)------------------------------
% 3.07/1.64 % (22868)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_22545 for (2999ds/1041Mi)
% 3.07/1.64 % (22866)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_22545 for (2999ds/15Mi)
% 3.07/1.65 % (22870)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22545 for (2999ds/16Mi)
% 3.07/1.65 % (22871)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_22545 for (2999ds/3Mi)
% 3.07/1.65 % (22871)Instruction limit reached!
% 3.07/1.65 % (22871)------------------------------
% 3.07/1.65 % (22871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.65 % (22871)Termination reason: Unknown
% 3.07/1.65 % (22871)Termination phase: shuffling
% 3.07/1.65
% 3.07/1.65 % (22871)Memory used [KB]: 1407
% 3.07/1.65 % (22871)Time elapsed: 0.002 s
% 3.07/1.65 % (22871)Instructions burned: 3 (million)
% 3.07/1.65 % (22871)------------------------------
% 3.07/1.65 % (22871)------------------------------
% 3.07/1.65 % (22869)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22545 for (2999ds/7Mi)
% 3.07/1.65 % (22866)Instruction limit reached!
% 3.07/1.65 % (22866)------------------------------
% 3.07/1.65 % (22866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.65 % (22866)Termination reason: Unknown
% 3.07/1.65 % (22866)Termination phase: shuffling
% 3.07/1.65
% 3.07/1.65 % (22866)Memory used [KB]: 1663
% 3.07/1.65 % (22866)Time elapsed: 0.011 s
% 3.07/1.65 % (22866)Instructions burned: 15 (million)
% 3.07/1.65 % (22866)------------------------------
% 3.07/1.65 % (22866)------------------------------
% 3.07/1.65 % (22869)Instruction limit reached!
% 3.07/1.65 % (22869)------------------------------
% 3.07/1.65 % (22869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.65 % (22869)Termination reason: Unknown
% 3.07/1.65 % (22869)Termination phase: shuffling
% 3.07/1.65
% 3.07/1.65 % (22869)Memory used [KB]: 1535
% 3.07/1.65 % (22869)Time elapsed: 0.005 s
% 3.07/1.65 % (22869)Instructions burned: 7 (million)
% 3.07/1.65 % (22869)------------------------------
% 3.07/1.65 % (22869)------------------------------
% 3.07/1.65 % (22870)Instruction limit reached!
% 3.07/1.65 % (22870)------------------------------
% 3.07/1.65 % (22870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.65 % (22870)Termination reason: Unknown
% 3.07/1.65 % (22870)Termination phase: shuffling
% 3.07/1.65
% 3.07/1.65 % (22870)Memory used [KB]: 1663
% 3.07/1.65 % (22870)Time elapsed: 0.008 s
% 3.07/1.65 % (22870)Instructions burned: 18 (million)
% 3.07/1.65 % (22870)------------------------------
% 3.07/1.65 % (22870)------------------------------
% 3.07/1.66 % (22872)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_22545 for (2999ds/3Mi)
% 3.07/1.66 % (22872)Instruction limit reached!
% 3.07/1.66 % (22872)------------------------------
% 3.07/1.66 % (22872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.66 % (22872)Termination reason: Unknown
% 3.07/1.66 % (22872)Termination phase: shuffling
% 3.07/1.66
% 3.07/1.66 % (22872)Memory used [KB]: 1407
% 3.07/1.66 % (22872)Time elapsed: 0.002 s
% 3.07/1.66 % (22872)Instructions burned: 3 (million)
% 3.07/1.66 % (22872)------------------------------
% 3.07/1.66 % (22872)------------------------------
% 3.07/1.66 % (22875)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22545 for (2999ds/4Mi)
% 3.07/1.66 % (22874)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22545 for (2999ds/3Mi)
% 3.07/1.67 % (22874)Instruction limit reached!
% 3.07/1.67 % (22874)------------------------------
% 3.07/1.67 % (22874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.67 % (22874)Termination reason: Unknown
% 3.07/1.67 % (22874)Termination phase: shuffling
% 3.07/1.67
% 3.07/1.67 % (22874)Memory used [KB]: 1407
% 3.07/1.67 % (22874)Time elapsed: 0.003 s
% 3.07/1.67 % (22874)Instructions burned: 4 (million)
% 3.07/1.67 % (22874)------------------------------
% 3.07/1.67 % (22874)------------------------------
% 3.07/1.67 % (22875)Instruction limit reached!
% 3.07/1.67 % (22875)------------------------------
% 3.07/1.67 % (22875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.67 % (22875)Termination reason: Unknown
% 3.07/1.67 % (22875)Termination phase: shuffling
% 3.07/1.67
% 3.07/1.67 % (22875)Memory used [KB]: 1535
% 3.07/1.67 % (22875)Time elapsed: 0.004 s
% 3.07/1.67 % (22875)Instructions burned: 6 (million)
% 3.07/1.67 % (22875)------------------------------
% 3.07/1.67 % (22875)------------------------------
% 3.07/1.67 % (22873)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22545 for (2999ds/7Mi)
% 3.07/1.67 % (22876)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22545 for (2999ds/18Mi)
% 3.07/1.67 % (22862)Refutation not found, incomplete strategy
% 3.07/1.67 % (22862)------------------------------
% 3.07/1.67 % (22862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.67 % (22862)Termination reason: Refutation not found, incomplete strategy
% 3.07/1.67
% 3.07/1.67
% 3.07/1.67 % (22862)Memory used [KB]: 6652
% 3.07/1.67 % (22862)Time elapsed: 0.047 s
% 3.07/1.67 % (22862)Instructions burned: 78 (million)
% 3.07/1.67 % (22862)------------------------------
% 3.07/1.67 % (22862)------------------------------
% 3.07/1.67 % (22873)Instruction limit reached!
% 3.07/1.67 % (22873)------------------------------
% 3.07/1.67 % (22873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.67 % (22873)Termination reason: Unknown
% 3.07/1.67 % (22873)Termination phase: shuffling
% 3.07/1.67
% 3.07/1.67 % (22873)Memory used [KB]: 1535
% 3.07/1.67 % (22873)Time elapsed: 0.006 s
% 3.07/1.67 % (22873)Instructions burned: 8 (million)
% 3.07/1.67 % (22873)------------------------------
% 3.07/1.67 % (22873)------------------------------
% 3.07/1.67 % (22857)Instruction limit reached!
% 3.07/1.67 % (22857)------------------------------
% 3.07/1.67 % (22857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.67 % (22857)Termination reason: Unknown
% 3.07/1.67 % (22857)Termination phase: Saturation
% 3.07/1.67
% 3.07/1.67 % (22857)Memory used [KB]: 7291
% 3.07/1.67 % (22857)Time elapsed: 0.059 s
% 3.07/1.67 % (22857)Instructions burned: 183 (million)
% 3.07/1.67 % (22857)------------------------------
% 3.07/1.67 % (22857)------------------------------
% 3.07/1.68 % (22876)Instruction limit reached!
% 3.07/1.68 % (22876)------------------------------
% 3.07/1.68 % (22876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.68 % (22876)Termination reason: Unknown
% 3.07/1.68 % (22876)Termination phase: shuffling
% 3.07/1.68
% 3.07/1.68 % (22876)Memory used [KB]: 1663
% 3.07/1.68 % (22876)Time elapsed: 0.007 s
% 3.07/1.68 % (22876)Instructions burned: 18 (million)
% 3.07/1.68 % (22876)------------------------------
% 3.07/1.68 % (22876)------------------------------
% 3.07/1.68 % (22877)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_22545 for (2999ds/710Mi)
% 3.07/1.68 % (22878)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22545 for (2999ds/6Mi)
% 3.07/1.68 % (22878)Instruction limit reached!
% 3.07/1.68 % (22878)------------------------------
% 3.07/1.68 % (22878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.68 % (22878)Termination reason: Unknown
% 3.07/1.68 % (22878)Termination phase: shuffling
% 3.07/1.68
% 3.07/1.68 % (22878)Memory used [KB]: 1535
% 3.07/1.68 % (22878)Time elapsed: 0.004 s
% 3.07/1.68 % (22878)Instructions burned: 7 (million)
% 3.07/1.68 % (22878)------------------------------
% 3.07/1.68 % (22878)------------------------------
% 3.07/1.68 % (22882)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_22545 for (2999ds/6Mi)
% 3.07/1.68 % (22880)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_22545 for (2999ds/21Mi)
% 3.07/1.69 % (22882)Instruction limit reached!
% 3.07/1.69 % (22882)------------------------------
% 3.07/1.69 % (22882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.69 % (22882)Termination reason: Unknown
% 3.07/1.69 % (22882)Termination phase: shuffling
% 3.07/1.69
% 3.07/1.69 % (22882)Memory used [KB]: 1535
% 3.07/1.69 % (22882)Time elapsed: 0.003 s
% 3.07/1.69 % (22882)Instructions burned: 7 (million)
% 3.07/1.69 % (22882)------------------------------
% 3.07/1.69 % (22882)------------------------------
% 3.07/1.69 % (22879)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_22545 for (2999ds/902Mi)
% 3.07/1.69 % (22883)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_22545 for (2999ds/377Mi)
% 3.07/1.69 % (22880)Instruction limit reached!
% 3.07/1.69 % (22880)------------------------------
% 3.07/1.69 % (22880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.69 % (22880)Termination reason: Unknown
% 3.07/1.69 % (22880)Termination phase: shuffling
% 3.07/1.69
% 3.07/1.69 % (22880)Memory used [KB]: 1663
% 3.07/1.69 % (22880)Time elapsed: 0.008 s
% 3.07/1.69 % (22880)Instructions burned: 22 (million)
% 3.07/1.69 % (22880)------------------------------
% 3.07/1.69 % (22880)------------------------------
% 3.07/1.69 % (22881)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_22545 for (2999ds/5Mi)
% 3.07/1.70 % (22881)Instruction limit reached!
% 3.07/1.70 % (22881)------------------------------
% 3.07/1.70 % (22881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.70 % (22881)Termination reason: Unknown
% 3.07/1.70 % (22881)Termination phase: shuffling
% 3.07/1.70
% 3.07/1.70 % (22881)Memory used [KB]: 1535
% 3.07/1.70 % (22881)Time elapsed: 0.005 s
% 3.07/1.70 % (22881)Instructions burned: 5 (million)
% 3.07/1.70 % (22881)------------------------------
% 3.07/1.70 % (22881)------------------------------
% 3.07/1.70 % (22884)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_22545 for (2999ds/779Mi)
% 3.07/1.70 % (22885)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_22545 for (2999ds/19Mi)
% 3.07/1.71 % (22885)Instruction limit reached!
% 3.07/1.71 % (22885)------------------------------
% 3.07/1.71 % (22885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.71 % (22885)Termination reason: Unknown
% 3.07/1.71 % (22885)Termination phase: shuffling
% 3.07/1.71
% 3.07/1.71 % (22885)Memory used [KB]: 1918
% 3.07/1.71 % (22885)Time elapsed: 0.007 s
% 3.07/1.71 % (22885)Instructions burned: 21 (million)
% 3.07/1.71 % (22885)------------------------------
% 3.07/1.71 % (22885)------------------------------
% 3.07/1.71 % (22886)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_22545 for (2998ds/879Mi)
% 3.07/1.72 % (22887)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_22545 for (2998ds/17Mi)
% 3.07/1.72 % (22887)Instruction limit reached!
% 3.07/1.72 % (22887)------------------------------
% 3.07/1.72 % (22887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.72 % (22887)Termination reason: Unknown
% 3.07/1.72 % (22887)Termination phase: shuffling
% 3.07/1.72
% 3.07/1.72 % (22887)Memory used [KB]: 1663
% 3.07/1.72 % (22887)Time elapsed: 0.007 s
% 3.07/1.72 % (22887)Instructions burned: 17 (million)
% 3.07/1.72 % (22887)------------------------------
% 3.07/1.72 % (22887)------------------------------
% 3.07/1.73 % (22888)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_22545 for (2998ds/3Mi)
% 3.07/1.73 % (22888)Instruction limit reached!
% 3.07/1.73 % (22888)------------------------------
% 3.07/1.73 % (22888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.73 % (22888)Termination reason: Unknown
% 3.07/1.73 % (22888)Termination phase: shuffling
% 3.07/1.73
% 3.07/1.73 % (22888)Memory used [KB]: 1407
% 3.07/1.73 % (22888)Time elapsed: 0.002 s
% 3.07/1.73 % (22888)Instructions burned: 3 (million)
% 3.07/1.73 % (22888)------------------------------
% 3.07/1.73 % (22888)------------------------------
% 3.07/1.74 % (22889)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_22545 for (2998ds/30Mi)
% 3.07/1.75 % (22889)Instruction limit reached!
% 3.07/1.75 % (22889)------------------------------
% 3.07/1.75 % (22889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.75 % (22889)Termination reason: Unknown
% 3.07/1.75 % (22889)Termination phase: shuffling
% 3.07/1.75
% 3.07/1.75 % (22889)Memory used [KB]: 1918
% 3.07/1.75 % (22889)Time elapsed: 0.011 s
% 3.07/1.75 % (22889)Instructions burned: 32 (million)
% 3.07/1.75 % (22889)------------------------------
% 3.07/1.75 % (22889)------------------------------
% 3.07/1.76 % (22890)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_22545 for (2998ds/127Mi)
% 3.07/1.80 % (22890)Instruction limit reached!
% 3.07/1.80 % (22890)------------------------------
% 3.07/1.80 % (22890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.80 % (22890)Termination reason: Unknown
% 3.07/1.80 % (22890)Termination phase: Saturation
% 3.07/1.80
% 3.07/1.80 % (22890)Memory used [KB]: 6780
% 3.07/1.80 % (22890)Time elapsed: 0.039 s
% 3.07/1.80 % (22890)Instructions burned: 127 (million)
% 3.07/1.80 % (22890)------------------------------
% 3.07/1.80 % (22890)------------------------------
% 3.07/1.81 % (22886)First to succeed.
% 3.07/1.81 % (22891)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_22545 for (2997ds/100Mi)
% 3.07/1.81 % (22883)Instruction limit reached!
% 3.07/1.81 % (22883)------------------------------
% 3.07/1.81 % (22883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.81 % (22883)Termination reason: Unknown
% 3.07/1.81 % (22883)Termination phase: Saturation
% 3.07/1.81
% 3.07/1.81 % (22883)Memory used [KB]: 7931
% 3.07/1.81 % (22883)Time elapsed: 0.143 s
% 3.07/1.81 % (22883)Instructions burned: 379 (million)
% 3.07/1.81 % (22883)------------------------------
% 3.07/1.81 % (22883)------------------------------
% 3.07/1.81 % (22886)Refutation found. Thanks to Tanya!
% 3.07/1.81 % SZS status Theorem for DTF2THF_22545
% 3.07/1.81 % SZS output start Proof for DTF2THF_22545
% 3.07/1.81 thf(type_def_6, type, option: ($tType) > $tType).
% 3.07/1.81 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 3.07/1.81 thf(type_def_8, type, set: ($tType) > $tType).
% 3.07/1.81 thf(type_def_9, type, fml: $tType).
% 3.07/1.81 thf(type_def_10, type, variable: $tType).
% 3.07/1.81 thf(type_def_11, type, trm: $tType).
% 3.07/1.81 thf(type_def_12, type, char: $tType).
% 3.07/1.81 thf(type_def_13, type, game: $tType).
% 3.07/1.81 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 3.07/1.81 thf(func_def_1, type, variable: $tType).
% 3.07/1.81 thf(func_def_2, type, option: ($tType) > $tType).
% 3.07/1.81 thf(func_def_3, type, game: $tType).
% 3.07/1.81 thf(func_def_4, type, char: $tType).
% 3.07/1.81 thf(func_def_5, type, trm: $tType).
% 3.07/1.81 thf(func_def_6, type, fml: $tType).
% 3.07/1.81 thf(func_def_7, type, set: ($tType) > $tType).
% 3.07/1.81 thf(func_def_8, type, bounded_lattice: !>[X0: $tType]:($o)).
% 3.07/1.81 thf(func_def_9, type, type: !>[X0: $tType]:($o)).
% 3.07/1.81 thf(func_def_10, type, bot: !>[X0: $tType]:($o)).
% 3.07/1.81 thf(func_def_11, type, ord: !>[X0: $tType]:($o)).
% 3.07/1.81 thf(func_def_12, type, order: !>[X0: $tType]:($o)).
% 3.07/1.81 thf(func_def_13, type, lattice: !>[X0: $tType]:($o)).
% 3.07/1.81 thf(func_def_14, type, linorder: !>[X0: $tType]:($o)).
% 3.07/1.81 thf(func_def_15, type, preorder: !>[X0: $tType]:($o)).
% 3.07/1.81 thf(func_def_16, type, order_bot: !>[X0: $tType]:($o)).
% 3.07/1.81 thf(func_def_17, type, semilattice_inf: !>[X0: $tType]:($o)).
% 3.07/1.81 thf(func_def_18, type, bounded_lattice_bot: !>[X0: $tType]:($o)).
% 3.07/1.81 thf(func_def_19, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 3.07/1.81 thf(func_def_20, type, inf_inf: !>[X0: $tType]:(X0 > X0 > X0)).
% 3.07/1.81 thf(func_def_21, type, none: !>[X0: $tType]:(option @ X0)).
% 3.07/1.81 thf(func_def_22, type, some: !>[X0: $tType]:(X0 > option @ X0)).
% 3.07/1.81 thf(func_def_23, type, case_option: !>[X0: $tType, X1: $tType]:(X0 > (X1 > X0) > option @ X1 > X0)).
% 3.07/1.81 thf(func_def_24, type, the: !>[X0: $tType]:(option @ X0 > X0)).
% 3.07/1.81 thf(func_def_25, type, bot_bot: !>[X0: $tType]:(X0)).
% 3.07/1.81 thf(func_def_26, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 3.07/1.81 thf(func_def_27, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 3.07/1.81 thf(func_def_28, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 3.07/1.81 thf(func_def_29, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 3.07/1.81 thf(func_def_30, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 3.07/1.81 thf(func_def_31, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 3.07/1.81 thf(func_def_32, type, static_FVF: fml > set @ variable).
% 3.07/1.81 thf(func_def_33, type, static_FVT: trm > set @ variable).
% 3.07/1.81 thf(func_def_34, type, geq: trm > trm > fml).
% 3.07/1.81 thf(func_def_35, type, pred: char > trm > fml).
% 3.07/1.81 thf(func_def_36, type, const: char > trm).
% 3.07/1.81 thf(func_def_37, type, func: char > trm > trm).
% 3.07/1.81 thf(func_def_38, type, uSubst1556497037e_Geqo: option @ trm > option @ trm > option @ fml).
% 3.07/1.81 thf(func_def_39, type, uSubst969145931substt: trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 3.07/1.81 thf(func_def_40, 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).
% 3.07/1.81 thf(func_def_41, 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).
% 3.07/1.81 thf(func_def_42, 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).
% 3.07/1.81 thf(func_def_43, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 3.07/1.81 thf(func_def_44, type, ua: set @ variable).
% 3.07/1.81 thf(func_def_45, type, va: set @ variable).
% 3.07/1.81 thf(func_def_46, type, sigma: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 3.07/1.81 thf(func_def_47, type, theta: trm).
% 3.07/1.81 thf(func_def_48, type, p: char).
% 3.07/1.81 thf(func_def_49, type, vv: set @ variable > set @ variable > variable).
% 3.07/1.81 thf(func_def_50, type, vva: set @ variable > set @ variable > variable).
% 3.07/1.81 thf(func_def_67, type, sP0: option @ trm > option @ fml > option @ trm > $o).
% 3.07/1.81 thf(func_def_68, type, sK1: option @ fml > fml).
% 3.07/1.81 thf(func_def_69, type, sK2: (char > option @ trm > $o) > char).
% 3.07/1.81 thf(func_def_70, type, sK3: (char > option @ trm > $o) > trm).
% 3.07/1.81 thf(func_def_71, type, sK4: (char > option @ trm > $o) > char).
% 3.07/1.81 thf(func_def_72, type, sK5: char > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > trm).
% 3.07/1.81 thf(func_def_73, type, sK6: char > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > trm).
% 3.07/1.81 thf(func_def_74, type, sK7: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 3.07/1.81 thf(func_def_75, type, sK8: (option @ fml > $o) > fml).
% 3.07/1.81 thf(func_def_76, type, sK9: (option @ game > option @ fml > $o) > game).
% 3.07/1.81 thf(func_def_77, type, sK10: (option @ game > option @ fml > $o) > fml).
% 3.07/1.81 thf(func_def_78, type, sK11: (option @ game > option @ fml > $o) > option @ fml).
% 3.07/1.81 thf(func_def_79, type, sK12: (option @ game > option @ fml > $o) > game).
% 3.07/1.81 thf(func_def_80, type, sK13: (option @ trm > option @ trm > $o) > option @ trm).
% 3.07/1.81 thf(func_def_81, type, sK14: (option @ trm > option @ trm > $o) > trm).
% 3.07/1.81 thf(func_def_82, type, sK15: (option @ trm > option @ trm > $o) > trm).
% 3.07/1.81 thf(func_def_83, type, sK16: (option @ trm > option @ trm > $o) > trm).
% 3.07/1.81 thf(func_def_84, type, sK17: (variable > option @ trm > $o) > variable).
% 3.07/1.81 thf(func_def_85, type, sK18: (variable > option @ trm > $o) > variable).
% 3.07/1.81 thf(func_def_86, type, sK19: (variable > option @ trm > $o) > trm).
% 3.07/1.81 thf(func_def_87, type, sK20: (variable > option @ fml > $o) > variable).
% 3.07/1.81 thf(func_def_88, type, sK21: (variable > option @ fml > $o) > variable).
% 3.07/1.81 thf(func_def_89, type, sK22: (variable > option @ fml > $o) > fml).
% 3.07/1.81 thf(func_def_90, type, sK23: (option @ fml > option @ fml > $o) > fml).
% 3.07/1.81 thf(func_def_91, type, sK24: (option @ fml > option @ fml > $o) > fml).
% 3.07/1.81 thf(func_def_92, type, sK25: (option @ fml > option @ fml > $o) > fml).
% 3.07/1.81 thf(func_def_93, type, sK26: (option @ fml > option @ fml > $o) > option @ fml).
% 3.07/1.81 thf(func_def_94, type, sK27: (option @ game > option @ game > $o) > game).
% 3.07/1.81 thf(func_def_95, type, sK28: (option @ game > option @ game > $o) > game).
% 3.07/1.81 thf(func_def_96, type, sK29: (option @ game > option @ game > $o) > game).
% 3.07/1.81 thf(func_def_97, type, sK30: (option @ game > option @ game > $o) > option @ game).
% 3.07/1.81 thf(func_def_98, type, sK31: option @ trm > trm).
% 3.07/1.81 thf(func_def_99, type, sK32: option @ fml > option @ trm > option @ trm > trm).
% 3.07/1.81 thf(func_def_100, type, sK33: option @ fml > option @ trm > option @ trm > trm).
% 3.07/1.81 thf(func_def_101, type, sK34: set @ variable > set @ variable > variable).
% 3.07/1.81 thf(func_def_102, type, sK35: (option @ game > $o) > game).
% 3.07/1.81 thf(func_def_103, type, sK36: char > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > trm).
% 3.07/1.81 thf(func_def_104, type, sK37: option @ game > game).
% 3.07/1.81 thf(func_def_105, type, sK38: (option @ trm > $o) > trm).
% 3.07/1.81 thf(func_def_106, type, sK39: option @ trm > trm).
% 3.07/1.81 thf(func_def_107, type, sK40: product_prod @ option @ game @ option @ fml > game).
% 3.07/1.81 thf(func_def_108, type, sK41: product_prod @ option @ game @ option @ fml > fml).
% 3.07/1.81 thf(func_def_109, type, sK42: product_prod @ option @ game @ option @ fml > option @ fml).
% 3.07/1.81 thf(func_def_110, type, sK43: product_prod @ option @ game @ option @ fml > game).
% 3.07/1.81 thf(func_def_111, type, sK44: char > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > fml).
% 3.07/1.81 thf(func_def_113, type, sK46: set @ variable > set @ variable > variable).
% 3.07/1.81 thf(func_def_114, type, sK47: set @ variable > set @ variable > variable).
% 3.07/1.81 thf(func_def_115, type, sK48: set @ variable > set @ variable > variable).
% 3.07/1.81 thf(func_def_116, type, sK49: option @ game > game).
% 3.07/1.81 thf(func_def_117, type, sK50: option @ fml > fml).
% 3.07/1.81 thf(func_def_118, type, sK51: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 3.07/1.81 thf(func_def_119, type, sK52: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 3.07/1.81 thf(f1310,plain,(
% 3.07/1.81 $false),
% 3.07/1.81 inference(subsumption_resolution,[status(thm)],[f1309,f1290])).
% 3.07/1.81 thf(f1290,plain,(
% 3.07/1.81 (none @ fml = (uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ ua @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))),
% 3.07/1.81 inference(forward_demodulation,[status(thm)],[f1289,f982])).
% 3.07/1.81 thf(f982,plain,(
% 3.07/1.81 (none @ fml = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)))),
% 3.07/1.81 inference(cnf_transformation,[status(thm)],[f826])).
% 3.07/1.81 thf(f826,plain,(
% 3.07/1.81 (none @ fml != (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)) & (none @ fml = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)))),
% 3.07/1.81 inference(ennf_transformation,[status(thm)],[f537])).
% 3.07/1.81 thf(f537,plain,(
% 3.07/1.81 ~((none @ fml != (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))) | (none @ fml = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))),
% 3.07/1.81 inference(fool_elimination,[status(thm)],[f536])).
% 3.07/1.81 thf(f536,plain,(
% 3.07/1.81 ~((none @ fml != (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))) | (none @ fml = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : char > option @ fml, X3 : char > option @ game] : (X2)))))) @ sigma @ p)))),
% 3.07/1.81 inference(rectify,[status(thm)],[f288])).
% 3.07/1.81 thf(f288,negated_conjecture,(
% 3.07/1.81 ~((none @ fml != (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))) | (none @ fml = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X9)))))) @ sigma @ p)))),
% 3.07/1.81 inference(negated_conjecture,[status(cth)],[f287])).
% 3.07/1.81 thf(f287,conjecture,(
% 3.07/1.81 (none @ fml != (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))) | (none @ fml = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X9)))))) @ sigma @ p))),
% 3.07/1.81 file('/export/starexec/sandbox/tmp/tmp.JL8G97Ngch/DTF2THF_22545.p',conj_0)).
% 3.07/1.81 thf(f1289,plain,(
% 3.07/1.81 ((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)) = (uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ ua @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))),
% 3.07/1.81 inference(forward_demodulation,[status(thm)],[f1288,f1003])).
% 3.07/1.81 thf(f1003,plain,(
% 3.07/1.81 ((uSubst95898992stappt @ sigma @ va @ theta) = (uSubst95898992stappt @ sigma @ ua @ theta))),
% 3.07/1.81 inference(cnf_transformation,[status(thm)],[f9])).
% 3.07/1.81 thf(f9,axiom,(
% 3.07/1.81 ((uSubst95898992stappt @ sigma @ va @ theta) = (uSubst95898992stappt @ sigma @ ua @ theta))),
% 3.07/1.81 file('/export/starexec/sandbox/tmp/tmp.JL8G97Ngch/DTF2THF_22545.p',fact_8_f7)).
% 3.07/1.81 thf(f1288,plain,(
% 3.07/1.81 ((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)) = (uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))),
% 3.07/1.81 inference(subsumption_resolution,[status(thm)],[f1287,f1285])).
% 3.07/1.81 thf(f1285,plain,(
% 3.07/1.81 (none @ fml != (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))),
% 3.07/1.81 inference(subsumption_resolution,[status(thm)],[f1284,f977])).
% 3.07/1.81 thf(f977,plain,(
% 3.07/1.81 ((uSubst95898978stappf @ sigma @ ua @ (pred @ p @ theta)) != none @ fml)),
% 3.07/1.81 inference(cnf_transformation,[status(thm)],[f2])).
% 3.07/1.81 thf(f2,axiom,(
% 3.07/1.81 ((uSubst95898978stappf @ sigma @ ua @ (pred @ p @ theta)) != none @ fml)),
% 3.07/1.81 file('/export/starexec/sandbox/tmp/tmp.JL8G97Ngch/DTF2THF_22545.p',fact_1_Pred_Oprems_I2_J)).
% 3.07/1.81 thf(f1284,plain,(
% 3.07/1.81 (none @ fml != (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)) | ((uSubst95898978stappf @ sigma @ ua @ (pred @ p @ theta)) = none @ fml)),
% 3.07/1.81 inference(forward_demodulation,[status(thm)],[f1080,f982])).
% 3.07/1.81 thf(f1080,plain,(
% 3.07/1.81 ((uSubst95898978stappf @ sigma @ ua @ (pred @ p @ theta)) = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))) | (none @ fml != (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))),
% 3.07/1.81 inference(definition_unfolding,[status(thm)],[f972,f989,f989,f989])).
% 3.07/1.81 thf(f989,plain,(
% 3.07/1.81 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : ((product_case_prod @ X2 @ X1 @ X0 = produc2004651681e_prod @ X2 @ X1 @ X0)) )),
% 3.07/1.81 inference(cnf_transformation,[status(thm)],[f802])).
% 3.07/1.81 thf(f802,plain,(
% 3.07/1.81 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (product_case_prod @ X2 @ X1 @ X0 = produc2004651681e_prod @ X2 @ X1 @ X0)),
% 3.07/1.81 inference(rectify,[status(thm)],[f238])).
% 3.07/1.81 thf(f238,axiom,(
% 3.07/1.81 ! [X2 : $tType,X1 : $tType,X0 : $tType] : (product_case_prod @ X0 @ X1 @ X2 = produc2004651681e_prod @ X0 @ X1 @ X2)),
% 3.07/1.81 file('/export/starexec/sandbox/tmp/tmp.JL8G97Ngch/DTF2THF_22545.p',fact_237_internal__case__prod__def)).
% 3.07/1.81 thf(f972,plain,(
% 3.07/1.81 (none @ fml != (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)) | ((uSubst95898978stappf @ sigma @ ua @ (pred @ p @ theta)) = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)))),
% 3.07/1.81 inference(cnf_transformation,[status(thm)],[f821])).
% 3.07/1.81 thf(f821,plain,(
% 3.07/1.81 (none @ fml != (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)) | ((uSubst95898978stappf @ sigma @ ua @ (pred @ p @ theta)) = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)))),
% 3.07/1.81 inference(ennf_transformation,[status(thm)],[f705])).
% 3.07/1.81 thf(f705,plain,(
% 3.07/1.81 (none @ fml = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)) => ((uSubst95898978stappf @ sigma @ ua @ (pred @ p @ theta)) = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)))),
% 3.07/1.81 inference(fool_elimination,[status(thm)],[f704])).
% 3.07/1.81 thf(f704,plain,(
% 3.07/1.81 ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : char > option @ fml, X3 : char > option @ game] : (X2)))))) @ sigma @ p) = none @ fml) => ((uSubst95898978stappf @ sigma @ ua @ (pred @ p @ theta)) = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)))),
% 3.07/1.81 inference(rectify,[status(thm)],[f6])).
% 3.07/1.81 thf(f6,axiom,(
% 3.07/1.81 ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X9)))))) @ sigma @ p) = none @ fml) => ((uSubst95898978stappf @ sigma @ ua @ (pred @ p @ theta)) = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)))),
% 3.07/1.81 file('/export/starexec/sandbox/tmp/tmp.JL8G97Ngch/DTF2THF_22545.p',fact_5_f8)).
% 3.07/1.81 thf(f1287,plain,(
% 3.07/1.81 ((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)) = (uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) | (none @ fml = (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))),
% 3.07/1.81 inference(subsumption_resolution,[status(thm)],[f1075,f1094])).
% 3.07/1.81 thf(f1094,plain,(
% 3.07/1.81 (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va))),
% 3.07/1.81 inference(definition_unfolding,[status(thm)],[f1033,f989,f989,f989])).
% 3.07/1.81 thf(f1033,plain,(
% 3.07/1.81 (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va))),
% 3.07/1.81 inference(cnf_transformation,[status(thm)],[f844])).
% 3.07/1.81 thf(f844,plain,(
% 3.07/1.81 (none @ fml != (uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) & (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va))),
% 3.07/1.81 inference(ennf_transformation,[status(thm)],[f327])).
% 3.07/1.81 thf(f327,plain,(
% 3.07/1.81 ~((bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va)) => (none @ fml = (uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))))),
% 3.07/1.81 inference(fool_elimination,[status(thm)],[f326])).
% 3.07/1.81 thf(f326,plain,(
% 3.07/1.81 ~(((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : char > option @ fml, X3 : char > option @ game] : (X2)))))) @ sigma @ p))) @ va) = bot_bot @ set @ variable) => ((uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X4 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X5 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X6 : char > option @ fml, X7 : char > option @ game] : (X6)))))) @ sigma @ p))) = none @ fml))),
% 3.07/1.81 inference(rectify,[status(thm)],[f3])).
% 3.07/1.81 thf(f3,axiom,(
% 3.07/1.81 ~(((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X9)))))) @ sigma @ p))) @ va) = bot_bot @ set @ variable) => ((uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X9)))))) @ sigma @ p))) = none @ fml))),
% 3.07/1.81 file('/export/starexec/sandbox/tmp/tmp.JL8G97Ngch/DTF2THF_22545.p',fact_2__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Aundeff_092_060close_062)).
% 3.07/1.81 thf(f1075,plain,(
% 3.07/1.81 (bot_bot @ set @ variable != (inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va)) | ((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)) = (uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) | (none @ fml = (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))),
% 3.07/1.81 inference(definition_unfolding,[status(thm)],[f959,f989,f989,f989,f989,f989,f989,f989,f989,f989])).
% 3.07/1.81 thf(f959,plain,(
% 3.07/1.81 ((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)) = (uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) | (bot_bot @ set @ variable != (inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va)) | (none @ fml = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))),
% 3.07/1.81 inference(cnf_transformation,[status(thm)],[f811])).
% 3.07/1.81 thf(f811,plain,(
% 3.07/1.81 (((none @ fml = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))) | (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va))) & (((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)) = (uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) | (bot_bot @ set @ variable != (inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va)))) | (none @ fml = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))),
% 3.07/1.81 inference(ennf_transformation,[status(thm)],[f625])).
% 3.07/1.81 thf(f625,plain,(
% 3.07/1.81 ~(((bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va)) => ((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)) = (uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))) & ((bot_bot @ set @ variable != (inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va)) => (none @ fml = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))))) => (none @ fml = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))),
% 3.07/1.81 inference(fool_elimination,[status(thm)],[f624])).
% 3.07/1.81 thf(f624,plain,(
% 3.07/1.81 ~((((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : char > option @ fml, X3 : char > option @ game] : (X2)))))) @ sigma @ p))) @ va) != bot_bot @ set @ variable) => (none @ fml = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)))) & ((bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X4 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X5 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X6 : char > option @ fml, X7 : char > option @ game] : (X6)))))) @ sigma @ p))) @ va)) => ((uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X9 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X10 : char > option @ fml, X11 : char > option @ game] : (X10)))))) @ sigma @ p))) = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))))) => ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X12 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X13 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X14 : char > option @ fml, X15 : char > option @ game] : (X14)))))) @ sigma @ p) = none @ fml)),
% 3.07/1.81 inference(rectify,[status(thm)],[f4])).
% 3.07/1.81 thf(f4,axiom,(
% 3.07/1.81 ~((((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X9)))))) @ sigma @ p))) @ va) != bot_bot @ set @ variable) => (none @ fml = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)))) & ((bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X9)))))) @ sigma @ p))) @ va)) => ((uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X9)))))) @ sigma @ p))) = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))))) => ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X7 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X8 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X9 : char > option @ fml, X10 : char > option @ game] : (X9)))))) @ sigma @ p) = none @ fml)),
% 3.07/1.81 file('/export/starexec/sandbox/tmp/tmp.JL8G97Ngch/DTF2THF_22545.p',fact_3__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_A_092_060Longrightarrow_062_ASPreds_A_092_060sigma_062_Ap_A_061_Aundeff_092_060close_062)).
% 3.07/1.81 thf(f1309,plain,(
% 3.07/1.81 (none @ fml != (uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ ua @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))),
% 3.07/1.81 inference(forward_demodulation,[status(thm)],[f1093,f1003])).
% 3.07/1.81 thf(f1093,plain,(
% 3.07/1.81 (none @ fml != (uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (produc2004651681e_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))),
% 3.07/1.81 inference(definition_unfolding,[status(thm)],[f1034,f989,f989,f989])).
% 3.07/1.81 thf(f1034,plain,(
% 3.07/1.81 (none @ fml != (uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))),
% 3.07/1.81 inference(cnf_transformation,[status(thm)],[f844])).
% 3.07/1.81 % SZS output end Proof for DTF2THF_22545
% 3.07/1.81 % (22886)------------------------------
% 3.07/1.81 % (22886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.81 % (22886)Termination reason: Refutation
% 3.07/1.81
% 3.07/1.81 % (22886)Memory used [KB]: 7419
% 3.07/1.81 % (22886)Time elapsed: 0.099 s
% 3.07/1.81 % (22886)Instructions burned: 184 (million)
% 3.07/1.81 % (22886)------------------------------
% 3.07/1.81 % (22886)------------------------------
% 3.07/1.81 % (22856)Success in time 0.236 s
%------------------------------------------------------------------------------