%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP205^2 : 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 : n024.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 08:56:25 AM UTC 2026
% Result : Theorem 21.64s 4.24s
% Output : Refutation 21.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : ITP205^2 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 03:29:40 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.36 ---- Original DTF file ---
% 0.13/0.36 thf(spec,logic,$$dhol).
% 0.13/0.36 %------------------------------------------------------------------------------
% 0.13/0.36 % File : ITP205^2 : TPTP v9.2.1. Released v7.5.0.
% 0.13/0.36 % Domain : Interactive Theorem Proving
% 0.13/0.36 % Problem : Sledgehammer USubst problem prob_966__6345404_1
% 0.13/0.36 % Version : Especial.
% 0.13/0.36 % English :
% 0.13/0.36
% 0.13/0.36 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.13/0.36 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.13/0.36 % Source : [Des21]
% 0.13/0.36 % Names : USubst/prob_966__6345404_1 [Des21]
% 0.13/0.36
% 0.13/0.36 % Status : Theorem
% 0.13/0.36 % Rating : 0.67 v8.1.0, 0.75 v7.5.0
% 0.13/0.36 % Syntax : Number of formulae : 322 ( 119 unt; 50 typ; 0 def)
% 0.13/0.36 % Number of atoms : 673 ( 291 equ; 0 cnn)
% 0.13/0.36 % Maximal formula atoms : 13 ( 2 avg)
% 0.13/0.36 % Number of connectives : 4420 ( 83 ~; 9 |; 37 &;3977 @)
% 0.13/0.36 % ( 0 <=>; 314 =>; 0 <=; 0 <~>)
% 0.13/0.36 % Maximal formula depth : 28 ( 8 avg)
% 0.13/0.36 % Number of types : 6 ( 5 usr)
% 0.13/0.36 % Number of type conns : 300 ( 300 >; 0 *; 0 +; 0 <<)
% 0.13/0.36 % Number of symbols : 46 ( 45 usr; 4 con; 0-9 aty)
% 0.13/0.36 % Number of variables : 1179 ( 117 ^; 993 !; 13 ?;1179 :)
% 0.13/0.36 % ( 56 !>; 0 ?*; 0 @-; 0 @+)
% 0.13/0.36 % SPC : TH1_THM_EQU_NAR
% 0.13/0.36
% 0.13/0.36 % Comments : This file was generated by Sledgehammer 2021-02-23 16:21:34.396
% 0.13/0.36 %------------------------------------------------------------------------------
% 0.13/0.36 % Could-be-implicit typings (8)
% 0.13/0.36 thf(ty_t_Product__Type_Oprod,type,
% 0.13/0.36 product_prod: $tType > $tType > $tType ).
% 0.13/0.36
% 0.13/0.36 thf(ty_t_Syntax_Ovariable,type,
% 0.13/0.36 variable: $tType ).
% 0.13/0.36
% 0.13/0.36 thf(ty_t_Option_Ooption,type,
% 0.13/0.36 option: $tType > $tType ).
% 0.13/0.36
% 0.13/0.36 thf(ty_t_Syntax_Ogame,type,
% 0.13/0.36 game: $tType ).
% 0.13/0.36
% 0.13/0.36 thf(ty_t_String_Ochar,type,
% 0.13/0.36 char: $tType ).
% 0.13/0.36
% 0.13/0.36 thf(ty_t_Syntax_Otrm,type,
% 0.13/0.36 trm: $tType ).
% 0.13/0.36
% 0.13/0.36 thf(ty_t_Syntax_Ofml,type,
% 0.13/0.36 fml: $tType ).
% 0.13/0.36
% 0.13/0.36 thf(ty_t_Set_Oset,type,
% 0.13/0.36 set: $tType > $tType ).
% 0.13/0.36
% 0.13/0.36 % Explicit typings (42)
% 0.13/0.36 thf(sy_cl_HOL_Otype,type,
% 0.13/0.36 type:
% 0.13/0.36 !>[A: $tType] : $o ).
% 0.13/0.36
% 0.13/0.36 thf(sy_cl_Orderings_Oord,type,
% 0.13/0.36 ord:
% 0.13/0.36 !>[A: $tType] : $o ).
% 0.13/0.36
% 0.13/0.36 thf(sy_cl_Orderings_Oorder,type,
% 0.13/0.36 order:
% 0.13/0.36 !>[A: $tType] : $o ).
% 0.13/0.36
% 0.13/0.36 thf(sy_cl_Lattices_Olattice,type,
% 0.13/0.36 lattice:
% 0.13/0.36 !>[A: $tType] : $o ).
% 0.13/0.36
% 0.13/0.36 thf(sy_cl_Orderings_Olinorder,type,
% 0.13/0.36 linorder:
% 0.13/0.36 !>[A: $tType] : $o ).
% 0.13/0.36
% 0.13/0.36 thf(sy_cl_Orderings_Opreorder,type,
% 0.13/0.36 preorder:
% 0.13/0.36 !>[A: $tType] : $o ).
% 0.13/0.36
% 0.13/0.36 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.13/0.36 semilattice_sup:
% 0.13/0.36 !>[A: $tType] : $o ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain,type,
% 0.13/0.36 bNF_Ca1785829860lChain:
% 0.13/0.36 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( A > B ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_BNF__Def_Ocsquare,type,
% 0.13/0.36 bNF_csquare:
% 0.13/0.36 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( set @ A ) > ( B > C ) > ( D > C ) > ( A > B ) > ( A > D ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_BNF__Def_OfstOp,type,
% 0.13/0.36 bNF_fstOp:
% 0.13/0.36 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > $o ) > ( B > C > $o ) > ( product_prod @ A @ C ) > ( product_prod @ A @ B ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_BNF__Def_Opick__middlep,type,
% 0.13/0.36 bNF_pick_middlep:
% 0.13/0.36 !>[B: $tType,A: $tType,C: $tType] : ( ( B > A > $o ) > ( A > C > $o ) > B > C > A ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_BNF__Def_OsndOp,type,
% 0.13/0.36 bNF_sndOp:
% 0.13/0.36 !>[C: $tType,A: $tType,B: $tType] : ( ( C > A > $o ) > ( A > B > $o ) > ( product_prod @ C @ B ) > ( product_prod @ A @ B ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2,type,
% 0.13/0.36 bNF_Greatest_image2:
% 0.13/0.36 !>[C: $tType,A: $tType,B: $tType] : ( ( set @ C ) > ( C > A ) > ( C > B ) > ( set @ ( product_prod @ A @ B ) ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.13/0.36 sup_sup:
% 0.13/0.36 !>[A: $tType] : ( A > A > A ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Option_Ooption_ONone,type,
% 0.13/0.36 none:
% 0.13/0.36 !>[A: $tType] : ( option @ A ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Option_Ooption_OSome,type,
% 0.13/0.36 some:
% 0.13/0.36 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Option_Ooption_Ocase__option,type,
% 0.13/0.36 case_option:
% 0.13/0.36 !>[B: $tType,A: $tType] : ( B > ( A > B ) > ( option @ A ) > B ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Option_Ooption_Othe,type,
% 0.13/0.36 the:
% 0.13/0.36 !>[A: $tType] : ( ( option @ A ) > A ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.13/0.36 ord_less_eq:
% 0.13/0.36 !>[A: $tType] : ( A > A > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Orderings_Oorder__class_OGreatest,type,
% 0.13/0.36 order_Greatest:
% 0.13/0.36 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Product__Type_OPair,type,
% 0.13/0.36 product_Pair:
% 0.13/0.36 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.13/0.36 produc2004651681e_prod:
% 0.13/0.36 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.13/0.36 product_rec_prod:
% 0.13/0.36 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Product__Type_Oprod_Ofst,type,
% 0.13/0.36 product_fst:
% 0.13/0.36 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > A ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Product__Type_Oprod_Osnd,type,
% 0.13/0.36 product_snd:
% 0.13/0.36 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > B ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Product__Type_Oprod_Oswap,type,
% 0.13/0.36 product_swap:
% 0.13/0.36 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > ( product_prod @ B @ A ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Product__Type_Oscomp,type,
% 0.13/0.36 product_scomp:
% 0.13/0.36 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( A > ( product_prod @ B @ C ) ) > ( B > C > D ) > A > D ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Relation_Orelcompp,type,
% 0.13/0.36 relcompp:
% 0.13/0.36 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > $o ) > ( B > C > $o ) > A > C > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Set_OCollect,type,
% 0.13/0.36 collect:
% 0.13/0.36 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Static__Semantics_OBVG,type,
% 0.13/0.36 static_BVG: game > ( set @ variable ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Syntax_Ogame_OChoice,type,
% 0.13/0.36 choice: game > game > game ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Syntax_Ogame_OCompose,type,
% 0.13/0.36 compose: game > game > game ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Syntax_Ogame_OLoop,type,
% 0.13/0.36 loop: game > game ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OChoiceo,type,
% 0.13/0.36 uSubst1976112797hoiceo: ( option @ game ) > ( option @ game ) > ( option @ game ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OComposeo,type,
% 0.13/0.36 uSubst1385204910mposeo: ( option @ game ) > ( option @ game ) > ( option @ game ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OLoopo,type,
% 0.13/0.36 uSubst993936602_Loopo: ( option @ game ) > ( option @ game ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappp,type,
% 0.13/0.36 uSubst95898988stappp: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > game > ( product_prod @ ( set @ variable ) @ ( option @ game ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_member,type,
% 0.13/0.36 member:
% 0.13/0.36 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_v_Ua____,type,
% 0.13/0.36 ua: set @ variable ).
% 0.13/0.36
% 0.13/0.36 thf(sy_v__092_060alpha_062_H____,type,
% 0.13/0.36 alpha: game ).
% 0.13/0.36
% 0.13/0.36 thf(sy_v__092_060beta_062____,type,
% 0.13/0.36 beta: game ).
% 0.13/0.36
% 0.13/0.36 thf(sy_v__092_060sigma_062,type,
% 0.13/0.36 sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Relevant facts (255)
% 0.13/0.36 thf(fact_0__092_060open_062U_A_092_060union_062_ABVG_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_J_A_092_060union_062_ABVG_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_A_Ifst_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_A_092_060beta_062_J_J_J_A_092_060subseteq_062_Afst_A_Iusubstappp_A_092_060sigma_062_A_Ifst_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_A_092_060beta_062_J_092_060close_062,axiom,
% 0.13/0.36 ord_less_eq @ ( set @ variable ) @ ( sup_sup @ ( set @ variable ) @ ( sup_sup @ ( set @ variable ) @ ua @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) ) ) ) @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ).
% 0.13/0.36
% 0.13/0.36 % \<open>U \<union> BVG (the (snd (usubstappp \<sigma> U \<alpha>))) \<union> BVG (the (snd (usubstappp \<sigma> (fst (usubstappp \<sigma> U \<alpha>)) \<beta>))) \<subseteq> fst (usubstappp \<sigma> (fst (usubstappp \<sigma> U \<alpha>)) \<beta>)\<close>
% 0.13/0.36 thf(fact_1_fact,axiom,
% 0.13/0.36 ord_less_eq @ ( set @ variable ) @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) @ ( sup_sup @ ( set @ variable ) @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) ) ) @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % fact
% 0.13/0.36 thf(fact_2_IHa,axiom,
% 0.13/0.36 ord_less_eq @ ( set @ variable ) @ ( sup_sup @ ( set @ variable ) @ ua @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) ) ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) ).
% 0.13/0.36
% 0.13/0.36 % IHa
% 0.13/0.36 thf(fact_3_IHb,axiom,
% 0.13/0.36 ord_less_eq @ ( set @ variable ) @ ( sup_sup @ ( set @ variable ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ).
% 0.13/0.36
% 0.13/0.36 % IHb
% 0.13/0.36 thf(fact_4_Compose_Oprems,axiom,
% 0.13/0.36 ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) )
% 0.13/0.36 != ( none @ game ) ) ).
% 0.13/0.36
% 0.13/0.36 % Compose.prems
% 0.13/0.36 thf(fact_5_usubst__taboos__mon,axiom,
% 0.13/0.36 ! [U: set @ variable,Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),Alpha: game] : ( ord_less_eq @ ( set @ variable ) @ U @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % usubst_taboos_mon
% 0.13/0.36 thf(fact_6_usubstappp__fst__mon,axiom,
% 0.13/0.36 ! [U: set @ variable,V: set @ variable,Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),Alpha: game] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ variable ) @ U @ V )
% 0.13/0.36 => ( ord_less_eq @ ( set @ variable ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ V @ Alpha ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % usubstappp_fst_mon
% 0.13/0.36 thf(fact_7_Compose_OIH_I2_J,axiom,
% 0.13/0.36 ! [U: set @ variable] :
% 0.13/0.36 ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ U @ beta ) )
% 0.13/0.36 != ( none @ game ) )
% 0.13/0.36 => ( ord_less_eq @ ( set @ variable ) @ ( sup_sup @ ( set @ variable ) @ U @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ U @ beta ) ) ) ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ U @ beta ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Compose.IH(2)
% 0.13/0.36 thf(fact_8_Compose_OIH_I1_J,axiom,
% 0.13/0.36 ! [U: set @ variable] :
% 0.13/0.36 ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ U @ alpha ) )
% 0.13/0.36 != ( none @ game ) )
% 0.13/0.36 => ( ord_less_eq @ ( set @ variable ) @ ( sup_sup @ ( set @ variable ) @ U @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ U @ alpha ) ) ) ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ U @ alpha ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Compose.IH(1)
% 0.13/0.36 thf(fact_9_Un__subset__iff,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,B2: set @ A,C2: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C2 )
% 0.13/0.36 = ( ( ord_less_eq @ ( set @ A ) @ A2 @ C2 )
% 0.13/0.36 & ( ord_less_eq @ ( set @ A ) @ B2 @ C2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_subset_iff
% 0.13/0.36 thf(fact_10_le__sup__iff,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [X: A,Y: A,Z: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.13/0.36 = ( ( ord_less_eq @ A @ X @ Z )
% 0.13/0.36 & ( ord_less_eq @ A @ Y @ Z ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_sup_iff
% 0.13/0.36 thf(fact_11_sup_Obounded__iff,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [B3: A,C3: A,A3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C3 ) @ A3 )
% 0.13/0.36 = ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.13/0.36 & ( ord_less_eq @ A @ C3 @ A3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.bounded_iff
% 0.13/0.36 thf(fact_12_BVG__compose,axiom,
% 0.13/0.36 ! [Alpha: game,Beta: game] : ( ord_less_eq @ ( set @ variable ) @ ( static_BVG @ ( compose @ Alpha @ Beta ) ) @ ( sup_sup @ ( set @ variable ) @ ( static_BVG @ Alpha ) @ ( static_BVG @ Beta ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % BVG_compose
% 0.13/0.36 thf(fact_13_game_Oinject_I5_J,axiom,
% 0.13/0.36 ! [X51: game,X52: game,Y51: game,Y52: game] :
% 0.13/0.36 ( ( ( compose @ X51 @ X52 )
% 0.13/0.36 = ( compose @ Y51 @ Y52 ) )
% 0.13/0.36 = ( ( X51 = Y51 )
% 0.13/0.36 & ( X52 = Y52 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % game.inject(5)
% 0.13/0.36 thf(fact_14_UnCI,axiom,
% 0.13/0.36 ! [A: $tType,C3: A,B2: set @ A,A2: set @ A] :
% 0.13/0.36 ( ( ~ ( member @ A @ C3 @ B2 )
% 0.13/0.36 => ( member @ A @ C3 @ A2 ) )
% 0.13/0.36 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % UnCI
% 0.13/0.36 thf(fact_15_union__or,axiom,
% 0.13/0.36 ! [A: $tType,C3: A,A2: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.13/0.36 = ( ( member @ A @ C3 @ A2 )
% 0.13/0.36 | ( member @ A @ C3 @ B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % union_or
% 0.13/0.36 thf(fact_16_sup__apply,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ B )
% 0.13/0.36 => ( ( sup_sup @ ( A > B ) )
% 0.13/0.36 = ( ^ [F: A > B,G: A > B,X2: A] : ( sup_sup @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_apply
% 0.13/0.36 thf(fact_17_sup_Oidem,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [A3: A] :
% 0.13/0.36 ( ( sup_sup @ A @ A3 @ A3 )
% 0.13/0.36 = A3 ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.idem
% 0.13/0.36 thf(fact_18_sup__idem,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [X: A] :
% 0.13/0.36 ( ( sup_sup @ A @ X @ X )
% 0.13/0.36 = X ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_idem
% 0.13/0.36 thf(fact_19_subset__antisym,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.13/0.36 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 0.13/0.36 => ( A2 = B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % subset_antisym
% 0.13/0.36 thf(fact_20_subsetI,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.13/0.36 ( ! [X3: A] :
% 0.13/0.36 ( ( member @ A @ X3 @ A2 )
% 0.13/0.36 => ( member @ A @ X3 @ B2 ) )
% 0.13/0.36 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % subsetI
% 0.13/0.36 thf(fact_21_sup_Oright__idem,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [A3: A,B3: A] :
% 0.13/0.36 ( ( sup_sup @ A @ ( sup_sup @ A @ A3 @ B3 ) @ B3 )
% 0.13/0.36 = ( sup_sup @ A @ A3 @ B3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.right_idem
% 0.13/0.36 thf(fact_22_sup__left__idem,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [X: A,Y: A] :
% 0.13/0.36 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.13/0.36 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_left_idem
% 0.13/0.36 thf(fact_23_sup_Oleft__idem,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [A3: A,B3: A] :
% 0.13/0.36 ( ( sup_sup @ A @ A3 @ ( sup_sup @ A @ A3 @ B3 ) )
% 0.13/0.36 = ( sup_sup @ A @ A3 @ B3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.left_idem
% 0.13/0.36 thf(fact_24_usubstappp__det,axiom,
% 0.13/0.36 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Alpha: game,V: set @ variable] :
% 0.13/0.36 ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) )
% 0.13/0.36 != ( none @ game ) )
% 0.13/0.36 => ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ V @ Alpha ) )
% 0.13/0.36 != ( none @ game ) )
% 0.13/0.36 => ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) )
% 0.13/0.36 = ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ V @ Alpha ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % usubstappp_det
% 0.13/0.36 thf(fact_25_Collect__mono__iff,axiom,
% 0.13/0.36 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.13/0.36 = ( ! [X2: A] :
% 0.13/0.36 ( ( P @ X2 )
% 0.13/0.36 => ( Q @ X2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Collect_mono_iff
% 0.13/0.36 thf(fact_26_set__eq__subset,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ^ [Y2: set @ A,Z2: set @ A] : ( Y2 = Z2 ) )
% 0.13/0.36 = ( ^ [A4: set @ A,B4: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.13/0.36 & ( ord_less_eq @ ( set @ A ) @ B4 @ A4 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % set_eq_subset
% 0.13/0.36 thf(fact_27_subset__trans,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,B2: set @ A,C2: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.13/0.36 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C2 )
% 0.13/0.36 => ( ord_less_eq @ ( set @ A ) @ A2 @ C2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % subset_trans
% 0.13/0.36 thf(fact_28_Collect__mono,axiom,
% 0.13/0.36 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.13/0.36 ( ! [X3: A] :
% 0.13/0.36 ( ( P @ X3 )
% 0.13/0.36 => ( Q @ X3 ) )
% 0.13/0.36 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Collect_mono
% 0.13/0.36 thf(fact_29_subset__refl,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 0.13/0.36
% 0.13/0.36 % subset_refl
% 0.13/0.36 thf(fact_30_subset__iff,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) )
% 0.13/0.36 = ( ^ [A4: set @ A,B4: set @ A] :
% 0.13/0.36 ! [T2: A] :
% 0.13/0.36 ( ( member @ A @ T2 @ A4 )
% 0.13/0.36 => ( member @ A @ T2 @ B4 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % subset_iff
% 0.13/0.36 thf(fact_31_equalityD2,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( A2 = B2 )
% 0.13/0.36 => ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % equalityD2
% 0.13/0.36 thf(fact_32_equalityD1,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( A2 = B2 )
% 0.13/0.36 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % equalityD1
% 0.13/0.36 thf(fact_33_subset__eq,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) )
% 0.13/0.36 = ( ^ [A4: set @ A,B4: set @ A] :
% 0.13/0.36 ! [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ A4 )
% 0.13/0.36 => ( member @ A @ X2 @ B4 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % subset_eq
% 0.13/0.36 thf(fact_34_equalityE,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( A2 = B2 )
% 0.13/0.36 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.13/0.36 => ~ ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % equalityE
% 0.13/0.36 thf(fact_35_subsetD,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,B2: set @ A,C3: A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.13/0.36 => ( ( member @ A @ C3 @ A2 )
% 0.13/0.36 => ( member @ A @ C3 @ B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % subsetD
% 0.13/0.36 thf(fact_36_in__mono,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,B2: set @ A,X: A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.13/0.36 => ( ( member @ A @ X @ A2 )
% 0.13/0.36 => ( member @ A @ X @ B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % in_mono
% 0.13/0.36 thf(fact_37_sup__left__commute,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [X: A,Y: A,Z: A] :
% 0.13/0.36 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.13/0.36 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_left_commute
% 0.13/0.36 thf(fact_38_sup_Oleft__commute,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [B3: A,A3: A,C3: A] :
% 0.13/0.36 ( ( sup_sup @ A @ B3 @ ( sup_sup @ A @ A3 @ C3 ) )
% 0.13/0.36 = ( sup_sup @ A @ A3 @ ( sup_sup @ A @ B3 @ C3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.left_commute
% 0.13/0.36 thf(fact_39_sup__commute,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ( ( sup_sup @ A )
% 0.13/0.36 = ( ^ [X2: A,Y3: A] : ( sup_sup @ A @ Y3 @ X2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_commute
% 0.13/0.36 thf(fact_40_sup_Ocommute,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ( ( sup_sup @ A )
% 0.13/0.36 = ( ^ [A5: A,B5: A] : ( sup_sup @ A @ B5 @ A5 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.commute
% 0.13/0.36 thf(fact_41_sup__assoc,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [X: A,Y: A,Z: A] :
% 0.13/0.36 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.13/0.36 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_assoc
% 0.13/0.36 thf(fact_42_sup_Oassoc,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [A3: A,B3: A,C3: A] :
% 0.13/0.36 ( ( sup_sup @ A @ ( sup_sup @ A @ A3 @ B3 ) @ C3 )
% 0.13/0.36 = ( sup_sup @ A @ A3 @ ( sup_sup @ A @ B3 @ C3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.assoc
% 0.13/0.36 thf(fact_43_boolean__algebra__cancel_Osup2,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [B2: A,K: A,B3: A,A3: A] :
% 0.13/0.36 ( ( B2
% 0.13/0.36 = ( sup_sup @ A @ K @ B3 ) )
% 0.13/0.36 => ( ( sup_sup @ A @ A3 @ B2 )
% 0.13/0.36 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A3 @ B3 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % boolean_algebra_cancel.sup2
% 0.13/0.36 thf(fact_44_boolean__algebra__cancel_Osup1,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [A2: A,K: A,A3: A,B3: A] :
% 0.13/0.36 ( ( A2
% 0.13/0.36 = ( sup_sup @ A @ K @ A3 ) )
% 0.13/0.36 => ( ( sup_sup @ A @ A2 @ B3 )
% 0.13/0.36 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A3 @ B3 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % boolean_algebra_cancel.sup1
% 0.13/0.36 thf(fact_45_mem__Collect__eq,axiom,
% 0.13/0.36 ! [A: $tType,A3: A,P: A > $o] :
% 0.13/0.36 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 0.13/0.36 = ( P @ A3 ) ) ).
% 0.13/0.36
% 0.13/0.36 % mem_Collect_eq
% 0.13/0.36 thf(fact_46_Collect__mem__eq,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A] :
% 0.13/0.36 ( ( collect @ A
% 0.13/0.36 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 0.13/0.36 = A2 ) ).
% 0.13/0.36
% 0.13/0.36 % Collect_mem_eq
% 0.13/0.36 thf(fact_47_Collect__cong,axiom,
% 0.13/0.36 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.13/0.36 ( ! [X3: A] :
% 0.13/0.36 ( ( P @ X3 )
% 0.13/0.36 = ( Q @ X3 ) )
% 0.13/0.36 => ( ( collect @ A @ P )
% 0.13/0.36 = ( collect @ A @ Q ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Collect_cong
% 0.13/0.36 thf(fact_48_ext,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,F2: A > B,G2: A > B] :
% 0.13/0.36 ( ! [X3: A] :
% 0.13/0.36 ( ( F2 @ X3 )
% 0.13/0.36 = ( G2 @ X3 ) )
% 0.13/0.36 => ( F2 = G2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % ext
% 0.13/0.36 thf(fact_49_sup__fun__def,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ B )
% 0.13/0.36 => ( ( sup_sup @ ( A > B ) )
% 0.13/0.36 = ( ^ [F: A > B,G: A > B,X2: A] : ( sup_sup @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_fun_def
% 0.13/0.36 thf(fact_50_inf__sup__aci_I5_J,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( lattice @ A )
% 0.13/0.36 => ( ( sup_sup @ A )
% 0.13/0.36 = ( ^ [X2: A,Y3: A] : ( sup_sup @ A @ Y3 @ X2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % inf_sup_aci(5)
% 0.13/0.36 thf(fact_51_inf__sup__aci_I6_J,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( lattice @ A )
% 0.13/0.36 => ! [X: A,Y: A,Z: A] :
% 0.13/0.36 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.13/0.36 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % inf_sup_aci(6)
% 0.13/0.36 thf(fact_52_inf__sup__aci_I7_J,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( lattice @ A )
% 0.13/0.36 => ! [X: A,Y: A,Z: A] :
% 0.13/0.36 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.13/0.36 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % inf_sup_aci(7)
% 0.13/0.36 thf(fact_53_inf__sup__aci_I8_J,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( lattice @ A )
% 0.13/0.36 => ! [X: A,Y: A] :
% 0.13/0.36 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.13/0.36 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % inf_sup_aci(8)
% 0.13/0.36 thf(fact_54_not__union__or,axiom,
% 0.13/0.36 ! [A: $tType,X: A,A2: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( ~ ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) )
% 0.13/0.36 = ( ~ ( member @ A @ X @ A2 )
% 0.13/0.36 & ~ ( member @ A @ X @ B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % not_union_or
% 0.13/0.36 thf(fact_55_Un__left__commute,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,B2: set @ A,C2: set @ A] :
% 0.13/0.36 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C2 ) )
% 0.13/0.36 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A2 @ C2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_left_commute
% 0.13/0.36 thf(fact_56_Un__left__absorb,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.13/0.36 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_left_absorb
% 0.13/0.36 thf(fact_57_Un__commute,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( sup_sup @ ( set @ A ) )
% 0.13/0.36 = ( ^ [A4: set @ A,B4: set @ A] : ( sup_sup @ ( set @ A ) @ B4 @ A4 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_commute
% 0.13/0.36 thf(fact_58_Un__absorb,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A] :
% 0.13/0.36 ( ( sup_sup @ ( set @ A ) @ A2 @ A2 )
% 0.13/0.36 = A2 ) ).
% 0.13/0.36
% 0.13/0.36 % Un_absorb
% 0.13/0.36 thf(fact_59_Un__assoc,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,B2: set @ A,C2: set @ A] :
% 0.13/0.36 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C2 )
% 0.13/0.36 = ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_assoc
% 0.13/0.36 thf(fact_60_ball__Un,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 0.13/0.36 ( ( ! [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.13/0.36 => ( P @ X2 ) ) )
% 0.13/0.36 = ( ! [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ A2 )
% 0.13/0.36 => ( P @ X2 ) )
% 0.13/0.36 & ! [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ B2 )
% 0.13/0.36 => ( P @ X2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % ball_Un
% 0.13/0.36 thf(fact_61_bex__Un,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 0.13/0.36 ( ( ? [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.13/0.36 & ( P @ X2 ) ) )
% 0.13/0.36 = ( ? [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ A2 )
% 0.13/0.36 & ( P @ X2 ) )
% 0.13/0.36 | ? [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ B2 )
% 0.13/0.36 & ( P @ X2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % bex_Un
% 0.13/0.36 thf(fact_62_UnI2,axiom,
% 0.13/0.36 ! [A: $tType,C3: A,B2: set @ A,A2: set @ A] :
% 0.13/0.36 ( ( member @ A @ C3 @ B2 )
% 0.13/0.36 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % UnI2
% 0.13/0.36 thf(fact_63_UnI1,axiom,
% 0.13/0.36 ! [A: $tType,C3: A,A2: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( member @ A @ C3 @ A2 )
% 0.13/0.36 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % UnI1
% 0.13/0.36 thf(fact_64_UnE,axiom,
% 0.13/0.36 ! [A: $tType,C3: A,A2: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.13/0.36 => ( ~ ( member @ A @ C3 @ A2 )
% 0.13/0.36 => ( member @ A @ C3 @ B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % UnE
% 0.13/0.36 thf(fact_65_usubstappp__antimon,axiom,
% 0.13/0.36 ! [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 ) ) ) ),Alpha: game] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ variable ) @ V @ U )
% 0.13/0.36 => ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) )
% 0.13/0.36 != ( none @ game ) )
% 0.13/0.36 => ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) )
% 0.13/0.36 = ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ V @ Alpha ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % usubstappp_antimon
% 0.13/0.36 thf(fact_66_sup_OcoboundedI2,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [C3: A,B3: A,A3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ C3 @ B3 )
% 0.13/0.36 => ( ord_less_eq @ A @ C3 @ ( sup_sup @ A @ A3 @ B3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.coboundedI2
% 0.13/0.36 thf(fact_67_sup_OcoboundedI1,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [C3: A,A3: A,B3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ C3 @ A3 )
% 0.13/0.36 => ( ord_less_eq @ A @ C3 @ ( sup_sup @ A @ A3 @ B3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.coboundedI1
% 0.13/0.36 thf(fact_68_sup_Oabsorb__iff2,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ( ( ord_less_eq @ A )
% 0.13/0.36 = ( ^ [A5: A,B5: A] :
% 0.13/0.36 ( ( sup_sup @ A @ A5 @ B5 )
% 0.13/0.36 = B5 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.absorb_iff2
% 0.13/0.36 thf(fact_69_sup_Oabsorb__iff1,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ( ( ord_less_eq @ A )
% 0.13/0.36 = ( ^ [B5: A,A5: A] :
% 0.13/0.36 ( ( sup_sup @ A @ A5 @ B5 )
% 0.13/0.36 = A5 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.absorb_iff1
% 0.13/0.36 thf(fact_70_sup_Ocobounded2,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [B3: A,A3: A] : ( ord_less_eq @ A @ B3 @ ( sup_sup @ A @ A3 @ B3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.cobounded2
% 0.13/0.36 thf(fact_71_sup_Ocobounded1,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [A3: A,B3: A] : ( ord_less_eq @ A @ A3 @ ( sup_sup @ A @ A3 @ B3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.cobounded1
% 0.13/0.36 thf(fact_72_sup_Oorder__iff,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ( ( ord_less_eq @ A )
% 0.13/0.36 = ( ^ [B5: A,A5: A] :
% 0.13/0.36 ( A5
% 0.13/0.36 = ( sup_sup @ A @ A5 @ B5 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.order_iff
% 0.13/0.36 thf(fact_73_sup_OboundedI,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [B3: A,A3: A,C3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.13/0.36 => ( ( ord_less_eq @ A @ C3 @ A3 )
% 0.13/0.36 => ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C3 ) @ A3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.boundedI
% 0.13/0.36 thf(fact_74_sup_OboundedE,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [B3: A,C3: A,A3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C3 ) @ A3 )
% 0.13/0.36 => ~ ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.13/0.36 => ~ ( ord_less_eq @ A @ C3 @ A3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.boundedE
% 0.13/0.36 thf(fact_75_sup__absorb2,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [X: A,Y: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X @ Y )
% 0.13/0.36 => ( ( sup_sup @ A @ X @ Y )
% 0.13/0.36 = Y ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_absorb2
% 0.13/0.36 thf(fact_76_sup__absorb1,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [Y: A,X: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ Y @ X )
% 0.13/0.36 => ( ( sup_sup @ A @ X @ Y )
% 0.13/0.36 = X ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_absorb1
% 0.13/0.36 thf(fact_77_sup_Oabsorb2,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [A3: A,B3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.13/0.36 => ( ( sup_sup @ A @ A3 @ B3 )
% 0.13/0.36 = B3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.absorb2
% 0.13/0.36 thf(fact_78_sup_Oabsorb1,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [B3: A,A3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.13/0.36 => ( ( sup_sup @ A @ A3 @ B3 )
% 0.13/0.36 = A3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.absorb1
% 0.13/0.36 thf(fact_79_sup__unique,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [F2: A > A > A,X: A,Y: A] :
% 0.13/0.36 ( ! [X3: A,Y4: A] : ( ord_less_eq @ A @ X3 @ ( F2 @ X3 @ Y4 ) )
% 0.13/0.36 => ( ! [X3: A,Y4: A] : ( ord_less_eq @ A @ Y4 @ ( F2 @ X3 @ Y4 ) )
% 0.13/0.36 => ( ! [X3: A,Y4: A,Z3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ Y4 @ X3 )
% 0.13/0.36 => ( ( ord_less_eq @ A @ Z3 @ X3 )
% 0.13/0.36 => ( ord_less_eq @ A @ ( F2 @ Y4 @ Z3 ) @ X3 ) ) )
% 0.13/0.36 => ( ( sup_sup @ A @ X @ Y )
% 0.13/0.36 = ( F2 @ X @ Y ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_unique
% 0.13/0.36 thf(fact_80_sup_OorderI,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [A3: A,B3: A] :
% 0.13/0.36 ( ( A3
% 0.13/0.36 = ( sup_sup @ A @ A3 @ B3 ) )
% 0.13/0.36 => ( ord_less_eq @ A @ B3 @ A3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.orderI
% 0.13/0.36 thf(fact_81_sup_OorderE,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [B3: A,A3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.13/0.36 => ( A3
% 0.13/0.36 = ( sup_sup @ A @ A3 @ B3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.orderE
% 0.13/0.36 thf(fact_82_le__iff__sup,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ( ( ord_less_eq @ A )
% 0.13/0.36 = ( ^ [X2: A,Y3: A] :
% 0.13/0.36 ( ( sup_sup @ A @ X2 @ Y3 )
% 0.13/0.36 = Y3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_iff_sup
% 0.13/0.36 thf(fact_83_sup__least,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [Y: A,X: A,Z: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ Y @ X )
% 0.13/0.36 => ( ( ord_less_eq @ A @ Z @ X )
% 0.13/0.36 => ( ord_less_eq @ A @ ( sup_sup @ A @ Y @ Z ) @ X ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_least
% 0.13/0.36 thf(fact_84_sup__mono,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [A3: A,C3: A,B3: A,D2: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A3 @ C3 )
% 0.13/0.36 => ( ( ord_less_eq @ A @ B3 @ D2 )
% 0.13/0.36 => ( ord_less_eq @ A @ ( sup_sup @ A @ A3 @ B3 ) @ ( sup_sup @ A @ C3 @ D2 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_mono
% 0.13/0.36 thf(fact_85_sup_Omono,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [C3: A,A3: A,D2: A,B3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ C3 @ A3 )
% 0.13/0.36 => ( ( ord_less_eq @ A @ D2 @ B3 )
% 0.13/0.36 => ( ord_less_eq @ A @ ( sup_sup @ A @ C3 @ D2 ) @ ( sup_sup @ A @ A3 @ B3 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.mono
% 0.13/0.36 thf(fact_86_le__supI2,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [X: A,B3: A,A3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X @ B3 )
% 0.13/0.36 => ( ord_less_eq @ A @ X @ ( sup_sup @ A @ A3 @ B3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_supI2
% 0.13/0.36 thf(fact_87_le__supI1,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [X: A,A3: A,B3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X @ A3 )
% 0.13/0.36 => ( ord_less_eq @ A @ X @ ( sup_sup @ A @ A3 @ B3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_supI1
% 0.13/0.36 thf(fact_88_sup__ge2,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [Y: A,X: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_ge2
% 0.13/0.36 thf(fact_89_sup__ge1,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [X: A,Y: A] : ( ord_less_eq @ A @ X @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_ge1
% 0.13/0.36 thf(fact_90_le__supI,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [A3: A,X: A,B3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A3 @ X )
% 0.13/0.36 => ( ( ord_less_eq @ A @ B3 @ X )
% 0.13/0.36 => ( ord_less_eq @ A @ ( sup_sup @ A @ A3 @ B3 ) @ X ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_supI
% 0.13/0.36 thf(fact_91_le__supE,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A )
% 0.13/0.36 => ! [A3: A,B3: A,X: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ ( sup_sup @ A @ A3 @ B3 ) @ X )
% 0.13/0.36 => ~ ( ( ord_less_eq @ A @ A3 @ X )
% 0.13/0.36 => ~ ( ord_less_eq @ A @ B3 @ X ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_supE
% 0.13/0.36 thf(fact_92_inf__sup__ord_I3_J,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( lattice @ A )
% 0.13/0.36 => ! [X: A,Y: A] : ( ord_less_eq @ A @ X @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % inf_sup_ord(3)
% 0.13/0.36 thf(fact_93_inf__sup__ord_I4_J,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( lattice @ A )
% 0.13/0.36 => ! [Y: A,X: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % inf_sup_ord(4)
% 0.13/0.36 thf(fact_94_subset__Un__eq,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) )
% 0.13/0.36 = ( ^ [A4: set @ A,B4: set @ A] :
% 0.13/0.36 ( ( sup_sup @ ( set @ A ) @ A4 @ B4 )
% 0.13/0.36 = B4 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % subset_Un_eq
% 0.13/0.36 thf(fact_95_subset__UnE,axiom,
% 0.13/0.36 ! [A: $tType,C2: set @ A,A2: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.13/0.36 => ~ ! [A6: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A6 @ A2 )
% 0.13/0.36 => ! [B6: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ B6 @ B2 )
% 0.13/0.36 => ( C2
% 0.13/0.36 != ( sup_sup @ ( set @ A ) @ A6 @ B6 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % subset_UnE
% 0.13/0.36 thf(fact_96_Un__absorb2,axiom,
% 0.13/0.36 ! [A: $tType,B2: set @ A,A2: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 0.13/0.36 => ( ( sup_sup @ ( set @ A ) @ A2 @ B2 )
% 0.13/0.36 = A2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_absorb2
% 0.13/0.36 thf(fact_97_Un__absorb1,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.13/0.36 => ( ( sup_sup @ ( set @ A ) @ A2 @ B2 )
% 0.13/0.36 = B2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_absorb1
% 0.13/0.36 thf(fact_98_Un__upper2,axiom,
% 0.13/0.36 ! [A: $tType,B2: set @ A,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_upper2
% 0.13/0.36 thf(fact_99_Un__upper1,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,B2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_upper1
% 0.13/0.36 thf(fact_100_Un__least,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,C2: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C2 )
% 0.13/0.36 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C2 )
% 0.13/0.36 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_least
% 0.13/0.36 thf(fact_101_Un__mono,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,C2: set @ A,B2: set @ A,D3: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C2 )
% 0.13/0.36 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ D3 )
% 0.13/0.36 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ ( sup_sup @ ( set @ A ) @ C2 @ D3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_mono
% 0.13/0.36 thf(fact_102_order__refl,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( preorder @ A )
% 0.13/0.36 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.13/0.36
% 0.13/0.36 % order_refl
% 0.13/0.36 thf(fact_103_option_Oexpand,axiom,
% 0.13/0.36 ! [A: $tType,Option: option @ A,Option2: option @ A] :
% 0.13/0.36 ( ( ( Option
% 0.13/0.36 = ( none @ A ) )
% 0.13/0.36 = ( Option2
% 0.13/0.36 = ( none @ A ) ) )
% 0.13/0.36 => ( ( ( Option
% 0.13/0.36 != ( none @ A ) )
% 0.13/0.36 => ( ( Option2
% 0.13/0.36 != ( none @ A ) )
% 0.13/0.36 => ( ( the @ A @ Option )
% 0.13/0.36 = ( the @ A @ Option2 ) ) ) )
% 0.13/0.36 => ( Option = Option2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % option.expand
% 0.13/0.36 thf(fact_104_prod__eq__iff,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType] :
% 0.13/0.36 ( ( ^ [Y2: product_prod @ A @ B,Z2: product_prod @ A @ B] : ( Y2 = Z2 ) )
% 0.13/0.36 = ( ^ [S: product_prod @ A @ B,T2: product_prod @ A @ B] :
% 0.13/0.36 ( ( ( product_fst @ A @ B @ S )
% 0.13/0.36 = ( product_fst @ A @ B @ T2 ) )
% 0.13/0.36 & ( ( product_snd @ A @ B @ S )
% 0.13/0.36 = ( product_snd @ A @ B @ T2 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % prod_eq_iff
% 0.13/0.36 thf(fact_105_prod_Oexpand,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B,Prod2: product_prod @ A @ B] :
% 0.13/0.36 ( ( ( ( product_fst @ A @ B @ Prod )
% 0.13/0.36 = ( product_fst @ A @ B @ Prod2 ) )
% 0.13/0.36 & ( ( product_snd @ A @ B @ Prod )
% 0.13/0.36 = ( product_snd @ A @ B @ Prod2 ) ) )
% 0.13/0.36 => ( Prod = Prod2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % prod.expand
% 0.13/0.36 thf(fact_106_exE__realizer_H,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,P: A > B > $o,P2: product_prod @ B @ A] :
% 0.13/0.36 ( ( P @ ( product_snd @ B @ A @ P2 ) @ ( product_fst @ B @ A @ P2 ) )
% 0.13/0.36 => ~ ! [X3: B,Y4: A] :
% 0.13/0.36 ~ ( P @ Y4 @ X3 ) ) ).
% 0.13/0.36
% 0.13/0.36 % exE_realizer'
% 0.13/0.36 thf(fact_107_prod__eqI,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,P2: product_prod @ A @ B,Q2: product_prod @ A @ B] :
% 0.13/0.36 ( ( ( product_fst @ A @ B @ P2 )
% 0.13/0.36 = ( product_fst @ A @ B @ Q2 ) )
% 0.13/0.36 => ( ( ( product_snd @ A @ B @ P2 )
% 0.13/0.36 = ( product_snd @ A @ B @ Q2 ) )
% 0.13/0.36 => ( P2 = Q2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % prod_eqI
% 0.13/0.36 thf(fact_108_usubstappp__loop__conv,axiom,
% 0.13/0.36 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Alpha: game] :
% 0.13/0.36 ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ ( loop @ Alpha ) ) )
% 0.13/0.36 != ( none @ game ) )
% 0.13/0.36 => ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) )
% 0.13/0.36 != ( none @ game ) )
% 0.13/0.36 & ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) )
% 0.13/0.36 != ( none @ game ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % usubstappp_loop_conv
% 0.13/0.36 thf(fact_109_BVG__choice,axiom,
% 0.13/0.36 ! [Alpha: game,Beta: game] : ( ord_less_eq @ ( set @ variable ) @ ( static_BVG @ ( choice @ Alpha @ Beta ) ) @ ( sup_sup @ ( set @ variable ) @ ( static_BVG @ Alpha ) @ ( static_BVG @ Beta ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % BVG_choice
% 0.13/0.36 thf(fact_110_usubstappp__choice__conv,axiom,
% 0.13/0.36 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Alpha: game,Beta: game] :
% 0.13/0.36 ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ ( choice @ Alpha @ Beta ) ) )
% 0.13/0.36 != ( none @ game ) )
% 0.13/0.36 => ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) )
% 0.13/0.36 != ( none @ game ) )
% 0.13/0.36 & ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Beta ) )
% 0.13/0.36 != ( none @ game ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % usubstappp_choice_conv
% 0.13/0.36 thf(fact_111_game_Oinject_I6_J,axiom,
% 0.13/0.36 ! [X6: game,Y6: game] :
% 0.13/0.36 ( ( ( loop @ X6 )
% 0.13/0.36 = ( loop @ Y6 ) )
% 0.13/0.36 = ( X6 = Y6 ) ) ).
% 0.13/0.36
% 0.13/0.36 % game.inject(6)
% 0.13/0.36 thf(fact_112_game_Oinject_I4_J,axiom,
% 0.13/0.36 ! [X41: game,X42: game,Y41: game,Y42: game] :
% 0.13/0.36 ( ( ( choice @ X41 @ X42 )
% 0.13/0.36 = ( choice @ Y41 @ Y42 ) )
% 0.13/0.36 = ( ( X41 = Y41 )
% 0.13/0.36 & ( X42 = Y42 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % game.inject(4)
% 0.13/0.36 thf(fact_113_game_Odistinct_I39_J,axiom,
% 0.13/0.36 ! [X41: game,X42: game,X6: game] :
% 0.13/0.36 ( ( choice @ X41 @ X42 )
% 0.13/0.36 != ( loop @ X6 ) ) ).
% 0.13/0.36
% 0.13/0.36 % game.distinct(39)
% 0.13/0.36 thf(fact_114_game_Odistinct_I45_J,axiom,
% 0.13/0.36 ! [X51: game,X52: game,X6: game] :
% 0.13/0.36 ( ( compose @ X51 @ X52 )
% 0.13/0.36 != ( loop @ X6 ) ) ).
% 0.13/0.36
% 0.13/0.36 % game.distinct(45)
% 0.13/0.36 thf(fact_115_game_Odistinct_I37_J,axiom,
% 0.13/0.36 ! [X41: game,X42: game,X51: game,X52: game] :
% 0.13/0.36 ( ( choice @ X41 @ X42 )
% 0.13/0.36 != ( compose @ X51 @ X52 ) ) ).
% 0.13/0.36
% 0.13/0.36 % game.distinct(37)
% 0.13/0.36 thf(fact_116_BVG__loop,axiom,
% 0.13/0.36 ! [Alpha: game] : ( ord_less_eq @ ( set @ variable ) @ ( static_BVG @ ( loop @ Alpha ) ) @ ( static_BVG @ Alpha ) ) ).
% 0.13/0.36
% 0.13/0.36 % BVG_loop
% 0.13/0.36 thf(fact_117_le__funD,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType] :
% 0.13/0.36 ( ( ord @ B )
% 0.13/0.36 => ! [F2: A > B,G2: A > B,X: A] :
% 0.13/0.36 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 0.13/0.36 => ( ord_less_eq @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_funD
% 0.13/0.36 thf(fact_118_le__funE,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType] :
% 0.13/0.36 ( ( ord @ B )
% 0.13/0.36 => ! [F2: A > B,G2: A > B,X: A] :
% 0.13/0.36 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 0.13/0.36 => ( ord_less_eq @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_funE
% 0.13/0.36 thf(fact_119_le__funI,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType] :
% 0.13/0.36 ( ( ord @ B )
% 0.13/0.36 => ! [F2: A > B,G2: A > B] :
% 0.13/0.36 ( ! [X3: A] : ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 0.13/0.36 => ( ord_less_eq @ ( A > B ) @ F2 @ G2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_funI
% 0.13/0.36 thf(fact_120_le__fun__def,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType] :
% 0.13/0.36 ( ( ord @ B )
% 0.13/0.36 => ( ( ord_less_eq @ ( A > B ) )
% 0.13/0.36 = ( ^ [F: A > B,G: A > B] :
% 0.13/0.36 ! [X2: A] : ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_fun_def
% 0.13/0.36 thf(fact_121_order__subst1,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType] :
% 0.13/0.36 ( ( ( order @ B )
% 0.13/0.36 & ( order @ A ) )
% 0.13/0.36 => ! [A3: A,F2: B > A,B3: B,C3: B] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A3 @ ( F2 @ B3 ) )
% 0.13/0.36 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 0.13/0.36 => ( ! [X3: B,Y4: B] :
% 0.13/0.36 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 0.13/0.36 => ( ord_less_eq @ A @ ( F2 @ X3 ) @ ( F2 @ Y4 ) ) )
% 0.13/0.36 => ( ord_less_eq @ A @ A3 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % order_subst1
% 0.13/0.36 thf(fact_122_order__subst2,axiom,
% 0.13/0.36 ! [A: $tType,C: $tType] :
% 0.13/0.36 ( ( ( order @ C )
% 0.13/0.36 & ( order @ A ) )
% 0.13/0.36 => ! [A3: A,B3: A,F2: A > C,C3: C] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.13/0.36 => ( ( ord_less_eq @ C @ ( F2 @ B3 ) @ C3 )
% 0.13/0.36 => ( ! [X3: A,Y4: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.13/0.36 => ( ord_less_eq @ C @ ( F2 @ X3 ) @ ( F2 @ Y4 ) ) )
% 0.13/0.36 => ( ord_less_eq @ C @ ( F2 @ A3 ) @ C3 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % order_subst2
% 0.13/0.36 thf(fact_123_ord__eq__le__subst,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType] :
% 0.13/0.36 ( ( ( ord @ B )
% 0.13/0.36 & ( ord @ A ) )
% 0.13/0.36 => ! [A3: A,F2: B > A,B3: B,C3: B] :
% 0.13/0.36 ( ( A3
% 0.13/0.36 = ( F2 @ B3 ) )
% 0.13/0.36 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 0.13/0.36 => ( ! [X3: B,Y4: B] :
% 0.13/0.36 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 0.13/0.36 => ( ord_less_eq @ A @ ( F2 @ X3 ) @ ( F2 @ Y4 ) ) )
% 0.13/0.36 => ( ord_less_eq @ A @ A3 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % ord_eq_le_subst
% 0.13/0.36 thf(fact_124_ord__le__eq__subst,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType] :
% 0.13/0.36 ( ( ( ord @ B )
% 0.13/0.36 & ( ord @ A ) )
% 0.13/0.36 => ! [A3: A,B3: A,F2: A > B,C3: B] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.13/0.36 => ( ( ( F2 @ B3 )
% 0.13/0.36 = C3 )
% 0.13/0.36 => ( ! [X3: A,Y4: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.13/0.36 => ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( F2 @ Y4 ) ) )
% 0.13/0.36 => ( ord_less_eq @ B @ ( F2 @ A3 ) @ C3 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % ord_le_eq_subst
% 0.13/0.36 thf(fact_125_eq__iff,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A )
% 0.13/0.36 => ( ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 0.13/0.36 = ( ^ [X2: A,Y3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.13/0.36 & ( ord_less_eq @ A @ Y3 @ X2 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % eq_iff
% 0.13/0.36 thf(fact_126_antisym,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A )
% 0.13/0.36 => ! [X: A,Y: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X @ Y )
% 0.13/0.36 => ( ( ord_less_eq @ A @ Y @ X )
% 0.13/0.36 => ( X = Y ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % antisym
% 0.13/0.36 thf(fact_127_linear,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( linorder @ A )
% 0.13/0.36 => ! [X: A,Y: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X @ Y )
% 0.13/0.36 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % linear
% 0.13/0.36 thf(fact_128_eq__refl,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( preorder @ A )
% 0.13/0.36 => ! [X: A,Y: A] :
% 0.13/0.36 ( ( X = Y )
% 0.13/0.36 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % eq_refl
% 0.13/0.36 thf(fact_129_le__cases,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( linorder @ A )
% 0.13/0.36 => ! [X: A,Y: A] :
% 0.13/0.36 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.13/0.36 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_cases
% 0.13/0.36 thf(fact_130_order_Otrans,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A )
% 0.13/0.36 => ! [A3: A,B3: A,C3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.13/0.36 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 0.13/0.36 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % order.trans
% 0.13/0.36 thf(fact_131_le__cases3,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( linorder @ A )
% 0.13/0.36 => ! [X: A,Y: A,Z: A] :
% 0.13/0.36 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.13/0.36 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 0.13/0.36 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.13/0.36 => ~ ( ord_less_eq @ A @ X @ Z ) )
% 0.13/0.36 => ( ( ( ord_less_eq @ A @ X @ Z )
% 0.13/0.36 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 0.13/0.36 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 0.13/0.36 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.13/0.36 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 0.13/0.36 => ~ ( ord_less_eq @ A @ Z @ X ) )
% 0.13/0.36 => ~ ( ( ord_less_eq @ A @ Z @ X )
% 0.13/0.36 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_cases3
% 0.13/0.36 thf(fact_132_antisym__conv,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A )
% 0.13/0.36 => ! [Y: A,X: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ Y @ X )
% 0.13/0.36 => ( ( ord_less_eq @ A @ X @ Y )
% 0.13/0.36 = ( X = Y ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % antisym_conv
% 0.13/0.36 thf(fact_133_order__class_Oorder_Oeq__iff,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A )
% 0.13/0.36 => ( ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 0.13/0.36 = ( ^ [A5: A,B5: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A5 @ B5 )
% 0.13/0.36 & ( ord_less_eq @ A @ B5 @ A5 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % order_class.order.eq_iff
% 0.13/0.36 thf(fact_134_ord__eq__le__trans,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord @ A )
% 0.13/0.36 => ! [A3: A,B3: A,C3: A] :
% 0.13/0.36 ( ( A3 = B3 )
% 0.13/0.36 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 0.13/0.36 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % ord_eq_le_trans
% 0.13/0.36 thf(fact_135_ord__le__eq__trans,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord @ A )
% 0.13/0.36 => ! [A3: A,B3: A,C3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.13/0.36 => ( ( B3 = C3 )
% 0.13/0.36 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % ord_le_eq_trans
% 0.13/0.36 thf(fact_136_order__class_Oorder_Oantisym,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A )
% 0.13/0.36 => ! [A3: A,B3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.13/0.36 => ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.13/0.36 => ( A3 = B3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % order_class.order.antisym
% 0.13/0.36 thf(fact_137_order__trans,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( preorder @ A )
% 0.13/0.36 => ! [X: A,Y: A,Z: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X @ Y )
% 0.13/0.36 => ( ( ord_less_eq @ A @ Y @ Z )
% 0.13/0.36 => ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % order_trans
% 0.13/0.36 thf(fact_138_dual__order_Orefl,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A )
% 0.13/0.36 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 0.13/0.36
% 0.13/0.36 % dual_order.refl
% 0.13/0.36 thf(fact_139_linorder__wlog,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( linorder @ A )
% 0.13/0.36 => ! [P: A > A > $o,A3: A,B3: A] :
% 0.13/0.36 ( ! [A7: A,B7: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A7 @ B7 )
% 0.13/0.36 => ( P @ A7 @ B7 ) )
% 0.13/0.36 => ( ! [A7: A,B7: A] :
% 0.13/0.36 ( ( P @ B7 @ A7 )
% 0.13/0.36 => ( P @ A7 @ B7 ) )
% 0.13/0.36 => ( P @ A3 @ B3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % linorder_wlog
% 0.13/0.36 thf(fact_140_dual__order_Otrans,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A )
% 0.13/0.36 => ! [B3: A,A3: A,C3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.13/0.36 => ( ( ord_less_eq @ A @ C3 @ B3 )
% 0.13/0.36 => ( ord_less_eq @ A @ C3 @ A3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % dual_order.trans
% 0.13/0.36 thf(fact_141_dual__order_Oeq__iff,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A )
% 0.13/0.36 => ( ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 0.13/0.36 = ( ^ [A5: A,B5: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ B5 @ A5 )
% 0.13/0.36 & ( ord_less_eq @ A @ A5 @ B5 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % dual_order.eq_iff
% 0.13/0.36 thf(fact_142_dual__order_Oantisym,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A )
% 0.13/0.36 => ! [B3: A,A3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.13/0.36 => ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.13/0.36 => ( A3 = B3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % dual_order.antisym
% 0.13/0.36 thf(fact_143_fst__swap,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,X: product_prod @ B @ A] :
% 0.13/0.36 ( ( product_fst @ A @ B @ ( product_swap @ B @ A @ X ) )
% 0.13/0.36 = ( product_snd @ B @ A @ X ) ) ).
% 0.13/0.36
% 0.13/0.36 % fst_swap
% 0.13/0.36 thf(fact_144_snd__swap,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,X: product_prod @ A @ B] :
% 0.13/0.36 ( ( product_snd @ B @ A @ ( product_swap @ A @ B @ X ) )
% 0.13/0.36 = ( product_fst @ A @ B @ X ) ) ).
% 0.13/0.36
% 0.13/0.36 % snd_swap
% 0.13/0.36 thf(fact_145_usubstappp__choice,axiom,
% 0.13/0.36 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Alpha: game,Beta: game] :
% 0.13/0.36 ( ( uSubst95898988stappp @ Sigma @ U @ ( choice @ Alpha @ Beta ) )
% 0.13/0.36 = ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( sup_sup @ ( set @ variable ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Beta ) ) ) @ ( uSubst1976112797hoiceo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Beta ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % usubstappp_choice
% 0.13/0.36 thf(fact_146_GreatestI2__order,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A )
% 0.13/0.36 => ! [P: A > $o,X: A,Q: A > $o] :
% 0.13/0.36 ( ( P @ X )
% 0.13/0.36 => ( ! [Y4: A] :
% 0.13/0.36 ( ( P @ Y4 )
% 0.13/0.36 => ( ord_less_eq @ A @ Y4 @ X ) )
% 0.13/0.36 => ( ! [X3: A] :
% 0.13/0.36 ( ( P @ X3 )
% 0.13/0.36 => ( ! [Y5: A] :
% 0.13/0.36 ( ( P @ Y5 )
% 0.13/0.36 => ( ord_less_eq @ A @ Y5 @ X3 ) )
% 0.13/0.36 => ( Q @ X3 ) ) )
% 0.13/0.36 => ( Q @ ( order_Greatest @ A @ P ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % GreatestI2_order
% 0.13/0.36 thf(fact_147_Greatest__equality,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A )
% 0.13/0.36 => ! [P: A > $o,X: A] :
% 0.13/0.36 ( ( P @ X )
% 0.13/0.36 => ( ! [Y4: A] :
% 0.13/0.36 ( ( P @ Y4 )
% 0.13/0.36 => ( ord_less_eq @ A @ Y4 @ X ) )
% 0.13/0.36 => ( ( order_Greatest @ A @ P )
% 0.13/0.36 = X ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Greatest_equality
% 0.13/0.36 thf(fact_148_old_Oprod_Oinject,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,A3: A,B3: B,A8: A,B8: B] :
% 0.13/0.36 ( ( ( product_Pair @ A @ B @ A3 @ B3 )
% 0.13/0.36 = ( product_Pair @ A @ B @ A8 @ B8 ) )
% 0.13/0.36 = ( ( A3 = A8 )
% 0.13/0.36 & ( B3 = B8 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % old.prod.inject
% 0.13/0.36 thf(fact_149_prod_Oinject,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y22: B] :
% 0.13/0.36 ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 0.13/0.36 = ( product_Pair @ A @ B @ Y1 @ Y22 ) )
% 0.13/0.36 = ( ( X1 = Y1 )
% 0.13/0.36 & ( X22 = Y22 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % prod.inject
% 0.13/0.36 thf(fact_150_swap__swap,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,P2: product_prod @ A @ B] :
% 0.13/0.36 ( ( product_swap @ B @ A @ ( product_swap @ A @ B @ P2 ) )
% 0.13/0.36 = P2 ) ).
% 0.13/0.36
% 0.13/0.36 % swap_swap
% 0.13/0.36 thf(fact_151_swap__simp,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,X: B,Y: A] :
% 0.13/0.36 ( ( product_swap @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) )
% 0.13/0.36 = ( product_Pair @ A @ B @ Y @ X ) ) ).
% 0.13/0.36
% 0.13/0.36 % swap_simp
% 0.13/0.36 thf(fact_152_prod_Ocollapse,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 0.13/0.36 ( ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) )
% 0.13/0.36 = Prod ) ).
% 0.13/0.36
% 0.13/0.36 % prod.collapse
% 0.13/0.36 thf(fact_153_old_Oprod_Oinducts,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.13/0.36 ( ! [A7: A,B7: B] : ( P @ ( product_Pair @ A @ B @ A7 @ B7 ) )
% 0.13/0.36 => ( P @ Prod ) ) ).
% 0.13/0.36
% 0.13/0.36 % old.prod.inducts
% 0.13/0.36 thf(fact_154_old_Oprod_Oexhaust,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.13/0.36 ~ ! [A7: A,B7: B] :
% 0.13/0.36 ( Y
% 0.13/0.36 != ( product_Pair @ A @ B @ A7 @ B7 ) ) ).
% 0.13/0.36
% 0.13/0.36 % old.prod.exhaust
% 0.13/0.36 thf(fact_155_prod__induct7,axiom,
% 0.13/0.36 ! [G3: $tType,F3: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) )] :
% 0.13/0.36 ( ! [A7: A,B7: B,C4: C,D4: D,E2: E,F4: F3,G4: G3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) @ B7 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) @ D4 @ ( product_Pair @ E @ ( product_prod @ F3 @ G3 ) @ E2 @ ( product_Pair @ F3 @ G3 @ F4 @ G4 ) ) ) ) ) ) )
% 0.13/0.36 => ( P @ X ) ) ).
% 0.13/0.36
% 0.13/0.36 % prod_induct7
% 0.13/0.36 thf(fact_156_prod__induct6,axiom,
% 0.13/0.36 ! [F3: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) )] :
% 0.13/0.36 ( ! [A7: A,B7: B,C4: C,D4: D,E2: E,F4: F3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B7 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D4 @ ( product_Pair @ E @ F3 @ E2 @ F4 ) ) ) ) ) )
% 0.13/0.36 => ( P @ X ) ) ).
% 0.13/0.36
% 0.13/0.36 % prod_induct6
% 0.13/0.36 thf(fact_157_prod__induct5,axiom,
% 0.13/0.36 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.13/0.36 ( ! [A7: A,B7: B,C4: C,D4: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B7 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C4 @ ( product_Pair @ D @ E @ D4 @ E2 ) ) ) ) )
% 0.13/0.36 => ( P @ X ) ) ).
% 0.13/0.36
% 0.13/0.36 % prod_induct5
% 0.13/0.36 thf(fact_158_prod__induct4,axiom,
% 0.13/0.36 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.13/0.36 ( ! [A7: A,B7: B,C4: C,D4: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B7 @ ( product_Pair @ C @ D @ C4 @ D4 ) ) ) )
% 0.13/0.36 => ( P @ X ) ) ).
% 0.13/0.36
% 0.13/0.36 % prod_induct4
% 0.13/0.36 thf(fact_159_prod__induct3,axiom,
% 0.13/0.36 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.13/0.36 ( ! [A7: A,B7: B,C4: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A7 @ ( product_Pair @ B @ C @ B7 @ C4 ) ) )
% 0.13/0.36 => ( P @ X ) ) ).
% 0.13/0.36
% 0.13/0.36 % prod_induct3
% 0.13/0.36 thf(fact_160_prod__cases7,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,G3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) )] :
% 0.13/0.36 ~ ! [A7: A,B7: B,C4: C,D4: D,E2: E,F4: F3,G4: G3] :
% 0.13/0.36 ( Y
% 0.13/0.36 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) @ B7 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) @ D4 @ ( product_Pair @ E @ ( product_prod @ F3 @ G3 ) @ E2 @ ( product_Pair @ F3 @ G3 @ F4 @ G4 ) ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % prod_cases7
% 0.13/0.36 thf(fact_161_prod__cases6,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) )] :
% 0.13/0.36 ~ ! [A7: A,B7: B,C4: C,D4: D,E2: E,F4: F3] :
% 0.13/0.36 ( Y
% 0.13/0.36 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B7 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D4 @ ( product_Pair @ E @ F3 @ E2 @ F4 ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % prod_cases6
% 0.13/0.36 thf(fact_162_prod__cases5,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.13/0.36 ~ ! [A7: A,B7: B,C4: C,D4: D,E2: E] :
% 0.13/0.36 ( Y
% 0.13/0.36 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B7 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C4 @ ( product_Pair @ D @ E @ D4 @ E2 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % prod_cases5
% 0.13/0.36 thf(fact_163_prod__cases4,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.13/0.36 ~ ! [A7: A,B7: B,C4: C,D4: D] :
% 0.13/0.36 ( Y
% 0.13/0.36 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B7 @ ( product_Pair @ C @ D @ C4 @ D4 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % prod_cases4
% 0.13/0.36 thf(fact_164_prod__cases3,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.13/0.36 ~ ! [A7: A,B7: B,C4: C] :
% 0.13/0.36 ( Y
% 0.13/0.36 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A7 @ ( product_Pair @ B @ C @ B7 @ C4 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % prod_cases3
% 0.13/0.36 thf(fact_165_Pair__inject,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,A3: A,B3: B,A8: A,B8: B] :
% 0.13/0.36 ( ( ( product_Pair @ A @ B @ A3 @ B3 )
% 0.13/0.36 = ( product_Pair @ A @ B @ A8 @ B8 ) )
% 0.13/0.36 => ~ ( ( A3 = A8 )
% 0.13/0.36 => ( B3 != B8 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Pair_inject
% 0.13/0.36 thf(fact_166_prod__cases,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 0.13/0.36 ( ! [A7: A,B7: B] : ( P @ ( product_Pair @ A @ B @ A7 @ B7 ) )
% 0.13/0.36 => ( P @ P2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % prod_cases
% 0.13/0.36 thf(fact_167_surj__pair,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 0.13/0.36 ? [X3: A,Y4: B] :
% 0.13/0.36 ( P2
% 0.13/0.36 = ( product_Pair @ A @ B @ X3 @ Y4 ) ) ).
% 0.13/0.36
% 0.13/0.36 % surj_pair
% 0.13/0.36 thf(fact_168_fst__eqD,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,X: A,Y: B,A3: A] :
% 0.13/0.36 ( ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X @ Y ) )
% 0.13/0.36 = A3 )
% 0.13/0.36 => ( X = A3 ) ) ).
% 0.13/0.36
% 0.13/0.36 % fst_eqD
% 0.13/0.36 thf(fact_169_fst__conv,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,X1: A,X22: B] :
% 0.13/0.36 ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X1 @ X22 ) )
% 0.13/0.36 = X1 ) ).
% 0.13/0.36
% 0.13/0.36 % fst_conv
% 0.13/0.36 thf(fact_170_snd__eqD,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,X: B,Y: A,A3: A] :
% 0.13/0.36 ( ( ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) )
% 0.13/0.36 = A3 )
% 0.13/0.36 => ( Y = A3 ) ) ).
% 0.13/0.36
% 0.13/0.36 % snd_eqD
% 0.13/0.36 thf(fact_171_snd__conv,axiom,
% 0.13/0.36 ! [Aa: $tType,A: $tType,X1: Aa,X22: A] :
% 0.13/0.36 ( ( product_snd @ Aa @ A @ ( product_Pair @ Aa @ A @ X1 @ X22 ) )
% 0.13/0.36 = X22 ) ).
% 0.13/0.36
% 0.13/0.36 % snd_conv
% 0.13/0.36 thf(fact_172_prod_Oswap__def,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType] :
% 0.13/0.36 ( ( product_swap @ A @ B )
% 0.13/0.36 = ( ^ [P3: product_prod @ A @ B] : ( product_Pair @ B @ A @ ( product_snd @ A @ B @ P3 ) @ ( product_fst @ A @ B @ P3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % prod.swap_def
% 0.13/0.36 thf(fact_173_fst__pair,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,A3: A,B3: B] :
% 0.13/0.36 ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.13/0.36 = A3 ) ).
% 0.13/0.36
% 0.13/0.36 % fst_pair
% 0.13/0.36 thf(fact_174_snd__pair,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,A3: B,B3: A] :
% 0.13/0.36 ( ( product_snd @ B @ A @ ( product_Pair @ B @ A @ A3 @ B3 ) )
% 0.13/0.36 = B3 ) ).
% 0.13/0.36
% 0.13/0.36 % snd_pair
% 0.13/0.36 thf(fact_175_surjective__pairing,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,T3: product_prod @ A @ B] :
% 0.13/0.36 ( T3
% 0.13/0.36 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ T3 ) @ ( product_snd @ A @ B @ T3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % surjective_pairing
% 0.13/0.36 thf(fact_176_prod_Oexhaust__sel,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 0.13/0.36 ( Prod
% 0.13/0.36 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % prod.exhaust_sel
% 0.13/0.36 thf(fact_177_conjI__realizer,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,P: A > $o,P2: A,Q: B > $o,Q2: B] :
% 0.13/0.36 ( ( P @ P2 )
% 0.13/0.36 => ( ( Q @ Q2 )
% 0.13/0.36 => ( ( P @ ( product_fst @ A @ B @ ( product_Pair @ A @ B @ P2 @ Q2 ) ) )
% 0.13/0.36 & ( Q @ ( product_snd @ A @ B @ ( product_Pair @ A @ B @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % conjI_realizer
% 0.13/0.36 thf(fact_178_exI__realizer,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,P: A > B > $o,Y: A,X: B] :
% 0.13/0.36 ( ( P @ Y @ X )
% 0.13/0.36 => ( P @ ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) ) @ ( product_fst @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % exI_realizer
% 0.13/0.36 thf(fact_179_Choiceo_Osimps_I2_J,axiom,
% 0.13/0.36 ! [Alpha: option @ game] :
% 0.13/0.36 ( ( uSubst1976112797hoiceo @ Alpha @ ( none @ game ) )
% 0.13/0.36 = ( none @ game ) ) ).
% 0.13/0.36
% 0.13/0.36 % Choiceo.simps(2)
% 0.13/0.36 thf(fact_180_Choiceo__undef,axiom,
% 0.13/0.36 ! [Alpha: option @ game,Beta: option @ game] :
% 0.13/0.36 ( ( ( uSubst1976112797hoiceo @ Alpha @ Beta )
% 0.13/0.36 = ( none @ game ) )
% 0.13/0.36 = ( ( Alpha
% 0.13/0.36 = ( none @ game ) )
% 0.13/0.36 | ( Beta
% 0.13/0.36 = ( none @ game ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Choiceo_undef
% 0.13/0.36 thf(fact_181_usubstappp__compose,axiom,
% 0.13/0.36 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Alpha: game,Beta: game] :
% 0.13/0.36 ( ( uSubst95898988stappp @ Sigma @ U @ ( compose @ Alpha @ Beta ) )
% 0.13/0.36 = ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ Beta ) ) @ ( uSubst1385204910mposeo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ Beta ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % usubstappp_compose
% 0.13/0.36 thf(fact_182_old_Oprod_Orec,axiom,
% 0.13/0.36 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A3: A,B3: B] :
% 0.13/0.36 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.13/0.36 = ( F1 @ A3 @ B3 ) ) ).
% 0.13/0.36
% 0.13/0.36 % old.prod.rec
% 0.13/0.36 thf(fact_183_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,P: A > B > $o,X: A,Y: B,A3: product_prod @ A @ B] :
% 0.13/0.36 ( ( P @ X @ Y )
% 0.13/0.36 => ( ( A3
% 0.13/0.36 = ( product_Pair @ A @ B @ X @ Y ) )
% 0.13/0.36 => ( P @ ( product_fst @ A @ B @ A3 ) @ ( product_snd @ A @ B @ A3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % BNF_Greatest_Fixpoint.subst_Pair
% 0.13/0.36 thf(fact_184_Composeo__undef,axiom,
% 0.13/0.36 ! [Alpha: option @ game,Beta: option @ game] :
% 0.13/0.36 ( ( ( uSubst1385204910mposeo @ Alpha @ Beta )
% 0.13/0.36 = ( none @ game ) )
% 0.13/0.36 = ( ( Alpha
% 0.13/0.36 = ( none @ game ) )
% 0.13/0.36 | ( Beta
% 0.13/0.36 = ( none @ game ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Composeo_undef
% 0.13/0.36 thf(fact_185_Composeo_Osimps_I2_J,axiom,
% 0.13/0.36 ! [Alpha: option @ game] :
% 0.13/0.36 ( ( uSubst1385204910mposeo @ Alpha @ ( none @ game ) )
% 0.13/0.36 = ( none @ game ) ) ).
% 0.13/0.36
% 0.13/0.36 % Composeo.simps(2)
% 0.13/0.36 thf(fact_186_usubstappp__loop,axiom,
% 0.13/0.36 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Alpha: game] :
% 0.13/0.36 ( ( uSubst95898988stappp @ Sigma @ U @ ( loop @ Alpha ) )
% 0.13/0.36 = ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ ( uSubst993936602_Loopo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % usubstappp_loop
% 0.13/0.36 thf(fact_187_eq__snd__iff,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,B3: A,P2: product_prod @ B @ A] :
% 0.13/0.36 ( ( B3
% 0.13/0.36 = ( product_snd @ B @ A @ P2 ) )
% 0.13/0.36 = ( ? [A5: B] :
% 0.13/0.36 ( P2
% 0.13/0.36 = ( product_Pair @ B @ A @ A5 @ B3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % eq_snd_iff
% 0.13/0.36 thf(fact_188_sndI,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,X: product_prod @ A @ B,Y: A,Z: B] :
% 0.13/0.36 ( ( X
% 0.13/0.36 = ( product_Pair @ A @ B @ Y @ Z ) )
% 0.13/0.36 => ( ( product_snd @ A @ B @ X )
% 0.13/0.36 = Z ) ) ).
% 0.13/0.36
% 0.13/0.36 % sndI
% 0.13/0.36 thf(fact_189_Loopo_Osimps_I2_J,axiom,
% 0.13/0.36 ( ( uSubst993936602_Loopo @ ( none @ game ) )
% 0.13/0.36 = ( none @ game ) ) ).
% 0.13/0.36
% 0.13/0.36 % Loopo.simps(2)
% 0.13/0.36 thf(fact_190_Loopo__undef,axiom,
% 0.13/0.36 ! [Alpha: option @ game] :
% 0.13/0.36 ( ( ( uSubst993936602_Loopo @ Alpha )
% 0.13/0.36 = ( none @ game ) )
% 0.13/0.36 = ( Alpha
% 0.13/0.36 = ( none @ game ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Loopo_undef
% 0.13/0.36 thf(fact_191_fstI,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,X: product_prod @ A @ B,Y: A,Z: B] :
% 0.13/0.36 ( ( X
% 0.13/0.36 = ( product_Pair @ A @ B @ Y @ Z ) )
% 0.13/0.36 => ( ( product_fst @ A @ B @ X )
% 0.13/0.36 = Y ) ) ).
% 0.13/0.36
% 0.13/0.36 % fstI
% 0.13/0.36 thf(fact_192_eq__fst__iff,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,A3: A,P2: product_prod @ A @ B] :
% 0.13/0.36 ( ( A3
% 0.13/0.36 = ( product_fst @ A @ B @ P2 ) )
% 0.13/0.36 = ( ? [B5: B] :
% 0.13/0.36 ( P2
% 0.13/0.36 = ( product_Pair @ A @ B @ A3 @ B5 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % eq_fst_iff
% 0.13/0.36 thf(fact_193_internal__case__prod__conv,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A3: B,B3: C] :
% 0.13/0.36 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A3 @ B3 ) )
% 0.13/0.36 = ( C3 @ A3 @ B3 ) ) ).
% 0.13/0.36
% 0.13/0.36 % internal_case_prod_conv
% 0.13/0.36 thf(fact_194_relChain__def,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType] :
% 0.13/0.36 ( ( ord @ B )
% 0.13/0.36 => ( ( bNF_Ca1785829860lChain @ A @ B )
% 0.13/0.36 = ( ^ [R: set @ ( product_prod @ A @ A ),As: A > B] :
% 0.13/0.36 ! [I: A,J: A] :
% 0.13/0.36 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ I @ J ) @ R )
% 0.13/0.36 => ( ord_less_eq @ B @ ( As @ I ) @ ( As @ J ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % relChain_def
% 0.13/0.36 thf(fact_195_sndOp__def,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,C: $tType] :
% 0.13/0.36 ( ( bNF_sndOp @ C @ A @ B )
% 0.13/0.36 = ( ^ [P4: C > A > $o,Q3: A > B > $o,Ac: product_prod @ C @ B] : ( product_Pair @ A @ B @ ( bNF_pick_middlep @ C @ A @ B @ P4 @ Q3 @ ( product_fst @ C @ B @ Ac ) @ ( product_snd @ C @ B @ Ac ) ) @ ( product_snd @ C @ B @ Ac ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sndOp_def
% 0.13/0.36 thf(fact_196_fstOp__def,axiom,
% 0.13/0.36 ! [C: $tType,B: $tType,A: $tType] :
% 0.13/0.36 ( ( bNF_fstOp @ A @ B @ C )
% 0.13/0.36 = ( ^ [P4: A > B > $o,Q3: B > C > $o,Ac: product_prod @ A @ C] : ( product_Pair @ A @ B @ ( product_fst @ A @ C @ Ac ) @ ( bNF_pick_middlep @ A @ B @ C @ P4 @ Q3 @ ( product_fst @ A @ C @ Ac ) @ ( product_snd @ A @ C @ Ac ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % fstOp_def
% 0.13/0.36 thf(fact_197_csquare__fstOp__sndOp,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,C: $tType,F2: ( A > B > $o ) > ( product_prod @ A @ B ) > $o,P: A > C > $o,Q: C > B > $o] : ( bNF_csquare @ ( product_prod @ A @ B ) @ ( product_prod @ A @ C ) @ C @ ( product_prod @ C @ B ) @ ( collect @ ( product_prod @ A @ B ) @ ( F2 @ ( relcompp @ A @ C @ B @ P @ Q ) ) ) @ ( product_snd @ A @ C ) @ ( product_fst @ C @ B ) @ ( bNF_fstOp @ A @ C @ B @ P @ Q ) @ ( bNF_sndOp @ A @ C @ B @ P @ Q ) ) ).
% 0.13/0.36
% 0.13/0.36 % csquare_fstOp_sndOp
% 0.13/0.36 thf(fact_198_usubstappp_Osimps_I4_J,axiom,
% 0.13/0.36 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Alpha: game,Beta: game] :
% 0.13/0.36 ( ( uSubst95898988stappp @ Sigma @ U @ ( choice @ Alpha @ Beta ) )
% 0.13/0.36 = ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( sup_sup @ ( set @ variable ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Beta ) ) ) @ ( uSubst1976112797hoiceo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Beta ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % usubstappp.simps(4)
% 0.13/0.36 thf(fact_199_pick__middlep,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,C: $tType,P: A > B > $o,Q: B > C > $o,A3: A,C3: C] :
% 0.13/0.36 ( ( relcompp @ A @ B @ C @ P @ Q @ A3 @ C3 )
% 0.13/0.36 => ( ( P @ A3 @ ( bNF_pick_middlep @ A @ B @ C @ P @ Q @ A3 @ C3 ) )
% 0.13/0.36 & ( Q @ ( bNF_pick_middlep @ A @ B @ C @ P @ Q @ A3 @ C3 ) @ C3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % pick_middlep
% 0.13/0.36 thf(fact_200_csquare__def,axiom,
% 0.13/0.36 ! [B: $tType,C: $tType,D: $tType,A: $tType] :
% 0.13/0.36 ( ( bNF_csquare @ A @ B @ C @ D )
% 0.13/0.36 = ( ^ [A4: set @ A,F12: B > C,F22: D > C,P1: A > B,P22: A > D] :
% 0.13/0.36 ! [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ A4 )
% 0.13/0.36 => ( ( F12 @ ( P1 @ X2 ) )
% 0.13/0.36 = ( F22 @ ( P22 @ X2 ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % csquare_def
% 0.13/0.36 thf(fact_201_leq__OOI,axiom,
% 0.13/0.36 ! [A: $tType,R2: A > A > $o] :
% 0.13/0.36 ( ( R2
% 0.13/0.36 = ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) ) )
% 0.13/0.36 => ( ord_less_eq @ ( A > A > $o ) @ R2 @ ( relcompp @ A @ A @ A @ R2 @ R2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % leq_OOI
% 0.13/0.36 thf(fact_202_less__eq__set__def,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) )
% 0.13/0.36 = ( ^ [A4: set @ A,B4: set @ A] :
% 0.13/0.36 ( ord_less_eq @ ( A > $o )
% 0.13/0.36 @ ^ [X2: A] : ( member @ A @ X2 @ A4 )
% 0.13/0.36 @ ^ [X2: A] : ( member @ A @ X2 @ B4 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % less_eq_set_def
% 0.13/0.36 thf(fact_203_Collect__subset,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,P: A > $o] :
% 0.13/0.36 ( ord_less_eq @ ( set @ A )
% 0.13/0.36 @ ( collect @ A
% 0.13/0.36 @ ^ [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ A2 )
% 0.13/0.36 & ( P @ X2 ) ) )
% 0.13/0.36 @ A2 ) ).
% 0.13/0.36
% 0.13/0.36 % Collect_subset
% 0.13/0.36 thf(fact_204_Un__def,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( sup_sup @ ( set @ A ) )
% 0.13/0.36 = ( ^ [A4: set @ A,B4: set @ A] :
% 0.13/0.36 ( collect @ A
% 0.13/0.36 @ ^ [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ A4 )
% 0.13/0.36 | ( member @ A @ X2 @ B4 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_def
% 0.13/0.36 thf(fact_205_sup__set__def,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( sup_sup @ ( set @ A ) )
% 0.13/0.36 = ( ^ [A4: set @ A,B4: set @ A] :
% 0.13/0.36 ( collect @ A
% 0.13/0.36 @ ( sup_sup @ ( A > $o )
% 0.13/0.36 @ ^ [X2: A] : ( member @ A @ X2 @ A4 )
% 0.13/0.36 @ ^ [X2: A] : ( member @ A @ X2 @ B4 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_set_def
% 0.13/0.36 thf(fact_206_Collect__disj__eq,axiom,
% 0.13/0.36 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.13/0.36 ( ( collect @ A
% 0.13/0.36 @ ^ [X2: A] :
% 0.13/0.36 ( ( P @ X2 )
% 0.13/0.36 | ( Q @ X2 ) ) )
% 0.13/0.36 = ( sup_sup @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Collect_disj_eq
% 0.13/0.36 thf(fact_207_subset__CollectI,axiom,
% 0.13/0.36 ! [A: $tType,B2: set @ A,A2: set @ A,Q: A > $o,P: A > $o] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 0.13/0.36 => ( ! [X3: A] :
% 0.13/0.36 ( ( member @ A @ X3 @ B2 )
% 0.13/0.36 => ( ( Q @ X3 )
% 0.13/0.36 => ( P @ X3 ) ) )
% 0.13/0.36 => ( ord_less_eq @ ( set @ A )
% 0.13/0.36 @ ( collect @ A
% 0.13/0.36 @ ^ [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ B2 )
% 0.13/0.36 & ( Q @ X2 ) ) )
% 0.13/0.36 @ ( collect @ A
% 0.13/0.36 @ ^ [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ A2 )
% 0.13/0.36 & ( P @ X2 ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % subset_CollectI
% 0.13/0.36 thf(fact_208_subset__Collect__iff,axiom,
% 0.13/0.36 ! [A: $tType,B2: set @ A,A2: set @ A,P: A > $o] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 0.13/0.36 => ( ( ord_less_eq @ ( set @ A ) @ B2
% 0.13/0.36 @ ( collect @ A
% 0.13/0.36 @ ^ [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ A2 )
% 0.13/0.36 & ( P @ X2 ) ) ) )
% 0.13/0.36 = ( ! [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ B2 )
% 0.13/0.36 => ( P @ X2 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % subset_Collect_iff
% 0.13/0.36 thf(fact_209_usubstappp_Osimps_I5_J,axiom,
% 0.13/0.36 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Alpha: game,Beta: game] :
% 0.13/0.36 ( ( uSubst95898988stappp @ Sigma @ U @ ( compose @ Alpha @ Beta ) )
% 0.13/0.36 = ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ Beta ) ) @ ( uSubst1385204910mposeo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ Beta ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % usubstappp.simps(5)
% 0.13/0.36 thf(fact_210_usubstappp_Osimps_I6_J,axiom,
% 0.13/0.36 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Alpha: game] :
% 0.13/0.36 ( ( uSubst95898988stappp @ Sigma @ U @ ( loop @ Alpha ) )
% 0.13/0.36 = ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ ( uSubst993936602_Loopo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % usubstappp.simps(6)
% 0.13/0.36 thf(fact_211_scomp__unfold,axiom,
% 0.13/0.36 ! [D: $tType,C: $tType,B: $tType,A: $tType] :
% 0.13/0.36 ( ( product_scomp @ A @ B @ C @ D )
% 0.13/0.36 = ( ^ [F: A > ( product_prod @ B @ C ),G: B > C > D,X2: A] : ( G @ ( product_fst @ B @ C @ ( F @ X2 ) ) @ ( product_snd @ B @ C @ ( F @ X2 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % scomp_unfold
% 0.13/0.36 thf(fact_212_sup__Un__eq,axiom,
% 0.13/0.36 ! [A: $tType,R2: set @ A,S2: set @ A] :
% 0.13/0.36 ( ( sup_sup @ ( A > $o )
% 0.13/0.36 @ ^ [X2: A] : ( member @ A @ X2 @ R2 )
% 0.13/0.36 @ ^ [X2: A] : ( member @ A @ X2 @ S2 ) )
% 0.13/0.36 = ( ^ [X2: A] : ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ R2 @ S2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_Un_eq
% 0.13/0.36 thf(fact_213_scomp__scomp,axiom,
% 0.13/0.36 ! [A: $tType,C: $tType,D: $tType,B: $tType,F3: $tType,E: $tType,F2: A > ( product_prod @ E @ F3 ),G2: E > F3 > ( product_prod @ C @ D ),H: C > D > B] :
% 0.13/0.36 ( ( product_scomp @ A @ C @ D @ B @ ( product_scomp @ A @ E @ F3 @ ( product_prod @ C @ D ) @ F2 @ G2 ) @ H )
% 0.13/0.36 = ( product_scomp @ A @ E @ F3 @ B @ F2
% 0.13/0.36 @ ^ [X2: E] : ( product_scomp @ F3 @ C @ D @ B @ ( G2 @ X2 ) @ H ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % scomp_scomp
% 0.13/0.36 thf(fact_214_scomp__Pair,axiom,
% 0.13/0.36 ! [C: $tType,B: $tType,A: $tType,X: A > ( product_prod @ B @ C )] :
% 0.13/0.36 ( ( product_scomp @ A @ B @ C @ ( product_prod @ B @ C ) @ X @ ( product_Pair @ B @ C ) )
% 0.13/0.36 = X ) ).
% 0.13/0.36
% 0.13/0.36 % scomp_Pair
% 0.13/0.36 thf(fact_215_Pair__scomp,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,C: $tType,X: C,F2: C > A > B] :
% 0.13/0.36 ( ( product_scomp @ A @ C @ A @ B @ ( product_Pair @ C @ A @ X ) @ F2 )
% 0.13/0.36 = ( F2 @ X ) ) ).
% 0.13/0.36
% 0.13/0.36 % Pair_scomp
% 0.13/0.36 thf(fact_216_refl__ge__eq,axiom,
% 0.13/0.36 ! [A: $tType,R2: A > A > $o] :
% 0.13/0.36 ( ! [X3: A] : ( R2 @ X3 @ X3 )
% 0.13/0.36 => ( ord_less_eq @ ( A > A > $o )
% 0.13/0.36 @ ^ [Y2: A,Z2: A] : ( Y2 = Z2 )
% 0.13/0.36 @ R2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % refl_ge_eq
% 0.13/0.36 thf(fact_217_ge__eq__refl,axiom,
% 0.13/0.36 ! [A: $tType,R2: A > A > $o,X: A] :
% 0.13/0.36 ( ( ord_less_eq @ ( A > A > $o )
% 0.13/0.36 @ ^ [Y2: A,Z2: A] : ( Y2 = Z2 )
% 0.13/0.36 @ R2 )
% 0.13/0.36 => ( R2 @ X @ X ) ) ).
% 0.13/0.36
% 0.13/0.36 % ge_eq_refl
% 0.13/0.36 thf(fact_218_subrelI,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),S3: set @ ( product_prod @ A @ B )] :
% 0.13/0.36 ( ! [X3: A,Y4: B] :
% 0.13/0.36 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y4 ) @ R3 )
% 0.13/0.36 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y4 ) @ S3 ) )
% 0.13/0.36 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R3 @ S3 ) ) ).
% 0.13/0.36
% 0.13/0.36 % subrelI
% 0.13/0.36 thf(fact_219_pred__equals__eq2,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,R2: set @ ( product_prod @ A @ B ),S2: set @ ( product_prod @ A @ B )] :
% 0.13/0.36 ( ( ( ^ [X2: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ R2 ) )
% 0.13/0.36 = ( ^ [X2: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ S2 ) ) )
% 0.13/0.36 = ( R2 = S2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % pred_equals_eq2
% 0.13/0.36 thf(fact_220_pred__subset__eq2,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,R2: set @ ( product_prod @ A @ B ),S2: set @ ( product_prod @ A @ B )] :
% 0.13/0.36 ( ( ord_less_eq @ ( A > B > $o )
% 0.13/0.36 @ ^ [X2: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ R2 )
% 0.13/0.36 @ ^ [X2: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ S2 ) )
% 0.13/0.36 = ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R2 @ S2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % pred_subset_eq2
% 0.13/0.36 thf(fact_221_sup__Un__eq2,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,R2: set @ ( product_prod @ A @ B ),S2: set @ ( product_prod @ A @ B )] :
% 0.13/0.36 ( ( sup_sup @ ( A > B > $o )
% 0.13/0.36 @ ^ [X2: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ R2 )
% 0.13/0.36 @ ^ [X2: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ S2 ) )
% 0.13/0.36 = ( ^ [X2: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ ( sup_sup @ ( set @ ( product_prod @ A @ B ) ) @ R2 @ S2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_Un_eq2
% 0.13/0.36 thf(fact_222_pred__subset__eq,axiom,
% 0.13/0.36 ! [A: $tType,R2: set @ A,S2: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( A > $o )
% 0.13/0.36 @ ^ [X2: A] : ( member @ A @ X2 @ R2 )
% 0.13/0.36 @ ^ [X2: A] : ( member @ A @ X2 @ S2 ) )
% 0.13/0.36 = ( ord_less_eq @ ( set @ A ) @ R2 @ S2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % pred_subset_eq
% 0.13/0.36 thf(fact_223_conj__subset__def,axiom,
% 0.13/0.36 ! [A: $tType,A2: set @ A,P: A > $o,Q: A > $o] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A2
% 0.13/0.36 @ ( collect @ A
% 0.13/0.36 @ ^ [X2: A] :
% 0.13/0.36 ( ( P @ X2 )
% 0.13/0.36 & ( Q @ X2 ) ) ) )
% 0.13/0.36 = ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( collect @ A @ P ) )
% 0.13/0.36 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( collect @ A @ Q ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % conj_subset_def
% 0.13/0.36 thf(fact_224_prop__restrict,axiom,
% 0.13/0.36 ! [A: $tType,X: A,Z4: set @ A,X4: set @ A,P: A > $o] :
% 0.13/0.36 ( ( member @ A @ X @ Z4 )
% 0.13/0.36 => ( ( ord_less_eq @ ( set @ A ) @ Z4
% 0.13/0.36 @ ( collect @ A
% 0.13/0.36 @ ^ [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ X4 )
% 0.13/0.36 & ( P @ X2 ) ) ) )
% 0.13/0.36 => ( P @ X ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % prop_restrict
% 0.13/0.36 thf(fact_225_ssubst__Pair__rhs,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,R3: A,S3: B,R2: set @ ( product_prod @ A @ B ),S4: B] :
% 0.13/0.36 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S3 ) @ R2 )
% 0.13/0.36 => ( ( S4 = S3 )
% 0.13/0.36 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S4 ) @ R2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % ssubst_Pair_rhs
% 0.13/0.36 thf(fact_226_Collect__restrict,axiom,
% 0.13/0.36 ! [A: $tType,X4: set @ A,P: A > $o] :
% 0.13/0.36 ( ord_less_eq @ ( set @ A )
% 0.13/0.36 @ ( collect @ A
% 0.13/0.36 @ ^ [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ X4 )
% 0.13/0.36 & ( P @ X2 ) ) )
% 0.13/0.36 @ X4 ) ).
% 0.13/0.36
% 0.13/0.36 % Collect_restrict
% 0.13/0.36 thf(fact_227_image2__eqI,axiom,
% 0.13/0.36 ! [A: $tType,C: $tType,B: $tType,B3: A,F2: B > A,X: B,C3: C,G2: B > C,A2: set @ B] :
% 0.13/0.36 ( ( B3
% 0.13/0.36 = ( F2 @ X ) )
% 0.13/0.36 => ( ( C3
% 0.13/0.36 = ( G2 @ X ) )
% 0.13/0.36 => ( ( member @ B @ X @ A2 )
% 0.13/0.36 => ( member @ ( product_prod @ A @ C ) @ ( product_Pair @ A @ C @ B3 @ C3 ) @ ( bNF_Greatest_image2 @ B @ A @ C @ A2 @ F2 @ G2 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % image2_eqI
% 0.13/0.36 thf(fact_228_Loopo_Oelims,axiom,
% 0.13/0.36 ! [X: option @ game,Y: option @ game] :
% 0.13/0.36 ( ( ( uSubst993936602_Loopo @ X )
% 0.13/0.36 = Y )
% 0.13/0.36 => ( ! [Alpha2: game] :
% 0.13/0.36 ( ( X
% 0.13/0.36 = ( some @ game @ Alpha2 ) )
% 0.13/0.36 => ( Y
% 0.13/0.36 != ( some @ game @ ( loop @ Alpha2 ) ) ) )
% 0.13/0.36 => ~ ( ( X
% 0.13/0.36 = ( none @ game ) )
% 0.13/0.36 => ( Y
% 0.13/0.36 != ( none @ game ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Loopo.elims
% 0.13/0.36 thf(fact_229_option_Oinject,axiom,
% 0.13/0.36 ! [A: $tType,X22: A,Y22: A] :
% 0.13/0.36 ( ( ( some @ A @ X22 )
% 0.13/0.36 = ( some @ A @ Y22 ) )
% 0.13/0.36 = ( X22 = Y22 ) ) ).
% 0.13/0.36
% 0.13/0.36 % option.inject
% 0.13/0.36 thf(fact_230_not__Some__eq,axiom,
% 0.13/0.36 ! [A: $tType,X: option @ A] :
% 0.13/0.36 ( ( ! [Y3: A] :
% 0.13/0.36 ( X
% 0.13/0.36 != ( some @ A @ Y3 ) ) )
% 0.13/0.36 = ( X
% 0.13/0.36 = ( none @ A ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % not_Some_eq
% 0.13/0.36 thf(fact_231_not__None__eq,axiom,
% 0.13/0.36 ! [A: $tType,X: option @ A] :
% 0.13/0.36 ( ( X
% 0.13/0.36 != ( none @ A ) )
% 0.13/0.36 = ( ? [Y3: A] :
% 0.13/0.36 ( X
% 0.13/0.36 = ( some @ A @ Y3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % not_None_eq
% 0.13/0.36 thf(fact_232_option_Ocollapse,axiom,
% 0.13/0.36 ! [A: $tType,Option: option @ A] :
% 0.13/0.36 ( ( Option
% 0.13/0.36 != ( none @ A ) )
% 0.13/0.36 => ( ( some @ A @ ( the @ A @ Option ) )
% 0.13/0.36 = Option ) ) ).
% 0.13/0.36
% 0.13/0.36 % option.collapse
% 0.13/0.36 thf(fact_233_Composeo_Ocases,axiom,
% 0.13/0.36 ! [X: product_prod @ ( option @ game ) @ ( option @ game )] :
% 0.13/0.36 ( ! [Alpha2: game,Beta2: game] :
% 0.13/0.36 ( X
% 0.13/0.36 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ ( some @ game @ Alpha2 ) @ ( some @ game @ Beta2 ) ) )
% 0.13/0.36 => ( ! [Alpha2: option @ game] :
% 0.13/0.36 ( X
% 0.13/0.36 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ Alpha2 @ ( none @ game ) ) )
% 0.13/0.36 => ~ ! [V2: game] :
% 0.13/0.36 ( X
% 0.13/0.36 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ ( none @ game ) @ ( some @ game @ V2 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Composeo.cases
% 0.13/0.36 thf(fact_234_option_Oexhaust__sel,axiom,
% 0.13/0.36 ! [A: $tType,Option: option @ A] :
% 0.13/0.36 ( ( Option
% 0.13/0.36 != ( none @ A ) )
% 0.13/0.36 => ( Option
% 0.13/0.36 = ( some @ A @ ( the @ A @ Option ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % option.exhaust_sel
% 0.13/0.36 thf(fact_235_combine__options__cases,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,X: option @ A,P: ( option @ A ) > ( option @ B ) > $o,Y: option @ B] :
% 0.13/0.36 ( ( ( X
% 0.13/0.36 = ( none @ A ) )
% 0.13/0.36 => ( P @ X @ Y ) )
% 0.13/0.36 => ( ( ( Y
% 0.13/0.36 = ( none @ B ) )
% 0.13/0.36 => ( P @ X @ Y ) )
% 0.13/0.36 => ( ! [A7: A,B7: B] :
% 0.13/0.36 ( ( X
% 0.13/0.36 = ( some @ A @ A7 ) )
% 0.13/0.36 => ( ( Y
% 0.13/0.36 = ( some @ B @ B7 ) )
% 0.13/0.36 => ( P @ X @ Y ) ) )
% 0.13/0.36 => ( P @ X @ Y ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % combine_options_cases
% 0.13/0.36 thf(fact_236_split__option__all,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ^ [P5: ( option @ A ) > $o] :
% 0.13/0.36 ! [X5: option @ A] : ( P5 @ X5 ) )
% 0.13/0.36 = ( ^ [P4: ( option @ A ) > $o] :
% 0.13/0.36 ( ( P4 @ ( none @ A ) )
% 0.13/0.36 & ! [X2: A] : ( P4 @ ( some @ A @ X2 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % split_option_all
% 0.13/0.36 thf(fact_237_split__option__ex,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ^ [P5: ( option @ A ) > $o] :
% 0.13/0.36 ? [X5: option @ A] : ( P5 @ X5 ) )
% 0.13/0.36 = ( ^ [P4: ( option @ A ) > $o] :
% 0.13/0.36 ( ( P4 @ ( none @ A ) )
% 0.13/0.36 | ? [X2: A] : ( P4 @ ( some @ A @ X2 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % split_option_ex
% 0.13/0.36 thf(fact_238_option_Oinducts,axiom,
% 0.13/0.36 ! [A: $tType,P: ( option @ A ) > $o,Option: option @ A] :
% 0.13/0.36 ( ( P @ ( none @ A ) )
% 0.13/0.36 => ( ! [X3: A] : ( P @ ( some @ A @ X3 ) )
% 0.13/0.36 => ( P @ Option ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % option.inducts
% 0.13/0.36 thf(fact_239_option_Oexhaust,axiom,
% 0.13/0.36 ! [A: $tType,Y: option @ A] :
% 0.13/0.36 ( ( Y
% 0.13/0.36 != ( none @ A ) )
% 0.13/0.36 => ~ ! [X23: A] :
% 0.13/0.36 ( Y
% 0.13/0.36 != ( some @ A @ X23 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % option.exhaust
% 0.13/0.36 thf(fact_240_option_OdiscI,axiom,
% 0.13/0.36 ! [A: $tType,Option: option @ A,X22: A] :
% 0.13/0.36 ( ( Option
% 0.13/0.36 = ( some @ A @ X22 ) )
% 0.13/0.36 => ( Option
% 0.13/0.36 != ( none @ A ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % option.discI
% 0.13/0.36 thf(fact_241_option_Odistinct_I1_J,axiom,
% 0.13/0.36 ! [A: $tType,X22: A] :
% 0.13/0.36 ( ( none @ A )
% 0.13/0.36 != ( some @ A @ X22 ) ) ).
% 0.13/0.36
% 0.13/0.36 % option.distinct(1)
% 0.13/0.36 thf(fact_242_option_Osel,axiom,
% 0.13/0.36 ! [A: $tType,X22: A] :
% 0.13/0.36 ( ( the @ A @ ( some @ A @ X22 ) )
% 0.13/0.36 = X22 ) ).
% 0.13/0.36
% 0.13/0.36 % option.sel
% 0.13/0.36 thf(fact_243_Composeo_Oinduct,axiom,
% 0.13/0.36 ! [P: ( option @ game ) > ( option @ game ) > $o,A0: option @ game,A1: option @ game] :
% 0.13/0.36 ( ! [Alpha2: game,Beta2: game] : ( P @ ( some @ game @ Alpha2 ) @ ( some @ game @ Beta2 ) )
% 0.13/0.36 => ( ! [Alpha2: option @ game] : ( P @ Alpha2 @ ( none @ game ) )
% 0.13/0.36 => ( ! [V2: game] : ( P @ ( none @ game ) @ ( some @ game @ V2 ) )
% 0.13/0.36 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Composeo.induct
% 0.13/0.36 thf(fact_244_undefg__equiv,axiom,
% 0.13/0.36 ! [Alpha: option @ game] :
% 0.13/0.36 ( ( Alpha
% 0.13/0.36 != ( none @ game ) )
% 0.13/0.36 = ( ? [G: game] :
% 0.13/0.36 ( Alpha
% 0.13/0.36 = ( some @ game @ G ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % undefg_equiv
% 0.13/0.36 thf(fact_245_Loopo_Oinduct,axiom,
% 0.13/0.36 ! [P: ( option @ game ) > $o,A0: option @ game] :
% 0.13/0.36 ( ! [Alpha2: game] : ( P @ ( some @ game @ Alpha2 ) )
% 0.13/0.36 => ( ( P @ ( none @ game ) )
% 0.13/0.36 => ( P @ A0 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Loopo.induct
% 0.13/0.36 thf(fact_246_Loopo_Ocases,axiom,
% 0.13/0.36 ! [X: option @ game] :
% 0.13/0.36 ( ! [Alpha2: game] :
% 0.13/0.36 ( X
% 0.13/0.36 != ( some @ game @ Alpha2 ) )
% 0.13/0.36 => ( X
% 0.13/0.36 = ( none @ game ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Loopo.cases
% 0.13/0.36 thf(fact_247_Loopo_Osimps_I1_J,axiom,
% 0.13/0.36 ! [Alpha: game] :
% 0.13/0.36 ( ( uSubst993936602_Loopo @ ( some @ game @ Alpha ) )
% 0.13/0.36 = ( some @ game @ ( loop @ Alpha ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Loopo.simps(1)
% 0.13/0.36 thf(fact_248_Choiceo_Osimps_I1_J,axiom,
% 0.13/0.36 ! [Alpha: game,Beta: game] :
% 0.13/0.36 ( ( uSubst1976112797hoiceo @ ( some @ game @ Alpha ) @ ( some @ game @ Beta ) )
% 0.13/0.36 = ( some @ game @ ( choice @ Alpha @ Beta ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Choiceo.simps(1)
% 0.13/0.36 thf(fact_249_Composeo_Osimps_I1_J,axiom,
% 0.13/0.36 ! [Alpha: game,Beta: game] :
% 0.13/0.36 ( ( uSubst1385204910mposeo @ ( some @ game @ Alpha ) @ ( some @ game @ Beta ) )
% 0.13/0.36 = ( some @ game @ ( compose @ Alpha @ Beta ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Composeo.simps(1)
% 0.13/0.36 thf(fact_250_Composeo_Osimps_I3_J,axiom,
% 0.13/0.36 ! [V3: game] :
% 0.13/0.36 ( ( uSubst1385204910mposeo @ ( none @ game ) @ ( some @ game @ V3 ) )
% 0.13/0.36 = ( none @ game ) ) ).
% 0.13/0.36
% 0.13/0.36 % Composeo.simps(3)
% 0.13/0.36 thf(fact_251_Choiceo_Osimps_I3_J,axiom,
% 0.13/0.36 ! [V3: game] :
% 0.13/0.36 ( ( uSubst1976112797hoiceo @ ( none @ game ) @ ( some @ game @ V3 ) )
% 0.13/0.36 = ( none @ game ) ) ).
% 0.13/0.36
% 0.13/0.36 % Choiceo.simps(3)
% 0.13/0.36 thf(fact_252_Composeo_Oelims,axiom,
% 0.13/0.36 ! [X: option @ game,Xa: option @ game,Y: option @ game] :
% 0.13/0.36 ( ( ( uSubst1385204910mposeo @ X @ Xa )
% 0.13/0.36 = Y )
% 0.13/0.36 => ( ! [Alpha2: game] :
% 0.13/0.36 ( ( X
% 0.13/0.36 = ( some @ game @ Alpha2 ) )
% 0.13/0.36 => ! [Beta2: game] :
% 0.13/0.36 ( ( Xa
% 0.13/0.36 = ( some @ game @ Beta2 ) )
% 0.13/0.36 => ( Y
% 0.13/0.36 != ( some @ game @ ( compose @ Alpha2 @ Beta2 ) ) ) ) )
% 0.13/0.36 => ( ( ( Xa
% 0.13/0.36 = ( none @ game ) )
% 0.13/0.36 => ( Y
% 0.13/0.36 != ( none @ game ) ) )
% 0.13/0.36 => ~ ( ( X
% 0.13/0.36 = ( none @ game ) )
% 0.13/0.36 => ( ? [V2: game] :
% 0.13/0.36 ( Xa
% 0.13/0.36 = ( some @ game @ V2 ) )
% 0.13/0.36 => ( Y
% 0.13/0.36 != ( none @ game ) ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Composeo.elims
% 0.13/0.36 thf(fact_253_Choiceo_Oelims,axiom,
% 0.13/0.36 ! [X: option @ game,Xa: option @ game,Y: option @ game] :
% 0.13/0.36 ( ( ( uSubst1976112797hoiceo @ X @ Xa )
% 0.13/0.36 = Y )
% 0.13/0.36 => ( ! [Alpha2: game] :
% 0.13/0.36 ( ( X
% 0.13/0.36 = ( some @ game @ Alpha2 ) )
% 0.13/0.36 => ! [Beta2: game] :
% 0.13/0.36 ( ( Xa
% 0.13/0.36 = ( some @ game @ Beta2 ) )
% 0.13/0.36 => ( Y
% 0.13/0.36 != ( some @ game @ ( choice @ Alpha2 @ Beta2 ) ) ) ) )
% 0.13/0.36 => ( ( ( Xa
% 0.13/0.36 = ( none @ game ) )
% 0.13/0.36 => ( Y
% 0.13/0.36 != ( none @ game ) ) )
% 0.13/0.36 => ~ ( ( X
% 0.13/0.36 = ( none @ game ) )
% 0.13/0.36 => ( ? [V2: game] :
% 0.13/0.36 ( Xa
% 0.13/0.36 = ( some @ game @ V2 ) )
% 0.13/0.36 => ( Y
% 0.13/0.36 != ( none @ game ) ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Choiceo.elims
% 0.13/0.36 thf(fact_254_option_Osplit__sel__asm,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,P: B > $o,F1: B,F23: A > B,Option: option @ A] :
% 0.13/0.36 ( ( P @ ( case_option @ B @ A @ F1 @ F23 @ Option ) )
% 0.13/0.36 = ( ~ ( ( ( Option
% 0.13/0.36 = ( none @ A ) )
% 0.13/0.36 & ~ ( P @ F1 ) )
% 0.13/0.36 | ( ( Option
% 0.13/0.36 = ( some @ A @ ( the @ A @ Option ) ) )
% 0.13/0.36 & ~ ( P @ ( F23 @ ( the @ A @ Option ) ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % option.split_sel_asm
% 0.13/0.36
% 0.13/0.36 % Type constructors (16)
% 0.13/0.36 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.13/0.36 ! [A9: $tType,A10: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A10 )
% 0.13/0.36 => ( semilattice_sup @ ( A9 > A10 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.13/0.36 ! [A9: $tType,A10: $tType] :
% 0.13/0.36 ( ( preorder @ A10 )
% 0.13/0.36 => ( preorder @ ( A9 > A10 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.13/0.36 ! [A9: $tType,A10: $tType] :
% 0.13/0.36 ( ( lattice @ A10 )
% 0.13/0.36 => ( lattice @ ( A9 > A10 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.13/0.36 ! [A9: $tType,A10: $tType] :
% 0.13/0.36 ( ( order @ A10 )
% 0.13/0.36 => ( order @ ( A9 > A10 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_fun___Orderings_Oord,axiom,
% 0.13/0.36 ! [A9: $tType,A10: $tType] :
% 0.13/0.36 ( ( ord @ A10 )
% 0.13/0.36 => ( ord @ ( A9 > A10 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_1,axiom,
% 0.13/0.36 ! [A9: $tType] : ( semilattice_sup @ ( set @ A9 ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_Set_Oset___Orderings_Opreorder_2,axiom,
% 0.13/0.36 ! [A9: $tType] : ( preorder @ ( set @ A9 ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_Set_Oset___Lattices_Olattice_3,axiom,
% 0.13/0.36 ! [A9: $tType] : ( lattice @ ( set @ A9 ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_Set_Oset___Orderings_Oorder_4,axiom,
% 0.13/0.36 ! [A9: $tType] : ( order @ ( set @ A9 ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_Set_Oset___Orderings_Oord_5,axiom,
% 0.13/0.36 ! [A9: $tType] : ( ord @ ( set @ A9 ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_6,axiom,
% 0.13/0.36 semilattice_sup @ $o ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_HOL_Obool___Orderings_Opreorder_7,axiom,
% 0.13/0.36 preorder @ $o ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.13/0.36 linorder @ $o ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_HOL_Obool___Lattices_Olattice_8,axiom,
% 0.13/0.36 lattice @ $o ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_HOL_Obool___Orderings_Oorder_9,axiom,
% 0.13/0.36 order @ $o ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_HOL_Obool___Orderings_Oord_10,axiom,
% 0.13/0.36 ord @ $o ).
% 0.13/0.36
% 0.13/0.36 % Conjectures (1)
% 0.13/0.36 thf(conj_0,conjecture,
% 0.13/0.36 ord_less_eq @ ( set @ variable ) @ ( sup_sup @ ( set @ variable ) @ ua @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ).
% 0.13/0.36
% 0.13/0.36 %------------------------------------------------------------------------------
% 0.13/0.36 ------------------------
% 1.99/1.26 ---- Embedded in THF ---
% 1.99/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.99/1.26 %%% Generated on Tue Feb 24 03:29:41 EST 2026
% 1.99/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.99/1.26 %%% Logic specification used:
% 1.99/1.26 %%% thf(spec, logic, $$dhol).
% 1.99/1.26
% 1.99/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.WDfDZbBGZy/DTF2DTF14850.p
% 1.99/1.26 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 1.99/1.26 thf(ty_t_Syntax_Ovariable, type, variable: $tType).
% 1.99/1.26 thf(ty_t_Option_Ooption, type, option: ($tType > $tType)).
% 1.99/1.26 thf(ty_t_Syntax_Ogame, type, game: $tType).
% 1.99/1.26 thf(ty_t_String_Ochar, type, char: $tType).
% 1.99/1.26 thf(ty_t_Syntax_Otrm, type, trm: $tType).
% 1.99/1.26 thf(ty_t_Syntax_Ofml, type, fml: $tType).
% 1.99/1.26 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 1.99/1.26 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 1.99/1.26 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 1.99/1.26 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 1.99/1.26 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: ($o))).
% 1.99/1.26 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 1.99/1.26 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 1.99/1.26 thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: ($o))).
% 1.99/1.26 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain, type, bNF_Ca1785829860lChain: (!> [A:$tType,B:$tType]: (((set @ ((product_prod @ A) @ A)) > ((A > B) > $o))))).
% 1.99/1.26 thf(sy_c_BNF__Def_Ocsquare, type, bNF_csquare: (!> [A:$tType,B:$tType,C:$tType,D:$tType]: (((set @ A) > ((B > C) > ((D > C) > ((A > B) > ((A > D) > $o)))))))).
% 1.99/1.26 thf(sy_c_BNF__Def_OfstOp, type, bNF_fstOp: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > $o)) > ((B > (C > $o)) > (((product_prod @ A) @ C) > ((product_prod @ A) @ B))))))).
% 1.99/1.26 thf(sy_c_BNF__Def_Opick__middlep, type, bNF_pick_middlep: (!> [B:$tType,A:$tType,C:$tType]: (((B > (A > $o)) > ((A > (C > $o)) > (B > (C > A))))))).
% 1.99/1.26 thf(sy_c_BNF__Def_OsndOp, type, bNF_sndOp: (!> [C:$tType,A:$tType,B:$tType]: (((C > (A > $o)) > ((A > (B > $o)) > (((product_prod @ C) @ B) > ((product_prod @ A) @ B))))))).
% 1.99/1.26 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2, type, bNF_Greatest_image2: (!> [C:$tType,A:$tType,B:$tType]: (((set @ C) > ((C > A) > ((C > B) > (set @ ((product_prod @ A) @ B)))))))).
% 1.99/1.26 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 1.99/1.26 thf(sy_c_Option_Ooption_ONone, type, none: (!> [A:$tType]: ((option @ A)))).
% 1.99/1.26 thf(sy_c_Option_Ooption_OSome, type, some: (!> [A:$tType]: ((A > (option @ A))))).
% 1.99/1.26 thf(sy_c_Option_Ooption_Ocase__option, type, case_option: (!> [B:$tType,A:$tType]: ((B > ((A > B) > ((option @ A) > B)))))).
% 1.99/1.26 thf(sy_c_Option_Ooption_Othe, type, the: (!> [A:$tType]: (((option @ A) > A)))).
% 1.99/1.26 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 1.99/1.26 thf(sy_c_Orderings_Oorder__class_OGreatest, type, order_Greatest: (!> [A:$tType]: (((A > $o) > A)))).
% 1.99/1.26 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 1.99/1.26 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 1.99/1.26 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 1.99/1.26 thf(sy_c_Product__Type_Oprod_Ofst, type, product_fst: (!> [A:$tType,B:$tType]: ((((product_prod @ A) @ B) > A)))).
% 1.99/1.26 thf(sy_c_Product__Type_Oprod_Osnd, type, product_snd: (!> [A:$tType,B:$tType]: ((((product_prod @ A) @ B) > B)))).
% 1.99/1.26 thf(sy_c_Product__Type_Oprod_Oswap, type, product_swap: (!> [A:$tType,B:$tType]: ((((product_prod @ A) @ B) > ((product_prod @ B) @ A))))).
% 1.99/1.26 thf(sy_c_Product__Type_Oscomp, type, product_scomp: (!> [A:$tType,B:$tType,C:$tType,D:$tType]: (((A > ((product_prod @ B) @ C)) > ((B > (C > D)) > (A > D)))))).
% 1.99/1.26 thf(sy_c_Relation_Orelcompp, type, relcompp: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > $o)) > ((B > (C > $o)) > (A > (C > $o))))))).
% 1.99/1.26 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 1.99/1.26 thf(sy_c_Static__Semantics_OBVG, type, static_BVG: (game > (set @ variable))).
% 1.99/1.26 thf(sy_c_Syntax_Ogame_OChoice, type, choice: (game > (game > game))).
% 1.99/1.26 thf(sy_c_Syntax_Ogame_OCompose, type, compose: (game > (game > game))).
% 1.99/1.26 thf(sy_c_Syntax_Ogame_OLoop, type, loop: (game > game)).
% 1.99/1.26 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OChoiceo, type, uSubst1976112797hoiceo: ((option @ game) > ((option @ game) > (option @ game)))).
% 1.99/1.26 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OComposeo, type, uSubst1385204910mposeo: ((option @ game) > ((option @ game) > (option @ game)))).
% 1.99/1.26 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OLoopo, type, uSubst993936602_Loopo: ((option @ game) > (option @ game))).
% 1.99/1.26 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappp, type, uSubst95898988stappp: (((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) > ((set @ variable) > (game > ((product_prod @ (set @ variable)) @ (option @ game)))))).
% 1.99/1.26 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 1.99/1.26 thf(sy_v_Ua____, type, ua: (set @ variable)).
% 1.99/1.26 thf(sy_v__092_060alpha_062_H____, type, alpha: game).
% 1.99/1.26 thf(sy_v__092_060beta_062____, type, beta: game).
% 1.99/1.26 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)))))).
% 1.99/1.26 thf(fact_0__092_060open_062U_A_092_060union_062_ABVG_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_J_A_092_060union_062_ABVG_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_A_Ifst_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_A_092_060beta_062_J_J_J_A_092_060subseteq_062_Afst_A_Iusubstappp_A_092_060sigma_062_A_Ifst_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_A_092_060beta_062_J_092_060close_062, axiom, (((ord_less_eq @ (set @ variable)) @ (((sup_sup @ (set @ variable)) @ (((sup_sup @ (set @ variable)) @ ua) @ (static_BVG @ ((the @ game) @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ ua) @ alpha)))))) @ (static_BVG @ ((the @ game) @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ ua) @ alpha))) @ beta)))))) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ ua) @ alpha))) @ beta)))).
% 1.99/1.26 thf(fact_1_fact, axiom, (((ord_less_eq @ (set @ variable)) @ (static_BVG @ ((the @ game) @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ ua) @ ((compose @ alpha) @ beta)))))) @ (((sup_sup @ (set @ variable)) @ (static_BVG @ ((the @ game) @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ ua) @ alpha))))) @ (static_BVG @ ((the @ game) @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ ua) @ alpha))) @ beta))))))).
% 1.99/1.26 thf(fact_2_IHa, axiom, (((ord_less_eq @ (set @ variable)) @ (((sup_sup @ (set @ variable)) @ ua) @ (static_BVG @ ((the @ game) @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ ua) @ alpha)))))) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ ua) @ alpha)))).
% 1.99/1.26 thf(fact_3_IHb, axiom, (((ord_less_eq @ (set @ variable)) @ (((sup_sup @ (set @ variable)) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ ua) @ alpha))) @ (static_BVG @ ((the @ game) @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ ua) @ alpha))) @ beta)))))) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ ua) @ alpha))) @ beta)))).
% 1.99/1.26 thf(fact_4_Compose_Oprems, axiom, ((((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ ua) @ ((compose @ alpha) @ beta))) != (none @ game))).
% 1.99/1.26 thf(fact_5_usubst__taboos__mon, axiom, (! [U:(set @ variable),Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),Alpha:game]: ((((ord_less_eq @ (set @ variable)) @ U) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha)))))).
% 1.99/1.26 thf(fact_6_usubstappp__fst__mon, axiom, (! [U:(set @ variable),V:(set @ variable),Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),Alpha:game]: (((((ord_less_eq @ (set @ variable)) @ U) @ V) => (((ord_less_eq @ (set @ variable)) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha))) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ V) @ Alpha))))))).
% 1.99/1.26 thf(fact_7_Compose_OIH_I2_J, axiom, (! [U:(set @ variable)]: ((((((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ U) @ beta)) != (none @ game)) => (((ord_less_eq @ (set @ variable)) @ (((sup_sup @ (set @ variable)) @ U) @ (static_BVG @ ((the @ game) @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ U) @ beta)))))) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ U) @ beta))))))).
% 1.99/1.26 thf(fact_8_Compose_OIH_I1_J, axiom, (! [U:(set @ variable)]: ((((((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ U) @ alpha)) != (none @ game)) => (((ord_less_eq @ (set @ variable)) @ (((sup_sup @ (set @ variable)) @ U) @ (static_BVG @ ((the @ game) @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ U) @ alpha)))))) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ U) @ alpha))))))).
% 1.99/1.26 thf(fact_9_Un__subset__iff, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ C2) = ((((ord_less_eq @ (set @ A)) @ A2) @ C2) & (((ord_less_eq @ (set @ A)) @ B2) @ C2)))))).
% 1.99/1.26 thf(fact_10_le__sup__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z) = ((((ord_less_eq @ A) @ X) @ Z) & (((ord_less_eq @ A) @ Y) @ Z))))))))).
% 1.99/1.26 thf(fact_11_sup_Obounded__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B3:A,C3:A,A3:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ B3) @ C3)) @ A3) = ((((ord_less_eq @ A) @ B3) @ A3) & (((ord_less_eq @ A) @ C3) @ A3))))))))).
% 1.99/1.26 thf(fact_12_BVG__compose, axiom, (! [Alpha:game,Beta:game]: ((((ord_less_eq @ (set @ variable)) @ (static_BVG @ ((compose @ Alpha) @ Beta))) @ (((sup_sup @ (set @ variable)) @ (static_BVG @ Alpha)) @ (static_BVG @ Beta)))))).
% 1.99/1.26 thf(fact_13_game_Oinject_I5_J, axiom, (! [X51:game,X52:game,Y51:game,Y52:game]: (((((compose @ X51) @ X52) = ((compose @ Y51) @ Y52)) = ((X51 = Y51) & (X52 = Y52)))))).
% 1.99/1.26 thf(fact_14_UnCI, axiom, (! [A:$tType,C3:A,B2:(set @ A),A2:(set @ A)]: ((((~ ((((member @ A) @ C3) @ B2))) => (((member @ A) @ C3) @ A2)) => (((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 1.99/1.26 thf(fact_15_union__or, axiom, (! [A:$tType,C3:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) = ((((member @ A) @ C3) @ A2) | (((member @ A) @ C3) @ B2)))))).
% 1.99/1.26 thf(fact_16_sup__apply, axiom, (! [B:$tType,A:$tType]: (((semilattice_sup @ B) => ((sup_sup @ (A > B)) = (^ [F:(A > B),G:(A > B),X2:A]: ((((sup_sup @ B) @ (F @ X2)) @ (G @ X2))))))))).
% 1.99/1.26 thf(fact_17_sup_Oidem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A3:A]: (((((sup_sup @ A) @ A3) @ A3) = A3))))))).
% 1.99/1.26 thf(fact_18_sup__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X:A]: (((((sup_sup @ A) @ X) @ X) = X))))))).
% 1.99/1.26 thf(fact_19_subset__antisym, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((ord_less_eq @ (set @ A)) @ B2) @ A2) => (A2 = B2)))))).
% 1.99/1.26 thf(fact_20_subsetI, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A2) => (((member @ A) @ X3) @ B2)))) => (((ord_less_eq @ (set @ A)) @ A2) @ B2))))).
% 1.99/1.26 thf(fact_21_sup_Oright__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A3:A,B3:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A3) @ B3)) @ B3) = (((sup_sup @ A) @ A3) @ B3)))))))).
% 1.99/1.26 thf(fact_22_sup__left__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = (((sup_sup @ A) @ X) @ Y)))))))).
% 1.99/1.26 thf(fact_23_sup_Oleft__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A3:A,B3:A]: (((((sup_sup @ A) @ A3) @ (((sup_sup @ A) @ A3) @ B3)) = (((sup_sup @ A) @ A3) @ B3)))))))).
% 1.99/1.26 thf(fact_24_usubstappp__det, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Alpha:game,V:(set @ variable)]: ((((((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha)) != (none @ game)) => (((((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ V) @ Alpha)) != (none @ game)) => ((((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha)) = (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ V) @ Alpha)))))))).
% 1.99/1.26 thf(fact_25_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X2:A]: (((P @ X2) => (Q @ X2)))))))).
% 1.99/1.26 thf(fact_26_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y2:(set @ A),Z2:(set @ A)]: ((Y2 = Z2))) = (^ [A4:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) & (((ord_less_eq @ (set @ A)) @ B4) @ A4)))))))).
% 1.99/1.26 thf(fact_27_subset__trans, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((ord_less_eq @ (set @ A)) @ B2) @ C2) => (((ord_less_eq @ (set @ A)) @ A2) @ C2)))))).
% 1.99/1.26 thf(fact_28_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) => (Q @ X3)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 1.99/1.26 thf(fact_29_subset__refl, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ A2)))).
% 1.99/1.26 thf(fact_30_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B4:(set @ A)]: ((! [T2:A]: (((((member @ A) @ T2) @ A4) => (((member @ A) @ T2) @ B4)))))))))).
% 1.99/1.26 thf(fact_31_equalityD2, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((A2 = B2) => (((ord_less_eq @ (set @ A)) @ B2) @ A2))))).
% 1.99/1.26 thf(fact_32_equalityD1, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((A2 = B2) => (((ord_less_eq @ (set @ A)) @ A2) @ B2))))).
% 1.99/1.26 thf(fact_33_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B4:(set @ A)]: ((! [X2:A]: (((((member @ A) @ X2) @ A4) => (((member @ A) @ X2) @ B4)))))))))).
% 1.99/1.26 thf(fact_34_equalityE, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((A2 = B2) => (~ (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => (~ ((((ord_less_eq @ (set @ A)) @ B2) @ A2)))))))))).
% 1.99/1.26 thf(fact_35_subsetD, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((member @ A) @ C3) @ A2) => (((member @ A) @ C3) @ B2)))))).
% 1.99/1.26 thf(fact_36_in__mono, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((member @ A) @ X) @ A2) => (((member @ A) @ X) @ B2)))))).
% 1.99/1.26 thf(fact_37_sup__left__commute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X) @ Z))))))))).
% 1.99/1.26 thf(fact_38_sup_Oleft__commute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B3:A,A3:A,C3:A]: (((((sup_sup @ A) @ B3) @ (((sup_sup @ A) @ A3) @ C3)) = (((sup_sup @ A) @ A3) @ (((sup_sup @ A) @ B3) @ C3))))))))).
% 1.99/1.26 thf(fact_39_sup__commute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((sup_sup @ A) = (^ [X2:A,Y3:A]: ((((sup_sup @ A) @ Y3) @ X2)))))))).
% 1.99/1.26 thf(fact_40_sup_Ocommute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((sup_sup @ A) = (^ [A5:A,B5:A]: ((((sup_sup @ A) @ B5) @ A5)))))))).
% 1.99/1.26 thf(fact_41_sup__assoc, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z) = (((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z))))))))).
% 1.99/1.26 thf(fact_42_sup_Oassoc, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A3:A,B3:A,C3:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A3) @ B3)) @ C3) = (((sup_sup @ A) @ A3) @ (((sup_sup @ A) @ B3) @ C3))))))))).
% 1.99/1.26 thf(fact_43_boolean__algebra__cancel_Osup2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B2:A,K:A,B3:A,A3:A]: (((B2 = (((sup_sup @ A) @ K) @ B3)) => ((((sup_sup @ A) @ A3) @ B2) = (((sup_sup @ A) @ K) @ (((sup_sup @ A) @ A3) @ B3)))))))))).
% 1.99/1.26 thf(fact_44_boolean__algebra__cancel_Osup1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,K:A,A3:A,B3:A]: (((A2 = (((sup_sup @ A) @ K) @ A3)) => ((((sup_sup @ A) @ A2) @ B3) = (((sup_sup @ A) @ K) @ (((sup_sup @ A) @ A3) @ B3)))))))))).
% 1.99/1.26 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P)) = (P @ A3))))).
% 1.99/1.26 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A2)))) = A2)))).
% 1.99/1.26 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 1.99/1.26 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F2:(A > B),G2:(A > B)]: (((! [X3:A]: (((F2 @ X3) = (G2 @ X3)))) => (F2 = G2))))).
% 1.99/1.26 thf(fact_49_sup__fun__def, axiom, (! [B:$tType,A:$tType]: (((semilattice_sup @ B) => ((sup_sup @ (A > B)) = (^ [F:(A > B),G:(A > B),X2:A]: ((((sup_sup @ B) @ (F @ X2)) @ (G @ X2))))))))).
% 1.99/1.26 thf(fact_50_inf__sup__aci_I5_J, axiom, (! [A:$tType]: (((lattice @ A) => ((sup_sup @ A) = (^ [X2:A,Y3:A]: ((((sup_sup @ A) @ Y3) @ X2)))))))).
% 1.99/1.26 thf(fact_51_inf__sup__aci_I6_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z) = (((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z))))))))).
% 1.99/1.26 thf(fact_52_inf__sup__aci_I7_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X) @ Z))))))))).
% 1.99/1.26 thf(fact_53_inf__sup__aci_I8_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = (((sup_sup @ A) @ X) @ Y)))))))).
% 1.99/1.26 thf(fact_54_not__union__or, axiom, (! [A:$tType,X:A,A2:(set @ A),B2:(set @ A)]: (((~ ((((member @ A) @ X) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))) = ((~ ((((member @ A) @ X) @ A2))) & (~ ((((member @ A) @ X) @ B2)))))))).
% 1.99/1.26 thf(fact_55_Un__left__commute, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B2) @ C2)) = (((sup_sup @ (set @ A)) @ B2) @ (((sup_sup @ (set @ A)) @ A2) @ C2)))))).
% 1.99/1.26 thf(fact_56_Un__left__absorb, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) = (((sup_sup @ (set @ A)) @ A2) @ B2))))).
% 1.99/1.26 thf(fact_57_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A4:(set @ A),B4:(set @ A)]: ((((sup_sup @ (set @ A)) @ B4) @ A4))))))).
% 1.99/1.26 thf(fact_58_Un__absorb, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ A2) = A2)))).
% 1.99/1.26 thf(fact_59_Un__assoc, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ C2) = (((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B2) @ C2)))))).
% 1.99/1.26 thf(fact_60_ball__Un, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),P:(A > $o)]: (((! [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) => (P @ X2)))) = ((! [X2:A]: (((((member @ A) @ X2) @ A2) => (P @ X2)))) & (! [X2:A]: (((((member @ A) @ X2) @ B2) => (P @ X2))))))))).
% 1.99/1.26 thf(fact_61_bex__Un, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) & (P @ X2)))) = ((? [X2:A]: (((((member @ A) @ X2) @ A2) & (P @ X2)))) | (? [X2:A]: (((((member @ A) @ X2) @ B2) & (P @ X2))))))))).
% 1.99/1.26 thf(fact_62_UnI2, axiom, (! [A:$tType,C3:A,B2:(set @ A),A2:(set @ A)]: (((((member @ A) @ C3) @ B2) => (((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 1.99/1.26 thf(fact_63_UnI1, axiom, (! [A:$tType,C3:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C3) @ A2) => (((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 1.99/1.26 thf(fact_64_UnE, axiom, (! [A:$tType,C3:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) => ((~ ((((member @ A) @ C3) @ A2))) => (((member @ A) @ C3) @ B2)))))).
% 1.99/1.26 thf(fact_65_usubstappp__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))))),Alpha:game]: (((((ord_less_eq @ (set @ variable)) @ V) @ U) => (((((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha)) != (none @ game)) => ((((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha)) = (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ V) @ Alpha)))))))).
% 1.99/1.26 thf(fact_66_sup_OcoboundedI2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C3:A,B3:A,A3:A]: (((((ord_less_eq @ A) @ C3) @ B3) => (((ord_less_eq @ A) @ C3) @ (((sup_sup @ A) @ A3) @ B3))))))))).
% 1.99/1.26 thf(fact_67_sup_OcoboundedI1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C3:A,A3:A,B3:A]: (((((ord_less_eq @ A) @ C3) @ A3) => (((ord_less_eq @ A) @ C3) @ (((sup_sup @ A) @ A3) @ B3))))))))).
% 1.99/1.26 thf(fact_68_sup_Oabsorb__iff2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less_eq @ A) = (^ [A5:A,B5:A]: (((((sup_sup @ A) @ A5) @ B5) = B5)))))))).
% 1.99/1.26 thf(fact_69_sup_Oabsorb__iff1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less_eq @ A) = (^ [B5:A,A5:A]: (((((sup_sup @ A) @ A5) @ B5) = A5)))))))).
% 1.99/1.26 thf(fact_70_sup_Ocobounded2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B3:A,A3:A]: ((((ord_less_eq @ A) @ B3) @ (((sup_sup @ A) @ A3) @ B3)))))))).
% 1.99/1.26 thf(fact_71_sup_Ocobounded1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A3:A,B3:A]: ((((ord_less_eq @ A) @ A3) @ (((sup_sup @ A) @ A3) @ B3)))))))).
% 1.99/1.26 thf(fact_72_sup_Oorder__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less_eq @ A) = (^ [B5:A,A5:A]: ((A5 = (((sup_sup @ A) @ A5) @ B5))))))))).
% 1.99/1.26 thf(fact_73_sup_OboundedI, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B3:A,A3:A,C3:A]: (((((ord_less_eq @ A) @ B3) @ A3) => ((((ord_less_eq @ A) @ C3) @ A3) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ B3) @ C3)) @ A3))))))))).
% 1.99/1.26 thf(fact_74_sup_OboundedE, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B3:A,C3:A,A3:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ B3) @ C3)) @ A3) => (~ (((((ord_less_eq @ A) @ B3) @ A3) => (~ ((((ord_less_eq @ A) @ C3) @ A3))))))))))))).
% 1.99/1.26 thf(fact_75_sup__absorb2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((sup_sup @ A) @ X) @ Y) = Y)))))))).
% 1.99/1.26 thf(fact_76_sup__absorb1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((sup_sup @ A) @ X) @ Y) = X)))))))).
% 1.99/1.26 thf(fact_77_sup_Oabsorb2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((((sup_sup @ A) @ A3) @ B3) = B3)))))))).
% 1.99/1.26 thf(fact_78_sup_Oabsorb1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B3:A,A3:A]: (((((ord_less_eq @ A) @ B3) @ A3) => ((((sup_sup @ A) @ A3) @ B3) = A3)))))))).
% 1.99/1.26 thf(fact_79_sup__unique, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [F2:(A > (A > A)),X:A,Y:A]: (((! [X3:A,Y4:A]: ((((ord_less_eq @ A) @ X3) @ ((F2 @ X3) @ Y4)))) => ((! [X3:A,Y4:A]: ((((ord_less_eq @ A) @ Y4) @ ((F2 @ X3) @ Y4)))) => ((! [X3:A,Y4:A,Z3:A]: (((((ord_less_eq @ A) @ Y4) @ X3) => ((((ord_less_eq @ A) @ Z3) @ X3) => (((ord_less_eq @ A) @ ((F2 @ Y4) @ Z3)) @ X3))))) => ((((sup_sup @ A) @ X) @ Y) = ((F2 @ X) @ Y))))))))))).
% 1.99/1.26 thf(fact_80_sup_OorderI, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A3:A,B3:A]: (((A3 = (((sup_sup @ A) @ A3) @ B3)) => (((ord_less_eq @ A) @ B3) @ A3)))))))).
% 1.99/1.26 thf(fact_81_sup_OorderE, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B3:A,A3:A]: (((((ord_less_eq @ A) @ B3) @ A3) => (A3 = (((sup_sup @ A) @ A3) @ B3))))))))).
% 1.99/1.26 thf(fact_82_le__iff__sup, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less_eq @ A) = (^ [X2:A,Y3:A]: (((((sup_sup @ A) @ X2) @ Y3) = Y3)))))))).
% 1.99/1.26 thf(fact_83_sup__least, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [Y:A,X:A,Z:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ Z) @ X) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ Y) @ Z)) @ X))))))))).
% 1.99/1.26 thf(fact_84_sup__mono, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A3:A,C3:A,B3:A,D2:A]: (((((ord_less_eq @ A) @ A3) @ C3) => ((((ord_less_eq @ A) @ B3) @ D2) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ A3) @ B3)) @ (((sup_sup @ A) @ C3) @ D2)))))))))).
% 1.99/1.26 thf(fact_85_sup_Omono, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C3:A,A3:A,D2:A,B3:A]: (((((ord_less_eq @ A) @ C3) @ A3) => ((((ord_less_eq @ A) @ D2) @ B3) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ C3) @ D2)) @ (((sup_sup @ A) @ A3) @ B3)))))))))).
% 1.99/1.26 thf(fact_86_le__supI2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X:A,B3:A,A3:A]: (((((ord_less_eq @ A) @ X) @ B3) => (((ord_less_eq @ A) @ X) @ (((sup_sup @ A) @ A3) @ B3))))))))).
% 1.99/1.26 thf(fact_87_le__supI1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X:A,A3:A,B3:A]: (((((ord_less_eq @ A) @ X) @ A3) => (((ord_less_eq @ A) @ X) @ (((sup_sup @ A) @ A3) @ B3))))))))).
% 1.99/1.26 thf(fact_88_sup__ge2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [Y:A,X:A]: ((((ord_less_eq @ A) @ Y) @ (((sup_sup @ A) @ X) @ Y)))))))).
% 1.99/1.26 thf(fact_89_sup__ge1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X:A,Y:A]: ((((ord_less_eq @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)))))))).
% 1.99/1.26 thf(fact_90_le__supI, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A3:A,X:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ X) => ((((ord_less_eq @ A) @ B3) @ X) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ A3) @ B3)) @ X))))))))).
% 1.99/1.26 thf(fact_91_le__supE, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A3:A,B3:A,X:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ A3) @ B3)) @ X) => (~ (((((ord_less_eq @ A) @ A3) @ X) => (~ ((((ord_less_eq @ A) @ B3) @ X))))))))))))).
% 1.99/1.26 thf(fact_92_inf__sup__ord_I3_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X:A,Y:A]: ((((ord_less_eq @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)))))))).
% 1.99/1.26 thf(fact_93_inf__sup__ord_I4_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [Y:A,X:A]: ((((ord_less_eq @ A) @ Y) @ (((sup_sup @ A) @ X) @ Y)))))))).
% 1.99/1.26 thf(fact_94_subset__Un__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ B4) = B4))))))).
% 1.99/1.26 thf(fact_95_subset__UnE, axiom, (! [A:$tType,C2:(set @ A),A2:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) => (~ ((! [A6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ A2) => (! [B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B6) @ B2) => (C2 != (((sup_sup @ (set @ A)) @ A6) @ B6)))))))))))))).
% 1.99/1.26 thf(fact_96_Un__absorb2, axiom, (! [A:$tType,B2:(set @ A),A2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B2) @ A2) => ((((sup_sup @ (set @ A)) @ A2) @ B2) = A2))))).
% 1.99/1.26 thf(fact_97_Un__absorb1, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((sup_sup @ (set @ A)) @ A2) @ B2) = B2))))).
% 1.99/1.26 thf(fact_98_Un__upper2, axiom, (! [A:$tType,B2:(set @ A),A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ B2) @ (((sup_sup @ (set @ A)) @ A2) @ B2))))).
% 1.99/1.26 thf(fact_99_Un__upper1, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ A2) @ B2))))).
% 1.99/1.26 thf(fact_100_Un__least, axiom, (! [A:$tType,A2:(set @ A),C2:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ C2) => ((((ord_less_eq @ (set @ A)) @ B2) @ C2) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ C2)))))).
% 1.99/1.26 thf(fact_101_Un__mono, axiom, (! [A:$tType,A2:(set @ A),C2:(set @ A),B2:(set @ A),D3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ C2) => ((((ord_less_eq @ (set @ A)) @ B2) @ D3) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ (((sup_sup @ (set @ A)) @ C2) @ D3))))))).
% 1.99/1.26 thf(fact_102_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 1.99/1.26 thf(fact_103_option_Oexpand, axiom, (! [A:$tType,Option:(option @ A),Option2:(option @ A)]: ((((Option = (none @ A)) = (Option2 = (none @ A))) => (((Option != (none @ A)) => ((Option2 != (none @ A)) => (((the @ A) @ Option) = ((the @ A) @ Option2)))) => (Option = Option2)))))).
% 1.99/1.26 thf(fact_104_prod__eq__iff, axiom, (! [B:$tType,A:$tType]: (((^ [Y2:((product_prod @ A) @ B),Z2:((product_prod @ A) @ B)]: ((Y2 = Z2))) = (^ [S:((product_prod @ A) @ B),T2:((product_prod @ A) @ B)]: ((((((product_fst @ A) @ B) @ S) = (((product_fst @ A) @ B) @ T2)) & ((((product_snd @ A) @ B) @ S) = (((product_snd @ A) @ B) @ T2))))))))).
% 1.99/1.26 thf(fact_105_prod_Oexpand, axiom, (! [B:$tType,A:$tType,Prod:((product_prod @ A) @ B),Prod2:((product_prod @ A) @ B)]: (((((((product_fst @ A) @ B) @ Prod) = (((product_fst @ A) @ B) @ Prod2)) & ((((product_snd @ A) @ B) @ Prod) = (((product_snd @ A) @ B) @ Prod2))) => (Prod = Prod2))))).
% 1.99/1.26 thf(fact_106_exE__realizer_H, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),P2:((product_prod @ B) @ A)]: ((((P @ (((product_snd @ B) @ A) @ P2)) @ (((product_fst @ B) @ A) @ P2)) => (~ ((! [X3:B,Y4:A]: ((~ (((P @ Y4) @ X3))))))))))).
% 1.99/1.26 thf(fact_107_prod__eqI, axiom, (! [B:$tType,A:$tType,P2:((product_prod @ A) @ B),Q2:((product_prod @ A) @ B)]: ((((((product_fst @ A) @ B) @ P2) = (((product_fst @ A) @ B) @ Q2)) => (((((product_snd @ A) @ B) @ P2) = (((product_snd @ A) @ B) @ Q2)) => (P2 = Q2)))))).
% 1.99/1.26 thf(fact_108_usubstappp__loop__conv, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Alpha:game]: ((((((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ (loop @ Alpha))) != (none @ game)) => (((((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha)) != (none @ game)) & ((((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha))) @ Alpha)) != (none @ game))))))).
% 1.99/1.26 thf(fact_109_BVG__choice, axiom, (! [Alpha:game,Beta:game]: ((((ord_less_eq @ (set @ variable)) @ (static_BVG @ ((choice @ Alpha) @ Beta))) @ (((sup_sup @ (set @ variable)) @ (static_BVG @ Alpha)) @ (static_BVG @ Beta)))))).
% 1.99/1.26 thf(fact_110_usubstappp__choice__conv, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Alpha:game,Beta:game]: ((((((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ ((choice @ Alpha) @ Beta))) != (none @ game)) => (((((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha)) != (none @ game)) & ((((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Beta)) != (none @ game))))))).
% 1.99/1.26 thf(fact_111_game_Oinject_I6_J, axiom, (! [X6:game,Y6:game]: ((((loop @ X6) = (loop @ Y6)) = (X6 = Y6))))).
% 1.99/1.26 thf(fact_112_game_Oinject_I4_J, axiom, (! [X41:game,X42:game,Y41:game,Y42:game]: (((((choice @ X41) @ X42) = ((choice @ Y41) @ Y42)) = ((X41 = Y41) & (X42 = Y42)))))).
% 1.99/1.26 thf(fact_113_game_Odistinct_I39_J, axiom, (! [X41:game,X42:game,X6:game]: ((((choice @ X41) @ X42) != (loop @ X6))))).
% 1.99/1.26 thf(fact_114_game_Odistinct_I45_J, axiom, (! [X51:game,X52:game,X6:game]: ((((compose @ X51) @ X52) != (loop @ X6))))).
% 1.99/1.26 thf(fact_115_game_Odistinct_I37_J, axiom, (! [X41:game,X42:game,X51:game,X52:game]: ((((choice @ X41) @ X42) != ((compose @ X51) @ X52))))).
% 1.99/1.26 thf(fact_116_BVG__loop, axiom, (! [Alpha:game]: ((((ord_less_eq @ (set @ variable)) @ (static_BVG @ (loop @ Alpha))) @ (static_BVG @ Alpha))))).
% 1.99/1.26 thf(fact_117_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F2:(A > B),G2:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F2) @ G2) => (((ord_less_eq @ B) @ (F2 @ X)) @ (G2 @ X))))))))).
% 1.99/1.26 thf(fact_118_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F2:(A > B),G2:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F2) @ G2) => (((ord_less_eq @ B) @ (F2 @ X)) @ (G2 @ X))))))))).
% 1.99/1.26 thf(fact_119_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F2:(A > B),G2:(A > B)]: (((! [X3:A]: ((((ord_less_eq @ B) @ (F2 @ X3)) @ (G2 @ X3)))) => (((ord_less_eq @ (A > B)) @ F2) @ G2)))))))).
% 1.99/1.26 thf(fact_120_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F:(A > B),G:(A > B)]: ((! [X2:A]: ((((ord_less_eq @ B) @ (F @ X2)) @ (G @ X2))))))))))).
% 1.99/1.26 thf(fact_121_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A3:A,F2:(B > A),B3:B,C3:B]: (((((ord_less_eq @ A) @ A3) @ (F2 @ B3)) => ((((ord_less_eq @ B) @ B3) @ C3) => ((! [X3:B,Y4:B]: (((((ord_less_eq @ B) @ X3) @ Y4) => (((ord_less_eq @ A) @ (F2 @ X3)) @ (F2 @ Y4))))) => (((ord_less_eq @ A) @ A3) @ (F2 @ C3))))))))))).
% 1.99/1.26 thf(fact_122_order__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A3:A,B3:A,F2:(A > C),C3:C]: (((((ord_less_eq @ A) @ A3) @ B3) => ((((ord_less_eq @ C) @ (F2 @ B3)) @ C3) => ((! [X3:A,Y4:A]: (((((ord_less_eq @ A) @ X3) @ Y4) => (((ord_less_eq @ C) @ (F2 @ X3)) @ (F2 @ Y4))))) => (((ord_less_eq @ C) @ (F2 @ A3)) @ C3)))))))))).
% 1.99/1.26 thf(fact_123_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A3:A,F2:(B > A),B3:B,C3:B]: (((A3 = (F2 @ B3)) => ((((ord_less_eq @ B) @ B3) @ C3) => ((! [X3:B,Y4:B]: (((((ord_less_eq @ B) @ X3) @ Y4) => (((ord_less_eq @ A) @ (F2 @ X3)) @ (F2 @ Y4))))) => (((ord_less_eq @ A) @ A3) @ (F2 @ C3))))))))))).
% 1.99/1.26 thf(fact_124_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A3:A,B3:A,F2:(A > B),C3:B]: (((((ord_less_eq @ A) @ A3) @ B3) => (((F2 @ B3) = C3) => ((! [X3:A,Y4:A]: (((((ord_less_eq @ A) @ X3) @ Y4) => (((ord_less_eq @ B) @ (F2 @ X3)) @ (F2 @ Y4))))) => (((ord_less_eq @ B) @ (F2 @ A3)) @ C3)))))))))).
% 1.99/1.26 thf(fact_125_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y2:A,Z2:A]: ((Y2 = Z2))) = (^ [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) & (((ord_less_eq @ A) @ Y3) @ X2))))))))).
% 1.99/1.26 thf(fact_126_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ X) => (X = Y))))))))).
% 1.99/1.26 thf(fact_127_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less_eq @ A) @ Y) @ X)))))))).
% 1.99/1.26 thf(fact_128_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((X = Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 1.99/1.26 thf(fact_129_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 1.99/1.26 thf(fact_130_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B3:A,C3:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((((ord_less_eq @ A) @ B3) @ C3) => (((ord_less_eq @ A) @ A3) @ C3))))))))).
% 1.99/1.26 thf(fact_131_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A,Z:A]: ((((((ord_less_eq @ A) @ X) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z)))) => (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z)))) => (((((ord_less_eq @ A) @ X) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ Y)))) => (((((ord_less_eq @ A) @ Z) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X)))) => (((((ord_less_eq @ A) @ Y) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ X)))) => (~ (((((ord_less_eq @ A) @ Z) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y))))))))))))))))).
% 1.99/1.26 thf(fact_132_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 1.99/1.26 thf(fact_133_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y2:A,Z2:A]: ((Y2 = Z2))) = (^ [A5:A,B5:A]: (((((ord_less_eq @ A) @ A5) @ B5) & (((ord_less_eq @ A) @ B5) @ A5))))))))).
% 1.99/1.26 thf(fact_134_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B3:A,C3:A]: (((A3 = B3) => ((((ord_less_eq @ A) @ B3) @ C3) => (((ord_less_eq @ A) @ A3) @ C3))))))))).
% 1.99/1.26 thf(fact_135_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B3:A,C3:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((B3 = C3) => (((ord_less_eq @ A) @ A3) @ C3))))))))).
% 1.99/1.26 thf(fact_136_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((((ord_less_eq @ A) @ B3) @ A3) => (A3 = B3))))))))).
% 1.99/1.26 thf(fact_137_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z) => (((ord_less_eq @ A) @ X) @ Z))))))))).
% 1.99/1.26 thf(fact_138_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A]: ((((ord_less_eq @ A) @ A3) @ A3))))))).
% 1.99/1.26 thf(fact_139_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A3:A,B3:A]: (((! [A7:A,B7:A]: (((((ord_less_eq @ A) @ A7) @ B7) => ((P @ A7) @ B7)))) => ((! [A7:A,B7:A]: ((((P @ B7) @ A7) => ((P @ A7) @ B7)))) => ((P @ A3) @ B3))))))))).
% 1.99/1.26 thf(fact_140_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A3:A,C3:A]: (((((ord_less_eq @ A) @ B3) @ A3) => ((((ord_less_eq @ A) @ C3) @ B3) => (((ord_less_eq @ A) @ C3) @ A3))))))))).
% 1.99/1.26 thf(fact_141_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y2:A,Z2:A]: ((Y2 = Z2))) = (^ [A5:A,B5:A]: (((((ord_less_eq @ A) @ B5) @ A5) & (((ord_less_eq @ A) @ A5) @ B5))))))))).
% 1.99/1.26 thf(fact_142_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A3:A]: (((((ord_less_eq @ A) @ B3) @ A3) => ((((ord_less_eq @ A) @ A3) @ B3) => (A3 = B3))))))))).
% 1.99/1.26 thf(fact_143_fst__swap, axiom, (! [A:$tType,B:$tType,X:((product_prod @ B) @ A)]: (((((product_fst @ A) @ B) @ (((product_swap @ B) @ A) @ X)) = (((product_snd @ B) @ A) @ X))))).
% 1.99/1.26 thf(fact_144_snd__swap, axiom, (! [B:$tType,A:$tType,X:((product_prod @ A) @ B)]: (((((product_snd @ B) @ A) @ (((product_swap @ A) @ B) @ X)) = (((product_fst @ A) @ B) @ X))))).
% 1.99/1.26 thf(fact_145_usubstappp__choice, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Alpha:game,Beta:game]: (((((uSubst95898988stappp @ Sigma) @ U) @ ((choice @ Alpha) @ Beta)) = ((((product_Pair @ (set @ variable)) @ (option @ game)) @ (((sup_sup @ (set @ variable)) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha))) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Beta)))) @ ((uSubst1976112797hoiceo @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha))) @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Beta)))))))).
% 1.99/1.26 thf(fact_146_GreatestI2__order, axiom, (! [A:$tType]: (((order @ A) => (! [P:(A > $o),X:A,Q:(A > $o)]: (((P @ X) => ((! [Y4:A]: (((P @ Y4) => (((ord_less_eq @ A) @ Y4) @ X)))) => ((! [X3:A]: (((P @ X3) => ((! [Y5:A]: (((P @ Y5) => (((ord_less_eq @ A) @ Y5) @ X3)))) => (Q @ X3))))) => (Q @ ((order_Greatest @ A) @ P))))))))))).
% 1.99/1.26 thf(fact_147_Greatest__equality, axiom, (! [A:$tType]: (((order @ A) => (! [P:(A > $o),X:A]: (((P @ X) => ((! [Y4:A]: (((P @ Y4) => (((ord_less_eq @ A) @ Y4) @ X)))) => (((order_Greatest @ A) @ P) = X))))))))).
% 1.99/1.26 thf(fact_148_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A3:A,B3:B,A8:A,B8:B]: (((((((product_Pair @ A) @ B) @ A3) @ B3) = ((((product_Pair @ A) @ B) @ A8) @ B8)) = ((A3 = A8) & (B3 = B8)))))).
% 1.99/1.26 thf(fact_149_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X22:B,Y1:A,Y22:B]: (((((((product_Pair @ A) @ B) @ X1) @ X22) = ((((product_Pair @ A) @ B) @ Y1) @ Y22)) = ((X1 = Y1) & (X22 = Y22)))))).
% 1.99/1.26 thf(fact_150_swap__swap, axiom, (! [B:$tType,A:$tType,P2:((product_prod @ A) @ B)]: (((((product_swap @ B) @ A) @ (((product_swap @ A) @ B) @ P2)) = P2)))).
% 1.99/1.26 thf(fact_151_swap__simp, axiom, (! [A:$tType,B:$tType,X:B,Y:A]: (((((product_swap @ B) @ A) @ ((((product_Pair @ B) @ A) @ X) @ Y)) = ((((product_Pair @ A) @ B) @ Y) @ X))))).
% 1.99/1.26 thf(fact_152_prod_Ocollapse, axiom, (! [B:$tType,A:$tType,Prod:((product_prod @ A) @ B)]: ((((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ Prod)) @ (((product_snd @ A) @ B) @ Prod)) = Prod)))).
% 1.99/1.26 thf(fact_153_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A7:A,B7:B]: ((P @ ((((product_Pair @ A) @ B) @ A7) @ B7)))) => (P @ Prod))))).
% 1.99/1.26 thf(fact_154_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A7:A,B7:B]: ((Y != ((((product_Pair @ A) @ B) @ A7) @ B7))))))))).
% 1.99/1.26 thf(fact_155_prod__induct7, axiom, (! [G3:$tType,F3:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))))))]: (((! [A7:A,B7:B,C4:C,D4:D,E2:E,F4:F3,G4:G3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))))) @ A7) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))))) @ B7) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))) @ C4) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))) @ D4) @ ((((product_Pair @ E) @ ((product_prod @ F3) @ G3)) @ E2) @ ((((product_Pair @ F3) @ G3) @ F4) @ G4))))))))) => (P @ X))))).
% 1.99/1.26 thf(fact_156_prod__induct6, axiom, (! [F3:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))))]: (((! [A7:A,B7:B,C4:C,D4:D,E2:E,F4:F3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))))) @ A7) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))) @ B7) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))) @ C4) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F3)) @ D4) @ ((((product_Pair @ E) @ F3) @ E2) @ F4)))))))) => (P @ X))))).
% 1.99/1.26 thf(fact_157_prod__induct5, axiom, (! [E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: (((! [A7:A,B7:B,C4:C,D4:D,E2:E]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A7) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B7) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C4) @ ((((product_Pair @ D) @ E) @ D4) @ E2))))))) => (P @ X))))).
% 1.99/1.26 thf(fact_158_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A7:A,B7:B,C4:C,D4:D]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A7) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B7) @ ((((product_Pair @ C) @ D) @ C4) @ D4)))))) => (P @ X))))).
% 1.99/1.26 thf(fact_159_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A7:A,B7:B,C4:C]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A7) @ ((((product_Pair @ B) @ C) @ B7) @ C4))))) => (P @ X))))).
% 1.99/1.26 thf(fact_160_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F3:$tType,G3:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))))))]: ((~ ((! [A7:A,B7:B,C4:C,D4:D,E2:E,F4:F3,G4:G3]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))))) @ A7) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))))) @ B7) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))) @ C4) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))) @ D4) @ ((((product_Pair @ E) @ ((product_prod @ F3) @ G3)) @ E2) @ ((((product_Pair @ F3) @ G3) @ F4) @ G4)))))))))))))).
% 1.99/1.26 thf(fact_161_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F3:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))))]: ((~ ((! [A7:A,B7:B,C4:C,D4:D,E2:E,F4:F3]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))))) @ A7) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))) @ B7) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))) @ C4) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F3)) @ D4) @ ((((product_Pair @ E) @ F3) @ E2) @ F4))))))))))))).
% 1.99/1.26 thf(fact_162_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: ((~ ((! [A7:A,B7:B,C4:C,D4:D,E2:E]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A7) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B7) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C4) @ ((((product_Pair @ D) @ E) @ D4) @ E2)))))))))))).
% 1.99/1.26 thf(fact_163_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A7:A,B7:B,C4:C,D4:D]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A7) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B7) @ ((((product_Pair @ C) @ D) @ C4) @ D4))))))))))).
% 1.99/1.26 thf(fact_164_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A7:A,B7:B,C4:C]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A7) @ ((((product_Pair @ B) @ C) @ B7) @ C4)))))))))).
% 1.99/1.26 thf(fact_165_Pair__inject, axiom, (! [A:$tType,B:$tType,A3:A,B3:B,A8:A,B8:B]: (((((((product_Pair @ A) @ B) @ A3) @ B3) = ((((product_Pair @ A) @ B) @ A8) @ B8)) => (~ (((A3 = A8) => (B3 != B8)))))))).
% 1.99/1.26 thf(fact_166_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P2:((product_prod @ A) @ B)]: (((! [A7:A,B7:B]: ((P @ ((((product_Pair @ A) @ B) @ A7) @ B7)))) => (P @ P2))))).
% 1.99/1.26 thf(fact_167_surj__pair, axiom, (! [A:$tType,B:$tType,P2:((product_prod @ A) @ B)]: ((? [X3:A,Y4:B]: ((P2 = ((((product_Pair @ A) @ B) @ X3) @ Y4))))))).
% 1.99/1.26 thf(fact_168_fst__eqD, axiom, (! [B:$tType,A:$tType,X:A,Y:B,A3:A]: ((((((product_fst @ A) @ B) @ ((((product_Pair @ A) @ B) @ X) @ Y)) = A3) => (X = A3))))).
% 1.99/1.26 thf(fact_169_fst__conv, axiom, (! [B:$tType,A:$tType,X1:A,X22:B]: (((((product_fst @ A) @ B) @ ((((product_Pair @ A) @ B) @ X1) @ X22)) = X1)))).
% 1.99/1.26 thf(fact_170_snd__eqD, axiom, (! [B:$tType,A:$tType,X:B,Y:A,A3:A]: ((((((product_snd @ B) @ A) @ ((((product_Pair @ B) @ A) @ X) @ Y)) = A3) => (Y = A3))))).
% 1.99/1.26 thf(fact_171_snd__conv, axiom, (! [Aa:$tType,A:$tType,X1:Aa,X22:A]: (((((product_snd @ Aa) @ A) @ ((((product_Pair @ Aa) @ A) @ X1) @ X22)) = X22)))).
% 1.99/1.26 thf(fact_172_prod_Oswap__def, axiom, (! [B:$tType,A:$tType]: ((((product_swap @ A) @ B) = (^ [P3:((product_prod @ A) @ B)]: (((((product_Pair @ B) @ A) @ (((product_snd @ A) @ B) @ P3)) @ (((product_fst @ A) @ B) @ P3)))))))).
% 1.99/1.26 thf(fact_173_fst__pair, axiom, (! [B:$tType,A:$tType,A3:A,B3:B]: (((((product_fst @ A) @ B) @ ((((product_Pair @ A) @ B) @ A3) @ B3)) = A3)))).
% 1.99/1.26 thf(fact_174_snd__pair, axiom, (! [B:$tType,A:$tType,A3:B,B3:A]: (((((product_snd @ B) @ A) @ ((((product_Pair @ B) @ A) @ A3) @ B3)) = B3)))).
% 1.99/1.26 thf(fact_175_surjective__pairing, axiom, (! [B:$tType,A:$tType,T3:((product_prod @ A) @ B)]: ((T3 = ((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ T3)) @ (((product_snd @ A) @ B) @ T3)))))).
% 1.99/1.26 thf(fact_176_prod_Oexhaust__sel, axiom, (! [B:$tType,A:$tType,Prod:((product_prod @ A) @ B)]: ((Prod = ((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ Prod)) @ (((product_snd @ A) @ B) @ Prod)))))).
% 1.99/1.26 thf(fact_177_conjI__realizer, axiom, (! [A:$tType,B:$tType,P:(A > $o),P2:A,Q:(B > $o),Q2:B]: (((P @ P2) => ((Q @ Q2) => ((P @ (((product_fst @ A) @ B) @ ((((product_Pair @ A) @ B) @ P2) @ Q2))) & (Q @ (((product_snd @ A) @ B) @ ((((product_Pair @ A) @ B) @ P2) @ Q2))))))))).
% 1.99/1.26 thf(fact_178_exI__realizer, axiom, (! [B:$tType,A:$tType,P:(A > (B > $o)),Y:A,X:B]: ((((P @ Y) @ X) => ((P @ (((product_snd @ B) @ A) @ ((((product_Pair @ B) @ A) @ X) @ Y))) @ (((product_fst @ B) @ A) @ ((((product_Pair @ B) @ A) @ X) @ Y))))))).
% 1.99/1.26 thf(fact_179_Choiceo_Osimps_I2_J, axiom, (! [Alpha:(option @ game)]: ((((uSubst1976112797hoiceo @ Alpha) @ (none @ game)) = (none @ game))))).
% 1.99/1.26 thf(fact_180_Choiceo__undef, axiom, (! [Alpha:(option @ game),Beta:(option @ game)]: (((((uSubst1976112797hoiceo @ Alpha) @ Beta) = (none @ game)) = ((Alpha = (none @ game)) | (Beta = (none @ game))))))).
% 1.99/1.26 thf(fact_181_usubstappp__compose, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Alpha:game,Beta:game]: (((((uSubst95898988stappp @ Sigma) @ U) @ ((compose @ Alpha) @ Beta)) = ((((product_Pair @ (set @ variable)) @ (option @ game)) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha))) @ Beta))) @ ((uSubst1385204910mposeo @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha))) @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha))) @ Beta)))))))).
% 1.99/1.26 thf(fact_182_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A3:A,B3:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A3) @ B3)) = ((F1 @ A3) @ B3))))).
% 1.99/1.26 thf(fact_183_BNF__Greatest__Fixpoint_Osubst__Pair, axiom, (! [B:$tType,A:$tType,P:(A > (B > $o)),X:A,Y:B,A3:((product_prod @ A) @ B)]: ((((P @ X) @ Y) => ((A3 = ((((product_Pair @ A) @ B) @ X) @ Y)) => ((P @ (((product_fst @ A) @ B) @ A3)) @ (((product_snd @ A) @ B) @ A3))))))).
% 1.99/1.26 thf(fact_184_Composeo__undef, axiom, (! [Alpha:(option @ game),Beta:(option @ game)]: (((((uSubst1385204910mposeo @ Alpha) @ Beta) = (none @ game)) = ((Alpha = (none @ game)) | (Beta = (none @ game))))))).
% 1.99/1.26 thf(fact_185_Composeo_Osimps_I2_J, axiom, (! [Alpha:(option @ game)]: ((((uSubst1385204910mposeo @ Alpha) @ (none @ game)) = (none @ game))))).
% 1.99/1.26 thf(fact_186_usubstappp__loop, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Alpha:game]: (((((uSubst95898988stappp @ Sigma) @ U) @ (loop @ Alpha)) = ((((product_Pair @ (set @ variable)) @ (option @ game)) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha))) @ (uSubst993936602_Loopo @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha))) @ Alpha)))))))).
% 1.99/1.26 thf(fact_187_eq__snd__iff, axiom, (! [A:$tType,B:$tType,B3:A,P2:((product_prod @ B) @ A)]: (((B3 = (((product_snd @ B) @ A) @ P2)) = (? [A5:B]: ((P2 = ((((product_Pair @ B) @ A) @ A5) @ B3)))))))).
% 1.99/1.26 thf(fact_188_sndI, axiom, (! [A:$tType,B:$tType,X:((product_prod @ A) @ B),Y:A,Z:B]: (((X = ((((product_Pair @ A) @ B) @ Y) @ Z)) => ((((product_snd @ A) @ B) @ X) = Z))))).
% 1.99/1.26 thf(fact_189_Loopo_Osimps_I2_J, axiom, ((uSubst993936602_Loopo @ (none @ game)) = (none @ game))).
% 1.99/1.26 thf(fact_190_Loopo__undef, axiom, (! [Alpha:(option @ game)]: ((((uSubst993936602_Loopo @ Alpha) = (none @ game)) = (Alpha = (none @ game)))))).
% 1.99/1.26 thf(fact_191_fstI, axiom, (! [B:$tType,A:$tType,X:((product_prod @ A) @ B),Y:A,Z:B]: (((X = ((((product_Pair @ A) @ B) @ Y) @ Z)) => ((((product_fst @ A) @ B) @ X) = Y))))).
% 1.99/1.26 thf(fact_192_eq__fst__iff, axiom, (! [A:$tType,B:$tType,A3:A,P2:((product_prod @ A) @ B)]: (((A3 = (((product_fst @ A) @ B) @ P2)) = (? [B5:B]: ((P2 = ((((product_Pair @ A) @ B) @ A3) @ B5)))))))).
% 1.99/1.26 thf(fact_193_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C3:(B > (C > A)),A3:B,B3:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C3) @ ((((product_Pair @ B) @ C) @ A3) @ B3)) = ((C3 @ A3) @ B3))))).
% 1.99/1.26 thf(fact_194_relChain__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (((bNF_Ca1785829860lChain @ A) @ B) = (^ [R:(set @ ((product_prod @ A) @ A)),As:(A > B)]: ((! [I:A,J:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ I) @ J)) @ R) => (((ord_less_eq @ B) @ (As @ I)) @ (As @ J)))))))))))).
% 1.99/1.26 thf(fact_195_sndOp__def, axiom, (! [B:$tType,A:$tType,C:$tType]: (((((bNF_sndOp @ C) @ A) @ B) = (^ [P4:(C > (A > $o)),Q3:(A > (B > $o)),Ac:((product_prod @ C) @ B)]: (((((product_Pair @ A) @ B) @ (((((((bNF_pick_middlep @ C) @ A) @ B) @ P4) @ Q3) @ (((product_fst @ C) @ B) @ Ac)) @ (((product_snd @ C) @ B) @ Ac))) @ (((product_snd @ C) @ B) @ Ac)))))))).
% 1.99/1.26 thf(fact_196_fstOp__def, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((bNF_fstOp @ A) @ B) @ C) = (^ [P4:(A > (B > $o)),Q3:(B > (C > $o)),Ac:((product_prod @ A) @ C)]: (((((product_Pair @ A) @ B) @ (((product_fst @ A) @ C) @ Ac)) @ (((((((bNF_pick_middlep @ A) @ B) @ C) @ P4) @ Q3) @ (((product_fst @ A) @ C) @ Ac)) @ (((product_snd @ A) @ C) @ Ac))))))))).
% 1.99/1.26 thf(fact_197_csquare__fstOp__sndOp, axiom, (! [A:$tType,B:$tType,C:$tType,F2:((A > (B > $o)) > (((product_prod @ A) @ B) > $o)),P:(A > (C > $o)),Q:(C > (B > $o))]: ((((((((((bNF_csquare @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ C)) @ C) @ ((product_prod @ C) @ B)) @ ((collect @ ((product_prod @ A) @ B)) @ (F2 @ (((((relcompp @ A) @ C) @ B) @ P) @ Q)))) @ ((product_snd @ A) @ C)) @ ((product_fst @ C) @ B)) @ (((((bNF_fstOp @ A) @ C) @ B) @ P) @ Q)) @ (((((bNF_sndOp @ A) @ C) @ B) @ P) @ Q))))).
% 1.99/1.26 thf(fact_198_usubstappp_Osimps_I4_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Alpha:game,Beta:game]: (((((uSubst95898988stappp @ Sigma) @ U) @ ((choice @ Alpha) @ Beta)) = ((((product_Pair @ (set @ variable)) @ (option @ game)) @ (((sup_sup @ (set @ variable)) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha))) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Beta)))) @ ((uSubst1976112797hoiceo @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha))) @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Beta)))))))).
% 1.99/1.26 thf(fact_199_pick__middlep, axiom, (! [B:$tType,A:$tType,C:$tType,P:(A > (B > $o)),Q:(B > (C > $o)),A3:A,C3:C]: (((((((((relcompp @ A) @ B) @ C) @ P) @ Q) @ A3) @ C3) => (((P @ A3) @ (((((((bNF_pick_middlep @ A) @ B) @ C) @ P) @ Q) @ A3) @ C3)) & ((Q @ (((((((bNF_pick_middlep @ A) @ B) @ C) @ P) @ Q) @ A3) @ C3)) @ C3)))))).
% 1.99/1.26 thf(fact_200_csquare__def, axiom, (! [B:$tType,C:$tType,D:$tType,A:$tType]: ((((((bNF_csquare @ A) @ B) @ C) @ D) = (^ [A4:(set @ A),F12:(B > C),F22:(D > C),P1:(A > B),P22:(A > D)]: ((! [X2:A]: (((((member @ A) @ X2) @ A4) => ((F12 @ (P1 @ X2)) = (F22 @ (P22 @ X2)))))))))))).
% 1.99/1.26 thf(fact_201_leq__OOI, axiom, (! [A:$tType,R2:(A > (A > $o))]: (((R2 = (^ [Y2:A,Z2:A]: ((Y2 = Z2)))) => (((ord_less_eq @ (A > (A > $o))) @ R2) @ (((((relcompp @ A) @ A) @ A) @ R2) @ R2)))))).
% 1.99/1.26 thf(fact_202_less__eq__set__def, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B4:(set @ A)]: ((((ord_less_eq @ (A > $o)) @ (^ [X2:A]: ((((member @ A) @ X2) @ A4)))) @ (^ [X2:A]: ((((member @ A) @ X2) @ B4)))))))))).
% 1.99/1.26 thf(fact_203_Collect__subset, axiom, (! [A:$tType,A2:(set @ A),P:(A > $o)]: ((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X2:A]: (((((member @ A) @ X2) @ A2) & (P @ X2)))))) @ A2)))).
% 1.99/1.26 thf(fact_204_Un__def, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A4:(set @ A),B4:(set @ A)]: (((collect @ A) @ (^ [X2:A]: (((((member @ A) @ X2) @ A4) | (((member @ A) @ X2) @ B4))))))))))).
% 1.99/1.26 thf(fact_205_sup__set__def, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A4:(set @ A),B4:(set @ A)]: (((collect @ A) @ (((sup_sup @ (A > $o)) @ (^ [X2:A]: ((((member @ A) @ X2) @ A4)))) @ (^ [X2:A]: ((((member @ A) @ X2) @ B4))))))))))).
% 1.99/1.26 thf(fact_206_Collect__disj__eq, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: ((((collect @ A) @ (^ [X2:A]: (((P @ X2) | (Q @ X2))))) = (((sup_sup @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 1.99/1.26 thf(fact_207_subset__CollectI, axiom, (! [A:$tType,B2:(set @ A),A2:(set @ A),Q:(A > $o),P:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ B2) @ A2) => ((! [X3:A]: (((((member @ A) @ X3) @ B2) => ((Q @ X3) => (P @ X3))))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X2:A]: (((((member @ A) @ X2) @ B2) & (Q @ X2)))))) @ ((collect @ A) @ (^ [X2:A]: (((((member @ A) @ X2) @ A2) & (P @ X2))))))))))).
% 1.99/1.26 thf(fact_208_subset__Collect__iff, axiom, (! [A:$tType,B2:(set @ A),A2:(set @ A),P:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ B2) @ A2) => ((((ord_less_eq @ (set @ A)) @ B2) @ ((collect @ A) @ (^ [X2:A]: (((((member @ A) @ X2) @ A2) & (P @ X2)))))) = (! [X2:A]: (((((member @ A) @ X2) @ B2) => (P @ X2))))))))).
% 1.99/1.26 thf(fact_209_usubstappp_Osimps_I5_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Alpha:game,Beta:game]: (((((uSubst95898988stappp @ Sigma) @ U) @ ((compose @ Alpha) @ Beta)) = ((((product_Pair @ (set @ variable)) @ (option @ game)) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha))) @ Beta))) @ ((uSubst1385204910mposeo @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha))) @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha))) @ Beta)))))))).
% 1.99/1.26 thf(fact_210_usubstappp_Osimps_I6_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Alpha:game]: (((((uSubst95898988stappp @ Sigma) @ U) @ (loop @ Alpha)) = ((((product_Pair @ (set @ variable)) @ (option @ game)) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha))) @ (uSubst993936602_Loopo @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ Sigma) @ U) @ Alpha))) @ Alpha)))))))).
% 1.99/1.26 thf(fact_211_scomp__unfold, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType]: ((((((product_scomp @ A) @ B) @ C) @ D) = (^ [F:(A > ((product_prod @ B) @ C)),G:(B > (C > D)),X2:A]: (((G @ (((product_fst @ B) @ C) @ (F @ X2))) @ (((product_snd @ B) @ C) @ (F @ X2))))))))).
% 1.99/1.26 thf(fact_212_sup__Un__eq, axiom, (! [A:$tType,R2:(set @ A),S2:(set @ A)]: (((((sup_sup @ (A > $o)) @ (^ [X2:A]: ((((member @ A) @ X2) @ R2)))) @ (^ [X2:A]: ((((member @ A) @ X2) @ S2)))) = (^ [X2:A]: ((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ R2) @ S2)))))))).
% 1.99/1.26 thf(fact_213_scomp__scomp, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,F3:$tType,E:$tType,F2:(A > ((product_prod @ E) @ F3)),G2:(E > (F3 > ((product_prod @ C) @ D))),H:(C > (D > B))]: ((((((((product_scomp @ A) @ C) @ D) @ B) @ ((((((product_scomp @ A) @ E) @ F3) @ ((product_prod @ C) @ D)) @ F2) @ G2)) @ H) = ((((((product_scomp @ A) @ E) @ F3) @ B) @ F2) @ (^ [X2:E]: (((((((product_scomp @ F3) @ C) @ D) @ B) @ (G2 @ X2)) @ H)))))))).
% 1.99/1.26 thf(fact_214_scomp__Pair, axiom, (! [C:$tType,B:$tType,A:$tType,X:(A > ((product_prod @ B) @ C))]: ((((((((product_scomp @ A) @ B) @ C) @ ((product_prod @ B) @ C)) @ X) @ ((product_Pair @ B) @ C)) = X)))).
% 1.99/1.26 thf(fact_215_Pair__scomp, axiom, (! [A:$tType,B:$tType,C:$tType,X:C,F2:(C > (A > B))]: ((((((((product_scomp @ A) @ C) @ A) @ B) @ (((product_Pair @ C) @ A) @ X)) @ F2) = (F2 @ X))))).
% 1.99/1.26 thf(fact_216_refl__ge__eq, axiom, (! [A:$tType,R2:(A > (A > $o))]: (((! [X3:A]: (((R2 @ X3) @ X3))) => (((ord_less_eq @ (A > (A > $o))) @ (^ [Y2:A,Z2:A]: ((Y2 = Z2)))) @ R2))))).
% 1.99/1.26 thf(fact_217_ge__eq__refl, axiom, (! [A:$tType,R2:(A > (A > $o)),X:A]: (((((ord_less_eq @ (A > (A > $o))) @ (^ [Y2:A,Z2:A]: ((Y2 = Z2)))) @ R2) => ((R2 @ X) @ X))))).
% 1.99/1.26 thf(fact_218_subrelI, axiom, (! [B:$tType,A:$tType,R3:(set @ ((product_prod @ A) @ B)),S3:(set @ ((product_prod @ A) @ B))]: (((! [X3:A,Y4:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y4)) @ R3) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y4)) @ S3)))) => (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R3) @ S3))))).
% 1.99/1.26 thf(fact_219_pred__equals__eq2, axiom, (! [B:$tType,A:$tType,R2:(set @ ((product_prod @ A) @ B)),S2:(set @ ((product_prod @ A) @ B))]: ((((^ [X2:A,Y3:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X2) @ Y3)) @ R2))) = (^ [X2:A,Y3:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X2) @ Y3)) @ S2)))) = (R2 = S2))))).
% 1.99/1.26 thf(fact_220_pred__subset__eq2, axiom, (! [B:$tType,A:$tType,R2:(set @ ((product_prod @ A) @ B)),S2:(set @ ((product_prod @ A) @ B))]: (((((ord_less_eq @ (A > (B > $o))) @ (^ [X2:A,Y3:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X2) @ Y3)) @ R2)))) @ (^ [X2:A,Y3:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X2) @ Y3)) @ S2)))) = (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R2) @ S2))))).
% 1.99/1.26 thf(fact_221_sup__Un__eq2, axiom, (! [B:$tType,A:$tType,R2:(set @ ((product_prod @ A) @ B)),S2:(set @ ((product_prod @ A) @ B))]: (((((sup_sup @ (A > (B > $o))) @ (^ [X2:A,Y3:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X2) @ Y3)) @ R2)))) @ (^ [X2:A,Y3:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X2) @ Y3)) @ S2)))) = (^ [X2:A,Y3:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X2) @ Y3)) @ (((sup_sup @ (set @ ((product_prod @ A) @ B))) @ R2) @ S2)))))))).
% 1.99/1.26 thf(fact_222_pred__subset__eq, axiom, (! [A:$tType,R2:(set @ A),S2:(set @ A)]: (((((ord_less_eq @ (A > $o)) @ (^ [X2:A]: ((((member @ A) @ X2) @ R2)))) @ (^ [X2:A]: ((((member @ A) @ X2) @ S2)))) = (((ord_less_eq @ (set @ A)) @ R2) @ S2))))).
% 1.99/1.26 thf(fact_223_conj__subset__def, axiom, (! [A:$tType,A2:(set @ A),P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ A2) @ ((collect @ A) @ (^ [X2:A]: (((P @ X2) & (Q @ X2)))))) = ((((ord_less_eq @ (set @ A)) @ A2) @ ((collect @ A) @ P)) & (((ord_less_eq @ (set @ A)) @ A2) @ ((collect @ A) @ Q))))))).
% 1.99/1.26 thf(fact_224_prop__restrict, axiom, (! [A:$tType,X:A,Z4:(set @ A),X4:(set @ A),P:(A > $o)]: (((((member @ A) @ X) @ Z4) => ((((ord_less_eq @ (set @ A)) @ Z4) @ ((collect @ A) @ (^ [X2:A]: (((((member @ A) @ X2) @ X4) & (P @ X2)))))) => (P @ X)))))).
% 1.99/1.26 thf(fact_225_ssubst__Pair__rhs, axiom, (! [B:$tType,A:$tType,R3:A,S3:B,R2:(set @ ((product_prod @ A) @ B)),S4:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R3) @ S3)) @ R2) => ((S4 = S3) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R3) @ S4)) @ R2)))))).
% 1.99/1.26 thf(fact_226_Collect__restrict, axiom, (! [A:$tType,X4:(set @ A),P:(A > $o)]: ((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X2:A]: (((((member @ A) @ X2) @ X4) & (P @ X2)))))) @ X4)))).
% 1.99/1.26 thf(fact_227_image2__eqI, axiom, (! [A:$tType,C:$tType,B:$tType,B3:A,F2:(B > A),X:B,C3:C,G2:(B > C),A2:(set @ B)]: (((B3 = (F2 @ X)) => ((C3 = (G2 @ X)) => ((((member @ B) @ X) @ A2) => (((member @ ((product_prod @ A) @ C)) @ ((((product_Pair @ A) @ C) @ B3) @ C3)) @ ((((((bNF_Greatest_image2 @ B) @ A) @ C) @ A2) @ F2) @ G2)))))))).
% 1.99/1.26 thf(fact_228_Loopo_Oelims, axiom, (! [X:(option @ game),Y:(option @ game)]: ((((uSubst993936602_Loopo @ X) = Y) => ((! [Alpha2:game]: (((X = ((some @ game) @ Alpha2)) => (Y != ((some @ game) @ (loop @ Alpha2)))))) => (~ (((X = (none @ game)) => (Y != (none @ game)))))))))).
% 1.99/1.26 thf(fact_229_option_Oinject, axiom, (! [A:$tType,X22:A,Y22:A]: (((((some @ A) @ X22) = ((some @ A) @ Y22)) = (X22 = Y22))))).
% 1.99/1.26 thf(fact_230_not__Some__eq, axiom, (! [A:$tType,X:(option @ A)]: (((! [Y3:A]: ((X != ((some @ A) @ Y3)))) = (X = (none @ A)))))).
% 1.99/1.26 thf(fact_231_not__None__eq, axiom, (! [A:$tType,X:(option @ A)]: (((X != (none @ A)) = (? [Y3:A]: ((X = ((some @ A) @ Y3)))))))).
% 1.99/1.26 thf(fact_232_option_Ocollapse, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) => (((some @ A) @ ((the @ A) @ Option)) = Option))))).
% 1.99/1.26 thf(fact_233_Composeo_Ocases, axiom, (! [X:((product_prod @ (option @ game)) @ (option @ game))]: (((! [Alpha2:game,Beta2:game]: ((X != ((((product_Pair @ (option @ game)) @ (option @ game)) @ ((some @ game) @ Alpha2)) @ ((some @ game) @ Beta2))))) => ((! [Alpha2:(option @ game)]: ((X != ((((product_Pair @ (option @ game)) @ (option @ game)) @ Alpha2) @ (none @ game))))) => (~ ((! [V2:game]: ((X != ((((product_Pair @ (option @ game)) @ (option @ game)) @ (none @ game)) @ ((some @ game) @ V2)))))))))))).
% 1.99/1.26 thf(fact_234_option_Oexhaust__sel, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) => (Option = ((some @ A) @ ((the @ A) @ Option))))))).
% 1.99/1.26 thf(fact_235_combine__options__cases, axiom, (! [A:$tType,B:$tType,X:(option @ A),P:((option @ A) > ((option @ B) > $o)),Y:(option @ B)]: ((((X = (none @ A)) => ((P @ X) @ Y)) => (((Y = (none @ B)) => ((P @ X) @ Y)) => ((! [A7:A,B7:B]: (((X = ((some @ A) @ A7)) => ((Y = ((some @ B) @ B7)) => ((P @ X) @ Y))))) => ((P @ X) @ Y))))))).
% 1.99/1.26 thf(fact_236_split__option__all, axiom, (! [A:$tType]: (((^ [P5:((option @ A) > $o)]: ((! [X5:(option @ A)]: ((P5 @ X5))))) = (^ [P4:((option @ A) > $o)]: (((P4 @ (none @ A)) & (! [X2:A]: ((P4 @ ((some @ A) @ X2))))))))))).
% 1.99/1.26 thf(fact_237_split__option__ex, axiom, (! [A:$tType]: (((^ [P5:((option @ A) > $o)]: ((? [X5:(option @ A)]: ((P5 @ X5))))) = (^ [P4:((option @ A) > $o)]: (((P4 @ (none @ A)) | (? [X2:A]: ((P4 @ ((some @ A) @ X2))))))))))).
% 1.99/1.26 thf(fact_238_option_Oinducts, axiom, (! [A:$tType,P:((option @ A) > $o),Option:(option @ A)]: (((P @ (none @ A)) => ((! [X3:A]: ((P @ ((some @ A) @ X3)))) => (P @ Option)))))).
% 1.99/1.26 thf(fact_239_option_Oexhaust, axiom, (! [A:$tType,Y:(option @ A)]: (((Y != (none @ A)) => (~ ((! [X23:A]: ((Y != ((some @ A) @ X23)))))))))).
% 1.99/1.26 thf(fact_240_option_OdiscI, axiom, (! [A:$tType,Option:(option @ A),X22:A]: (((Option = ((some @ A) @ X22)) => (Option != (none @ A)))))).
% 1.99/1.26 thf(fact_241_option_Odistinct_I1_J, axiom, (! [A:$tType,X22:A]: (((none @ A) != ((some @ A) @ X22))))).
% 1.99/1.26 thf(fact_242_option_Osel, axiom, (! [A:$tType,X22:A]: ((((the @ A) @ ((some @ A) @ X22)) = X22)))).
% 1.99/1.26 thf(fact_243_Composeo_Oinduct, axiom, (! [P:((option @ game) > ((option @ game) > $o)),A0:(option @ game),A1:(option @ game)]: (((! [Alpha2:game,Beta2:game]: (((P @ ((some @ game) @ Alpha2)) @ ((some @ game) @ Beta2)))) => ((! [Alpha2:(option @ game)]: (((P @ Alpha2) @ (none @ game)))) => ((! [V2:game]: (((P @ (none @ game)) @ ((some @ game) @ V2)))) => ((P @ A0) @ A1))))))).
% 1.99/1.26 thf(fact_244_undefg__equiv, axiom, (! [Alpha:(option @ game)]: (((Alpha != (none @ game)) = (? [G:game]: ((Alpha = ((some @ game) @ G)))))))).
% 1.99/1.26 thf(fact_245_Loopo_Oinduct, axiom, (! [P:((option @ game) > $o),A0:(option @ game)]: (((! [Alpha2:game]: ((P @ ((some @ game) @ Alpha2)))) => ((P @ (none @ game)) => (P @ A0)))))).
% 1.99/1.26 thf(fact_246_Loopo_Ocases, axiom, (! [X:(option @ game)]: (((! [Alpha2:game]: ((X != ((some @ game) @ Alpha2)))) => (X = (none @ game)))))).
% 1.99/1.26 thf(fact_247_Loopo_Osimps_I1_J, axiom, (! [Alpha:game]: (((uSubst993936602_Loopo @ ((some @ game) @ Alpha)) = ((some @ game) @ (loop @ Alpha)))))).
% 1.99/1.26 thf(fact_248_Choiceo_Osimps_I1_J, axiom, (! [Alpha:game,Beta:game]: ((((uSubst1976112797hoiceo @ ((some @ game) @ Alpha)) @ ((some @ game) @ Beta)) = ((some @ game) @ ((choice @ Alpha) @ Beta)))))).
% 1.99/1.26 thf(fact_249_Composeo_Osimps_I1_J, axiom, (! [Alpha:game,Beta:game]: ((((uSubst1385204910mposeo @ ((some @ game) @ Alpha)) @ ((some @ game) @ Beta)) = ((some @ game) @ ((compose @ Alpha) @ Beta)))))).
% 1.99/1.26 thf(fact_250_Composeo_Osimps_I3_J, axiom, (! [V3:game]: ((((uSubst1385204910mposeo @ (none @ game)) @ ((some @ game) @ V3)) = (none @ game))))).
% 1.99/1.26 thf(fact_251_Choiceo_Osimps_I3_J, axiom, (! [V3:game]: ((((uSubst1976112797hoiceo @ (none @ game)) @ ((some @ game) @ V3)) = (none @ game))))).
% 1.99/1.26 thf(fact_252_Composeo_Oelims, axiom, (! [X:(option @ game),Xa:(option @ game),Y:(option @ game)]: (((((uSubst1385204910mposeo @ X) @ Xa) = Y) => ((! [Alpha2:game]: (((X = ((some @ game) @ Alpha2)) => (! [Beta2:game]: (((Xa = ((some @ game) @ Beta2)) => (Y != ((some @ game) @ ((compose @ Alpha2) @ Beta2))))))))) => (((Xa = (none @ game)) => (Y != (none @ game))) => (~ (((X = (none @ game)) => ((? [V2:game]: ((Xa = ((some @ game) @ V2)))) => (Y != (none @ game)))))))))))).
% 1.99/1.26 thf(fact_253_Choiceo_Oelims, axiom, (! [X:(option @ game),Xa:(option @ game),Y:(option @ game)]: (((((uSubst1976112797hoiceo @ X) @ Xa) = Y) => ((! [Alpha2:game]: (((X = ((some @ game) @ Alpha2)) => (! [Beta2:game]: (((Xa = ((some @ game) @ Beta2)) => (Y != ((some @ game) @ ((choice @ Alpha2) @ Beta2))))))))) => (((Xa = (none @ game)) => (Y != (none @ game))) => (~ (((X = (none @ game)) => ((? [V2:game]: ((Xa = ((some @ game) @ V2)))) => (Y != (none @ game)))))))))))).
% 1.99/1.26 thf(fact_254_option_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F23:(A > B),Option:(option @ A)]: (((P @ (((((case_option @ B) @ A) @ F1) @ F23) @ Option)) = (~ ((((Option = (none @ A)) & (~ ((P @ F1)))) | ((Option = ((some @ A) @ ((the @ A) @ Option))) & (~ ((P @ (F23 @ ((the @ A) @ Option))))))))))))).
% 1.99/1.26 thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A9:$tType,A10:$tType]: (((semilattice_sup @ A10) => (semilattice_sup @ (A9 > A10)))))).
% 1.99/1.26 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A9:$tType,A10:$tType]: (((preorder @ A10) => (preorder @ (A9 > A10)))))).
% 1.99/1.26 thf(tcon_fun___Lattices_Olattice, axiom, (! [A9:$tType,A10:$tType]: (((lattice @ A10) => (lattice @ (A9 > A10)))))).
% 1.99/1.26 thf(tcon_fun___Orderings_Oorder, axiom, (! [A9:$tType,A10:$tType]: (((order @ A10) => (order @ (A9 > A10)))))).
% 1.99/1.26 thf(tcon_fun___Orderings_Oord, axiom, (! [A9:$tType,A10:$tType]: (((ord @ A10) => (ord @ (A9 > A10)))))).
% 1.99/1.26 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_1, axiom, (! [A9:$tType]: ((semilattice_sup @ (set @ A9))))).
% 1.99/1.26 thf(tcon_Set_Oset___Orderings_Opreorder_2, axiom, (! [A9:$tType]: ((preorder @ (set @ A9))))).
% 1.99/1.26 thf(tcon_Set_Oset___Lattices_Olattice_3, axiom, (! [A9:$tType]: ((lattice @ (set @ A9))))).
% 1.99/1.26 thf(tcon_Set_Oset___Orderings_Oorder_4, axiom, (! [A9:$tType]: ((order @ (set @ A9))))).
% 1.99/1.26 thf(tcon_Set_Oset___Orderings_Oord_5, axiom, (! [A9:$tType]: ((ord @ (set @ A9))))).
% 1.99/1.26 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_6, axiom, (semilattice_sup @ $o)).
% 1.99/1.26 thf(tcon_HOL_Obool___Orderings_Opreorder_7, axiom, (preorder @ $o)).
% 1.99/1.26 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 1.99/1.26 thf(tcon_HOL_Obool___Lattices_Olattice_8, axiom, (lattice @ $o)).
% 1.99/1.26 thf(tcon_HOL_Obool___Orderings_Oorder_9, axiom, (order @ $o)).
% 1.99/1.26 thf(tcon_HOL_Obool___Orderings_Oord_10, axiom, (ord @ $o)).
% 1.99/1.26 thf(conj_0, conjecture, (((ord_less_eq @ (set @ variable)) @ (((sup_sup @ (set @ variable)) @ ua) @ (static_BVG @ ((the @ game) @ (((product_snd @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ ua) @ ((compose @ alpha) @ beta))))))) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ (((product_fst @ (set @ variable)) @ (option @ game)) @ (((uSubst95898988stappp @ sigma) @ ua) @ alpha))) @ beta)))).
% 1.99/1.26 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.WDfDZbBGZy/DTF2DTF14850.p
% 1.99/1.26 ------------------------
% 1.99/1.29 ---- Cleaned THF ---
% 1.99/1.29 thf(ty_t_Product__Type_Oprod,type,
% 1.99/1.29 product_prod: $tType > $tType > $tType ).
% 1.99/1.29
% 1.99/1.29 thf(ty_t_Syntax_Ovariable,type,
% 1.99/1.29 variable: $tType ).
% 1.99/1.29
% 1.99/1.29 thf(ty_t_Option_Ooption,type,
% 1.99/1.29 option: $tType > $tType ).
% 1.99/1.29
% 1.99/1.29 thf(ty_t_Syntax_Ogame,type,
% 1.99/1.29 game: $tType ).
% 1.99/1.29
% 1.99/1.29 thf(ty_t_String_Ochar,type,
% 1.99/1.29 char: $tType ).
% 1.99/1.29
% 1.99/1.29 thf(ty_t_Syntax_Otrm,type,
% 1.99/1.29 trm: $tType ).
% 1.99/1.29
% 1.99/1.29 thf(ty_t_Syntax_Ofml,type,
% 1.99/1.29 fml: $tType ).
% 1.99/1.29
% 1.99/1.29 thf(ty_t_Set_Oset,type,
% 1.99/1.29 set: $tType > $tType ).
% 1.99/1.29
% 1.99/1.29 thf(sy_cl_HOL_Otype,type,
% 1.99/1.29 type:
% 1.99/1.29 !>[A: $tType] : $o ).
% 1.99/1.29
% 1.99/1.29 thf(sy_cl_Orderings_Oord,type,
% 1.99/1.29 ord:
% 1.99/1.29 !>[A: $tType] : $o ).
% 1.99/1.29
% 1.99/1.29 thf(sy_cl_Orderings_Oorder,type,
% 1.99/1.29 order:
% 1.99/1.29 !>[A: $tType] : $o ).
% 1.99/1.29
% 1.99/1.29 thf(sy_cl_Lattices_Olattice,type,
% 1.99/1.29 lattice:
% 1.99/1.29 !>[A: $tType] : $o ).
% 1.99/1.29
% 1.99/1.29 thf(sy_cl_Orderings_Olinorder,type,
% 1.99/1.29 linorder:
% 1.99/1.29 !>[A: $tType] : $o ).
% 1.99/1.29
% 1.99/1.29 thf(sy_cl_Orderings_Opreorder,type,
% 1.99/1.29 preorder:
% 1.99/1.29 !>[A: $tType] : $o ).
% 1.99/1.29
% 1.99/1.29 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 1.99/1.29 semilattice_sup:
% 1.99/1.29 !>[A: $tType] : $o ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain,type,
% 1.99/1.29 bNF_Ca1785829860lChain:
% 1.99/1.29 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( A > B ) > $o ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_BNF__Def_Ocsquare,type,
% 1.99/1.29 bNF_csquare:
% 1.99/1.29 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( set @ A ) > ( B > C ) > ( D > C ) > ( A > B ) > ( A > D ) > $o ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_BNF__Def_OfstOp,type,
% 1.99/1.29 bNF_fstOp:
% 1.99/1.29 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > $o ) > ( B > C > $o ) > ( product_prod @ A @ C ) > ( product_prod @ A @ B ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_BNF__Def_Opick__middlep,type,
% 1.99/1.29 bNF_pick_middlep:
% 1.99/1.29 !>[B: $tType,A: $tType,C: $tType] : ( ( B > A > $o ) > ( A > C > $o ) > B > C > A ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_BNF__Def_OsndOp,type,
% 1.99/1.29 bNF_sndOp:
% 1.99/1.29 !>[C: $tType,A: $tType,B: $tType] : ( ( C > A > $o ) > ( A > B > $o ) > ( product_prod @ C @ B ) > ( product_prod @ A @ B ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2,type,
% 1.99/1.29 bNF_Greatest_image2:
% 1.99/1.29 !>[C: $tType,A: $tType,B: $tType] : ( ( set @ C ) > ( C > A ) > ( C > B ) > ( set @ ( product_prod @ A @ B ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Lattices_Osup__class_Osup,type,
% 1.99/1.29 sup_sup:
% 1.99/1.29 !>[A: $tType] : ( A > A > A ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Option_Ooption_ONone,type,
% 1.99/1.29 none:
% 1.99/1.29 !>[A: $tType] : ( option @ A ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Option_Ooption_OSome,type,
% 1.99/1.29 some:
% 1.99/1.29 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Option_Ooption_Ocase__option,type,
% 1.99/1.29 case_option:
% 1.99/1.29 !>[B: $tType,A: $tType] : ( B > ( A > B ) > ( option @ A ) > B ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Option_Ooption_Othe,type,
% 1.99/1.29 the:
% 1.99/1.29 !>[A: $tType] : ( ( option @ A ) > A ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 1.99/1.29 ord_less_eq:
% 1.99/1.29 !>[A: $tType] : ( A > A > $o ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Orderings_Oorder__class_OGreatest,type,
% 1.99/1.29 order_Greatest:
% 1.99/1.29 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Product__Type_OPair,type,
% 1.99/1.29 product_Pair:
% 1.99/1.29 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 1.99/1.29 produc2004651681e_prod:
% 1.99/1.29 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 1.99/1.29 product_rec_prod:
% 1.99/1.29 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Product__Type_Oprod_Ofst,type,
% 1.99/1.29 product_fst:
% 1.99/1.29 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > A ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Product__Type_Oprod_Osnd,type,
% 1.99/1.29 product_snd:
% 1.99/1.29 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > B ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Product__Type_Oprod_Oswap,type,
% 1.99/1.29 product_swap:
% 1.99/1.29 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > ( product_prod @ B @ A ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Product__Type_Oscomp,type,
% 1.99/1.29 product_scomp:
% 1.99/1.29 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( A > ( product_prod @ B @ C ) ) > ( B > C > D ) > A > D ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Relation_Orelcompp,type,
% 1.99/1.29 relcompp:
% 1.99/1.29 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > $o ) > ( B > C > $o ) > A > C > $o ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Set_OCollect,type,
% 1.99/1.29 collect:
% 1.99/1.29 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Static__Semantics_OBVG,type,
% 1.99/1.29 static_BVG: game > ( set @ variable ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Syntax_Ogame_OChoice,type,
% 1.99/1.29 choice: game > game > game ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Syntax_Ogame_OCompose,type,
% 1.99/1.29 compose: game > game > game ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_Syntax_Ogame_OLoop,type,
% 1.99/1.29 loop: game > game ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OChoiceo,type,
% 1.99/1.29 uSubst1976112797hoiceo: ( option @ game ) > ( option @ game ) > ( option @ game ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OComposeo,type,
% 1.99/1.29 uSubst1385204910mposeo: ( option @ game ) > ( option @ game ) > ( option @ game ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OLoopo,type,
% 1.99/1.29 uSubst993936602_Loopo: ( option @ game ) > ( option @ game ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappp,type,
% 1.99/1.29 uSubst95898988stappp: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > game > ( product_prod @ ( set @ variable ) @ ( option @ game ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_c_member,type,
% 1.99/1.29 member:
% 1.99/1.29 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 1.99/1.29
% 1.99/1.29 thf(sy_v_Ua____,type,
% 1.99/1.29 ua: set @ variable ).
% 1.99/1.29
% 1.99/1.29 thf(sy_v__092_060alpha_062_H____,type,
% 1.99/1.29 alpha: game ).
% 1.99/1.29
% 1.99/1.29 thf(sy_v__092_060beta_062____,type,
% 1.99/1.29 beta: game ).
% 1.99/1.29
% 1.99/1.29 thf(sy_v__092_060sigma_062,type,
% 1.99/1.29 sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_0__092_060open_062U_A_092_060union_062_ABVG_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_J_A_092_060union_062_ABVG_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_A_Ifst_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_A_092_060beta_062_J_J_J_A_092_060subseteq_062_Afst_A_Iusubstappp_A_092_060sigma_062_A_Ifst_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_A_092_060beta_062_J_092_060close_062,axiom,
% 1.99/1.29 ord_less_eq @ ( set @ variable ) @ ( sup_sup @ ( set @ variable ) @ ( sup_sup @ ( set @ variable ) @ ua @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) ) ) ) @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_1_fact,axiom,
% 1.99/1.29 ord_less_eq @ ( set @ variable ) @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) @ ( sup_sup @ ( set @ variable ) @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) ) ) @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_2_IHa,axiom,
% 1.99/1.29 ord_less_eq @ ( set @ variable ) @ ( sup_sup @ ( set @ variable ) @ ua @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) ) ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_3_IHb,axiom,
% 1.99/1.29 ord_less_eq @ ( set @ variable ) @ ( sup_sup @ ( set @ variable ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_4_Compose_Oprems,axiom,
% 1.99/1.29 ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) )
% 1.99/1.29 != ( none @ game ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_5_usubst__taboos__mon,axiom,
% 1.99/1.29 ! [U: set @ variable,Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),Alpha: game] : ( ord_less_eq @ ( set @ variable ) @ U @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_6_usubstappp__fst__mon,axiom,
% 1.99/1.29 ! [U: set @ variable,V: set @ variable,Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),Alpha: game] :
% 1.99/1.29 ( ( ord_less_eq @ ( set @ variable ) @ U @ V )
% 1.99/1.29 => ( ord_less_eq @ ( set @ variable ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ V @ Alpha ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_7_Compose_OIH_I2_J,axiom,
% 1.99/1.29 ! [U: set @ variable] :
% 1.99/1.29 ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ U @ beta ) )
% 1.99/1.29 != ( none @ game ) )
% 1.99/1.29 => ( ord_less_eq @ ( set @ variable ) @ ( sup_sup @ ( set @ variable ) @ U @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ U @ beta ) ) ) ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ U @ beta ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_8_Compose_OIH_I1_J,axiom,
% 1.99/1.29 ! [U: set @ variable] :
% 1.99/1.29 ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ U @ alpha ) )
% 1.99/1.29 != ( none @ game ) )
% 1.99/1.29 => ( ord_less_eq @ ( set @ variable ) @ ( sup_sup @ ( set @ variable ) @ U @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ U @ alpha ) ) ) ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ U @ alpha ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_9_Un__subset__iff,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A,B2: set @ A,C2: set @ A] :
% 1.99/1.29 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C2 )
% 1.99/1.29 = ( ( ord_less_eq @ ( set @ A ) @ A2 @ C2 )
% 1.99/1.29 & ( ord_less_eq @ ( set @ A ) @ B2 @ C2 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_10_le__sup__iff,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [X: A,Y: A,Z: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 1.99/1.29 = ( ( ord_less_eq @ A @ X @ Z )
% 1.99/1.29 & ( ord_less_eq @ A @ Y @ Z ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_11_sup_Obounded__iff,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [B3: A,C3: A,A3: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C3 ) @ A3 )
% 1.99/1.29 = ( ( ord_less_eq @ A @ B3 @ A3 )
% 1.99/1.29 & ( ord_less_eq @ A @ C3 @ A3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_12_BVG__compose,axiom,
% 1.99/1.29 ! [Alpha: game,Beta: game] : ( ord_less_eq @ ( set @ variable ) @ ( static_BVG @ ( compose @ Alpha @ Beta ) ) @ ( sup_sup @ ( set @ variable ) @ ( static_BVG @ Alpha ) @ ( static_BVG @ Beta ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_13_game_Oinject_I5_J,axiom,
% 1.99/1.29 ! [X51: game,X52: game,Y51: game,Y52: game] :
% 1.99/1.29 ( ( ( compose @ X51 @ X52 )
% 1.99/1.29 = ( compose @ Y51 @ Y52 ) )
% 1.99/1.29 = ( ( X51 = Y51 )
% 1.99/1.29 & ( X52 = Y52 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_14_UnCI,axiom,
% 1.99/1.29 ! [A: $tType,C3: A,B2: set @ A,A2: set @ A] :
% 1.99/1.29 ( ( ~ ( member @ A @ C3 @ B2 )
% 1.99/1.29 => ( member @ A @ C3 @ A2 ) )
% 1.99/1.29 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_15_union__or,axiom,
% 1.99/1.29 ! [A: $tType,C3: A,A2: set @ A,B2: set @ A] :
% 1.99/1.29 ( ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 1.99/1.29 = ( ( member @ A @ C3 @ A2 )
% 1.99/1.29 | ( member @ A @ C3 @ B2 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_16_sup__apply,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ B )
% 1.99/1.29 => ( ( sup_sup @ ( A > B ) )
% 1.99/1.29 = ( ^ [F: A > B,G: A > B,X2: A] : ( sup_sup @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_17_sup_Oidem,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [A3: A] :
% 1.99/1.29 ( ( sup_sup @ A @ A3 @ A3 )
% 1.99/1.29 = A3 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_18_sup__idem,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [X: A] :
% 1.99/1.29 ( ( sup_sup @ A @ X @ X )
% 1.99/1.29 = X ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_19_subset__antisym,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 1.99/1.29 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 1.99/1.29 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 1.99/1.29 => ( A2 = B2 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_20_subsetI,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 1.99/1.29 ( ! [X3: A] :
% 1.99/1.29 ( ( member @ A @ X3 @ A2 )
% 1.99/1.29 => ( member @ A @ X3 @ B2 ) )
% 1.99/1.29 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_21_sup_Oright__idem,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [A3: A,B3: A] :
% 1.99/1.29 ( ( sup_sup @ A @ ( sup_sup @ A @ A3 @ B3 ) @ B3 )
% 1.99/1.29 = ( sup_sup @ A @ A3 @ B3 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_22_sup__left__idem,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [X: A,Y: A] :
% 1.99/1.29 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 1.99/1.29 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_23_sup_Oleft__idem,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [A3: A,B3: A] :
% 1.99/1.29 ( ( sup_sup @ A @ A3 @ ( sup_sup @ A @ A3 @ B3 ) )
% 1.99/1.29 = ( sup_sup @ A @ A3 @ B3 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_24_usubstappp__det,axiom,
% 1.99/1.29 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Alpha: game,V: set @ variable] :
% 1.99/1.29 ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) )
% 1.99/1.29 != ( none @ game ) )
% 1.99/1.29 => ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ V @ Alpha ) )
% 1.99/1.29 != ( none @ game ) )
% 1.99/1.29 => ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) )
% 1.99/1.29 = ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ V @ Alpha ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_25_Collect__mono__iff,axiom,
% 1.99/1.29 ! [A: $tType,P: A > $o,Q: A > $o] :
% 1.99/1.29 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 1.99/1.29 = ( ! [X2: A] :
% 1.99/1.29 ( ( P @ X2 )
% 1.99/1.29 => ( Q @ X2 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_26_set__eq__subset,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( ^ [Y2: set @ A,Z2: set @ A] : ( Y2 = Z2 ) )
% 1.99/1.29 = ( ^ [A4: set @ A,B4: set @ A] :
% 1.99/1.29 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 1.99/1.29 & ( ord_less_eq @ ( set @ A ) @ B4 @ A4 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_27_subset__trans,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A,B2: set @ A,C2: set @ A] :
% 1.99/1.29 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 1.99/1.29 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C2 )
% 1.99/1.29 => ( ord_less_eq @ ( set @ A ) @ A2 @ C2 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_28_Collect__mono,axiom,
% 1.99/1.29 ! [A: $tType,P: A > $o,Q: A > $o] :
% 1.99/1.29 ( ! [X3: A] :
% 1.99/1.29 ( ( P @ X3 )
% 1.99/1.29 => ( Q @ X3 ) )
% 1.99/1.29 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_29_subset__refl,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_30_subset__iff,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( ord_less_eq @ ( set @ A ) )
% 1.99/1.29 = ( ^ [A4: set @ A,B4: set @ A] :
% 1.99/1.29 ! [T2: A] :
% 1.99/1.29 ( ( member @ A @ T2 @ A4 )
% 1.99/1.29 => ( member @ A @ T2 @ B4 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_31_equalityD2,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 1.99/1.29 ( ( A2 = B2 )
% 1.99/1.29 => ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_32_equalityD1,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 1.99/1.29 ( ( A2 = B2 )
% 1.99/1.29 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_33_subset__eq,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( ord_less_eq @ ( set @ A ) )
% 1.99/1.29 = ( ^ [A4: set @ A,B4: set @ A] :
% 1.99/1.29 ! [X2: A] :
% 1.99/1.29 ( ( member @ A @ X2 @ A4 )
% 1.99/1.29 => ( member @ A @ X2 @ B4 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_34_equalityE,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 1.99/1.29 ( ( A2 = B2 )
% 1.99/1.29 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 1.99/1.29 => ~ ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_35_subsetD,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A,B2: set @ A,C3: A] :
% 1.99/1.29 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 1.99/1.29 => ( ( member @ A @ C3 @ A2 )
% 1.99/1.29 => ( member @ A @ C3 @ B2 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_36_in__mono,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A,B2: set @ A,X: A] :
% 1.99/1.29 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 1.99/1.29 => ( ( member @ A @ X @ A2 )
% 1.99/1.29 => ( member @ A @ X @ B2 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_37_sup__left__commute,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [X: A,Y: A,Z: A] :
% 1.99/1.29 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 1.99/1.29 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_38_sup_Oleft__commute,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [B3: A,A3: A,C3: A] :
% 1.99/1.29 ( ( sup_sup @ A @ B3 @ ( sup_sup @ A @ A3 @ C3 ) )
% 1.99/1.29 = ( sup_sup @ A @ A3 @ ( sup_sup @ A @ B3 @ C3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_39_sup__commute,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ( ( sup_sup @ A )
% 1.99/1.29 = ( ^ [X2: A,Y3: A] : ( sup_sup @ A @ Y3 @ X2 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_40_sup_Ocommute,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ( ( sup_sup @ A )
% 1.99/1.29 = ( ^ [A5: A,B5: A] : ( sup_sup @ A @ B5 @ A5 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_41_sup__assoc,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [X: A,Y: A,Z: A] :
% 1.99/1.29 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 1.99/1.29 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_42_sup_Oassoc,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [A3: A,B3: A,C3: A] :
% 1.99/1.29 ( ( sup_sup @ A @ ( sup_sup @ A @ A3 @ B3 ) @ C3 )
% 1.99/1.29 = ( sup_sup @ A @ A3 @ ( sup_sup @ A @ B3 @ C3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_43_boolean__algebra__cancel_Osup2,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [B2: A,K: A,B3: A,A3: A] :
% 1.99/1.29 ( ( B2
% 1.99/1.29 = ( sup_sup @ A @ K @ B3 ) )
% 1.99/1.29 => ( ( sup_sup @ A @ A3 @ B2 )
% 1.99/1.29 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A3 @ B3 ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_44_boolean__algebra__cancel_Osup1,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [A2: A,K: A,A3: A,B3: A] :
% 1.99/1.29 ( ( A2
% 1.99/1.29 = ( sup_sup @ A @ K @ A3 ) )
% 1.99/1.29 => ( ( sup_sup @ A @ A2 @ B3 )
% 1.99/1.29 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A3 @ B3 ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_45_mem__Collect__eq,axiom,
% 1.99/1.29 ! [A: $tType,A3: A,P: A > $o] :
% 1.99/1.29 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 1.99/1.29 = ( P @ A3 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_46_Collect__mem__eq,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A] :
% 1.99/1.29 ( ( collect @ A
% 1.99/1.29 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 1.99/1.29 = A2 ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_47_Collect__cong,axiom,
% 1.99/1.29 ! [A: $tType,P: A > $o,Q: A > $o] :
% 1.99/1.29 ( ! [X3: A] :
% 1.99/1.29 ( ( P @ X3 )
% 1.99/1.29 = ( Q @ X3 ) )
% 1.99/1.29 => ( ( collect @ A @ P )
% 1.99/1.29 = ( collect @ A @ Q ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_48_ext,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType,F2: A > B,G2: A > B] :
% 1.99/1.29 ( ! [X3: A] :
% 1.99/1.29 ( ( F2 @ X3 )
% 1.99/1.29 = ( G2 @ X3 ) )
% 1.99/1.29 => ( F2 = G2 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_49_sup__fun__def,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ B )
% 1.99/1.29 => ( ( sup_sup @ ( A > B ) )
% 1.99/1.29 = ( ^ [F: A > B,G: A > B,X2: A] : ( sup_sup @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_50_inf__sup__aci_I5_J,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( lattice @ A )
% 1.99/1.29 => ( ( sup_sup @ A )
% 1.99/1.29 = ( ^ [X2: A,Y3: A] : ( sup_sup @ A @ Y3 @ X2 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_51_inf__sup__aci_I6_J,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( lattice @ A )
% 1.99/1.29 => ! [X: A,Y: A,Z: A] :
% 1.99/1.29 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 1.99/1.29 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_52_inf__sup__aci_I7_J,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( lattice @ A )
% 1.99/1.29 => ! [X: A,Y: A,Z: A] :
% 1.99/1.29 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 1.99/1.29 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_53_inf__sup__aci_I8_J,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( lattice @ A )
% 1.99/1.29 => ! [X: A,Y: A] :
% 1.99/1.29 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 1.99/1.29 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_54_not__union__or,axiom,
% 1.99/1.29 ! [A: $tType,X: A,A2: set @ A,B2: set @ A] :
% 1.99/1.29 ( ( ~ ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) )
% 1.99/1.29 = ( ~ ( member @ A @ X @ A2 )
% 1.99/1.29 & ~ ( member @ A @ X @ B2 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_55_Un__left__commute,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A,B2: set @ A,C2: set @ A] :
% 1.99/1.29 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C2 ) )
% 1.99/1.29 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A2 @ C2 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_56_Un__left__absorb,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 1.99/1.29 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 1.99/1.29 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_57_Un__commute,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( sup_sup @ ( set @ A ) )
% 1.99/1.29 = ( ^ [A4: set @ A,B4: set @ A] : ( sup_sup @ ( set @ A ) @ B4 @ A4 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_58_Un__absorb,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A] :
% 1.99/1.29 ( ( sup_sup @ ( set @ A ) @ A2 @ A2 )
% 1.99/1.29 = A2 ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_59_Un__assoc,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A,B2: set @ A,C2: set @ A] :
% 1.99/1.29 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C2 )
% 1.99/1.29 = ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C2 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_60_ball__Un,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 1.99/1.29 ( ( ! [X2: A] :
% 1.99/1.29 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 1.99/1.29 => ( P @ X2 ) ) )
% 1.99/1.29 = ( ! [X2: A] :
% 1.99/1.29 ( ( member @ A @ X2 @ A2 )
% 1.99/1.29 => ( P @ X2 ) )
% 1.99/1.29 & ! [X2: A] :
% 1.99/1.29 ( ( member @ A @ X2 @ B2 )
% 1.99/1.29 => ( P @ X2 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_61_bex__Un,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 1.99/1.29 ( ( ? [X2: A] :
% 1.99/1.29 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 1.99/1.29 & ( P @ X2 ) ) )
% 1.99/1.29 = ( ? [X2: A] :
% 1.99/1.29 ( ( member @ A @ X2 @ A2 )
% 1.99/1.29 & ( P @ X2 ) )
% 1.99/1.29 | ? [X2: A] :
% 1.99/1.29 ( ( member @ A @ X2 @ B2 )
% 1.99/1.29 & ( P @ X2 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_62_UnI2,axiom,
% 1.99/1.29 ! [A: $tType,C3: A,B2: set @ A,A2: set @ A] :
% 1.99/1.29 ( ( member @ A @ C3 @ B2 )
% 1.99/1.29 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_63_UnI1,axiom,
% 1.99/1.29 ! [A: $tType,C3: A,A2: set @ A,B2: set @ A] :
% 1.99/1.29 ( ( member @ A @ C3 @ A2 )
% 1.99/1.29 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_64_UnE,axiom,
% 1.99/1.29 ! [A: $tType,C3: A,A2: set @ A,B2: set @ A] :
% 1.99/1.29 ( ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 1.99/1.29 => ( ~ ( member @ A @ C3 @ A2 )
% 1.99/1.29 => ( member @ A @ C3 @ B2 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_65_usubstappp__antimon,axiom,
% 1.99/1.29 ! [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 ) ) ) ),Alpha: game] :
% 1.99/1.29 ( ( ord_less_eq @ ( set @ variable ) @ V @ U )
% 1.99/1.29 => ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) )
% 1.99/1.29 != ( none @ game ) )
% 1.99/1.29 => ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) )
% 1.99/1.29 = ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ V @ Alpha ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_66_sup_OcoboundedI2,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [C3: A,B3: A,A3: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ C3 @ B3 )
% 1.99/1.29 => ( ord_less_eq @ A @ C3 @ ( sup_sup @ A @ A3 @ B3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_67_sup_OcoboundedI1,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [C3: A,A3: A,B3: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ C3 @ A3 )
% 1.99/1.29 => ( ord_less_eq @ A @ C3 @ ( sup_sup @ A @ A3 @ B3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_68_sup_Oabsorb__iff2,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ( ( ord_less_eq @ A )
% 1.99/1.29 = ( ^ [A5: A,B5: A] :
% 1.99/1.29 ( ( sup_sup @ A @ A5 @ B5 )
% 1.99/1.29 = B5 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_69_sup_Oabsorb__iff1,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ( ( ord_less_eq @ A )
% 1.99/1.29 = ( ^ [B5: A,A5: A] :
% 1.99/1.29 ( ( sup_sup @ A @ A5 @ B5 )
% 1.99/1.29 = A5 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_70_sup_Ocobounded2,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [B3: A,A3: A] : ( ord_less_eq @ A @ B3 @ ( sup_sup @ A @ A3 @ B3 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_71_sup_Ocobounded1,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [A3: A,B3: A] : ( ord_less_eq @ A @ A3 @ ( sup_sup @ A @ A3 @ B3 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_72_sup_Oorder__iff,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ( ( ord_less_eq @ A )
% 1.99/1.29 = ( ^ [B5: A,A5: A] :
% 1.99/1.29 ( A5
% 1.99/1.29 = ( sup_sup @ A @ A5 @ B5 ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_73_sup_OboundedI,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [B3: A,A3: A,C3: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ B3 @ A3 )
% 1.99/1.29 => ( ( ord_less_eq @ A @ C3 @ A3 )
% 1.99/1.29 => ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C3 ) @ A3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_74_sup_OboundedE,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [B3: A,C3: A,A3: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C3 ) @ A3 )
% 1.99/1.29 => ~ ( ( ord_less_eq @ A @ B3 @ A3 )
% 1.99/1.29 => ~ ( ord_less_eq @ A @ C3 @ A3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_75_sup__absorb2,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [X: A,Y: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ X @ Y )
% 1.99/1.29 => ( ( sup_sup @ A @ X @ Y )
% 1.99/1.29 = Y ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_76_sup__absorb1,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [Y: A,X: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ Y @ X )
% 1.99/1.29 => ( ( sup_sup @ A @ X @ Y )
% 1.99/1.29 = X ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_77_sup_Oabsorb2,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [A3: A,B3: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ A3 @ B3 )
% 1.99/1.29 => ( ( sup_sup @ A @ A3 @ B3 )
% 1.99/1.29 = B3 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_78_sup_Oabsorb1,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [B3: A,A3: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ B3 @ A3 )
% 1.99/1.29 => ( ( sup_sup @ A @ A3 @ B3 )
% 1.99/1.29 = A3 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_79_sup__unique,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [F2: A > A > A,X: A,Y: A] :
% 1.99/1.29 ( ! [X3: A,Y4: A] : ( ord_less_eq @ A @ X3 @ ( F2 @ X3 @ Y4 ) )
% 1.99/1.29 => ( ! [X3: A,Y4: A] : ( ord_less_eq @ A @ Y4 @ ( F2 @ X3 @ Y4 ) )
% 1.99/1.29 => ( ! [X3: A,Y4: A,Z3: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ Y4 @ X3 )
% 1.99/1.29 => ( ( ord_less_eq @ A @ Z3 @ X3 )
% 1.99/1.29 => ( ord_less_eq @ A @ ( F2 @ Y4 @ Z3 ) @ X3 ) ) )
% 1.99/1.29 => ( ( sup_sup @ A @ X @ Y )
% 1.99/1.29 = ( F2 @ X @ Y ) ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_80_sup_OorderI,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [A3: A,B3: A] :
% 1.99/1.29 ( ( A3
% 1.99/1.29 = ( sup_sup @ A @ A3 @ B3 ) )
% 1.99/1.29 => ( ord_less_eq @ A @ B3 @ A3 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_81_sup_OorderE,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [B3: A,A3: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ B3 @ A3 )
% 1.99/1.29 => ( A3
% 1.99/1.29 = ( sup_sup @ A @ A3 @ B3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_82_le__iff__sup,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ( ( ord_less_eq @ A )
% 1.99/1.29 = ( ^ [X2: A,Y3: A] :
% 1.99/1.29 ( ( sup_sup @ A @ X2 @ Y3 )
% 1.99/1.29 = Y3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_83_sup__least,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [Y: A,X: A,Z: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ Y @ X )
% 1.99/1.29 => ( ( ord_less_eq @ A @ Z @ X )
% 1.99/1.29 => ( ord_less_eq @ A @ ( sup_sup @ A @ Y @ Z ) @ X ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_84_sup__mono,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [A3: A,C3: A,B3: A,D2: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ A3 @ C3 )
% 1.99/1.29 => ( ( ord_less_eq @ A @ B3 @ D2 )
% 1.99/1.29 => ( ord_less_eq @ A @ ( sup_sup @ A @ A3 @ B3 ) @ ( sup_sup @ A @ C3 @ D2 ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_85_sup_Omono,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [C3: A,A3: A,D2: A,B3: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ C3 @ A3 )
% 1.99/1.29 => ( ( ord_less_eq @ A @ D2 @ B3 )
% 1.99/1.29 => ( ord_less_eq @ A @ ( sup_sup @ A @ C3 @ D2 ) @ ( sup_sup @ A @ A3 @ B3 ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_86_le__supI2,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [X: A,B3: A,A3: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ X @ B3 )
% 1.99/1.29 => ( ord_less_eq @ A @ X @ ( sup_sup @ A @ A3 @ B3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_87_le__supI1,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [X: A,A3: A,B3: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ X @ A3 )
% 1.99/1.29 => ( ord_less_eq @ A @ X @ ( sup_sup @ A @ A3 @ B3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_88_sup__ge2,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [Y: A,X: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_89_sup__ge1,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [X: A,Y: A] : ( ord_less_eq @ A @ X @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_90_le__supI,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [A3: A,X: A,B3: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ A3 @ X )
% 1.99/1.29 => ( ( ord_less_eq @ A @ B3 @ X )
% 1.99/1.29 => ( ord_less_eq @ A @ ( sup_sup @ A @ A3 @ B3 ) @ X ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_91_le__supE,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( semilattice_sup @ A )
% 1.99/1.29 => ! [A3: A,B3: A,X: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ ( sup_sup @ A @ A3 @ B3 ) @ X )
% 1.99/1.29 => ~ ( ( ord_less_eq @ A @ A3 @ X )
% 1.99/1.29 => ~ ( ord_less_eq @ A @ B3 @ X ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_92_inf__sup__ord_I3_J,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( lattice @ A )
% 1.99/1.29 => ! [X: A,Y: A] : ( ord_less_eq @ A @ X @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_93_inf__sup__ord_I4_J,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( lattice @ A )
% 1.99/1.29 => ! [Y: A,X: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_94_subset__Un__eq,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( ord_less_eq @ ( set @ A ) )
% 1.99/1.29 = ( ^ [A4: set @ A,B4: set @ A] :
% 1.99/1.29 ( ( sup_sup @ ( set @ A ) @ A4 @ B4 )
% 1.99/1.29 = B4 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_95_subset__UnE,axiom,
% 1.99/1.29 ! [A: $tType,C2: set @ A,A2: set @ A,B2: set @ A] :
% 1.99/1.29 ( ( ord_less_eq @ ( set @ A ) @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 1.99/1.29 => ~ ! [A6: set @ A] :
% 1.99/1.29 ( ( ord_less_eq @ ( set @ A ) @ A6 @ A2 )
% 1.99/1.29 => ! [B6: set @ A] :
% 1.99/1.29 ( ( ord_less_eq @ ( set @ A ) @ B6 @ B2 )
% 1.99/1.29 => ( C2
% 1.99/1.29 != ( sup_sup @ ( set @ A ) @ A6 @ B6 ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_96_Un__absorb2,axiom,
% 1.99/1.29 ! [A: $tType,B2: set @ A,A2: set @ A] :
% 1.99/1.29 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 1.99/1.29 => ( ( sup_sup @ ( set @ A ) @ A2 @ B2 )
% 1.99/1.29 = A2 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_97_Un__absorb1,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 1.99/1.29 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 1.99/1.29 => ( ( sup_sup @ ( set @ A ) @ A2 @ B2 )
% 1.99/1.29 = B2 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_98_Un__upper2,axiom,
% 1.99/1.29 ! [A: $tType,B2: set @ A,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_99_Un__upper1,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A,B2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_100_Un__least,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A,C2: set @ A,B2: set @ A] :
% 1.99/1.29 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C2 )
% 1.99/1.29 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C2 )
% 1.99/1.29 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C2 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_101_Un__mono,axiom,
% 1.99/1.29 ! [A: $tType,A2: set @ A,C2: set @ A,B2: set @ A,D3: set @ A] :
% 1.99/1.29 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C2 )
% 1.99/1.29 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ D3 )
% 1.99/1.29 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ ( sup_sup @ ( set @ A ) @ C2 @ D3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_102_order__refl,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( preorder @ A )
% 1.99/1.29 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_103_option_Oexpand,axiom,
% 1.99/1.29 ! [A: $tType,Option: option @ A,Option2: option @ A] :
% 1.99/1.29 ( ( ( Option
% 1.99/1.29 = ( none @ A ) )
% 1.99/1.29 = ( Option2
% 1.99/1.29 = ( none @ A ) ) )
% 1.99/1.29 => ( ( ( Option
% 1.99/1.29 != ( none @ A ) )
% 1.99/1.29 => ( ( Option2
% 1.99/1.29 != ( none @ A ) )
% 1.99/1.29 => ( ( the @ A @ Option )
% 1.99/1.29 = ( the @ A @ Option2 ) ) ) )
% 1.99/1.29 => ( Option = Option2 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_104_prod__eq__iff,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType] :
% 1.99/1.29 ( ( ^ [Y2: product_prod @ A @ B,Z2: product_prod @ A @ B] : ( Y2 = Z2 ) )
% 1.99/1.29 = ( ^ [S: product_prod @ A @ B,T2: product_prod @ A @ B] :
% 1.99/1.29 ( ( ( product_fst @ A @ B @ S )
% 1.99/1.29 = ( product_fst @ A @ B @ T2 ) )
% 1.99/1.29 & ( ( product_snd @ A @ B @ S )
% 1.99/1.29 = ( product_snd @ A @ B @ T2 ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_105_prod_Oexpand,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B,Prod2: product_prod @ A @ B] :
% 1.99/1.29 ( ( ( ( product_fst @ A @ B @ Prod )
% 1.99/1.29 = ( product_fst @ A @ B @ Prod2 ) )
% 1.99/1.29 & ( ( product_snd @ A @ B @ Prod )
% 1.99/1.29 = ( product_snd @ A @ B @ Prod2 ) ) )
% 1.99/1.29 => ( Prod = Prod2 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_106_exE__realizer_H,axiom,
% 1.99/1.29 ! [A: $tType,B: $tType,P: A > B > $o,P2: product_prod @ B @ A] :
% 1.99/1.29 ( ( P @ ( product_snd @ B @ A @ P2 ) @ ( product_fst @ B @ A @ P2 ) )
% 1.99/1.29 => ~ ! [X3: B,Y4: A] :
% 1.99/1.29 ~ ( P @ Y4 @ X3 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_107_prod__eqI,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType,P2: product_prod @ A @ B,Q2: product_prod @ A @ B] :
% 1.99/1.29 ( ( ( product_fst @ A @ B @ P2 )
% 1.99/1.29 = ( product_fst @ A @ B @ Q2 ) )
% 1.99/1.29 => ( ( ( product_snd @ A @ B @ P2 )
% 1.99/1.29 = ( product_snd @ A @ B @ Q2 ) )
% 1.99/1.29 => ( P2 = Q2 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_108_usubstappp__loop__conv,axiom,
% 1.99/1.29 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Alpha: game] :
% 1.99/1.29 ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ ( loop @ Alpha ) ) )
% 1.99/1.29 != ( none @ game ) )
% 1.99/1.29 => ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) )
% 1.99/1.29 != ( none @ game ) )
% 1.99/1.29 & ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) )
% 1.99/1.29 != ( none @ game ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_109_BVG__choice,axiom,
% 1.99/1.29 ! [Alpha: game,Beta: game] : ( ord_less_eq @ ( set @ variable ) @ ( static_BVG @ ( choice @ Alpha @ Beta ) ) @ ( sup_sup @ ( set @ variable ) @ ( static_BVG @ Alpha ) @ ( static_BVG @ Beta ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_110_usubstappp__choice__conv,axiom,
% 1.99/1.29 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Alpha: game,Beta: game] :
% 1.99/1.29 ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ ( choice @ Alpha @ Beta ) ) )
% 1.99/1.29 != ( none @ game ) )
% 1.99/1.29 => ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) )
% 1.99/1.29 != ( none @ game ) )
% 1.99/1.29 & ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Beta ) )
% 1.99/1.29 != ( none @ game ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_111_game_Oinject_I6_J,axiom,
% 1.99/1.29 ! [X6: game,Y6: game] :
% 1.99/1.29 ( ( ( loop @ X6 )
% 1.99/1.29 = ( loop @ Y6 ) )
% 1.99/1.29 = ( X6 = Y6 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_112_game_Oinject_I4_J,axiom,
% 1.99/1.29 ! [X41: game,X42: game,Y41: game,Y42: game] :
% 1.99/1.29 ( ( ( choice @ X41 @ X42 )
% 1.99/1.29 = ( choice @ Y41 @ Y42 ) )
% 1.99/1.29 = ( ( X41 = Y41 )
% 1.99/1.29 & ( X42 = Y42 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_113_game_Odistinct_I39_J,axiom,
% 1.99/1.29 ! [X41: game,X42: game,X6: game] :
% 1.99/1.29 ( ( choice @ X41 @ X42 )
% 1.99/1.29 != ( loop @ X6 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_114_game_Odistinct_I45_J,axiom,
% 1.99/1.29 ! [X51: game,X52: game,X6: game] :
% 1.99/1.29 ( ( compose @ X51 @ X52 )
% 1.99/1.29 != ( loop @ X6 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_115_game_Odistinct_I37_J,axiom,
% 1.99/1.29 ! [X41: game,X42: game,X51: game,X52: game] :
% 1.99/1.29 ( ( choice @ X41 @ X42 )
% 1.99/1.29 != ( compose @ X51 @ X52 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_116_BVG__loop,axiom,
% 1.99/1.29 ! [Alpha: game] : ( ord_less_eq @ ( set @ variable ) @ ( static_BVG @ ( loop @ Alpha ) ) @ ( static_BVG @ Alpha ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_117_le__funD,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType] :
% 1.99/1.29 ( ( ord @ B )
% 1.99/1.29 => ! [F2: A > B,G2: A > B,X: A] :
% 1.99/1.29 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 1.99/1.29 => ( ord_less_eq @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_118_le__funE,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType] :
% 1.99/1.29 ( ( ord @ B )
% 1.99/1.29 => ! [F2: A > B,G2: A > B,X: A] :
% 1.99/1.29 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 1.99/1.29 => ( ord_less_eq @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_119_le__funI,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType] :
% 1.99/1.29 ( ( ord @ B )
% 1.99/1.29 => ! [F2: A > B,G2: A > B] :
% 1.99/1.29 ( ! [X3: A] : ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 1.99/1.29 => ( ord_less_eq @ ( A > B ) @ F2 @ G2 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_120_le__fun__def,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType] :
% 1.99/1.29 ( ( ord @ B )
% 1.99/1.29 => ( ( ord_less_eq @ ( A > B ) )
% 1.99/1.29 = ( ^ [F: A > B,G: A > B] :
% 1.99/1.29 ! [X2: A] : ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_121_order__subst1,axiom,
% 1.99/1.29 ! [A: $tType,B: $tType] :
% 1.99/1.29 ( ( ( order @ B )
% 1.99/1.29 & ( order @ A ) )
% 1.99/1.29 => ! [A3: A,F2: B > A,B3: B,C3: B] :
% 1.99/1.29 ( ( ord_less_eq @ A @ A3 @ ( F2 @ B3 ) )
% 1.99/1.29 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 1.99/1.29 => ( ! [X3: B,Y4: B] :
% 1.99/1.29 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 1.99/1.29 => ( ord_less_eq @ A @ ( F2 @ X3 ) @ ( F2 @ Y4 ) ) )
% 1.99/1.29 => ( ord_less_eq @ A @ A3 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_122_order__subst2,axiom,
% 1.99/1.29 ! [A: $tType,C: $tType] :
% 1.99/1.29 ( ( ( order @ C )
% 1.99/1.29 & ( order @ A ) )
% 1.99/1.29 => ! [A3: A,B3: A,F2: A > C,C3: C] :
% 1.99/1.29 ( ( ord_less_eq @ A @ A3 @ B3 )
% 1.99/1.29 => ( ( ord_less_eq @ C @ ( F2 @ B3 ) @ C3 )
% 1.99/1.29 => ( ! [X3: A,Y4: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 1.99/1.29 => ( ord_less_eq @ C @ ( F2 @ X3 ) @ ( F2 @ Y4 ) ) )
% 1.99/1.29 => ( ord_less_eq @ C @ ( F2 @ A3 ) @ C3 ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_123_ord__eq__le__subst,axiom,
% 1.99/1.29 ! [A: $tType,B: $tType] :
% 1.99/1.29 ( ( ( ord @ B )
% 1.99/1.29 & ( ord @ A ) )
% 1.99/1.29 => ! [A3: A,F2: B > A,B3: B,C3: B] :
% 1.99/1.29 ( ( A3
% 1.99/1.29 = ( F2 @ B3 ) )
% 1.99/1.29 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 1.99/1.29 => ( ! [X3: B,Y4: B] :
% 1.99/1.29 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 1.99/1.29 => ( ord_less_eq @ A @ ( F2 @ X3 ) @ ( F2 @ Y4 ) ) )
% 1.99/1.29 => ( ord_less_eq @ A @ A3 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_124_ord__le__eq__subst,axiom,
% 1.99/1.29 ! [A: $tType,B: $tType] :
% 1.99/1.29 ( ( ( ord @ B )
% 1.99/1.29 & ( ord @ A ) )
% 1.99/1.29 => ! [A3: A,B3: A,F2: A > B,C3: B] :
% 1.99/1.29 ( ( ord_less_eq @ A @ A3 @ B3 )
% 1.99/1.29 => ( ( ( F2 @ B3 )
% 1.99/1.29 = C3 )
% 1.99/1.29 => ( ! [X3: A,Y4: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 1.99/1.29 => ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( F2 @ Y4 ) ) )
% 1.99/1.29 => ( ord_less_eq @ B @ ( F2 @ A3 ) @ C3 ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_125_eq__iff,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( order @ A )
% 1.99/1.29 => ( ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 1.99/1.29 = ( ^ [X2: A,Y3: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 1.99/1.29 & ( ord_less_eq @ A @ Y3 @ X2 ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_126_antisym,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( order @ A )
% 1.99/1.29 => ! [X: A,Y: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ X @ Y )
% 1.99/1.29 => ( ( ord_less_eq @ A @ Y @ X )
% 1.99/1.29 => ( X = Y ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_127_linear,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( linorder @ A )
% 1.99/1.29 => ! [X: A,Y: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ X @ Y )
% 1.99/1.29 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_128_eq__refl,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( preorder @ A )
% 1.99/1.29 => ! [X: A,Y: A] :
% 1.99/1.29 ( ( X = Y )
% 1.99/1.29 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_129_le__cases,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( linorder @ A )
% 1.99/1.29 => ! [X: A,Y: A] :
% 1.99/1.29 ( ~ ( ord_less_eq @ A @ X @ Y )
% 1.99/1.29 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_130_order_Otrans,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( order @ A )
% 1.99/1.29 => ! [A3: A,B3: A,C3: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ A3 @ B3 )
% 1.99/1.29 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 1.99/1.29 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_131_le__cases3,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( linorder @ A )
% 1.99/1.29 => ! [X: A,Y: A,Z: A] :
% 1.99/1.29 ( ( ( ord_less_eq @ A @ X @ Y )
% 1.99/1.29 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 1.99/1.29 => ( ( ( ord_less_eq @ A @ Y @ X )
% 1.99/1.29 => ~ ( ord_less_eq @ A @ X @ Z ) )
% 1.99/1.29 => ( ( ( ord_less_eq @ A @ X @ Z )
% 1.99/1.29 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 1.99/1.29 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 1.99/1.29 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 1.99/1.29 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 1.99/1.29 => ~ ( ord_less_eq @ A @ Z @ X ) )
% 1.99/1.29 => ~ ( ( ord_less_eq @ A @ Z @ X )
% 1.99/1.29 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_132_antisym__conv,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( order @ A )
% 1.99/1.29 => ! [Y: A,X: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ Y @ X )
% 1.99/1.29 => ( ( ord_less_eq @ A @ X @ Y )
% 1.99/1.29 = ( X = Y ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_133_order__class_Oorder_Oeq__iff,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( order @ A )
% 1.99/1.29 => ( ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 1.99/1.29 = ( ^ [A5: A,B5: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ A5 @ B5 )
% 1.99/1.29 & ( ord_less_eq @ A @ B5 @ A5 ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_134_ord__eq__le__trans,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( ord @ A )
% 1.99/1.29 => ! [A3: A,B3: A,C3: A] :
% 1.99/1.29 ( ( A3 = B3 )
% 1.99/1.29 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 1.99/1.29 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_135_ord__le__eq__trans,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( ord @ A )
% 1.99/1.29 => ! [A3: A,B3: A,C3: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ A3 @ B3 )
% 1.99/1.29 => ( ( B3 = C3 )
% 1.99/1.29 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_136_order__class_Oorder_Oantisym,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( order @ A )
% 1.99/1.29 => ! [A3: A,B3: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ A3 @ B3 )
% 1.99/1.29 => ( ( ord_less_eq @ A @ B3 @ A3 )
% 1.99/1.29 => ( A3 = B3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_137_order__trans,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( preorder @ A )
% 1.99/1.29 => ! [X: A,Y: A,Z: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ X @ Y )
% 1.99/1.29 => ( ( ord_less_eq @ A @ Y @ Z )
% 1.99/1.29 => ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_138_dual__order_Orefl,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( order @ A )
% 1.99/1.29 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_139_linorder__wlog,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( linorder @ A )
% 1.99/1.29 => ! [P: A > A > $o,A3: A,B3: A] :
% 1.99/1.29 ( ! [A7: A,B7: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ A7 @ B7 )
% 1.99/1.29 => ( P @ A7 @ B7 ) )
% 1.99/1.29 => ( ! [A7: A,B7: A] :
% 1.99/1.29 ( ( P @ B7 @ A7 )
% 1.99/1.29 => ( P @ A7 @ B7 ) )
% 1.99/1.29 => ( P @ A3 @ B3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_140_dual__order_Otrans,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( order @ A )
% 1.99/1.29 => ! [B3: A,A3: A,C3: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ B3 @ A3 )
% 1.99/1.29 => ( ( ord_less_eq @ A @ C3 @ B3 )
% 1.99/1.29 => ( ord_less_eq @ A @ C3 @ A3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_141_dual__order_Oeq__iff,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( order @ A )
% 1.99/1.29 => ( ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 1.99/1.29 = ( ^ [A5: A,B5: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ B5 @ A5 )
% 1.99/1.29 & ( ord_less_eq @ A @ A5 @ B5 ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_142_dual__order_Oantisym,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( order @ A )
% 1.99/1.29 => ! [B3: A,A3: A] :
% 1.99/1.29 ( ( ord_less_eq @ A @ B3 @ A3 )
% 1.99/1.29 => ( ( ord_less_eq @ A @ A3 @ B3 )
% 1.99/1.29 => ( A3 = B3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_143_fst__swap,axiom,
% 1.99/1.29 ! [A: $tType,B: $tType,X: product_prod @ B @ A] :
% 1.99/1.29 ( ( product_fst @ A @ B @ ( product_swap @ B @ A @ X ) )
% 1.99/1.29 = ( product_snd @ B @ A @ X ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_144_snd__swap,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType,X: product_prod @ A @ B] :
% 1.99/1.29 ( ( product_snd @ B @ A @ ( product_swap @ A @ B @ X ) )
% 1.99/1.29 = ( product_fst @ A @ B @ X ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_145_usubstappp__choice,axiom,
% 1.99/1.29 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Alpha: game,Beta: game] :
% 1.99/1.29 ( ( uSubst95898988stappp @ Sigma @ U @ ( choice @ Alpha @ Beta ) )
% 1.99/1.29 = ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( sup_sup @ ( set @ variable ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Beta ) ) ) @ ( uSubst1976112797hoiceo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Beta ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_146_GreatestI2__order,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( order @ A )
% 1.99/1.29 => ! [P: A > $o,X: A,Q: A > $o] :
% 1.99/1.29 ( ( P @ X )
% 1.99/1.29 => ( ! [Y4: A] :
% 1.99/1.29 ( ( P @ Y4 )
% 1.99/1.29 => ( ord_less_eq @ A @ Y4 @ X ) )
% 1.99/1.29 => ( ! [X3: A] :
% 1.99/1.29 ( ( P @ X3 )
% 1.99/1.29 => ( ! [Y5: A] :
% 1.99/1.29 ( ( P @ Y5 )
% 1.99/1.29 => ( ord_less_eq @ A @ Y5 @ X3 ) )
% 1.99/1.29 => ( Q @ X3 ) ) )
% 1.99/1.29 => ( Q @ ( order_Greatest @ A @ P ) ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_147_Greatest__equality,axiom,
% 1.99/1.29 ! [A: $tType] :
% 1.99/1.29 ( ( order @ A )
% 1.99/1.29 => ! [P: A > $o,X: A] :
% 1.99/1.29 ( ( P @ X )
% 1.99/1.29 => ( ! [Y4: A] :
% 1.99/1.29 ( ( P @ Y4 )
% 1.99/1.29 => ( ord_less_eq @ A @ Y4 @ X ) )
% 1.99/1.29 => ( ( order_Greatest @ A @ P )
% 1.99/1.29 = X ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_148_old_Oprod_Oinject,axiom,
% 1.99/1.29 ! [A: $tType,B: $tType,A3: A,B3: B,A8: A,B8: B] :
% 1.99/1.29 ( ( ( product_Pair @ A @ B @ A3 @ B3 )
% 1.99/1.29 = ( product_Pair @ A @ B @ A8 @ B8 ) )
% 1.99/1.29 = ( ( A3 = A8 )
% 1.99/1.29 & ( B3 = B8 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_149_prod_Oinject,axiom,
% 1.99/1.29 ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y22: B] :
% 1.99/1.29 ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 1.99/1.29 = ( product_Pair @ A @ B @ Y1 @ Y22 ) )
% 1.99/1.29 = ( ( X1 = Y1 )
% 1.99/1.29 & ( X22 = Y22 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_150_swap__swap,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType,P2: product_prod @ A @ B] :
% 1.99/1.29 ( ( product_swap @ B @ A @ ( product_swap @ A @ B @ P2 ) )
% 1.99/1.29 = P2 ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_151_swap__simp,axiom,
% 1.99/1.29 ! [A: $tType,B: $tType,X: B,Y: A] :
% 1.99/1.29 ( ( product_swap @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) )
% 1.99/1.29 = ( product_Pair @ A @ B @ Y @ X ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_152_prod_Ocollapse,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 1.99/1.29 ( ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) )
% 1.99/1.29 = Prod ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_153_old_Oprod_Oinducts,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 1.99/1.29 ( ! [A7: A,B7: B] : ( P @ ( product_Pair @ A @ B @ A7 @ B7 ) )
% 1.99/1.29 => ( P @ Prod ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_154_old_Oprod_Oexhaust,axiom,
% 1.99/1.29 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 1.99/1.29 ~ ! [A7: A,B7: B] :
% 1.99/1.29 ( Y
% 1.99/1.29 != ( product_Pair @ A @ B @ A7 @ B7 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_155_prod__induct7,axiom,
% 1.99/1.29 ! [G3: $tType,F3: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) )] :
% 1.99/1.29 ( ! [A7: A,B7: B,C4: C,D4: D,E2: E,F4: F3,G4: G3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) @ B7 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) @ D4 @ ( product_Pair @ E @ ( product_prod @ F3 @ G3 ) @ E2 @ ( product_Pair @ F3 @ G3 @ F4 @ G4 ) ) ) ) ) ) )
% 1.99/1.29 => ( P @ X ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_156_prod__induct6,axiom,
% 1.99/1.29 ! [F3: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) )] :
% 1.99/1.29 ( ! [A7: A,B7: B,C4: C,D4: D,E2: E,F4: F3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B7 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D4 @ ( product_Pair @ E @ F3 @ E2 @ F4 ) ) ) ) ) )
% 1.99/1.29 => ( P @ X ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_157_prod__induct5,axiom,
% 1.99/1.29 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 1.99/1.29 ( ! [A7: A,B7: B,C4: C,D4: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B7 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C4 @ ( product_Pair @ D @ E @ D4 @ E2 ) ) ) ) )
% 1.99/1.29 => ( P @ X ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_158_prod__induct4,axiom,
% 1.99/1.29 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 1.99/1.29 ( ! [A7: A,B7: B,C4: C,D4: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B7 @ ( product_Pair @ C @ D @ C4 @ D4 ) ) ) )
% 1.99/1.29 => ( P @ X ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_159_prod__induct3,axiom,
% 1.99/1.29 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 1.99/1.29 ( ! [A7: A,B7: B,C4: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A7 @ ( product_Pair @ B @ C @ B7 @ C4 ) ) )
% 1.99/1.29 => ( P @ X ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_160_prod__cases7,axiom,
% 1.99/1.29 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,G3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) )] :
% 1.99/1.29 ~ ! [A7: A,B7: B,C4: C,D4: D,E2: E,F4: F3,G4: G3] :
% 1.99/1.29 ( Y
% 1.99/1.29 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) @ B7 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) @ D4 @ ( product_Pair @ E @ ( product_prod @ F3 @ G3 ) @ E2 @ ( product_Pair @ F3 @ G3 @ F4 @ G4 ) ) ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_161_prod__cases6,axiom,
% 1.99/1.29 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) )] :
% 1.99/1.29 ~ ! [A7: A,B7: B,C4: C,D4: D,E2: E,F4: F3] :
% 1.99/1.29 ( Y
% 1.99/1.29 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B7 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D4 @ ( product_Pair @ E @ F3 @ E2 @ F4 ) ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_162_prod__cases5,axiom,
% 1.99/1.29 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 1.99/1.29 ~ ! [A7: A,B7: B,C4: C,D4: D,E2: E] :
% 1.99/1.29 ( Y
% 1.99/1.29 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B7 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C4 @ ( product_Pair @ D @ E @ D4 @ E2 ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_163_prod__cases4,axiom,
% 1.99/1.29 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 1.99/1.29 ~ ! [A7: A,B7: B,C4: C,D4: D] :
% 1.99/1.29 ( Y
% 1.99/1.29 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B7 @ ( product_Pair @ C @ D @ C4 @ D4 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_164_prod__cases3,axiom,
% 1.99/1.29 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 1.99/1.29 ~ ! [A7: A,B7: B,C4: C] :
% 1.99/1.29 ( Y
% 1.99/1.29 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A7 @ ( product_Pair @ B @ C @ B7 @ C4 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_165_Pair__inject,axiom,
% 1.99/1.29 ! [A: $tType,B: $tType,A3: A,B3: B,A8: A,B8: B] :
% 1.99/1.29 ( ( ( product_Pair @ A @ B @ A3 @ B3 )
% 1.99/1.29 = ( product_Pair @ A @ B @ A8 @ B8 ) )
% 1.99/1.29 => ~ ( ( A3 = A8 )
% 1.99/1.29 => ( B3 != B8 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_166_prod__cases,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 1.99/1.29 ( ! [A7: A,B7: B] : ( P @ ( product_Pair @ A @ B @ A7 @ B7 ) )
% 1.99/1.29 => ( P @ P2 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_167_surj__pair,axiom,
% 1.99/1.29 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 1.99/1.29 ? [X3: A,Y4: B] :
% 1.99/1.29 ( P2
% 1.99/1.29 = ( product_Pair @ A @ B @ X3 @ Y4 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_168_fst__eqD,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType,X: A,Y: B,A3: A] :
% 1.99/1.29 ( ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X @ Y ) )
% 1.99/1.29 = A3 )
% 1.99/1.29 => ( X = A3 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_169_fst__conv,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType,X1: A,X22: B] :
% 1.99/1.29 ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X1 @ X22 ) )
% 1.99/1.29 = X1 ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_170_snd__eqD,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType,X: B,Y: A,A3: A] :
% 1.99/1.29 ( ( ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) )
% 1.99/1.29 = A3 )
% 1.99/1.29 => ( Y = A3 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_171_snd__conv,axiom,
% 1.99/1.29 ! [Aa: $tType,A: $tType,X1: Aa,X22: A] :
% 1.99/1.29 ( ( product_snd @ Aa @ A @ ( product_Pair @ Aa @ A @ X1 @ X22 ) )
% 1.99/1.29 = X22 ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_172_prod_Oswap__def,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType] :
% 1.99/1.29 ( ( product_swap @ A @ B )
% 1.99/1.29 = ( ^ [P3: product_prod @ A @ B] : ( product_Pair @ B @ A @ ( product_snd @ A @ B @ P3 ) @ ( product_fst @ A @ B @ P3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_173_fst__pair,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType,A3: A,B3: B] :
% 1.99/1.29 ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ A3 @ B3 ) )
% 1.99/1.29 = A3 ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_174_snd__pair,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType,A3: B,B3: A] :
% 1.99/1.29 ( ( product_snd @ B @ A @ ( product_Pair @ B @ A @ A3 @ B3 ) )
% 1.99/1.29 = B3 ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_175_surjective__pairing,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType,T3: product_prod @ A @ B] :
% 1.99/1.29 ( T3
% 1.99/1.29 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ T3 ) @ ( product_snd @ A @ B @ T3 ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_176_prod_Oexhaust__sel,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 1.99/1.29 ( Prod
% 1.99/1.29 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_177_conjI__realizer,axiom,
% 1.99/1.29 ! [A: $tType,B: $tType,P: A > $o,P2: A,Q: B > $o,Q2: B] :
% 1.99/1.29 ( ( P @ P2 )
% 1.99/1.29 => ( ( Q @ Q2 )
% 1.99/1.29 => ( ( P @ ( product_fst @ A @ B @ ( product_Pair @ A @ B @ P2 @ Q2 ) ) )
% 1.99/1.29 & ( Q @ ( product_snd @ A @ B @ ( product_Pair @ A @ B @ P2 @ Q2 ) ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_178_exI__realizer,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType,P: A > B > $o,Y: A,X: B] :
% 1.99/1.29 ( ( P @ Y @ X )
% 1.99/1.29 => ( P @ ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) ) @ ( product_fst @ B @ A @ ( product_Pair @ B @ A @ X @ Y ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_179_Choiceo_Osimps_I2_J,axiom,
% 1.99/1.29 ! [Alpha: option @ game] :
% 1.99/1.29 ( ( uSubst1976112797hoiceo @ Alpha @ ( none @ game ) )
% 1.99/1.29 = ( none @ game ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_180_Choiceo__undef,axiom,
% 1.99/1.29 ! [Alpha: option @ game,Beta: option @ game] :
% 1.99/1.29 ( ( ( uSubst1976112797hoiceo @ Alpha @ Beta )
% 1.99/1.29 = ( none @ game ) )
% 1.99/1.29 = ( ( Alpha
% 1.99/1.29 = ( none @ game ) )
% 1.99/1.29 | ( Beta
% 1.99/1.29 = ( none @ game ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_181_usubstappp__compose,axiom,
% 1.99/1.29 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Alpha: game,Beta: game] :
% 1.99/1.29 ( ( uSubst95898988stappp @ Sigma @ U @ ( compose @ Alpha @ Beta ) )
% 1.99/1.29 = ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ Beta ) ) @ ( uSubst1385204910mposeo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ Beta ) ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_182_old_Oprod_Orec,axiom,
% 1.99/1.29 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A3: A,B3: B] :
% 1.99/1.29 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A3 @ B3 ) )
% 1.99/1.29 = ( F1 @ A3 @ B3 ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_183_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 1.99/1.29 ! [B: $tType,A: $tType,P: A > B > $o,X: A,Y: B,A3: product_prod @ A @ B] :
% 1.99/1.29 ( ( P @ X @ Y )
% 1.99/1.29 => ( ( A3
% 1.99/1.29 = ( product_Pair @ A @ B @ X @ Y ) )
% 1.99/1.29 => ( P @ ( product_fst @ A @ B @ A3 ) @ ( product_snd @ A @ B @ A3 ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_184_Composeo__undef,axiom,
% 1.99/1.29 ! [Alpha: option @ game,Beta: option @ game] :
% 1.99/1.29 ( ( ( uSubst1385204910mposeo @ Alpha @ Beta )
% 1.99/1.29 = ( none @ game ) )
% 1.99/1.29 = ( ( Alpha
% 1.99/1.29 = ( none @ game ) )
% 1.99/1.29 | ( Beta
% 1.99/1.29 = ( none @ game ) ) ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_185_Composeo_Osimps_I2_J,axiom,
% 1.99/1.29 ! [Alpha: option @ game] :
% 1.99/1.29 ( ( uSubst1385204910mposeo @ Alpha @ ( none @ game ) )
% 1.99/1.29 = ( none @ game ) ) ).
% 1.99/1.29
% 1.99/1.29 thf(fact_186_usubstappp__loop,axiom,
% 1.99/1.29 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Alpha: game] :
% 1.99/1.29 ( ( uSubst95898988stappp @ Sigma @ U @ ( loop @ Alpha ) )
% 1.99/1.29 = ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ ( uSubst993936602_Loopo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_187_eq__snd__iff,axiom,
% 1.99/1.30 ! [A: $tType,B: $tType,B3: A,P2: product_prod @ B @ A] :
% 1.99/1.30 ( ( B3
% 1.99/1.30 = ( product_snd @ B @ A @ P2 ) )
% 1.99/1.30 = ( ? [A5: B] :
% 1.99/1.30 ( P2
% 1.99/1.30 = ( product_Pair @ B @ A @ A5 @ B3 ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_188_sndI,axiom,
% 1.99/1.30 ! [A: $tType,B: $tType,X: product_prod @ A @ B,Y: A,Z: B] :
% 1.99/1.30 ( ( X
% 1.99/1.30 = ( product_Pair @ A @ B @ Y @ Z ) )
% 1.99/1.30 => ( ( product_snd @ A @ B @ X )
% 1.99/1.30 = Z ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_189_Loopo_Osimps_I2_J,axiom,
% 1.99/1.30 ( ( uSubst993936602_Loopo @ ( none @ game ) )
% 1.99/1.30 = ( none @ game ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_190_Loopo__undef,axiom,
% 1.99/1.30 ! [Alpha: option @ game] :
% 1.99/1.30 ( ( ( uSubst993936602_Loopo @ Alpha )
% 1.99/1.30 = ( none @ game ) )
% 1.99/1.30 = ( Alpha
% 1.99/1.30 = ( none @ game ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_191_fstI,axiom,
% 1.99/1.30 ! [B: $tType,A: $tType,X: product_prod @ A @ B,Y: A,Z: B] :
% 1.99/1.30 ( ( X
% 1.99/1.30 = ( product_Pair @ A @ B @ Y @ Z ) )
% 1.99/1.30 => ( ( product_fst @ A @ B @ X )
% 1.99/1.30 = Y ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_192_eq__fst__iff,axiom,
% 1.99/1.30 ! [A: $tType,B: $tType,A3: A,P2: product_prod @ A @ B] :
% 1.99/1.30 ( ( A3
% 1.99/1.30 = ( product_fst @ A @ B @ P2 ) )
% 1.99/1.30 = ( ? [B5: B] :
% 1.99/1.30 ( P2
% 1.99/1.30 = ( product_Pair @ A @ B @ A3 @ B5 ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_193_internal__case__prod__conv,axiom,
% 1.99/1.30 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A3: B,B3: C] :
% 1.99/1.30 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A3 @ B3 ) )
% 1.99/1.30 = ( C3 @ A3 @ B3 ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_194_relChain__def,axiom,
% 1.99/1.30 ! [B: $tType,A: $tType] :
% 1.99/1.30 ( ( ord @ B )
% 1.99/1.30 => ( ( bNF_Ca1785829860lChain @ A @ B )
% 1.99/1.30 = ( ^ [R: set @ ( product_prod @ A @ A ),As: A > B] :
% 1.99/1.30 ! [I: A,J: A] :
% 1.99/1.30 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ I @ J ) @ R )
% 1.99/1.30 => ( ord_less_eq @ B @ ( As @ I ) @ ( As @ J ) ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_195_sndOp__def,axiom,
% 1.99/1.30 ! [B: $tType,A: $tType,C: $tType] :
% 1.99/1.30 ( ( bNF_sndOp @ C @ A @ B )
% 1.99/1.30 = ( ^ [P4: C > A > $o,Q3: A > B > $o,Ac: product_prod @ C @ B] : ( product_Pair @ A @ B @ ( bNF_pick_middlep @ C @ A @ B @ P4 @ Q3 @ ( product_fst @ C @ B @ Ac ) @ ( product_snd @ C @ B @ Ac ) ) @ ( product_snd @ C @ B @ Ac ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_196_fstOp__def,axiom,
% 1.99/1.30 ! [C: $tType,B: $tType,A: $tType] :
% 1.99/1.30 ( ( bNF_fstOp @ A @ B @ C )
% 1.99/1.30 = ( ^ [P4: A > B > $o,Q3: B > C > $o,Ac: product_prod @ A @ C] : ( product_Pair @ A @ B @ ( product_fst @ A @ C @ Ac ) @ ( bNF_pick_middlep @ A @ B @ C @ P4 @ Q3 @ ( product_fst @ A @ C @ Ac ) @ ( product_snd @ A @ C @ Ac ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_197_csquare__fstOp__sndOp,axiom,
% 1.99/1.30 ! [A: $tType,B: $tType,C: $tType,F2: ( A > B > $o ) > ( product_prod @ A @ B ) > $o,P: A > C > $o,Q: C > B > $o] : ( bNF_csquare @ ( product_prod @ A @ B ) @ ( product_prod @ A @ C ) @ C @ ( product_prod @ C @ B ) @ ( collect @ ( product_prod @ A @ B ) @ ( F2 @ ( relcompp @ A @ C @ B @ P @ Q ) ) ) @ ( product_snd @ A @ C ) @ ( product_fst @ C @ B ) @ ( bNF_fstOp @ A @ C @ B @ P @ Q ) @ ( bNF_sndOp @ A @ C @ B @ P @ Q ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_198_usubstappp_Osimps_I4_J,axiom,
% 1.99/1.30 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Alpha: game,Beta: game] :
% 1.99/1.30 ( ( uSubst95898988stappp @ Sigma @ U @ ( choice @ Alpha @ Beta ) )
% 1.99/1.30 = ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( sup_sup @ ( set @ variable ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Beta ) ) ) @ ( uSubst1976112797hoiceo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Beta ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_199_pick__middlep,axiom,
% 1.99/1.30 ! [B: $tType,A: $tType,C: $tType,P: A > B > $o,Q: B > C > $o,A3: A,C3: C] :
% 1.99/1.30 ( ( relcompp @ A @ B @ C @ P @ Q @ A3 @ C3 )
% 1.99/1.30 => ( ( P @ A3 @ ( bNF_pick_middlep @ A @ B @ C @ P @ Q @ A3 @ C3 ) )
% 1.99/1.30 & ( Q @ ( bNF_pick_middlep @ A @ B @ C @ P @ Q @ A3 @ C3 ) @ C3 ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_200_csquare__def,axiom,
% 1.99/1.30 ! [B: $tType,C: $tType,D: $tType,A: $tType] :
% 1.99/1.30 ( ( bNF_csquare @ A @ B @ C @ D )
% 1.99/1.30 = ( ^ [A4: set @ A,F12: B > C,F22: D > C,P1: A > B,P22: A > D] :
% 1.99/1.30 ! [X2: A] :
% 1.99/1.30 ( ( member @ A @ X2 @ A4 )
% 1.99/1.30 => ( ( F12 @ ( P1 @ X2 ) )
% 1.99/1.30 = ( F22 @ ( P22 @ X2 ) ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_201_leq__OOI,axiom,
% 1.99/1.30 ! [A: $tType,R2: A > A > $o] :
% 1.99/1.30 ( ( R2
% 1.99/1.30 = ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) ) )
% 1.99/1.30 => ( ord_less_eq @ ( A > A > $o ) @ R2 @ ( relcompp @ A @ A @ A @ R2 @ R2 ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_202_less__eq__set__def,axiom,
% 1.99/1.30 ! [A: $tType] :
% 1.99/1.30 ( ( ord_less_eq @ ( set @ A ) )
% 1.99/1.30 = ( ^ [A4: set @ A,B4: set @ A] :
% 1.99/1.30 ( ord_less_eq @ ( A > $o )
% 1.99/1.30 @ ^ [X2: A] : ( member @ A @ X2 @ A4 )
% 1.99/1.30 @ ^ [X2: A] : ( member @ A @ X2 @ B4 ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_203_Collect__subset,axiom,
% 1.99/1.30 ! [A: $tType,A2: set @ A,P: A > $o] :
% 1.99/1.30 ( ord_less_eq @ ( set @ A )
% 1.99/1.30 @ ( collect @ A
% 1.99/1.30 @ ^ [X2: A] :
% 1.99/1.30 ( ( member @ A @ X2 @ A2 )
% 1.99/1.30 & ( P @ X2 ) ) )
% 1.99/1.30 @ A2 ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_204_Un__def,axiom,
% 1.99/1.30 ! [A: $tType] :
% 1.99/1.30 ( ( sup_sup @ ( set @ A ) )
% 1.99/1.30 = ( ^ [A4: set @ A,B4: set @ A] :
% 1.99/1.30 ( collect @ A
% 1.99/1.30 @ ^ [X2: A] :
% 1.99/1.30 ( ( member @ A @ X2 @ A4 )
% 1.99/1.30 | ( member @ A @ X2 @ B4 ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_205_sup__set__def,axiom,
% 1.99/1.30 ! [A: $tType] :
% 1.99/1.30 ( ( sup_sup @ ( set @ A ) )
% 1.99/1.30 = ( ^ [A4: set @ A,B4: set @ A] :
% 1.99/1.30 ( collect @ A
% 1.99/1.30 @ ( sup_sup @ ( A > $o )
% 1.99/1.30 @ ^ [X2: A] : ( member @ A @ X2 @ A4 )
% 1.99/1.30 @ ^ [X2: A] : ( member @ A @ X2 @ B4 ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_206_Collect__disj__eq,axiom,
% 1.99/1.30 ! [A: $tType,P: A > $o,Q: A > $o] :
% 1.99/1.30 ( ( collect @ A
% 1.99/1.30 @ ^ [X2: A] :
% 1.99/1.30 ( ( P @ X2 )
% 1.99/1.30 | ( Q @ X2 ) ) )
% 1.99/1.30 = ( sup_sup @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_207_subset__CollectI,axiom,
% 1.99/1.30 ! [A: $tType,B2: set @ A,A2: set @ A,Q: A > $o,P: A > $o] :
% 1.99/1.30 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 1.99/1.30 => ( ! [X3: A] :
% 1.99/1.30 ( ( member @ A @ X3 @ B2 )
% 1.99/1.30 => ( ( Q @ X3 )
% 1.99/1.30 => ( P @ X3 ) ) )
% 1.99/1.30 => ( ord_less_eq @ ( set @ A )
% 1.99/1.30 @ ( collect @ A
% 1.99/1.30 @ ^ [X2: A] :
% 1.99/1.30 ( ( member @ A @ X2 @ B2 )
% 1.99/1.30 & ( Q @ X2 ) ) )
% 1.99/1.30 @ ( collect @ A
% 1.99/1.30 @ ^ [X2: A] :
% 1.99/1.30 ( ( member @ A @ X2 @ A2 )
% 1.99/1.30 & ( P @ X2 ) ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_208_subset__Collect__iff,axiom,
% 1.99/1.30 ! [A: $tType,B2: set @ A,A2: set @ A,P: A > $o] :
% 1.99/1.30 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 1.99/1.30 => ( ( ord_less_eq @ ( set @ A ) @ B2
% 1.99/1.30 @ ( collect @ A
% 1.99/1.30 @ ^ [X2: A] :
% 1.99/1.30 ( ( member @ A @ X2 @ A2 )
% 1.99/1.30 & ( P @ X2 ) ) ) )
% 1.99/1.30 = ( ! [X2: A] :
% 1.99/1.30 ( ( member @ A @ X2 @ B2 )
% 1.99/1.30 => ( P @ X2 ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_209_usubstappp_Osimps_I5_J,axiom,
% 1.99/1.30 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Alpha: game,Beta: game] :
% 1.99/1.30 ( ( uSubst95898988stappp @ Sigma @ U @ ( compose @ Alpha @ Beta ) )
% 1.99/1.30 = ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ Beta ) ) @ ( uSubst1385204910mposeo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ Beta ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_210_usubstappp_Osimps_I6_J,axiom,
% 1.99/1.30 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Alpha: game] :
% 1.99/1.30 ( ( uSubst95898988stappp @ Sigma @ U @ ( loop @ Alpha ) )
% 1.99/1.30 = ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ ( uSubst993936602_Loopo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_211_scomp__unfold,axiom,
% 1.99/1.30 ! [D: $tType,C: $tType,B: $tType,A: $tType] :
% 1.99/1.30 ( ( product_scomp @ A @ B @ C @ D )
% 1.99/1.30 = ( ^ [F: A > ( product_prod @ B @ C ),G: B > C > D,X2: A] : ( G @ ( product_fst @ B @ C @ ( F @ X2 ) ) @ ( product_snd @ B @ C @ ( F @ X2 ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_212_sup__Un__eq,axiom,
% 1.99/1.30 ! [A: $tType,R2: set @ A,S2: set @ A] :
% 1.99/1.30 ( ( sup_sup @ ( A > $o )
% 1.99/1.30 @ ^ [X2: A] : ( member @ A @ X2 @ R2 )
% 1.99/1.30 @ ^ [X2: A] : ( member @ A @ X2 @ S2 ) )
% 1.99/1.30 = ( ^ [X2: A] : ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ R2 @ S2 ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_213_scomp__scomp,axiom,
% 1.99/1.30 ! [A: $tType,C: $tType,D: $tType,B: $tType,F3: $tType,E: $tType,F2: A > ( product_prod @ E @ F3 ),G2: E > F3 > ( product_prod @ C @ D ),H: C > D > B] :
% 1.99/1.30 ( ( product_scomp @ A @ C @ D @ B @ ( product_scomp @ A @ E @ F3 @ ( product_prod @ C @ D ) @ F2 @ G2 ) @ H )
% 1.99/1.30 = ( product_scomp @ A @ E @ F3 @ B @ F2
% 1.99/1.30 @ ^ [X2: E] : ( product_scomp @ F3 @ C @ D @ B @ ( G2 @ X2 ) @ H ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_214_scomp__Pair,axiom,
% 1.99/1.30 ! [C: $tType,B: $tType,A: $tType,X: A > ( product_prod @ B @ C )] :
% 1.99/1.30 ( ( product_scomp @ A @ B @ C @ ( product_prod @ B @ C ) @ X @ ( product_Pair @ B @ C ) )
% 1.99/1.30 = X ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_215_Pair__scomp,axiom,
% 1.99/1.30 ! [A: $tType,B: $tType,C: $tType,X: C,F2: C > A > B] :
% 1.99/1.30 ( ( product_scomp @ A @ C @ A @ B @ ( product_Pair @ C @ A @ X ) @ F2 )
% 1.99/1.30 = ( F2 @ X ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_216_refl__ge__eq,axiom,
% 1.99/1.30 ! [A: $tType,R2: A > A > $o] :
% 1.99/1.30 ( ! [X3: A] : ( R2 @ X3 @ X3 )
% 1.99/1.30 => ( ord_less_eq @ ( A > A > $o )
% 1.99/1.30 @ ^ [Y2: A,Z2: A] : ( Y2 = Z2 )
% 1.99/1.30 @ R2 ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_217_ge__eq__refl,axiom,
% 1.99/1.30 ! [A: $tType,R2: A > A > $o,X: A] :
% 1.99/1.30 ( ( ord_less_eq @ ( A > A > $o )
% 1.99/1.30 @ ^ [Y2: A,Z2: A] : ( Y2 = Z2 )
% 1.99/1.30 @ R2 )
% 1.99/1.30 => ( R2 @ X @ X ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_218_subrelI,axiom,
% 1.99/1.30 ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),S3: set @ ( product_prod @ A @ B )] :
% 1.99/1.30 ( ! [X3: A,Y4: B] :
% 1.99/1.30 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y4 ) @ R3 )
% 1.99/1.30 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y4 ) @ S3 ) )
% 1.99/1.30 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R3 @ S3 ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_219_pred__equals__eq2,axiom,
% 1.99/1.30 ! [B: $tType,A: $tType,R2: set @ ( product_prod @ A @ B ),S2: set @ ( product_prod @ A @ B )] :
% 1.99/1.30 ( ( ( ^ [X2: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ R2 ) )
% 1.99/1.30 = ( ^ [X2: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ S2 ) ) )
% 1.99/1.30 = ( R2 = S2 ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_220_pred__subset__eq2,axiom,
% 1.99/1.30 ! [B: $tType,A: $tType,R2: set @ ( product_prod @ A @ B ),S2: set @ ( product_prod @ A @ B )] :
% 1.99/1.30 ( ( ord_less_eq @ ( A > B > $o )
% 1.99/1.30 @ ^ [X2: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ R2 )
% 1.99/1.30 @ ^ [X2: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ S2 ) )
% 1.99/1.30 = ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R2 @ S2 ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_221_sup__Un__eq2,axiom,
% 1.99/1.30 ! [B: $tType,A: $tType,R2: set @ ( product_prod @ A @ B ),S2: set @ ( product_prod @ A @ B )] :
% 1.99/1.30 ( ( sup_sup @ ( A > B > $o )
% 1.99/1.30 @ ^ [X2: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ R2 )
% 1.99/1.30 @ ^ [X2: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ S2 ) )
% 1.99/1.30 = ( ^ [X2: A,Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ ( sup_sup @ ( set @ ( product_prod @ A @ B ) ) @ R2 @ S2 ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_222_pred__subset__eq,axiom,
% 1.99/1.30 ! [A: $tType,R2: set @ A,S2: set @ A] :
% 1.99/1.30 ( ( ord_less_eq @ ( A > $o )
% 1.99/1.30 @ ^ [X2: A] : ( member @ A @ X2 @ R2 )
% 1.99/1.30 @ ^ [X2: A] : ( member @ A @ X2 @ S2 ) )
% 1.99/1.30 = ( ord_less_eq @ ( set @ A ) @ R2 @ S2 ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_223_conj__subset__def,axiom,
% 1.99/1.30 ! [A: $tType,A2: set @ A,P: A > $o,Q: A > $o] :
% 1.99/1.30 ( ( ord_less_eq @ ( set @ A ) @ A2
% 1.99/1.30 @ ( collect @ A
% 1.99/1.30 @ ^ [X2: A] :
% 1.99/1.30 ( ( P @ X2 )
% 1.99/1.30 & ( Q @ X2 ) ) ) )
% 1.99/1.30 = ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( collect @ A @ P ) )
% 1.99/1.30 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( collect @ A @ Q ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_224_prop__restrict,axiom,
% 1.99/1.30 ! [A: $tType,X: A,Z4: set @ A,X4: set @ A,P: A > $o] :
% 1.99/1.30 ( ( member @ A @ X @ Z4 )
% 1.99/1.30 => ( ( ord_less_eq @ ( set @ A ) @ Z4
% 1.99/1.30 @ ( collect @ A
% 1.99/1.30 @ ^ [X2: A] :
% 1.99/1.30 ( ( member @ A @ X2 @ X4 )
% 1.99/1.30 & ( P @ X2 ) ) ) )
% 1.99/1.30 => ( P @ X ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_225_ssubst__Pair__rhs,axiom,
% 1.99/1.30 ! [B: $tType,A: $tType,R3: A,S3: B,R2: set @ ( product_prod @ A @ B ),S4: B] :
% 1.99/1.30 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S3 ) @ R2 )
% 1.99/1.30 => ( ( S4 = S3 )
% 1.99/1.30 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S4 ) @ R2 ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_226_Collect__restrict,axiom,
% 1.99/1.30 ! [A: $tType,X4: set @ A,P: A > $o] :
% 1.99/1.30 ( ord_less_eq @ ( set @ A )
% 1.99/1.30 @ ( collect @ A
% 1.99/1.30 @ ^ [X2: A] :
% 1.99/1.30 ( ( member @ A @ X2 @ X4 )
% 1.99/1.30 & ( P @ X2 ) ) )
% 1.99/1.30 @ X4 ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_227_image2__eqI,axiom,
% 1.99/1.30 ! [A: $tType,C: $tType,B: $tType,B3: A,F2: B > A,X: B,C3: C,G2: B > C,A2: set @ B] :
% 1.99/1.30 ( ( B3
% 1.99/1.30 = ( F2 @ X ) )
% 1.99/1.30 => ( ( C3
% 1.99/1.30 = ( G2 @ X ) )
% 1.99/1.30 => ( ( member @ B @ X @ A2 )
% 1.99/1.30 => ( member @ ( product_prod @ A @ C ) @ ( product_Pair @ A @ C @ B3 @ C3 ) @ ( bNF_Greatest_image2 @ B @ A @ C @ A2 @ F2 @ G2 ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_228_Loopo_Oelims,axiom,
% 1.99/1.30 ! [X: option @ game,Y: option @ game] :
% 1.99/1.30 ( ( ( uSubst993936602_Loopo @ X )
% 1.99/1.30 = Y )
% 1.99/1.30 => ( ! [Alpha2: game] :
% 1.99/1.30 ( ( X
% 1.99/1.30 = ( some @ game @ Alpha2 ) )
% 1.99/1.30 => ( Y
% 1.99/1.30 != ( some @ game @ ( loop @ Alpha2 ) ) ) )
% 1.99/1.30 => ~ ( ( X
% 1.99/1.30 = ( none @ game ) )
% 1.99/1.30 => ( Y
% 1.99/1.30 != ( none @ game ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_229_option_Oinject,axiom,
% 1.99/1.30 ! [A: $tType,X22: A,Y22: A] :
% 1.99/1.30 ( ( ( some @ A @ X22 )
% 1.99/1.30 = ( some @ A @ Y22 ) )
% 1.99/1.30 = ( X22 = Y22 ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_230_not__Some__eq,axiom,
% 1.99/1.30 ! [A: $tType,X: option @ A] :
% 1.99/1.30 ( ( ! [Y3: A] :
% 1.99/1.30 ( X
% 1.99/1.30 != ( some @ A @ Y3 ) ) )
% 1.99/1.30 = ( X
% 1.99/1.30 = ( none @ A ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_231_not__None__eq,axiom,
% 1.99/1.30 ! [A: $tType,X: option @ A] :
% 1.99/1.30 ( ( X
% 1.99/1.30 != ( none @ A ) )
% 1.99/1.30 = ( ? [Y3: A] :
% 1.99/1.30 ( X
% 1.99/1.30 = ( some @ A @ Y3 ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_232_option_Ocollapse,axiom,
% 1.99/1.30 ! [A: $tType,Option: option @ A] :
% 1.99/1.30 ( ( Option
% 1.99/1.30 != ( none @ A ) )
% 1.99/1.30 => ( ( some @ A @ ( the @ A @ Option ) )
% 1.99/1.30 = Option ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_233_Composeo_Ocases,axiom,
% 1.99/1.30 ! [X: product_prod @ ( option @ game ) @ ( option @ game )] :
% 1.99/1.30 ( ! [Alpha2: game,Beta2: game] :
% 1.99/1.30 ( X
% 1.99/1.30 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ ( some @ game @ Alpha2 ) @ ( some @ game @ Beta2 ) ) )
% 1.99/1.30 => ( ! [Alpha2: option @ game] :
% 1.99/1.30 ( X
% 1.99/1.30 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ Alpha2 @ ( none @ game ) ) )
% 1.99/1.30 => ~ ! [V2: game] :
% 1.99/1.30 ( X
% 1.99/1.30 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ ( none @ game ) @ ( some @ game @ V2 ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_234_option_Oexhaust__sel,axiom,
% 1.99/1.30 ! [A: $tType,Option: option @ A] :
% 1.99/1.30 ( ( Option
% 1.99/1.30 != ( none @ A ) )
% 1.99/1.30 => ( Option
% 1.99/1.30 = ( some @ A @ ( the @ A @ Option ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_235_combine__options__cases,axiom,
% 1.99/1.30 ! [A: $tType,B: $tType,X: option @ A,P: ( option @ A ) > ( option @ B ) > $o,Y: option @ B] :
% 1.99/1.30 ( ( ( X
% 1.99/1.30 = ( none @ A ) )
% 1.99/1.30 => ( P @ X @ Y ) )
% 1.99/1.30 => ( ( ( Y
% 1.99/1.30 = ( none @ B ) )
% 1.99/1.30 => ( P @ X @ Y ) )
% 1.99/1.30 => ( ! [A7: A,B7: B] :
% 1.99/1.30 ( ( X
% 1.99/1.30 = ( some @ A @ A7 ) )
% 1.99/1.30 => ( ( Y
% 1.99/1.30 = ( some @ B @ B7 ) )
% 1.99/1.30 => ( P @ X @ Y ) ) )
% 1.99/1.30 => ( P @ X @ Y ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_236_split__option__all,axiom,
% 1.99/1.30 ! [A: $tType] :
% 1.99/1.30 ( ( ^ [P5: ( option @ A ) > $o] :
% 1.99/1.30 ! [X5: option @ A] : ( P5 @ X5 ) )
% 1.99/1.30 = ( ^ [P4: ( option @ A ) > $o] :
% 1.99/1.30 ( ( P4 @ ( none @ A ) )
% 1.99/1.30 & ! [X2: A] : ( P4 @ ( some @ A @ X2 ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_237_split__option__ex,axiom,
% 1.99/1.30 ! [A: $tType] :
% 1.99/1.30 ( ( ^ [P5: ( option @ A ) > $o] :
% 1.99/1.30 ? [X5: option @ A] : ( P5 @ X5 ) )
% 1.99/1.30 = ( ^ [P4: ( option @ A ) > $o] :
% 1.99/1.30 ( ( P4 @ ( none @ A ) )
% 1.99/1.30 | ? [X2: A] : ( P4 @ ( some @ A @ X2 ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_238_option_Oinducts,axiom,
% 1.99/1.30 ! [A: $tType,P: ( option @ A ) > $o,Option: option @ A] :
% 1.99/1.30 ( ( P @ ( none @ A ) )
% 1.99/1.30 => ( ! [X3: A] : ( P @ ( some @ A @ X3 ) )
% 1.99/1.30 => ( P @ Option ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_239_option_Oexhaust,axiom,
% 1.99/1.30 ! [A: $tType,Y: option @ A] :
% 1.99/1.30 ( ( Y
% 1.99/1.30 != ( none @ A ) )
% 1.99/1.30 => ~ ! [X23: A] :
% 1.99/1.30 ( Y
% 1.99/1.30 != ( some @ A @ X23 ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_240_option_OdiscI,axiom,
% 1.99/1.30 ! [A: $tType,Option: option @ A,X22: A] :
% 1.99/1.30 ( ( Option
% 1.99/1.30 = ( some @ A @ X22 ) )
% 1.99/1.30 => ( Option
% 1.99/1.30 != ( none @ A ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_241_option_Odistinct_I1_J,axiom,
% 1.99/1.30 ! [A: $tType,X22: A] :
% 1.99/1.30 ( ( none @ A )
% 1.99/1.30 != ( some @ A @ X22 ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_242_option_Osel,axiom,
% 1.99/1.30 ! [A: $tType,X22: A] :
% 1.99/1.30 ( ( the @ A @ ( some @ A @ X22 ) )
% 1.99/1.30 = X22 ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_243_Composeo_Oinduct,axiom,
% 1.99/1.30 ! [P: ( option @ game ) > ( option @ game ) > $o,A0: option @ game,A1: option @ game] :
% 1.99/1.30 ( ! [Alpha2: game,Beta2: game] : ( P @ ( some @ game @ Alpha2 ) @ ( some @ game @ Beta2 ) )
% 1.99/1.30 => ( ! [Alpha2: option @ game] : ( P @ Alpha2 @ ( none @ game ) )
% 1.99/1.30 => ( ! [V2: game] : ( P @ ( none @ game ) @ ( some @ game @ V2 ) )
% 1.99/1.30 => ( P @ A0 @ A1 ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_244_undefg__equiv,axiom,
% 1.99/1.30 ! [Alpha: option @ game] :
% 1.99/1.30 ( ( Alpha
% 1.99/1.30 != ( none @ game ) )
% 1.99/1.30 = ( ? [G: game] :
% 1.99/1.30 ( Alpha
% 1.99/1.30 = ( some @ game @ G ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_245_Loopo_Oinduct,axiom,
% 1.99/1.30 ! [P: ( option @ game ) > $o,A0: option @ game] :
% 1.99/1.30 ( ! [Alpha2: game] : ( P @ ( some @ game @ Alpha2 ) )
% 1.99/1.30 => ( ( P @ ( none @ game ) )
% 1.99/1.30 => ( P @ A0 ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_246_Loopo_Ocases,axiom,
% 1.99/1.30 ! [X: option @ game] :
% 1.99/1.30 ( ! [Alpha2: game] :
% 1.99/1.30 ( X
% 1.99/1.30 != ( some @ game @ Alpha2 ) )
% 1.99/1.30 => ( X
% 1.99/1.30 = ( none @ game ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_247_Loopo_Osimps_I1_J,axiom,
% 1.99/1.30 ! [Alpha: game] :
% 1.99/1.30 ( ( uSubst993936602_Loopo @ ( some @ game @ Alpha ) )
% 1.99/1.30 = ( some @ game @ ( loop @ Alpha ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_248_Choiceo_Osimps_I1_J,axiom,
% 1.99/1.30 ! [Alpha: game,Beta: game] :
% 1.99/1.30 ( ( uSubst1976112797hoiceo @ ( some @ game @ Alpha ) @ ( some @ game @ Beta ) )
% 1.99/1.30 = ( some @ game @ ( choice @ Alpha @ Beta ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_249_Composeo_Osimps_I1_J,axiom,
% 1.99/1.30 ! [Alpha: game,Beta: game] :
% 1.99/1.30 ( ( uSubst1385204910mposeo @ ( some @ game @ Alpha ) @ ( some @ game @ Beta ) )
% 1.99/1.30 = ( some @ game @ ( compose @ Alpha @ Beta ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_250_Composeo_Osimps_I3_J,axiom,
% 1.99/1.30 ! [V3: game] :
% 1.99/1.30 ( ( uSubst1385204910mposeo @ ( none @ game ) @ ( some @ game @ V3 ) )
% 1.99/1.30 = ( none @ game ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_251_Choiceo_Osimps_I3_J,axiom,
% 1.99/1.30 ! [V3: game] :
% 1.99/1.30 ( ( uSubst1976112797hoiceo @ ( none @ game ) @ ( some @ game @ V3 ) )
% 1.99/1.30 = ( none @ game ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_252_Composeo_Oelims,axiom,
% 1.99/1.30 ! [X: option @ game,Xa: option @ game,Y: option @ game] :
% 1.99/1.30 ( ( ( uSubst1385204910mposeo @ X @ Xa )
% 1.99/1.30 = Y )
% 1.99/1.30 => ( ! [Alpha2: game] :
% 1.99/1.30 ( ( X
% 1.99/1.30 = ( some @ game @ Alpha2 ) )
% 1.99/1.30 => ! [Beta2: game] :
% 1.99/1.30 ( ( Xa
% 1.99/1.30 = ( some @ game @ Beta2 ) )
% 1.99/1.30 => ( Y
% 1.99/1.30 != ( some @ game @ ( compose @ Alpha2 @ Beta2 ) ) ) ) )
% 1.99/1.30 => ( ( ( Xa
% 1.99/1.30 = ( none @ game ) )
% 1.99/1.30 => ( Y
% 1.99/1.30 != ( none @ game ) ) )
% 1.99/1.30 => ~ ( ( X
% 1.99/1.30 = ( none @ game ) )
% 1.99/1.30 => ( ? [V2: game] :
% 1.99/1.30 ( Xa
% 1.99/1.30 = ( some @ game @ V2 ) )
% 1.99/1.30 => ( Y
% 1.99/1.30 != ( none @ game ) ) ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_253_Choiceo_Oelims,axiom,
% 1.99/1.30 ! [X: option @ game,Xa: option @ game,Y: option @ game] :
% 1.99/1.30 ( ( ( uSubst1976112797hoiceo @ X @ Xa )
% 1.99/1.30 = Y )
% 1.99/1.30 => ( ! [Alpha2: game] :
% 1.99/1.30 ( ( X
% 1.99/1.30 = ( some @ game @ Alpha2 ) )
% 1.99/1.30 => ! [Beta2: game] :
% 1.99/1.30 ( ( Xa
% 1.99/1.30 = ( some @ game @ Beta2 ) )
% 1.99/1.30 => ( Y
% 1.99/1.30 != ( some @ game @ ( choice @ Alpha2 @ Beta2 ) ) ) ) )
% 1.99/1.30 => ( ( ( Xa
% 1.99/1.30 = ( none @ game ) )
% 1.99/1.30 => ( Y
% 1.99/1.30 != ( none @ game ) ) )
% 1.99/1.30 => ~ ( ( X
% 1.99/1.30 = ( none @ game ) )
% 1.99/1.30 => ( ? [V2: game] :
% 1.99/1.30 ( Xa
% 1.99/1.30 = ( some @ game @ V2 ) )
% 1.99/1.30 => ( Y
% 1.99/1.30 != ( none @ game ) ) ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(fact_254_option_Osplit__sel__asm,axiom,
% 1.99/1.30 ! [B: $tType,A: $tType,P: B > $o,F1: B,F23: A > B,Option: option @ A] :
% 1.99/1.30 ( ( P @ ( case_option @ B @ A @ F1 @ F23 @ Option ) )
% 1.99/1.30 = ( ~ ( ( ( Option
% 1.99/1.30 = ( none @ A ) )
% 1.99/1.30 & ~ ( P @ F1 ) )
% 1.99/1.30 | ( ( Option
% 1.99/1.30 = ( some @ A @ ( the @ A @ Option ) ) )
% 1.99/1.30 & ~ ( P @ ( F23 @ ( the @ A @ Option ) ) ) ) ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 1.99/1.30 ! [A9: $tType,A10: $tType] :
% 1.99/1.30 ( ( semilattice_sup @ A10 )
% 1.99/1.30 => ( semilattice_sup @ ( A9 > A10 ) ) ) ).
% 1.99/1.30
% 1.99/1.30 thf(tcon_fun___Orderings_Opreorder,axiom,
% 1.99/1.30 ! [A9: $tType,A10: $tType] :
% 1.99/1.30 ( ( preorder @ A10 )
% 1.99/1.30 => ( preorder @ ( A9 > A10 ) ) ) ).
% 2.21/1.30
% 2.21/1.30 thf(tcon_fun___Lattices_Olattice,axiom,
% 2.21/1.30 ! [A9: $tType,A10: $tType] :
% 2.21/1.30 ( ( lattice @ A10 )
% 2.21/1.30 => ( lattice @ ( A9 > A10 ) ) ) ).
% 2.21/1.30
% 2.21/1.30 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.21/1.30 ! [A9: $tType,A10: $tType] :
% 2.21/1.30 ( ( order @ A10 )
% 2.21/1.30 => ( order @ ( A9 > A10 ) ) ) ).
% 2.21/1.30
% 2.21/1.30 thf(tcon_fun___Orderings_Oord,axiom,
% 2.21/1.30 ! [A9: $tType,A10: $tType] :
% 2.21/1.30 ( ( ord @ A10 )
% 2.21/1.30 => ( ord @ ( A9 > A10 ) ) ) ).
% 2.21/1.30
% 2.21/1.30 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_1,axiom,
% 2.21/1.30 ! [A9: $tType] : ( semilattice_sup @ ( set @ A9 ) ) ).
% 2.21/1.30
% 2.21/1.30 thf(tcon_Set_Oset___Orderings_Opreorder_2,axiom,
% 2.21/1.30 ! [A9: $tType] : ( preorder @ ( set @ A9 ) ) ).
% 2.21/1.30
% 2.21/1.30 thf(tcon_Set_Oset___Lattices_Olattice_3,axiom,
% 2.21/1.30 ! [A9: $tType] : ( lattice @ ( set @ A9 ) ) ).
% 2.21/1.30
% 2.21/1.30 thf(tcon_Set_Oset___Orderings_Oorder_4,axiom,
% 2.21/1.30 ! [A9: $tType] : ( order @ ( set @ A9 ) ) ).
% 2.21/1.30
% 2.21/1.30 thf(tcon_Set_Oset___Orderings_Oord_5,axiom,
% 2.21/1.30 ! [A9: $tType] : ( ord @ ( set @ A9 ) ) ).
% 2.21/1.30
% 2.21/1.30 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_6,axiom,
% 2.21/1.30 semilattice_sup @ $o ).
% 2.21/1.30
% 2.21/1.30 thf(tcon_HOL_Obool___Orderings_Opreorder_7,axiom,
% 2.21/1.30 preorder @ $o ).
% 2.21/1.30
% 2.21/1.30 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.21/1.30 linorder @ $o ).
% 2.21/1.30
% 2.21/1.30 thf(tcon_HOL_Obool___Lattices_Olattice_8,axiom,
% 2.21/1.30 lattice @ $o ).
% 2.21/1.30
% 2.21/1.30 thf(tcon_HOL_Obool___Orderings_Oorder_9,axiom,
% 2.21/1.30 order @ $o ).
% 2.21/1.30
% 2.21/1.30 thf(tcon_HOL_Obool___Orderings_Oord_10,axiom,
% 2.21/1.30 ord @ $o ).
% 2.21/1.30
% 2.21/1.30 thf(conj_0,conjecture,
% 2.21/1.30 ord_less_eq @ ( set @ variable ) @ ( sup_sup @ ( set @ variable ) @ ua @ ( static_BVG @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ).
% 2.21/1.30 ------------------------
% 2.21/1.32 % (15043)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14850 for (2999ds/183Mi)
% 2.21/1.32 % (15047)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_14850 for (2999ds/2Mi)
% 2.21/1.32 % (15046)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14850 for (2999ds/2Mi)
% 2.21/1.32 % (15047)Instruction limit reached!
% 2.21/1.32 % (15047)------------------------------
% 2.21/1.32 % (15047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.32 % (15047)Termination reason: Unknown
% 2.21/1.32 % (15047)Termination phase: shuffling
% 2.21/1.32
% 2.21/1.32 % (15047)Memory used [KB]: 1407
% 2.21/1.32 % (15047)Time elapsed: 0.002 s
% 2.21/1.32 % (15047)Instructions burned: 3 (million)
% 2.21/1.32 % (15047)------------------------------
% 2.21/1.32 % (15047)------------------------------
% 2.21/1.32 % (15046)Instruction limit reached!
% 2.21/1.32 % (15046)------------------------------
% 2.21/1.32 % (15046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.32 % (15046)Termination reason: Unknown
% 2.21/1.32 % (15046)Termination phase: shuffling
% 2.21/1.32
% 2.21/1.32 % (15046)Memory used [KB]: 1407
% 2.21/1.32 % (15046)Time elapsed: 0.003 s
% 2.21/1.32 % (15046)Instructions burned: 3 (million)
% 2.21/1.32 % (15046)------------------------------
% 2.21/1.32 % (15046)------------------------------
% 2.21/1.32 % (15044)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_14850 for (2999ds/4Mi)
% 2.21/1.32 % (15044)Instruction limit reached!
% 2.21/1.32 % (15044)------------------------------
% 2.21/1.32 % (15044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.32 % (15044)Termination reason: Unknown
% 2.21/1.32 % (15044)Termination phase: shuffling
% 2.21/1.32
% 2.21/1.32 % (15044)Memory used [KB]: 1407
% 2.21/1.32 % (15044)Time elapsed: 0.003 s
% 2.21/1.32 % (15044)Instructions burned: 5 (million)
% 2.21/1.32 % (15044)------------------------------
% 2.21/1.32 % (15044)------------------------------
% 2.21/1.32 % (15048)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_14850 for (2999ds/275Mi)
% 2.21/1.32 % (15049)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14850 for (2999ds/18Mi)
% 2.21/1.32 % (15045)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_14850 for (2999ds/27Mi)
% 2.21/1.33 % (15051)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_14850 for (2999ds/37Mi)
% 2.21/1.33 % (15049)Instruction limit reached!
% 2.21/1.33 % (15049)------------------------------
% 2.21/1.33 % (15049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.33 % (15049)Termination reason: Unknown
% 2.21/1.33 % (15049)Termination phase: shuffling
% 2.21/1.33
% 2.21/1.33 % (15049)Memory used [KB]: 1663
% 2.21/1.33 % (15049)Time elapsed: 0.011 s
% 2.21/1.33 % (15049)Instructions burned: 19 (million)
% 2.21/1.33 % (15049)------------------------------
% 2.21/1.33 % (15049)------------------------------
% 2.21/1.33 % (15045)Instruction limit reached!
% 2.21/1.33 % (15045)------------------------------
% 2.21/1.33 % (15045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.33 % (15045)Termination reason: Unknown
% 2.21/1.33 % (15045)Termination phase: Property scanning
% 2.21/1.33
% 2.21/1.33 % (15045)Memory used [KB]: 1918
% 2.21/1.33 % (15045)Time elapsed: 0.011 s
% 2.21/1.33 % (15045)Instructions burned: 29 (million)
% 2.21/1.33 % (15045)------------------------------
% 2.21/1.33 % (15045)------------------------------
% 2.21/1.33 % (15050)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14850 for (2999ds/3Mi)
% 2.21/1.34 % (15050)Instruction limit reached!
% 2.21/1.34 % (15050)------------------------------
% 2.21/1.34 % (15050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.34 % (15050)Termination reason: Unknown
% 2.21/1.34 % (15050)Termination phase: shuffling
% 2.21/1.34
% 2.21/1.34 % (15050)Memory used [KB]: 1407
% 2.21/1.34 % (15050)Time elapsed: 0.003 s
% 2.21/1.34 % (15050)Instructions burned: 3 (million)
% 2.21/1.34 % (15050)------------------------------
% 2.21/1.34 % (15050)------------------------------
% 2.21/1.34 % (15052)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_14850 for (2999ds/15Mi)
% 2.21/1.34 % (15051)Instruction limit reached!
% 2.21/1.34 % (15051)------------------------------
% 2.21/1.34 % (15051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.34 % (15051)Termination reason: Unknown
% 2.21/1.34 % (15051)Termination phase: shuffling
% 2.21/1.34
% 2.21/1.34 % (15051)Memory used [KB]: 2174
% 2.21/1.34 % (15051)Time elapsed: 0.012 s
% 2.21/1.34 % (15051)Instructions burned: 39 (million)
% 2.21/1.34 % (15051)------------------------------
% 2.21/1.34 % (15051)------------------------------
% 2.21/1.34 % (15054)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_14850 for (2999ds/1041Mi)
% 2.21/1.35 % (15052)Instruction limit reached!
% 2.21/1.35 % (15052)------------------------------
% 2.21/1.35 % (15052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.35 % (15052)Termination reason: Unknown
% 2.21/1.35 % (15052)Termination phase: shuffling
% 2.21/1.35
% 2.21/1.35 % (15052)Memory used [KB]: 1663
% 2.21/1.35 % (15052)Time elapsed: 0.009 s
% 2.21/1.35 % (15052)Instructions burned: 16 (million)
% 2.21/1.35 % (15052)------------------------------
% 2.21/1.35 % (15052)------------------------------
% 2.21/1.35 % (15053)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_14850 for (2999ds/3Mi)
% 2.21/1.35 % (15053)Instruction limit reached!
% 2.21/1.35 % (15053)------------------------------
% 2.21/1.35 % (15053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.35 % (15053)Termination reason: Unknown
% 2.21/1.35 % (15053)Termination phase: shuffling
% 2.21/1.35
% 2.21/1.35 % (15053)Memory used [KB]: 1407
% 2.21/1.35 % (15053)Time elapsed: 0.003 s
% 2.21/1.35 % (15053)Instructions burned: 3 (million)
% 2.21/1.35 % (15053)------------------------------
% 2.21/1.35 % (15053)------------------------------
% 2.21/1.35 % (15056)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_14850 for (2999ds/16Mi)
% 2.21/1.36 % (15055)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14850 for (2999ds/7Mi)
% 2.21/1.36 % (15056)Instruction limit reached!
% 2.21/1.36 % (15056)------------------------------
% 2.21/1.36 % (15056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.36 % (15056)Termination reason: Unknown
% 2.21/1.36 % (15056)Termination phase: shuffling
% 2.21/1.36
% 2.21/1.36 % (15056)Memory used [KB]: 1791
% 2.21/1.36 % (15056)Time elapsed: 0.007 s
% 2.21/1.36 % (15056)Instructions burned: 18 (million)
% 2.21/1.36 % (15056)------------------------------
% 2.21/1.36 % (15056)------------------------------
% 2.21/1.36 % (15055)Instruction limit reached!
% 2.21/1.36 % (15055)------------------------------
% 2.21/1.36 % (15055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.36 % (15055)Termination reason: Unknown
% 2.21/1.36 % (15055)Termination phase: shuffling
% 2.21/1.36
% 2.21/1.36 % (15055)Memory used [KB]: 1535
% 2.21/1.36 % (15055)Time elapsed: 0.006 s
% 2.21/1.36 % (15055)Instructions burned: 8 (million)
% 2.21/1.36 % (15055)------------------------------
% 2.21/1.36 % (15055)------------------------------
% 2.21/1.36 % (15058)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_14850 for (2999ds/3Mi)
% 2.21/1.36 % (15058)Instruction limit reached!
% 2.21/1.36 % (15058)------------------------------
% 2.21/1.36 % (15058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.36 % (15058)Termination reason: Unknown
% 2.21/1.36 % (15058)Termination phase: shuffling
% 2.21/1.36
% 2.21/1.36 % (15058)Memory used [KB]: 1407
% 2.21/1.36 % (15058)Time elapsed: 0.003 s
% 2.21/1.36 % (15058)Instructions burned: 3 (million)
% 2.21/1.36 % (15058)------------------------------
% 2.21/1.36 % (15058)------------------------------
% 2.21/1.37 % (15059)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_14850 for (2999ds/7Mi)
% 2.21/1.37 % (15057)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_14850 for (2999ds/3Mi)
% 2.21/1.37 % (15057)Instruction limit reached!
% 2.21/1.37 % (15057)------------------------------
% 2.21/1.37 % (15057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.37 % (15057)Termination reason: Unknown
% 2.21/1.37 % (15057)Termination phase: shuffling
% 2.21/1.37
% 2.21/1.37 % (15057)Memory used [KB]: 1407
% 2.21/1.37 % (15057)Time elapsed: 0.004 s
% 2.21/1.37 % (15057)Instructions burned: 4 (million)
% 2.21/1.37 % (15057)------------------------------
% 2.21/1.37 % (15057)------------------------------
% 2.21/1.37 % (15059)Instruction limit reached!
% 2.21/1.37 % (15059)------------------------------
% 2.21/1.37 % (15059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.37 % (15059)Termination reason: Unknown
% 2.21/1.37 % (15059)Termination phase: shuffling
% 2.21/1.37
% 2.21/1.37 % (15059)Memory used [KB]: 1535
% 2.21/1.37 % (15059)Time elapsed: 0.004 s
% 2.21/1.37 % (15059)Instructions burned: 9 (million)
% 2.21/1.37 % (15059)------------------------------
% 2.21/1.37 % (15059)------------------------------
% 2.21/1.37 % (15060)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_14850 for (2999ds/3Mi)
% 2.21/1.37 % (15060)Instruction limit reached!
% 2.21/1.37 % (15060)------------------------------
% 2.21/1.37 % (15060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.37 % (15060)Termination reason: Unknown
% 2.21/1.37 % (15060)Termination phase: shuffling
% 2.21/1.37
% 2.21/1.37 % (15060)Memory used [KB]: 1407
% 2.21/1.37 % (15060)Time elapsed: 0.004 s
% 2.21/1.37 % (15060)Instructions burned: 4 (million)
% 2.21/1.37 % (15060)------------------------------
% 2.21/1.37 % (15060)------------------------------
% 2.21/1.37 % (15043)Instruction limit reached!
% 2.21/1.37 % (15043)------------------------------
% 2.21/1.37 % (15043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.37 % (15043)Termination reason: Unknown
% 2.21/1.37 % (15043)Termination phase: Saturation
% 2.21/1.37
% 2.21/1.37 % (15043)Memory used [KB]: 7291
% 2.21/1.37 % (15043)Time elapsed: 0.058 s
% 2.21/1.37 % (15043)Instructions burned: 185 (million)
% 2.21/1.37 % (15043)------------------------------
% 2.21/1.37 % (15043)------------------------------
% 2.21/1.37 % (15061)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_14850 for (2999ds/4Mi)
% 2.21/1.38 % (15061)Instruction limit reached!
% 2.21/1.38 % (15061)------------------------------
% 2.21/1.38 % (15061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.38 % (15061)Termination reason: Unknown
% 2.21/1.38 % (15061)Termination phase: shuffling
% 2.21/1.38
% 2.21/1.38 % (15061)Memory used [KB]: 1407
% 2.21/1.38 % (15061)Time elapsed: 0.004 s
% 2.21/1.38 % (15061)Instructions burned: 5 (million)
% 2.21/1.38 % (15061)------------------------------
% 2.21/1.38 % (15061)------------------------------
% 2.21/1.38 % (15062)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_14850 for (2999ds/18Mi)
% 2.21/1.38 % (15065)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_14850 for (2999ds/902Mi)
% 2.21/1.38 % (15062)Instruction limit reached!
% 2.21/1.38 % (15062)------------------------------
% 2.21/1.38 % (15062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.38 % (15062)Termination reason: Unknown
% 2.21/1.38 % (15062)Termination phase: shuffling
% 2.21/1.38
% 2.21/1.38 % (15062)Memory used [KB]: 1791
% 2.21/1.38 % (15062)Time elapsed: 0.007 s
% 2.21/1.38 % (15062)Instructions burned: 19 (million)
% 2.21/1.38 % (15062)------------------------------
% 2.21/1.38 % (15062)------------------------------
% 2.21/1.38 % (15063)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_14850 for (2999ds/710Mi)
% 2.21/1.39 % (15064)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14850 for (2999ds/6Mi)
% 2.21/1.39 % (15066)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_14850 for (2999ds/21Mi)
% 2.21/1.39 % (15064)Instruction limit reached!
% 2.21/1.39 % (15064)------------------------------
% 2.21/1.39 % (15064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.39 % (15064)Termination reason: Unknown
% 2.21/1.39 % (15064)Termination phase: shuffling
% 2.21/1.39
% 2.21/1.39 % (15064)Memory used [KB]: 1535
% 2.21/1.39 % (15064)Time elapsed: 0.005 s
% 2.21/1.39 % (15064)Instructions burned: 6 (million)
% 2.21/1.39 % (15064)------------------------------
% 2.21/1.39 % (15064)------------------------------
% 2.21/1.39 % (15067)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_14850 for (2999ds/5Mi)
% 2.21/1.40 % (15067)Instruction limit reached!
% 2.21/1.40 % (15067)------------------------------
% 2.21/1.40 % (15067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.40 % (15067)Termination reason: Unknown
% 2.21/1.40 % (15067)Termination phase: shuffling
% 2.21/1.40
% 2.21/1.40 % (15067)Memory used [KB]: 1535
% 2.21/1.40 % (15067)Time elapsed: 0.003 s
% 2.21/1.40 % (15067)Instructions burned: 7 (million)
% 2.21/1.40 % (15067)------------------------------
% 2.21/1.40 % (15067)------------------------------
% 2.21/1.40 % (15066)Instruction limit reached!
% 2.21/1.40 % (15066)------------------------------
% 2.21/1.40 % (15066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.40 % (15066)Termination reason: Unknown
% 2.21/1.40 % (15066)Termination phase: shuffling
% 2.21/1.40
% 2.21/1.40 % (15066)Memory used [KB]: 1791
% 2.21/1.40 % (15066)Time elapsed: 0.009 s
% 2.21/1.40 % (15066)Instructions burned: 23 (million)
% 2.21/1.40 % (15066)------------------------------
% 2.21/1.40 % (15066)------------------------------
% 2.21/1.41 % (15069)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_14850 for (2999ds/377Mi)
% 2.21/1.41 % (15070)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_14850 for (2999ds/779Mi)
% 2.21/1.41 % (15068)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_14850 for (2999ds/6Mi)
% 2.21/1.41 % (15068)Instruction limit reached!
% 2.21/1.41 % (15068)------------------------------
% 2.21/1.41 % (15068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.41 % (15068)Termination reason: Unknown
% 2.21/1.41 % (15068)Termination phase: shuffling
% 2.21/1.41
% 2.21/1.41 % (15068)Memory used [KB]: 1407
% 2.21/1.41 % (15068)Time elapsed: 0.004 s
% 2.21/1.41 % (15068)Instructions burned: 6 (million)
% 2.21/1.41 % (15068)------------------------------
% 2.21/1.41 % (15068)------------------------------
% 2.21/1.43 % (15071)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_14850 for (2998ds/19Mi)
% 2.21/1.44 % (15071)Instruction limit reached!
% 2.21/1.44 % (15071)------------------------------
% 2.21/1.44 % (15071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.44 % (15071)Termination reason: Unknown
% 2.21/1.44 % (15071)Termination phase: shuffling
% 2.21/1.44
% 2.21/1.44 % (15071)Memory used [KB]: 1791
% 2.21/1.44 % (15071)Time elapsed: 0.011 s
% 2.21/1.44 % (15071)Instructions burned: 20 (million)
% 2.21/1.44 % (15071)------------------------------
% 2.21/1.44 % (15071)------------------------------
% 2.21/1.45 % (15048)Instruction limit reached!
% 2.21/1.45 % (15048)------------------------------
% 2.21/1.45 % (15048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.45 % (15048)Termination reason: Unknown
% 2.21/1.45 % (15048)Termination phase: Saturation
% 2.21/1.45
% 2.21/1.45 % (15048)Memory used [KB]: 7164
% 2.21/1.45 % (15048)Time elapsed: 0.130 s
% 2.21/1.45 % (15048)Instructions burned: 277 (million)
% 2.21/1.45 % (15048)------------------------------
% 2.21/1.45 % (15048)------------------------------
% 2.21/1.45 % (15072)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_14850 for (2998ds/879Mi)
% 2.21/1.46 % (15073)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_14850 for (2998ds/17Mi)
% 2.21/1.47 % (15073)Instruction limit reached!
% 2.21/1.47 % (15073)------------------------------
% 2.21/1.47 % (15073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.47 % (15073)Termination reason: Unknown
% 2.21/1.47 % (15073)Termination phase: shuffling
% 2.21/1.47
% 2.21/1.47 % (15073)Memory used [KB]: 1663
% 2.21/1.47 % (15073)Time elapsed: 0.007 s
% 2.21/1.47 % (15073)Instructions burned: 17 (million)
% 2.21/1.47 % (15073)------------------------------
% 2.21/1.47 % (15073)------------------------------
% 2.21/1.48 % (15075)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_14850 for (2998ds/3Mi)
% 2.21/1.48 % (15075)Instruction limit reached!
% 2.21/1.48 % (15075)------------------------------
% 2.21/1.48 % (15075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.48 % (15075)Termination reason: Unknown
% 2.21/1.48 % (15075)Termination phase: shuffling
% 2.21/1.48
% 2.21/1.48 % (15075)Memory used [KB]: 1407
% 2.21/1.48 % (15075)Time elapsed: 0.003 s
% 2.21/1.48 % (15075)Instructions burned: 5 (million)
% 2.21/1.48 % (15075)------------------------------
% 2.21/1.48 % (15075)------------------------------
% 2.21/1.49 % (15076)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_14850 for (2998ds/30Mi)
% 2.21/1.50 % (15076)Instruction limit reached!
% 2.21/1.50 % (15076)------------------------------
% 2.21/1.50 % (15076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.50 % (15076)Termination reason: Unknown
% 2.21/1.50 % (15076)Termination phase: shuffling
% 2.21/1.50
% 2.21/1.50 % (15076)Memory used [KB]: 2046
% 2.21/1.50 % (15076)Time elapsed: 0.012 s
% 2.21/1.50 % (15076)Instructions burned: 31 (million)
% 2.21/1.50 % (15076)------------------------------
% 2.21/1.50 % (15076)------------------------------
% 2.21/1.51 % (15077)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_14850 for (2998ds/127Mi)
% 2.21/1.52 % (15069)Instruction limit reached!
% 2.21/1.52 % (15069)------------------------------
% 2.21/1.52 % (15069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.52 % (15069)Termination reason: Unknown
% 2.21/1.52 % (15069)Termination phase: Saturation
% 2.21/1.52
% 2.21/1.52 % (15069)Memory used [KB]: 8315
% 2.21/1.52 % (15069)Time elapsed: 0.119 s
% 2.21/1.52 % (15069)Instructions burned: 377 (million)
% 2.21/1.52 % (15069)------------------------------
% 2.21/1.52 % (15069)------------------------------
% 2.21/1.53 % (15078)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_14850 for (2997ds/100Mi)
% 2.21/1.55 % (15077)Instruction limit reached!
% 2.21/1.55 % (15077)------------------------------
% 2.21/1.55 % (15077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.55 % (15077)Termination reason: Unknown
% 2.21/1.55 % (15077)Termination phase: Saturation
% 2.21/1.55
% 2.21/1.55 % (15077)Memory used [KB]: 7036
% 2.21/1.55 % (15077)Time elapsed: 0.040 s
% 2.21/1.55 % (15077)Instructions burned: 129 (million)
% 2.21/1.55 % (15077)------------------------------
% 2.21/1.55 % (15077)------------------------------
% 2.21/1.56 % (15079)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_14850 for (2997ds/3Mi)
% 2.21/1.56 % (15079)Instruction limit reached!
% 2.21/1.56 % (15079)------------------------------
% 2.21/1.56 % (15079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.56 % (15079)Termination reason: Unknown
% 2.21/1.56 % (15079)Termination phase: shuffling
% 2.21/1.56
% 2.21/1.56 % (15079)Memory used [KB]: 1407
% 2.21/1.56 % (15079)Time elapsed: 0.003 s
% 2.21/1.56 % (15079)Instructions burned: 5 (million)
% 2.21/1.56 % (15079)------------------------------
% 2.21/1.56 % (15079)------------------------------
% 2.21/1.56 % (15078)Instruction limit reached!
% 2.21/1.56 % (15078)------------------------------
% 2.21/1.56 % (15078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.56 % (15078)Termination reason: Unknown
% 2.21/1.56 % (15078)Termination phase: Property scanning
% 2.21/1.56
% 2.21/1.56 % (15078)Memory used [KB]: 2430
% 2.21/1.56 % (15078)Time elapsed: 0.029 s
% 2.21/1.56 % (15078)Instructions burned: 100 (million)
% 2.21/1.56 % (15078)------------------------------
% 2.21/1.56 % (15078)------------------------------
% 2.21/1.57 % (15080)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_14850 for (2997ds/20Mi)
% 2.21/1.57 % (15081)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_14850 for (2997ds/86Mi)
% 2.21/1.58 % (15080)Instruction limit reached!
% 2.21/1.58 % (15080)------------------------------
% 2.21/1.58 % (15080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.58 % (15080)Termination reason: Unknown
% 2.21/1.58 % (15080)Termination phase: shuffling
% 2.21/1.58
% 2.21/1.58 % (15080)Memory used [KB]: 1791
% 2.21/1.58 % (15080)Time elapsed: 0.008 s
% 2.21/1.58 % (15080)Instructions burned: 21 (million)
% 2.21/1.58 % (15080)------------------------------
% 2.21/1.58 % (15080)------------------------------
% 2.21/1.58 % (15082)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_14850 for (2997ds/107Mi)
% 2.21/1.60 % (15081)Instruction limit reached!
% 2.21/1.60 % (15081)------------------------------
% 2.21/1.60 % (15081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.60 % (15081)Termination reason: Unknown
% 2.21/1.60 % (15081)Termination phase: Saturation
% 2.21/1.60
% 2.21/1.60 % (15081)Memory used [KB]: 2302
% 2.21/1.60 % (15081)Time elapsed: 0.027 s
% 2.21/1.60 % (15081)Instructions burned: 88 (million)
% 2.21/1.60 % (15081)------------------------------
% 2.21/1.60 % (15081)------------------------------
% 2.21/1.61 % (15083)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_14850 for (2996ds/39Mi)
% 2.21/1.62 % (15082)Instruction limit reached!
% 2.21/1.62 % (15082)------------------------------
% 2.21/1.62 % (15082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.62 % (15082)Termination reason: Unknown
% 2.21/1.62 % (15082)Termination phase: Saturation
% 2.21/1.62
% 2.21/1.62 % (15082)Memory used [KB]: 6780
% 2.21/1.62 % (15082)Time elapsed: 0.033 s
% 2.21/1.62 % (15082)Instructions burned: 107 (million)
% 2.21/1.62 % (15082)------------------------------
% 2.21/1.62 % (15082)------------------------------
% 2.21/1.62 % (15083)Instruction limit reached!
% 2.21/1.62 % (15083)------------------------------
% 2.21/1.62 % (15083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.62 % (15083)Termination reason: Unknown
% 2.21/1.62 % (15083)Termination phase: shuffling
% 2.21/1.62
% 2.21/1.62 % (15083)Memory used [KB]: 2174
% 2.21/1.62 % (15083)Time elapsed: 0.013 s
% 2.21/1.62 % (15083)Instructions burned: 41 (million)
% 2.21/1.62 % (15083)------------------------------
% 2.21/1.62 % (15083)------------------------------
% 2.21/1.63 % (15084)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_14850 for (2996ds/448Mi)
% 2.21/1.63 % (15085)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_14850 for (2996ds/46Mi)
% 2.21/1.64 % (15085)Instruction limit reached!
% 2.21/1.64 % (15085)------------------------------
% 2.21/1.64 % (15085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.64 % (15085)Termination reason: Unknown
% 2.21/1.64 % (15085)Termination phase: Preprocessing 2
% 2.21/1.64
% 2.21/1.64 % (15085)Memory used [KB]: 2046
% 2.21/1.64 % (15085)Time elapsed: 0.016 s
% 2.21/1.64 % (15085)Instructions burned: 48 (million)
% 2.21/1.64 % (15085)------------------------------
% 2.21/1.64 % (15085)------------------------------
% 2.21/1.65 % (15086)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_14850 for (2996ds/98Mi)
% 2.21/1.66 % (15065)Instruction limit reached!
% 2.21/1.66 % (15065)------------------------------
% 2.21/1.66 % (15065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.66 % (15065)Termination reason: Unknown
% 2.21/1.66 % (15065)Termination phase: Saturation
% 2.21/1.66
% 2.21/1.66 % (15065)Memory used [KB]: 7931
% 2.21/1.66 % (15065)Time elapsed: 0.275 s
% 2.21/1.66 % (15065)Instructions burned: 904 (million)
% 2.21/1.66 % (15065)------------------------------
% 2.21/1.66 % (15065)------------------------------
% 2.21/1.67 % (15087)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_14850 for (2996ds/507Mi)
% 2.21/1.68 % (15063)Refutation not found, non-redundant clauses discarded% (15063)------------------------------
% 2.21/1.68 % (15063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.68 % (15063)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.21/1.68
% 2.21/1.68 % (15063)Memory used [KB]: 8059
% 2.21/1.68 % (15063)Time elapsed: 0.292 s
% 2.21/1.68 % (15063)Instructions burned: 700 (million)
% 2.21/1.68 % (15063)------------------------------
% 2.21/1.68 % (15063)------------------------------
% 2.21/1.68 % (15086)Instruction limit reached!
% 2.21/1.68 % (15086)------------------------------
% 2.21/1.68 % (15086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.68 % (15086)Termination reason: Unknown
% 2.21/1.68 % (15086)Termination phase: Property scanning
% 2.21/1.68
% 2.21/1.68 % (15086)Memory used [KB]: 2430
% 2.21/1.68 % (15086)Time elapsed: 0.028 s
% 2.21/1.68 % (15086)Instructions burned: 98 (million)
% 2.21/1.68 % (15086)------------------------------
% 2.21/1.68 % (15086)------------------------------
% 2.21/1.69 % (15088)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_14850 for (2996ds/149Mi)
% 2.21/1.69 % (15089)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_14850 for (2996ds/39Mi)
% 2.21/1.70 % (15089)Instruction limit reached!
% 2.21/1.70 % (15089)------------------------------
% 2.21/1.70 % (15089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.70 % (15089)Termination reason: Unknown
% 2.21/1.70 % (15089)Termination phase: shuffling
% 2.21/1.70
% 2.21/1.70 % (15089)Memory used [KB]: 2046
% 2.21/1.70 % (15089)Time elapsed: 0.014 s
% 2.21/1.70 % (15089)Instructions burned: 41 (million)
% 2.21/1.70 % (15089)------------------------------
% 2.21/1.70 % (15089)------------------------------
% 2.21/1.71 % (15090)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_14850 for (2995ds/6Mi)
% 2.21/1.71 % (15090)Instruction limit reached!
% 2.21/1.71 % (15090)------------------------------
% 2.21/1.71 % (15090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.71 % (15090)Termination reason: Unknown
% 2.21/1.71 % (15090)Termination phase: shuffling
% 2.21/1.71
% 2.21/1.71 % (15090)Memory used [KB]: 1535
% 2.21/1.71 % (15090)Time elapsed: 0.004 s
% 2.21/1.71 % (15090)Instructions burned: 9 (million)
% 2.21/1.71 % (15090)------------------------------
% 2.21/1.71 % (15090)------------------------------
% 2.21/1.72 % (15091)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_14850 for (2995ds/1087Mi)
% 2.21/1.73 % (15054)Instruction limit reached!
% 2.21/1.73 % (15054)------------------------------
% 2.21/1.73 % (15054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.73 % (15054)Termination reason: Unknown
% 2.21/1.73 % (15054)Termination phase: Saturation
% 2.21/1.73
% 2.21/1.73 % (15054)Memory used [KB]: 9978
% 2.21/1.73 % (15054)Time elapsed: 0.388 s
% 2.21/1.73 % (15054)Instructions burned: 1043 (million)
% 2.21/1.73 % (15054)------------------------------
% 2.21/1.73 % (15054)------------------------------
% 2.21/1.74 % (15088)Instruction limit reached!
% 2.21/1.74 % (15088)------------------------------
% 2.21/1.74 % (15088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.74 % (15088)Termination reason: Unknown
% 2.21/1.74 % (15088)Termination phase: Saturation
% 2.21/1.74
% 2.21/1.74 % (15088)Memory used [KB]: 7164
% 2.21/1.74 % (15088)Time elapsed: 0.052 s
% 2.21/1.74 % (15088)Instructions burned: 150 (million)
% 2.21/1.74 % (15088)------------------------------
% 2.21/1.74 % (15088)------------------------------
% 2.21/1.74 % (15092)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_14850 for (2995ds/47Mi)
% 2.21/1.75 % (15093)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_14850 for (2995ds/44Mi)
% 2.21/1.75 % (15092)Instruction limit reached!
% 2.21/1.75 % (15092)------------------------------
% 2.21/1.75 % (15092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.75 % (15092)Termination reason: Unknown
% 2.21/1.75 % (15092)Termination phase: Preprocessing 3
% 2.21/1.75
% 2.21/1.75 % (15092)Memory used [KB]: 2046
% 2.21/1.75 % (15092)Time elapsed: 0.016 s
% 2.21/1.75 % (15092)Instructions burned: 47 (million)
% 2.21/1.75 % (15092)------------------------------
% 2.21/1.75 % (15092)------------------------------
% 2.21/1.76 % (15070)Instruction limit reached!
% 2.21/1.76 % (15070)------------------------------
% 2.21/1.76 % (15070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.76 % (15070)Termination reason: Unknown
% 2.21/1.76 % (15070)Termination phase: Saturation
% 2.21/1.76
% 2.21/1.76 % (15070)Memory used [KB]: 8315
% 2.21/1.76 % (15070)Time elapsed: 0.354 s
% 2.21/1.76 % (15070)Instructions burned: 780 (million)
% 2.21/1.76 % (15070)------------------------------
% 2.21/1.76 % (15070)------------------------------
% 2.21/1.76 % (15084)Instruction limit reached!
% 2.21/1.76 % (15084)------------------------------
% 2.21/1.76 % (15084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.76 % (15084)Termination reason: Unknown
% 2.21/1.76 % (15084)Termination phase: Saturation
% 2.21/1.76
% 2.21/1.76 % (15084)Memory used [KB]: 8827
% 2.21/1.76 % (15084)Time elapsed: 0.134 s
% 2.21/1.76 % (15084)Instructions burned: 449 (million)
% 2.21/1.76 % (15084)------------------------------
% 2.21/1.76 % (15084)------------------------------
% 2.21/1.76 % (15094)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_14850 for (2995ds/432Mi)
% 2.21/1.77 % (15096)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_14850 for (2995ds/31Mi)
% 2.21/1.77 % (15093)Instruction limit reached!
% 2.21/1.77 % (15093)------------------------------
% 2.21/1.77 % (15093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.77 % (15093)Termination reason: Unknown
% 2.21/1.77 % (15093)Termination phase: Property scanning
% 2.21/1.77
% 2.21/1.77 % (15093)Memory used [KB]: 2174
% 2.21/1.77 % (15093)Time elapsed: 0.019 s
% 2.21/1.77 % (15093)Instructions burned: 46 (million)
% 2.21/1.77 % (15093)------------------------------
% 2.21/1.77 % (15093)------------------------------
% 2.21/1.77 % (15095)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_14850 for (2995ds/62Mi)
% 2.21/1.78 % (15096)Instruction limit reached!
% 2.21/1.78 % (15096)------------------------------
% 2.21/1.78 % (15096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.78 % (15096)Termination reason: Unknown
% 2.21/1.78 % (15096)Termination phase: Property scanning
% 2.21/1.78
% 2.21/1.78 % (15096)Memory used [KB]: 1918
% 2.21/1.78 % (15096)Time elapsed: 0.011 s
% 2.21/1.78 % (15096)Instructions burned: 32 (million)
% 2.21/1.78 % (15096)------------------------------
% 2.21/1.78 % (15096)------------------------------
% 2.21/1.78 % (15097)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_14850 for (2995ds/96Mi)
% 2.21/1.79 % (15098)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_14850 for (2995ds/453Mi)
% 2.21/1.79 % (15095)Instruction limit reached!
% 2.21/1.79 % (15095)------------------------------
% 2.21/1.79 % (15095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.79 % (15095)Termination reason: Unknown
% 2.21/1.79 % (15095)Termination phase: Property scanning
% 2.21/1.79
% 2.21/1.79 % (15095)Memory used [KB]: 2174
% 2.21/1.79 % (15095)Time elapsed: 0.019 s
% 2.21/1.79 % (15095)Instructions burned: 64 (million)
% 2.21/1.79 % (15095)------------------------------
% 2.21/1.79 % (15095)------------------------------
% 2.21/1.80 % (15099)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_14850 for (2995ds/71Mi)
% 2.21/1.82 % (15072)Instruction limit reached!
% 2.21/1.82 % (15072)------------------------------
% 2.21/1.82 % (15072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.82 % (15072)Termination reason: Unknown
% 2.21/1.82 % (15072)Termination phase: Saturation
% 2.21/1.82
% 2.21/1.82 % (15072)Memory used [KB]: 7675
% 2.21/1.82 % (15072)Time elapsed: 0.365 s
% 2.21/1.82 % (15072)Instructions burned: 880 (million)
% 2.21/1.82 % (15072)------------------------------
% 2.21/1.82 % (15072)------------------------------
% 2.21/1.82 % (15099)Instruction limit reached!
% 2.21/1.82 % (15099)------------------------------
% 2.21/1.82 % (15099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.82 % (15099)Termination reason: Unknown
% 2.21/1.82 % (15099)Termination phase: Property scanning
% 2.21/1.82
% 2.21/1.82 % (15099)Memory used [KB]: 2302
% 2.21/1.82 % (15099)Time elapsed: 0.023 s
% 2.21/1.82 % (15099)Instructions burned: 73 (million)
% 2.21/1.82 % (15099)------------------------------
% 2.21/1.82 % (15099)------------------------------
% 2.21/1.83 % (15097)Instruction limit reached!
% 2.21/1.83 % (15097)------------------------------
% 2.21/1.83 % (15097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.83 % (15097)Termination reason: Unknown
% 2.21/1.83 % (15097)Termination phase: Saturation
% 2.21/1.83
% 2.21/1.83 % (15097)Memory used [KB]: 6780
% 2.21/1.83 % (15097)Time elapsed: 0.047 s
% 2.21/1.83 % (15097)Instructions burned: 96 (million)
% 2.21/1.83 % (15097)------------------------------
% 2.21/1.83 % (15097)------------------------------
% 2.21/1.83 % (15100)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_14850 for (2994ds/83Mi)
% 2.21/1.84 % (15101)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_14850 for (2994ds/11Mi)
% 2.21/1.84 % (15102)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_14850 for (2994ds/41Mi)
% 2.21/1.84 % (15101)Instruction limit reached!
% 2.21/1.84 % (15101)------------------------------
% 2.21/1.84 % (15101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.84 % (15101)Termination reason: Unknown
% 2.21/1.84 % (15101)Termination phase: shuffling
% 2.21/1.84
% 2.21/1.84 % (15101)Memory used [KB]: 1663
% 2.21/1.84 % (15101)Time elapsed: 0.007 s
% 2.21/1.84 % (15101)Instructions burned: 12 (million)
% 2.21/1.84 % (15101)------------------------------
% 2.21/1.84 % (15101)------------------------------
% 2.21/1.85 % (15087)Instruction limit reached!
% 2.21/1.85 % (15087)------------------------------
% 2.21/1.85 % (15087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.85 % (15087)Termination reason: Unknown
% 2.21/1.85 % (15087)Termination phase: Saturation
% 2.21/1.85
% 2.21/1.85 % (15087)Memory used [KB]: 7803
% 2.21/1.85 % (15087)Time elapsed: 0.183 s
% 2.21/1.85 % (15087)Instructions burned: 510 (million)
% 2.21/1.85 % (15087)------------------------------
% 2.21/1.85 % (15087)------------------------------
% 2.21/1.86 % (15103)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14850 for (2994ds/6Mi)
% 2.21/1.86 % (15102)Instruction limit reached!
% 2.21/1.86 % (15102)------------------------------
% 2.21/1.86 % (15102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.86 % (15102)Termination reason: Unknown
% 2.21/1.86 % (15102)Termination phase: Property scanning
% 2.21/1.86
% 2.21/1.86 % (15102)Memory used [KB]: 2174
% 2.21/1.86 % (15102)Time elapsed: 0.022 s
% 2.21/1.86 % (15102)Instructions burned: 42 (million)
% 2.21/1.86 % (15102)------------------------------
% 2.21/1.86 % (15102)------------------------------
% 2.21/1.86 % (15104)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_14850 for (2994ds/150Mi)
% 2.21/1.86 % (15103)Instruction limit reached!
% 2.21/1.86 % (15103)------------------------------
% 2.21/1.86 % (15103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.86 % (15103)Termination reason: Unknown
% 2.21/1.86 % (15103)Termination phase: shuffling
% 2.21/1.86
% 2.21/1.86 % (15103)Memory used [KB]: 1535
% 2.21/1.86 % (15103)Time elapsed: 0.005 s
% 2.21/1.86 % (15103)Instructions burned: 7 (million)
% 2.21/1.86 % (15103)------------------------------
% 2.21/1.86 % (15103)------------------------------
% 2.21/1.87 % (15100)Instruction limit reached!
% 2.21/1.87 % (15100)------------------------------
% 2.21/1.87 % (15100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.87 % (15100)Termination reason: Unknown
% 2.21/1.87 % (15100)Termination phase: Saturation
% 2.21/1.87
% 2.21/1.87 % (15100)Memory used [KB]: 6652
% 2.21/1.87 % (15100)Time elapsed: 0.042 s
% 2.21/1.87 % (15100)Instructions burned: 84 (million)
% 2.21/1.87 % (15100)------------------------------
% 2.21/1.87 % (15100)------------------------------
% 2.21/1.88 % (15106)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_14850 for (2994ds/109Mi)
% 2.21/1.88 % (15105)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_14850 for (2994ds/343Mi)
% 2.21/1.89 % (15107)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_14850 for (2994ds/253Mi)
% 2.21/1.92 % (15098)Instruction limit reached!
% 2.21/1.92 % (15098)------------------------------
% 2.21/1.92 % (15098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.92 % (15098)Termination reason: Unknown
% 2.21/1.92 % (15098)Termination phase: Saturation
% 2.21/1.92
% 2.21/1.92 % (15098)Memory used [KB]: 7931
% 2.21/1.92 % (15098)Time elapsed: 0.134 s
% 2.21/1.92 % (15098)Instructions burned: 455 (million)
% 2.21/1.92 % (15098)------------------------------
% 2.21/1.92 % (15098)------------------------------
% 2.21/1.92 % (15094)Instruction limit reached!
% 2.21/1.92 % (15094)------------------------------
% 2.21/1.92 % (15094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.92 % (15094)Termination reason: Unknown
% 2.21/1.92 % (15094)Termination phase: Saturation
% 2.21/1.92
% 2.21/1.92 % (15094)Memory used [KB]: 3709
% 2.21/1.92 % (15094)Time elapsed: 0.161 s
% 2.21/1.92 % (15094)Instructions burned: 432 (million)
% 2.21/1.92 % (15094)------------------------------
% 2.21/1.92 % (15094)------------------------------
% 2.21/1.92 % (15104)Instruction limit reached!
% 2.21/1.92 % (15104)------------------------------
% 2.21/1.92 % (15104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.92 % (15104)Termination reason: Unknown
% 2.21/1.92 % (15106)Instruction limit reached!
% 2.21/1.92 % (15106)------------------------------
% 2.21/1.92 % (15106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.92 % (15106)Termination reason: Unknown
% 2.21/1.92 % (15106)Termination phase: Saturation
% 2.21/1.92
% 2.21/1.92 % (15106)Memory used [KB]: 6780
% 2.21/1.92 % (15106)Time elapsed: 0.047 s
% 2.21/1.92 % (15106)Instructions burned: 109 (million)
% 2.21/1.92 % (15106)------------------------------
% 2.21/1.92 % (15106)------------------------------
% 2.21/1.92 % (15104)Termination phase: Saturation
% 2.21/1.92
% 2.21/1.92 % (15104)Memory used [KB]: 7164
% 2.21/1.92 % (15104)Time elapsed: 0.062 s
% 2.21/1.92 % (15104)Instructions burned: 150 (million)
% 2.21/1.92 % (15104)------------------------------
% 2.21/1.92 % (15104)------------------------------
% 2.21/1.93 % (15108)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_14850 for (2993ds/140Mi)
% 2.21/1.93 % (15109)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_14850 for (2993ds/614Mi)
% 2.21/1.94 % (15111)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_14850 for (2993ds/339Mi)
% 2.21/1.94 % (15110)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_14850 for (2993ds/202Mi)
% 2.21/1.98 % (15108)Instruction limit reached!
% 2.21/1.98 % (15108)------------------------------
% 2.21/1.98 % (15108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.98 % (15108)Termination reason: Unknown
% 2.21/1.98 % (15108)Termination phase: Saturation
% 2.21/1.98
% 2.21/1.98 % (15108)Memory used [KB]: 7036
% 2.21/1.98 % (15108)Time elapsed: 0.046 s
% 2.21/1.98 % (15108)Instructions burned: 140 (million)
% 2.21/1.98 % (15108)------------------------------
% 2.21/1.98 % (15108)------------------------------
% 2.21/1.98 % (15107)Instruction limit reached!
% 2.21/1.98 % (15107)------------------------------
% 2.21/1.98 % (15107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.98 % (15107)Termination reason: Unknown
% 2.21/1.98 % (15107)Termination phase: Saturation
% 2.21/1.98
% 2.21/1.98 % (15107)Memory used [KB]: 7547
% 2.21/1.98 % (15107)Time elapsed: 0.093 s
% 2.21/1.98 % (15107)Instructions burned: 254 (million)
% 2.21/1.98 % (15107)------------------------------
% 2.21/1.98 % (15107)------------------------------
% 2.21/1.99 % (15112)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_14850 for (2993ds/283Mi)
% 2.21/1.99 % (15113)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_14850 for (2993ds/134Mi)
% 7.12/2.03 % (15113)Instruction limit reached!
% 7.12/2.03 % (15113)------------------------------
% 7.12/2.03 % (15113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.03 % (15113)Termination reason: Unknown
% 7.12/2.03 % (15113)Termination phase: Saturation
% 7.12/2.03
% 7.12/2.03 % (15113)Memory used [KB]: 7036
% 7.12/2.03 % (15113)Time elapsed: 0.042 s
% 7.12/2.03 % (15113)Instructions burned: 134 (million)
% 7.12/2.03 % (15113)------------------------------
% 7.12/2.03 % (15113)------------------------------
% 7.12/2.04 % (15110)Instruction limit reached!
% 7.12/2.04 % (15110)------------------------------
% 7.12/2.04 % (15110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.04 % (15110)Termination reason: Unknown
% 7.12/2.04 % (15110)Termination phase: Saturation
% 7.12/2.04
% 7.12/2.04 % (15110)Memory used [KB]: 7675
% 7.12/2.04 % (15110)Time elapsed: 0.099 s
% 7.12/2.04 % (15110)Instructions burned: 202 (million)
% 7.12/2.04 % (15110)------------------------------
% 7.12/2.04 % (15110)------------------------------
% 7.12/2.04 % (15114)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_14850 for (2992ds/298Mi)
% 7.12/2.05 % (15115)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_14850 for (2992ds/192Mi)
% 7.12/2.05 % (15105)Instruction limit reached!
% 7.12/2.05 % (15105)------------------------------
% 7.12/2.05 % (15105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.05 % (15105)Termination reason: Unknown
% 7.12/2.05 % (15105)Termination phase: Saturation
% 7.12/2.05
% 7.12/2.05 % (15105)Memory used [KB]: 7931
% 7.12/2.05 % (15105)Time elapsed: 0.173 s
% 7.12/2.05 % (15105)Instructions burned: 343 (million)
% 7.12/2.05 % (15105)------------------------------
% 7.12/2.05 % (15105)------------------------------
% 7.12/2.06 % (15091)Instruction limit reached!
% 7.12/2.06 % (15091)------------------------------
% 7.12/2.06 % (15091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.06 % (15091)Termination reason: Unknown
% 7.12/2.06 % (15091)Termination phase: Saturation
% 7.12/2.06
% 7.12/2.06 % (15091)Memory used [KB]: 8059
% 7.12/2.06 % (15091)Time elapsed: 0.339 s
% 7.12/2.06 % (15091)Instructions burned: 1088 (million)
% 7.12/2.06 % (15091)------------------------------
% 7.12/2.06 % (15091)------------------------------
% 7.12/2.06 % (15116)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_14850 for (2992ds/258Mi)
% 7.12/2.07 % (15112)Instruction limit reached!
% 7.12/2.07 % (15112)------------------------------
% 7.12/2.07 % (15112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.07 % (15112)Termination reason: Unknown
% 7.12/2.07 % (15112)Termination phase: Saturation
% 7.12/2.07
% 7.12/2.07 % (15112)Memory used [KB]: 7547
% 7.12/2.07 % (15112)Time elapsed: 0.085 s
% 7.12/2.07 % (15112)Instructions burned: 284 (million)
% 7.12/2.07 % (15112)------------------------------
% 7.12/2.07 % (15112)------------------------------
% 7.12/2.07 % (15117)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_14850 for (2992ds/90Mi)
% 7.12/2.08 % (15118)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_14850 for (2992ds/231Mi)
% 7.12/2.09 % (15111)Instruction limit reached!
% 7.12/2.09 % (15111)------------------------------
% 7.12/2.09 % (15111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.09 % (15111)Termination reason: Unknown
% 7.12/2.09 % (15111)Termination phase: Saturation
% 7.12/2.09
% 7.12/2.09 % (15111)Memory used [KB]: 7675
% 7.12/2.09 % (15111)Time elapsed: 0.148 s
% 7.12/2.09 % (15111)Instructions burned: 339 (million)
% 7.12/2.09 % (15111)------------------------------
% 7.12/2.09 % (15111)------------------------------
% 7.12/2.10 % (15119)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_14850 for (2992ds/458Mi)
% 7.12/2.10 % (15117)Instruction limit reached!
% 7.12/2.10 % (15117)------------------------------
% 7.12/2.10 % (15117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.10 % (15117)Termination reason: Unknown
% 7.12/2.10 % (15117)Termination phase: Saturation
% 7.12/2.10
% 7.12/2.10 % (15117)Memory used [KB]: 2302
% 7.12/2.10 % (15117)Time elapsed: 0.027 s
% 7.12/2.10 % (15117)Instructions burned: 90 (million)
% 7.12/2.10 % (15117)------------------------------
% 7.12/2.10 % (15117)------------------------------
% 7.12/2.11 % (15120)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_14850 for (2991ds/31Mi)
% 7.12/2.12 % (15120)Instruction limit reached!
% 7.12/2.12 % (15120)------------------------------
% 7.12/2.12 % (15120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.12 % (15120)Termination reason: Unknown
% 7.12/2.12 % (15120)Termination phase: Property scanning
% 7.12/2.12
% 7.12/2.12 % (15120)Memory used [KB]: 1918
% 7.12/2.12 % (15120)Time elapsed: 0.011 s
% 7.12/2.12 % (15120)Instructions burned: 32 (million)
% 7.12/2.12 % (15120)------------------------------
% 7.12/2.12 % (15120)------------------------------
% 7.12/2.12 % (15115)Instruction limit reached!
% 7.12/2.12 % (15115)------------------------------
% 7.12/2.12 % (15115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.12 % (15115)Termination reason: Unknown
% 7.12/2.12 % (15115)Termination phase: Saturation
% 7.12/2.12
% 7.12/2.12 % (15115)Memory used [KB]: 8059
% 7.12/2.12 % (15115)Time elapsed: 0.078 s
% 7.12/2.12 % (15115)Instructions burned: 193 (million)
% 7.12/2.12 % (15115)------------------------------
% 7.12/2.12 % (15115)------------------------------
% 7.62/2.13 % (15128)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_14850 for (2991ds/297Mi)
% 7.62/2.14 % (15118)Instruction limit reached!
% 7.62/2.14 % (15118)------------------------------
% 7.62/2.14 % (15118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.62/2.14 % (15118)Termination reason: Unknown
% 7.62/2.14 % (15118)Termination phase: Saturation
% 7.62/2.14
% 7.62/2.14 % (15118)Memory used [KB]: 7036
% 7.62/2.14 % (15118)Time elapsed: 0.063 s
% 7.62/2.14 % (15118)Instructions burned: 232 (million)
% 7.62/2.14 % (15118)------------------------------
% 7.62/2.14 % (15118)------------------------------
% 7.62/2.14 % (15114)Instruction limit reached!
% 7.62/2.14 % (15114)------------------------------
% 7.62/2.14 % (15114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.62/2.14 % (15114)Termination reason: Unknown
% 7.62/2.14 % (15114)Termination phase: Saturation
% 7.62/2.14
% 7.62/2.14 % (15114)Memory used [KB]: 8699
% 7.62/2.14 % (15114)Time elapsed: 0.103 s
% 7.62/2.14 % (15114)Instructions burned: 299 (million)
% 7.62/2.14 % (15114)------------------------------
% 7.62/2.14 % (15114)------------------------------
% 7.62/2.15 % (15129)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_14850 for (2991ds/987Mi)
% 7.62/2.15 % (15130)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_14850 for (2991ds/182Mi)
% 7.62/2.17 % (15131)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_14850 for (2991ds/182Mi)
% 7.62/2.17 % (15116)Instruction limit reached!
% 7.62/2.17 % (15116)------------------------------
% 7.62/2.17 % (15116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.62/2.17 % (15116)Termination reason: Unknown
% 7.62/2.17 % (15116)Termination phase: Saturation
% 7.62/2.17
% 7.62/2.17 % (15116)Memory used [KB]: 7547
% 7.62/2.17 % (15116)Time elapsed: 0.129 s
% 7.62/2.17 % (15116)Instructions burned: 258 (million)
% 7.62/2.17 % (15116)------------------------------
% 7.62/2.17 % (15116)------------------------------
% 7.62/2.17 % (15109)Instruction limit reached!
% 7.62/2.17 % (15109)------------------------------
% 7.62/2.17 % (15109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.62/2.17 % (15109)Termination reason: Unknown
% 7.62/2.17 % (15109)Termination phase: Saturation
% 7.62/2.17
% 7.62/2.17 % (15109)Memory used [KB]: 8059
% 7.62/2.17 % (15109)Time elapsed: 0.240 s
% 7.62/2.17 % (15109)Instructions burned: 615 (million)
% 7.62/2.17 % (15109)------------------------------
% 7.62/2.17 % (15109)------------------------------
% 7.62/2.18 % (15132)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_14850 for (2991ds/154Mi)
% 7.62/2.19 % (15133)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_14850 for (2991ds/79Mi)
% 7.98/2.21 % (15133)Instruction limit reached!
% 7.98/2.21 % (15133)------------------------------
% 7.98/2.21 % (15133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/2.21 % (15133)Termination reason: Unknown
% 7.98/2.21 % (15133)Termination phase: Property scanning
% 7.98/2.21
% 7.98/2.21 % (15133)Memory used [KB]: 2302
% 7.98/2.21 % (15133)Time elapsed: 0.025 s
% 7.98/2.21 % (15133)Instructions burned: 80 (million)
% 7.98/2.22 % (15133)------------------------------
% 7.98/2.22 % (15133)------------------------------
% 7.98/2.22 % (15130)Instruction limit reached!
% 7.98/2.22 % (15130)------------------------------
% 7.98/2.22 % (15130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/2.22 % (15130)Termination reason: Unknown
% 7.98/2.22 % (15130)Termination phase: Saturation
% 7.98/2.22
% 7.98/2.22 % (15130)Memory used [KB]: 7291
% 7.98/2.22 % (15130)Time elapsed: 0.057 s
% 7.98/2.22 % (15130)Instructions burned: 184 (million)
% 7.98/2.22 % (15130)------------------------------
% 7.98/2.22 % (15130)------------------------------
% 7.98/2.22 % (15134)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_14850 for (2990ds/216Mi)
% 7.98/2.23 % (15132)Instruction limit reached!
% 7.98/2.23 % (15132)------------------------------
% 7.98/2.23 % (15132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/2.23 % (15132)Termination reason: Unknown
% 7.98/2.23 % (15132)Termination phase: Saturation
% 7.98/2.23
% 7.98/2.23 % (15132)Memory used [KB]: 2942
% 7.98/2.23 % (15132)Time elapsed: 0.044 s
% 7.98/2.23 % (15132)Instructions burned: 154 (million)
% 7.98/2.23 % (15132)------------------------------
% 7.98/2.23 % (15132)------------------------------
% 7.98/2.23 % (15135)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_14850 for (2990ds/114Mi)
% 7.98/2.23 % (15131)Instruction limit reached!
% 7.98/2.23 % (15131)------------------------------
% 7.98/2.23 % (15131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/2.23 % (15131)Termination reason: Unknown
% 7.98/2.23 % (15131)Termination phase: Saturation
% 7.98/2.23
% 7.98/2.23 % (15131)Memory used [KB]: 7291
% 7.98/2.23 % (15131)Time elapsed: 0.065 s
% 7.98/2.23 % (15131)Instructions burned: 184 (million)
% 7.98/2.23 % (15131)------------------------------
% 7.98/2.23 % (15131)------------------------------
% 7.98/2.24 % (15136)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_14850 for (2990ds/922Mi)
% 7.98/2.24 % (15137)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_14850 for (2990ds/182Mi)
% 7.98/2.26 % (15135)Instruction limit reached!
% 7.98/2.26 % (15135)------------------------------
% 7.98/2.26 % (15135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/2.26 % (15135)Termination reason: Unknown
% 7.98/2.26 % (15135)Termination phase: Saturation
% 7.98/2.26
% 7.98/2.26 % (15135)Memory used [KB]: 7036
% 7.98/2.26 % (15135)Time elapsed: 0.035 s
% 7.98/2.26 % (15135)Instructions burned: 116 (million)
% 7.98/2.26 % (15135)------------------------------
% 7.98/2.26 % (15135)------------------------------
% 7.98/2.27 % (15128)Instruction limit reached!
% 7.98/2.27 % (15128)------------------------------
% 7.98/2.27 % (15128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/2.27 % (15128)Termination reason: Unknown
% 7.98/2.27 % (15128)Termination phase: Saturation
% 7.98/2.27
% 7.98/2.27 % (15128)Memory used [KB]: 7675
% 7.98/2.27 % (15128)Time elapsed: 0.145 s
% 7.98/2.27 % (15128)Instructions burned: 298 (million)
% 7.98/2.27 % (15128)------------------------------
% 7.98/2.27 % (15128)------------------------------
% 7.98/2.27 % (15138)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_14850 for (2990ds/164Mi)
% 7.98/2.29 % (15134)Instruction limit reached!
% 7.98/2.29 % (15134)------------------------------
% 7.98/2.29 % (15134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/2.29 % (15134)Termination reason: Unknown
% 7.98/2.29 % (15134)Termination phase: Saturation
% 7.98/2.29
% 7.98/2.29 % (15134)Memory used [KB]: 7419
% 7.98/2.29 % (15134)Time elapsed: 0.063 s
% 7.98/2.29 % (15134)Instructions burned: 216 (million)
% 7.98/2.29 % (15134)------------------------------
% 7.98/2.29 % (15134)------------------------------
% 7.98/2.29 % (15139)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_14850 for (2990ds/50Mi)
% 7.98/2.29 % (15137)Instruction limit reached!
% 7.98/2.29 % (15137)------------------------------
% 7.98/2.29 % (15137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/2.29 % (15137)Termination reason: Unknown
% 7.98/2.29 % (15137)Termination phase: Saturation
% 7.98/2.29
% 7.98/2.29 % (15137)Memory used [KB]: 7291
% 7.98/2.29 % (15137)Time elapsed: 0.054 s
% 7.98/2.29 % (15137)Instructions burned: 185 (million)
% 7.98/2.29 % (15137)------------------------------
% 7.98/2.29 % (15137)------------------------------
% 8.54/2.30 % (15140)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_14850 for (2990ds/368Mi)
% 8.54/2.30 % (15141)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_14850 for (2990ds/1021Mi)
% 8.54/2.30 % (15119)Instruction limit reached!
% 8.54/2.30 % (15119)------------------------------
% 8.54/2.30 % (15119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.54/2.30 % (15119)Termination reason: Unknown
% 8.54/2.30 % (15119)Termination phase: Saturation
% 8.54/2.30
% 8.54/2.30 % (15119)Memory used [KB]: 8315
% 8.54/2.30 % (15119)Time elapsed: 0.198 s
% 8.54/2.30 % (15119)Instructions burned: 459 (million)
% 8.54/2.30 % (15119)------------------------------
% 8.54/2.30 % (15119)------------------------------
% 8.54/2.31 % (15139)Instruction limit reached!
% 8.54/2.31 % (15139)------------------------------
% 8.54/2.31 % (15139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.54/2.31 % (15139)Termination reason: Unknown
% 8.54/2.31 % (15139)Termination phase: Property scanning
% 8.54/2.31
% 8.54/2.31 % (15139)Memory used [KB]: 2174
% 8.54/2.31 % (15139)Time elapsed: 0.025 s
% 8.54/2.31 % (15139)Instructions burned: 51 (million)
% 8.54/2.31 % (15139)------------------------------
% 8.54/2.31 % (15139)------------------------------
% 8.54/2.31 % (15142)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_14850 for (2989ds/267Mi)
% 8.54/2.32 % (15138)Instruction limit reached!
% 8.54/2.32 % (15138)------------------------------
% 8.54/2.32 % (15138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.54/2.32 % (15138)Termination reason: Unknown
% 8.54/2.32 % (15138)Termination phase: Saturation
% 8.54/2.32
% 8.54/2.32 % (15138)Memory used [KB]: 2814
% 8.54/2.32 % (15138)Time elapsed: 0.048 s
% 8.54/2.32 % (15138)Instructions burned: 166 (million)
% 8.54/2.32 % (15138)------------------------------
% 8.54/2.32 % (15138)------------------------------
% 8.54/2.32 % (15143)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_14850 for (2989ds/204Mi)
% 8.54/2.33 % (15144)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_14850 for (2989ds/26Mi)
% 8.54/2.34 % (15144)Instruction limit reached!
% 8.54/2.34 % (15144)------------------------------
% 8.54/2.34 % (15144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.54/2.34 % (15144)Termination reason: Unknown
% 8.54/2.34 % (15144)Termination phase: shuffling
% 8.54/2.34
% 8.54/2.34 % (15144)Memory used [KB]: 2046
% 8.54/2.34 % (15144)Time elapsed: 0.009 s
% 8.54/2.34 % (15144)Instructions burned: 28 (million)
% 8.54/2.34 % (15144)------------------------------
% 8.54/2.34 % (15144)------------------------------
% 8.54/2.35 % (15145)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_14850 for (2989ds/53Mi)
% 8.54/2.36 % (15145)Instruction limit reached!
% 8.54/2.36 % (15145)------------------------------
% 8.54/2.36 % (15145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.54/2.36 % (15145)Termination reason: Unknown
% 8.54/2.36 % (15145)Termination phase: Property scanning
% 8.54/2.36
% 8.54/2.36 % (15145)Memory used [KB]: 2174
% 8.54/2.36 % (15145)Time elapsed: 0.016 s
% 8.54/2.36 % (15145)Instructions burned: 54 (million)
% 8.54/2.36 % (15145)------------------------------
% 8.54/2.36 % (15145)------------------------------
% 8.54/2.37 % (15146)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_14850 for (2989ds/4436Mi)
% 8.89/2.40 % (15142)Instruction limit reached!
% 8.89/2.40 % (15142)------------------------------
% 8.89/2.40 % (15142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.40 % (15142)Termination reason: Unknown
% 8.89/2.40 % (15142)Termination phase: Saturation
% 8.89/2.40
% 8.89/2.40 % (15142)Memory used [KB]: 7547
% 8.89/2.40 % (15142)Time elapsed: 0.084 s
% 8.89/2.40 % (15142)Instructions burned: 268 (million)
% 8.89/2.40 % (15142)------------------------------
% 8.89/2.40 % (15142)------------------------------
% 8.89/2.40 % (15143)Instruction limit reached!
% 8.89/2.40 % (15143)------------------------------
% 8.89/2.40 % (15143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.40 % (15143)Termination reason: Unknown
% 8.89/2.40 % (15143)Termination phase: Saturation
% 8.89/2.40
% 8.89/2.40 % (15143)Memory used [KB]: 7036
% 8.89/2.40 % (15143)Time elapsed: 0.077 s
% 8.89/2.40 % (15143)Instructions burned: 204 (million)
% 8.89/2.40 % (15143)------------------------------
% 8.89/2.40 % (15143)------------------------------
% 8.89/2.41 % (15152)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_14850 for (2989ds/1539Mi)
% 8.89/2.41 % (15153)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_14850 for (2989ds/408Mi)
% 8.89/2.41 % (15140)Instruction limit reached!
% 8.89/2.41 % (15140)------------------------------
% 8.89/2.41 % (15140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.41 % (15140)Termination reason: Unknown
% 8.89/2.41 % (15140)Termination phase: Saturation
% 8.89/2.41
% 8.89/2.41 % (15140)Memory used [KB]: 7547
% 8.89/2.41 % (15140)Time elapsed: 0.115 s
% 8.89/2.41 % (15140)Instructions burned: 369 (million)
% 8.89/2.41 % (15140)------------------------------
% 8.89/2.41 % (15140)------------------------------
% 8.89/2.42 % (15154)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_14850 for (2988ds/5205Mi)
% 9.19/2.51 % (15129)Instruction limit reached!
% 9.19/2.51 % (15129)------------------------------
% 9.19/2.51 % (15129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.19/2.51 % (15129)Termination reason: Unknown
% 9.19/2.51 % (15129)Termination phase: Saturation
% 9.19/2.51
% 9.19/2.51 % (15129)Memory used [KB]: 9594
% 9.19/2.51 % (15129)Time elapsed: 0.359 s
% 9.19/2.51 % (15129)Instructions burned: 988 (million)
% 9.19/2.51 % (15129)------------------------------
% 9.19/2.51 % (15129)------------------------------
% 9.19/2.51 % (15155)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_14850 for (2987ds/1913Mi)
% 9.19/2.53 % (15136)Instruction limit reached!
% 9.19/2.53 % (15136)------------------------------
% 9.19/2.53 % (15136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.19/2.53 % (15136)Termination reason: Unknown
% 9.19/2.53 % (15136)Termination phase: Saturation
% 9.19/2.53
% 9.19/2.53 % (15136)Memory used [KB]: 7547
% 9.19/2.53 % (15136)Time elapsed: 0.291 s
% 9.19/2.53 % (15136)Instructions burned: 924 (million)
% 9.19/2.53 % (15136)------------------------------
% 9.19/2.53 % (15136)------------------------------
% 9.19/2.53 % (15153)Instruction limit reached!
% 9.19/2.53 % (15153)------------------------------
% 9.19/2.53 % (15153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.19/2.53 % (15153)Termination reason: Unknown
% 9.19/2.53 % (15153)Termination phase: Saturation
% 9.19/2.53
% 9.19/2.53 % (15153)Memory used [KB]: 8059
% 9.19/2.53 % (15153)Time elapsed: 0.125 s
% 9.19/2.53 % (15153)Instructions burned: 409 (million)
% 9.19/2.53 % (15153)------------------------------
% 9.19/2.53 % (15153)------------------------------
% 9.19/2.53 % (15156)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_14850 for (2987ds/4350Mi)
% 9.19/2.54 % (15157)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_14850 for (2987ds/68Mi)
% 9.19/2.56 % (15157)Instruction limit reached!
% 9.19/2.56 % (15157)------------------------------
% 9.19/2.56 % (15157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.19/2.56 % (15157)Termination reason: Unknown
% 9.19/2.56 % (15157)Termination phase: Property scanning
% 9.19/2.56
% 9.19/2.56 % (15157)Memory used [KB]: 2174
% 9.19/2.56 % (15157)Time elapsed: 0.022 s
% 9.19/2.56 % (15157)Instructions burned: 69 (million)
% 9.19/2.56 % (15157)------------------------------
% 9.19/2.56 % (15157)------------------------------
% 9.19/2.57 % (15158)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_14850 for (2987ds/358Mi)
% 10.02/2.62 % (15141)Instruction limit reached!
% 10.02/2.62 % (15141)------------------------------
% 10.02/2.62 % (15141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.02/2.62 % (15141)Termination reason: Unknown
% 10.02/2.62 % (15141)Termination phase: Saturation
% 10.02/2.62
% 10.02/2.62 % (15141)Memory used [KB]: 8571
% 10.02/2.62 % (15141)Time elapsed: 0.320 s
% 10.02/2.62 % (15141)Instructions burned: 1023 (million)
% 10.02/2.62 % (15141)------------------------------
% 10.02/2.62 % (15141)------------------------------
% 10.02/2.63 % (15159)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_14850 for (2986ds/31Mi)
% 10.02/2.64 % (15159)Instruction limit reached!
% 10.02/2.64 % (15159)------------------------------
% 10.02/2.64 % (15159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.02/2.64 % (15159)Termination reason: Unknown
% 10.02/2.64 % (15159)Termination phase: Property scanning
% 10.02/2.64
% 10.02/2.64 % (15159)Memory used [KB]: 1918
% 10.02/2.64 % (15159)Time elapsed: 0.011 s
% 10.02/2.64 % (15159)Instructions burned: 32 (million)
% 10.02/2.64 % (15159)------------------------------
% 10.02/2.64 % (15159)------------------------------
% 10.02/2.65 % (15160)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_14850 for (2986ds/279Mi)
% 10.02/2.68 % (15158)Instruction limit reached!
% 10.02/2.68 % (15158)------------------------------
% 10.02/2.68 % (15158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.02/2.68 % (15158)Termination reason: Unknown
% 10.02/2.68 % (15158)Termination phase: Saturation
% 10.02/2.68
% 10.02/2.68 % (15158)Memory used [KB]: 7419
% 10.02/2.68 % (15158)Time elapsed: 0.113 s
% 10.02/2.68 % (15158)Instructions burned: 359 (million)
% 10.02/2.68 % (15158)------------------------------
% 10.02/2.68 % (15158)------------------------------
% 10.02/2.69 % (15160)Refutation not found, incomplete strategy
% 10.02/2.69 % (15160)------------------------------
% 10.02/2.69 % (15160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.02/2.69 % (15160)Termination reason: Refutation not found, incomplete strategy
% 10.02/2.69
% 10.02/2.69
% 10.02/2.69 % (15160)Memory used [KB]: 7164
% 10.02/2.69 % (15160)Time elapsed: 0.041 s
% 10.02/2.69 % (15160)Instructions burned: 145 (million)
% 10.02/2.69 % (15160)------------------------------
% 10.02/2.69 % (15160)------------------------------
% 10.02/2.69 % (15161)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_14850 for (2986ds/258Mi)
% 10.54/2.70 % (15162)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_14850 for (2986ds/26Mi)
% 10.54/2.71 % (15162)Instruction limit reached!
% 10.54/2.71 % (15162)------------------------------
% 10.54/2.71 % (15162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.54/2.71 % (15162)Termination reason: Unknown
% 10.54/2.71 % (15162)Termination phase: shuffling
% 10.54/2.71
% 10.54/2.71 % (15162)Memory used [KB]: 2046
% 10.54/2.71 % (15162)Time elapsed: 0.009 s
% 10.54/2.71 % (15162)Instructions burned: 29 (million)
% 10.54/2.71 % (15162)------------------------------
% 10.54/2.71 % (15162)------------------------------
% 10.54/2.72 % (15163)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_14850 for (2985ds/995Mi)
% 10.54/2.77 % (15161)Instruction limit reached!
% 10.54/2.77 % (15161)------------------------------
% 10.54/2.77 % (15161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.54/2.77 % (15161)Termination reason: Unknown
% 10.54/2.77 % (15161)Termination phase: Saturation
% 10.54/2.77
% 10.54/2.77 % (15161)Memory used [KB]: 7675
% 10.54/2.77 % (15161)Time elapsed: 0.080 s
% 10.54/2.77 % (15161)Instructions burned: 260 (million)
% 10.54/2.77 % (15161)------------------------------
% 10.54/2.77 % (15161)------------------------------
% 10.54/2.78 % (15164)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_14850 for (2985ds/373Mi)
% 10.65/2.87 % (15152)Instruction limit reached!
% 10.65/2.87 % (15152)------------------------------
% 10.65/2.87 % (15152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.65/2.87 % (15152)Termination reason: Unknown
% 10.65/2.87 % (15152)Termination phase: Saturation
% 10.65/2.87
% 10.65/2.87 % (15152)Memory used [KB]: 10362
% 10.65/2.87 % (15152)Time elapsed: 0.462 s
% 10.65/2.87 % (15152)Instructions burned: 1539 (million)
% 10.65/2.87 % (15152)------------------------------
% 10.65/2.87 % (15152)------------------------------
% 10.65/2.88 % (15165)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_14850 for (2984ds/253Mi)
% 10.65/2.90 % (15164)Instruction limit reached!
% 10.65/2.90 % (15164)------------------------------
% 10.65/2.90 % (15164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.65/2.90 % (15164)Termination reason: Unknown
% 10.65/2.90 % (15164)Termination phase: Saturation
% 10.65/2.90
% 10.65/2.90 % (15164)Memory used [KB]: 7803
% 10.65/2.90 % (15164)Time elapsed: 0.116 s
% 10.65/2.90 % (15164)Instructions burned: 374 (million)
% 10.65/2.90 % (15164)------------------------------
% 10.65/2.90 % (15164)------------------------------
% 11.12/2.91 % (15166)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_14850 for (2984ds/832Mi)
% 11.12/2.95 % (15165)Instruction limit reached!
% 11.12/2.95 % (15165)------------------------------
% 11.12/2.95 % (15165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/2.95 % (15165)Termination reason: Unknown
% 11.12/2.95 % (15165)Termination phase: Saturation
% 11.12/2.95
% 11.12/2.95 % (15165)Memory used [KB]: 7803
% 11.12/2.95 % (15165)Time elapsed: 0.073 s
% 11.12/2.95 % (15165)Instructions burned: 255 (million)
% 11.12/2.95 % (15165)------------------------------
% 11.12/2.95 % (15165)------------------------------
% 11.12/2.96 % (15167)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_14850 for (2983ds/668Mi)
% 11.12/3.01 % (15163)Instruction limit reached!
% 11.12/3.01 % (15163)------------------------------
% 11.12/3.01 % (15163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/3.01 % (15163)Termination reason: Unknown
% 11.12/3.01 % (15163)Termination phase: Saturation
% 11.12/3.01
% 11.12/3.01 % (15163)Memory used [KB]: 9722
% 11.12/3.01 % (15163)Time elapsed: 0.292 s
% 11.12/3.01 % (15163)Instructions burned: 995 (million)
% 11.12/3.01 % (15163)------------------------------
% 11.12/3.01 % (15163)------------------------------
% 13.65/3.02 % (15168)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_14850 for (2983ds/40Mi)
% 13.65/3.03 % (15168)Instruction limit reached!
% 13.65/3.03 % (15168)------------------------------
% 13.65/3.03 % (15168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.65/3.03 % (15168)Termination reason: Unknown
% 13.65/3.03 % (15168)Termination phase: Property scanning
% 13.65/3.03
% 13.65/3.03 % (15168)Memory used [KB]: 2174
% 13.65/3.03 % (15168)Time elapsed: 0.013 s
% 13.65/3.03 % (15168)Instructions burned: 43 (million)
% 13.65/3.03 % (15168)------------------------------
% 13.65/3.03 % (15168)------------------------------
% 13.65/3.04 % (15169)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_14850 for (2982ds/294Mi)
% 13.65/3.08 % (15169)Refutation not found, incomplete strategy
% 13.65/3.08 % (15169)------------------------------
% 13.65/3.08 % (15169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.65/3.08 % (15169)Termination reason: Refutation not found, incomplete strategy
% 13.65/3.08
% 13.65/3.08
% 13.65/3.08 % (15169)Memory used [KB]: 6908
% 13.65/3.08 % (15169)Time elapsed: 0.041 s
% 13.65/3.08 % (15169)Instructions burned: 104 (million)
% 13.65/3.08 % (15169)------------------------------
% 13.65/3.08 % (15169)------------------------------
% 13.65/3.09 % (15170)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_14850 for (2982ds/187Mi)
% 13.65/3.11 % (15155)Instruction limit reached!
% 13.65/3.11 % (15155)------------------------------
% 13.65/3.11 % (15155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.65/3.11 % (15155)Termination reason: Unknown
% 13.65/3.11 % (15155)Termination phase: Saturation
% 13.65/3.11
% 13.65/3.11 % (15155)Memory used [KB]: 4093
% 13.65/3.11 % (15155)Time elapsed: 0.594 s
% 13.65/3.11 % (15155)Instructions burned: 1913 (million)
% 13.65/3.11 % (15155)------------------------------
% 13.65/3.11 % (15155)------------------------------
% 14.65/3.12 % (15171)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_14850 for (2982ds/371Mi)
% 14.65/3.15 % (15166)Instruction limit reached!
% 14.65/3.15 % (15166)------------------------------
% 14.65/3.15 % (15166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.65/3.15 % (15166)Termination reason: Unknown
% 14.65/3.15 % (15166)Termination phase: Saturation
% 14.65/3.15
% 14.65/3.15 % (15166)Memory used [KB]: 7931
% 14.65/3.15 % (15166)Time elapsed: 0.245 s
% 14.65/3.15 % (15166)Instructions burned: 832 (million)
% 14.65/3.15 % (15166)------------------------------
% 14.65/3.15 % (15166)------------------------------
% 14.65/3.15 % (15170)Instruction limit reached!
% 14.65/3.15 % (15170)------------------------------
% 14.65/3.15 % (15170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.65/3.15 % (15170)Termination reason: Unknown
% 14.65/3.15 % (15170)Termination phase: Saturation
% 14.65/3.15
% 14.65/3.15 % (15170)Memory used [KB]: 7419
% 14.65/3.15 % (15170)Time elapsed: 0.082 s
% 14.65/3.15 % (15170)Instructions burned: 187 (million)
% 14.65/3.15 % (15170)------------------------------
% 14.65/3.15 % (15170)------------------------------
% 14.65/3.16 % (15172)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_14850 for (2981ds/1827Mi)
% 14.65/3.16 % (15167)Instruction limit reached!
% 14.65/3.16 % (15167)------------------------------
% 14.65/3.16 % (15167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.65/3.16 % (15167)Termination reason: Unknown
% 14.65/3.16 % (15167)Termination phase: Saturation
% 14.65/3.16
% 14.65/3.16 % (15167)Memory used [KB]: 13944
% 14.65/3.16 % (15167)Time elapsed: 0.202 s
% 14.65/3.16 % (15167)Instructions burned: 668 (million)
% 14.65/3.16 % (15167)------------------------------
% 14.65/3.16 % (15167)------------------------------
% 14.65/3.16 % (15173)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_14850 for (2981ds/70Mi)
% 14.65/3.17 % (15174)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_14850 for (2981ds/316Mi)
% 14.65/3.18 % (15173)Instruction limit reached!
% 14.65/3.18 % (15173)------------------------------
% 14.65/3.18 % (15173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.65/3.18 % (15173)Termination reason: Unknown
% 14.65/3.18 % (15173)Termination phase: Preprocessing 1
% 14.65/3.18
% 14.65/3.18 % (15173)Memory used [KB]: 2302
% 14.65/3.18 % (15173)Time elapsed: 0.020 s
% 14.65/3.18 % (15173)Instructions burned: 70 (million)
% 14.65/3.18 % (15173)------------------------------
% 14.65/3.18 % (15173)------------------------------
% 14.65/3.19 % (15175)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_14850 for (2981ds/932Mi)
% 15.10/3.23 % (15174)Refutation not found, incomplete strategy
% 15.10/3.23 % (15174)------------------------------
% 15.10/3.23 % (15174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.10/3.23 % (15174)Termination reason: Refutation not found, incomplete strategy
% 15.10/3.23
% 15.10/3.23
% 15.10/3.23 % (15174)Memory used [KB]: 7675
% 15.10/3.23 % (15174)Time elapsed: 0.057 s
% 15.10/3.23 % (15174)Instructions burned: 204 (million)
% 15.10/3.23 % (15174)------------------------------
% 15.10/3.23 % (15174)------------------------------
% 15.10/3.23 % (15171)Instruction limit reached!
% 15.10/3.23 % (15171)------------------------------
% 15.10/3.23 % (15171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.10/3.23 % (15171)Termination reason: Unknown
% 15.10/3.23 % (15171)Termination phase: Saturation
% 15.10/3.23
% 15.10/3.23 % (15171)Memory used [KB]: 8187
% 15.10/3.23 % (15171)Time elapsed: 0.140 s
% 15.10/3.23 % (15171)Instructions burned: 373 (million)
% 15.10/3.23 % (15171)------------------------------
% 15.10/3.23 % (15171)------------------------------
% 15.10/3.24 % (15176)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_14850 for (2980ds/4714Mi)
% 15.10/3.24 % (15177)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_14850 for (2980ds/8250Mi)
% 15.10/3.29 % (15176)Refutation not found, incomplete strategy
% 15.10/3.29 % (15176)------------------------------
% 15.10/3.29 % (15176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.10/3.29 % (15176)Termination reason: Refutation not found, incomplete strategy
% 15.10/3.29
% 15.10/3.29
% 15.10/3.29 % (15176)Memory used [KB]: 7803
% 15.10/3.29 % (15176)Time elapsed: 0.057 s
% 15.10/3.29 % (15176)Instructions burned: 201 (million)
% 15.10/3.29 % (15176)------------------------------
% 15.10/3.29 % (15176)------------------------------
% 15.66/3.30 % (15178)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_14850 for (2979ds/770Mi)
% 15.96/3.47 % (15175)Instruction limit reached!
% 15.96/3.47 % (15175)------------------------------
% 15.96/3.47 % (15175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.96/3.47 % (15175)Termination reason: Unknown
% 15.96/3.47 % (15175)Termination phase: Saturation
% 15.96/3.47
% 15.96/3.47 % (15175)Memory used [KB]: 11129
% 15.96/3.47 % (15175)Time elapsed: 0.278 s
% 15.96/3.47 % (15175)Instructions burned: 932 (million)
% 15.96/3.47 % (15175)------------------------------
% 15.96/3.47 % (15175)------------------------------
% 15.96/3.48 % (15179)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_14850 for (2978ds/794Mi)
% 16.55/3.53 % (15178)Instruction limit reached!
% 16.55/3.53 % (15178)------------------------------
% 16.55/3.53 % (15178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.55/3.53 % (15178)Termination reason: Unknown
% 16.55/3.53 % (15178)Termination phase: Saturation
% 16.55/3.53
% 16.55/3.53 % (15178)Memory used [KB]: 7675
% 16.55/3.53 % (15178)Time elapsed: 0.230 s
% 16.55/3.53 % (15178)Instructions burned: 771 (million)
% 16.55/3.53 % (15178)------------------------------
% 16.55/3.53 % (15178)------------------------------
% 16.55/3.54 % (15180)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_14850 for (2977ds/464Mi)
% 17.09/3.69 % (15180)Instruction limit reached!
% 17.09/3.69 % (15180)------------------------------
% 17.09/3.69 % (15180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.09/3.69 % (15180)Termination reason: Unknown
% 17.09/3.69 % (15180)Termination phase: Saturation
% 17.09/3.69
% 17.09/3.69 % (15180)Memory used [KB]: 7547
% 17.09/3.69 % (15180)Time elapsed: 0.151 s
% 17.09/3.69 % (15180)Instructions burned: 464 (million)
% 17.09/3.69 % (15180)------------------------------
% 17.09/3.69 % (15180)------------------------------
% 17.09/3.69 % (15146)Instruction limit reached!
% 17.09/3.69 % (15146)------------------------------
% 17.09/3.69 % (15146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.09/3.69 % (15146)Termination reason: Unknown
% 17.09/3.69 % (15146)Termination phase: Saturation
% 17.09/3.69
% 17.09/3.69 % (15146)Memory used [KB]: 11257
% 17.09/3.69 % (15146)Time elapsed: 1.322 s
% 17.09/3.69 % (15146)Instructions burned: 4437 (million)
% 17.09/3.69 % (15146)------------------------------
% 17.09/3.69 % (15146)------------------------------
% 17.56/3.70 % (15181)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_14850 for (2976ds/1376Mi)
% 17.56/3.70 % (15182)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_14850 for (2975ds/906Mi)
% 17.56/3.72 % (15179)Instruction limit reached!
% 17.56/3.72 % (15179)------------------------------
% 17.56/3.72 % (15179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.56/3.72 % (15179)Termination reason: Unknown
% 17.56/3.72 % (15179)Termination phase: Saturation
% 17.56/3.72
% 17.56/3.72 % (15179)Memory used [KB]: 5756
% 17.56/3.72 % (15179)Time elapsed: 0.245 s
% 17.56/3.72 % (15179)Instructions burned: 796 (million)
% 17.56/3.72 % (15179)------------------------------
% 17.56/3.72 % (15179)------------------------------
% 17.56/3.73 % (15172)Instruction limit reached!
% 17.56/3.73 % (15172)------------------------------
% 17.56/3.73 % (15172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.56/3.73 % (15172)Termination reason: Unknown
% 17.56/3.73 % (15172)Termination phase: Saturation
% 17.56/3.73
% 17.56/3.73 % (15172)Memory used [KB]: 9850
% 17.56/3.73 % (15172)Time elapsed: 0.591 s
% 17.56/3.73 % (15172)Instructions burned: 1827 (million)
% 17.56/3.73 % (15172)------------------------------
% 17.56/3.73 % (15172)------------------------------
% 17.56/3.73 % (15183)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_14850 for (2975ds/434Mi)
% 17.56/3.74 % (15184)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_14850 for (2975ds/865Mi)
% 18.59/3.83 % (15156)Instruction limit reached!
% 18.59/3.83 % (15156)------------------------------
% 18.59/3.83 % (15156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.59/3.83 % (15156)Termination reason: Unknown
% 18.59/3.83 % (15156)Termination phase: Saturation
% 18.59/3.83
% 18.59/3.83 % (15156)Memory used [KB]: 10618
% 18.59/3.83 % (15156)Time elapsed: 1.299 s
% 18.59/3.83 % (15156)Instructions burned: 4352 (million)
% 18.59/3.83 % (15156)------------------------------
% 18.59/3.83 % (15156)------------------------------
% 18.59/3.85 % (15185)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_14850 for (2974ds/593Mi)
% 18.59/3.86 % (15183)Instruction limit reached!
% 18.59/3.86 % (15183)------------------------------
% 18.59/3.86 % (15183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.59/3.86 % (15183)Termination reason: Unknown
% 18.59/3.86 % (15183)Termination phase: Saturation
% 18.59/3.86
% 18.59/3.86 % (15183)Memory used [KB]: 7675
% 18.59/3.86 % (15183)Time elapsed: 0.131 s
% 18.59/3.86 % (15183)Instructions burned: 435 (million)
% 18.59/3.86 % (15183)------------------------------
% 18.59/3.86 % (15183)------------------------------
% 18.59/3.87 % (15186)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_14850 for (2974ds/443Mi)
% 18.59/3.89 % (15154)Instruction limit reached!
% 18.59/3.89 % (15154)------------------------------
% 18.59/3.89 % (15154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.59/3.89 % (15154)Termination reason: Unknown
% 18.59/3.89 % (15154)Termination phase: Saturation
% 18.59/3.89
% 18.59/3.89 % (15154)Memory used [KB]: 14072
% 18.59/3.89 % (15154)Time elapsed: 1.473 s
% 18.59/3.89 % (15154)Instructions burned: 5205 (million)
% 18.59/3.89 % (15154)------------------------------
% 18.59/3.89 % (15154)------------------------------
% 18.89/3.90 % (15187)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_14850 for (2974ds/594Mi)
% 18.89/4.01 % (15182)Instruction limit reached!
% 18.89/4.01 % (15182)------------------------------
% 18.89/4.01 % (15182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.89/4.01 % (15182)Termination reason: Unknown
% 18.89/4.01 % (15182)Termination phase: Saturation
% 18.89/4.01
% 18.89/4.01 % (15182)Memory used [KB]: 10618
% 18.89/4.01 % (15182)Time elapsed: 0.307 s
% 18.89/4.01 % (15182)Instructions burned: 908 (million)
% 18.89/4.01 % (15182)------------------------------
% 18.89/4.01 % (15182)------------------------------
% 18.89/4.02 % (15189)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_14850 for (2972ds/327Mi)
% 18.89/4.02 % (15185)Instruction limit reached!
% 18.89/4.02 % (15185)------------------------------
% 18.89/4.02 % (15185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.89/4.02 % (15185)Termination reason: Unknown
% 18.89/4.02 % (15185)Termination phase: Saturation
% 18.89/4.02
% 18.89/4.02 % (15185)Memory used [KB]: 9338
% 18.89/4.02 % (15185)Time elapsed: 0.180 s
% 18.89/4.02 % (15185)Instructions burned: 594 (million)
% 18.89/4.02 % (15185)------------------------------
% 18.89/4.02 % (15185)------------------------------
% 21.02/4.03 % (15186)Instruction limit reached!
% 21.02/4.03 % (15186)------------------------------
% 21.02/4.03 % (15186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.02/4.03 % (15186)Termination reason: Unknown
% 21.02/4.03 % (15186)Termination phase: Saturation
% 21.02/4.03
% 21.02/4.03 % (15186)Memory used [KB]: 7675
% 21.02/4.03 % (15186)Time elapsed: 0.143 s
% 21.02/4.03 % (15186)Instructions burned: 445 (million)
% 21.02/4.03 % (15186)------------------------------
% 21.02/4.03 % (15186)------------------------------
% 21.02/4.03 % (15184)Instruction limit reached!
% 21.02/4.03 % (15184)------------------------------
% 21.02/4.03 % (15184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.02/4.03 % (15184)Termination reason: Unknown
% 21.02/4.03 % (15184)Termination phase: Saturation
% 21.02/4.03
% 21.02/4.03 % (15184)Memory used [KB]: 8955
% 21.02/4.03 % (15184)Time elapsed: 0.291 s
% 21.02/4.03 % (15184)Instructions burned: 865 (million)
% 21.02/4.03 % (15184)------------------------------
% 21.02/4.03 % (15184)------------------------------
% 21.02/4.03 % (15190)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_14850 for (2972ds/5411Mi)
% 21.02/4.04 % (15191)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_14850 for (2972ds/1762Mi)
% 21.02/4.04 % (15192)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_14850 for (2972ds/96Mi)
% 21.02/4.07 % (15192)Instruction limit reached!
% 21.02/4.07 % (15192)------------------------------
% 21.02/4.07 % (15192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.02/4.07 % (15192)Termination reason: Unknown
% 21.02/4.07 % (15192)Termination phase: Property scanning
% 21.02/4.07
% 21.02/4.07 % (15192)Memory used [KB]: 2430
% 21.02/4.07 % (15192)Time elapsed: 0.029 s
% 21.02/4.07 % (15192)Instructions burned: 99 (million)
% 21.02/4.07 % (15192)------------------------------
% 21.02/4.07 % (15192)------------------------------
% 21.02/4.07 % (15194)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_14850 for (2972ds/503Mi)
% 21.02/4.09 % (15187)Instruction limit reached!
% 21.02/4.09 % (15187)------------------------------
% 21.02/4.09 % (15187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.02/4.09 % (15187)Termination reason: Unknown
% 21.02/4.09 % (15187)Termination phase: Saturation
% 21.02/4.09
% 21.02/4.09 % (15187)Memory used [KB]: 7931
% 21.02/4.09 % (15187)Time elapsed: 0.188 s
% 21.02/4.09 % (15187)Instructions burned: 596 (million)
% 21.02/4.09 % (15187)------------------------------
% 21.02/4.09 % (15187)------------------------------
% 21.02/4.10 % (15181)Instruction limit reached!
% 21.02/4.10 % (15181)------------------------------
% 21.02/4.10 % (15181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.02/4.10 % (15181)Termination reason: Unknown
% 21.02/4.10 % (15181)Termination phase: Saturation
% 21.02/4.10
% 21.02/4.10 % (15181)Memory used [KB]: 11897
% 21.02/4.10 % (15181)Time elapsed: 0.399 s
% 21.02/4.10 % (15181)Instructions burned: 1378 (million)
% 21.02/4.10 % (15181)------------------------------
% 21.02/4.10 % (15181)------------------------------
% 21.02/4.10 % (15195)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_14850 for (2972ds/90Mi)
% 21.02/4.11 % (15196)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_14850 for (2972ds/593Mi)
% 21.02/4.12 % (15194)Refutation not found, incomplete strategy
% 21.02/4.12 % (15194)------------------------------
% 21.02/4.12 % (15194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.02/4.12 % (15194)Termination reason: Refutation not found, incomplete strategy
% 21.02/4.12
% 21.02/4.12
% 21.02/4.12 % (15194)Memory used [KB]: 7547
% 21.02/4.12 % (15194)Time elapsed: 0.047 s
% 21.02/4.12 % (15194)Instructions burned: 155 (million)
% 21.02/4.12 % (15194)------------------------------
% 21.02/4.12 % (15194)------------------------------
% 21.42/4.13 % (15195)Instruction limit reached!
% 21.42/4.13 % (15195)------------------------------
% 21.42/4.13 % (15195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.42/4.13 % (15195)Termination reason: Unknown
% 21.42/4.13 % (15195)Termination phase: Saturation
% 21.42/4.13
% 21.42/4.13 % (15195)Memory used [KB]: 6780
% 21.42/4.13 % (15195)Time elapsed: 0.027 s
% 21.42/4.13 % (15195)Instructions burned: 91 (million)
% 21.42/4.13 % (15195)------------------------------
% 21.42/4.13 % (15195)------------------------------
% 21.42/4.13 % (15197)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_14850 for (2971ds/1512Mi)
% 21.42/4.14 % (15198)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_14850 for (2971ds/569Mi)
% 21.42/4.14 % (15189)Instruction limit reached!
% 21.42/4.14 % (15189)------------------------------
% 21.42/4.14 % (15189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.42/4.14 % (15189)Termination reason: Unknown
% 21.42/4.14 % (15189)Termination phase: Saturation
% 21.42/4.14
% 21.42/4.14 % (15189)Memory used [KB]: 7931
% 21.42/4.14 % (15189)Time elapsed: 0.117 s
% 21.42/4.14 % (15189)Instructions burned: 329 (million)
% 21.42/4.14 % (15189)------------------------------
% 21.42/4.14 % (15189)------------------------------
% 21.42/4.15 % (15199)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_14850 for (2971ds/501Mi)
% 21.64/4.24 % (15190)First to succeed.
% 21.64/4.24 % (15190)Refutation found. Thanks to Tanya!
% 21.64/4.24 % SZS status Theorem for DTF2THF_14850
% 21.64/4.24 % SZS output start Proof for DTF2THF_14850
% 21.64/4.24 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 21.64/4.24 thf(type_def_6, type, set: ($tType) > $tType).
% 21.64/4.24 thf(type_def_8, type, option: ($tType) > $tType).
% 21.64/4.24 thf(type_def_9, type, game: $tType).
% 21.64/4.24 thf(type_def_10, type, variable: $tType).
% 21.64/4.24 thf(type_def_11, type, char: $tType).
% 21.64/4.24 thf(type_def_12, type, trm: $tType).
% 21.64/4.24 thf(type_def_13, type, fml: $tType).
% 21.64/4.24 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 21.64/4.24 thf(func_def_1, type, variable: $tType).
% 21.64/4.24 thf(func_def_2, type, option: ($tType) > $tType).
% 21.64/4.24 thf(func_def_3, type, game: $tType).
% 21.64/4.24 thf(func_def_4, type, char: $tType).
% 21.64/4.24 thf(func_def_5, type, trm: $tType).
% 21.64/4.24 thf(func_def_6, type, fml: $tType).
% 21.64/4.24 thf(func_def_7, type, set: ($tType) > $tType).
% 21.64/4.24 thf(func_def_8, type, type: !>[X0: $tType]:($o)).
% 21.64/4.24 thf(func_def_9, type, ord: !>[X0: $tType]:($o)).
% 21.64/4.24 thf(func_def_10, type, order: !>[X0: $tType]:($o)).
% 21.64/4.24 thf(func_def_11, type, lattice: !>[X0: $tType]:($o)).
% 21.64/4.24 thf(func_def_12, type, linorder: !>[X0: $tType]:($o)).
% 21.64/4.24 thf(func_def_13, type, preorder: !>[X0: $tType]:($o)).
% 21.64/4.24 thf(func_def_14, type, semilattice_sup: !>[X0: $tType]:($o)).
% 21.64/4.24 thf(func_def_15, type, bNF_Ca1785829860lChain: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X0 > (X0 > X1) > $o)).
% 21.64/4.24 thf(func_def_16, type, bNF_csquare: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(set @ X0 > (X1 > X2) > (X3 > X2) > (X0 > X1) > (X0 > X3) > $o)).
% 21.64/4.24 thf(func_def_17, type, bNF_fstOp: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > $o) > (X1 > X2 > $o) > product_prod @ X0 @ X2 > product_prod @ X0 @ X1)).
% 21.64/4.24 thf(func_def_18, type, bNF_pick_middlep: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > $o) > (X1 > X2 > $o) > X0 > X2 > X1)).
% 21.64/4.24 thf(func_def_19, type, bNF_sndOp: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > $o) > (X1 > X2 > $o) > product_prod @ X0 @ X2 > product_prod @ X1 @ X2)).
% 21.64/4.24 thf(func_def_20, type, bNF_Greatest_image2: !>[X0: $tType, X1: $tType, X2: $tType]:(set @ X0 > (X0 > X1) > (X0 > X2) > set @ product_prod @ X1 @ X2)).
% 21.64/4.24 thf(func_def_21, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 21.64/4.24 thf(func_def_22, type, none: !>[X0: $tType]:(option @ X0)).
% 21.64/4.24 thf(func_def_23, type, some: !>[X0: $tType]:(X0 > option @ X0)).
% 21.64/4.24 thf(func_def_24, type, case_option: !>[X0: $tType, X1: $tType]:(X0 > (X1 > X0) > option @ X1 > X0)).
% 21.64/4.24 thf(func_def_25, type, the: !>[X0: $tType]:(option @ X0 > X0)).
% 21.64/4.24 thf(func_def_26, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 21.64/4.24 thf(func_def_27, type, order_Greatest: !>[X0: $tType]:((X0 > $o) > X0)).
% 21.64/4.24 thf(func_def_28, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 21.64/4.24 thf(func_def_29, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 21.64/4.24 thf(func_def_30, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 21.64/4.24 thf(func_def_31, type, product_fst: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 21.64/4.24 thf(func_def_32, type, product_snd: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 21.64/4.24 thf(func_def_33, type, product_swap: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > product_prod @ X1 @ X0)).
% 21.64/4.24 thf(func_def_34, type, product_scomp: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > product_prod @ X1 @ X2) > (X1 > X2 > X3) > X0 > X3)).
% 21.64/4.24 thf(func_def_35, type, relcompp: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > $o) > (X1 > X2 > $o) > X0 > X2 > $o)).
% 21.64/4.24 thf(func_def_36, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 21.64/4.24 thf(func_def_37, type, static_BVG: game > set @ variable).
% 21.64/4.24 thf(func_def_38, type, choice: game > game > game).
% 21.64/4.24 thf(func_def_39, type, compose: game > game > game).
% 21.64/4.24 thf(func_def_40, type, loop: game > game).
% 21.64/4.24 thf(func_def_41, type, uSubst1976112797hoiceo: option @ game > option @ game > option @ game).
% 21.64/4.24 thf(func_def_42, type, uSubst1385204910mposeo: option @ game > option @ game > option @ game).
% 21.64/4.24 thf(func_def_43, type, uSubst993936602_Loopo: option @ game > option @ game).
% 21.64/4.24 thf(func_def_44, type, uSubst95898988stappp: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > game > product_prod @ set @ variable @ option @ game).
% 21.64/4.24 thf(func_def_45, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 21.64/4.24 thf(func_def_46, type, ua: set @ variable).
% 21.64/4.24 thf(func_def_47, type, alpha: game).
% 21.64/4.24 thf(func_def_48, type, beta: game).
% 21.64/4.24 thf(func_def_49, type, sigma: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 21.64/4.24 thf(func_def_66, type, sP0: !>[X0: $tType, X1: $tType]:((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > $o)).
% 21.64/4.24 thf(func_def_67, type, sK1: !>[X0: $tType]:(option @ X0 > X0)).
% 21.64/4.24 thf(func_def_68, type, sK2: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0)).
% 21.64/4.24 thf(func_def_69, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1)).
% 21.64/4.24 thf(func_def_70, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2)).
% 21.64/4.24 thf(func_def_71, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3)).
% 21.64/4.24 thf(func_def_72, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4)).
% 21.64/4.24 thf(func_def_73, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5)).
% 21.64/4.24 thf(func_def_74, type, sK8: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 21.64/4.24 thf(func_def_75, type, sK9: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 21.64/4.24 thf(func_def_76, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6)).
% 21.64/4.24 thf(func_def_77, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 21.64/4.24 thf(func_def_78, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 21.64/4.24 thf(func_def_79, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 21.64/4.24 thf(func_def_80, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 21.64/4.24 thf(func_def_81, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 21.64/4.24 thf(func_def_82, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 21.64/4.24 thf(func_def_83, type, sK17: option @ game > game).
% 21.64/4.24 thf(func_def_84, type, sK18: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X1)).
% 21.64/4.24 thf(func_def_85, type, sK19: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0)).
% 21.64/4.24 thf(func_def_86, type, sK20: option @ game > game).
% 21.64/4.24 thf(func_def_87, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0)).
% 21.64/4.24 thf(func_def_88, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1)).
% 21.64/4.24 thf(func_def_89, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2)).
% 21.64/4.24 thf(func_def_90, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3)).
% 21.64/4.24 thf(func_def_91, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4)).
% 21.64/4.24 thf(func_def_92, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5)).
% 21.64/4.24 thf(func_def_93, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6)).
% 21.64/4.24 thf(func_def_94, type, sK28: !>[X0: $tType, X1: $tType]:((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > X1)).
% 21.64/4.24 thf(func_def_95, type, sK29: !>[X0: $tType, X1: $tType]:((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > X0)).
% 21.64/4.24 thf(func_def_96, type, sK30: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ X0 > X0 > X1)).
% 21.64/4.24 thf(func_def_97, type, sK31: !>[X0: $tType]:(option @ X0 > X0)).
% 21.64/4.24 thf(func_def_98, type, sK32: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 21.64/4.24 thf(func_def_99, type, sK33: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 21.64/4.24 thf(func_def_100, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 21.64/4.24 thf(func_def_101, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 21.64/4.24 thf(func_def_102, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 21.64/4.24 thf(func_def_103, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 21.64/4.24 thf(func_def_104, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 21.64/4.24 thf(func_def_105, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 21.64/4.24 thf(func_def_106, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 21.64/4.24 thf(func_def_107, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 21.64/4.24 thf(func_def_108, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 21.64/4.24 thf(func_def_109, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 21.64/4.24 thf(func_def_110, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 21.64/4.24 thf(func_def_111, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 21.64/4.24 thf(func_def_112, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 21.64/4.24 thf(func_def_113, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 21.64/4.24 thf(func_def_114, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 21.64/4.24 thf(func_def_115, type, sK49: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0 > X1)).
% 21.64/4.24 thf(func_def_116, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0)).
% 21.64/4.24 thf(func_def_117, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1)).
% 21.64/4.24 thf(func_def_118, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2)).
% 21.64/4.24 thf(func_def_119, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3)).
% 21.64/4.24 thf(func_def_120, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4)).
% 21.64/4.24 thf(func_def_121, type, sK55: (option @ game > option @ game > $o) > game).
% 21.64/4.24 thf(func_def_122, type, sK56: (option @ game > option @ game > $o) > game).
% 21.64/4.24 thf(func_def_123, type, sK57: (option @ game > option @ game > $o) > option @ game).
% 21.64/4.24 thf(func_def_124, type, sK58: (option @ game > option @ game > $o) > game).
% 21.64/4.24 thf(func_def_125, type, sK59: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 21.64/4.24 thf(func_def_126, type, sK60: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 21.64/4.24 thf(func_def_127, type, sK61: !>[X0: $tType]:((option @ X0 > $o) > X0)).
% 21.64/4.24 thf(func_def_128, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 21.64/4.24 thf(func_def_129, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 21.64/4.24 thf(func_def_130, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 21.64/4.24 thf(func_def_131, type, sK65: !>[X0: $tType]:(option @ X0 > X0)).
% 21.64/4.24 thf(func_def_132, type, sK66: (option @ game > $o) > game).
% 21.64/4.24 thf(func_def_133, type, sK67: product_prod @ option @ game @ option @ game > game).
% 21.64/4.24 thf(func_def_134, type, sK68: product_prod @ option @ game @ option @ game > game).
% 21.64/4.24 thf(func_def_135, type, sK69: product_prod @ option @ game @ option @ game > game).
% 21.64/4.24 thf(func_def_136, type, sK70: product_prod @ option @ game @ option @ game > option @ game).
% 21.64/4.24 thf(func_def_137, type, sK71: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 21.64/4.24 thf(func_def_138, type, sK72: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 21.64/4.24 thf(func_def_139, type, sK73: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 21.64/4.24 thf(func_def_140, type, sK74: !>[X0: $tType]:(set @ X0 > set @ X0 > set @ X0 > set @ X0)).
% 21.64/4.24 thf(func_def_141, type, sK75: !>[X0: $tType]:(set @ X0 > set @ X0 > set @ X0 > set @ X0)).
% 21.64/4.24 thf(func_def_142, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X0)).
% 21.64/4.24 thf(func_def_143, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X1)).
% 21.64/4.24 thf(func_def_144, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X2)).
% 21.64/4.24 thf(func_def_145, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0)).
% 21.64/4.24 thf(func_def_146, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1)).
% 21.64/4.24 thf(func_def_147, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2)).
% 21.64/4.24 thf(func_def_148, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3)).
% 21.64/4.24 thf(func_def_150, type, ph84: !>[X0: $tType]:(X0)).
% 21.64/4.24 thf(f1962,plain,(
% 21.64/4.24 $false),
% 21.64/4.24 inference(subsumption_resolution,[status(thm)],[f1961,f981])).
% 21.64/4.24 thf(f981,plain,(
% 21.64/4.24 ((ord_less_eq @ set @ variable @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (sup_sup @ set @ variable @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)))) @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta)))))) = $true)),
% 21.64/4.24 inference(cnf_transformation,[status(thm)],[f664])).
% 21.64/4.24 thf(f664,plain,(
% 21.64/4.24 ((ord_less_eq @ set @ variable @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (sup_sup @ set @ variable @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)))) @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta)))))) = $true)),
% 21.64/4.24 inference(fool_elimination,[status(thm)],[f663])).
% 21.64/4.24 thf(f663,plain,(
% 21.64/4.24 (ord_less_eq @ set @ variable @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (sup_sup @ set @ variable @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)))) @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta))))))),
% 21.64/4.24 inference(rectify,[status(thm)],[f2])).
% 21.64/4.24 thf(f2,axiom,(
% 21.64/4.24 (ord_less_eq @ set @ variable @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (sup_sup @ set @ variable @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)))) @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta))))))),
% 21.64/4.24 file('/export/starexec/sandbox/tmp/tmp.WDfDZbBGZy/DTF2THF_14850.p',fact_1_fact)).
% 21.64/4.24 thf(f1961,plain,(
% 21.64/4.24 ((ord_less_eq @ set @ variable @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (sup_sup @ set @ variable @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)))) @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta)))))) != $true)),
% 21.64/4.24 inference(subsumption_resolution,[status(thm)],[f1930,f998])).
% 21.64/4.24 thf(f998,plain,(
% 21.64/4.24 ( ! [X0 : $tType,X2 : set @ X0] : (((ord_less_eq @ set @ X0 @ X2 @ X2) = $true)) )),
% 21.64/4.24 inference(equality_resolution,[status(thm)],[f896])).
% 21.64/4.24 thf(f896,plain,(
% 21.64/4.24 ( ! [X0 : $tType,X2 : set @ X0,X1 : set @ X0] : ((X1 != X2) | ((ord_less_eq @ set @ X0 @ X1 @ X2) = $true)) )),
% 21.64/4.24 inference(cnf_transformation,[status(thm)],[f766])).
% 21.64/4.24 thf(f766,plain,(
% 21.64/4.24 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : ((X1 != X2) | (((ord_less_eq @ set @ X0 @ X1 @ X2) = $true) & ((ord_less_eq @ set @ X0 @ X2 @ X1) = $true)))),
% 21.64/4.24 inference(ennf_transformation,[status(thm)],[f684])).
% 21.64/4.24 thf(f684,plain,(
% 21.64/4.24 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : ((X1 = X2) => ~(((ord_less_eq @ set @ X0 @ X1 @ X2) = $true) => ((ord_less_eq @ set @ X0 @ X2 @ X1) != $true)))),
% 21.64/4.24 inference(flattening,[status(thm)],[f560])).
% 21.64/4.24 thf(f560,plain,(
% 21.64/4.24 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : ((X1 = X2) => ~(((ord_less_eq @ set @ X0 @ X1 @ X2) = $true) => ~((ord_less_eq @ set @ X0 @ X2 @ X1) = $true)))),
% 21.64/4.24 inference(fool_elimination,[status(thm)],[f559])).
% 21.64/4.24 thf(f559,plain,(
% 21.64/4.24 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : ((X1 = X2) => ~((ord_less_eq @ set @ X0 @ X1 @ X2) => ~(ord_less_eq @ set @ X0 @ X2 @ X1)))),
% 21.64/4.24 inference(rectify,[status(thm)],[f35])).
% 21.64/4.24 thf(f35,axiom,(
% 21.64/4.24 ! [X0 : $tType,X9 : set @ X0,X10 : set @ X0] : ((X9 = X10) => ~((ord_less_eq @ set @ X0 @ X9 @ X10) => ~(ord_less_eq @ set @ X0 @ X10 @ X9)))),
% 21.64/4.24 file('/export/starexec/sandbox/tmp/tmp.WDfDZbBGZy/DTF2THF_14850.p',fact_34_equalityE)).
% 21.64/4.24 thf(f1930,plain,(
% 21.64/4.24 ($true != (ord_less_eq @ set @ variable @ ua @ ua)) | ((ord_less_eq @ set @ variable @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (sup_sup @ set @ variable @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)))) @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta)))))) != $true)),
% 21.64/4.24 inference(trivial_inequality_removal,[status(thm)],[f1925])).
% 21.64/4.24 thf(f1925,plain,(
% 21.64/4.24 ($true != $true) | ((ord_less_eq @ set @ variable @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (sup_sup @ set @ variable @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)))) @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta)))))) != $true) | ($true != (ord_less_eq @ set @ variable @ ua @ ua))),
% 21.64/4.24 inference(superposition,[status(thm)],[f1223,f962])).
% 21.64/4.24 thf(f962,plain,(
% 21.64/4.24 ( ! [X0 : $tType,X2 : set @ X0,X3 : set @ X0,X1 : set @ X0,X4 : set @ X0] : (((ord_less_eq @ set @ X0 @ (sup_sup @ set @ X0 @ X1 @ X3) @ (sup_sup @ set @ X0 @ X2 @ X4)) = $true) | ((ord_less_eq @ set @ X0 @ X3 @ X4) != $true) | ((ord_less_eq @ set @ X0 @ X1 @ X2) != $true)) )),
% 21.64/4.24 inference(cnf_transformation,[status(thm)],[f733])).
% 21.64/4.24 thf(f733,plain,(
% 21.64/4.24 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : set @ X0,X4 : set @ X0] : (((ord_less_eq @ set @ X0 @ X3 @ X4) != $true) | ((ord_less_eq @ set @ X0 @ X1 @ X2) != $true) | ((ord_less_eq @ set @ X0 @ (sup_sup @ set @ X0 @ X1 @ X3) @ (sup_sup @ set @ X0 @ X2 @ X4)) = $true))),
% 21.64/4.24 inference(flattening,[status(thm)],[f732])).
% 21.64/4.24 thf(f732,plain,(
% 21.64/4.24 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : set @ X0,X4 : set @ X0] : ((((ord_less_eq @ set @ X0 @ (sup_sup @ set @ X0 @ X1 @ X3) @ (sup_sup @ set @ X0 @ X2 @ X4)) = $true) | ((ord_less_eq @ set @ X0 @ X3 @ X4) != $true)) | ((ord_less_eq @ set @ X0 @ X1 @ X2) != $true))),
% 21.64/4.24 inference(ennf_transformation,[status(thm)],[f676])).
% 21.64/4.24 thf(f676,plain,(
% 21.64/4.24 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : set @ X0,X4 : set @ X0] : (((ord_less_eq @ set @ X0 @ X1 @ X2) = $true) => (((ord_less_eq @ set @ X0 @ X3 @ X4) = $true) => ((ord_less_eq @ set @ X0 @ (sup_sup @ set @ X0 @ X1 @ X3) @ (sup_sup @ set @ X0 @ X2 @ X4)) = $true)))),
% 21.64/4.24 inference(fool_elimination,[status(thm)],[f675])).
% 21.64/4.24 thf(f675,plain,(
% 21.64/4.24 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : set @ X0,X4 : set @ X0] : ((ord_less_eq @ set @ X0 @ X1 @ X2) => ((ord_less_eq @ set @ X0 @ X3 @ X4) => (ord_less_eq @ set @ X0 @ (sup_sup @ set @ X0 @ X1 @ X3) @ (sup_sup @ set @ X0 @ X2 @ X4))))),
% 21.64/4.24 inference(rectify,[status(thm)],[f102])).
% 21.64/4.24 thf(f102,axiom,(
% 21.64/4.24 ! [X0 : $tType,X9 : set @ X0,X11 : set @ X0,X10 : set @ X0,X45 : set @ X0] : ((ord_less_eq @ set @ X0 @ X9 @ X11) => ((ord_less_eq @ set @ X0 @ X10 @ X45) => (ord_less_eq @ set @ X0 @ (sup_sup @ set @ X0 @ X9 @ X10) @ (sup_sup @ set @ X0 @ X11 @ X45))))),
% 21.64/4.24 file('/export/starexec/sandbox/tmp/tmp.WDfDZbBGZy/DTF2THF_14850.p',fact_101_Un__mono)).
% 21.64/4.24 thf(f1223,plain,(
% 21.64/4.24 ((ord_less_eq @ set @ variable @ (sup_sup @ set @ variable @ ua @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ (compose @ alpha @ beta)))))) @ (sup_sup @ set @ variable @ ua @ (sup_sup @ set @ variable @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)))) @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta))))))) != $true)),
% 21.64/4.24 inference(forward_demodulation,[status(thm)],[f1216,f878])).
% 21.64/4.24 thf(f878,plain,(
% 21.64/4.24 ( ! [X0 : $tType,X2 : set @ X0,X3 : set @ X0,X1 : set @ X0] : (((sup_sup @ set @ X0 @ X1 @ (sup_sup @ set @ X0 @ X2 @ X3)) = (sup_sup @ set @ X0 @ (sup_sup @ set @ X0 @ X1 @ X2) @ X3))) )),
% 21.64/4.24 inference(cnf_transformation,[status(thm)],[f688])).
% 21.64/4.24 thf(f688,plain,(
% 21.64/4.24 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : set @ X0] : ((sup_sup @ set @ X0 @ X1 @ (sup_sup @ set @ X0 @ X2 @ X3)) = (sup_sup @ set @ X0 @ (sup_sup @ set @ X0 @ X1 @ X2) @ X3))),
% 21.64/4.24 inference(rectify,[status(thm)],[f60])).
% 21.64/4.24 thf(f60,axiom,(
% 21.64/4.24 ! [X0 : $tType,X9 : set @ X0,X10 : set @ X0,X11 : set @ X0] : ((sup_sup @ set @ X0 @ X9 @ (sup_sup @ set @ X0 @ X10 @ X11)) = (sup_sup @ set @ X0 @ (sup_sup @ set @ X0 @ X9 @ X10) @ X11))),
% 21.64/4.24 file('/export/starexec/sandbox/tmp/tmp.WDfDZbBGZy/DTF2THF_14850.p',fact_59_Un__assoc)).
% 21.64/4.24 thf(f1216,plain,(
% 21.64/4.24 ((ord_less_eq @ set @ variable @ (sup_sup @ set @ variable @ ua @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ (compose @ alpha @ beta)))))) @ (sup_sup @ set @ variable @ (sup_sup @ set @ variable @ ua @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha))))) @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta)))))) != $true)),
% 21.64/4.24 inference(trivial_inequality_removal,[status(thm)],[f1192])).
% 21.64/4.24 thf(f1192,plain,(
% 21.64/4.24 ((ord_less_eq @ set @ variable @ (sup_sup @ set @ variable @ ua @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ (compose @ alpha @ beta)))))) @ (sup_sup @ set @ variable @ (sup_sup @ set @ variable @ ua @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha))))) @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta)))))) != $true) | ($true != $true)),
% 21.64/4.24 inference(superposition,[status(thm)],[f1037,f956])).
% 21.64/4.24 thf(f956,plain,(
% 21.64/4.24 ((ord_less_eq @ set @ variable @ (sup_sup @ set @ variable @ (sup_sup @ set @ variable @ ua @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha))))) @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta))))) @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta))) = $true)),
% 21.64/4.24 inference(cnf_transformation,[status(thm)],[f570])).
% 21.64/4.24 thf(f570,plain,(
% 21.64/4.24 ((ord_less_eq @ set @ variable @ (sup_sup @ set @ variable @ (sup_sup @ set @ variable @ ua @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha))))) @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta))))) @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta))) = $true)),
% 21.64/4.24 inference(fool_elimination,[status(thm)],[f569])).
% 21.64/4.24 thf(f569,plain,(
% 21.64/4.24 (ord_less_eq @ set @ variable @ (sup_sup @ set @ variable @ (sup_sup @ set @ variable @ ua @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha))))) @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta))))) @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta)))),
% 21.64/4.24 inference(rectify,[status(thm)],[f1])).
% 21.64/4.24 thf(f1,axiom,(
% 21.64/4.24 (ord_less_eq @ set @ variable @ (sup_sup @ set @ variable @ (sup_sup @ set @ variable @ ua @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha))))) @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta))))) @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta)))),
% 21.64/4.24 file('/export/starexec/sandbox/tmp/tmp.WDfDZbBGZy/DTF2THF_14850.p',fact_0__092_060open_062U_A_092_060union_062_ABVG_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_J_A_092_060union_062_ABVG_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_A_Ifst_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_A_092_060beta_062_J_J_J_A_092_060subseteq_062_Afst_A_Iusubstappp_A_092_060sigma_062_A_Ifst_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_A_092_060beta_062_J_092_060close_062)).
% 21.64/4.24 thf(f1037,plain,(
% 21.64/4.24 ( ! [X0 : set @ variable] : (((ord_less_eq @ set @ variable @ X0 @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta))) != $true) | ((ord_less_eq @ set @ variable @ (sup_sup @ set @ variable @ ua @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ (compose @ alpha @ beta)))))) @ X0) != $true)) )),
% 21.64/4.24 inference(trivial_inequality_removal,[status(thm)],[f1035])).
% 21.64/4.24 thf(f1035,plain,(
% 21.64/4.24 ( ! [X0 : set @ variable] : (($true != $true) | ((ord_less_eq @ set @ variable @ X0 @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta))) != $true) | ((ord_less_eq @ set @ variable @ (sup_sup @ set @ variable @ ua @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ (compose @ alpha @ beta)))))) @ X0) != $true)) )),
% 21.64/4.24 inference(superposition,[status(thm)],[f922,f975])).
% 21.64/4.24 thf(f975,plain,(
% 21.64/4.24 ( ! [X0 : $tType,X2 : set @ X0,X3 : set @ X0,X1 : set @ X0] : (((ord_less_eq @ set @ X0 @ X1 @ X3) = $true) | ((ord_less_eq @ set @ X0 @ X2 @ X3) != $true) | ((ord_less_eq @ set @ X0 @ X1 @ X2) != $true)) )),
% 21.64/4.24 inference(cnf_transformation,[status(thm)],[f771])).
% 21.64/4.24 thf(f771,plain,(
% 21.64/4.24 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : set @ X0] : (((ord_less_eq @ set @ X0 @ X1 @ X2) != $true) | ((ord_less_eq @ set @ X0 @ X2 @ X3) != $true) | ((ord_less_eq @ set @ X0 @ X1 @ X3) = $true))),
% 21.64/4.24 inference(flattening,[status(thm)],[f770])).
% 21.64/4.24 thf(f770,plain,(
% 21.64/4.24 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : set @ X0] : ((((ord_less_eq @ set @ X0 @ X1 @ X3) = $true) | ((ord_less_eq @ set @ X0 @ X2 @ X3) != $true)) | ((ord_less_eq @ set @ X0 @ X1 @ X2) != $true))),
% 21.64/4.24 inference(ennf_transformation,[status(thm)],[f394])).
% 21.64/4.24 thf(f394,plain,(
% 21.64/4.24 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : set @ X0] : (((ord_less_eq @ set @ X0 @ X1 @ X2) = $true) => (((ord_less_eq @ set @ X0 @ X2 @ X3) = $true) => ((ord_less_eq @ set @ X0 @ X1 @ X3) = $true)))),
% 21.64/4.24 inference(fool_elimination,[status(thm)],[f393])).
% 21.64/4.24 thf(f393,plain,(
% 21.64/4.24 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : set @ X0] : ((ord_less_eq @ set @ X0 @ X1 @ X2) => ((ord_less_eq @ set @ X0 @ X2 @ X3) => (ord_less_eq @ set @ X0 @ X1 @ X3)))),
% 21.64/4.24 inference(rectify,[status(thm)],[f28])).
% 21.64/4.24 thf(f28,axiom,(
% 21.64/4.24 ! [X0 : $tType,X9 : set @ X0,X10 : set @ X0,X11 : set @ X0] : ((ord_less_eq @ set @ X0 @ X9 @ X10) => ((ord_less_eq @ set @ X0 @ X10 @ X11) => (ord_less_eq @ set @ X0 @ X9 @ X11)))),
% 21.64/4.24 file('/export/starexec/sandbox/tmp/tmp.WDfDZbBGZy/DTF2THF_14850.p',fact_27_subset__trans)).
% 21.64/4.24 thf(f922,plain,(
% 21.64/4.24 ((ord_less_eq @ set @ variable @ (sup_sup @ set @ variable @ ua @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ (compose @ alpha @ beta)))))) @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta))) != $true)),
% 21.64/4.24 inference(cnf_transformation,[status(thm)],[f683])).
% 21.64/4.24 thf(f683,plain,(
% 21.64/4.24 ((ord_less_eq @ set @ variable @ (sup_sup @ set @ variable @ ua @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ (compose @ alpha @ beta)))))) @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta))) != $true)),
% 21.64/4.24 inference(flattening,[status(thm)],[f666])).
% 21.64/4.24 thf(f666,plain,(
% 21.64/4.24 ~((ord_less_eq @ set @ variable @ (sup_sup @ set @ variable @ ua @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ (compose @ alpha @ beta)))))) @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta))) = $true)),
% 21.64/4.24 inference(fool_elimination,[status(thm)],[f665])).
% 21.64/4.24 thf(f665,plain,(
% 21.64/4.24 ~(ord_less_eq @ set @ variable @ (sup_sup @ set @ variable @ ua @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ (compose @ alpha @ beta)))))) @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta)))),
% 21.64/4.24 inference(rectify,[status(thm)],[f273])).
% 21.64/4.24 thf(f273,negated_conjecture,(
% 21.64/4.24 ~(ord_less_eq @ set @ variable @ (sup_sup @ set @ variable @ ua @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ (compose @ alpha @ beta)))))) @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta)))),
% 21.64/4.24 inference(negated_conjecture,[status(cth)],[f272])).
% 21.64/4.24 thf(f272,conjecture,(
% 21.64/4.24 (ord_less_eq @ set @ variable @ (sup_sup @ set @ variable @ ua @ (static_BVG @ (the @ game @ (product_snd @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ (compose @ alpha @ beta)))))) @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ (product_fst @ set @ variable @ option @ game @ (uSubst95898988stappp @ sigma @ ua @ alpha)) @ beta)))),
% 21.64/4.24 file('/export/starexec/sandbox/tmp/tmp.WDfDZbBGZy/DTF2THF_14850.p',conj_0)).
% 21.64/4.24 % SZS output end Proof for DTF2THF_14850
% 21.64/4.24 % (15190)------------------------------
% 21.64/4.24 % (15190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.64/4.24 % (15190)Termination reason: Refutation
% 21.64/4.24
% 21.64/4.24 % (15190)Memory used [KB]: 7547
% 21.64/4.24 % (15190)Time elapsed: 0.209 s
% 21.64/4.24 % (15190)Instructions burned: 715 (million)
% 21.64/4.24 % (15190)------------------------------
% 21.64/4.24 % (15190)------------------------------
% 21.64/4.24 % (15042)Success in time 2.941 s
%------------------------------------------------------------------------------