%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP203^2 : 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 : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:56:23 AM UTC 2026
% Result : Theorem 165.61s 24.94s
% Output : Refutation 165.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : ITP203^2 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.35 % Computer : n027.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue Feb 24 08:30:07 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.48 ---- Original DTF file ---
% 0.27/0.48 thf(spec,logic,$$dhol).
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 % File : ITP203^2 : TPTP v9.2.1. Released v7.5.0.
% 0.27/0.48 % Domain : Interactive Theorem Proving
% 0.27/0.48 % Problem : Sledgehammer USubst problem prob_534__6335794_1
% 0.27/0.48 % Version : Especial.
% 0.27/0.48 % English :
% 0.27/0.48
% 0.27/0.48 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.27/0.48 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.27/0.48 % Source : [Des21]
% 0.27/0.48 % Names : USubst/prob_534__6335794_1 [Des21]
% 0.27/0.48
% 0.27/0.48 % Status : Theorem
% 0.27/0.48 % Rating : 0.67 v9.1.0, 0.33 v9.0.0, 0.67 v8.1.0, 0.50 v7.5.0
% 0.27/0.48 % Syntax : Number of formulae : 334 ( 154 unt; 58 typ; 0 def)
% 0.27/0.48 % Number of atoms : 608 ( 443 equ; 0 cnn)
% 0.27/0.48 % Maximal formula atoms : 31 ( 2 avg)
% 0.27/0.48 % Number of connectives : 7417 ( 175 ~; 10 |; 28 &;6919 @)
% 0.27/0.48 % ( 0 <=>; 285 =>; 0 <=; 0 <~>)
% 0.27/0.48 % Maximal formula depth : 29 ( 7 avg)
% 0.27/0.48 % Number of types : 7 ( 6 usr)
% 0.27/0.48 % Number of type conns : 1365 (1365 >; 0 *; 0 +; 0 <<)
% 0.27/0.48 % Number of symbols : 55 ( 52 usr; 8 con; 0-8 aty)
% 0.27/0.48 % Number of variables : 1347 ( 269 ^;1035 !; 14 ?;1347 :)
% 0.27/0.48 % ( 29 !>; 0 ?*; 0 @-; 0 @+)
% 0.27/0.48 % SPC : TH1_THM_EQU_NAR
% 0.27/0.48
% 0.27/0.48 % Comments : This file was generated by Sledgehammer 2021-02-23 16:19:55.955
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 % Could-be-implicit typings (9)
% 0.27/0.48 thf(ty_t_Product__Type_Oprod,type,
% 0.27/0.48 product_prod: $tType > $tType > $tType ).
% 0.27/0.48
% 0.27/0.48 thf(ty_t_Syntax_Ovariable,type,
% 0.27/0.48 variable: $tType ).
% 0.27/0.48
% 0.27/0.48 thf(ty_t_Option_Ooption,type,
% 0.27/0.48 option: $tType > $tType ).
% 0.27/0.48
% 0.27/0.48 thf(ty_t_Syntax_Ogame,type,
% 0.27/0.48 game: $tType ).
% 0.27/0.48
% 0.27/0.48 thf(ty_t_String_Ochar,type,
% 0.27/0.48 char: $tType ).
% 0.27/0.48
% 0.27/0.48 thf(ty_t_Syntax_Otrm,type,
% 0.27/0.48 trm: $tType ).
% 0.27/0.48
% 0.27/0.48 thf(ty_t_Syntax_Ofml,type,
% 0.27/0.48 fml: $tType ).
% 0.27/0.48
% 0.27/0.48 thf(ty_t_Real_Oreal,type,
% 0.27/0.48 real: $tType ).
% 0.27/0.48
% 0.27/0.48 thf(ty_t_Set_Oset,type,
% 0.27/0.48 set: $tType > $tType ).
% 0.27/0.48
% 0.27/0.48 % Explicit typings (49)
% 0.27/0.48 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.27/0.48 bounded_lattice:
% 0.27/0.48 !>[A: $tType] : $o ).
% 0.27/0.48
% 0.27/0.48 thf(sy_cl_HOL_Otype,type,
% 0.27/0.48 type:
% 0.27/0.48 !>[A: $tType] : $o ).
% 0.27/0.48
% 0.27/0.48 thf(sy_cl_Orderings_Obot,type,
% 0.27/0.48 bot:
% 0.27/0.48 !>[A: $tType] : $o ).
% 0.27/0.48
% 0.27/0.48 thf(sy_cl_Lattices_Olattice,type,
% 0.27/0.48 lattice:
% 0.27/0.48 !>[A: $tType] : $o ).
% 0.27/0.48
% 0.27/0.48 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 0.27/0.48 semilattice_inf:
% 0.27/0.48 !>[A: $tType] : $o ).
% 0.27/0.48
% 0.27/0.48 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 0.27/0.48 bounded_lattice_bot:
% 0.27/0.48 !>[A: $tType] : $o ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_If,type,
% 0.27/0.48 if:
% 0.27/0.48 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.27/0.48 inf_inf:
% 0.27/0.48 !>[A: $tType] : ( A > A > A ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Option_Ooption_ONone,type,
% 0.27/0.48 none:
% 0.27/0.48 !>[A: $tType] : ( option @ A ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Option_Ooption_OSome,type,
% 0.27/0.48 some:
% 0.27/0.48 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Option_Ooption_Ocase__option,type,
% 0.27/0.48 case_option:
% 0.27/0.48 !>[B: $tType,A: $tType] : ( B > ( A > B ) > ( option @ A ) > B ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Option_Ooption_Othe,type,
% 0.27/0.48 the:
% 0.27/0.48 !>[A: $tType] : ( ( option @ A ) > A ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.27/0.48 bot_bot:
% 0.27/0.48 !>[A: $tType] : A ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Product__Type_OPair,type,
% 0.27/0.48 product_Pair:
% 0.27/0.48 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.27/0.48 produc2004651681e_prod:
% 0.27/0.48 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.27/0.48 product_rec_prod:
% 0.27/0.48 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Product__Type_Oprod_Ocase__prod,type,
% 0.27/0.48 product_case_prod:
% 0.27/0.48 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Set_OCollect,type,
% 0.27/0.48 collect:
% 0.27/0.48 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Set_Ois__empty,type,
% 0.27/0.48 is_empty:
% 0.27/0.48 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Static__Semantics_OFVF,type,
% 0.27/0.48 static_FVF: fml > ( set @ variable ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Static__Semantics_OFVT,type,
% 0.27/0.48 static_FVT: trm > ( set @ variable ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_String_Ochar_OChar,type,
% 0.27/0.48 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Syntax_Ofml_OGeq,type,
% 0.27/0.48 geq: trm > trm > fml ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Syntax_Ofml_OPred,type,
% 0.27/0.48 pred: char > trm > fml ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Syntax_Otrm_OConst,type,
% 0.27/0.48 const: char > trm ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Syntax_Otrm_ODifferential,type,
% 0.27/0.48 differential: trm > trm ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Syntax_Otrm_OFunc,type,
% 0.27/0.48 func: char > trm > trm ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Syntax_Otrm_ONumber,type,
% 0.27/0.48 number: real > trm ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Syntax_Otrm_OPlus,type,
% 0.27/0.48 plus: trm > trm > trm ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Syntax_Otrm_OTimes,type,
% 0.27/0.48 times: trm > trm > trm ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Syntax_Otrm_OVar,type,
% 0.27/0.48 var: variable > trm ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_USubst__Mirabelle__nnnzepxswx_ODifferentialo,type,
% 0.27/0.48 uSubst259074819ntialo: ( option @ trm ) > ( option @ trm ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OGeqo,type,
% 0.27/0.48 uSubst1556497037e_Geqo: ( option @ trm ) > ( option @ trm ) > ( option @ fml ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OPluso,type,
% 0.27/0.48 uSubst1112714340_Pluso: ( option @ trm ) > ( option @ trm ) > ( option @ trm ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTesto,type,
% 0.27/0.48 uSubst190403692_Testo: ( option @ fml ) > ( option @ game ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTimeso,type,
% 0.27/0.48 uSubst277968634Timeso: ( option @ trm ) > ( option @ trm ) > ( option @ trm ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Odot,type,
% 0.27/0.48 uSubst_Mirabelle_dot: trm ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Odotsubstt,type,
% 0.27/0.48 uSubst969145931substt: trm > ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousappconst,type,
% 0.27/0.48 uSubst1138577137pconst: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > char > ( option @ trm ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappf,type,
% 0.27/0.48 uSubst95898978stappf: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > fml > ( option @ fml ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappt,type,
% 0.27/0.48 uSubst95898992stappt: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > trm > ( option @ trm ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappt__rel,type,
% 0.27/0.48 uSubst2096773001pt_rel: ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) > ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) > $o ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_Wellfounded_Oaccp,type,
% 0.27/0.48 accp:
% 0.27/0.48 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_c_member,type,
% 0.27/0.48 member:
% 0.27/0.48 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_v_Ua____,type,
% 0.27/0.48 ua: set @ variable ).
% 0.27/0.48
% 0.27/0.48 thf(sy_v_Va____,type,
% 0.27/0.48 va: set @ variable ).
% 0.27/0.48
% 0.27/0.48 thf(sy_v__092_060sigma_062,type,
% 0.27/0.48 sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(sy_v__092_060theta_062____,type,
% 0.27/0.48 theta: trm ).
% 0.27/0.48
% 0.27/0.48 thf(sy_v_p____,type,
% 0.27/0.48 p: char ).
% 0.27/0.48
% 0.27/0.48 % Relevant facts (255)
% 0.27/0.48 thf(fact_0_f7,axiom,
% 0.27/0.48 ! [Z: option @ fml,F: fml > ( option @ fml ),Za: option @ fml] :
% 0.27/0.48 ( ( ( Za
% 0.27/0.48 = ( none @ fml ) )
% 0.27/0.48 => ( ( case_option @ ( option @ fml ) @ fml @ Z @ F @ Za )
% 0.27/0.48 = Z ) )
% 0.27/0.48 & ( ( Za
% 0.27/0.48 != ( none @ fml ) )
% 0.27/0.48 => ( ( case_option @ ( option @ fml ) @ fml @ Z @ F @ Za )
% 0.27/0.48 = ( F @ ( the @ fml @ Za ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % f7
% 0.27/0.48 thf(fact_1_Pred_Oprems_I2_J,axiom,
% 0.27/0.48 ( ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) )
% 0.27/0.48 != ( none @ fml ) ) ).
% 0.27/0.48
% 0.27/0.48 % Pred.prems(2)
% 0.27/0.48 thf(fact_2_case__prod__app,axiom,
% 0.27/0.48 ! [A: $tType,D: $tType,C: $tType,B: $tType] :
% 0.27/0.48 ( ( product_case_prod @ B @ C @ ( D > A ) )
% 0.27/0.48 = ( ^ [F2: B > C > D > A,X: product_prod @ B @ C,Y: D] :
% 0.27/0.48 ( product_case_prod @ B @ C @ A
% 0.27/0.48 @ ^ [L: B,R: C] : ( F2 @ L @ R @ Y )
% 0.27/0.48 @ X ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % case_prod_app
% 0.27/0.48 thf(fact_3_Pred_Oprems_I1_J,axiom,
% 0.27/0.48 ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.27/0.48 != ( none @ fml ) ) ).
% 0.27/0.48
% 0.27/0.48 % Pred.prems(1)
% 0.27/0.48 thf(fact_4__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_092_060close_062,axiom,
% 0.27/0.48 ~ ( ( ( inf_inf @ ( set @ variable )
% 0.27/0.48 @ ( static_FVF
% 0.27/0.48 @ ( the @ fml
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p ) ) )
% 0.27/0.48 @ va )
% 0.27/0.48 != ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.48 => ( ( none @ fml )
% 0.27/0.48 = ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) )
% 0.27/0.48 @ ( the @ fml
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % \<open>(if FVF (the (SPreds \<sigma> p)) \<inter> V = {} then usubstappf (dotsubstt (the (usubstappt \<sigma> V \<theta>))) {} (the (SPreds \<sigma> p)) else undeff) \<noteq> usubstappf (dotsubstt (the (usubstappt \<sigma> V \<theta>))) {} (the (SPreds \<sigma> p))\<close>
% 0.27/0.48 thf(fact_5_f9,axiom,
% 0.27/0.48 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p )
% 0.27/0.48 = ( none @ fml ) )
% 0.27/0.48 => ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.27/0.48 = ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % f9
% 0.27/0.48 thf(fact_6__092_060open_062_Icase_ASPreds_A_092_060sigma_062_Ap_Aof_ANone_A_092_060Rightarrow_062_AAfml_A_IPred_Ap_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_124_ASome_Af_A_092_060Rightarrow_062_Aif_AFVF_Af_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_Af_Aelse_Aundeff_J_A_092_060noteq_062_A_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_092_060close_062,axiom,
% 0.27/0.48 ~ ( ( ( ( inf_inf @ ( set @ variable )
% 0.27/0.48 @ ( static_FVF
% 0.27/0.48 @ ( the @ fml
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p ) ) )
% 0.27/0.48 @ va )
% 0.27/0.48 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.48 => ( ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) )
% 0.27/0.48 @ ^ [F2: fml] :
% 0.27/0.48 ( if @ ( option @ fml )
% 0.27/0.48 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ va )
% 0.27/0.48 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.48 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 0.27/0.48 @ ( none @ fml ) )
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p ) )
% 0.27/0.48 = ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) )
% 0.27/0.48 @ ( the @ fml
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p ) ) ) ) )
% 0.27/0.48 & ( ( ( inf_inf @ ( set @ variable )
% 0.27/0.48 @ ( static_FVF
% 0.27/0.48 @ ( the @ fml
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p ) ) )
% 0.27/0.48 @ va )
% 0.27/0.48 != ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.48 => ( ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) )
% 0.27/0.48 @ ^ [F2: fml] :
% 0.27/0.48 ( if @ ( option @ fml )
% 0.27/0.48 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ va )
% 0.27/0.48 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.48 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 0.27/0.48 @ ( none @ fml ) )
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p ) )
% 0.27/0.48 = ( none @ fml ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % \<open>(case SPreds \<sigma> p of None \<Rightarrow> Afml (Pred p (the (usubstappt \<sigma> V \<theta>))) | Some f \<Rightarrow> if FVF f \<inter> V = {} then usubstappf (dotsubstt (the (usubstappt \<sigma> V \<theta>))) {} f else undeff) \<noteq> (if FVF (the (SPreds \<sigma> p)) \<inter> V = {} then usubstappf (dotsubstt (the (usubstappt \<sigma> V \<theta>))) {} (the (SPreds \<sigma> p)) else undeff)\<close>
% 0.27/0.48 thf(fact_7_Ando_Oinduct,axiom,
% 0.27/0.48 ! [P2: ( option @ fml ) > ( option @ fml ) > $o,A0: option @ fml,A1: option @ fml] :
% 0.27/0.48 ( ! [Phi: fml,Psi: fml] : ( P2 @ ( some @ fml @ Phi ) @ ( some @ fml @ Psi ) )
% 0.27/0.48 => ( ! [X_1: option @ fml] : ( P2 @ ( none @ fml ) @ X_1 )
% 0.27/0.48 => ( ! [V: fml] : ( P2 @ ( some @ fml @ V ) @ ( none @ fml ) )
% 0.27/0.48 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Ando.induct
% 0.27/0.48 thf(fact_8_Testo_Ocases,axiom,
% 0.27/0.48 ! [X2: option @ fml] :
% 0.27/0.48 ( ! [Phi: fml] :
% 0.27/0.48 ( X2
% 0.27/0.48 != ( some @ fml @ Phi ) )
% 0.27/0.48 => ( X2
% 0.27/0.48 = ( none @ fml ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Testo.cases
% 0.27/0.48 thf(fact_9_Testo_Oinduct,axiom,
% 0.27/0.48 ! [P2: ( option @ fml ) > $o,A0: option @ fml] :
% 0.27/0.48 ( ! [Phi: fml] : ( P2 @ ( some @ fml @ Phi ) )
% 0.27/0.48 => ( ( P2 @ ( none @ fml ) )
% 0.27/0.48 => ( P2 @ A0 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Testo.induct
% 0.27/0.48 thf(fact_10_undeff__equiv,axiom,
% 0.27/0.48 ! [Phi2: option @ fml] :
% 0.27/0.48 ( ( Phi2
% 0.27/0.48 != ( none @ fml ) )
% 0.27/0.48 = ( ? [F2: fml] :
% 0.27/0.48 ( Phi2
% 0.27/0.48 = ( some @ fml @ F2 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % undeff_equiv
% 0.27/0.48 thf(fact_11_Existso_Oinduct,axiom,
% 0.27/0.48 ! [P2: variable > ( option @ fml ) > $o,A0: variable,A1: option @ fml] :
% 0.27/0.48 ( ! [X3: variable,Phi: fml] : ( P2 @ X3 @ ( some @ fml @ Phi ) )
% 0.27/0.48 => ( ! [X3: variable] : ( P2 @ X3 @ ( none @ fml ) )
% 0.27/0.48 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Existso.induct
% 0.27/0.48 thf(fact_12_prod_Ocase__distrib,axiom,
% 0.27/0.48 ! [C: $tType,D: $tType,B: $tType,A: $tType,H: C > D,F3: A > B > C,Prod: product_prod @ A @ B] :
% 0.27/0.48 ( ( H @ ( product_case_prod @ A @ B @ C @ F3 @ Prod ) )
% 0.27/0.48 = ( product_case_prod @ A @ B @ D
% 0.27/0.48 @ ^ [X1: A,X22: B] : ( H @ ( F3 @ X1 @ X22 ) )
% 0.27/0.48 @ Prod ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod.case_distrib
% 0.27/0.48 thf(fact_13__092_060open_062usubstappf_A_092_060sigma_062_AU_A_IPred_Ap_A_092_060theta_062_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_092_060close_062,axiom,
% 0.27/0.48 ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.27/0.48 != ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % \<open>usubstappf \<sigma> U (Pred p \<theta>) \<noteq> usubstappf \<sigma> V (Pred p \<theta>)\<close>
% 0.27/0.48 thf(fact_14_f5,axiom,
% 0.27/0.48 ( ( uSubst95898992stappt @ sigma @ ua @ theta )
% 0.27/0.48 = ( uSubst95898992stappt @ sigma @ va @ theta ) ) ).
% 0.27/0.48
% 0.27/0.48 % f5
% 0.27/0.48 thf(fact_15_calculation_I1_J,axiom,
% 0.27/0.48 ~ ( ( ( ( inf_inf @ ( set @ variable )
% 0.27/0.48 @ ( static_FVF
% 0.27/0.48 @ ( the @ fml
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p ) ) )
% 0.27/0.48 @ va )
% 0.27/0.48 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.48 => ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.27/0.48 = ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) )
% 0.27/0.48 @ ( the @ fml
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p ) ) ) ) )
% 0.27/0.48 & ( ( ( inf_inf @ ( set @ variable )
% 0.27/0.48 @ ( static_FVF
% 0.27/0.48 @ ( the @ fml
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p ) ) )
% 0.27/0.48 @ va )
% 0.27/0.48 != ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.48 => ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.27/0.48 = ( none @ fml ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % calculation(1)
% 0.27/0.48 thf(fact_16_calculation_I2_J,axiom,
% 0.27/0.48 ( ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.27/0.48 != ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) )
% 0.27/0.48 @ ( the @ fml
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p ) ) ) )
% 0.27/0.48 => ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p )
% 0.27/0.48 = ( none @ fml ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % calculation(2)
% 0.27/0.48 thf(fact_17_f6,axiom,
% 0.27/0.48 ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.27/0.48 = ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) )
% 0.27/0.48 @ ^ [F2: fml] :
% 0.27/0.48 ( if @ ( option @ fml )
% 0.27/0.48 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ ua )
% 0.27/0.48 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.48 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 0.27/0.48 @ ( none @ fml ) )
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % f6
% 0.27/0.48 thf(fact_18__092_060open_062usubstappf_A_092_060sigma_062_AU_A_IPred_Ap_A_092_060theta_062_J_A_092_060noteq_062_A_Icase_ASPreds_A_092_060sigma_062_Ap_Aof_ANone_A_092_060Rightarrow_062_AAfml_A_IPred_Ap_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_124_ASome_Af_A_092_060Rightarrow_062_Aif_AFVF_Af_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_Af_Aelse_Aundeff_J_092_060close_062,axiom,
% 0.27/0.48 ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.27/0.48 != ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) )
% 0.27/0.48 @ ^ [F2: fml] :
% 0.27/0.48 ( if @ ( option @ fml )
% 0.27/0.48 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ va )
% 0.27/0.48 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.48 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 0.27/0.48 @ ( none @ fml ) )
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % \<open>usubstappf \<sigma> U (Pred p \<theta>) \<noteq> (case SPreds \<sigma> p of None \<Rightarrow> Afml (Pred p (the (usubstappt \<sigma> V \<theta>))) | Some f \<Rightarrow> if FVF f \<inter> V = {} then usubstappf (dotsubstt (the (usubstappt \<sigma> V \<theta>))) {} f else undeff)\<close>
% 0.27/0.48 thf(fact_19_usubstappf__pred2,axiom,
% 0.27/0.48 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),P3: char,R2: fml,U: set @ variable,Theta: trm] :
% 0.27/0.48 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ Sigma
% 0.27/0.48 @ P3 )
% 0.27/0.48 = ( some @ fml @ R2 ) )
% 0.27/0.48 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R2 ) @ U )
% 0.27/0.48 != ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.48 => ( ( uSubst95898978stappf @ Sigma @ U @ ( pred @ P3 @ Theta ) )
% 0.27/0.48 = ( none @ fml ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % usubstappf_pred2
% 0.27/0.48 thf(fact_20_f3,axiom,
% 0.27/0.48 ( ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
% 0.27/0.48 @ ^ [T2: trm] :
% 0.27/0.48 ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ T2 ) )
% 0.27/0.48 @ ^ [F2: fml] :
% 0.27/0.48 ( if @ ( option @ fml )
% 0.27/0.48 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ ua )
% 0.27/0.48 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.48 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ T2 ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 0.27/0.48 @ ( none @ fml ) )
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p ) )
% 0.27/0.48 @ ( uSubst95898992stappt @ sigma @ ua @ theta ) )
% 0.27/0.48 = ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ua @ theta ) ) ) )
% 0.27/0.48 @ ^ [F2: fml] :
% 0.27/0.48 ( if @ ( option @ fml )
% 0.27/0.48 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ ua )
% 0.27/0.48 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.48 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ua @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 0.27/0.48 @ ( none @ fml ) )
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % f3
% 0.27/0.48 thf(fact_21_f8,axiom,
% 0.27/0.48 ( ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
% 0.27/0.48 @ ^ [T2: trm] :
% 0.27/0.48 ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ T2 ) )
% 0.27/0.48 @ ^ [F2: fml] :
% 0.27/0.48 ( if @ ( option @ fml )
% 0.27/0.48 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ va )
% 0.27/0.48 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.48 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ T2 ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 0.27/0.48 @ ( none @ fml ) )
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p ) )
% 0.27/0.48 @ ( uSubst95898992stappt @ sigma @ va @ theta ) )
% 0.27/0.48 = ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) )
% 0.27/0.48 @ ^ [F2: fml] :
% 0.27/0.48 ( if @ ( option @ fml )
% 0.27/0.48 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ va )
% 0.27/0.48 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.48 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 0.27/0.48 @ ( none @ fml ) )
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % f8
% 0.27/0.48 thf(fact_22_f1,axiom,
% 0.27/0.48 ( ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
% 0.27/0.48 @ ^ [T2: trm] :
% 0.27/0.48 ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ T2 ) )
% 0.27/0.48 @ ^ [F2: fml] :
% 0.27/0.48 ( if @ ( option @ fml )
% 0.27/0.48 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ ua )
% 0.27/0.48 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.48 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ T2 ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 0.27/0.48 @ ( none @ fml ) )
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p ) )
% 0.27/0.48 @ ( uSubst95898992stappt @ sigma @ ua @ theta ) )
% 0.27/0.48 != ( none @ fml ) ) ).
% 0.27/0.48
% 0.27/0.48 % f1
% 0.27/0.48 thf(fact_23_f4,axiom,
% 0.27/0.48 ( ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
% 0.27/0.48 @ ^ [T2: trm] :
% 0.27/0.48 ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ T2 ) )
% 0.27/0.48 @ ^ [F2: fml] :
% 0.27/0.48 ( if @ ( option @ fml )
% 0.27/0.48 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ va )
% 0.27/0.48 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.48 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ T2 ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 0.27/0.48 @ ( none @ fml ) )
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ sigma
% 0.27/0.48 @ p ) )
% 0.27/0.48 @ ( uSubst95898992stappt @ sigma @ va @ theta ) )
% 0.27/0.48 != ( none @ fml ) ) ).
% 0.27/0.48
% 0.27/0.48 % f4
% 0.27/0.48 thf(fact_24_option_Ocollapse,axiom,
% 0.27/0.48 ! [A: $tType,Option: option @ A] :
% 0.27/0.48 ( ( Option
% 0.27/0.48 != ( none @ A ) )
% 0.27/0.48 => ( ( some @ A @ ( the @ A @ Option ) )
% 0.27/0.48 = Option ) ) ).
% 0.27/0.48
% 0.27/0.48 % option.collapse
% 0.27/0.48 thf(fact_25_not__Some__eq,axiom,
% 0.27/0.48 ! [A: $tType,X2: option @ A] :
% 0.27/0.48 ( ( ! [Y: A] :
% 0.27/0.48 ( X2
% 0.27/0.48 != ( some @ A @ Y ) ) )
% 0.27/0.48 = ( X2
% 0.27/0.48 = ( none @ A ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % not_Some_eq
% 0.27/0.48 thf(fact_26_not__None__eq,axiom,
% 0.27/0.48 ! [A: $tType,X2: option @ A] :
% 0.27/0.48 ( ( X2
% 0.27/0.48 != ( none @ A ) )
% 0.27/0.48 = ( ? [Y: A] :
% 0.27/0.48 ( X2
% 0.27/0.48 = ( some @ A @ Y ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % not_None_eq
% 0.27/0.48 thf(fact_27_usubstappf_Osimps_I1_J,axiom,
% 0.27/0.48 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,P3: char,Theta: trm] :
% 0.27/0.48 ( ( uSubst95898978stappf @ Sigma @ U @ ( pred @ P3 @ Theta ) )
% 0.27/0.48 = ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
% 0.27/0.48 @ ^ [Sigma_theta: trm] :
% 0.27/0.48 ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ P3 @ Sigma_theta ) )
% 0.27/0.48 @ ^ [R: fml] :
% 0.27/0.48 ( if @ ( option @ fml )
% 0.27/0.48 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R ) @ U )
% 0.27/0.48 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.48 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ Sigma_theta ) @ ( bot_bot @ ( set @ variable ) ) @ R )
% 0.27/0.48 @ ( none @ fml ) )
% 0.27/0.48 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ Sigma
% 0.27/0.48 @ P3 ) )
% 0.27/0.48 @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % usubstappf.simps(1)
% 0.27/0.48 thf(fact_28_inf__bot__left,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( bounded_lattice_bot @ A )
% 0.27/0.48 => ! [X2: A] :
% 0.27/0.48 ( ( inf_inf @ A @ ( bot_bot @ A ) @ X2 )
% 0.27/0.48 = ( bot_bot @ A ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf_bot_left
% 0.27/0.48 thf(fact_29_inf__bot__right,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( bounded_lattice_bot @ A )
% 0.27/0.48 => ! [X2: A] :
% 0.27/0.48 ( ( inf_inf @ A @ X2 @ ( bot_bot @ A ) )
% 0.27/0.48 = ( bot_bot @ A ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf_bot_right
% 0.27/0.48 thf(fact_30_option_Osplit__sel__asm,axiom,
% 0.27/0.48 ! [B: $tType,A: $tType,P2: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 0.27/0.48 ( ( P2 @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 0.27/0.48 = ( ~ ( ( ( Option
% 0.27/0.48 = ( none @ A ) )
% 0.27/0.48 & ~ ( P2 @ F1 ) )
% 0.27/0.48 | ( ( Option
% 0.27/0.48 = ( some @ A @ ( the @ A @ Option ) ) )
% 0.27/0.48 & ~ ( P2 @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % option.split_sel_asm
% 0.27/0.48 thf(fact_31_f2,axiom,
% 0.27/0.48 ! [Z: option @ fml,F: trm > ( option @ fml ),Za: option @ trm] :
% 0.27/0.48 ( ( ( Za
% 0.27/0.48 = ( none @ trm ) )
% 0.27/0.48 => ( ( case_option @ ( option @ fml ) @ trm @ Z @ F @ Za )
% 0.27/0.48 = Z ) )
% 0.27/0.48 & ( ( Za
% 0.27/0.48 != ( none @ trm ) )
% 0.27/0.48 => ( ( case_option @ ( option @ fml ) @ trm @ Z @ F @ Za )
% 0.27/0.48 = ( F @ ( the @ trm @ Za ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % f2
% 0.27/0.48 thf(fact_32_inf__right__idem,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( semilattice_inf @ A )
% 0.27/0.48 => ! [X2: A,Y2: A] :
% 0.27/0.48 ( ( inf_inf @ A @ ( inf_inf @ A @ X2 @ Y2 ) @ Y2 )
% 0.27/0.48 = ( inf_inf @ A @ X2 @ Y2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf_right_idem
% 0.27/0.48 thf(fact_33_inf_Oright__idem,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( semilattice_inf @ A )
% 0.27/0.48 => ! [A2: A,B2: A] :
% 0.27/0.48 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 )
% 0.27/0.48 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf.right_idem
% 0.27/0.48 thf(fact_34_inf__left__idem,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( semilattice_inf @ A )
% 0.27/0.48 => ! [X2: A,Y2: A] :
% 0.27/0.48 ( ( inf_inf @ A @ X2 @ ( inf_inf @ A @ X2 @ Y2 ) )
% 0.27/0.48 = ( inf_inf @ A @ X2 @ Y2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf_left_idem
% 0.27/0.48 thf(fact_35_inf_Oleft__idem,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( semilattice_inf @ A )
% 0.27/0.48 => ! [A2: A,B2: A] :
% 0.27/0.48 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B2 ) )
% 0.27/0.48 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf.left_idem
% 0.27/0.48 thf(fact_36_inf__idem,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( semilattice_inf @ A )
% 0.27/0.48 => ! [X2: A] :
% 0.27/0.48 ( ( inf_inf @ A @ X2 @ X2 )
% 0.27/0.48 = X2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf_idem
% 0.27/0.48 thf(fact_37_inf_Oidem,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( semilattice_inf @ A )
% 0.27/0.48 => ! [A2: A] :
% 0.27/0.48 ( ( inf_inf @ A @ A2 @ A2 )
% 0.27/0.48 = A2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf.idem
% 0.27/0.48 thf(fact_38_inf__apply,axiom,
% 0.27/0.48 ! [B: $tType,A: $tType] :
% 0.27/0.48 ( ( semilattice_inf @ B )
% 0.27/0.48 => ( ( inf_inf @ ( A > B ) )
% 0.27/0.48 = ( ^ [F2: A > B,G: A > B,X: A] : ( inf_inf @ B @ ( F2 @ X ) @ ( G @ X ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf_apply
% 0.27/0.48 thf(fact_39_option_Oinject,axiom,
% 0.27/0.48 ! [A: $tType,X23: A,Y22: A] :
% 0.27/0.48 ( ( ( some @ A @ X23 )
% 0.27/0.48 = ( some @ A @ Y22 ) )
% 0.27/0.48 = ( X23 = Y22 ) ) ).
% 0.27/0.48
% 0.27/0.48 % option.inject
% 0.27/0.48 thf(fact_40_usubstappf__pred,axiom,
% 0.27/0.48 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),P3: char,R2: fml,U: set @ variable,Theta: trm,Sigma_theta2: trm] :
% 0.27/0.48 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.48 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.48 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.48 @ Sigma
% 0.27/0.48 @ P3 )
% 0.27/0.48 = ( some @ fml @ R2 ) )
% 0.27/0.48 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R2 ) @ U )
% 0.27/0.48 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.48 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.27/0.48 = ( some @ trm @ Sigma_theta2 ) )
% 0.27/0.48 => ( ( uSubst95898978stappf @ Sigma @ U @ ( pred @ P3 @ Theta ) )
% 0.27/0.48 = ( uSubst95898978stappf @ ( uSubst969145931substt @ Sigma_theta2 ) @ ( bot_bot @ ( set @ variable ) ) @ R2 ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % usubstappf_pred
% 0.27/0.48 thf(fact_41_Diamondo_Oinduct,axiom,
% 0.27/0.48 ! [P2: ( option @ game ) > ( option @ fml ) > $o,A0: option @ game,A1: option @ fml] :
% 0.27/0.48 ( ! [Alpha: game,Phi: fml] : ( P2 @ ( some @ game @ Alpha ) @ ( some @ fml @ Phi ) )
% 0.27/0.48 => ( ! [X_1: option @ fml] : ( P2 @ ( none @ game ) @ X_1 )
% 0.27/0.48 => ( ! [V: game] : ( P2 @ ( some @ game @ V ) @ ( none @ fml ) )
% 0.27/0.48 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Diamondo.induct
% 0.27/0.48 thf(fact_42_option_Odisc__eq__case_I2_J,axiom,
% 0.27/0.48 ! [A: $tType,Option: option @ A] :
% 0.27/0.48 ( ( Option
% 0.27/0.48 != ( none @ A ) )
% 0.27/0.48 = ( case_option @ $o @ A @ $false
% 0.27/0.48 @ ^ [Uu: A] : $true
% 0.27/0.48 @ Option ) ) ).
% 0.27/0.48
% 0.27/0.48 % option.disc_eq_case(2)
% 0.27/0.48 thf(fact_43_option_Odisc__eq__case_I1_J,axiom,
% 0.27/0.48 ! [A: $tType,Option: option @ A] :
% 0.27/0.48 ( ( Option
% 0.27/0.48 = ( none @ A ) )
% 0.27/0.48 = ( case_option @ $o @ A @ $true
% 0.27/0.48 @ ^ [Uu: A] : $false
% 0.27/0.48 @ Option ) ) ).
% 0.27/0.48
% 0.27/0.48 % option.disc_eq_case(1)
% 0.27/0.48 thf(fact_44_usubstappt__det,axiom,
% 0.27/0.48 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,V2: set @ variable] :
% 0.27/0.48 ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.27/0.48 != ( none @ trm ) )
% 0.27/0.48 => ( ( ( uSubst95898992stappt @ Sigma @ V2 @ Theta )
% 0.27/0.48 != ( none @ trm ) )
% 0.27/0.48 => ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.27/0.48 = ( uSubst95898992stappt @ Sigma @ V2 @ Theta ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % usubstappt_det
% 0.27/0.48 thf(fact_45_mem__Collect__eq,axiom,
% 0.27/0.48 ! [A: $tType,A2: A,P2: A > $o] :
% 0.27/0.48 ( ( member @ A @ A2 @ ( collect @ A @ P2 ) )
% 0.27/0.48 = ( P2 @ A2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % mem_Collect_eq
% 0.27/0.48 thf(fact_46_Collect__mem__eq,axiom,
% 0.27/0.48 ! [A: $tType,A3: set @ A] :
% 0.27/0.48 ( ( collect @ A
% 0.27/0.48 @ ^ [X: A] : ( member @ A @ X @ A3 ) )
% 0.27/0.48 = A3 ) ).
% 0.27/0.48
% 0.27/0.48 % Collect_mem_eq
% 0.27/0.48 thf(fact_47_Collect__cong,axiom,
% 0.27/0.48 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.27/0.48 ( ! [X3: A] :
% 0.27/0.48 ( ( P2 @ X3 )
% 0.27/0.48 = ( Q @ X3 ) )
% 0.27/0.48 => ( ( collect @ A @ P2 )
% 0.27/0.48 = ( collect @ A @ Q ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Collect_cong
% 0.27/0.48 thf(fact_48_ext,axiom,
% 0.27/0.48 ! [B: $tType,A: $tType,F3: A > B,G2: A > B] :
% 0.27/0.48 ( ! [X3: A] :
% 0.27/0.48 ( ( F3 @ X3 )
% 0.27/0.48 = ( G2 @ X3 ) )
% 0.27/0.48 => ( F3 = G2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % ext
% 0.27/0.48 thf(fact_49_case__optionE,axiom,
% 0.27/0.48 ! [A: $tType,P2: $o,Q: A > $o,X2: option @ A] :
% 0.27/0.48 ( ( case_option @ $o @ A @ P2 @ Q @ X2 )
% 0.27/0.48 => ( ( ( X2
% 0.27/0.48 = ( none @ A ) )
% 0.27/0.48 => ~ P2 )
% 0.27/0.48 => ~ ! [Y3: A] :
% 0.27/0.48 ( ( X2
% 0.27/0.48 = ( some @ A @ Y3 ) )
% 0.27/0.48 => ~ ( Q @ Y3 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % case_optionE
% 0.27/0.48 thf(fact_50_inf__left__commute,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( semilattice_inf @ A )
% 0.27/0.48 => ! [X2: A,Y2: A,Z2: A] :
% 0.27/0.48 ( ( inf_inf @ A @ X2 @ ( inf_inf @ A @ Y2 @ Z2 ) )
% 0.27/0.48 = ( inf_inf @ A @ Y2 @ ( inf_inf @ A @ X2 @ Z2 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf_left_commute
% 0.27/0.48 thf(fact_51_inf_Oleft__commute,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( semilattice_inf @ A )
% 0.27/0.48 => ! [B2: A,A2: A,C2: A] :
% 0.27/0.48 ( ( inf_inf @ A @ B2 @ ( inf_inf @ A @ A2 @ C2 ) )
% 0.27/0.48 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf.left_commute
% 0.27/0.48 thf(fact_52_inf__commute,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( semilattice_inf @ A )
% 0.27/0.48 => ( ( inf_inf @ A )
% 0.27/0.48 = ( ^ [X: A,Y: A] : ( inf_inf @ A @ Y @ X ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf_commute
% 0.27/0.48 thf(fact_53_inf_Ocommute,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( semilattice_inf @ A )
% 0.27/0.48 => ( ( inf_inf @ A )
% 0.27/0.48 = ( ^ [A4: A,B3: A] : ( inf_inf @ A @ B3 @ A4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf.commute
% 0.27/0.48 thf(fact_54_inf__assoc,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( semilattice_inf @ A )
% 0.27/0.48 => ! [X2: A,Y2: A,Z2: A] :
% 0.27/0.48 ( ( inf_inf @ A @ ( inf_inf @ A @ X2 @ Y2 ) @ Z2 )
% 0.27/0.48 = ( inf_inf @ A @ X2 @ ( inf_inf @ A @ Y2 @ Z2 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf_assoc
% 0.27/0.48 thf(fact_55_inf_Oassoc,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( semilattice_inf @ A )
% 0.27/0.48 => ! [A2: A,B2: A,C2: A] :
% 0.27/0.48 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C2 )
% 0.27/0.48 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf.assoc
% 0.27/0.48 thf(fact_56_boolean__algebra__cancel_Oinf2,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( semilattice_inf @ A )
% 0.27/0.48 => ! [B4: A,K: A,B2: A,A2: A] :
% 0.27/0.48 ( ( B4
% 0.27/0.48 = ( inf_inf @ A @ K @ B2 ) )
% 0.27/0.48 => ( ( inf_inf @ A @ A2 @ B4 )
% 0.27/0.48 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % boolean_algebra_cancel.inf2
% 0.27/0.48 thf(fact_57_boolean__algebra__cancel_Oinf1,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( semilattice_inf @ A )
% 0.27/0.48 => ! [A3: A,K: A,A2: A,B2: A] :
% 0.27/0.48 ( ( A3
% 0.27/0.48 = ( inf_inf @ A @ K @ A2 ) )
% 0.27/0.48 => ( ( inf_inf @ A @ A3 @ B2 )
% 0.27/0.48 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % boolean_algebra_cancel.inf1
% 0.27/0.48 thf(fact_58_inf__fun__def,axiom,
% 0.27/0.48 ! [B: $tType,A: $tType] :
% 0.27/0.48 ( ( semilattice_inf @ B )
% 0.27/0.48 => ( ( inf_inf @ ( A > B ) )
% 0.27/0.48 = ( ^ [F2: A > B,G: A > B,X: A] : ( inf_inf @ B @ ( F2 @ X ) @ ( G @ X ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf_fun_def
% 0.27/0.48 thf(fact_59_inf__sup__aci_I1_J,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( lattice @ A )
% 0.27/0.48 => ( ( inf_inf @ A )
% 0.27/0.48 = ( ^ [X: A,Y: A] : ( inf_inf @ A @ Y @ X ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf_sup_aci(1)
% 0.27/0.48 thf(fact_60_inf__sup__aci_I2_J,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( lattice @ A )
% 0.27/0.48 => ! [X2: A,Y2: A,Z2: A] :
% 0.27/0.48 ( ( inf_inf @ A @ ( inf_inf @ A @ X2 @ Y2 ) @ Z2 )
% 0.27/0.48 = ( inf_inf @ A @ X2 @ ( inf_inf @ A @ Y2 @ Z2 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf_sup_aci(2)
% 0.27/0.48 thf(fact_61_inf__sup__aci_I3_J,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( lattice @ A )
% 0.27/0.48 => ! [X2: A,Y2: A,Z2: A] :
% 0.27/0.48 ( ( inf_inf @ A @ X2 @ ( inf_inf @ A @ Y2 @ Z2 ) )
% 0.27/0.48 = ( inf_inf @ A @ Y2 @ ( inf_inf @ A @ X2 @ Z2 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf_sup_aci(3)
% 0.27/0.48 thf(fact_62_inf__sup__aci_I4_J,axiom,
% 0.27/0.48 ! [A: $tType] :
% 0.27/0.48 ( ( lattice @ A )
% 0.27/0.48 => ! [X2: A,Y2: A] :
% 0.27/0.48 ( ( inf_inf @ A @ X2 @ ( inf_inf @ A @ X2 @ Y2 ) )
% 0.27/0.48 = ( inf_inf @ A @ X2 @ Y2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % inf_sup_aci(4)
% 0.27/0.48 thf(fact_63_option_Ocase__distrib,axiom,
% 0.27/0.48 ! [C: $tType,B: $tType,A: $tType,H: B > C,F1: B,F22: A > B,Option: option @ A] :
% 0.27/0.48 ( ( H @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 0.27/0.48 = ( case_option @ C @ A @ ( H @ F1 )
% 0.27/0.49 @ ^ [X: A] : ( H @ ( F22 @ X ) )
% 0.27/0.49 @ Option ) ) ).
% 0.27/0.49
% 0.27/0.49 % option.case_distrib
% 0.27/0.49 thf(fact_64_option_Odistinct_I1_J,axiom,
% 0.27/0.49 ! [A: $tType,X23: A] :
% 0.27/0.49 ( ( none @ A )
% 0.27/0.49 != ( some @ A @ X23 ) ) ).
% 0.27/0.49
% 0.27/0.49 % option.distinct(1)
% 0.27/0.49 thf(fact_65_option_OdiscI,axiom,
% 0.27/0.49 ! [A: $tType,Option: option @ A,X23: A] :
% 0.27/0.49 ( ( Option
% 0.27/0.49 = ( some @ A @ X23 ) )
% 0.27/0.49 => ( Option
% 0.27/0.49 != ( none @ A ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % option.discI
% 0.27/0.49 thf(fact_66_option_Oexhaust,axiom,
% 0.27/0.49 ! [A: $tType,Y2: option @ A] :
% 0.27/0.49 ( ( Y2
% 0.27/0.49 != ( none @ A ) )
% 0.27/0.49 => ~ ! [X24: A] :
% 0.27/0.49 ( Y2
% 0.27/0.49 != ( some @ A @ X24 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % option.exhaust
% 0.27/0.49 thf(fact_67_option_Oinducts,axiom,
% 0.27/0.49 ! [A: $tType,P2: ( option @ A ) > $o,Option: option @ A] :
% 0.27/0.49 ( ( P2 @ ( none @ A ) )
% 0.27/0.49 => ( ! [X3: A] : ( P2 @ ( some @ A @ X3 ) )
% 0.27/0.49 => ( P2 @ Option ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % option.inducts
% 0.27/0.49 thf(fact_68_split__option__ex,axiom,
% 0.27/0.49 ! [A: $tType] :
% 0.27/0.49 ( ( ^ [P4: ( option @ A ) > $o] :
% 0.27/0.49 ? [X4: option @ A] : ( P4 @ X4 ) )
% 0.27/0.49 = ( ^ [P: ( option @ A ) > $o] :
% 0.27/0.49 ( ( P @ ( none @ A ) )
% 0.27/0.49 | ? [X: A] : ( P @ ( some @ A @ X ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % split_option_ex
% 0.27/0.49 thf(fact_69_split__option__all,axiom,
% 0.27/0.49 ! [A: $tType] :
% 0.27/0.49 ( ( ^ [P4: ( option @ A ) > $o] :
% 0.27/0.49 ! [X4: option @ A] : ( P4 @ X4 ) )
% 0.27/0.49 = ( ^ [P: ( option @ A ) > $o] :
% 0.27/0.49 ( ( P @ ( none @ A ) )
% 0.27/0.49 & ! [X: A] : ( P @ ( some @ A @ X ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % split_option_all
% 0.27/0.49 thf(fact_70_combine__options__cases,axiom,
% 0.27/0.49 ! [A: $tType,B: $tType,X2: option @ A,P2: ( option @ A ) > ( option @ B ) > $o,Y2: option @ B] :
% 0.27/0.49 ( ( ( X2
% 0.27/0.49 = ( none @ A ) )
% 0.27/0.49 => ( P2 @ X2 @ Y2 ) )
% 0.27/0.49 => ( ( ( Y2
% 0.27/0.49 = ( none @ B ) )
% 0.27/0.49 => ( P2 @ X2 @ Y2 ) )
% 0.27/0.49 => ( ! [A5: A,B5: B] :
% 0.27/0.49 ( ( X2
% 0.27/0.49 = ( some @ A @ A5 ) )
% 0.27/0.49 => ( ( Y2
% 0.27/0.49 = ( some @ B @ B5 ) )
% 0.27/0.49 => ( P2 @ X2 @ Y2 ) ) )
% 0.27/0.49 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % combine_options_cases
% 0.27/0.49 thf(fact_71_option_Osimps_I4_J,axiom,
% 0.27/0.49 ! [A: $tType,B: $tType,F1: B,F22: A > B] :
% 0.27/0.49 ( ( case_option @ B @ A @ F1 @ F22 @ ( none @ A ) )
% 0.27/0.49 = F1 ) ).
% 0.27/0.49
% 0.27/0.49 % option.simps(4)
% 0.27/0.49 thf(fact_72_option_Oexpand,axiom,
% 0.27/0.49 ! [A: $tType,Option: option @ A,Option2: option @ A] :
% 0.27/0.49 ( ( ( Option
% 0.27/0.49 = ( none @ A ) )
% 0.27/0.49 = ( Option2
% 0.27/0.49 = ( none @ A ) ) )
% 0.27/0.49 => ( ( ( Option
% 0.27/0.49 != ( none @ A ) )
% 0.27/0.49 => ( ( Option2
% 0.27/0.49 != ( none @ A ) )
% 0.27/0.49 => ( ( the @ A @ Option )
% 0.27/0.49 = ( the @ A @ Option2 ) ) ) )
% 0.27/0.49 => ( Option = Option2 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % option.expand
% 0.27/0.49 thf(fact_73_option_Osimps_I5_J,axiom,
% 0.27/0.49 ! [B: $tType,A: $tType,F1: B,F22: A > B,X23: A] :
% 0.27/0.49 ( ( case_option @ B @ A @ F1 @ F22 @ ( some @ A @ X23 ) )
% 0.27/0.49 = ( F22 @ X23 ) ) ).
% 0.27/0.49
% 0.27/0.49 % option.simps(5)
% 0.27/0.49 thf(fact_74_option_Osel,axiom,
% 0.27/0.49 ! [A: $tType,X23: A] :
% 0.27/0.49 ( ( the @ A @ ( some @ A @ X23 ) )
% 0.27/0.49 = X23 ) ).
% 0.27/0.49
% 0.27/0.49 % option.sel
% 0.27/0.49 thf(fact_75_option_Oexhaust__sel,axiom,
% 0.27/0.49 ! [A: $tType,Option: option @ A] :
% 0.27/0.49 ( ( Option
% 0.27/0.49 != ( none @ A ) )
% 0.27/0.49 => ( Option
% 0.27/0.49 = ( some @ A @ ( the @ A @ Option ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % option.exhaust_sel
% 0.27/0.49 thf(fact_76_option_Ocase__eq__if,axiom,
% 0.27/0.49 ! [A: $tType,B: $tType] :
% 0.27/0.49 ( ( case_option @ B @ A )
% 0.27/0.49 = ( ^ [F12: B,F23: A > B,Option3: option @ A] :
% 0.27/0.49 ( if @ B
% 0.27/0.49 @ ( Option3
% 0.27/0.49 = ( none @ A ) )
% 0.27/0.49 @ F12
% 0.27/0.49 @ ( F23 @ ( the @ A @ Option3 ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % option.case_eq_if
% 0.27/0.49 thf(fact_77_usubstappf__pred__conv,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,P3: char,Theta: trm] :
% 0.27/0.49 ( ( ( uSubst95898978stappf @ Sigma @ U @ ( pred @ P3 @ Theta ) )
% 0.27/0.49 != ( none @ fml ) )
% 0.27/0.49 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.27/0.49 != ( none @ trm ) )
% 0.27/0.49 & ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.49 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.49 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.49 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.49 @ Sigma
% 0.27/0.49 @ P3 )
% 0.27/0.49 = ( none @ fml ) )
% 0.27/0.49 | ? [R3: fml] :
% 0.27/0.49 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.49 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.49 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.49 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.49 @ Sigma
% 0.27/0.49 @ P3 )
% 0.27/0.49 = ( some @ fml @ R3 ) )
% 0.27/0.49 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R3 ) @ U )
% 0.27/0.49 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappf_pred_conv
% 0.27/0.49 thf(fact_78_option_Osplit__sel,axiom,
% 0.27/0.49 ! [B: $tType,A: $tType,P2: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 0.27/0.49 ( ( P2 @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 0.27/0.49 = ( ( ( Option
% 0.27/0.49 = ( none @ A ) )
% 0.27/0.49 => ( P2 @ F1 ) )
% 0.27/0.49 & ( ( Option
% 0.27/0.49 = ( some @ A @ ( the @ A @ Option ) ) )
% 0.27/0.49 => ( P2 @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % option.split_sel
% 0.27/0.49 thf(fact_79_fml_Oinject_I1_J,axiom,
% 0.27/0.49 ! [X11: char,X12: trm,Y11: char,Y12: trm] :
% 0.27/0.49 ( ( ( pred @ X11 @ X12 )
% 0.27/0.49 = ( pred @ Y11 @ Y12 ) )
% 0.27/0.49 = ( ( X11 = Y11 )
% 0.27/0.49 & ( X12 = Y12 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % fml.inject(1)
% 0.27/0.49 thf(fact_80_Int__iff,axiom,
% 0.27/0.49 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 0.27/0.49 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.27/0.49 = ( ( member @ A @ C2 @ A3 )
% 0.27/0.49 & ( member @ A @ C2 @ B4 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Int_iff
% 0.27/0.49 thf(fact_81_IntI,axiom,
% 0.27/0.49 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 0.27/0.49 ( ( member @ A @ C2 @ A3 )
% 0.27/0.49 => ( ( member @ A @ C2 @ B4 )
% 0.27/0.49 => ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % IntI
% 0.27/0.49 thf(fact_82_empty__Collect__eq,axiom,
% 0.27/0.49 ! [A: $tType,P2: A > $o] :
% 0.27/0.49 ( ( ( bot_bot @ ( set @ A ) )
% 0.27/0.49 = ( collect @ A @ P2 ) )
% 0.27/0.49 = ( ! [X: A] :
% 0.27/0.49 ~ ( P2 @ X ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % empty_Collect_eq
% 0.27/0.49 thf(fact_83_Collect__empty__eq,axiom,
% 0.27/0.49 ! [A: $tType,P2: A > $o] :
% 0.27/0.49 ( ( ( collect @ A @ P2 )
% 0.27/0.49 = ( bot_bot @ ( set @ A ) ) )
% 0.27/0.49 = ( ! [X: A] :
% 0.27/0.49 ~ ( P2 @ X ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Collect_empty_eq
% 0.27/0.49 thf(fact_84_all__not__in__conv,axiom,
% 0.27/0.49 ! [A: $tType,A3: set @ A] :
% 0.27/0.49 ( ( ! [X: A] :
% 0.27/0.49 ~ ( member @ A @ X @ A3 ) )
% 0.27/0.49 = ( A3
% 0.27/0.49 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % all_not_in_conv
% 0.27/0.49 thf(fact_85_empty__iff,axiom,
% 0.27/0.49 ! [A: $tType,C2: A] :
% 0.27/0.49 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % empty_iff
% 0.27/0.49 thf(fact_86_bot__apply,axiom,
% 0.27/0.49 ! [C: $tType,D: $tType] :
% 0.27/0.49 ( ( bot @ C )
% 0.27/0.49 => ( ( bot_bot @ ( D > C ) )
% 0.27/0.49 = ( ^ [X: D] : ( bot_bot @ C ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % bot_apply
% 0.27/0.49 thf(fact_87_disjoint__iff__not__equal,axiom,
% 0.27/0.49 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.27/0.49 ( ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 0.27/0.49 = ( bot_bot @ ( set @ A ) ) )
% 0.27/0.49 = ( ! [X: A] :
% 0.27/0.49 ( ( member @ A @ X @ A3 )
% 0.27/0.49 => ! [Y: A] :
% 0.27/0.49 ( ( member @ A @ Y @ B4 )
% 0.27/0.49 => ( X != Y ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % disjoint_iff_not_equal
% 0.27/0.49 thf(fact_88_Aterm__Some,axiom,
% 0.27/0.49 ( ( some @ trm )
% 0.27/0.49 = ( some @ trm ) ) ).
% 0.27/0.49
% 0.27/0.49 % Aterm_Some
% 0.27/0.49 thf(fact_89_Loopo_Ocases,axiom,
% 0.27/0.49 ! [X2: option @ game] :
% 0.27/0.49 ( ! [Alpha: game] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( some @ game @ Alpha ) )
% 0.27/0.49 => ( X2
% 0.27/0.49 = ( none @ game ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Loopo.cases
% 0.27/0.49 thf(fact_90_ODEo_Oinduct,axiom,
% 0.27/0.49 ! [P2: char > ( option @ trm ) > $o,A0: char,A1: option @ trm] :
% 0.27/0.49 ( ! [X3: char,Theta2: trm] : ( P2 @ X3 @ ( some @ trm @ Theta2 ) )
% 0.27/0.49 => ( ! [X3: char] : ( P2 @ X3 @ ( none @ trm ) )
% 0.27/0.49 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % ODEo.induct
% 0.27/0.49 thf(fact_91_Loopo_Oinduct,axiom,
% 0.27/0.49 ! [P2: ( option @ game ) > $o,A0: option @ game] :
% 0.27/0.49 ( ! [Alpha: game] : ( P2 @ ( some @ game @ Alpha ) )
% 0.27/0.49 => ( ( P2 @ ( none @ game ) )
% 0.27/0.49 => ( P2 @ A0 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Loopo.induct
% 0.27/0.49 thf(fact_92_undefg__equiv,axiom,
% 0.27/0.49 ! [Alpha2: option @ game] :
% 0.27/0.49 ( ( Alpha2
% 0.27/0.49 != ( none @ game ) )
% 0.27/0.49 = ( ? [G: game] :
% 0.27/0.49 ( Alpha2
% 0.27/0.49 = ( some @ game @ G ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % undefg_equiv
% 0.27/0.49 thf(fact_93_undeft__equiv,axiom,
% 0.27/0.49 ! [Theta: option @ trm] :
% 0.27/0.49 ( ( Theta
% 0.27/0.49 != ( none @ trm ) )
% 0.27/0.49 = ( ? [T2: trm] :
% 0.27/0.49 ( Theta
% 0.27/0.49 = ( some @ trm @ T2 ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % undeft_equiv
% 0.27/0.49 thf(fact_94_Timeso_Oinduct,axiom,
% 0.27/0.49 ! [P2: ( option @ trm ) > ( option @ trm ) > $o,A0: option @ trm,A1: option @ trm] :
% 0.27/0.49 ( ! [Theta2: trm,Eta: trm] : ( P2 @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta ) )
% 0.27/0.49 => ( ! [X_1: option @ trm] : ( P2 @ ( none @ trm ) @ X_1 )
% 0.27/0.49 => ( ! [V: trm] : ( P2 @ ( some @ trm @ V ) @ ( none @ trm ) )
% 0.27/0.49 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Timeso.induct
% 0.27/0.49 thf(fact_95_Assigno_Oinduct,axiom,
% 0.27/0.49 ! [P2: variable > ( option @ trm ) > $o,A0: variable,A1: option @ trm] :
% 0.27/0.49 ( ! [X3: variable,Theta2: trm] : ( P2 @ X3 @ ( some @ trm @ Theta2 ) )
% 0.27/0.49 => ( ! [X3: variable] : ( P2 @ X3 @ ( none @ trm ) )
% 0.27/0.49 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Assigno.induct
% 0.27/0.49 thf(fact_96_Composeo_Oinduct,axiom,
% 0.27/0.49 ! [P2: ( option @ game ) > ( option @ game ) > $o,A0: option @ game,A1: option @ game] :
% 0.27/0.49 ( ! [Alpha: game,Beta: game] : ( P2 @ ( some @ game @ Alpha ) @ ( some @ game @ Beta ) )
% 0.27/0.49 => ( ! [Alpha: option @ game] : ( P2 @ Alpha @ ( none @ game ) )
% 0.27/0.49 => ( ! [V: game] : ( P2 @ ( none @ game ) @ ( some @ game @ V ) )
% 0.27/0.49 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Composeo.induct
% 0.27/0.49 thf(fact_97_Differentialo_Ocases,axiom,
% 0.27/0.49 ! [X2: option @ trm] :
% 0.27/0.49 ( ! [Theta2: trm] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( some @ trm @ Theta2 ) )
% 0.27/0.49 => ( X2
% 0.27/0.49 = ( none @ trm ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Differentialo.cases
% 0.27/0.49 thf(fact_98_Differentialo_Oinduct,axiom,
% 0.27/0.49 ! [P2: ( option @ trm ) > $o,A0: option @ trm] :
% 0.27/0.49 ( ! [Theta2: trm] : ( P2 @ ( some @ trm @ Theta2 ) )
% 0.27/0.49 => ( ( P2 @ ( none @ trm ) )
% 0.27/0.49 => ( P2 @ A0 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Differentialo.induct
% 0.27/0.49 thf(fact_99_undeft__None,axiom,
% 0.27/0.49 ( ( none @ trm )
% 0.27/0.49 = ( none @ trm ) ) ).
% 0.27/0.49
% 0.27/0.49 % undeft_None
% 0.27/0.49 thf(fact_100_bot__fun__def,axiom,
% 0.27/0.49 ! [B: $tType,A: $tType] :
% 0.27/0.49 ( ( bot @ B )
% 0.27/0.49 => ( ( bot_bot @ ( A > B ) )
% 0.27/0.49 = ( ^ [X: A] : ( bot_bot @ B ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % bot_fun_def
% 0.27/0.49 thf(fact_101_emptyE,axiom,
% 0.27/0.49 ! [A: $tType,A2: A] :
% 0.27/0.49 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % emptyE
% 0.27/0.49 thf(fact_102_equals0D,axiom,
% 0.27/0.49 ! [A: $tType,A3: set @ A,A2: A] :
% 0.27/0.49 ( ( A3
% 0.27/0.49 = ( bot_bot @ ( set @ A ) ) )
% 0.27/0.49 => ~ ( member @ A @ A2 @ A3 ) ) ).
% 0.27/0.49
% 0.27/0.49 % equals0D
% 0.27/0.49 thf(fact_103_equals0I,axiom,
% 0.27/0.49 ! [A: $tType,A3: set @ A] :
% 0.27/0.49 ( ! [Y3: A] :
% 0.27/0.49 ~ ( member @ A @ Y3 @ A3 )
% 0.27/0.49 => ( A3
% 0.27/0.49 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % equals0I
% 0.27/0.49 thf(fact_104_ex__in__conv,axiom,
% 0.27/0.49 ! [A: $tType,A3: set @ A] :
% 0.27/0.49 ( ( ? [X: A] : ( member @ A @ X @ A3 ) )
% 0.27/0.49 = ( A3
% 0.27/0.49 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % ex_in_conv
% 0.27/0.49 thf(fact_105_bot__set__def,axiom,
% 0.27/0.49 ! [A: $tType] :
% 0.27/0.49 ( ( bot_bot @ ( set @ A ) )
% 0.27/0.49 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % bot_set_def
% 0.27/0.49 thf(fact_106_IntE,axiom,
% 0.27/0.49 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 0.27/0.49 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.27/0.49 => ~ ( ( member @ A @ C2 @ A3 )
% 0.27/0.49 => ~ ( member @ A @ C2 @ B4 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % IntE
% 0.27/0.49 thf(fact_107_IntD1,axiom,
% 0.27/0.49 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 0.27/0.49 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.27/0.49 => ( member @ A @ C2 @ A3 ) ) ).
% 0.27/0.49
% 0.27/0.49 % IntD1
% 0.27/0.49 thf(fact_108_IntD2,axiom,
% 0.27/0.49 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 0.27/0.49 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.27/0.49 => ( member @ A @ C2 @ B4 ) ) ).
% 0.27/0.49
% 0.27/0.49 % IntD2
% 0.27/0.49 thf(fact_109_Int__assoc,axiom,
% 0.27/0.49 ! [A: $tType,A3: set @ A,B4: set @ A,C3: set @ A] :
% 0.27/0.49 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) @ C3 )
% 0.27/0.49 = ( inf_inf @ ( set @ A ) @ A3 @ ( inf_inf @ ( set @ A ) @ B4 @ C3 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Int_assoc
% 0.27/0.49 thf(fact_110_Int__absorb,axiom,
% 0.27/0.49 ! [A: $tType,A3: set @ A] :
% 0.27/0.49 ( ( inf_inf @ ( set @ A ) @ A3 @ A3 )
% 0.27/0.49 = A3 ) ).
% 0.27/0.49
% 0.27/0.49 % Int_absorb
% 0.27/0.49 thf(fact_111_Int__commute,axiom,
% 0.27/0.49 ! [A: $tType] :
% 0.27/0.49 ( ( inf_inf @ ( set @ A ) )
% 0.27/0.49 = ( ^ [A6: set @ A,B6: set @ A] : ( inf_inf @ ( set @ A ) @ B6 @ A6 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Int_commute
% 0.27/0.49 thf(fact_112_Int__left__absorb,axiom,
% 0.27/0.49 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.27/0.49 ( ( inf_inf @ ( set @ A ) @ A3 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.27/0.49 = ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ).
% 0.27/0.49
% 0.27/0.49 % Int_left_absorb
% 0.27/0.49 thf(fact_113_Int__left__commute,axiom,
% 0.27/0.49 ! [A: $tType,A3: set @ A,B4: set @ A,C3: set @ A] :
% 0.27/0.49 ( ( inf_inf @ ( set @ A ) @ A3 @ ( inf_inf @ ( set @ A ) @ B4 @ C3 ) )
% 0.27/0.49 = ( inf_inf @ ( set @ A ) @ B4 @ ( inf_inf @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Int_left_commute
% 0.27/0.49 thf(fact_114_empty__def,axiom,
% 0.27/0.49 ! [A: $tType] :
% 0.27/0.49 ( ( bot_bot @ ( set @ A ) )
% 0.27/0.49 = ( collect @ A
% 0.27/0.49 @ ^ [X: A] : $false ) ) ).
% 0.27/0.49
% 0.27/0.49 % empty_def
% 0.27/0.49 thf(fact_115_Collect__conj__eq,axiom,
% 0.27/0.49 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.27/0.49 ( ( collect @ A
% 0.27/0.49 @ ^ [X: A] :
% 0.27/0.49 ( ( P2 @ X )
% 0.27/0.49 & ( Q @ X ) ) )
% 0.27/0.49 = ( inf_inf @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Collect_conj_eq
% 0.27/0.49 thf(fact_116_Int__Collect,axiom,
% 0.27/0.49 ! [A: $tType,X2: A,A3: set @ A,P2: A > $o] :
% 0.27/0.49 ( ( member @ A @ X2 @ ( inf_inf @ ( set @ A ) @ A3 @ ( collect @ A @ P2 ) ) )
% 0.27/0.49 = ( ( member @ A @ X2 @ A3 )
% 0.27/0.49 & ( P2 @ X2 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Int_Collect
% 0.27/0.49 thf(fact_117_Int__def,axiom,
% 0.27/0.49 ! [A: $tType] :
% 0.27/0.49 ( ( inf_inf @ ( set @ A ) )
% 0.27/0.49 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.27/0.49 ( collect @ A
% 0.27/0.49 @ ^ [X: A] :
% 0.27/0.49 ( ( member @ A @ X @ A6 )
% 0.27/0.49 & ( member @ A @ X @ B6 ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Int_def
% 0.27/0.49 thf(fact_118_inf__set__def,axiom,
% 0.27/0.49 ! [A: $tType] :
% 0.27/0.49 ( ( inf_inf @ ( set @ A ) )
% 0.27/0.49 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.27/0.49 ( collect @ A
% 0.27/0.49 @ ( inf_inf @ ( A > $o )
% 0.27/0.49 @ ^ [X: A] : ( member @ A @ X @ A6 )
% 0.27/0.49 @ ^ [X: A] : ( member @ A @ X @ B6 ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % inf_set_def
% 0.27/0.49 thf(fact_119_Int__emptyI,axiom,
% 0.27/0.49 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.27/0.49 ( ! [X3: A] :
% 0.27/0.49 ( ( member @ A @ X3 @ A3 )
% 0.27/0.49 => ~ ( member @ A @ X3 @ B4 ) )
% 0.27/0.49 => ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 0.27/0.49 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Int_emptyI
% 0.27/0.49 thf(fact_120_disjoint__iff,axiom,
% 0.27/0.49 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.27/0.49 ( ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 0.27/0.49 = ( bot_bot @ ( set @ A ) ) )
% 0.27/0.49 = ( ! [X: A] :
% 0.27/0.49 ( ( member @ A @ X @ A3 )
% 0.27/0.49 => ~ ( member @ A @ X @ B4 ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % disjoint_iff
% 0.27/0.49 thf(fact_121_Int__empty__left,axiom,
% 0.27/0.49 ! [A: $tType,B4: set @ A] :
% 0.27/0.49 ( ( inf_inf @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B4 )
% 0.27/0.49 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Int_empty_left
% 0.27/0.49 thf(fact_122_Int__empty__right,axiom,
% 0.27/0.49 ! [A: $tType,A3: set @ A] :
% 0.27/0.49 ( ( inf_inf @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.27/0.49 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Int_empty_right
% 0.27/0.49 thf(fact_123_disjE__realizer2,axiom,
% 0.27/0.49 ! [B: $tType,A: $tType,P2: $o,Q: A > $o,X2: option @ A,R4: B > $o,F3: B,G2: A > B] :
% 0.27/0.49 ( ( case_option @ $o @ A @ P2 @ Q @ X2 )
% 0.27/0.49 => ( ( P2
% 0.27/0.49 => ( R4 @ F3 ) )
% 0.27/0.49 => ( ! [Q2: A] :
% 0.27/0.49 ( ( Q @ Q2 )
% 0.27/0.49 => ( R4 @ ( G2 @ Q2 ) ) )
% 0.27/0.49 => ( R4 @ ( case_option @ B @ A @ F3 @ G2 @ X2 ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % disjE_realizer2
% 0.27/0.49 thf(fact_124_usubstappf__geqr,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,Eta2: trm] :
% 0.27/0.49 ( ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.27/0.49 != ( none @ fml ) )
% 0.27/0.49 => ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.27/0.49 = ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Eta2 ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappf_geqr
% 0.27/0.49 thf(fact_125_usubstappf__geq,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,Eta2: trm] :
% 0.27/0.49 ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.27/0.49 != ( none @ trm ) )
% 0.27/0.49 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Eta2 )
% 0.27/0.49 != ( none @ trm ) )
% 0.27/0.49 => ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.27/0.49 = ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Eta2 ) ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappf_geq
% 0.27/0.49 thf(fact_126_Geqo_Osimps_I3_J,axiom,
% 0.27/0.49 ! [V3: trm] :
% 0.27/0.49 ( ( uSubst1556497037e_Geqo @ ( some @ trm @ V3 ) @ ( none @ trm ) )
% 0.27/0.49 = ( none @ fml ) ) ).
% 0.27/0.49
% 0.27/0.49 % Geqo.simps(3)
% 0.27/0.49 thf(fact_127_Set_Ois__empty__def,axiom,
% 0.27/0.49 ! [A: $tType] :
% 0.27/0.49 ( ( is_empty @ A )
% 0.27/0.49 = ( ^ [A6: set @ A] :
% 0.27/0.49 ( A6
% 0.27/0.49 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Set.is_empty_def
% 0.27/0.49 thf(fact_128_usubstappf__geq__conv,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,Eta2: trm] :
% 0.27/0.49 ( ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.27/0.49 != ( none @ fml ) )
% 0.27/0.49 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.27/0.49 != ( none @ trm ) )
% 0.27/0.49 & ( ( uSubst95898992stappt @ Sigma @ U @ Eta2 )
% 0.27/0.49 != ( none @ trm ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappf_geq_conv
% 0.27/0.49 thf(fact_129_fml_Oinject_I2_J,axiom,
% 0.27/0.49 ! [X21: trm,X222: trm,Y21: trm,Y222: trm] :
% 0.27/0.49 ( ( ( geq @ X21 @ X222 )
% 0.27/0.49 = ( geq @ Y21 @ Y222 ) )
% 0.27/0.49 = ( ( X21 = Y21 )
% 0.27/0.49 & ( X222 = Y222 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % fml.inject(2)
% 0.27/0.49 thf(fact_130_inf1I,axiom,
% 0.27/0.49 ! [A: $tType,A3: A > $o,X2: A,B4: A > $o] :
% 0.27/0.49 ( ( A3 @ X2 )
% 0.27/0.49 => ( ( B4 @ X2 )
% 0.27/0.49 => ( inf_inf @ ( A > $o ) @ A3 @ B4 @ X2 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % inf1I
% 0.27/0.49 thf(fact_131_inf1E,axiom,
% 0.27/0.49 ! [A: $tType,A3: A > $o,B4: A > $o,X2: A] :
% 0.27/0.49 ( ( inf_inf @ ( A > $o ) @ A3 @ B4 @ X2 )
% 0.27/0.49 => ~ ( ( A3 @ X2 )
% 0.27/0.49 => ~ ( B4 @ X2 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % inf1E
% 0.27/0.49 thf(fact_132_inf1D1,axiom,
% 0.27/0.49 ! [A: $tType,A3: A > $o,B4: A > $o,X2: A] :
% 0.27/0.49 ( ( inf_inf @ ( A > $o ) @ A3 @ B4 @ X2 )
% 0.27/0.49 => ( A3 @ X2 ) ) ).
% 0.27/0.49
% 0.27/0.49 % inf1D1
% 0.27/0.49 thf(fact_133_inf1D2,axiom,
% 0.27/0.49 ! [A: $tType,A3: A > $o,B4: A > $o,X2: A] :
% 0.27/0.49 ( ( inf_inf @ ( A > $o ) @ A3 @ B4 @ X2 )
% 0.27/0.49 => ( B4 @ X2 ) ) ).
% 0.27/0.49
% 0.27/0.49 % inf1D2
% 0.27/0.49 thf(fact_134_fml_Odistinct_I1_J,axiom,
% 0.27/0.49 ! [X11: char,X12: trm,X21: trm,X222: trm] :
% 0.27/0.49 ( ( pred @ X11 @ X12 )
% 0.27/0.49 != ( geq @ X21 @ X222 ) ) ).
% 0.27/0.49
% 0.27/0.49 % fml.distinct(1)
% 0.27/0.49 thf(fact_135_usubstappf_Osimps_I2_J,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,Eta2: trm] :
% 0.27/0.49 ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.27/0.49 = ( uSubst1556497037e_Geqo @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) @ ( uSubst95898992stappt @ Sigma @ U @ Eta2 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappf.simps(2)
% 0.27/0.49 thf(fact_136_Geqo_Osimps_I1_J,axiom,
% 0.27/0.49 ! [Theta: trm,Eta2: trm] :
% 0.27/0.49 ( ( uSubst1556497037e_Geqo @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta2 ) )
% 0.27/0.49 = ( some @ fml @ ( geq @ Theta @ Eta2 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Geqo.simps(1)
% 0.27/0.49 thf(fact_137_Geqo_Oelims,axiom,
% 0.27/0.49 ! [X2: option @ trm,Xa: option @ trm,Y2: option @ fml] :
% 0.27/0.49 ( ( ( uSubst1556497037e_Geqo @ X2 @ Xa )
% 0.27/0.49 = Y2 )
% 0.27/0.49 => ( ! [Theta2: trm] :
% 0.27/0.49 ( ( X2
% 0.27/0.49 = ( some @ trm @ Theta2 ) )
% 0.27/0.49 => ! [Eta: trm] :
% 0.27/0.49 ( ( Xa
% 0.27/0.49 = ( some @ trm @ Eta ) )
% 0.27/0.49 => ( Y2
% 0.27/0.49 != ( some @ fml @ ( geq @ Theta2 @ Eta ) ) ) ) )
% 0.27/0.49 => ( ( ( X2
% 0.27/0.49 = ( none @ trm ) )
% 0.27/0.49 => ( Y2
% 0.27/0.49 != ( none @ fml ) ) )
% 0.27/0.49 => ~ ( ? [V: trm] :
% 0.27/0.49 ( X2
% 0.27/0.49 = ( some @ trm @ V ) )
% 0.27/0.49 => ( ( Xa
% 0.27/0.49 = ( none @ trm ) )
% 0.27/0.49 => ( Y2
% 0.27/0.49 != ( none @ fml ) ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Geqo.elims
% 0.27/0.49 thf(fact_138_Geqo_Osimps_I2_J,axiom,
% 0.27/0.49 ! [Eta2: option @ trm] :
% 0.27/0.49 ( ( uSubst1556497037e_Geqo @ ( none @ trm ) @ Eta2 )
% 0.27/0.49 = ( none @ fml ) ) ).
% 0.27/0.49
% 0.27/0.49 % Geqo.simps(2)
% 0.27/0.49 thf(fact_139_Geqo__undef,axiom,
% 0.27/0.49 ! [Theta: option @ trm,Eta2: option @ trm] :
% 0.27/0.49 ( ( ( uSubst1556497037e_Geqo @ Theta @ Eta2 )
% 0.27/0.49 = ( none @ fml ) )
% 0.27/0.49 = ( ( Theta
% 0.27/0.49 = ( none @ trm ) )
% 0.27/0.49 | ( Eta2
% 0.27/0.49 = ( none @ trm ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Geqo_undef
% 0.27/0.49 thf(fact_140_inf__Int__eq,axiom,
% 0.27/0.49 ! [A: $tType,R4: set @ A,S: set @ A] :
% 0.27/0.49 ( ( inf_inf @ ( A > $o )
% 0.27/0.49 @ ^ [X: A] : ( member @ A @ X @ R4 )
% 0.27/0.49 @ ^ [X: A] : ( member @ A @ X @ S ) )
% 0.27/0.49 = ( ^ [X: A] : ( member @ A @ X @ ( inf_inf @ ( set @ A ) @ R4 @ S ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % inf_Int_eq
% 0.27/0.49 thf(fact_141_Collect__empty__eq__bot,axiom,
% 0.27/0.49 ! [A: $tType,P2: A > $o] :
% 0.27/0.49 ( ( ( collect @ A @ P2 )
% 0.27/0.49 = ( bot_bot @ ( set @ A ) ) )
% 0.27/0.49 = ( P2
% 0.27/0.49 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Collect_empty_eq_bot
% 0.27/0.49 thf(fact_142_bot__empty__eq,axiom,
% 0.27/0.49 ! [A: $tType] :
% 0.27/0.49 ( ( bot_bot @ ( A > $o ) )
% 0.27/0.49 = ( ^ [X: A] : ( member @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % bot_empty_eq
% 0.27/0.49 thf(fact_143_internal__case__prod__def,axiom,
% 0.27/0.49 ! [C: $tType,B: $tType,A: $tType] :
% 0.27/0.49 ( ( produc2004651681e_prod @ A @ B @ C )
% 0.27/0.49 = ( product_case_prod @ A @ B @ C ) ) ).
% 0.27/0.49
% 0.27/0.49 % internal_case_prod_def
% 0.27/0.49 thf(fact_144_usubstappt_Osimps_I4_J,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F3: char,Theta: trm] :
% 0.27/0.49 ( ( uSubst95898992stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 0.27/0.49 = ( case_option @ ( option @ trm ) @ trm @ ( none @ trm )
% 0.27/0.49 @ ^ [Sigma_theta: trm] :
% 0.27/0.49 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( func @ F3 @ Sigma_theta ) )
% 0.27/0.49 @ ^ [R: trm] :
% 0.27/0.49 ( if @ ( option @ trm )
% 0.27/0.49 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R ) @ U )
% 0.27/0.49 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.49 @ ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta ) @ ( bot_bot @ ( set @ variable ) ) @ R )
% 0.27/0.49 @ ( none @ trm ) )
% 0.27/0.49 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [F4: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 0.27/0.49 @ Sigma
% 0.27/0.49 @ F3 ) )
% 0.27/0.49 @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt.simps(4)
% 0.27/0.49 thf(fact_145_Diamondo_Ocases,axiom,
% 0.27/0.49 ! [X2: product_prod @ ( option @ game ) @ ( option @ fml )] :
% 0.27/0.49 ( ! [Alpha: game,Phi: fml] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ Alpha ) @ ( some @ fml @ Phi ) ) )
% 0.27/0.49 => ( ! [Phi: option @ fml] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( none @ game ) @ Phi ) )
% 0.27/0.49 => ~ ! [V: game] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ V ) @ ( none @ fml ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Diamondo.cases
% 0.27/0.49 thf(fact_146_Testo__undef,axiom,
% 0.27/0.49 ! [Phi2: option @ fml] :
% 0.27/0.49 ( ( ( uSubst190403692_Testo @ Phi2 )
% 0.27/0.49 = ( none @ game ) )
% 0.27/0.49 = ( Phi2
% 0.27/0.49 = ( none @ fml ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Testo_undef
% 0.27/0.49 thf(fact_147_prod_Oinject,axiom,
% 0.27/0.49 ! [A: $tType,B: $tType,X13: A,X23: B,Y1: A,Y22: B] :
% 0.27/0.49 ( ( ( product_Pair @ A @ B @ X13 @ X23 )
% 0.27/0.49 = ( product_Pair @ A @ B @ Y1 @ Y22 ) )
% 0.27/0.49 = ( ( X13 = Y1 )
% 0.27/0.49 & ( X23 = Y22 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % prod.inject
% 0.27/0.49 thf(fact_148_old_Oprod_Oinject,axiom,
% 0.27/0.49 ! [A: $tType,B: $tType,A2: A,B2: B,A7: A,B7: B] :
% 0.27/0.49 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.27/0.49 = ( product_Pair @ A @ B @ A7 @ B7 ) )
% 0.27/0.49 = ( ( A2 = A7 )
% 0.27/0.49 & ( B2 = B7 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % old.prod.inject
% 0.27/0.49 thf(fact_149_trm_Oinject_I4_J,axiom,
% 0.27/0.49 ! [X41: char,X42: trm,Y41: char,Y42: trm] :
% 0.27/0.49 ( ( ( func @ X41 @ X42 )
% 0.27/0.49 = ( func @ Y41 @ Y42 ) )
% 0.27/0.49 = ( ( X41 = Y41 )
% 0.27/0.49 & ( X42 = Y42 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.inject(4)
% 0.27/0.49 thf(fact_150_case__prodI,axiom,
% 0.27/0.49 ! [A: $tType,B: $tType,F3: A > B > $o,A2: A,B2: B] :
% 0.27/0.49 ( ( F3 @ A2 @ B2 )
% 0.27/0.49 => ( product_case_prod @ A @ B @ $o @ F3 @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % case_prodI
% 0.27/0.49 thf(fact_151_case__prodI2,axiom,
% 0.27/0.49 ! [B: $tType,A: $tType,P3: product_prod @ A @ B,C2: A > B > $o] :
% 0.27/0.49 ( ! [A5: A,B5: B] :
% 0.27/0.49 ( ( P3
% 0.27/0.49 = ( product_Pair @ A @ B @ A5 @ B5 ) )
% 0.27/0.49 => ( C2 @ A5 @ B5 ) )
% 0.27/0.49 => ( product_case_prod @ A @ B @ $o @ C2 @ P3 ) ) ).
% 0.27/0.49
% 0.27/0.49 % case_prodI2
% 0.27/0.49 thf(fact_152_case__prodI2_H,axiom,
% 0.27/0.49 ! [A: $tType,B: $tType,C: $tType,P3: product_prod @ A @ B,C2: A > B > C > $o,X2: C] :
% 0.27/0.49 ( ! [A5: A,B5: B] :
% 0.27/0.49 ( ( ( product_Pair @ A @ B @ A5 @ B5 )
% 0.27/0.49 = P3 )
% 0.27/0.49 => ( C2 @ A5 @ B5 @ X2 ) )
% 0.27/0.49 => ( product_case_prod @ A @ B @ ( C > $o ) @ C2 @ P3 @ X2 ) ) ).
% 0.27/0.49
% 0.27/0.49 % case_prodI2'
% 0.27/0.49 thf(fact_153_mem__case__prodI,axiom,
% 0.27/0.49 ! [A: $tType,B: $tType,C: $tType,Z2: A,C2: B > C > ( set @ A ),A2: B,B2: C] :
% 0.27/0.49 ( ( member @ A @ Z2 @ ( C2 @ A2 @ B2 ) )
% 0.27/0.49 => ( member @ A @ Z2 @ ( product_case_prod @ B @ C @ ( set @ A ) @ C2 @ ( product_Pair @ B @ C @ A2 @ B2 ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % mem_case_prodI
% 0.27/0.49 thf(fact_154_mem__case__prodI2,axiom,
% 0.27/0.49 ! [C: $tType,B: $tType,A: $tType,P3: product_prod @ A @ B,Z2: C,C2: A > B > ( set @ C )] :
% 0.27/0.49 ( ! [A5: A,B5: B] :
% 0.27/0.49 ( ( P3
% 0.27/0.49 = ( product_Pair @ A @ B @ A5 @ B5 ) )
% 0.27/0.49 => ( member @ C @ Z2 @ ( C2 @ A5 @ B5 ) ) )
% 0.27/0.49 => ( member @ C @ Z2 @ ( product_case_prod @ A @ B @ ( set @ C ) @ C2 @ P3 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % mem_case_prodI2
% 0.27/0.49 thf(fact_155_case__prod__conv,axiom,
% 0.27/0.49 ! [B: $tType,A: $tType,C: $tType,F3: B > C > A,A2: B,B2: C] :
% 0.27/0.49 ( ( product_case_prod @ B @ C @ A @ F3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.27/0.49 = ( F3 @ A2 @ B2 ) ) ).
% 0.27/0.49
% 0.27/0.49 % case_prod_conv
% 0.27/0.49 thf(fact_156_usubstappt__func2,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F3: char,R2: trm,U: set @ variable,Theta: trm] :
% 0.27/0.49 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [F4: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 0.27/0.49 @ Sigma
% 0.27/0.49 @ F3 )
% 0.27/0.49 = ( some @ trm @ R2 ) )
% 0.27/0.49 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U )
% 0.27/0.49 != ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.49 => ( ( uSubst95898992stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 0.27/0.49 = ( none @ trm ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt_func2
% 0.27/0.49 thf(fact_157_usubstappt__func,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F3: char,R2: trm,U: set @ variable,Theta: trm,Sigma_theta2: trm] :
% 0.27/0.49 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [F4: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 0.27/0.49 @ Sigma
% 0.27/0.49 @ F3 )
% 0.27/0.49 = ( some @ trm @ R2 ) )
% 0.27/0.49 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U )
% 0.27/0.49 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.49 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.27/0.49 = ( some @ trm @ Sigma_theta2 ) )
% 0.27/0.49 => ( ( uSubst95898992stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 0.27/0.49 = ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta2 ) @ ( bot_bot @ ( set @ variable ) ) @ R2 ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt_func
% 0.27/0.49 thf(fact_158_inf__Int__eq2,axiom,
% 0.27/0.49 ! [B: $tType,A: $tType,R4: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.27/0.49 ( ( inf_inf @ ( A > B > $o )
% 0.27/0.49 @ ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ R4 )
% 0.27/0.49 @ ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ S ) )
% 0.27/0.49 = ( ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ ( inf_inf @ ( set @ ( product_prod @ A @ B ) ) @ R4 @ S ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % inf_Int_eq2
% 0.27/0.49 thf(fact_159_bot__empty__eq2,axiom,
% 0.27/0.49 ! [B: $tType,A: $tType] :
% 0.27/0.49 ( ( bot_bot @ ( A > B > $o ) )
% 0.27/0.49 = ( ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ ( bot_bot @ ( set @ ( product_prod @ A @ B ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % bot_empty_eq2
% 0.27/0.49 thf(fact_160_pred__equals__eq2,axiom,
% 0.27/0.49 ! [B: $tType,A: $tType,R4: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.27/0.49 ( ( ( ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ R4 ) )
% 0.27/0.49 = ( ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ S ) ) )
% 0.27/0.49 = ( R4 = S ) ) ).
% 0.27/0.49
% 0.27/0.49 % pred_equals_eq2
% 0.27/0.49 thf(fact_161_cond__case__prod__eta,axiom,
% 0.27/0.49 ! [C: $tType,B: $tType,A: $tType,F3: A > B > C,G2: ( product_prod @ A @ B ) > C] :
% 0.27/0.49 ( ! [X3: A,Y3: B] :
% 0.27/0.49 ( ( F3 @ X3 @ Y3 )
% 0.27/0.49 = ( G2 @ ( product_Pair @ A @ B @ X3 @ Y3 ) ) )
% 0.27/0.49 => ( ( product_case_prod @ A @ B @ C @ F3 )
% 0.27/0.49 = G2 ) ) ).
% 0.27/0.49
% 0.27/0.49 % cond_case_prod_eta
% 0.27/0.49 thf(fact_162_case__prod__eta,axiom,
% 0.27/0.49 ! [C: $tType,B: $tType,A: $tType,F3: ( product_prod @ A @ B ) > C] :
% 0.27/0.49 ( ( product_case_prod @ A @ B @ C
% 0.27/0.49 @ ^ [X: A,Y: B] : ( F3 @ ( product_Pair @ A @ B @ X @ Y ) ) )
% 0.27/0.49 = F3 ) ).
% 0.27/0.49
% 0.27/0.49 % case_prod_eta
% 0.27/0.49 thf(fact_163_case__prodE2,axiom,
% 0.27/0.49 ! [B: $tType,A: $tType,C: $tType,Q: A > $o,P2: B > C > A,Z2: product_prod @ B @ C] :
% 0.27/0.49 ( ( Q @ ( product_case_prod @ B @ C @ A @ P2 @ Z2 ) )
% 0.27/0.49 => ~ ! [X3: B,Y3: C] :
% 0.27/0.49 ( ( Z2
% 0.27/0.49 = ( product_Pair @ B @ C @ X3 @ Y3 ) )
% 0.27/0.49 => ~ ( Q @ ( P2 @ X3 @ Y3 ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % case_prodE2
% 0.27/0.49 thf(fact_164_surj__pair,axiom,
% 0.27/0.49 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 0.27/0.49 ? [X3: A,Y3: B] :
% 0.27/0.49 ( P3
% 0.27/0.49 = ( product_Pair @ A @ B @ X3 @ Y3 ) ) ).
% 0.27/0.49
% 0.27/0.49 % surj_pair
% 0.27/0.49 thf(fact_165_prod__cases,axiom,
% 0.27/0.49 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 0.27/0.49 ( ! [A5: A,B5: B] : ( P2 @ ( product_Pair @ A @ B @ A5 @ B5 ) )
% 0.27/0.49 => ( P2 @ P3 ) ) ).
% 0.27/0.49
% 0.27/0.49 % prod_cases
% 0.27/0.49 thf(fact_166_Pair__inject,axiom,
% 0.27/0.49 ! [A: $tType,B: $tType,A2: A,B2: B,A7: A,B7: B] :
% 0.27/0.49 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.27/0.49 = ( product_Pair @ A @ B @ A7 @ B7 ) )
% 0.27/0.49 => ~ ( ( A2 = A7 )
% 0.27/0.49 => ( B2 != B7 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Pair_inject
% 0.27/0.49 thf(fact_167_prod__cases3,axiom,
% 0.27/0.49 ! [A: $tType,B: $tType,C: $tType,Y2: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.27/0.49 ~ ! [A5: A,B5: B,C4: C] :
% 0.27/0.49 ( Y2
% 0.27/0.49 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B5 @ C4 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % prod_cases3
% 0.27/0.49 thf(fact_168_prod__cases4,axiom,
% 0.27/0.49 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.27/0.49 ~ ! [A5: A,B5: B,C4: C,D2: D] :
% 0.27/0.49 ( Y2
% 0.27/0.49 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C4 @ D2 ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % prod_cases4
% 0.27/0.49 thf(fact_169_prod__cases5,axiom,
% 0.27/0.49 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.27/0.49 ~ ! [A5: A,B5: B,C4: C,D2: D,E2: E] :
% 0.27/0.49 ( Y2
% 0.27/0.49 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C4 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % prod_cases5
% 0.27/0.49 thf(fact_170_prod__cases6,axiom,
% 0.27/0.49 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F5: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) )] :
% 0.27/0.49 ~ ! [A5: A,B5: B,C4: C,D2: D,E2: E,F6: F5] :
% 0.27/0.49 ( Y2
% 0.27/0.49 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ F5 ) @ D2 @ ( product_Pair @ E @ F5 @ E2 @ F6 ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % prod_cases6
% 0.27/0.49 thf(fact_171_prod__cases7,axiom,
% 0.27/0.49 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F5: $tType,G3: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) )] :
% 0.27/0.49 ~ ! [A5: A,B5: B,C4: C,D2: D,E2: E,F6: F5,G4: G3] :
% 0.27/0.49 ( Y2
% 0.27/0.49 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F5 @ G3 ) @ E2 @ ( product_Pair @ F5 @ G3 @ F6 @ G4 ) ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % prod_cases7
% 0.27/0.49 thf(fact_172_prod__induct3,axiom,
% 0.27/0.49 ! [C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.27/0.49 ( ! [A5: A,B5: B,C4: C] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B5 @ C4 ) ) )
% 0.27/0.49 => ( P2 @ X2 ) ) ).
% 0.27/0.49
% 0.27/0.49 % prod_induct3
% 0.27/0.49 thf(fact_173_prod__induct4,axiom,
% 0.27/0.49 ! [D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.27/0.49 ( ! [A5: A,B5: B,C4: C,D2: D] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C4 @ D2 ) ) ) )
% 0.27/0.49 => ( P2 @ X2 ) ) ).
% 0.27/0.49
% 0.27/0.49 % prod_induct4
% 0.27/0.49 thf(fact_174_prod__induct5,axiom,
% 0.27/0.49 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.27/0.49 ( ! [A5: A,B5: B,C4: C,D2: D,E2: E] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C4 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 0.27/0.49 => ( P2 @ X2 ) ) ).
% 0.27/0.49
% 0.27/0.49 % prod_induct5
% 0.27/0.49 thf(fact_175_prod__induct6,axiom,
% 0.27/0.49 ! [F5: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) )] :
% 0.27/0.49 ( ! [A5: A,B5: B,C4: C,D2: D,E2: E,F6: F5] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ F5 ) @ D2 @ ( product_Pair @ E @ F5 @ E2 @ F6 ) ) ) ) ) )
% 0.27/0.49 => ( P2 @ X2 ) ) ).
% 0.27/0.49
% 0.27/0.49 % prod_induct6
% 0.27/0.49 thf(fact_176_prod__induct7,axiom,
% 0.27/0.49 ! [G3: $tType,F5: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) )] :
% 0.27/0.49 ( ! [A5: A,B5: B,C4: C,D2: D,E2: E,F6: F5,G4: G3] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F5 @ G3 ) @ E2 @ ( product_Pair @ F5 @ G3 @ F6 @ G4 ) ) ) ) ) ) )
% 0.27/0.49 => ( P2 @ X2 ) ) ).
% 0.27/0.49
% 0.27/0.49 % prod_induct7
% 0.27/0.49 thf(fact_177_mem__case__prodE,axiom,
% 0.27/0.49 ! [B: $tType,A: $tType,C: $tType,Z2: A,C2: B > C > ( set @ A ),P3: product_prod @ B @ C] :
% 0.27/0.49 ( ( member @ A @ Z2 @ ( product_case_prod @ B @ C @ ( set @ A ) @ C2 @ P3 ) )
% 0.27/0.49 => ~ ! [X3: B,Y3: C] :
% 0.27/0.49 ( ( P3
% 0.27/0.49 = ( product_Pair @ B @ C @ X3 @ Y3 ) )
% 0.27/0.49 => ~ ( member @ A @ Z2 @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % mem_case_prodE
% 0.27/0.49 thf(fact_178_old_Oprod_Oexhaust,axiom,
% 0.27/0.49 ! [A: $tType,B: $tType,Y2: product_prod @ A @ B] :
% 0.27/0.49 ~ ! [A5: A,B5: B] :
% 0.27/0.49 ( Y2
% 0.27/0.49 != ( product_Pair @ A @ B @ A5 @ B5 ) ) ).
% 0.27/0.49
% 0.27/0.49 % old.prod.exhaust
% 0.27/0.49 thf(fact_179_old_Oprod_Oinducts,axiom,
% 0.27/0.49 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.27/0.49 ( ! [A5: A,B5: B] : ( P2 @ ( product_Pair @ A @ B @ A5 @ B5 ) )
% 0.27/0.49 => ( P2 @ Prod ) ) ).
% 0.27/0.49
% 0.27/0.49 % old.prod.inducts
% 0.27/0.49 thf(fact_180_case__prodD,axiom,
% 0.27/0.49 ! [A: $tType,B: $tType,F3: A > B > $o,A2: A,B2: B] :
% 0.27/0.49 ( ( product_case_prod @ A @ B @ $o @ F3 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.27/0.49 => ( F3 @ A2 @ B2 ) ) ).
% 0.27/0.49
% 0.27/0.49 % case_prodD
% 0.27/0.49 thf(fact_181_case__prodE,axiom,
% 0.27/0.49 ! [A: $tType,B: $tType,C2: A > B > $o,P3: product_prod @ A @ B] :
% 0.27/0.49 ( ( product_case_prod @ A @ B @ $o @ C2 @ P3 )
% 0.27/0.49 => ~ ! [X3: A,Y3: B] :
% 0.27/0.49 ( ( P3
% 0.27/0.49 = ( product_Pair @ A @ B @ X3 @ Y3 ) )
% 0.27/0.49 => ~ ( C2 @ X3 @ Y3 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % case_prodE
% 0.27/0.49 thf(fact_182_case__prodD_H,axiom,
% 0.27/0.49 ! [B: $tType,A: $tType,C: $tType,R4: A > B > C > $o,A2: A,B2: B,C2: C] :
% 0.27/0.49 ( ( product_case_prod @ A @ B @ ( C > $o ) @ R4 @ ( product_Pair @ A @ B @ A2 @ B2 ) @ C2 )
% 0.27/0.49 => ( R4 @ A2 @ B2 @ C2 ) ) ).
% 0.27/0.49
% 0.27/0.49 % case_prodD'
% 0.27/0.49 thf(fact_183_case__prodE_H,axiom,
% 0.27/0.49 ! [B: $tType,A: $tType,C: $tType,C2: A > B > C > $o,P3: product_prod @ A @ B,Z2: C] :
% 0.27/0.49 ( ( product_case_prod @ A @ B @ ( C > $o ) @ C2 @ P3 @ Z2 )
% 0.27/0.49 => ~ ! [X3: A,Y3: B] :
% 0.27/0.49 ( ( P3
% 0.27/0.49 = ( product_Pair @ A @ B @ X3 @ Y3 ) )
% 0.27/0.49 => ~ ( C2 @ X3 @ Y3 @ Z2 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % case_prodE'
% 0.27/0.49 thf(fact_184_case__prod__Pair__iden,axiom,
% 0.27/0.49 ! [B: $tType,A: $tType,P3: product_prod @ A @ B] :
% 0.27/0.49 ( ( product_case_prod @ A @ B @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B ) @ P3 )
% 0.27/0.49 = P3 ) ).
% 0.27/0.49
% 0.27/0.49 % case_prod_Pair_iden
% 0.27/0.49 thf(fact_185_old_Oprod_Ocase,axiom,
% 0.27/0.49 ! [A: $tType,C: $tType,B: $tType,F3: A > B > C,X13: A,X23: B] :
% 0.27/0.49 ( ( product_case_prod @ A @ B @ C @ F3 @ ( product_Pair @ A @ B @ X13 @ X23 ) )
% 0.27/0.49 = ( F3 @ X13 @ X23 ) ) ).
% 0.27/0.49
% 0.27/0.49 % old.prod.case
% 0.27/0.49 thf(fact_186_internal__case__prod__conv,axiom,
% 0.27/0.49 ! [B: $tType,A: $tType,C: $tType,C2: B > C > A,A2: B,B2: C] :
% 0.27/0.49 ( ( produc2004651681e_prod @ B @ C @ A @ C2 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.27/0.49 = ( C2 @ A2 @ B2 ) ) ).
% 0.27/0.49
% 0.27/0.49 % internal_case_prod_conv
% 0.27/0.49 thf(fact_187_usubstappt__func__conv,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F3: char,Theta: trm] :
% 0.27/0.49 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 0.27/0.49 != ( none @ trm ) )
% 0.27/0.49 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.27/0.49 != ( none @ trm ) )
% 0.27/0.49 & ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [F4: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 0.27/0.49 @ Sigma
% 0.27/0.49 @ F3 )
% 0.27/0.49 = ( none @ trm ) )
% 0.27/0.49 | ? [R3: trm] :
% 0.27/0.49 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [F4: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 0.27/0.49 @ Sigma
% 0.27/0.49 @ F3 )
% 0.27/0.49 = ( some @ trm @ R3 ) )
% 0.27/0.49 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R3 ) @ U )
% 0.27/0.49 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt_func_conv
% 0.27/0.49 thf(fact_188_Testo_Osimps_I2_J,axiom,
% 0.27/0.49 ( ( uSubst190403692_Testo @ ( none @ fml ) )
% 0.27/0.49 = ( none @ game ) ) ).
% 0.27/0.49
% 0.27/0.49 % Testo.simps(2)
% 0.27/0.49 thf(fact_189_usappconst__simp,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F3: char,R2: trm,U: set @ variable] :
% 0.27/0.49 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [F0: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.27/0.49 @ Sigma
% 0.27/0.49 @ F3 )
% 0.27/0.49 = ( some @ trm @ R2 ) )
% 0.27/0.49 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U )
% 0.27/0.49 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.49 => ( ( uSubst1138577137pconst @ Sigma @ U @ F3 )
% 0.27/0.49 = ( some @ trm @ R2 ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usappconst_simp
% 0.27/0.49 thf(fact_190_usappconst__conv,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F3: char] :
% 0.27/0.49 ( ( ( uSubst1138577137pconst @ Sigma @ U @ F3 )
% 0.27/0.49 != ( none @ trm ) )
% 0.27/0.49 => ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [F0: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.27/0.49 @ Sigma
% 0.27/0.49 @ F3 )
% 0.27/0.49 = ( none @ trm ) )
% 0.27/0.49 | ? [R3: trm] :
% 0.27/0.49 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [F0: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.27/0.49 @ Sigma
% 0.27/0.49 @ F3 )
% 0.27/0.49 = ( some @ trm @ R3 ) )
% 0.27/0.49 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R3 ) @ U )
% 0.27/0.49 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usappconst_conv
% 0.27/0.49 thf(fact_191_usubstappt__const,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F3: char,R2: trm,U: set @ variable] :
% 0.27/0.49 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [F0: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.27/0.49 @ Sigma
% 0.27/0.49 @ F3 )
% 0.27/0.49 = ( some @ trm @ R2 ) )
% 0.27/0.49 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U )
% 0.27/0.49 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.49 => ( ( uSubst95898992stappt @ Sigma @ U @ ( const @ F3 ) )
% 0.27/0.49 = ( some @ trm @ R2 ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt_const
% 0.27/0.49 thf(fact_192_trm_Oinject_I3_J,axiom,
% 0.27/0.49 ! [X32: char,Y32: char] :
% 0.27/0.49 ( ( ( const @ X32 )
% 0.27/0.49 = ( const @ Y32 ) )
% 0.27/0.49 = ( X32 = Y32 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.inject(3)
% 0.27/0.49 thf(fact_193_trm_Odistinct_I23_J,axiom,
% 0.27/0.49 ! [X32: char,X41: char,X42: trm] :
% 0.27/0.49 ( ( const @ X32 )
% 0.27/0.49 != ( func @ X41 @ X42 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(23)
% 0.27/0.49 thf(fact_194_usubstappt_Osimps_I3_J,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F3: char] :
% 0.27/0.49 ( ( uSubst95898992stappt @ Sigma @ U @ ( const @ F3 ) )
% 0.27/0.49 = ( uSubst1138577137pconst @ Sigma @ U @ F3 ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt.simps(3)
% 0.27/0.49 thf(fact_195_ODEo_Ocases,axiom,
% 0.27/0.49 ! [X2: product_prod @ char @ ( option @ trm )] :
% 0.27/0.49 ( ! [X3: char,Theta2: trm] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ char @ ( option @ trm ) @ X3 @ ( some @ trm @ Theta2 ) ) )
% 0.27/0.49 => ~ ! [X3: char] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ char @ ( option @ trm ) @ X3 @ ( none @ trm ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % ODEo.cases
% 0.27/0.49 thf(fact_196_Assigno_Ocases,axiom,
% 0.27/0.49 ! [X2: product_prod @ variable @ ( option @ trm )] :
% 0.27/0.49 ( ! [X3: variable,Theta2: trm] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ variable @ ( option @ trm ) @ X3 @ ( some @ trm @ Theta2 ) ) )
% 0.27/0.49 => ~ ! [X3: variable] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ variable @ ( option @ trm ) @ X3 @ ( none @ trm ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Assigno.cases
% 0.27/0.49 thf(fact_197_Timeso_Ocases,axiom,
% 0.27/0.49 ! [X2: product_prod @ ( option @ trm ) @ ( option @ trm )] :
% 0.27/0.49 ( ! [Theta2: trm,Eta: trm] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta ) ) )
% 0.27/0.49 => ( ! [Eta: option @ trm] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( none @ trm ) @ Eta ) )
% 0.27/0.49 => ~ ! [V: trm] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ V ) @ ( none @ trm ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Timeso.cases
% 0.27/0.49 thf(fact_198_Existso_Ocases,axiom,
% 0.27/0.49 ! [X2: product_prod @ variable @ ( option @ fml )] :
% 0.27/0.49 ( ! [X3: variable,Phi: fml] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ variable @ ( option @ fml ) @ X3 @ ( some @ fml @ Phi ) ) )
% 0.27/0.49 => ~ ! [X3: variable] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ variable @ ( option @ fml ) @ X3 @ ( none @ fml ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Existso.cases
% 0.27/0.49 thf(fact_199_Ando_Ocases,axiom,
% 0.27/0.49 ! [X2: product_prod @ ( option @ fml ) @ ( option @ fml )] :
% 0.27/0.49 ( ! [Phi: fml,Psi: fml] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ ( option @ fml ) @ ( option @ fml ) @ ( some @ fml @ Phi ) @ ( some @ fml @ Psi ) ) )
% 0.27/0.49 => ( ! [Psi: option @ fml] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ ( option @ fml ) @ ( option @ fml ) @ ( none @ fml ) @ Psi ) )
% 0.27/0.49 => ~ ! [V: fml] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ ( option @ fml ) @ ( option @ fml ) @ ( some @ fml @ V ) @ ( none @ fml ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Ando.cases
% 0.27/0.49 thf(fact_200_Composeo_Ocases,axiom,
% 0.27/0.49 ! [X2: product_prod @ ( option @ game ) @ ( option @ game )] :
% 0.27/0.49 ( ! [Alpha: game,Beta: game] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ ( some @ game @ Alpha ) @ ( some @ game @ Beta ) ) )
% 0.27/0.49 => ( ! [Alpha: option @ game] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ Alpha @ ( none @ game ) ) )
% 0.27/0.49 => ~ ! [V: game] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ ( none @ game ) @ ( some @ game @ V ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Composeo.cases
% 0.27/0.49 thf(fact_201_usappconst__def,axiom,
% 0.27/0.49 ( uSubst1138577137pconst
% 0.27/0.49 = ( ^ [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,F2: char] :
% 0.27/0.49 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( const @ F2 ) )
% 0.27/0.49 @ ^ [R: trm] :
% 0.27/0.49 ( if @ ( option @ trm )
% 0.27/0.49 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R ) @ U2 )
% 0.27/0.49 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.49 @ ( some @ trm @ R )
% 0.27/0.49 @ ( none @ trm ) )
% 0.27/0.49 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [F0: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.27/0.49 @ Sigma2
% 0.27/0.49 @ F2 ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usappconst_def
% 0.27/0.49 thf(fact_202_usubstappt__const__conv,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F3: char] :
% 0.27/0.49 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( const @ F3 ) )
% 0.27/0.49 != ( none @ trm ) )
% 0.27/0.49 => ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [F0: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.27/0.49 @ Sigma
% 0.27/0.49 @ F3 )
% 0.27/0.49 = ( none @ trm ) )
% 0.27/0.49 | ? [R3: trm] :
% 0.27/0.49 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [F0: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 0.27/0.49 @ Sigma
% 0.27/0.49 @ F3 )
% 0.27/0.49 = ( some @ trm @ R3 ) )
% 0.27/0.49 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R3 ) @ U )
% 0.27/0.49 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt_const_conv
% 0.27/0.49 thf(fact_203_old_Oprod_Orec,axiom,
% 0.27/0.49 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.27/0.49 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.27/0.49 = ( F1 @ A2 @ B2 ) ) ).
% 0.27/0.49
% 0.27/0.49 % old.prod.rec
% 0.27/0.49 thf(fact_204_usubstappt_Opsimps_I4_J,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F3: char,Theta: trm] :
% 0.27/0.49 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( func @ F3 @ Theta ) ) ) )
% 0.27/0.49 => ( ( uSubst95898992stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 0.27/0.49 = ( case_option @ ( option @ trm ) @ trm @ ( none @ trm )
% 0.27/0.49 @ ^ [Sigma_theta: trm] :
% 0.27/0.49 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( func @ F3 @ Sigma_theta ) )
% 0.27/0.49 @ ^ [R: trm] :
% 0.27/0.49 ( if @ ( option @ trm )
% 0.27/0.49 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R ) @ U )
% 0.27/0.49 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.49 @ ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta ) @ ( bot_bot @ ( set @ variable ) ) @ R )
% 0.27/0.49 @ ( none @ trm ) )
% 0.27/0.49 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [F4: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 0.27/0.49 @ Sigma
% 0.27/0.49 @ F3 ) )
% 0.27/0.49 @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt.psimps(4)
% 0.27/0.49 thf(fact_205_usubstappt_Opsimps_I3_J,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F3: char] :
% 0.27/0.49 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( const @ F3 ) ) ) )
% 0.27/0.49 => ( ( uSubst95898992stappt @ Sigma @ U @ ( const @ F3 ) )
% 0.27/0.49 = ( uSubst1138577137pconst @ Sigma @ U @ F3 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt.psimps(3)
% 0.27/0.49 thf(fact_206_usubstappt_Opsimps_I1_J,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,X2: variable] :
% 0.27/0.49 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( var @ X2 ) ) ) )
% 0.27/0.49 => ( ( uSubst95898992stappt @ Sigma @ U @ ( var @ X2 ) )
% 0.27/0.49 = ( some @ trm @ ( var @ X2 ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt.psimps(1)
% 0.27/0.49 thf(fact_207_usubstappt_Opsimps_I2_J,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,R2: real] :
% 0.27/0.49 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( number @ R2 ) ) ) )
% 0.27/0.49 => ( ( uSubst95898992stappt @ Sigma @ U @ ( number @ R2 ) )
% 0.27/0.49 = ( some @ trm @ ( number @ R2 ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt.psimps(2)
% 0.27/0.49 thf(fact_208_trm_Oinject_I2_J,axiom,
% 0.27/0.49 ! [X23: real,Y22: real] :
% 0.27/0.49 ( ( ( number @ X23 )
% 0.27/0.49 = ( number @ Y22 ) )
% 0.27/0.49 = ( X23 = Y22 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.inject(2)
% 0.27/0.49 thf(fact_209_trm_Oinject_I1_J,axiom,
% 0.27/0.49 ! [X13: variable,Y1: variable] :
% 0.27/0.49 ( ( ( var @ X13 )
% 0.27/0.49 = ( var @ Y1 ) )
% 0.27/0.49 = ( X13 = Y1 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.inject(1)
% 0.27/0.49 thf(fact_210_trm_Odistinct_I15_J,axiom,
% 0.27/0.49 ! [X23: real,X41: char,X42: trm] :
% 0.27/0.49 ( ( number @ X23 )
% 0.27/0.49 != ( func @ X41 @ X42 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(15)
% 0.27/0.49 thf(fact_211_trm_Odistinct_I5_J,axiom,
% 0.27/0.49 ! [X13: variable,X41: char,X42: trm] :
% 0.27/0.49 ( ( var @ X13 )
% 0.27/0.49 != ( func @ X41 @ X42 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(5)
% 0.27/0.49 thf(fact_212_trm_Odistinct_I1_J,axiom,
% 0.27/0.49 ! [X13: variable,X23: real] :
% 0.27/0.49 ( ( var @ X13 )
% 0.27/0.49 != ( number @ X23 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(1)
% 0.27/0.49 thf(fact_213_trm_Odistinct_I13_J,axiom,
% 0.27/0.49 ! [X23: real,X32: char] :
% 0.27/0.49 ( ( number @ X23 )
% 0.27/0.49 != ( const @ X32 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(13)
% 0.27/0.49 thf(fact_214_trm_Odistinct_I3_J,axiom,
% 0.27/0.49 ! [X13: variable,X32: char] :
% 0.27/0.49 ( ( var @ X13 )
% 0.27/0.49 != ( const @ X32 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(3)
% 0.27/0.49 thf(fact_215_usubstappt_Osimps_I2_J,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,R2: real] :
% 0.27/0.49 ( ( uSubst95898992stappt @ Sigma @ U @ ( number @ R2 ) )
% 0.27/0.49 = ( some @ trm @ ( number @ R2 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt.simps(2)
% 0.27/0.49 thf(fact_216_usubstappt_Osimps_I1_J,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,X2: variable] :
% 0.27/0.49 ( ( uSubst95898992stappt @ Sigma @ U @ ( var @ X2 ) )
% 0.27/0.49 = ( some @ trm @ ( var @ X2 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt.simps(1)
% 0.27/0.49 thf(fact_217_usubstappt_Opinduct,axiom,
% 0.27/0.49 ! [A0: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),A1: set @ variable,A22: trm,P2: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > trm > $o] :
% 0.27/0.49 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ A0 @ ( product_Pair @ ( set @ variable ) @ trm @ A1 @ A22 ) ) )
% 0.27/0.49 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,X3: variable] :
% 0.27/0.49 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( var @ X3 ) ) ) )
% 0.27/0.49 => ( P2 @ Sigma3 @ U3 @ ( var @ X3 ) ) )
% 0.27/0.49 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,R3: real] :
% 0.27/0.49 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( number @ R3 ) ) ) )
% 0.27/0.49 => ( P2 @ Sigma3 @ U3 @ ( number @ R3 ) ) )
% 0.27/0.49 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F6: char] :
% 0.27/0.49 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( const @ F6 ) ) ) )
% 0.27/0.49 => ( P2 @ Sigma3 @ U3 @ ( const @ F6 ) ) )
% 0.27/0.49 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F6: char,Theta2: trm] :
% 0.27/0.49 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( func @ F6 @ Theta2 ) ) ) )
% 0.27/0.49 => ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 0.27/0.49 => ( ! [X25: trm] :
% 0.27/0.49 ( ( ( uSubst95898992stappt @ Sigma3 @ U3 @ Theta2 )
% 0.27/0.49 = ( some @ trm @ X25 ) )
% 0.27/0.49 => ! [X2a: trm] :
% 0.27/0.49 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [F4: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 0.27/0.49 @ Sigma3
% 0.27/0.49 @ F6 )
% 0.27/0.49 = ( some @ trm @ X2a ) )
% 0.27/0.49 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ X2a ) @ U3 )
% 0.27/0.49 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.49 => ( P2 @ ( uSubst969145931substt @ X25 ) @ ( bot_bot @ ( set @ variable ) ) @ X2a ) ) ) )
% 0.27/0.49 => ( P2 @ Sigma3 @ U3 @ ( func @ F6 @ Theta2 ) ) ) ) )
% 0.27/0.49 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm,Eta: trm] :
% 0.27/0.49 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( plus @ Theta2 @ Eta ) ) ) )
% 0.27/0.49 => ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 0.27/0.49 => ( ( P2 @ Sigma3 @ U3 @ Eta )
% 0.27/0.49 => ( P2 @ Sigma3 @ U3 @ ( plus @ Theta2 @ Eta ) ) ) ) )
% 0.27/0.49 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm,Eta: trm] :
% 0.27/0.49 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( times @ Theta2 @ Eta ) ) ) )
% 0.27/0.49 => ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 0.27/0.49 => ( ( P2 @ Sigma3 @ U3 @ Eta )
% 0.27/0.49 => ( P2 @ Sigma3 @ U3 @ ( times @ Theta2 @ Eta ) ) ) ) )
% 0.27/0.49 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm] :
% 0.27/0.49 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( differential @ Theta2 ) ) ) )
% 0.27/0.49 => ( ( P2 @ Sigma3
% 0.27/0.49 @ ( collect @ variable
% 0.27/0.49 @ ^ [X: variable] : $true )
% 0.27/0.49 @ Theta2 )
% 0.27/0.49 => ( P2 @ Sigma3 @ U3 @ ( differential @ Theta2 ) ) ) )
% 0.27/0.49 => ( P2 @ A0 @ A1 @ A22 ) ) ) ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt.pinduct
% 0.27/0.49 thf(fact_218_dotsubstt__def,axiom,
% 0.27/0.49 ( uSubst969145931substt
% 0.27/0.49 = ( ^ [Theta3: trm] :
% 0.27/0.49 ( product_Pair @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) )
% 0.27/0.49 @ ^ [F2: char] :
% 0.27/0.49 ( if @ ( option @ trm )
% 0.27/0.49 @ ( F2
% 0.27/0.49 = ( char2 @ $false @ $true @ $true @ $true @ $false @ $true @ $false @ $false ) )
% 0.27/0.49 @ ( some @ trm @ Theta3 )
% 0.27/0.49 @ ( none @ trm ) )
% 0.27/0.49 @ ( product_Pair @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) )
% 0.27/0.49 @ ^ [Uu: char] : ( none @ trm )
% 0.27/0.49 @ ( product_Pair @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) )
% 0.27/0.49 @ ^ [Uu: char] : ( none @ fml )
% 0.27/0.49 @ ^ [Uu: char] : ( none @ game ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % dotsubstt_def
% 0.27/0.49 thf(fact_219_trm_Oinject_I6_J,axiom,
% 0.27/0.49 ! [X61: trm,X62: trm,Y61: trm,Y62: trm] :
% 0.27/0.49 ( ( ( times @ X61 @ X62 )
% 0.27/0.49 = ( times @ Y61 @ Y62 ) )
% 0.27/0.49 = ( ( X61 = Y61 )
% 0.27/0.49 & ( X62 = Y62 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.inject(6)
% 0.27/0.49 thf(fact_220_trm_Oinject_I5_J,axiom,
% 0.27/0.49 ! [X51: trm,X52: trm,Y51: trm,Y52: trm] :
% 0.27/0.49 ( ( ( plus @ X51 @ X52 )
% 0.27/0.49 = ( plus @ Y51 @ Y52 ) )
% 0.27/0.49 = ( ( X51 = Y51 )
% 0.27/0.49 & ( X52 = Y52 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.inject(5)
% 0.27/0.49 thf(fact_221_trm_Oinject_I7_J,axiom,
% 0.27/0.49 ! [X7: trm,Y7: trm] :
% 0.27/0.49 ( ( ( differential @ X7 )
% 0.27/0.49 = ( differential @ Y7 ) )
% 0.27/0.49 = ( X7 = Y7 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.inject(7)
% 0.27/0.49 thf(fact_222_trm_Odistinct_I7_J,axiom,
% 0.27/0.49 ! [X13: variable,X51: trm,X52: trm] :
% 0.27/0.49 ( ( var @ X13 )
% 0.27/0.49 != ( plus @ X51 @ X52 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(7)
% 0.27/0.49 thf(fact_223_trm_Odistinct_I9_J,axiom,
% 0.27/0.49 ! [X13: variable,X61: trm,X62: trm] :
% 0.27/0.49 ( ( var @ X13 )
% 0.27/0.49 != ( times @ X61 @ X62 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(9)
% 0.27/0.49 thf(fact_224_trm_Odistinct_I11_J,axiom,
% 0.27/0.49 ! [X13: variable,X7: trm] :
% 0.27/0.49 ( ( var @ X13 )
% 0.27/0.49 != ( differential @ X7 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(11)
% 0.27/0.49 thf(fact_225_trm_Odistinct_I17_J,axiom,
% 0.27/0.49 ! [X23: real,X51: trm,X52: trm] :
% 0.27/0.49 ( ( number @ X23 )
% 0.27/0.49 != ( plus @ X51 @ X52 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(17)
% 0.27/0.49 thf(fact_226_trm_Odistinct_I19_J,axiom,
% 0.27/0.49 ! [X23: real,X61: trm,X62: trm] :
% 0.27/0.49 ( ( number @ X23 )
% 0.27/0.49 != ( times @ X61 @ X62 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(19)
% 0.27/0.49 thf(fact_227_trm_Odistinct_I21_J,axiom,
% 0.27/0.49 ! [X23: real,X7: trm] :
% 0.27/0.49 ( ( number @ X23 )
% 0.27/0.49 != ( differential @ X7 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(21)
% 0.27/0.49 thf(fact_228_trm_Oexhaust,axiom,
% 0.27/0.49 ! [Y2: trm] :
% 0.27/0.49 ( ! [X14: variable] :
% 0.27/0.49 ( Y2
% 0.27/0.49 != ( var @ X14 ) )
% 0.27/0.49 => ( ! [X24: real] :
% 0.27/0.49 ( Y2
% 0.27/0.49 != ( number @ X24 ) )
% 0.27/0.49 => ( ! [X33: char] :
% 0.27/0.49 ( Y2
% 0.27/0.49 != ( const @ X33 ) )
% 0.27/0.49 => ( ! [X412: char,X422: trm] :
% 0.27/0.49 ( Y2
% 0.27/0.49 != ( func @ X412 @ X422 ) )
% 0.27/0.49 => ( ! [X512: trm,X522: trm] :
% 0.27/0.49 ( Y2
% 0.27/0.49 != ( plus @ X512 @ X522 ) )
% 0.27/0.49 => ( ! [X612: trm,X622: trm] :
% 0.27/0.49 ( Y2
% 0.27/0.49 != ( times @ X612 @ X622 ) )
% 0.27/0.49 => ~ ! [X72: trm] :
% 0.27/0.49 ( Y2
% 0.27/0.49 != ( differential @ X72 ) ) ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.exhaust
% 0.27/0.49 thf(fact_229_trm_Oinduct,axiom,
% 0.27/0.49 ! [P2: trm > $o,Trm: trm] :
% 0.27/0.49 ( ! [X3: variable] : ( P2 @ ( var @ X3 ) )
% 0.27/0.49 => ( ! [X3: real] : ( P2 @ ( number @ X3 ) )
% 0.27/0.49 => ( ! [X3: char] : ( P2 @ ( const @ X3 ) )
% 0.27/0.49 => ( ! [X1a: char,X2a2: trm] :
% 0.27/0.49 ( ( P2 @ X2a2 )
% 0.27/0.49 => ( P2 @ ( func @ X1a @ X2a2 ) ) )
% 0.27/0.49 => ( ! [X1a: trm,X2a2: trm] :
% 0.27/0.49 ( ( P2 @ X1a )
% 0.27/0.49 => ( ( P2 @ X2a2 )
% 0.27/0.49 => ( P2 @ ( plus @ X1a @ X2a2 ) ) ) )
% 0.27/0.49 => ( ! [X1a: trm,X2a2: trm] :
% 0.27/0.49 ( ( P2 @ X1a )
% 0.27/0.49 => ( ( P2 @ X2a2 )
% 0.27/0.49 => ( P2 @ ( times @ X1a @ X2a2 ) ) ) )
% 0.27/0.49 => ( ! [X3: trm] :
% 0.27/0.49 ( ( P2 @ X3 )
% 0.27/0.49 => ( P2 @ ( differential @ X3 ) ) )
% 0.27/0.49 => ( P2 @ Trm ) ) ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.induct
% 0.27/0.49 thf(fact_230_trm_Odistinct_I25_J,axiom,
% 0.27/0.49 ! [X32: char,X51: trm,X52: trm] :
% 0.27/0.49 ( ( const @ X32 )
% 0.27/0.49 != ( plus @ X51 @ X52 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(25)
% 0.27/0.49 thf(fact_231_trm_Odistinct_I27_J,axiom,
% 0.27/0.49 ! [X32: char,X61: trm,X62: trm] :
% 0.27/0.49 ( ( const @ X32 )
% 0.27/0.49 != ( times @ X61 @ X62 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(27)
% 0.27/0.49 thf(fact_232_trm_Odistinct_I29_J,axiom,
% 0.27/0.49 ! [X32: char,X7: trm] :
% 0.27/0.49 ( ( const @ X32 )
% 0.27/0.49 != ( differential @ X7 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(29)
% 0.27/0.49 thf(fact_233_trm_Odistinct_I41_J,axiom,
% 0.27/0.49 ! [X61: trm,X62: trm,X7: trm] :
% 0.27/0.49 ( ( times @ X61 @ X62 )
% 0.27/0.49 != ( differential @ X7 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(41)
% 0.27/0.49 thf(fact_234_trm_Odistinct_I39_J,axiom,
% 0.27/0.49 ! [X51: trm,X52: trm,X7: trm] :
% 0.27/0.49 ( ( plus @ X51 @ X52 )
% 0.27/0.49 != ( differential @ X7 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(39)
% 0.27/0.49 thf(fact_235_trm_Odistinct_I37_J,axiom,
% 0.27/0.49 ! [X51: trm,X52: trm,X61: trm,X62: trm] :
% 0.27/0.49 ( ( plus @ X51 @ X52 )
% 0.27/0.49 != ( times @ X61 @ X62 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(37)
% 0.27/0.49 thf(fact_236_trm_Odistinct_I31_J,axiom,
% 0.27/0.49 ! [X41: char,X42: trm,X51: trm,X52: trm] :
% 0.27/0.49 ( ( func @ X41 @ X42 )
% 0.27/0.49 != ( plus @ X51 @ X52 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(31)
% 0.27/0.49 thf(fact_237_trm_Odistinct_I33_J,axiom,
% 0.27/0.49 ! [X41: char,X42: trm,X61: trm,X62: trm] :
% 0.27/0.49 ( ( func @ X41 @ X42 )
% 0.27/0.49 != ( times @ X61 @ X62 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(33)
% 0.27/0.49 thf(fact_238_trm_Odistinct_I35_J,axiom,
% 0.27/0.49 ! [X41: char,X42: trm,X7: trm] :
% 0.27/0.49 ( ( func @ X41 @ X42 )
% 0.27/0.49 != ( differential @ X7 ) ) ).
% 0.27/0.49
% 0.27/0.49 % trm.distinct(35)
% 0.27/0.49 thf(fact_239_usubstappt_Ocases,axiom,
% 0.27/0.49 ! [X2: product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm )] :
% 0.27/0.49 ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,X3: variable] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( var @ X3 ) ) ) )
% 0.27/0.49 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,R3: real] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( number @ R3 ) ) ) )
% 0.27/0.49 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F6: char] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( const @ F6 ) ) ) )
% 0.27/0.49 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F6: char,Theta2: trm] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( func @ F6 @ Theta2 ) ) ) )
% 0.27/0.49 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm,Eta: trm] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( plus @ Theta2 @ Eta ) ) ) )
% 0.27/0.49 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm,Eta: trm] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( times @ Theta2 @ Eta ) ) ) )
% 0.27/0.49 => ~ ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm] :
% 0.27/0.49 ( X2
% 0.27/0.49 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( differential @ Theta2 ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt.cases
% 0.27/0.49 thf(fact_240_usubstappt__times__conv,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,Eta2: trm] :
% 0.27/0.49 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( times @ Theta @ Eta2 ) )
% 0.27/0.49 != ( none @ trm ) )
% 0.27/0.49 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.27/0.49 != ( none @ trm ) )
% 0.27/0.49 & ( ( uSubst95898992stappt @ Sigma @ U @ Eta2 )
% 0.27/0.49 != ( none @ trm ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt_times_conv
% 0.27/0.49 thf(fact_241_usubstappt__plus__conv,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,Eta2: trm] :
% 0.27/0.49 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( plus @ Theta @ Eta2 ) )
% 0.27/0.49 != ( none @ trm ) )
% 0.27/0.49 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 0.27/0.49 != ( none @ trm ) )
% 0.27/0.49 & ( ( uSubst95898992stappt @ Sigma @ U @ Eta2 )
% 0.27/0.49 != ( none @ trm ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt_plus_conv
% 0.27/0.49 thf(fact_242_usubstappt__differential__conv,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm] :
% 0.27/0.49 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( differential @ Theta ) )
% 0.27/0.49 != ( none @ trm ) )
% 0.27/0.49 => ( ( uSubst95898992stappt @ Sigma
% 0.27/0.49 @ ( collect @ variable
% 0.27/0.49 @ ^ [X: variable] : $true )
% 0.27/0.49 @ Theta )
% 0.27/0.49 != ( none @ trm ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt_differential_conv
% 0.27/0.49 thf(fact_243_usubstappt__induct,axiom,
% 0.27/0.49 ! [P2: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > trm > $o,A0: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),A1: set @ variable,A22: trm] :
% 0.27/0.49 ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,X3: variable] : ( P2 @ Sigma3 @ U3 @ ( var @ X3 ) )
% 0.27/0.49 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,R3: real] : ( P2 @ Sigma3 @ U3 @ ( number @ R3 ) )
% 0.27/0.49 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F6: char] : ( P2 @ Sigma3 @ U3 @ ( const @ F6 ) )
% 0.27/0.49 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F6: char,Theta2: trm] :
% 0.27/0.49 ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 0.27/0.49 => ( ! [X25: trm] :
% 0.27/0.49 ( ( ( uSubst95898992stappt @ Sigma3 @ U3 @ Theta2 )
% 0.27/0.49 = ( some @ trm @ X25 ) )
% 0.27/0.49 => ! [X2a: trm] :
% 0.27/0.49 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [F4: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 0.27/0.49 @ Sigma3
% 0.27/0.49 @ F6 )
% 0.27/0.49 = ( some @ trm @ X2a ) )
% 0.27/0.49 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ X2a ) @ U3 )
% 0.27/0.49 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.49 => ( P2 @ ( uSubst969145931substt @ X25 ) @ ( bot_bot @ ( set @ variable ) ) @ X2a ) ) ) )
% 0.27/0.49 => ( P2 @ Sigma3 @ U3 @ ( func @ F6 @ Theta2 ) ) ) )
% 0.27/0.49 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm] :
% 0.27/0.49 ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 0.27/0.49 => ! [Eta: trm] :
% 0.27/0.49 ( ( P2 @ Sigma3 @ U3 @ Eta )
% 0.27/0.49 => ( P2 @ Sigma3 @ U3 @ ( plus @ Theta2 @ Eta ) ) ) )
% 0.27/0.49 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm] :
% 0.27/0.49 ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 0.27/0.49 => ! [Eta: trm] :
% 0.27/0.49 ( ( P2 @ Sigma3 @ U3 @ Eta )
% 0.27/0.49 => ( P2 @ Sigma3 @ U3 @ ( times @ Theta2 @ Eta ) ) ) )
% 0.27/0.49 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm] :
% 0.27/0.49 ( ( P2 @ Sigma3
% 0.27/0.49 @ ( collect @ variable
% 0.27/0.49 @ ^ [X: variable] : $true )
% 0.27/0.49 @ Theta2 )
% 0.27/0.49 => ( P2 @ Sigma3 @ U3 @ ( differential @ Theta2 ) ) )
% 0.27/0.49 => ( P2 @ A0 @ A1 @ A22 ) ) ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt_induct
% 0.27/0.49 thf(fact_244_dot__def,axiom,
% 0.27/0.49 ( uSubst_Mirabelle_dot
% 0.27/0.49 = ( const @ ( char2 @ $false @ $true @ $true @ $true @ $false @ $true @ $false @ $false ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % dot_def
% 0.27/0.49 thf(fact_245_usubstappt_Opelims,axiom,
% 0.27/0.49 ! [X2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),Xa: set @ variable,Xb: trm,Y2: option @ trm] :
% 0.27/0.49 ( ( ( uSubst95898992stappt @ X2 @ Xa @ Xb )
% 0.27/0.49 = Y2 )
% 0.27/0.49 => ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ X2 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ Xb ) ) )
% 0.27/0.49 => ( ! [X3: variable] :
% 0.27/0.49 ( ( Xb
% 0.27/0.49 = ( var @ X3 ) )
% 0.27/0.49 => ( ( Y2
% 0.27/0.49 = ( some @ trm @ ( var @ X3 ) ) )
% 0.27/0.49 => ~ ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ X2 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( var @ X3 ) ) ) ) ) )
% 0.27/0.49 => ( ! [R3: real] :
% 0.27/0.49 ( ( Xb
% 0.27/0.49 = ( number @ R3 ) )
% 0.27/0.49 => ( ( Y2
% 0.27/0.49 = ( some @ trm @ ( number @ R3 ) ) )
% 0.27/0.49 => ~ ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ X2 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( number @ R3 ) ) ) ) ) )
% 0.27/0.49 => ( ! [F6: char] :
% 0.27/0.49 ( ( Xb
% 0.27/0.49 = ( const @ F6 ) )
% 0.27/0.49 => ( ( Y2
% 0.27/0.49 = ( uSubst1138577137pconst @ X2 @ Xa @ F6 ) )
% 0.27/0.49 => ~ ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ X2 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( const @ F6 ) ) ) ) ) )
% 0.27/0.49 => ( ! [F6: char,Theta2: trm] :
% 0.27/0.49 ( ( Xb
% 0.27/0.49 = ( func @ F6 @ Theta2 ) )
% 0.27/0.49 => ( ( Y2
% 0.27/0.49 = ( case_option @ ( option @ trm ) @ trm @ ( none @ trm )
% 0.27/0.49 @ ^ [Sigma_theta: trm] :
% 0.27/0.49 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( func @ F6 @ Sigma_theta ) )
% 0.27/0.49 @ ^ [R: trm] :
% 0.27/0.49 ( if @ ( option @ trm )
% 0.27/0.49 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R ) @ Xa )
% 0.27/0.49 = ( bot_bot @ ( set @ variable ) ) )
% 0.27/0.49 @ ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta ) @ ( bot_bot @ ( set @ variable ) ) @ R )
% 0.27/0.49 @ ( none @ trm ) )
% 0.27/0.49 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [F4: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 0.27/0.49 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 0.27/0.49 @ X2
% 0.27/0.49 @ F6 ) )
% 0.27/0.49 @ ( uSubst95898992stappt @ X2 @ Xa @ Theta2 ) ) )
% 0.27/0.49 => ~ ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ X2 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( func @ F6 @ Theta2 ) ) ) ) ) )
% 0.27/0.49 => ( ! [Theta2: trm,Eta: trm] :
% 0.27/0.49 ( ( Xb
% 0.27/0.49 = ( plus @ Theta2 @ Eta ) )
% 0.27/0.49 => ( ( Y2
% 0.27/0.49 = ( uSubst1112714340_Pluso @ ( uSubst95898992stappt @ X2 @ Xa @ Theta2 ) @ ( uSubst95898992stappt @ X2 @ Xa @ Eta ) ) )
% 0.27/0.49 => ~ ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ X2 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( plus @ Theta2 @ Eta ) ) ) ) ) )
% 0.27/0.49 => ( ! [Theta2: trm,Eta: trm] :
% 0.27/0.49 ( ( Xb
% 0.27/0.49 = ( times @ Theta2 @ Eta ) )
% 0.27/0.49 => ( ( Y2
% 0.27/0.49 = ( uSubst277968634Timeso @ ( uSubst95898992stappt @ X2 @ Xa @ Theta2 ) @ ( uSubst95898992stappt @ X2 @ Xa @ Eta ) ) )
% 0.27/0.49 => ~ ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ X2 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( times @ Theta2 @ Eta ) ) ) ) ) )
% 0.27/0.49 => ~ ! [Theta2: trm] :
% 0.27/0.49 ( ( Xb
% 0.27/0.49 = ( differential @ Theta2 ) )
% 0.27/0.49 => ( ( Y2
% 0.27/0.49 = ( uSubst259074819ntialo
% 0.27/0.49 @ ( uSubst95898992stappt @ X2
% 0.27/0.49 @ ( collect @ variable
% 0.27/0.49 @ ^ [X: variable] : $true )
% 0.27/0.49 @ Theta2 ) ) )
% 0.27/0.49 => ~ ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ X2 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( differential @ Theta2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt.pelims
% 0.27/0.49 thf(fact_246_Differentialo_Osimps_I2_J,axiom,
% 0.27/0.49 ( ( uSubst259074819ntialo @ ( none @ trm ) )
% 0.27/0.49 = ( none @ trm ) ) ).
% 0.27/0.49
% 0.27/0.49 % Differentialo.simps(2)
% 0.27/0.49 thf(fact_247_Differentialo__undef,axiom,
% 0.27/0.49 ! [Theta: option @ trm] :
% 0.27/0.49 ( ( ( uSubst259074819ntialo @ Theta )
% 0.27/0.49 = ( none @ trm ) )
% 0.27/0.49 = ( Theta
% 0.27/0.49 = ( none @ trm ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Differentialo_undef
% 0.27/0.49 thf(fact_248_Pluso_Osimps_I2_J,axiom,
% 0.27/0.49 ! [Eta2: option @ trm] :
% 0.27/0.49 ( ( uSubst1112714340_Pluso @ ( none @ trm ) @ Eta2 )
% 0.27/0.49 = ( none @ trm ) ) ).
% 0.27/0.49
% 0.27/0.49 % Pluso.simps(2)
% 0.27/0.49 thf(fact_249_Timeso_Osimps_I2_J,axiom,
% 0.27/0.49 ! [Eta2: option @ trm] :
% 0.27/0.49 ( ( uSubst277968634Timeso @ ( none @ trm ) @ Eta2 )
% 0.27/0.49 = ( none @ trm ) ) ).
% 0.27/0.49
% 0.27/0.49 % Timeso.simps(2)
% 0.27/0.49 thf(fact_250_Pluso__undef,axiom,
% 0.27/0.49 ! [Theta: option @ trm,Eta2: option @ trm] :
% 0.27/0.49 ( ( ( uSubst1112714340_Pluso @ Theta @ Eta2 )
% 0.27/0.49 = ( none @ trm ) )
% 0.27/0.49 = ( ( Theta
% 0.27/0.49 = ( none @ trm ) )
% 0.27/0.49 | ( Eta2
% 0.27/0.49 = ( none @ trm ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Pluso_undef
% 0.27/0.49 thf(fact_251_Timeso__undef,axiom,
% 0.27/0.49 ! [Theta: option @ trm,Eta2: option @ trm] :
% 0.27/0.49 ( ( ( uSubst277968634Timeso @ Theta @ Eta2 )
% 0.27/0.49 = ( none @ trm ) )
% 0.27/0.49 = ( ( Theta
% 0.27/0.49 = ( none @ trm ) )
% 0.27/0.49 | ( Eta2
% 0.27/0.49 = ( none @ trm ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Timeso_undef
% 0.27/0.49 thf(fact_252_Pluso_Osimps_I3_J,axiom,
% 0.27/0.49 ! [V3: trm] :
% 0.27/0.49 ( ( uSubst1112714340_Pluso @ ( some @ trm @ V3 ) @ ( none @ trm ) )
% 0.27/0.49 = ( none @ trm ) ) ).
% 0.27/0.49
% 0.27/0.49 % Pluso.simps(3)
% 0.27/0.49 thf(fact_253_Timeso_Osimps_I3_J,axiom,
% 0.27/0.49 ! [V3: trm] :
% 0.27/0.49 ( ( uSubst277968634Timeso @ ( some @ trm @ V3 ) @ ( none @ trm ) )
% 0.27/0.49 = ( none @ trm ) ) ).
% 0.27/0.49
% 0.27/0.49 % Timeso.simps(3)
% 0.27/0.49 thf(fact_254_usubstappt_Osimps_I5_J,axiom,
% 0.27/0.49 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,Eta2: trm] :
% 0.27/0.49 ( ( uSubst95898992stappt @ Sigma @ U @ ( plus @ Theta @ Eta2 ) )
% 0.27/0.49 = ( uSubst1112714340_Pluso @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) @ ( uSubst95898992stappt @ Sigma @ U @ Eta2 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % usubstappt.simps(5)
% 0.27/0.49
% 0.27/0.49 % Type constructors (17)
% 0.27/0.49 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.27/0.49 bounded_lattice @ $o ).
% 0.27/0.49
% 0.27/0.49 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.27/0.49 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.27/0.49 ! [A8: $tType,A9: $tType] :
% 0.27/0.49 ( ( bounded_lattice @ A9 )
% 0.27/0.49 => ( bounded_lattice @ ( A8 > A9 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 0.27/0.49 ! [A8: $tType,A9: $tType] :
% 0.27/0.49 ( ( bounded_lattice @ A9 )
% 0.27/0.49 => ( bounded_lattice_bot @ ( A8 > A9 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 0.27/0.49 ! [A8: $tType,A9: $tType] :
% 0.27/0.49 ( ( semilattice_inf @ A9 )
% 0.27/0.49 => ( semilattice_inf @ ( A8 > A9 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.27/0.49 ! [A8: $tType,A9: $tType] :
% 0.27/0.49 ( ( lattice @ A9 )
% 0.27/0.49 => ( lattice @ ( A8 > A9 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(tcon_fun___Orderings_Obot,axiom,
% 0.27/0.49 ! [A8: $tType,A9: $tType] :
% 0.27/0.49 ( ( bot @ A9 )
% 0.27/0.49 => ( bot @ ( A8 > A9 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_3,axiom,
% 0.27/0.49 ! [A8: $tType] : ( bounded_lattice_bot @ ( set @ A8 ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_4,axiom,
% 0.27/0.49 ! [A8: $tType] : ( semilattice_inf @ ( set @ A8 ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(tcon_Set_Oset___Lattices_Olattice_5,axiom,
% 0.27/0.49 ! [A8: $tType] : ( lattice @ ( set @ A8 ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(tcon_Set_Oset___Orderings_Obot_6,axiom,
% 0.27/0.49 ! [A8: $tType] : ( bot @ ( set @ A8 ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_7,axiom,
% 0.27/0.49 bounded_lattice_bot @ $o ).
% 0.27/0.49
% 0.27/0.49 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_8,axiom,
% 0.27/0.49 semilattice_inf @ $o ).
% 0.27/0.49
% 0.27/0.49 thf(tcon_HOL_Obool___Lattices_Olattice_9,axiom,
% 0.27/0.49 lattice @ $o ).
% 0.27/0.49
% 0.27/0.49 thf(tcon_HOL_Obool___Orderings_Obot_10,axiom,
% 0.27/0.49 bot @ $o ).
% 0.27/0.49
% 0.27/0.49 thf(tcon_Real_Oreal___Lattices_Osemilattice__inf_11,axiom,
% 0.27/0.49 semilattice_inf @ real ).
% 0.27/0.49
% 0.27/0.49 thf(tcon_Real_Oreal___Lattices_Olattice_12,axiom,
% 0.27/0.49 lattice @ real ).
% 0.27/0.49
% 0.27/0.49 % Helper facts (3)
% 0.27/0.49 thf(help_If_3_1_T,axiom,
% 0.27/0.49 ! [P2: $o] :
% 0.27/0.49 ( ( P2 = $true )
% 0.27/0.49 | ( P2 = $false ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(help_If_2_1_T,axiom,
% 0.27/0.49 ! [A: $tType,X2: A,Y2: A] :
% 0.27/0.49 ( ( if @ A @ $false @ X2 @ Y2 )
% 0.27/0.49 = Y2 ) ).
% 0.27/0.49
% 0.27/0.49 thf(help_If_1_1_T,axiom,
% 0.27/0.49 ! [A: $tType,X2: A,Y2: A] :
% 0.27/0.49 ( ( if @ A @ $true @ X2 @ Y2 )
% 0.27/0.49 = X2 ) ).
% 0.27/0.49
% 0.27/0.49 % Conjectures (1)
% 0.27/0.49 thf(conj_0,conjecture,
% 0.27/0.49 ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.49 @ ^ [Uu: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 0.27/0.49 @ ^ [Uv: char > ( option @ trm )] :
% 0.27/0.49 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 0.27/0.49 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 0.27/0.49 @ sigma
% 0.27/0.49 @ p )
% 0.27/0.49 = ( none @ fml ) ) ).
% 0.27/0.49
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 ------------------------
% 2.81/1.58 ---- Embedded in THF ---
% 2.81/1.58 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.81/1.58 %%% Generated on Tue Feb 24 08:30:08 EST 2026
% 2.81/1.58 %%% using '$$dhol' embedding, version 1.3.0.
% 2.81/1.58 %%% Logic specification used:
% 2.81/1.58 %%% thf(spec, logic, $$dhol).
% 2.81/1.58
% 2.81/1.58 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.oidpnoGwex/DTF2DTF3332.p
% 2.81/1.58 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.81/1.58 thf(ty_t_Syntax_Ovariable, type, variable: $tType).
% 2.81/1.58 thf(ty_t_Option_Ooption, type, option: ($tType > $tType)).
% 2.81/1.58 thf(ty_t_Syntax_Ogame, type, game: $tType).
% 2.81/1.58 thf(ty_t_String_Ochar, type, char: $tType).
% 2.81/1.58 thf(ty_t_Syntax_Otrm, type, trm: $tType).
% 2.81/1.58 thf(ty_t_Syntax_Ofml, type, fml: $tType).
% 2.81/1.58 thf(ty_t_Real_Oreal, type, real: $tType).
% 2.81/1.58 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.81/1.58 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: ($o))).
% 2.81/1.58 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.81/1.58 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: ($o))).
% 2.81/1.58 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: ($o))).
% 2.81/1.58 thf(sy_cl_Lattices_Osemilattice__inf, type, semilattice_inf: (!> [A:$tType]: ($o))).
% 2.81/1.58 thf(sy_cl_Lattices_Obounded__lattice__bot, type, bounded_lattice_bot: (!> [A:$tType]: ($o))).
% 2.81/1.58 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.81/1.58 thf(sy_c_Lattices_Oinf__class_Oinf, type, inf_inf: (!> [A:$tType]: ((A > (A > A))))).
% 2.81/1.58 thf(sy_c_Option_Ooption_ONone, type, none: (!> [A:$tType]: ((option @ A)))).
% 2.81/1.58 thf(sy_c_Option_Ooption_OSome, type, some: (!> [A:$tType]: ((A > (option @ A))))).
% 2.81/1.58 thf(sy_c_Option_Ooption_Ocase__option, type, case_option: (!> [B:$tType,A:$tType]: ((B > ((A > B) > ((option @ A) > B)))))).
% 2.81/1.58 thf(sy_c_Option_Ooption_Othe, type, the: (!> [A:$tType]: (((option @ A) > A)))).
% 2.81/1.58 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.81/1.58 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.81/1.58 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 2.81/1.58 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 2.81/1.58 thf(sy_c_Product__Type_Oprod_Ocase__prod, type, product_case_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 2.81/1.58 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.81/1.58 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.81/1.58 thf(sy_c_Static__Semantics_OFVF, type, static_FVF: (fml > (set @ variable))).
% 2.81/1.58 thf(sy_c_Static__Semantics_OFVT, type, static_FVT: (trm > (set @ variable))).
% 2.81/1.58 thf(sy_c_String_Ochar_OChar, type, char2: ($o > ($o > ($o > ($o > ($o > ($o > ($o > ($o > char))))))))).
% 2.81/1.58 thf(sy_c_Syntax_Ofml_OGeq, type, geq: (trm > (trm > fml))).
% 2.81/1.58 thf(sy_c_Syntax_Ofml_OPred, type, pred: (char > (trm > fml))).
% 2.81/1.58 thf(sy_c_Syntax_Otrm_OConst, type, const: (char > trm)).
% 2.81/1.58 thf(sy_c_Syntax_Otrm_ODifferential, type, differential: (trm > trm)).
% 2.81/1.58 thf(sy_c_Syntax_Otrm_OFunc, type, func: (char > (trm > trm))).
% 2.81/1.58 thf(sy_c_Syntax_Otrm_ONumber, type, number: (real > trm)).
% 2.81/1.58 thf(sy_c_Syntax_Otrm_OPlus, type, plus: (trm > (trm > trm))).
% 2.81/1.58 thf(sy_c_Syntax_Otrm_OTimes, type, times: (trm > (trm > trm))).
% 2.81/1.58 thf(sy_c_Syntax_Otrm_OVar, type, var: (variable > trm)).
% 2.81/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_ODifferentialo, type, uSubst259074819ntialo: ((option @ trm) > (option @ trm))).
% 2.81/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OGeqo, type, uSubst1556497037e_Geqo: ((option @ trm) > ((option @ trm) > (option @ fml)))).
% 2.81/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OPluso, type, uSubst1112714340_Pluso: ((option @ trm) > ((option @ trm) > (option @ trm)))).
% 2.81/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTesto, type, uSubst190403692_Testo: ((option @ fml) > (option @ game))).
% 2.81/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTimeso, type, uSubst277968634Timeso: ((option @ trm) > ((option @ trm) > (option @ trm)))).
% 2.81/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Odot, type, uSubst_Mirabelle_dot: trm).
% 2.81/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Odotsubstt, type, uSubst969145931substt: (trm > ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))))).
% 2.81/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousappconst, type, uSubst1138577137pconst: (((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) > ((set @ variable) > (char > (option @ trm))))).
% 2.81/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappf, type, uSubst95898978stappf: (((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) > ((set @ variable) > (fml > (option @ fml))))).
% 2.81/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappt, type, uSubst95898992stappt: (((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) > ((set @ variable) > (trm > (option @ trm))))).
% 2.81/1.58 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappt__rel, type, uSubst2096773001pt_rel: (((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) > (((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) > $o))).
% 2.81/1.58 thf(sy_c_Wellfounded_Oaccp, type, accp: (!> [A:$tType]: (((A > (A > $o)) > (A > $o))))).
% 2.81/1.58 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.81/1.58 thf(sy_v_Ua____, type, ua: (set @ variable)).
% 2.81/1.58 thf(sy_v_Va____, type, va: (set @ variable)).
% 2.81/1.58 thf(sy_v__092_060sigma_062, type, sigma: ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))).
% 2.81/1.58 thf(sy_v__092_060theta_062____, type, theta: trm).
% 2.81/1.58 thf(sy_v_p____, type, p: char).
% 2.81/1.58 thf(fact_0_f7, axiom, (! [Z:(option @ fml),F:(fml > (option @ fml)),Za:(option @ fml)]: ((((Za = (none @ fml)) => ((((((case_option @ (option @ fml)) @ fml) @ Z) @ F) @ Za) = Z)) & ((Za != (none @ fml)) => ((((((case_option @ (option @ fml)) @ fml) @ Z) @ F) @ Za) = (F @ ((the @ fml) @ Za)))))))).
% 2.81/1.58 thf(fact_1_Pred_Oprems_I2_J, axiom, ((((uSubst95898978stappf @ sigma) @ va) @ ((pred @ p) @ theta)) != (none @ fml))).
% 2.81/1.58 thf(fact_2_case__prod__app, axiom, (! [A:$tType,D:$tType,C:$tType,B:$tType]: (((((product_case_prod @ B) @ C) @ (D > A)) = (^ [F2:(B > (C > (D > A))),X:((product_prod @ B) @ C),Y:D]: ((((((product_case_prod @ B) @ C) @ A) @ (^ [L:B,R:C]: ((((F2 @ L) @ R) @ Y)))) @ X))))))).
% 2.81/1.58 thf(fact_3_Pred_Oprems_I1_J, axiom, ((((uSubst95898978stappf @ sigma) @ ua) @ ((pred @ p) @ theta)) != (none @ fml))).
% 2.81/1.58 thf(fact_4__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_092_060close_062, axiom, (~ ((((((inf_inf @ (set @ variable)) @ (static_FVF @ ((the @ fml) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))) @ va) != (bot_bot @ (set @ variable))) => ((none @ fml) = (((uSubst95898978stappf @ (uSubst969145931substt @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ va) @ theta)))) @ (bot_bot @ (set @ variable))) @ ((the @ fml) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))))))).
% 2.81/1.58 thf(fact_5_f9, axiom, ((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p) = (none @ fml)) => ((((uSubst95898978stappf @ sigma) @ ua) @ ((pred @ p) @ theta)) = (((uSubst95898978stappf @ sigma) @ va) @ ((pred @ p) @ theta))))).
% 2.81/1.58 thf(fact_6__092_060open_062_Icase_ASPreds_A_092_060sigma_062_Ap_Aof_ANone_A_092_060Rightarrow_062_AAfml_A_IPred_Ap_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_124_ASome_Af_A_092_060Rightarrow_062_Aif_AFVF_Af_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_Af_Aelse_Aundeff_J_A_092_060noteq_062_A_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_092_060close_062, axiom, (~ (((((((inf_inf @ (set @ variable)) @ (static_FVF @ ((the @ fml) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))) @ va) = (bot_bot @ (set @ variable))) => ((((((case_option @ (option @ fml)) @ fml) @ ((some @ fml) @ ((pred @ p) @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ va) @ theta))))) @ (^ [F2:fml]: (((((if @ (option @ fml)) @ ((((inf_inf @ (set @ variable)) @ (static_FVF @ F2)) @ va) = (bot_bot @ (set @ variable)))) @ (((uSubst95898978stappf @ (uSubst969145931substt @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ va) @ theta)))) @ (bot_bot @ (set @ variable))) @ F2)) @ (none @ fml))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)) = (((uSubst95898978stappf @ (uSubst969145931substt @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ va) @ theta)))) @ (bot_bot @ (set @ variable))) @ ((the @ fml) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p))))) & (((((inf_inf @ (set @ variable)) @ (static_FVF @ ((the @ fml) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))) @ va) != (bot_bot @ (set @ variable))) => ((((((case_option @ (option @ fml)) @ fml) @ ((some @ fml) @ ((pred @ p) @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ va) @ theta))))) @ (^ [F2:fml]: (((((if @ (option @ fml)) @ ((((inf_inf @ (set @ variable)) @ (static_FVF @ F2)) @ va) = (bot_bot @ (set @ variable)))) @ (((uSubst95898978stappf @ (uSubst969145931substt @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ va) @ theta)))) @ (bot_bot @ (set @ variable))) @ F2)) @ (none @ fml))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)) = (none @ fml))))))).
% 2.81/1.58 thf(fact_7_Ando_Oinduct, axiom, (! [P2:((option @ fml) > ((option @ fml) > $o)),A0:(option @ fml),A1:(option @ fml)]: (((! [Phi:fml,Psi:fml]: (((P2 @ ((some @ fml) @ Phi)) @ ((some @ fml) @ Psi)))) => ((! [X_1:(option @ fml)]: (((P2 @ (none @ fml)) @ X_1))) => ((! [V:fml]: (((P2 @ ((some @ fml) @ V)) @ (none @ fml)))) => ((P2 @ A0) @ A1))))))).
% 2.81/1.58 thf(fact_8_Testo_Ocases, axiom, (! [X2:(option @ fml)]: (((! [Phi:fml]: ((X2 != ((some @ fml) @ Phi)))) => (X2 = (none @ fml)))))).
% 2.81/1.58 thf(fact_9_Testo_Oinduct, axiom, (! [P2:((option @ fml) > $o),A0:(option @ fml)]: (((! [Phi:fml]: ((P2 @ ((some @ fml) @ Phi)))) => ((P2 @ (none @ fml)) => (P2 @ A0)))))).
% 2.81/1.58 thf(fact_10_undeff__equiv, axiom, (! [Phi2:(option @ fml)]: (((Phi2 != (none @ fml)) = (? [F2:fml]: ((Phi2 = ((some @ fml) @ F2)))))))).
% 2.81/1.58 thf(fact_11_Existso_Oinduct, axiom, (! [P2:(variable > ((option @ fml) > $o)),A0:variable,A1:(option @ fml)]: (((! [X3:variable,Phi:fml]: (((P2 @ X3) @ ((some @ fml) @ Phi)))) => ((! [X3:variable]: (((P2 @ X3) @ (none @ fml)))) => ((P2 @ A0) @ A1)))))).
% 2.81/1.58 thf(fact_12_prod_Ocase__distrib, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,H:(C > D),F3:(A > (B > C)),Prod:((product_prod @ A) @ B)]: (((H @ (((((product_case_prod @ A) @ B) @ C) @ F3) @ Prod)) = (((((product_case_prod @ A) @ B) @ D) @ (^ [X1:A,X22:B]: ((H @ ((F3 @ X1) @ X22))))) @ Prod))))).
% 2.81/1.58 thf(fact_13__092_060open_062usubstappf_A_092_060sigma_062_AU_A_IPred_Ap_A_092_060theta_062_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_092_060close_062, axiom, ((((uSubst95898978stappf @ sigma) @ ua) @ ((pred @ p) @ theta)) != (((uSubst95898978stappf @ sigma) @ va) @ ((pred @ p) @ theta)))).
% 2.81/1.58 thf(fact_14_f5, axiom, ((((uSubst95898992stappt @ sigma) @ ua) @ theta) = (((uSubst95898992stappt @ sigma) @ va) @ theta))).
% 2.81/1.58 thf(fact_15_calculation_I1_J, axiom, (~ (((((((inf_inf @ (set @ variable)) @ (static_FVF @ ((the @ fml) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))) @ va) = (bot_bot @ (set @ variable))) => ((((uSubst95898978stappf @ sigma) @ ua) @ ((pred @ p) @ theta)) = (((uSubst95898978stappf @ (uSubst969145931substt @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ va) @ theta)))) @ (bot_bot @ (set @ variable))) @ ((the @ fml) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p))))) & (((((inf_inf @ (set @ variable)) @ (static_FVF @ ((the @ fml) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))) @ va) != (bot_bot @ (set @ variable))) => ((((uSubst95898978stappf @ sigma) @ ua) @ ((pred @ p) @ theta)) = (none @ fml))))))).
% 2.81/1.58 thf(fact_16_calculation_I2_J, axiom, (((((uSubst95898978stappf @ sigma) @ ua) @ ((pred @ p) @ theta)) != (((uSubst95898978stappf @ (uSubst969145931substt @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ va) @ theta)))) @ (bot_bot @ (set @ variable))) @ ((the @ fml) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))) => (((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p) = (none @ fml)))).
% 2.81/1.58 thf(fact_17_f6, axiom, ((((uSubst95898978stappf @ sigma) @ ua) @ ((pred @ p) @ theta)) = (((((case_option @ (option @ fml)) @ fml) @ ((some @ fml) @ ((pred @ p) @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ va) @ theta))))) @ (^ [F2:fml]: (((((if @ (option @ fml)) @ ((((inf_inf @ (set @ variable)) @ (static_FVF @ F2)) @ ua) = (bot_bot @ (set @ variable)))) @ (((uSubst95898978stappf @ (uSubst969145931substt @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ va) @ theta)))) @ (bot_bot @ (set @ variable))) @ F2)) @ (none @ fml))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))).
% 2.81/1.58 thf(fact_18__092_060open_062usubstappf_A_092_060sigma_062_AU_A_IPred_Ap_A_092_060theta_062_J_A_092_060noteq_062_A_Icase_ASPreds_A_092_060sigma_062_Ap_Aof_ANone_A_092_060Rightarrow_062_AAfml_A_IPred_Ap_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_124_ASome_Af_A_092_060Rightarrow_062_Aif_AFVF_Af_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_Af_Aelse_Aundeff_J_092_060close_062, axiom, ((((uSubst95898978stappf @ sigma) @ ua) @ ((pred @ p) @ theta)) != (((((case_option @ (option @ fml)) @ fml) @ ((some @ fml) @ ((pred @ p) @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ va) @ theta))))) @ (^ [F2:fml]: (((((if @ (option @ fml)) @ ((((inf_inf @ (set @ variable)) @ (static_FVF @ F2)) @ va) = (bot_bot @ (set @ variable)))) @ (((uSubst95898978stappf @ (uSubst969145931substt @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ va) @ theta)))) @ (bot_bot @ (set @ variable))) @ F2)) @ (none @ fml))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))).
% 2.81/1.58 thf(fact_19_usubstappf__pred2, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),P3:char,R2:fml,U:(set @ variable),Theta:trm]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ Sigma) @ P3) = ((some @ fml) @ R2)) => (((((inf_inf @ (set @ variable)) @ (static_FVF @ R2)) @ U) != (bot_bot @ (set @ variable))) => ((((uSubst95898978stappf @ Sigma) @ U) @ ((pred @ P3) @ Theta)) = (none @ fml))))))).
% 2.81/1.58 thf(fact_20_f3, axiom, ((((((case_option @ (option @ fml)) @ trm) @ (none @ fml)) @ (^ [T2:trm]: ((((((case_option @ (option @ fml)) @ fml) @ ((some @ fml) @ ((pred @ p) @ T2))) @ (^ [F2:fml]: (((((if @ (option @ fml)) @ ((((inf_inf @ (set @ variable)) @ (static_FVF @ F2)) @ ua) = (bot_bot @ (set @ variable)))) @ (((uSubst95898978stappf @ (uSubst969145931substt @ T2)) @ (bot_bot @ (set @ variable))) @ F2)) @ (none @ fml))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p))))) @ (((uSubst95898992stappt @ sigma) @ ua) @ theta)) = (((((case_option @ (option @ fml)) @ fml) @ ((some @ fml) @ ((pred @ p) @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ ua) @ theta))))) @ (^ [F2:fml]: (((((if @ (option @ fml)) @ ((((inf_inf @ (set @ variable)) @ (static_FVF @ F2)) @ ua) = (bot_bot @ (set @ variable)))) @ (((uSubst95898978stappf @ (uSubst969145931substt @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ ua) @ theta)))) @ (bot_bot @ (set @ variable))) @ F2)) @ (none @ fml))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))).
% 2.81/1.58 thf(fact_21_f8, axiom, ((((((case_option @ (option @ fml)) @ trm) @ (none @ fml)) @ (^ [T2:trm]: ((((((case_option @ (option @ fml)) @ fml) @ ((some @ fml) @ ((pred @ p) @ T2))) @ (^ [F2:fml]: (((((if @ (option @ fml)) @ ((((inf_inf @ (set @ variable)) @ (static_FVF @ F2)) @ va) = (bot_bot @ (set @ variable)))) @ (((uSubst95898978stappf @ (uSubst969145931substt @ T2)) @ (bot_bot @ (set @ variable))) @ F2)) @ (none @ fml))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p))))) @ (((uSubst95898992stappt @ sigma) @ va) @ theta)) = (((((case_option @ (option @ fml)) @ fml) @ ((some @ fml) @ ((pred @ p) @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ va) @ theta))))) @ (^ [F2:fml]: (((((if @ (option @ fml)) @ ((((inf_inf @ (set @ variable)) @ (static_FVF @ F2)) @ va) = (bot_bot @ (set @ variable)))) @ (((uSubst95898978stappf @ (uSubst969145931substt @ ((the @ trm) @ (((uSubst95898992stappt @ sigma) @ va) @ theta)))) @ (bot_bot @ (set @ variable))) @ F2)) @ (none @ fml))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p)))).
% 2.81/1.58 thf(fact_22_f1, axiom, ((((((case_option @ (option @ fml)) @ trm) @ (none @ fml)) @ (^ [T2:trm]: ((((((case_option @ (option @ fml)) @ fml) @ ((some @ fml) @ ((pred @ p) @ T2))) @ (^ [F2:fml]: (((((if @ (option @ fml)) @ ((((inf_inf @ (set @ variable)) @ (static_FVF @ F2)) @ ua) = (bot_bot @ (set @ variable)))) @ (((uSubst95898978stappf @ (uSubst969145931substt @ T2)) @ (bot_bot @ (set @ variable))) @ F2)) @ (none @ fml))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p))))) @ (((uSubst95898992stappt @ sigma) @ ua) @ theta)) != (none @ fml))).
% 2.81/1.58 thf(fact_23_f4, axiom, ((((((case_option @ (option @ fml)) @ trm) @ (none @ fml)) @ (^ [T2:trm]: ((((((case_option @ (option @ fml)) @ fml) @ ((some @ fml) @ ((pred @ p) @ T2))) @ (^ [F2:fml]: (((((if @ (option @ fml)) @ ((((inf_inf @ (set @ variable)) @ (static_FVF @ F2)) @ va) = (bot_bot @ (set @ variable)))) @ (((uSubst95898978stappf @ (uSubst969145931substt @ T2)) @ (bot_bot @ (set @ variable))) @ F2)) @ (none @ fml))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p))))) @ (((uSubst95898992stappt @ sigma) @ va) @ theta)) != (none @ fml))).
% 2.81/1.58 thf(fact_24_option_Ocollapse, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) => (((some @ A) @ ((the @ A) @ Option)) = Option))))).
% 2.81/1.58 thf(fact_25_not__Some__eq, axiom, (! [A:$tType,X2:(option @ A)]: (((! [Y:A]: ((X2 != ((some @ A) @ Y)))) = (X2 = (none @ A)))))).
% 2.81/1.58 thf(fact_26_not__None__eq, axiom, (! [A:$tType,X2:(option @ A)]: (((X2 != (none @ A)) = (? [Y:A]: ((X2 = ((some @ A) @ Y)))))))).
% 2.81/1.58 thf(fact_27_usubstappf_Osimps_I1_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),P3:char,Theta:trm]: (((((uSubst95898978stappf @ Sigma) @ U) @ ((pred @ P3) @ Theta)) = (((((case_option @ (option @ fml)) @ trm) @ (none @ fml)) @ (^ [Sigma_theta:trm]: ((((((case_option @ (option @ fml)) @ fml) @ ((some @ fml) @ ((pred @ P3) @ Sigma_theta))) @ (^ [R:fml]: (((((if @ (option @ fml)) @ ((((inf_inf @ (set @ variable)) @ (static_FVF @ R)) @ U) = (bot_bot @ (set @ variable)))) @ (((uSubst95898978stappf @ (uSubst969145931substt @ Sigma_theta)) @ (bot_bot @ (set @ variable))) @ R)) @ (none @ fml))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ Sigma) @ P3))))) @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta)))))).
% 2.81/1.58 thf(fact_28_inf__bot__left, axiom, (! [A:$tType]: (((bounded_lattice_bot @ A) => (! [X2:A]: (((((inf_inf @ A) @ (bot_bot @ A)) @ X2) = (bot_bot @ A)))))))).
% 2.81/1.58 thf(fact_29_inf__bot__right, axiom, (! [A:$tType]: (((bounded_lattice_bot @ A) => (! [X2:A]: (((((inf_inf @ A) @ X2) @ (bot_bot @ A)) = (bot_bot @ A)))))))).
% 2.81/1.58 thf(fact_30_option_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P2:(B > $o),F1:B,F22:(A > B),Option:(option @ A)]: (((P2 @ (((((case_option @ B) @ A) @ F1) @ F22) @ Option)) = (~ ((((Option = (none @ A)) & (~ ((P2 @ F1)))) | ((Option = ((some @ A) @ ((the @ A) @ Option))) & (~ ((P2 @ (F22 @ ((the @ A) @ Option))))))))))))).
% 2.81/1.58 thf(fact_31_f2, axiom, (! [Z:(option @ fml),F:(trm > (option @ fml)),Za:(option @ trm)]: ((((Za = (none @ trm)) => ((((((case_option @ (option @ fml)) @ trm) @ Z) @ F) @ Za) = Z)) & ((Za != (none @ trm)) => ((((((case_option @ (option @ fml)) @ trm) @ Z) @ F) @ Za) = (F @ ((the @ trm) @ Za)))))))).
% 2.81/1.58 thf(fact_32_inf__right__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X2:A,Y2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X2) @ Y2)) @ Y2) = (((inf_inf @ A) @ X2) @ Y2)))))))).
% 2.81/1.58 thf(fact_33_inf_Oright__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ B2) = (((inf_inf @ A) @ A2) @ B2)))))))).
% 2.81/1.58 thf(fact_34_inf__left__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X2:A,Y2:A]: (((((inf_inf @ A) @ X2) @ (((inf_inf @ A) @ X2) @ Y2)) = (((inf_inf @ A) @ X2) @ Y2)))))))).
% 2.81/1.58 thf(fact_35_inf_Oleft__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A]: (((((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ A2) @ B2)) = (((inf_inf @ A) @ A2) @ B2)))))))).
% 2.81/1.58 thf(fact_36_inf__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X2:A]: (((((inf_inf @ A) @ X2) @ X2) = X2))))))).
% 2.81/1.58 thf(fact_37_inf_Oidem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A]: (((((inf_inf @ A) @ A2) @ A2) = A2))))))).
% 2.81/1.58 thf(fact_38_inf__apply, axiom, (! [B:$tType,A:$tType]: (((semilattice_inf @ B) => ((inf_inf @ (A > B)) = (^ [F2:(A > B),G:(A > B),X:A]: ((((inf_inf @ B) @ (F2 @ X)) @ (G @ X))))))))).
% 2.81/1.58 thf(fact_39_option_Oinject, axiom, (! [A:$tType,X23:A,Y22:A]: (((((some @ A) @ X23) = ((some @ A) @ Y22)) = (X23 = Y22))))).
% 2.81/1.58 thf(fact_40_usubstappf__pred, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),P3:char,R2:fml,U:(set @ variable),Theta:trm,Sigma_theta2:trm]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ Sigma) @ P3) = ((some @ fml) @ R2)) => (((((inf_inf @ (set @ variable)) @ (static_FVF @ R2)) @ U) = (bot_bot @ (set @ variable))) => (((((uSubst95898992stappt @ Sigma) @ U) @ Theta) = ((some @ trm) @ Sigma_theta2)) => ((((uSubst95898978stappf @ Sigma) @ U) @ ((pred @ P3) @ Theta)) = (((uSubst95898978stappf @ (uSubst969145931substt @ Sigma_theta2)) @ (bot_bot @ (set @ variable))) @ R2)))))))).
% 2.81/1.58 thf(fact_41_Diamondo_Oinduct, axiom, (! [P2:((option @ game) > ((option @ fml) > $o)),A0:(option @ game),A1:(option @ fml)]: (((! [Alpha:game,Phi:fml]: (((P2 @ ((some @ game) @ Alpha)) @ ((some @ fml) @ Phi)))) => ((! [X_1:(option @ fml)]: (((P2 @ (none @ game)) @ X_1))) => ((! [V:game]: (((P2 @ ((some @ game) @ V)) @ (none @ fml)))) => ((P2 @ A0) @ A1))))))).
% 2.81/1.58 thf(fact_42_option_Odisc__eq__case_I2_J, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) = (((((case_option @ $o) @ A) @ $false) @ (^ [Uu:A]: ($true))) @ Option))))).
% 2.81/1.58 thf(fact_43_option_Odisc__eq__case_I1_J, axiom, (! [A:$tType,Option:(option @ A)]: (((Option = (none @ A)) = (((((case_option @ $o) @ A) @ $true) @ (^ [Uu:A]: ($false))) @ Option))))).
% 2.81/1.58 thf(fact_44_usubstappt__det, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm,V2:(set @ variable)]: ((((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (none @ trm)) => (((((uSubst95898992stappt @ Sigma) @ V2) @ Theta) != (none @ trm)) => ((((uSubst95898992stappt @ Sigma) @ U) @ Theta) = (((uSubst95898992stappt @ Sigma) @ V2) @ Theta))))))).
% 2.81/1.58 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P2:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P2)) = (P2 @ A2))))).
% 2.81/1.58 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A3)))) = A3)))).
% 2.81/1.58 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P2 @ X3) = (Q @ X3)))) => (((collect @ A) @ P2) = ((collect @ A) @ Q)))))).
% 2.81/1.58 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F3:(A > B),G2:(A > B)]: (((! [X3:A]: (((F3 @ X3) = (G2 @ X3)))) => (F3 = G2))))).
% 2.81/1.58 thf(fact_49_case__optionE, axiom, (! [A:$tType,P2:$o,Q:(A > $o),X2:(option @ A)]: (((((((case_option @ $o) @ A) @ P2) @ Q) @ X2) => (((X2 = (none @ A)) => (~ (P2))) => (~ ((! [Y3:A]: (((X2 = ((some @ A) @ Y3)) => (~ ((Q @ Y3))))))))))))).
% 2.81/1.58 thf(fact_50_inf__left__commute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X2:A,Y2:A,Z2:A]: (((((inf_inf @ A) @ X2) @ (((inf_inf @ A) @ Y2) @ Z2)) = (((inf_inf @ A) @ Y2) @ (((inf_inf @ A) @ X2) @ Z2))))))))).
% 2.81/1.58 thf(fact_51_inf_Oleft__commute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [B2:A,A2:A,C2:A]: (((((inf_inf @ A) @ B2) @ (((inf_inf @ A) @ A2) @ C2)) = (((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C2))))))))).
% 2.81/1.58 thf(fact_52_inf__commute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => ((inf_inf @ A) = (^ [X:A,Y:A]: ((((inf_inf @ A) @ Y) @ X)))))))).
% 2.81/1.58 thf(fact_53_inf_Ocommute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => ((inf_inf @ A) = (^ [A4:A,B3:A]: ((((inf_inf @ A) @ B3) @ A4)))))))).
% 2.81/1.58 thf(fact_54_inf__assoc, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X2:A,Y2:A,Z2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X2) @ Y2)) @ Z2) = (((inf_inf @ A) @ X2) @ (((inf_inf @ A) @ Y2) @ Z2))))))))).
% 2.81/1.58 thf(fact_55_inf_Oassoc, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A,C2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ C2) = (((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C2))))))))).
% 2.81/1.58 thf(fact_56_boolean__algebra__cancel_Oinf2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [B4:A,K:A,B2:A,A2:A]: (((B4 = (((inf_inf @ A) @ K) @ B2)) => ((((inf_inf @ A) @ A2) @ B4) = (((inf_inf @ A) @ K) @ (((inf_inf @ A) @ A2) @ B2)))))))))).
% 2.81/1.58 thf(fact_57_boolean__algebra__cancel_Oinf1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A3:A,K:A,A2:A,B2:A]: (((A3 = (((inf_inf @ A) @ K) @ A2)) => ((((inf_inf @ A) @ A3) @ B2) = (((inf_inf @ A) @ K) @ (((inf_inf @ A) @ A2) @ B2)))))))))).
% 2.81/1.58 thf(fact_58_inf__fun__def, axiom, (! [B:$tType,A:$tType]: (((semilattice_inf @ B) => ((inf_inf @ (A > B)) = (^ [F2:(A > B),G:(A > B),X:A]: ((((inf_inf @ B) @ (F2 @ X)) @ (G @ X))))))))).
% 2.81/1.58 thf(fact_59_inf__sup__aci_I1_J, axiom, (! [A:$tType]: (((lattice @ A) => ((inf_inf @ A) = (^ [X:A,Y:A]: ((((inf_inf @ A) @ Y) @ X)))))))).
% 2.81/1.58 thf(fact_60_inf__sup__aci_I2_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X2:A,Y2:A,Z2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X2) @ Y2)) @ Z2) = (((inf_inf @ A) @ X2) @ (((inf_inf @ A) @ Y2) @ Z2))))))))).
% 2.81/1.58 thf(fact_61_inf__sup__aci_I3_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X2:A,Y2:A,Z2:A]: (((((inf_inf @ A) @ X2) @ (((inf_inf @ A) @ Y2) @ Z2)) = (((inf_inf @ A) @ Y2) @ (((inf_inf @ A) @ X2) @ Z2))))))))).
% 2.81/1.58 thf(fact_62_inf__sup__aci_I4_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X2:A,Y2:A]: (((((inf_inf @ A) @ X2) @ (((inf_inf @ A) @ X2) @ Y2)) = (((inf_inf @ A) @ X2) @ Y2)))))))).
% 2.81/1.58 thf(fact_63_option_Ocase__distrib, axiom, (! [C:$tType,B:$tType,A:$tType,H:(B > C),F1:B,F22:(A > B),Option:(option @ A)]: (((H @ (((((case_option @ B) @ A) @ F1) @ F22) @ Option)) = (((((case_option @ C) @ A) @ (H @ F1)) @ (^ [X:A]: ((H @ (F22 @ X))))) @ Option))))).
% 2.81/1.58 thf(fact_64_option_Odistinct_I1_J, axiom, (! [A:$tType,X23:A]: (((none @ A) != ((some @ A) @ X23))))).
% 2.81/1.58 thf(fact_65_option_OdiscI, axiom, (! [A:$tType,Option:(option @ A),X23:A]: (((Option = ((some @ A) @ X23)) => (Option != (none @ A)))))).
% 2.81/1.58 thf(fact_66_option_Oexhaust, axiom, (! [A:$tType,Y2:(option @ A)]: (((Y2 != (none @ A)) => (~ ((! [X24:A]: ((Y2 != ((some @ A) @ X24)))))))))).
% 2.81/1.58 thf(fact_67_option_Oinducts, axiom, (! [A:$tType,P2:((option @ A) > $o),Option:(option @ A)]: (((P2 @ (none @ A)) => ((! [X3:A]: ((P2 @ ((some @ A) @ X3)))) => (P2 @ Option)))))).
% 2.81/1.58 thf(fact_68_split__option__ex, axiom, (! [A:$tType]: (((^ [P4:((option @ A) > $o)]: ((? [X4:(option @ A)]: ((P4 @ X4))))) = (^ [P:((option @ A) > $o)]: (((P @ (none @ A)) | (? [X:A]: ((P @ ((some @ A) @ X))))))))))).
% 2.81/1.58 thf(fact_69_split__option__all, axiom, (! [A:$tType]: (((^ [P4:((option @ A) > $o)]: ((! [X4:(option @ A)]: ((P4 @ X4))))) = (^ [P:((option @ A) > $o)]: (((P @ (none @ A)) & (! [X:A]: ((P @ ((some @ A) @ X))))))))))).
% 2.81/1.58 thf(fact_70_combine__options__cases, axiom, (! [A:$tType,B:$tType,X2:(option @ A),P2:((option @ A) > ((option @ B) > $o)),Y2:(option @ B)]: ((((X2 = (none @ A)) => ((P2 @ X2) @ Y2)) => (((Y2 = (none @ B)) => ((P2 @ X2) @ Y2)) => ((! [A5:A,B5:B]: (((X2 = ((some @ A) @ A5)) => ((Y2 = ((some @ B) @ B5)) => ((P2 @ X2) @ Y2))))) => ((P2 @ X2) @ Y2))))))).
% 2.81/1.58 thf(fact_71_option_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F1:B,F22:(A > B)]: (((((((case_option @ B) @ A) @ F1) @ F22) @ (none @ A)) = F1)))).
% 2.81/1.58 thf(fact_72_option_Oexpand, axiom, (! [A:$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)))))).
% 2.81/1.58 thf(fact_73_option_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:B,F22:(A > B),X23:A]: (((((((case_option @ B) @ A) @ F1) @ F22) @ ((some @ A) @ X23)) = (F22 @ X23))))).
% 2.81/1.58 thf(fact_74_option_Osel, axiom, (! [A:$tType,X23:A]: ((((the @ A) @ ((some @ A) @ X23)) = X23)))).
% 2.81/1.58 thf(fact_75_option_Oexhaust__sel, axiom, (! [A:$tType,Option:(option @ A)]: (((Option != (none @ A)) => (Option = ((some @ A) @ ((the @ A) @ Option))))))).
% 2.81/1.58 thf(fact_76_option_Ocase__eq__if, axiom, (! [A:$tType,B:$tType]: ((((case_option @ B) @ A) = (^ [F12:B,F23:(A > B),Option3:(option @ A)]: (((((if @ B) @ (Option3 = (none @ A))) @ F12) @ (F23 @ ((the @ A) @ Option3))))))))).
% 2.81/1.58 thf(fact_77_usubstappf__pred__conv, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),P3:char,Theta:trm]: ((((((uSubst95898978stappf @ Sigma) @ U) @ ((pred @ P3) @ Theta)) != (none @ fml)) => (((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (none @ trm)) & ((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ Sigma) @ P3) = (none @ fml)) | (? [R3:fml]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ Sigma) @ P3) = ((some @ fml) @ R3)) & ((((inf_inf @ (set @ variable)) @ (static_FVF @ R3)) @ U) = (bot_bot @ (set @ variable)))))))))))).
% 2.81/1.58 thf(fact_78_option_Osplit__sel, axiom, (! [B:$tType,A:$tType,P2:(B > $o),F1:B,F22:(A > B),Option:(option @ A)]: (((P2 @ (((((case_option @ B) @ A) @ F1) @ F22) @ Option)) = (((Option = (none @ A)) => (P2 @ F1)) & ((Option = ((some @ A) @ ((the @ A) @ Option))) => (P2 @ (F22 @ ((the @ A) @ Option))))))))).
% 2.81/1.58 thf(fact_79_fml_Oinject_I1_J, axiom, (! [X11:char,X12:trm,Y11:char,Y12:trm]: (((((pred @ X11) @ X12) = ((pred @ Y11) @ Y12)) = ((X11 = Y11) & (X12 = Y12)))))).
% 2.81/1.58 thf(fact_80_Int__iff, axiom, (! [A:$tType,C2:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) = ((((member @ A) @ C2) @ A3) & (((member @ A) @ C2) @ B4)))))).
% 2.81/1.58 thf(fact_81_IntI, axiom, (! [A:$tType,C2:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ A3) => ((((member @ A) @ C2) @ B4) => (((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A3) @ B4))))))).
% 2.81/1.58 thf(fact_82_empty__Collect__eq, axiom, (! [A:$tType,P2:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P2)) = (! [X:A]: ((~ ((P2 @ X))))))))).
% 2.81/1.58 thf(fact_83_Collect__empty__eq, axiom, (! [A:$tType,P2:(A > $o)]: (((((collect @ A) @ P2) = (bot_bot @ (set @ A))) = (! [X:A]: ((~ ((P2 @ X))))))))).
% 2.81/1.58 thf(fact_84_all__not__in__conv, axiom, (! [A:$tType,A3:(set @ A)]: (((! [X:A]: ((~ ((((member @ A) @ X) @ A3))))) = (A3 = (bot_bot @ (set @ A))))))).
% 2.81/1.58 thf(fact_85_empty__iff, axiom, (! [A:$tType,C2:A]: ((~ ((((member @ A) @ C2) @ (bot_bot @ (set @ A)))))))).
% 2.81/1.58 thf(fact_86_bot__apply, axiom, (! [C:$tType,D:$tType]: (((bot @ C) => ((bot_bot @ (D > C)) = (^ [X:D]: ((bot_bot @ C)))))))).
% 2.81/1.58 thf(fact_87_disjoint__iff__not__equal, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: ((((((inf_inf @ (set @ A)) @ A3) @ B4) = (bot_bot @ (set @ A))) = (! [X:A]: (((((member @ A) @ X) @ A3) => (! [Y:A]: (((((member @ A) @ Y) @ B4) => (X != Y))))))))))).
% 2.81/1.58 thf(fact_88_Aterm__Some, axiom, ((some @ trm) = (some @ trm))).
% 2.81/1.58 thf(fact_89_Loopo_Ocases, axiom, (! [X2:(option @ game)]: (((! [Alpha:game]: ((X2 != ((some @ game) @ Alpha)))) => (X2 = (none @ game)))))).
% 2.81/1.58 thf(fact_90_ODEo_Oinduct, axiom, (! [P2:(char > ((option @ trm) > $o)),A0:char,A1:(option @ trm)]: (((! [X3:char,Theta2:trm]: (((P2 @ X3) @ ((some @ trm) @ Theta2)))) => ((! [X3:char]: (((P2 @ X3) @ (none @ trm)))) => ((P2 @ A0) @ A1)))))).
% 2.81/1.58 thf(fact_91_Loopo_Oinduct, axiom, (! [P2:((option @ game) > $o),A0:(option @ game)]: (((! [Alpha:game]: ((P2 @ ((some @ game) @ Alpha)))) => ((P2 @ (none @ game)) => (P2 @ A0)))))).
% 2.81/1.58 thf(fact_92_undefg__equiv, axiom, (! [Alpha2:(option @ game)]: (((Alpha2 != (none @ game)) = (? [G:game]: ((Alpha2 = ((some @ game) @ G)))))))).
% 2.81/1.58 thf(fact_93_undeft__equiv, axiom, (! [Theta:(option @ trm)]: (((Theta != (none @ trm)) = (? [T2:trm]: ((Theta = ((some @ trm) @ T2)))))))).
% 2.81/1.58 thf(fact_94_Timeso_Oinduct, axiom, (! [P2:((option @ trm) > ((option @ trm) > $o)),A0:(option @ trm),A1:(option @ trm)]: (((! [Theta2:trm,Eta:trm]: (((P2 @ ((some @ trm) @ Theta2)) @ ((some @ trm) @ Eta)))) => ((! [X_1:(option @ trm)]: (((P2 @ (none @ trm)) @ X_1))) => ((! [V:trm]: (((P2 @ ((some @ trm) @ V)) @ (none @ trm)))) => ((P2 @ A0) @ A1))))))).
% 2.81/1.58 thf(fact_95_Assigno_Oinduct, axiom, (! [P2:(variable > ((option @ trm) > $o)),A0:variable,A1:(option @ trm)]: (((! [X3:variable,Theta2:trm]: (((P2 @ X3) @ ((some @ trm) @ Theta2)))) => ((! [X3:variable]: (((P2 @ X3) @ (none @ trm)))) => ((P2 @ A0) @ A1)))))).
% 2.81/1.58 thf(fact_96_Composeo_Oinduct, axiom, (! [P2:((option @ game) > ((option @ game) > $o)),A0:(option @ game),A1:(option @ game)]: (((! [Alpha:game,Beta:game]: (((P2 @ ((some @ game) @ Alpha)) @ ((some @ game) @ Beta)))) => ((! [Alpha:(option @ game)]: (((P2 @ Alpha) @ (none @ game)))) => ((! [V:game]: (((P2 @ (none @ game)) @ ((some @ game) @ V)))) => ((P2 @ A0) @ A1))))))).
% 2.81/1.58 thf(fact_97_Differentialo_Ocases, axiom, (! [X2:(option @ trm)]: (((! [Theta2:trm]: ((X2 != ((some @ trm) @ Theta2)))) => (X2 = (none @ trm)))))).
% 2.81/1.58 thf(fact_98_Differentialo_Oinduct, axiom, (! [P2:((option @ trm) > $o),A0:(option @ trm)]: (((! [Theta2:trm]: ((P2 @ ((some @ trm) @ Theta2)))) => ((P2 @ (none @ trm)) => (P2 @ A0)))))).
% 2.81/1.58 thf(fact_99_undeft__None, axiom, ((none @ trm) = (none @ trm))).
% 2.81/1.58 thf(fact_100_bot__fun__def, axiom, (! [B:$tType,A:$tType]: (((bot @ B) => ((bot_bot @ (A > B)) = (^ [X:A]: ((bot_bot @ B)))))))).
% 2.81/1.58 thf(fact_101_emptyE, axiom, (! [A:$tType,A2:A]: ((~ ((((member @ A) @ A2) @ (bot_bot @ (set @ A)))))))).
% 2.81/1.58 thf(fact_102_equals0D, axiom, (! [A:$tType,A3:(set @ A),A2:A]: (((A3 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A2) @ A3))))))).
% 2.81/1.58 thf(fact_103_equals0I, axiom, (! [A:$tType,A3:(set @ A)]: (((! [Y3:A]: ((~ ((((member @ A) @ Y3) @ A3))))) => (A3 = (bot_bot @ (set @ A))))))).
% 2.81/1.58 thf(fact_104_ex__in__conv, axiom, (! [A:$tType,A3:(set @ A)]: (((? [X:A]: ((((member @ A) @ X) @ A3))) = (A3 != (bot_bot @ (set @ A))))))).
% 2.81/1.58 thf(fact_105_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 2.81/1.58 thf(fact_106_IntE, axiom, (! [A:$tType,C2:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) => (~ (((((member @ A) @ C2) @ A3) => (~ ((((member @ A) @ C2) @ B4)))))))))).
% 2.81/1.58 thf(fact_107_IntD1, axiom, (! [A:$tType,C2:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) => (((member @ A) @ C2) @ A3))))).
% 2.81/1.58 thf(fact_108_IntD2, axiom, (! [A:$tType,C2:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) => (((member @ A) @ C2) @ B4))))).
% 2.81/1.58 thf(fact_109_Int__assoc, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),C3:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) @ C3) = (((inf_inf @ (set @ A)) @ A3) @ (((inf_inf @ (set @ A)) @ B4) @ C3)))))).
% 2.81/1.58 thf(fact_110_Int__absorb, axiom, (! [A:$tType,A3:(set @ A)]: (((((inf_inf @ (set @ A)) @ A3) @ A3) = A3)))).
% 2.81/1.58 thf(fact_111_Int__commute, axiom, (! [A:$tType]: (((inf_inf @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((((inf_inf @ (set @ A)) @ B6) @ A6))))))).
% 2.81/1.58 thf(fact_112_Int__left__absorb, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((((inf_inf @ (set @ A)) @ A3) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) = (((inf_inf @ (set @ A)) @ A3) @ B4))))).
% 2.81/1.58 thf(fact_113_Int__left__commute, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),C3:(set @ A)]: (((((inf_inf @ (set @ A)) @ A3) @ (((inf_inf @ (set @ A)) @ B4) @ C3)) = (((inf_inf @ (set @ A)) @ B4) @ (((inf_inf @ (set @ A)) @ A3) @ C3)))))).
% 2.81/1.58 thf(fact_114_empty__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (^ [X:A]: ($false))))))).
% 2.81/1.58 thf(fact_115_Collect__conj__eq, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: ((((collect @ A) @ (^ [X:A]: (((P2 @ X) & (Q @ X))))) = (((inf_inf @ (set @ A)) @ ((collect @ A) @ P2)) @ ((collect @ A) @ Q)))))).
% 2.81/1.58 thf(fact_116_Int__Collect, axiom, (! [A:$tType,X2:A,A3:(set @ A),P2:(A > $o)]: (((((member @ A) @ X2) @ (((inf_inf @ (set @ A)) @ A3) @ ((collect @ A) @ P2))) = ((((member @ A) @ X2) @ A3) & (P2 @ X2)))))).
% 2.81/1.58 thf(fact_117_Int__def, axiom, (! [A:$tType]: (((inf_inf @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: (((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ A6) & (((member @ A) @ X) @ B6))))))))))).
% 2.81/1.58 thf(fact_118_inf__set__def, axiom, (! [A:$tType]: (((inf_inf @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: (((collect @ A) @ (((inf_inf @ (A > $o)) @ (^ [X:A]: ((((member @ A) @ X) @ A6)))) @ (^ [X:A]: ((((member @ A) @ X) @ B6))))))))))).
% 2.81/1.58 thf(fact_119_Int__emptyI, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A3) => (~ ((((member @ A) @ X3) @ B4)))))) => ((((inf_inf @ (set @ A)) @ A3) @ B4) = (bot_bot @ (set @ A))))))).
% 2.81/1.58 thf(fact_120_disjoint__iff, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: ((((((inf_inf @ (set @ A)) @ A3) @ B4) = (bot_bot @ (set @ A))) = (! [X:A]: (((((member @ A) @ X) @ A3) => (~ ((((member @ A) @ X) @ B4)))))))))).
% 2.81/1.58 thf(fact_121_Int__empty__left, axiom, (! [A:$tType,B4:(set @ A)]: (((((inf_inf @ (set @ A)) @ (bot_bot @ (set @ A))) @ B4) = (bot_bot @ (set @ A)))))).
% 2.81/1.58 thf(fact_122_Int__empty__right, axiom, (! [A:$tType,A3:(set @ A)]: (((((inf_inf @ (set @ A)) @ A3) @ (bot_bot @ (set @ A))) = (bot_bot @ (set @ A)))))).
% 2.81/1.58 thf(fact_123_disjE__realizer2, axiom, (! [B:$tType,A:$tType,P2:$o,Q:(A > $o),X2:(option @ A),R4:(B > $o),F3:B,G2:(A > B)]: (((((((case_option @ $o) @ A) @ P2) @ Q) @ X2) => ((P2 => (R4 @ F3)) => ((! [Q2:A]: (((Q @ Q2) => (R4 @ (G2 @ Q2))))) => (R4 @ (((((case_option @ B) @ A) @ F3) @ G2) @ X2)))))))).
% 2.81/1.58 thf(fact_124_usubstappf__geqr, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm,Eta2:trm]: ((((((uSubst95898978stappf @ Sigma) @ U) @ ((geq @ Theta) @ Eta2)) != (none @ fml)) => ((((uSubst95898978stappf @ Sigma) @ U) @ ((geq @ Theta) @ Eta2)) = ((some @ fml) @ ((geq @ ((the @ trm) @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta))) @ ((the @ trm) @ (((uSubst95898992stappt @ Sigma) @ U) @ Eta2))))))))).
% 2.81/1.58 thf(fact_125_usubstappf__geq, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm,Eta2:trm]: ((((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (none @ trm)) => (((((uSubst95898992stappt @ Sigma) @ U) @ Eta2) != (none @ trm)) => ((((uSubst95898978stappf @ Sigma) @ U) @ ((geq @ Theta) @ Eta2)) = ((some @ fml) @ ((geq @ ((the @ trm) @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta))) @ ((the @ trm) @ (((uSubst95898992stappt @ Sigma) @ U) @ Eta2)))))))))).
% 2.81/1.58 thf(fact_126_Geqo_Osimps_I3_J, axiom, (! [V3:trm]: ((((uSubst1556497037e_Geqo @ ((some @ trm) @ V3)) @ (none @ trm)) = (none @ fml))))).
% 2.81/1.58 thf(fact_127_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A6:(set @ A)]: ((A6 = (bot_bot @ (set @ A))))))))).
% 2.81/1.58 thf(fact_128_usubstappf__geq__conv, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm,Eta2:trm]: ((((((uSubst95898978stappf @ Sigma) @ U) @ ((geq @ Theta) @ Eta2)) != (none @ fml)) => (((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (none @ trm)) & ((((uSubst95898992stappt @ Sigma) @ U) @ Eta2) != (none @ trm))))))).
% 2.81/1.58 thf(fact_129_fml_Oinject_I2_J, axiom, (! [X21:trm,X222:trm,Y21:trm,Y222:trm]: (((((geq @ X21) @ X222) = ((geq @ Y21) @ Y222)) = ((X21 = Y21) & (X222 = Y222)))))).
% 2.81/1.58 thf(fact_130_inf1I, axiom, (! [A:$tType,A3:(A > $o),X2:A,B4:(A > $o)]: (((A3 @ X2) => ((B4 @ X2) => ((((inf_inf @ (A > $o)) @ A3) @ B4) @ X2)))))).
% 2.81/1.58 thf(fact_131_inf1E, axiom, (! [A:$tType,A3:(A > $o),B4:(A > $o),X2:A]: ((((((inf_inf @ (A > $o)) @ A3) @ B4) @ X2) => (~ (((A3 @ X2) => (~ ((B4 @ X2)))))))))).
% 2.81/1.58 thf(fact_132_inf1D1, axiom, (! [A:$tType,A3:(A > $o),B4:(A > $o),X2:A]: ((((((inf_inf @ (A > $o)) @ A3) @ B4) @ X2) => (A3 @ X2))))).
% 2.81/1.58 thf(fact_133_inf1D2, axiom, (! [A:$tType,A3:(A > $o),B4:(A > $o),X2:A]: ((((((inf_inf @ (A > $o)) @ A3) @ B4) @ X2) => (B4 @ X2))))).
% 2.81/1.58 thf(fact_134_fml_Odistinct_I1_J, axiom, (! [X11:char,X12:trm,X21:trm,X222:trm]: ((((pred @ X11) @ X12) != ((geq @ X21) @ X222))))).
% 2.81/1.58 thf(fact_135_usubstappf_Osimps_I2_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm,Eta2:trm]: (((((uSubst95898978stappf @ Sigma) @ U) @ ((geq @ Theta) @ Eta2)) = ((uSubst1556497037e_Geqo @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta)) @ (((uSubst95898992stappt @ Sigma) @ U) @ Eta2)))))).
% 2.81/1.58 thf(fact_136_Geqo_Osimps_I1_J, axiom, (! [Theta:trm,Eta2:trm]: ((((uSubst1556497037e_Geqo @ ((some @ trm) @ Theta)) @ ((some @ trm) @ Eta2)) = ((some @ fml) @ ((geq @ Theta) @ Eta2)))))).
% 2.81/1.58 thf(fact_137_Geqo_Oelims, axiom, (! [X2:(option @ trm),Xa:(option @ trm),Y2:(option @ fml)]: (((((uSubst1556497037e_Geqo @ X2) @ Xa) = Y2) => ((! [Theta2:trm]: (((X2 = ((some @ trm) @ Theta2)) => (! [Eta:trm]: (((Xa = ((some @ trm) @ Eta)) => (Y2 != ((some @ fml) @ ((geq @ Theta2) @ Eta))))))))) => (((X2 = (none @ trm)) => (Y2 != (none @ fml))) => (~ (((? [V:trm]: ((X2 = ((some @ trm) @ V)))) => ((Xa = (none @ trm)) => (Y2 != (none @ fml)))))))))))).
% 2.81/1.58 thf(fact_138_Geqo_Osimps_I2_J, axiom, (! [Eta2:(option @ trm)]: ((((uSubst1556497037e_Geqo @ (none @ trm)) @ Eta2) = (none @ fml))))).
% 2.81/1.58 thf(fact_139_Geqo__undef, axiom, (! [Theta:(option @ trm),Eta2:(option @ trm)]: (((((uSubst1556497037e_Geqo @ Theta) @ Eta2) = (none @ fml)) = ((Theta = (none @ trm)) | (Eta2 = (none @ trm))))))).
% 2.81/1.58 thf(fact_140_inf__Int__eq, axiom, (! [A:$tType,R4:(set @ A),S:(set @ A)]: (((((inf_inf @ (A > $o)) @ (^ [X:A]: ((((member @ A) @ X) @ R4)))) @ (^ [X:A]: ((((member @ A) @ X) @ S)))) = (^ [X:A]: ((((member @ A) @ X) @ (((inf_inf @ (set @ A)) @ R4) @ S)))))))).
% 2.81/1.58 thf(fact_141_Collect__empty__eq__bot, axiom, (! [A:$tType,P2:(A > $o)]: (((((collect @ A) @ P2) = (bot_bot @ (set @ A))) = (P2 = (bot_bot @ (A > $o))))))).
% 2.81/1.58 thf(fact_142_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X:A]: ((((member @ A) @ X) @ (bot_bot @ (set @ A))))))))).
% 2.81/1.58 thf(fact_143_internal__case__prod__def, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((produc2004651681e_prod @ A) @ B) @ C) = (((product_case_prod @ A) @ B) @ C))))).
% 2.81/1.58 thf(fact_144_usubstappt_Osimps_I4_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),F3:char,Theta:trm]: (((((uSubst95898992stappt @ Sigma) @ U) @ ((func @ F3) @ Theta)) = (((((case_option @ (option @ trm)) @ trm) @ (none @ trm)) @ (^ [Sigma_theta:trm]: ((((((case_option @ (option @ trm)) @ trm) @ ((some @ trm) @ ((func @ F3) @ Sigma_theta))) @ (^ [R:trm]: (((((if @ (option @ trm)) @ ((((inf_inf @ (set @ variable)) @ (static_FVT @ R)) @ U) = (bot_bot @ (set @ variable)))) @ (((uSubst95898992stappt @ (uSubst969145931substt @ Sigma_theta)) @ (bot_bot @ (set @ variable))) @ R)) @ (none @ trm))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [F4:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F4))))))))) @ Sigma) @ F3))))) @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta)))))).
% 2.81/1.58 thf(fact_145_Diamondo_Ocases, axiom, (! [X2:((product_prod @ (option @ game)) @ (option @ fml))]: (((! [Alpha:game,Phi:fml]: ((X2 != ((((product_Pair @ (option @ game)) @ (option @ fml)) @ ((some @ game) @ Alpha)) @ ((some @ fml) @ Phi))))) => ((! [Phi:(option @ fml)]: ((X2 != ((((product_Pair @ (option @ game)) @ (option @ fml)) @ (none @ game)) @ Phi)))) => (~ ((! [V:game]: ((X2 != ((((product_Pair @ (option @ game)) @ (option @ fml)) @ ((some @ game) @ V)) @ (none @ fml)))))))))))).
% 2.81/1.58 thf(fact_146_Testo__undef, axiom, (! [Phi2:(option @ fml)]: ((((uSubst190403692_Testo @ Phi2) = (none @ game)) = (Phi2 = (none @ fml)))))).
% 2.81/1.58 thf(fact_147_prod_Oinject, axiom, (! [A:$tType,B:$tType,X13:A,X23:B,Y1:A,Y22:B]: (((((((product_Pair @ A) @ B) @ X13) @ X23) = ((((product_Pair @ A) @ B) @ Y1) @ Y22)) = ((X13 = Y1) & (X23 = Y22)))))).
% 2.81/1.58 thf(fact_148_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A7:A,B7:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A7) @ B7)) = ((A2 = A7) & (B2 = B7)))))).
% 2.81/1.58 thf(fact_149_trm_Oinject_I4_J, axiom, (! [X41:char,X42:trm,Y41:char,Y42:trm]: (((((func @ X41) @ X42) = ((func @ Y41) @ Y42)) = ((X41 = Y41) & (X42 = Y42)))))).
% 2.81/1.58 thf(fact_150_case__prodI, axiom, (! [A:$tType,B:$tType,F3:(A > (B > $o)),A2:A,B2:B]: ((((F3 @ A2) @ B2) => (((((product_case_prod @ A) @ B) @ $o) @ F3) @ ((((product_Pair @ A) @ B) @ A2) @ B2)))))).
% 2.81/1.58 thf(fact_151_case__prodI2, axiom, (! [B:$tType,A:$tType,P3:((product_prod @ A) @ B),C2:(A > (B > $o))]: (((! [A5:A,B5:B]: (((P3 = ((((product_Pair @ A) @ B) @ A5) @ B5)) => ((C2 @ A5) @ B5)))) => (((((product_case_prod @ A) @ B) @ $o) @ C2) @ P3))))).
% 2.81/1.58 thf(fact_152_case__prodI2_H, axiom, (! [A:$tType,B:$tType,C:$tType,P3:((product_prod @ A) @ B),C2:(A > (B > (C > $o))),X2:C]: (((! [A5:A,B5:B]: (((((((product_Pair @ A) @ B) @ A5) @ B5) = P3) => (((C2 @ A5) @ B5) @ X2)))) => ((((((product_case_prod @ A) @ B) @ (C > $o)) @ C2) @ P3) @ X2))))).
% 2.81/1.58 thf(fact_153_mem__case__prodI, axiom, (! [A:$tType,B:$tType,C:$tType,Z2:A,C2:(B > (C > (set @ A))),A2:B,B2:C]: (((((member @ A) @ Z2) @ ((C2 @ A2) @ B2)) => (((member @ A) @ Z2) @ (((((product_case_prod @ B) @ C) @ (set @ A)) @ C2) @ ((((product_Pair @ B) @ C) @ A2) @ B2))))))).
% 2.81/1.58 thf(fact_154_mem__case__prodI2, axiom, (! [C:$tType,B:$tType,A:$tType,P3:((product_prod @ A) @ B),Z2:C,C2:(A > (B > (set @ C)))]: (((! [A5:A,B5:B]: (((P3 = ((((product_Pair @ A) @ B) @ A5) @ B5)) => (((member @ C) @ Z2) @ ((C2 @ A5) @ B5))))) => (((member @ C) @ Z2) @ (((((product_case_prod @ A) @ B) @ (set @ C)) @ C2) @ P3)))))).
% 2.81/1.58 thf(fact_155_case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,F3:(B > (C > A)),A2:B,B2:C]: (((((((product_case_prod @ B) @ C) @ A) @ F3) @ ((((product_Pair @ B) @ C) @ A2) @ B2)) = ((F3 @ A2) @ B2))))).
% 2.81/1.58 thf(fact_156_usubstappt__func2, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),F3:char,R2:trm,U:(set @ variable),Theta:trm]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [F4:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F4))))))))) @ Sigma) @ F3) = ((some @ trm) @ R2)) => (((((inf_inf @ (set @ variable)) @ (static_FVT @ R2)) @ U) != (bot_bot @ (set @ variable))) => ((((uSubst95898992stappt @ Sigma) @ U) @ ((func @ F3) @ Theta)) = (none @ trm))))))).
% 2.81/1.58 thf(fact_157_usubstappt__func, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),F3:char,R2:trm,U:(set @ variable),Theta:trm,Sigma_theta2:trm]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [F4:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F4))))))))) @ Sigma) @ F3) = ((some @ trm) @ R2)) => (((((inf_inf @ (set @ variable)) @ (static_FVT @ R2)) @ U) = (bot_bot @ (set @ variable))) => (((((uSubst95898992stappt @ Sigma) @ U) @ Theta) = ((some @ trm) @ Sigma_theta2)) => ((((uSubst95898992stappt @ Sigma) @ U) @ ((func @ F3) @ Theta)) = (((uSubst95898992stappt @ (uSubst969145931substt @ Sigma_theta2)) @ (bot_bot @ (set @ variable))) @ R2)))))))).
% 2.81/1.58 thf(fact_158_inf__Int__eq2, axiom, (! [B:$tType,A:$tType,R4:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: (((((inf_inf @ (A > (B > $o))) @ (^ [X:A,Y:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y)) @ R4)))) @ (^ [X:A,Y:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y)) @ S)))) = (^ [X:A,Y:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y)) @ (((inf_inf @ (set @ ((product_prod @ A) @ B))) @ R4) @ S)))))))).
% 2.81/1.58 thf(fact_159_bot__empty__eq2, axiom, (! [B:$tType,A:$tType]: (((bot_bot @ (A > (B > $o))) = (^ [X:A,Y:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y)) @ (bot_bot @ (set @ ((product_prod @ A) @ B)))))))))).
% 2.81/1.58 thf(fact_160_pred__equals__eq2, axiom, (! [B:$tType,A:$tType,R4:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: ((((^ [X:A,Y:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y)) @ R4))) = (^ [X:A,Y:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y)) @ S)))) = (R4 = S))))).
% 2.81/1.58 thf(fact_161_cond__case__prod__eta, axiom, (! [C:$tType,B:$tType,A:$tType,F3:(A > (B > C)),G2:(((product_prod @ A) @ B) > C)]: (((! [X3:A,Y3:B]: ((((F3 @ X3) @ Y3) = (G2 @ ((((product_Pair @ A) @ B) @ X3) @ Y3))))) => (((((product_case_prod @ A) @ B) @ C) @ F3) = G2))))).
% 2.81/1.58 thf(fact_162_case__prod__eta, axiom, (! [C:$tType,B:$tType,A:$tType,F3:(((product_prod @ A) @ B) > C)]: ((((((product_case_prod @ A) @ B) @ C) @ (^ [X:A,Y:B]: ((F3 @ ((((product_Pair @ A) @ B) @ X) @ Y))))) = F3)))).
% 2.81/1.58 thf(fact_163_case__prodE2, axiom, (! [B:$tType,A:$tType,C:$tType,Q:(A > $o),P2:(B > (C > A)),Z2:((product_prod @ B) @ C)]: (((Q @ (((((product_case_prod @ B) @ C) @ A) @ P2) @ Z2)) => (~ ((! [X3:B,Y3:C]: (((Z2 = ((((product_Pair @ B) @ C) @ X3) @ Y3)) => (~ ((Q @ ((P2 @ X3) @ Y3))))))))))))).
% 2.81/1.58 thf(fact_164_surj__pair, axiom, (! [A:$tType,B:$tType,P3:((product_prod @ A) @ B)]: ((? [X3:A,Y3:B]: ((P3 = ((((product_Pair @ A) @ B) @ X3) @ Y3))))))).
% 2.81/1.58 thf(fact_165_prod__cases, axiom, (! [B:$tType,A:$tType,P2:(((product_prod @ A) @ B) > $o),P3:((product_prod @ A) @ B)]: (((! [A5:A,B5:B]: ((P2 @ ((((product_Pair @ A) @ B) @ A5) @ B5)))) => (P2 @ P3))))).
% 2.81/1.58 thf(fact_166_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A7:A,B7:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A7) @ B7)) => (~ (((A2 = A7) => (B2 != B7)))))))).
% 2.81/1.58 thf(fact_167_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A5:A,B5:B,C4:C]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A5) @ ((((product_Pair @ B) @ C) @ B5) @ C4)))))))))).
% 2.81/1.58 thf(fact_168_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A5:A,B5:B,C4:C,D2:D]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B5) @ ((((product_Pair @ C) @ D) @ C4) @ D2))))))))))).
% 2.81/1.58 thf(fact_169_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: ((~ ((! [A5:A,B5:B,C4:C,D2:D,E2:E]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C4) @ ((((product_Pair @ D) @ E) @ D2) @ E2)))))))))))).
% 2.81/1.58 thf(fact_170_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F5:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5)))))]: ((~ ((! [A5:A,B5:B,C4:C,D2:D,E2:E,F6:F5]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5)))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5))) @ C4) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F5)) @ D2) @ ((((product_Pair @ E) @ F5) @ E2) @ F6))))))))))))).
% 2.81/1.58 thf(fact_171_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F5:$tType,G3:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3))))))]: ((~ ((! [A5:A,B5:B,C4:C,D2:D,E2:E,F6:F5,G4:G3]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3)))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3))))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3)))) @ C4) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F5) @ G3)) @ E2) @ ((((product_Pair @ F5) @ G3) @ F6) @ G4)))))))))))))).
% 2.81/1.58 thf(fact_172_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A5:A,B5:B,C4:C]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A5) @ ((((product_Pair @ B) @ C) @ B5) @ C4))))) => (P2 @ X2))))).
% 2.81/1.58 thf(fact_173_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A5:A,B5:B,C4:C,D2:D]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B5) @ ((((product_Pair @ C) @ D) @ C4) @ D2)))))) => (P2 @ X2))))).
% 2.81/1.58 thf(fact_174_prod__induct5, axiom, (! [E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: (((! [A5:A,B5:B,C4:C,D2:D,E2:E]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C4) @ ((((product_Pair @ D) @ E) @ D2) @ E2))))))) => (P2 @ X2))))).
% 2.81/1.58 thf(fact_175_prod__induct6, axiom, (! [F5:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5))))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5)))))]: (((! [A5:A,B5:B,C4:C,D2:D,E2:E,F6:F5]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5)))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5))) @ C4) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F5)) @ D2) @ ((((product_Pair @ E) @ F5) @ E2) @ F6)))))))) => (P2 @ X2))))).
% 2.81/1.58 thf(fact_176_prod__induct7, axiom, (! [G3:$tType,F5:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3)))))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3))))))]: (((! [A5:A,B5:B,C4:C,D2:D,E2:E,F6:F5,G4:G3]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3)))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3))))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3)))) @ C4) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G3))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F5) @ G3)) @ E2) @ ((((product_Pair @ F5) @ G3) @ F6) @ G4))))))))) => (P2 @ X2))))).
% 2.81/1.58 thf(fact_177_mem__case__prodE, axiom, (! [B:$tType,A:$tType,C:$tType,Z2:A,C2:(B > (C > (set @ A))),P3:((product_prod @ B) @ C)]: (((((member @ A) @ Z2) @ (((((product_case_prod @ B) @ C) @ (set @ A)) @ C2) @ P3)) => (~ ((! [X3:B,Y3:C]: (((P3 = ((((product_Pair @ B) @ C) @ X3) @ Y3)) => (~ ((((member @ A) @ Z2) @ ((C2 @ X3) @ Y3))))))))))))).
% 2.81/1.58 thf(fact_178_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y2:((product_prod @ A) @ B)]: ((~ ((! [A5:A,B5:B]: ((Y2 != ((((product_Pair @ A) @ B) @ A5) @ B5))))))))).
% 2.81/1.58 thf(fact_179_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P2:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A5:A,B5:B]: ((P2 @ ((((product_Pair @ A) @ B) @ A5) @ B5)))) => (P2 @ Prod))))).
% 2.81/1.58 thf(fact_180_case__prodD, axiom, (! [A:$tType,B:$tType,F3:(A > (B > $o)),A2:A,B2:B]: (((((((product_case_prod @ A) @ B) @ $o) @ F3) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) => ((F3 @ A2) @ B2))))).
% 2.81/1.58 thf(fact_181_case__prodE, axiom, (! [A:$tType,B:$tType,C2:(A > (B > $o)),P3:((product_prod @ A) @ B)]: (((((((product_case_prod @ A) @ B) @ $o) @ C2) @ P3) => (~ ((! [X3:A,Y3:B]: (((P3 = ((((product_Pair @ A) @ B) @ X3) @ Y3)) => (~ (((C2 @ X3) @ Y3)))))))))))).
% 2.81/1.58 thf(fact_182_case__prodD_H, axiom, (! [B:$tType,A:$tType,C:$tType,R4:(A > (B > (C > $o))),A2:A,B2:B,C2:C]: ((((((((product_case_prod @ A) @ B) @ (C > $o)) @ R4) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) @ C2) => (((R4 @ A2) @ B2) @ C2))))).
% 2.81/1.58 thf(fact_183_case__prodE_H, axiom, (! [B:$tType,A:$tType,C:$tType,C2:(A > (B > (C > $o))),P3:((product_prod @ A) @ B),Z2:C]: ((((((((product_case_prod @ A) @ B) @ (C > $o)) @ C2) @ P3) @ Z2) => (~ ((! [X3:A,Y3:B]: (((P3 = ((((product_Pair @ A) @ B) @ X3) @ Y3)) => (~ ((((C2 @ X3) @ Y3) @ Z2)))))))))))).
% 2.81/1.58 thf(fact_184_case__prod__Pair__iden, axiom, (! [B:$tType,A:$tType,P3:((product_prod @ A) @ B)]: (((((((product_case_prod @ A) @ B) @ ((product_prod @ A) @ B)) @ ((product_Pair @ A) @ B)) @ P3) = P3)))).
% 2.81/1.58 thf(fact_185_old_Oprod_Ocase, axiom, (! [A:$tType,C:$tType,B:$tType,F3:(A > (B > C)),X13:A,X23:B]: (((((((product_case_prod @ A) @ B) @ C) @ F3) @ ((((product_Pair @ A) @ B) @ X13) @ X23)) = ((F3 @ X13) @ X23))))).
% 2.81/1.58 thf(fact_186_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C2:(B > (C > A)),A2:B,B2:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C2) @ ((((product_Pair @ B) @ C) @ A2) @ B2)) = ((C2 @ A2) @ B2))))).
% 2.81/1.58 thf(fact_187_usubstappt__func__conv, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),F3:char,Theta:trm]: ((((((uSubst95898992stappt @ Sigma) @ U) @ ((func @ F3) @ Theta)) != (none @ trm)) => (((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (none @ trm)) & ((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [F4:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F4))))))))) @ Sigma) @ F3) = (none @ trm)) | (? [R3:trm]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [F4:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F4))))))))) @ Sigma) @ F3) = ((some @ trm) @ R3)) & ((((inf_inf @ (set @ variable)) @ (static_FVT @ R3)) @ U) = (bot_bot @ (set @ variable)))))))))))).
% 2.81/1.58 thf(fact_188_Testo_Osimps_I2_J, axiom, ((uSubst190403692_Testo @ (none @ fml)) = (none @ game))).
% 2.81/1.58 thf(fact_189_usappconst__simp, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),F3:char,R2:trm,U:(set @ variable)]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ Sigma) @ F3) = ((some @ trm) @ R2)) => (((((inf_inf @ (set @ variable)) @ (static_FVT @ R2)) @ U) = (bot_bot @ (set @ variable))) => ((((uSubst1138577137pconst @ Sigma) @ U) @ F3) = ((some @ trm) @ R2))))))).
% 2.81/1.58 thf(fact_190_usappconst__conv, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),F3:char]: ((((((uSubst1138577137pconst @ Sigma) @ U) @ F3) != (none @ trm)) => ((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ Sigma) @ F3) = (none @ trm)) | (? [R3:trm]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ Sigma) @ F3) = ((some @ trm) @ R3)) & ((((inf_inf @ (set @ variable)) @ (static_FVT @ R3)) @ U) = (bot_bot @ (set @ variable))))))))))).
% 2.81/1.58 thf(fact_191_usubstappt__const, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),F3:char,R2:trm,U:(set @ variable)]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ Sigma) @ F3) = ((some @ trm) @ R2)) => (((((inf_inf @ (set @ variable)) @ (static_FVT @ R2)) @ U) = (bot_bot @ (set @ variable))) => ((((uSubst95898992stappt @ Sigma) @ U) @ (const @ F3)) = ((some @ trm) @ R2))))))).
% 2.81/1.58 thf(fact_192_trm_Oinject_I3_J, axiom, (! [X32:char,Y32:char]: ((((const @ X32) = (const @ Y32)) = (X32 = Y32))))).
% 2.81/1.58 thf(fact_193_trm_Odistinct_I23_J, axiom, (! [X32:char,X41:char,X42:trm]: (((const @ X32) != ((func @ X41) @ X42))))).
% 2.81/1.58 thf(fact_194_usubstappt_Osimps_I3_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),F3:char]: (((((uSubst95898992stappt @ Sigma) @ U) @ (const @ F3)) = (((uSubst1138577137pconst @ Sigma) @ U) @ F3))))).
% 2.81/1.58 thf(fact_195_ODEo_Ocases, axiom, (! [X2:((product_prod @ char) @ (option @ trm))]: (((! [X3:char,Theta2:trm]: ((X2 != ((((product_Pair @ char) @ (option @ trm)) @ X3) @ ((some @ trm) @ Theta2))))) => (~ ((! [X3:char]: ((X2 != ((((product_Pair @ char) @ (option @ trm)) @ X3) @ (none @ trm))))))))))).
% 2.81/1.58 thf(fact_196_Assigno_Ocases, axiom, (! [X2:((product_prod @ variable) @ (option @ trm))]: (((! [X3:variable,Theta2:trm]: ((X2 != ((((product_Pair @ variable) @ (option @ trm)) @ X3) @ ((some @ trm) @ Theta2))))) => (~ ((! [X3:variable]: ((X2 != ((((product_Pair @ variable) @ (option @ trm)) @ X3) @ (none @ trm))))))))))).
% 2.81/1.58 thf(fact_197_Timeso_Ocases, axiom, (! [X2:((product_prod @ (option @ trm)) @ (option @ trm))]: (((! [Theta2:trm,Eta:trm]: ((X2 != ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ ((some @ trm) @ Theta2)) @ ((some @ trm) @ Eta))))) => ((! [Eta:(option @ trm)]: ((X2 != ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ (none @ trm)) @ Eta)))) => (~ ((! [V:trm]: ((X2 != ((((product_Pair @ (option @ trm)) @ (option @ trm)) @ ((some @ trm) @ V)) @ (none @ trm)))))))))))).
% 2.81/1.58 thf(fact_198_Existso_Ocases, axiom, (! [X2:((product_prod @ variable) @ (option @ fml))]: (((! [X3:variable,Phi:fml]: ((X2 != ((((product_Pair @ variable) @ (option @ fml)) @ X3) @ ((some @ fml) @ Phi))))) => (~ ((! [X3:variable]: ((X2 != ((((product_Pair @ variable) @ (option @ fml)) @ X3) @ (none @ fml))))))))))).
% 2.81/1.58 thf(fact_199_Ando_Ocases, axiom, (! [X2:((product_prod @ (option @ fml)) @ (option @ fml))]: (((! [Phi:fml,Psi:fml]: ((X2 != ((((product_Pair @ (option @ fml)) @ (option @ fml)) @ ((some @ fml) @ Phi)) @ ((some @ fml) @ Psi))))) => ((! [Psi:(option @ fml)]: ((X2 != ((((product_Pair @ (option @ fml)) @ (option @ fml)) @ (none @ fml)) @ Psi)))) => (~ ((! [V:fml]: ((X2 != ((((product_Pair @ (option @ fml)) @ (option @ fml)) @ ((some @ fml) @ V)) @ (none @ fml)))))))))))).
% 2.81/1.58 thf(fact_200_Composeo_Ocases, axiom, (! [X2:((product_prod @ (option @ game)) @ (option @ game))]: (((! [Alpha:game,Beta:game]: ((X2 != ((((product_Pair @ (option @ game)) @ (option @ game)) @ ((some @ game) @ Alpha)) @ ((some @ game) @ Beta))))) => ((! [Alpha:(option @ game)]: ((X2 != ((((product_Pair @ (option @ game)) @ (option @ game)) @ Alpha) @ (none @ game))))) => (~ ((! [V:game]: ((X2 != ((((product_Pair @ (option @ game)) @ (option @ game)) @ (none @ game)) @ ((some @ game) @ V)))))))))))).
% 2.81/1.58 thf(fact_201_usappconst__def, axiom, (uSubst1138577137pconst = (^ [Sigma2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U2:(set @ variable),F2:char]: ((((((case_option @ (option @ trm)) @ trm) @ ((some @ trm) @ (const @ F2))) @ (^ [R:trm]: (((((if @ (option @ trm)) @ ((((inf_inf @ (set @ variable)) @ (static_FVT @ R)) @ U2) = (bot_bot @ (set @ variable)))) @ ((some @ trm) @ R)) @ (none @ trm))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ Sigma2) @ F2)))))).
% 2.81/1.58 thf(fact_202_usubstappt__const__conv, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),F3:char]: ((((((uSubst95898992stappt @ Sigma) @ U) @ (const @ F3)) != (none @ trm)) => ((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ Sigma) @ F3) = (none @ trm)) | (? [R3:trm]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [F0:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F0))))))))) @ Sigma) @ F3) = ((some @ trm) @ R3)) & ((((inf_inf @ (set @ variable)) @ (static_FVT @ R3)) @ U) = (bot_bot @ (set @ variable))))))))))).
% 2.81/1.58 thf(fact_203_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 2.81/1.58 thf(fact_204_usubstappt_Opsimps_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),F3:char,Theta:trm]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma) @ ((((product_Pair @ (set @ variable)) @ trm) @ U) @ ((func @ F3) @ Theta)))) => ((((uSubst95898992stappt @ Sigma) @ U) @ ((func @ F3) @ Theta)) = (((((case_option @ (option @ trm)) @ trm) @ (none @ trm)) @ (^ [Sigma_theta:trm]: ((((((case_option @ (option @ trm)) @ trm) @ ((some @ trm) @ ((func @ F3) @ Sigma_theta))) @ (^ [R:trm]: (((((if @ (option @ trm)) @ ((((inf_inf @ (set @ variable)) @ (static_FVT @ R)) @ U) = (bot_bot @ (set @ variable)))) @ (((uSubst95898992stappt @ (uSubst969145931substt @ Sigma_theta)) @ (bot_bot @ (set @ variable))) @ R)) @ (none @ trm))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [F4:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F4))))))))) @ Sigma) @ F3))))) @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta))))))).
% 2.81/1.58 thf(fact_205_usubstappt_Opsimps_I3_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),F3:char]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma) @ ((((product_Pair @ (set @ variable)) @ trm) @ U) @ (const @ F3)))) => ((((uSubst95898992stappt @ Sigma) @ U) @ (const @ F3)) = (((uSubst1138577137pconst @ Sigma) @ U) @ F3)))))).
% 2.81/1.58 thf(fact_206_usubstappt_Opsimps_I1_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),X2:variable]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma) @ ((((product_Pair @ (set @ variable)) @ trm) @ U) @ (var @ X2)))) => ((((uSubst95898992stappt @ Sigma) @ U) @ (var @ X2)) = ((some @ trm) @ (var @ X2))))))).
% 2.81/1.58 thf(fact_207_usubstappt_Opsimps_I2_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),R2:real]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma) @ ((((product_Pair @ (set @ variable)) @ trm) @ U) @ (number @ R2)))) => ((((uSubst95898992stappt @ Sigma) @ U) @ (number @ R2)) = ((some @ trm) @ (number @ R2))))))).
% 2.81/1.58 thf(fact_208_trm_Oinject_I2_J, axiom, (! [X23:real,Y22:real]: ((((number @ X23) = (number @ Y22)) = (X23 = Y22))))).
% 2.81/1.58 thf(fact_209_trm_Oinject_I1_J, axiom, (! [X13:variable,Y1:variable]: ((((var @ X13) = (var @ Y1)) = (X13 = Y1))))).
% 2.81/1.58 thf(fact_210_trm_Odistinct_I15_J, axiom, (! [X23:real,X41:char,X42:trm]: (((number @ X23) != ((func @ X41) @ X42))))).
% 2.81/1.58 thf(fact_211_trm_Odistinct_I5_J, axiom, (! [X13:variable,X41:char,X42:trm]: (((var @ X13) != ((func @ X41) @ X42))))).
% 2.81/1.58 thf(fact_212_trm_Odistinct_I1_J, axiom, (! [X13:variable,X23:real]: (((var @ X13) != (number @ X23))))).
% 2.81/1.58 thf(fact_213_trm_Odistinct_I13_J, axiom, (! [X23:real,X32:char]: (((number @ X23) != (const @ X32))))).
% 2.81/1.58 thf(fact_214_trm_Odistinct_I3_J, axiom, (! [X13:variable,X32:char]: (((var @ X13) != (const @ X32))))).
% 2.81/1.58 thf(fact_215_usubstappt_Osimps_I2_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),R2:real]: (((((uSubst95898992stappt @ Sigma) @ U) @ (number @ R2)) = ((some @ trm) @ (number @ R2)))))).
% 2.81/1.58 thf(fact_216_usubstappt_Osimps_I1_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),X2:variable]: (((((uSubst95898992stappt @ Sigma) @ U) @ (var @ X2)) = ((some @ trm) @ (var @ X2)))))).
% 2.81/1.58 thf(fact_217_usubstappt_Opinduct, axiom, (! [A0:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),A1:(set @ variable),A22:trm,P2:(((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) > ((set @ variable) > (trm > $o)))]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ A0) @ ((((product_Pair @ (set @ variable)) @ trm) @ A1) @ A22))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),X3:variable]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (var @ X3)))) => (((P2 @ Sigma3) @ U3) @ (var @ X3))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),R3:real]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (number @ R3)))) => (((P2 @ Sigma3) @ U3) @ (number @ R3))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),F6:char]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (const @ F6)))) => (((P2 @ Sigma3) @ U3) @ (const @ F6))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),F6:char,Theta2:trm]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ ((func @ F6) @ Theta2)))) => ((((P2 @ Sigma3) @ U3) @ Theta2) => ((! [X25:trm]: ((((((uSubst95898992stappt @ Sigma3) @ U3) @ Theta2) = ((some @ trm) @ X25)) => (! [X2a:trm]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [F4:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F4))))))))) @ Sigma3) @ F6) = ((some @ trm) @ X2a)) => (((((inf_inf @ (set @ variable)) @ (static_FVT @ X2a)) @ U3) = (bot_bot @ (set @ variable))) => (((P2 @ (uSubst969145931substt @ X25)) @ (bot_bot @ (set @ variable))) @ X2a)))))))) => (((P2 @ Sigma3) @ U3) @ ((func @ F6) @ Theta2))))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),Theta2:trm,Eta:trm]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ ((plus @ Theta2) @ Eta)))) => ((((P2 @ Sigma3) @ U3) @ Theta2) => ((((P2 @ Sigma3) @ U3) @ Eta) => (((P2 @ Sigma3) @ U3) @ ((plus @ Theta2) @ Eta))))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),Theta2:trm,Eta:trm]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ ((times @ Theta2) @ Eta)))) => ((((P2 @ Sigma3) @ U3) @ Theta2) => ((((P2 @ Sigma3) @ U3) @ Eta) => (((P2 @ Sigma3) @ U3) @ ((times @ Theta2) @ Eta))))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),Theta2:trm]: (((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (differential @ Theta2)))) => ((((P2 @ Sigma3) @ ((collect @ variable) @ (^ [X:variable]: ($true)))) @ Theta2) => (((P2 @ Sigma3) @ U3) @ (differential @ Theta2)))))) => (((P2 @ A0) @ A1) @ A22)))))))))))).
% 2.81/1.58 thf(fact_218_dotsubstt__def, axiom, (uSubst969145931substt = (^ [Theta3:trm]: (((((product_Pair @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (^ [F2:char]: (((((if @ (option @ trm)) @ (F2 = ((((((((char2 @ $false) @ $true) @ $true) @ $true) @ $false) @ $true) @ $false) @ $false))) @ ((some @ trm) @ Theta3)) @ (none @ trm))))) @ ((((product_Pair @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (^ [Uu:char]: ((none @ trm)))) @ ((((product_Pair @ (char > (option @ fml))) @ (char > (option @ game))) @ (^ [Uu:char]: ((none @ fml)))) @ (^ [Uu:char]: ((none @ game)))))))))).
% 2.81/1.58 thf(fact_219_trm_Oinject_I6_J, axiom, (! [X61:trm,X62:trm,Y61:trm,Y62:trm]: (((((times @ X61) @ X62) = ((times @ Y61) @ Y62)) = ((X61 = Y61) & (X62 = Y62)))))).
% 2.81/1.58 thf(fact_220_trm_Oinject_I5_J, axiom, (! [X51:trm,X52:trm,Y51:trm,Y52:trm]: (((((plus @ X51) @ X52) = ((plus @ Y51) @ Y52)) = ((X51 = Y51) & (X52 = Y52)))))).
% 2.81/1.58 thf(fact_221_trm_Oinject_I7_J, axiom, (! [X7:trm,Y7:trm]: ((((differential @ X7) = (differential @ Y7)) = (X7 = Y7))))).
% 2.81/1.58 thf(fact_222_trm_Odistinct_I7_J, axiom, (! [X13:variable,X51:trm,X52:trm]: (((var @ X13) != ((plus @ X51) @ X52))))).
% 2.81/1.58 thf(fact_223_trm_Odistinct_I9_J, axiom, (! [X13:variable,X61:trm,X62:trm]: (((var @ X13) != ((times @ X61) @ X62))))).
% 2.81/1.58 thf(fact_224_trm_Odistinct_I11_J, axiom, (! [X13:variable,X7:trm]: (((var @ X13) != (differential @ X7))))).
% 2.81/1.58 thf(fact_225_trm_Odistinct_I17_J, axiom, (! [X23:real,X51:trm,X52:trm]: (((number @ X23) != ((plus @ X51) @ X52))))).
% 2.81/1.58 thf(fact_226_trm_Odistinct_I19_J, axiom, (! [X23:real,X61:trm,X62:trm]: (((number @ X23) != ((times @ X61) @ X62))))).
% 2.81/1.58 thf(fact_227_trm_Odistinct_I21_J, axiom, (! [X23:real,X7:trm]: (((number @ X23) != (differential @ X7))))).
% 2.81/1.58 thf(fact_228_trm_Oexhaust, axiom, (! [Y2:trm]: (((! [X14:variable]: ((Y2 != (var @ X14)))) => ((! [X24:real]: ((Y2 != (number @ X24)))) => ((! [X33:char]: ((Y2 != (const @ X33)))) => ((! [X412:char,X422:trm]: ((Y2 != ((func @ X412) @ X422)))) => ((! [X512:trm,X522:trm]: ((Y2 != ((plus @ X512) @ X522)))) => ((! [X612:trm,X622:trm]: ((Y2 != ((times @ X612) @ X622)))) => (~ ((! [X72:trm]: ((Y2 != (differential @ X72))))))))))))))).
% 2.81/1.58 thf(fact_229_trm_Oinduct, axiom, (! [P2:(trm > $o),Trm:trm]: (((! [X3:variable]: ((P2 @ (var @ X3)))) => ((! [X3:real]: ((P2 @ (number @ X3)))) => ((! [X3:char]: ((P2 @ (const @ X3)))) => ((! [X1a:char,X2a2:trm]: (((P2 @ X2a2) => (P2 @ ((func @ X1a) @ X2a2))))) => ((! [X1a:trm,X2a2:trm]: (((P2 @ X1a) => ((P2 @ X2a2) => (P2 @ ((plus @ X1a) @ X2a2)))))) => ((! [X1a:trm,X2a2:trm]: (((P2 @ X1a) => ((P2 @ X2a2) => (P2 @ ((times @ X1a) @ X2a2)))))) => ((! [X3:trm]: (((P2 @ X3) => (P2 @ (differential @ X3))))) => (P2 @ Trm))))))))))).
% 2.81/1.58 thf(fact_230_trm_Odistinct_I25_J, axiom, (! [X32:char,X51:trm,X52:trm]: (((const @ X32) != ((plus @ X51) @ X52))))).
% 2.81/1.58 thf(fact_231_trm_Odistinct_I27_J, axiom, (! [X32:char,X61:trm,X62:trm]: (((const @ X32) != ((times @ X61) @ X62))))).
% 2.81/1.58 thf(fact_232_trm_Odistinct_I29_J, axiom, (! [X32:char,X7:trm]: (((const @ X32) != (differential @ X7))))).
% 2.81/1.58 thf(fact_233_trm_Odistinct_I41_J, axiom, (! [X61:trm,X62:trm,X7:trm]: ((((times @ X61) @ X62) != (differential @ X7))))).
% 2.81/1.58 thf(fact_234_trm_Odistinct_I39_J, axiom, (! [X51:trm,X52:trm,X7:trm]: ((((plus @ X51) @ X52) != (differential @ X7))))).
% 2.81/1.58 thf(fact_235_trm_Odistinct_I37_J, axiom, (! [X51:trm,X52:trm,X61:trm,X62:trm]: ((((plus @ X51) @ X52) != ((times @ X61) @ X62))))).
% 2.81/1.58 thf(fact_236_trm_Odistinct_I31_J, axiom, (! [X41:char,X42:trm,X51:trm,X52:trm]: ((((func @ X41) @ X42) != ((plus @ X51) @ X52))))).
% 2.81/1.58 thf(fact_237_trm_Odistinct_I33_J, axiom, (! [X41:char,X42:trm,X61:trm,X62:trm]: ((((func @ X41) @ X42) != ((times @ X61) @ X62))))).
% 2.81/1.58 thf(fact_238_trm_Odistinct_I35_J, axiom, (! [X41:char,X42:trm,X7:trm]: ((((func @ X41) @ X42) != (differential @ X7))))).
% 2.81/1.58 thf(fact_239_usubstappt_Ocases, axiom, (! [X2:((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))]: (((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),X3:variable]: ((X2 != ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (var @ X3)))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),R3:real]: ((X2 != ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (number @ R3)))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),F6:char]: ((X2 != ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (const @ F6)))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),F6:char,Theta2:trm]: ((X2 != ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ ((func @ F6) @ Theta2)))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),Theta2:trm,Eta:trm]: ((X2 != ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ ((plus @ Theta2) @ Eta)))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),Theta2:trm,Eta:trm]: ((X2 != ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ ((times @ Theta2) @ Eta)))))) => (~ ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),Theta2:trm]: ((X2 != ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ Sigma3) @ ((((product_Pair @ (set @ variable)) @ trm) @ U3) @ (differential @ Theta2))))))))))))))))).
% 2.81/1.58 thf(fact_240_usubstappt__times__conv, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm,Eta2:trm]: ((((((uSubst95898992stappt @ Sigma) @ U) @ ((times @ Theta) @ Eta2)) != (none @ trm)) => (((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (none @ trm)) & ((((uSubst95898992stappt @ Sigma) @ U) @ Eta2) != (none @ trm))))))).
% 2.81/1.58 thf(fact_241_usubstappt__plus__conv, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm,Eta2:trm]: ((((((uSubst95898992stappt @ Sigma) @ U) @ ((plus @ Theta) @ Eta2)) != (none @ trm)) => (((((uSubst95898992stappt @ Sigma) @ U) @ Theta) != (none @ trm)) & ((((uSubst95898992stappt @ Sigma) @ U) @ Eta2) != (none @ trm))))))).
% 2.81/1.58 thf(fact_242_usubstappt__differential__conv, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm]: ((((((uSubst95898992stappt @ Sigma) @ U) @ (differential @ Theta)) != (none @ trm)) => ((((uSubst95898992stappt @ Sigma) @ ((collect @ variable) @ (^ [X:variable]: ($true)))) @ Theta) != (none @ trm)))))).
% 2.81/1.58 thf(fact_243_usubstappt__induct, axiom, (! [P2:(((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) > ((set @ variable) > (trm > $o))),A0:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),A1:(set @ variable),A22:trm]: (((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),X3:variable]: ((((P2 @ Sigma3) @ U3) @ (var @ X3)))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),R3:real]: ((((P2 @ Sigma3) @ U3) @ (number @ R3)))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),F6:char]: ((((P2 @ Sigma3) @ U3) @ (const @ F6)))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),F6:char,Theta2:trm]: (((((P2 @ Sigma3) @ U3) @ Theta2) => ((! [X25:trm]: ((((((uSubst95898992stappt @ Sigma3) @ U3) @ Theta2) = ((some @ trm) @ X25)) => (! [X2a:trm]: (((((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [F4:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F4))))))))) @ Sigma3) @ F6) = ((some @ trm) @ X2a)) => (((((inf_inf @ (set @ variable)) @ (static_FVT @ X2a)) @ U3) = (bot_bot @ (set @ variable))) => (((P2 @ (uSubst969145931substt @ X25)) @ (bot_bot @ (set @ variable))) @ X2a)))))))) => (((P2 @ Sigma3) @ U3) @ ((func @ F6) @ Theta2)))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),Theta2:trm]: (((((P2 @ Sigma3) @ U3) @ Theta2) => (! [Eta:trm]: (((((P2 @ Sigma3) @ U3) @ Eta) => (((P2 @ Sigma3) @ U3) @ ((plus @ Theta2) @ Eta)))))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),Theta2:trm]: (((((P2 @ Sigma3) @ U3) @ Theta2) => (! [Eta:trm]: (((((P2 @ Sigma3) @ U3) @ Eta) => (((P2 @ Sigma3) @ U3) @ ((times @ Theta2) @ Eta)))))))) => ((! [Sigma3:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U3:(set @ variable),Theta2:trm]: (((((P2 @ Sigma3) @ ((collect @ variable) @ (^ [X:variable]: ($true)))) @ Theta2) => (((P2 @ Sigma3) @ U3) @ (differential @ Theta2))))) => (((P2 @ A0) @ A1) @ A22))))))))))).
% 2.81/1.58 thf(fact_244_dot__def, axiom, (uSubst_Mirabelle_dot = (const @ ((((((((char2 @ $false) @ $true) @ $true) @ $true) @ $false) @ $true) @ $false) @ $false)))).
% 2.81/1.58 thf(fact_245_usubstappt_Opelims, axiom, (! [X2:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),Xa:(set @ variable),Xb:trm,Y2:(option @ trm)]: ((((((uSubst95898992stappt @ X2) @ Xa) @ Xb) = Y2) => ((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ X2) @ ((((product_Pair @ (set @ variable)) @ trm) @ Xa) @ Xb))) => ((! [X3:variable]: (((Xb = (var @ X3)) => ((Y2 = ((some @ trm) @ (var @ X3))) => (~ ((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ X2) @ ((((product_Pair @ (set @ variable)) @ trm) @ Xa) @ (var @ X3)))))))))) => ((! [R3:real]: (((Xb = (number @ R3)) => ((Y2 = ((some @ trm) @ (number @ R3))) => (~ ((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ X2) @ ((((product_Pair @ (set @ variable)) @ trm) @ Xa) @ (number @ R3)))))))))) => ((! [F6:char]: (((Xb = (const @ F6)) => ((Y2 = (((uSubst1138577137pconst @ X2) @ Xa) @ F6)) => (~ ((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ X2) @ ((((product_Pair @ (set @ variable)) @ trm) @ Xa) @ (const @ F6)))))))))) => ((! [F6:char,Theta2:trm]: (((Xb = ((func @ F6) @ Theta2)) => ((Y2 = (((((case_option @ (option @ trm)) @ trm) @ (none @ trm)) @ (^ [Sigma_theta:trm]: ((((((case_option @ (option @ trm)) @ trm) @ ((some @ trm) @ ((func @ F6) @ Sigma_theta))) @ (^ [R:trm]: (((((if @ (option @ trm)) @ ((((inf_inf @ (set @ variable)) @ (static_FVT @ R)) @ Xa) = (bot_bot @ (set @ variable)))) @ (((uSubst95898992stappt @ (uSubst969145931substt @ Sigma_theta)) @ (bot_bot @ (set @ variable))) @ R)) @ (none @ trm))))) @ ((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ trm))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ trm))) @ (^ [F4:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ trm))) @ (^ [Uv:(char > (option @ fml)),Uw:(char > (option @ game))]: (F4))))))))) @ X2) @ F6))))) @ (((uSubst95898992stappt @ X2) @ Xa) @ Theta2))) => (~ ((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ X2) @ ((((product_Pair @ (set @ variable)) @ trm) @ Xa) @ ((func @ F6) @ Theta2)))))))))) => ((! [Theta2:trm,Eta:trm]: (((Xb = ((plus @ Theta2) @ Eta)) => ((Y2 = ((uSubst1112714340_Pluso @ (((uSubst95898992stappt @ X2) @ Xa) @ Theta2)) @ (((uSubst95898992stappt @ X2) @ Xa) @ Eta))) => (~ ((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ X2) @ ((((product_Pair @ (set @ variable)) @ trm) @ Xa) @ ((plus @ Theta2) @ Eta)))))))))) => ((! [Theta2:trm,Eta:trm]: (((Xb = ((times @ Theta2) @ Eta)) => ((Y2 = ((uSubst277968634Timeso @ (((uSubst95898992stappt @ X2) @ Xa) @ Theta2)) @ (((uSubst95898992stappt @ X2) @ Xa) @ Eta))) => (~ ((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ X2) @ ((((product_Pair @ (set @ variable)) @ trm) @ Xa) @ ((times @ Theta2) @ Eta)))))))))) => (~ ((! [Theta2:trm]: (((Xb = (differential @ Theta2)) => ((Y2 = (uSubst259074819ntialo @ (((uSubst95898992stappt @ X2) @ ((collect @ variable) @ (^ [X:variable]: ($true)))) @ Theta2))) => (~ ((((accp @ ((product_prod @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm))) @ uSubst2096773001pt_rel) @ ((((product_Pair @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))))) @ ((product_prod @ (set @ variable)) @ trm)) @ X2) @ ((((product_Pair @ (set @ variable)) @ trm) @ Xa) @ (differential @ Theta2))))))))))))))))))))))).
% 2.81/1.58 thf(fact_246_Differentialo_Osimps_I2_J, axiom, ((uSubst259074819ntialo @ (none @ trm)) = (none @ trm))).
% 2.81/1.58 thf(fact_247_Differentialo__undef, axiom, (! [Theta:(option @ trm)]: ((((uSubst259074819ntialo @ Theta) = (none @ trm)) = (Theta = (none @ trm)))))).
% 2.81/1.58 thf(fact_248_Pluso_Osimps_I2_J, axiom, (! [Eta2:(option @ trm)]: ((((uSubst1112714340_Pluso @ (none @ trm)) @ Eta2) = (none @ trm))))).
% 2.81/1.58 thf(fact_249_Timeso_Osimps_I2_J, axiom, (! [Eta2:(option @ trm)]: ((((uSubst277968634Timeso @ (none @ trm)) @ Eta2) = (none @ trm))))).
% 2.81/1.58 thf(fact_250_Pluso__undef, axiom, (! [Theta:(option @ trm),Eta2:(option @ trm)]: (((((uSubst1112714340_Pluso @ Theta) @ Eta2) = (none @ trm)) = ((Theta = (none @ trm)) | (Eta2 = (none @ trm))))))).
% 2.81/1.58 thf(fact_251_Timeso__undef, axiom, (! [Theta:(option @ trm),Eta2:(option @ trm)]: (((((uSubst277968634Timeso @ Theta) @ Eta2) = (none @ trm)) = ((Theta = (none @ trm)) | (Eta2 = (none @ trm))))))).
% 2.81/1.58 thf(fact_252_Pluso_Osimps_I3_J, axiom, (! [V3:trm]: ((((uSubst1112714340_Pluso @ ((some @ trm) @ V3)) @ (none @ trm)) = (none @ trm))))).
% 2.81/1.58 thf(fact_253_Timeso_Osimps_I3_J, axiom, (! [V3:trm]: ((((uSubst277968634Timeso @ ((some @ trm) @ V3)) @ (none @ trm)) = (none @ trm))))).
% 2.81/1.58 thf(fact_254_usubstappt_Osimps_I5_J, axiom, (! [Sigma:((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))),U:(set @ variable),Theta:trm,Eta2:trm]: (((((uSubst95898992stappt @ Sigma) @ U) @ ((plus @ Theta) @ Eta2)) = ((uSubst1112714340_Pluso @ (((uSubst95898992stappt @ Sigma) @ U) @ Theta)) @ (((uSubst95898992stappt @ Sigma) @ U) @ Eta2)))))).
% 2.81/1.58 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, (bounded_lattice @ $o)).
% 2.81/1.58 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A8:$tType]: ((bounded_lattice @ (set @ A8))))).
% 2.81/1.58 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounded_lattice @ (A8 > A9)))))).
% 2.81/1.58 thf(tcon_fun___Lattices_Obounded__lattice__bot, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounded_lattice_bot @ (A8 > A9)))))).
% 2.81/1.58 thf(tcon_fun___Lattices_Osemilattice__inf, axiom, (! [A8:$tType,A9:$tType]: (((semilattice_inf @ A9) => (semilattice_inf @ (A8 > A9)))))).
% 2.81/1.58 thf(tcon_fun___Lattices_Olattice, axiom, (! [A8:$tType,A9:$tType]: (((lattice @ A9) => (lattice @ (A8 > A9)))))).
% 2.81/1.58 thf(tcon_fun___Orderings_Obot, axiom, (! [A8:$tType,A9:$tType]: (((bot @ A9) => (bot @ (A8 > A9)))))).
% 2.81/1.58 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_3, axiom, (! [A8:$tType]: ((bounded_lattice_bot @ (set @ A8))))).
% 2.81/1.58 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_4, axiom, (! [A8:$tType]: ((semilattice_inf @ (set @ A8))))).
% 2.81/1.58 thf(tcon_Set_Oset___Lattices_Olattice_5, axiom, (! [A8:$tType]: ((lattice @ (set @ A8))))).
% 2.81/1.58 thf(tcon_Set_Oset___Orderings_Obot_6, axiom, (! [A8:$tType]: ((bot @ (set @ A8))))).
% 2.81/1.58 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_7, axiom, (bounded_lattice_bot @ $o)).
% 2.81/1.58 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_8, axiom, (semilattice_inf @ $o)).
% 2.81/1.58 thf(tcon_HOL_Obool___Lattices_Olattice_9, axiom, (lattice @ $o)).
% 2.81/1.58 thf(tcon_HOL_Obool___Orderings_Obot_10, axiom, (bot @ $o)).
% 2.81/1.58 thf(tcon_Real_Oreal___Lattices_Osemilattice__inf_11, axiom, (semilattice_inf @ real)).
% 2.81/1.58 thf(tcon_Real_Oreal___Lattices_Olattice_12, axiom, (lattice @ real)).
% 2.81/1.58 thf(help_If_3_1_T, axiom, (! [P2:$o]: (((P2 = $true) | (P2 = $false))))).
% 2.81/1.58 thf(help_If_2_1_T, axiom, (! [A:$tType,X2:A,Y2:A]: ((((((if @ A) @ $false) @ X2) @ Y2) = Y2)))).
% 2.81/1.58 thf(help_If_1_1_T, axiom, (! [A:$tType,X2:A,Y2:A]: ((((((if @ A) @ $true) @ X2) @ Y2) = X2)))).
% 2.81/1.58 thf(conj_0, conjecture, (((((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game))))) @ (char > (option @ fml))) @ (^ [Uu:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ trm))) @ ((product_prod @ (char > (option @ fml))) @ (char > (option @ game)))) @ (char > (option @ fml))) @ (^ [Uv:(char > (option @ trm))]: (((((product_case_prod @ (char > (option @ fml))) @ (char > (option @ game))) @ (char > (option @ fml))) @ (^ [P:(char > (option @ fml)),Uw:(char > (option @ game))]: (P))))))))) @ sigma) @ p) = (none @ fml))).
% 2.81/1.58 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.oidpnoGwex/DTF2DTF3332.p
% 2.81/1.58 ------------------------
% 3.06/1.66 ---- Cleaned THF ---
% 3.06/1.66 thf(ty_t_Product__Type_Oprod,type,
% 3.06/1.66 product_prod: $tType > $tType > $tType ).
% 3.06/1.66
% 3.06/1.66 thf(ty_t_Syntax_Ovariable,type,
% 3.06/1.66 variable: $tType ).
% 3.06/1.66
% 3.06/1.66 thf(ty_t_Option_Ooption,type,
% 3.06/1.66 option: $tType > $tType ).
% 3.06/1.66
% 3.06/1.66 thf(ty_t_Syntax_Ogame,type,
% 3.06/1.66 game: $tType ).
% 3.06/1.66
% 3.06/1.66 thf(ty_t_String_Ochar,type,
% 3.06/1.66 char: $tType ).
% 3.06/1.66
% 3.06/1.66 thf(ty_t_Syntax_Otrm,type,
% 3.06/1.66 trm: $tType ).
% 3.06/1.66
% 3.06/1.66 thf(ty_t_Syntax_Ofml,type,
% 3.06/1.66 fml: $tType ).
% 3.06/1.66
% 3.06/1.66 thf(ty_t_Real_Oreal,type,
% 3.06/1.66 real: $tType ).
% 3.06/1.66
% 3.06/1.66 thf(ty_t_Set_Oset,type,
% 3.06/1.66 set: $tType > $tType ).
% 3.06/1.66
% 3.06/1.66 thf(sy_cl_Lattices_Obounded__lattice,type,
% 3.06/1.66 bounded_lattice:
% 3.06/1.66 !>[A: $tType] : $o ).
% 3.06/1.66
% 3.06/1.66 thf(sy_cl_HOL_Otype,type,
% 3.06/1.66 type:
% 3.06/1.66 !>[A: $tType] : $o ).
% 3.06/1.66
% 3.06/1.66 thf(sy_cl_Orderings_Obot,type,
% 3.06/1.66 bot:
% 3.06/1.66 !>[A: $tType] : $o ).
% 3.06/1.66
% 3.06/1.66 thf(sy_cl_Lattices_Olattice,type,
% 3.06/1.66 lattice:
% 3.06/1.66 !>[A: $tType] : $o ).
% 3.06/1.66
% 3.06/1.66 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 3.06/1.66 semilattice_inf:
% 3.06/1.66 !>[A: $tType] : $o ).
% 3.06/1.66
% 3.06/1.66 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 3.06/1.66 bounded_lattice_bot:
% 3.06/1.66 !>[A: $tType] : $o ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_If,type,
% 3.06/1.66 if:
% 3.06/1.66 !>[A: $tType] : ( $o > A > A > A ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 3.06/1.66 inf_inf:
% 3.06/1.66 !>[A: $tType] : ( A > A > A ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Option_Ooption_ONone,type,
% 3.06/1.66 none:
% 3.06/1.66 !>[A: $tType] : ( option @ A ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Option_Ooption_OSome,type,
% 3.06/1.66 some:
% 3.06/1.66 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Option_Ooption_Ocase__option,type,
% 3.06/1.66 case_option:
% 3.06/1.66 !>[B: $tType,A: $tType] : ( B > ( A > B ) > ( option @ A ) > B ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Option_Ooption_Othe,type,
% 3.06/1.66 the:
% 3.06/1.66 !>[A: $tType] : ( ( option @ A ) > A ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Orderings_Obot__class_Obot,type,
% 3.06/1.66 bot_bot:
% 3.06/1.66 !>[A: $tType] : A ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Product__Type_OPair,type,
% 3.06/1.66 product_Pair:
% 3.06/1.66 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 3.06/1.66 produc2004651681e_prod:
% 3.06/1.66 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 3.06/1.66 product_rec_prod:
% 3.06/1.66 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Product__Type_Oprod_Ocase__prod,type,
% 3.06/1.66 product_case_prod:
% 3.06/1.66 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Set_OCollect,type,
% 3.06/1.66 collect:
% 3.06/1.66 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Set_Ois__empty,type,
% 3.06/1.66 is_empty:
% 3.06/1.66 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Static__Semantics_OFVF,type,
% 3.06/1.66 static_FVF: fml > ( set @ variable ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Static__Semantics_OFVT,type,
% 3.06/1.66 static_FVT: trm > ( set @ variable ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_String_Ochar_OChar,type,
% 3.06/1.66 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Syntax_Ofml_OGeq,type,
% 3.06/1.66 geq: trm > trm > fml ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Syntax_Ofml_OPred,type,
% 3.06/1.66 pred: char > trm > fml ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Syntax_Otrm_OConst,type,
% 3.06/1.66 const: char > trm ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Syntax_Otrm_ODifferential,type,
% 3.06/1.66 differential: trm > trm ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Syntax_Otrm_OFunc,type,
% 3.06/1.66 func: char > trm > trm ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Syntax_Otrm_ONumber,type,
% 3.06/1.66 number: real > trm ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Syntax_Otrm_OPlus,type,
% 3.06/1.66 plus: trm > trm > trm ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Syntax_Otrm_OTimes,type,
% 3.06/1.66 times: trm > trm > trm ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Syntax_Otrm_OVar,type,
% 3.06/1.66 var: variable > trm ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_USubst__Mirabelle__nnnzepxswx_ODifferentialo,type,
% 3.06/1.66 uSubst259074819ntialo: ( option @ trm ) > ( option @ trm ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OGeqo,type,
% 3.06/1.66 uSubst1556497037e_Geqo: ( option @ trm ) > ( option @ trm ) > ( option @ fml ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OPluso,type,
% 3.06/1.66 uSubst1112714340_Pluso: ( option @ trm ) > ( option @ trm ) > ( option @ trm ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTesto,type,
% 3.06/1.66 uSubst190403692_Testo: ( option @ fml ) > ( option @ game ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_USubst__Mirabelle__nnnzepxswx_OTimeso,type,
% 3.06/1.66 uSubst277968634Timeso: ( option @ trm ) > ( option @ trm ) > ( option @ trm ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Odot,type,
% 3.06/1.66 uSubst_Mirabelle_dot: trm ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Odotsubstt,type,
% 3.06/1.66 uSubst969145931substt: trm > ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousappconst,type,
% 3.06/1.66 uSubst1138577137pconst: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > char > ( option @ trm ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappf,type,
% 3.06/1.66 uSubst95898978stappf: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > fml > ( option @ fml ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappt,type,
% 3.06/1.66 uSubst95898992stappt: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > trm > ( option @ trm ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_USubst__Mirabelle__nnnzepxswx_Ousubstappt__rel,type,
% 3.06/1.66 uSubst2096773001pt_rel: ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) > ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) > $o ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_Wellfounded_Oaccp,type,
% 3.06/1.66 accp:
% 3.06/1.66 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_c_member,type,
% 3.06/1.66 member:
% 3.06/1.66 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_v_Ua____,type,
% 3.06/1.66 ua: set @ variable ).
% 3.06/1.66
% 3.06/1.66 thf(sy_v_Va____,type,
% 3.06/1.66 va: set @ variable ).
% 3.06/1.66
% 3.06/1.66 thf(sy_v__092_060sigma_062,type,
% 3.06/1.66 sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ).
% 3.06/1.66
% 3.06/1.66 thf(sy_v__092_060theta_062____,type,
% 3.06/1.66 theta: trm ).
% 3.06/1.66
% 3.06/1.66 thf(sy_v_p____,type,
% 3.06/1.66 p: char ).
% 3.06/1.66
% 3.06/1.66 thf(fact_0_f7,axiom,
% 3.06/1.66 ! [Z: option @ fml,F: fml > ( option @ fml ),Za: option @ fml] :
% 3.06/1.66 ( ( ( Za
% 3.06/1.66 = ( none @ fml ) )
% 3.06/1.66 => ( ( case_option @ ( option @ fml ) @ fml @ Z @ F @ Za )
% 3.06/1.66 = Z ) )
% 3.06/1.66 & ( ( Za
% 3.06/1.66 != ( none @ fml ) )
% 3.06/1.66 => ( ( case_option @ ( option @ fml ) @ fml @ Z @ F @ Za )
% 3.06/1.66 = ( F @ ( the @ fml @ Za ) ) ) ) ) ).
% 3.06/1.66
% 3.06/1.66 thf(fact_1_Pred_Oprems_I2_J,axiom,
% 3.06/1.66 ( ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) )
% 3.06/1.66 != ( none @ fml ) ) ).
% 3.06/1.66
% 3.06/1.66 thf(fact_2_case__prod__app,axiom,
% 3.06/1.66 ! [A: $tType,D: $tType,C: $tType,B: $tType] :
% 3.06/1.66 ( ( product_case_prod @ B @ C @ ( D > A ) )
% 3.06/1.66 = ( ^ [F2: B > C > D > A,X: product_prod @ B @ C,Y: D] :
% 3.06/1.66 ( product_case_prod @ B @ C @ A
% 3.06/1.67 @ ^ [L: B,R: C] : ( F2 @ L @ R @ Y )
% 3.06/1.67 @ X ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_3_Pred_Oprems_I1_J,axiom,
% 3.06/1.67 ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 3.06/1.67 != ( none @ fml ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_4__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_092_060close_062,axiom,
% 3.06/1.67 ~ ( ( ( inf_inf @ ( set @ variable )
% 3.06/1.67 @ ( static_FVF
% 3.06/1.67 @ ( the @ fml
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p ) ) )
% 3.06/1.67 @ va )
% 3.06/1.67 != ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 => ( ( none @ fml )
% 3.06/1.67 = ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) )
% 3.06/1.67 @ ( the @ fml
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_5_f9,axiom,
% 3.06/1.67 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p )
% 3.06/1.67 = ( none @ fml ) )
% 3.06/1.67 => ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 3.06/1.67 = ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_6__092_060open_062_Icase_ASPreds_A_092_060sigma_062_Ap_Aof_ANone_A_092_060Rightarrow_062_AAfml_A_IPred_Ap_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_124_ASome_Af_A_092_060Rightarrow_062_Aif_AFVF_Af_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_Af_Aelse_Aundeff_J_A_092_060noteq_062_A_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_092_060close_062,axiom,
% 3.06/1.67 ~ ( ( ( ( inf_inf @ ( set @ variable )
% 3.06/1.67 @ ( static_FVF
% 3.06/1.67 @ ( the @ fml
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p ) ) )
% 3.06/1.67 @ va )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 => ( ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) )
% 3.06/1.67 @ ^ [F2: fml] :
% 3.06/1.67 ( if @ ( option @ fml )
% 3.06/1.67 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ va )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 3.06/1.67 @ ( none @ fml ) )
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p ) )
% 3.06/1.67 = ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) )
% 3.06/1.67 @ ( the @ fml
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p ) ) ) ) )
% 3.06/1.67 & ( ( ( inf_inf @ ( set @ variable )
% 3.06/1.67 @ ( static_FVF
% 3.06/1.67 @ ( the @ fml
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p ) ) )
% 3.06/1.67 @ va )
% 3.06/1.67 != ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 => ( ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) )
% 3.06/1.67 @ ^ [F2: fml] :
% 3.06/1.67 ( if @ ( option @ fml )
% 3.06/1.67 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ va )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 3.06/1.67 @ ( none @ fml ) )
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p ) )
% 3.06/1.67 = ( none @ fml ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_7_Ando_Oinduct,axiom,
% 3.06/1.67 ! [P2: ( option @ fml ) > ( option @ fml ) > $o,A0: option @ fml,A1: option @ fml] :
% 3.06/1.67 ( ! [Phi: fml,Psi: fml] : ( P2 @ ( some @ fml @ Phi ) @ ( some @ fml @ Psi ) )
% 3.06/1.67 => ( ! [X_1: option @ fml] : ( P2 @ ( none @ fml ) @ X_1 )
% 3.06/1.67 => ( ! [V: fml] : ( P2 @ ( some @ fml @ V ) @ ( none @ fml ) )
% 3.06/1.67 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_8_Testo_Ocases,axiom,
% 3.06/1.67 ! [X2: option @ fml] :
% 3.06/1.67 ( ! [Phi: fml] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( some @ fml @ Phi ) )
% 3.06/1.67 => ( X2
% 3.06/1.67 = ( none @ fml ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_9_Testo_Oinduct,axiom,
% 3.06/1.67 ! [P2: ( option @ fml ) > $o,A0: option @ fml] :
% 3.06/1.67 ( ! [Phi: fml] : ( P2 @ ( some @ fml @ Phi ) )
% 3.06/1.67 => ( ( P2 @ ( none @ fml ) )
% 3.06/1.67 => ( P2 @ A0 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_10_undeff__equiv,axiom,
% 3.06/1.67 ! [Phi2: option @ fml] :
% 3.06/1.67 ( ( Phi2
% 3.06/1.67 != ( none @ fml ) )
% 3.06/1.67 = ( ? [F2: fml] :
% 3.06/1.67 ( Phi2
% 3.06/1.67 = ( some @ fml @ F2 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_11_Existso_Oinduct,axiom,
% 3.06/1.67 ! [P2: variable > ( option @ fml ) > $o,A0: variable,A1: option @ fml] :
% 3.06/1.67 ( ! [X3: variable,Phi: fml] : ( P2 @ X3 @ ( some @ fml @ Phi ) )
% 3.06/1.67 => ( ! [X3: variable] : ( P2 @ X3 @ ( none @ fml ) )
% 3.06/1.67 => ( P2 @ A0 @ A1 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_12_prod_Ocase__distrib,axiom,
% 3.06/1.67 ! [C: $tType,D: $tType,B: $tType,A: $tType,H: C > D,F3: A > B > C,Prod: product_prod @ A @ B] :
% 3.06/1.67 ( ( H @ ( product_case_prod @ A @ B @ C @ F3 @ Prod ) )
% 3.06/1.67 = ( product_case_prod @ A @ B @ D
% 3.06/1.67 @ ^ [X1: A,X22: B] : ( H @ ( F3 @ X1 @ X22 ) )
% 3.06/1.67 @ Prod ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_13__092_060open_062usubstappf_A_092_060sigma_062_AU_A_IPred_Ap_A_092_060theta_062_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_092_060close_062,axiom,
% 3.06/1.67 ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 3.06/1.67 != ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_14_f5,axiom,
% 3.06/1.67 ( ( uSubst95898992stappt @ sigma @ ua @ theta )
% 3.06/1.67 = ( uSubst95898992stappt @ sigma @ va @ theta ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_15_calculation_I1_J,axiom,
% 3.06/1.67 ~ ( ( ( ( inf_inf @ ( set @ variable )
% 3.06/1.67 @ ( static_FVF
% 3.06/1.67 @ ( the @ fml
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p ) ) )
% 3.06/1.67 @ va )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 => ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 3.06/1.67 = ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) )
% 3.06/1.67 @ ( the @ fml
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p ) ) ) ) )
% 3.06/1.67 & ( ( ( inf_inf @ ( set @ variable )
% 3.06/1.67 @ ( static_FVF
% 3.06/1.67 @ ( the @ fml
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p ) ) )
% 3.06/1.67 @ va )
% 3.06/1.67 != ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 => ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 3.06/1.67 = ( none @ fml ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_16_calculation_I2_J,axiom,
% 3.06/1.67 ( ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 3.06/1.67 != ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) )
% 3.06/1.67 @ ( the @ fml
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p ) ) ) )
% 3.06/1.67 => ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p )
% 3.06/1.67 = ( none @ fml ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_17_f6,axiom,
% 3.06/1.67 ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 3.06/1.67 = ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) )
% 3.06/1.67 @ ^ [F2: fml] :
% 3.06/1.67 ( if @ ( option @ fml )
% 3.06/1.67 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ ua )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 3.06/1.67 @ ( none @ fml ) )
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_18__092_060open_062usubstappf_A_092_060sigma_062_AU_A_IPred_Ap_A_092_060theta_062_J_A_092_060noteq_062_A_Icase_ASPreds_A_092_060sigma_062_Ap_Aof_ANone_A_092_060Rightarrow_062_AAfml_A_IPred_Ap_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_124_ASome_Af_A_092_060Rightarrow_062_Aif_AFVF_Af_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_Af_Aelse_Aundeff_J_092_060close_062,axiom,
% 3.06/1.67 ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 3.06/1.67 != ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) )
% 3.06/1.67 @ ^ [F2: fml] :
% 3.06/1.67 ( if @ ( option @ fml )
% 3.06/1.67 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ va )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 3.06/1.67 @ ( none @ fml ) )
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_19_usubstappf__pred2,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),P3: char,R2: fml,U: set @ variable,Theta: trm] :
% 3.06/1.67 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ Sigma
% 3.06/1.67 @ P3 )
% 3.06/1.67 = ( some @ fml @ R2 ) )
% 3.06/1.67 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R2 ) @ U )
% 3.06/1.67 != ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 => ( ( uSubst95898978stappf @ Sigma @ U @ ( pred @ P3 @ Theta ) )
% 3.06/1.67 = ( none @ fml ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_20_f3,axiom,
% 3.06/1.67 ( ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
% 3.06/1.67 @ ^ [T2: trm] :
% 3.06/1.67 ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ T2 ) )
% 3.06/1.67 @ ^ [F2: fml] :
% 3.06/1.67 ( if @ ( option @ fml )
% 3.06/1.67 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ ua )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ T2 ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 3.06/1.67 @ ( none @ fml ) )
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p ) )
% 3.06/1.67 @ ( uSubst95898992stappt @ sigma @ ua @ theta ) )
% 3.06/1.67 = ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ua @ theta ) ) ) )
% 3.06/1.67 @ ^ [F2: fml] :
% 3.06/1.67 ( if @ ( option @ fml )
% 3.06/1.67 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ ua )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ua @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 3.06/1.67 @ ( none @ fml ) )
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_21_f8,axiom,
% 3.06/1.67 ( ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
% 3.06/1.67 @ ^ [T2: trm] :
% 3.06/1.67 ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ T2 ) )
% 3.06/1.67 @ ^ [F2: fml] :
% 3.06/1.67 ( if @ ( option @ fml )
% 3.06/1.67 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ va )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ T2 ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 3.06/1.67 @ ( none @ fml ) )
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p ) )
% 3.06/1.67 @ ( uSubst95898992stappt @ sigma @ va @ theta ) )
% 3.06/1.67 = ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) )
% 3.06/1.67 @ ^ [F2: fml] :
% 3.06/1.67 ( if @ ( option @ fml )
% 3.06/1.67 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ va )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 3.06/1.67 @ ( none @ fml ) )
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_22_f1,axiom,
% 3.06/1.67 ( ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
% 3.06/1.67 @ ^ [T2: trm] :
% 3.06/1.67 ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ T2 ) )
% 3.06/1.67 @ ^ [F2: fml] :
% 3.06/1.67 ( if @ ( option @ fml )
% 3.06/1.67 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ ua )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ T2 ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 3.06/1.67 @ ( none @ fml ) )
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p ) )
% 3.06/1.67 @ ( uSubst95898992stappt @ sigma @ ua @ theta ) )
% 3.06/1.67 != ( none @ fml ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_23_f4,axiom,
% 3.06/1.67 ( ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
% 3.06/1.67 @ ^ [T2: trm] :
% 3.06/1.67 ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ T2 ) )
% 3.06/1.67 @ ^ [F2: fml] :
% 3.06/1.67 ( if @ ( option @ fml )
% 3.06/1.67 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F2 ) @ va )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ T2 ) @ ( bot_bot @ ( set @ variable ) ) @ F2 )
% 3.06/1.67 @ ( none @ fml ) )
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p ) )
% 3.06/1.67 @ ( uSubst95898992stappt @ sigma @ va @ theta ) )
% 3.06/1.67 != ( none @ fml ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_24_option_Ocollapse,axiom,
% 3.06/1.67 ! [A: $tType,Option: option @ A] :
% 3.06/1.67 ( ( Option
% 3.06/1.67 != ( none @ A ) )
% 3.06/1.67 => ( ( some @ A @ ( the @ A @ Option ) )
% 3.06/1.67 = Option ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_25_not__Some__eq,axiom,
% 3.06/1.67 ! [A: $tType,X2: option @ A] :
% 3.06/1.67 ( ( ! [Y: A] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( some @ A @ Y ) ) )
% 3.06/1.67 = ( X2
% 3.06/1.67 = ( none @ A ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_26_not__None__eq,axiom,
% 3.06/1.67 ! [A: $tType,X2: option @ A] :
% 3.06/1.67 ( ( X2
% 3.06/1.67 != ( none @ A ) )
% 3.06/1.67 = ( ? [Y: A] :
% 3.06/1.67 ( X2
% 3.06/1.67 = ( some @ A @ Y ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_27_usubstappf_Osimps_I1_J,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,P3: char,Theta: trm] :
% 3.06/1.67 ( ( uSubst95898978stappf @ Sigma @ U @ ( pred @ P3 @ Theta ) )
% 3.06/1.67 = ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
% 3.06/1.67 @ ^ [Sigma_theta: trm] :
% 3.06/1.67 ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ P3 @ Sigma_theta ) )
% 3.06/1.67 @ ^ [R: fml] :
% 3.06/1.67 ( if @ ( option @ fml )
% 3.06/1.67 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R ) @ U )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 @ ( uSubst95898978stappf @ ( uSubst969145931substt @ Sigma_theta ) @ ( bot_bot @ ( set @ variable ) ) @ R )
% 3.06/1.67 @ ( none @ fml ) )
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ Sigma
% 3.06/1.67 @ P3 ) )
% 3.06/1.67 @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_28_inf__bot__left,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( bounded_lattice_bot @ A )
% 3.06/1.67 => ! [X2: A] :
% 3.06/1.67 ( ( inf_inf @ A @ ( bot_bot @ A ) @ X2 )
% 3.06/1.67 = ( bot_bot @ A ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_29_inf__bot__right,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( bounded_lattice_bot @ A )
% 3.06/1.67 => ! [X2: A] :
% 3.06/1.67 ( ( inf_inf @ A @ X2 @ ( bot_bot @ A ) )
% 3.06/1.67 = ( bot_bot @ A ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_30_option_Osplit__sel__asm,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType,P2: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 3.06/1.67 ( ( P2 @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 3.06/1.67 = ( ~ ( ( ( Option
% 3.06/1.67 = ( none @ A ) )
% 3.06/1.67 & ~ ( P2 @ F1 ) )
% 3.06/1.67 | ( ( Option
% 3.06/1.67 = ( some @ A @ ( the @ A @ Option ) ) )
% 3.06/1.67 & ~ ( P2 @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_31_f2,axiom,
% 3.06/1.67 ! [Z: option @ fml,F: trm > ( option @ fml ),Za: option @ trm] :
% 3.06/1.67 ( ( ( Za
% 3.06/1.67 = ( none @ trm ) )
% 3.06/1.67 => ( ( case_option @ ( option @ fml ) @ trm @ Z @ F @ Za )
% 3.06/1.67 = Z ) )
% 3.06/1.67 & ( ( Za
% 3.06/1.67 != ( none @ trm ) )
% 3.06/1.67 => ( ( case_option @ ( option @ fml ) @ trm @ Z @ F @ Za )
% 3.06/1.67 = ( F @ ( the @ trm @ Za ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_32_inf__right__idem,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( semilattice_inf @ A )
% 3.06/1.67 => ! [X2: A,Y2: A] :
% 3.06/1.67 ( ( inf_inf @ A @ ( inf_inf @ A @ X2 @ Y2 ) @ Y2 )
% 3.06/1.67 = ( inf_inf @ A @ X2 @ Y2 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_33_inf_Oright__idem,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( semilattice_inf @ A )
% 3.06/1.67 => ! [A2: A,B2: A] :
% 3.06/1.67 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 )
% 3.06/1.67 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_34_inf__left__idem,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( semilattice_inf @ A )
% 3.06/1.67 => ! [X2: A,Y2: A] :
% 3.06/1.67 ( ( inf_inf @ A @ X2 @ ( inf_inf @ A @ X2 @ Y2 ) )
% 3.06/1.67 = ( inf_inf @ A @ X2 @ Y2 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_35_inf_Oleft__idem,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( semilattice_inf @ A )
% 3.06/1.67 => ! [A2: A,B2: A] :
% 3.06/1.67 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B2 ) )
% 3.06/1.67 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_36_inf__idem,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( semilattice_inf @ A )
% 3.06/1.67 => ! [X2: A] :
% 3.06/1.67 ( ( inf_inf @ A @ X2 @ X2 )
% 3.06/1.67 = X2 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_37_inf_Oidem,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( semilattice_inf @ A )
% 3.06/1.67 => ! [A2: A] :
% 3.06/1.67 ( ( inf_inf @ A @ A2 @ A2 )
% 3.06/1.67 = A2 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_38_inf__apply,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType] :
% 3.06/1.67 ( ( semilattice_inf @ B )
% 3.06/1.67 => ( ( inf_inf @ ( A > B ) )
% 3.06/1.67 = ( ^ [F2: A > B,G: A > B,X: A] : ( inf_inf @ B @ ( F2 @ X ) @ ( G @ X ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_39_option_Oinject,axiom,
% 3.06/1.67 ! [A: $tType,X23: A,Y22: A] :
% 3.06/1.67 ( ( ( some @ A @ X23 )
% 3.06/1.67 = ( some @ A @ Y22 ) )
% 3.06/1.67 = ( X23 = Y22 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_40_usubstappf__pred,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),P3: char,R2: fml,U: set @ variable,Theta: trm,Sigma_theta2: trm] :
% 3.06/1.67 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ Sigma
% 3.06/1.67 @ P3 )
% 3.06/1.67 = ( some @ fml @ R2 ) )
% 3.06/1.67 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R2 ) @ U )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 3.06/1.67 = ( some @ trm @ Sigma_theta2 ) )
% 3.06/1.67 => ( ( uSubst95898978stappf @ Sigma @ U @ ( pred @ P3 @ Theta ) )
% 3.06/1.67 = ( uSubst95898978stappf @ ( uSubst969145931substt @ Sigma_theta2 ) @ ( bot_bot @ ( set @ variable ) ) @ R2 ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_41_Diamondo_Oinduct,axiom,
% 3.06/1.67 ! [P2: ( option @ game ) > ( option @ fml ) > $o,A0: option @ game,A1: option @ fml] :
% 3.06/1.67 ( ! [Alpha: game,Phi: fml] : ( P2 @ ( some @ game @ Alpha ) @ ( some @ fml @ Phi ) )
% 3.06/1.67 => ( ! [X_1: option @ fml] : ( P2 @ ( none @ game ) @ X_1 )
% 3.06/1.67 => ( ! [V: game] : ( P2 @ ( some @ game @ V ) @ ( none @ fml ) )
% 3.06/1.67 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_42_option_Odisc__eq__case_I2_J,axiom,
% 3.06/1.67 ! [A: $tType,Option: option @ A] :
% 3.06/1.67 ( ( Option
% 3.06/1.67 != ( none @ A ) )
% 3.06/1.67 = ( case_option @ $o @ A @ $false
% 3.06/1.67 @ ^ [Uu: A] : $true
% 3.06/1.67 @ Option ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_43_option_Odisc__eq__case_I1_J,axiom,
% 3.06/1.67 ! [A: $tType,Option: option @ A] :
% 3.06/1.67 ( ( Option
% 3.06/1.67 = ( none @ A ) )
% 3.06/1.67 = ( case_option @ $o @ A @ $true
% 3.06/1.67 @ ^ [Uu: A] : $false
% 3.06/1.67 @ Option ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_44_usubstappt__det,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,V2: set @ variable] :
% 3.06/1.67 ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 3.06/1.67 != ( none @ trm ) )
% 3.06/1.67 => ( ( ( uSubst95898992stappt @ Sigma @ V2 @ Theta )
% 3.06/1.67 != ( none @ trm ) )
% 3.06/1.67 => ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 3.06/1.67 = ( uSubst95898992stappt @ Sigma @ V2 @ Theta ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_45_mem__Collect__eq,axiom,
% 3.06/1.67 ! [A: $tType,A2: A,P2: A > $o] :
% 3.06/1.67 ( ( member @ A @ A2 @ ( collect @ A @ P2 ) )
% 3.06/1.67 = ( P2 @ A2 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_46_Collect__mem__eq,axiom,
% 3.06/1.67 ! [A: $tType,A3: set @ A] :
% 3.06/1.67 ( ( collect @ A
% 3.06/1.67 @ ^ [X: A] : ( member @ A @ X @ A3 ) )
% 3.06/1.67 = A3 ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_47_Collect__cong,axiom,
% 3.06/1.67 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 3.06/1.67 ( ! [X3: A] :
% 3.06/1.67 ( ( P2 @ X3 )
% 3.06/1.67 = ( Q @ X3 ) )
% 3.06/1.67 => ( ( collect @ A @ P2 )
% 3.06/1.67 = ( collect @ A @ Q ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_48_ext,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType,F3: A > B,G2: A > B] :
% 3.06/1.67 ( ! [X3: A] :
% 3.06/1.67 ( ( F3 @ X3 )
% 3.06/1.67 = ( G2 @ X3 ) )
% 3.06/1.67 => ( F3 = G2 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_49_case__optionE,axiom,
% 3.06/1.67 ! [A: $tType,P2: $o,Q: A > $o,X2: option @ A] :
% 3.06/1.67 ( ( case_option @ $o @ A @ P2 @ Q @ X2 )
% 3.06/1.67 => ( ( ( X2
% 3.06/1.67 = ( none @ A ) )
% 3.06/1.67 => ~ P2 )
% 3.06/1.67 => ~ ! [Y3: A] :
% 3.06/1.67 ( ( X2
% 3.06/1.67 = ( some @ A @ Y3 ) )
% 3.06/1.67 => ~ ( Q @ Y3 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_50_inf__left__commute,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( semilattice_inf @ A )
% 3.06/1.67 => ! [X2: A,Y2: A,Z2: A] :
% 3.06/1.67 ( ( inf_inf @ A @ X2 @ ( inf_inf @ A @ Y2 @ Z2 ) )
% 3.06/1.67 = ( inf_inf @ A @ Y2 @ ( inf_inf @ A @ X2 @ Z2 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_51_inf_Oleft__commute,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( semilattice_inf @ A )
% 3.06/1.67 => ! [B2: A,A2: A,C2: A] :
% 3.06/1.67 ( ( inf_inf @ A @ B2 @ ( inf_inf @ A @ A2 @ C2 ) )
% 3.06/1.67 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_52_inf__commute,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( semilattice_inf @ A )
% 3.06/1.67 => ( ( inf_inf @ A )
% 3.06/1.67 = ( ^ [X: A,Y: A] : ( inf_inf @ A @ Y @ X ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_53_inf_Ocommute,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( semilattice_inf @ A )
% 3.06/1.67 => ( ( inf_inf @ A )
% 3.06/1.67 = ( ^ [A4: A,B3: A] : ( inf_inf @ A @ B3 @ A4 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_54_inf__assoc,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( semilattice_inf @ A )
% 3.06/1.67 => ! [X2: A,Y2: A,Z2: A] :
% 3.06/1.67 ( ( inf_inf @ A @ ( inf_inf @ A @ X2 @ Y2 ) @ Z2 )
% 3.06/1.67 = ( inf_inf @ A @ X2 @ ( inf_inf @ A @ Y2 @ Z2 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_55_inf_Oassoc,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( semilattice_inf @ A )
% 3.06/1.67 => ! [A2: A,B2: A,C2: A] :
% 3.06/1.67 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C2 )
% 3.06/1.67 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_56_boolean__algebra__cancel_Oinf2,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( semilattice_inf @ A )
% 3.06/1.67 => ! [B4: A,K: A,B2: A,A2: A] :
% 3.06/1.67 ( ( B4
% 3.06/1.67 = ( inf_inf @ A @ K @ B2 ) )
% 3.06/1.67 => ( ( inf_inf @ A @ A2 @ B4 )
% 3.06/1.67 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_57_boolean__algebra__cancel_Oinf1,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( semilattice_inf @ A )
% 3.06/1.67 => ! [A3: A,K: A,A2: A,B2: A] :
% 3.06/1.67 ( ( A3
% 3.06/1.67 = ( inf_inf @ A @ K @ A2 ) )
% 3.06/1.67 => ( ( inf_inf @ A @ A3 @ B2 )
% 3.06/1.67 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_58_inf__fun__def,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType] :
% 3.06/1.67 ( ( semilattice_inf @ B )
% 3.06/1.67 => ( ( inf_inf @ ( A > B ) )
% 3.06/1.67 = ( ^ [F2: A > B,G: A > B,X: A] : ( inf_inf @ B @ ( F2 @ X ) @ ( G @ X ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_59_inf__sup__aci_I1_J,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( lattice @ A )
% 3.06/1.67 => ( ( inf_inf @ A )
% 3.06/1.67 = ( ^ [X: A,Y: A] : ( inf_inf @ A @ Y @ X ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_60_inf__sup__aci_I2_J,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( lattice @ A )
% 3.06/1.67 => ! [X2: A,Y2: A,Z2: A] :
% 3.06/1.67 ( ( inf_inf @ A @ ( inf_inf @ A @ X2 @ Y2 ) @ Z2 )
% 3.06/1.67 = ( inf_inf @ A @ X2 @ ( inf_inf @ A @ Y2 @ Z2 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_61_inf__sup__aci_I3_J,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( lattice @ A )
% 3.06/1.67 => ! [X2: A,Y2: A,Z2: A] :
% 3.06/1.67 ( ( inf_inf @ A @ X2 @ ( inf_inf @ A @ Y2 @ Z2 ) )
% 3.06/1.67 = ( inf_inf @ A @ Y2 @ ( inf_inf @ A @ X2 @ Z2 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_62_inf__sup__aci_I4_J,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( lattice @ A )
% 3.06/1.67 => ! [X2: A,Y2: A] :
% 3.06/1.67 ( ( inf_inf @ A @ X2 @ ( inf_inf @ A @ X2 @ Y2 ) )
% 3.06/1.67 = ( inf_inf @ A @ X2 @ Y2 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_63_option_Ocase__distrib,axiom,
% 3.06/1.67 ! [C: $tType,B: $tType,A: $tType,H: B > C,F1: B,F22: A > B,Option: option @ A] :
% 3.06/1.67 ( ( H @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 3.06/1.67 = ( case_option @ C @ A @ ( H @ F1 )
% 3.06/1.67 @ ^ [X: A] : ( H @ ( F22 @ X ) )
% 3.06/1.67 @ Option ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_64_option_Odistinct_I1_J,axiom,
% 3.06/1.67 ! [A: $tType,X23: A] :
% 3.06/1.67 ( ( none @ A )
% 3.06/1.67 != ( some @ A @ X23 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_65_option_OdiscI,axiom,
% 3.06/1.67 ! [A: $tType,Option: option @ A,X23: A] :
% 3.06/1.67 ( ( Option
% 3.06/1.67 = ( some @ A @ X23 ) )
% 3.06/1.67 => ( Option
% 3.06/1.67 != ( none @ A ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_66_option_Oexhaust,axiom,
% 3.06/1.67 ! [A: $tType,Y2: option @ A] :
% 3.06/1.67 ( ( Y2
% 3.06/1.67 != ( none @ A ) )
% 3.06/1.67 => ~ ! [X24: A] :
% 3.06/1.67 ( Y2
% 3.06/1.67 != ( some @ A @ X24 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_67_option_Oinducts,axiom,
% 3.06/1.67 ! [A: $tType,P2: ( option @ A ) > $o,Option: option @ A] :
% 3.06/1.67 ( ( P2 @ ( none @ A ) )
% 3.06/1.67 => ( ! [X3: A] : ( P2 @ ( some @ A @ X3 ) )
% 3.06/1.67 => ( P2 @ Option ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_68_split__option__ex,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( ^ [P4: ( option @ A ) > $o] :
% 3.06/1.67 ? [X4: option @ A] : ( P4 @ X4 ) )
% 3.06/1.67 = ( ^ [P: ( option @ A ) > $o] :
% 3.06/1.67 ( ( P @ ( none @ A ) )
% 3.06/1.67 | ? [X: A] : ( P @ ( some @ A @ X ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_69_split__option__all,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( ^ [P4: ( option @ A ) > $o] :
% 3.06/1.67 ! [X4: option @ A] : ( P4 @ X4 ) )
% 3.06/1.67 = ( ^ [P: ( option @ A ) > $o] :
% 3.06/1.67 ( ( P @ ( none @ A ) )
% 3.06/1.67 & ! [X: A] : ( P @ ( some @ A @ X ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_70_combine__options__cases,axiom,
% 3.06/1.67 ! [A: $tType,B: $tType,X2: option @ A,P2: ( option @ A ) > ( option @ B ) > $o,Y2: option @ B] :
% 3.06/1.67 ( ( ( X2
% 3.06/1.67 = ( none @ A ) )
% 3.06/1.67 => ( P2 @ X2 @ Y2 ) )
% 3.06/1.67 => ( ( ( Y2
% 3.06/1.67 = ( none @ B ) )
% 3.06/1.67 => ( P2 @ X2 @ Y2 ) )
% 3.06/1.67 => ( ! [A5: A,B5: B] :
% 3.06/1.67 ( ( X2
% 3.06/1.67 = ( some @ A @ A5 ) )
% 3.06/1.67 => ( ( Y2
% 3.06/1.67 = ( some @ B @ B5 ) )
% 3.06/1.67 => ( P2 @ X2 @ Y2 ) ) )
% 3.06/1.67 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_71_option_Osimps_I4_J,axiom,
% 3.06/1.67 ! [A: $tType,B: $tType,F1: B,F22: A > B] :
% 3.06/1.67 ( ( case_option @ B @ A @ F1 @ F22 @ ( none @ A ) )
% 3.06/1.67 = F1 ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_72_option_Oexpand,axiom,
% 3.06/1.67 ! [A: $tType,Option: option @ A,Option2: option @ A] :
% 3.06/1.67 ( ( ( Option
% 3.06/1.67 = ( none @ A ) )
% 3.06/1.67 = ( Option2
% 3.06/1.67 = ( none @ A ) ) )
% 3.06/1.67 => ( ( ( Option
% 3.06/1.67 != ( none @ A ) )
% 3.06/1.67 => ( ( Option2
% 3.06/1.67 != ( none @ A ) )
% 3.06/1.67 => ( ( the @ A @ Option )
% 3.06/1.67 = ( the @ A @ Option2 ) ) ) )
% 3.06/1.67 => ( Option = Option2 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_73_option_Osimps_I5_J,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType,F1: B,F22: A > B,X23: A] :
% 3.06/1.67 ( ( case_option @ B @ A @ F1 @ F22 @ ( some @ A @ X23 ) )
% 3.06/1.67 = ( F22 @ X23 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_74_option_Osel,axiom,
% 3.06/1.67 ! [A: $tType,X23: A] :
% 3.06/1.67 ( ( the @ A @ ( some @ A @ X23 ) )
% 3.06/1.67 = X23 ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_75_option_Oexhaust__sel,axiom,
% 3.06/1.67 ! [A: $tType,Option: option @ A] :
% 3.06/1.67 ( ( Option
% 3.06/1.67 != ( none @ A ) )
% 3.06/1.67 => ( Option
% 3.06/1.67 = ( some @ A @ ( the @ A @ Option ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_76_option_Ocase__eq__if,axiom,
% 3.06/1.67 ! [A: $tType,B: $tType] :
% 3.06/1.67 ( ( case_option @ B @ A )
% 3.06/1.67 = ( ^ [F12: B,F23: A > B,Option3: option @ A] :
% 3.06/1.67 ( if @ B
% 3.06/1.67 @ ( Option3
% 3.06/1.67 = ( none @ A ) )
% 3.06/1.67 @ F12
% 3.06/1.67 @ ( F23 @ ( the @ A @ Option3 ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_77_usubstappf__pred__conv,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,P3: char,Theta: trm] :
% 3.06/1.67 ( ( ( uSubst95898978stappf @ Sigma @ U @ ( pred @ P3 @ Theta ) )
% 3.06/1.67 != ( none @ fml ) )
% 3.06/1.67 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 3.06/1.67 != ( none @ trm ) )
% 3.06/1.67 & ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ Sigma
% 3.06/1.67 @ P3 )
% 3.06/1.67 = ( none @ fml ) )
% 3.06/1.67 | ? [R3: fml] :
% 3.06/1.67 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ Sigma
% 3.06/1.67 @ P3 )
% 3.06/1.67 = ( some @ fml @ R3 ) )
% 3.06/1.67 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ R3 ) @ U )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_78_option_Osplit__sel,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType,P2: B > $o,F1: B,F22: A > B,Option: option @ A] :
% 3.06/1.67 ( ( P2 @ ( case_option @ B @ A @ F1 @ F22 @ Option ) )
% 3.06/1.67 = ( ( ( Option
% 3.06/1.67 = ( none @ A ) )
% 3.06/1.67 => ( P2 @ F1 ) )
% 3.06/1.67 & ( ( Option
% 3.06/1.67 = ( some @ A @ ( the @ A @ Option ) ) )
% 3.06/1.67 => ( P2 @ ( F22 @ ( the @ A @ Option ) ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_79_fml_Oinject_I1_J,axiom,
% 3.06/1.67 ! [X11: char,X12: trm,Y11: char,Y12: trm] :
% 3.06/1.67 ( ( ( pred @ X11 @ X12 )
% 3.06/1.67 = ( pred @ Y11 @ Y12 ) )
% 3.06/1.67 = ( ( X11 = Y11 )
% 3.06/1.67 & ( X12 = Y12 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_80_Int__iff,axiom,
% 3.06/1.67 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 3.06/1.67 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 3.06/1.67 = ( ( member @ A @ C2 @ A3 )
% 3.06/1.67 & ( member @ A @ C2 @ B4 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_81_IntI,axiom,
% 3.06/1.67 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 3.06/1.67 ( ( member @ A @ C2 @ A3 )
% 3.06/1.67 => ( ( member @ A @ C2 @ B4 )
% 3.06/1.67 => ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_82_empty__Collect__eq,axiom,
% 3.06/1.67 ! [A: $tType,P2: A > $o] :
% 3.06/1.67 ( ( ( bot_bot @ ( set @ A ) )
% 3.06/1.67 = ( collect @ A @ P2 ) )
% 3.06/1.67 = ( ! [X: A] :
% 3.06/1.67 ~ ( P2 @ X ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_83_Collect__empty__eq,axiom,
% 3.06/1.67 ! [A: $tType,P2: A > $o] :
% 3.06/1.67 ( ( ( collect @ A @ P2 )
% 3.06/1.67 = ( bot_bot @ ( set @ A ) ) )
% 3.06/1.67 = ( ! [X: A] :
% 3.06/1.67 ~ ( P2 @ X ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_84_all__not__in__conv,axiom,
% 3.06/1.67 ! [A: $tType,A3: set @ A] :
% 3.06/1.67 ( ( ! [X: A] :
% 3.06/1.67 ~ ( member @ A @ X @ A3 ) )
% 3.06/1.67 = ( A3
% 3.06/1.67 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_85_empty__iff,axiom,
% 3.06/1.67 ! [A: $tType,C2: A] :
% 3.06/1.67 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_86_bot__apply,axiom,
% 3.06/1.67 ! [C: $tType,D: $tType] :
% 3.06/1.67 ( ( bot @ C )
% 3.06/1.67 => ( ( bot_bot @ ( D > C ) )
% 3.06/1.67 = ( ^ [X: D] : ( bot_bot @ C ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_87_disjoint__iff__not__equal,axiom,
% 3.06/1.67 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 3.06/1.67 ( ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 3.06/1.67 = ( bot_bot @ ( set @ A ) ) )
% 3.06/1.67 = ( ! [X: A] :
% 3.06/1.67 ( ( member @ A @ X @ A3 )
% 3.06/1.67 => ! [Y: A] :
% 3.06/1.67 ( ( member @ A @ Y @ B4 )
% 3.06/1.67 => ( X != Y ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_88_Aterm__Some,axiom,
% 3.06/1.67 ( ( some @ trm )
% 3.06/1.67 = ( some @ trm ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_89_Loopo_Ocases,axiom,
% 3.06/1.67 ! [X2: option @ game] :
% 3.06/1.67 ( ! [Alpha: game] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( some @ game @ Alpha ) )
% 3.06/1.67 => ( X2
% 3.06/1.67 = ( none @ game ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_90_ODEo_Oinduct,axiom,
% 3.06/1.67 ! [P2: char > ( option @ trm ) > $o,A0: char,A1: option @ trm] :
% 3.06/1.67 ( ! [X3: char,Theta2: trm] : ( P2 @ X3 @ ( some @ trm @ Theta2 ) )
% 3.06/1.67 => ( ! [X3: char] : ( P2 @ X3 @ ( none @ trm ) )
% 3.06/1.67 => ( P2 @ A0 @ A1 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_91_Loopo_Oinduct,axiom,
% 3.06/1.67 ! [P2: ( option @ game ) > $o,A0: option @ game] :
% 3.06/1.67 ( ! [Alpha: game] : ( P2 @ ( some @ game @ Alpha ) )
% 3.06/1.67 => ( ( P2 @ ( none @ game ) )
% 3.06/1.67 => ( P2 @ A0 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_92_undefg__equiv,axiom,
% 3.06/1.67 ! [Alpha2: option @ game] :
% 3.06/1.67 ( ( Alpha2
% 3.06/1.67 != ( none @ game ) )
% 3.06/1.67 = ( ? [G: game] :
% 3.06/1.67 ( Alpha2
% 3.06/1.67 = ( some @ game @ G ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_93_undeft__equiv,axiom,
% 3.06/1.67 ! [Theta: option @ trm] :
% 3.06/1.67 ( ( Theta
% 3.06/1.67 != ( none @ trm ) )
% 3.06/1.67 = ( ? [T2: trm] :
% 3.06/1.67 ( Theta
% 3.06/1.67 = ( some @ trm @ T2 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_94_Timeso_Oinduct,axiom,
% 3.06/1.67 ! [P2: ( option @ trm ) > ( option @ trm ) > $o,A0: option @ trm,A1: option @ trm] :
% 3.06/1.67 ( ! [Theta2: trm,Eta: trm] : ( P2 @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta ) )
% 3.06/1.67 => ( ! [X_1: option @ trm] : ( P2 @ ( none @ trm ) @ X_1 )
% 3.06/1.67 => ( ! [V: trm] : ( P2 @ ( some @ trm @ V ) @ ( none @ trm ) )
% 3.06/1.67 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_95_Assigno_Oinduct,axiom,
% 3.06/1.67 ! [P2: variable > ( option @ trm ) > $o,A0: variable,A1: option @ trm] :
% 3.06/1.67 ( ! [X3: variable,Theta2: trm] : ( P2 @ X3 @ ( some @ trm @ Theta2 ) )
% 3.06/1.67 => ( ! [X3: variable] : ( P2 @ X3 @ ( none @ trm ) )
% 3.06/1.67 => ( P2 @ A0 @ A1 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_96_Composeo_Oinduct,axiom,
% 3.06/1.67 ! [P2: ( option @ game ) > ( option @ game ) > $o,A0: option @ game,A1: option @ game] :
% 3.06/1.67 ( ! [Alpha: game,Beta: game] : ( P2 @ ( some @ game @ Alpha ) @ ( some @ game @ Beta ) )
% 3.06/1.67 => ( ! [Alpha: option @ game] : ( P2 @ Alpha @ ( none @ game ) )
% 3.06/1.67 => ( ! [V: game] : ( P2 @ ( none @ game ) @ ( some @ game @ V ) )
% 3.06/1.67 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_97_Differentialo_Ocases,axiom,
% 3.06/1.67 ! [X2: option @ trm] :
% 3.06/1.67 ( ! [Theta2: trm] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( some @ trm @ Theta2 ) )
% 3.06/1.67 => ( X2
% 3.06/1.67 = ( none @ trm ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_98_Differentialo_Oinduct,axiom,
% 3.06/1.67 ! [P2: ( option @ trm ) > $o,A0: option @ trm] :
% 3.06/1.67 ( ! [Theta2: trm] : ( P2 @ ( some @ trm @ Theta2 ) )
% 3.06/1.67 => ( ( P2 @ ( none @ trm ) )
% 3.06/1.67 => ( P2 @ A0 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_99_undeft__None,axiom,
% 3.06/1.67 ( ( none @ trm )
% 3.06/1.67 = ( none @ trm ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_100_bot__fun__def,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType] :
% 3.06/1.67 ( ( bot @ B )
% 3.06/1.67 => ( ( bot_bot @ ( A > B ) )
% 3.06/1.67 = ( ^ [X: A] : ( bot_bot @ B ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_101_emptyE,axiom,
% 3.06/1.67 ! [A: $tType,A2: A] :
% 3.06/1.67 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_102_equals0D,axiom,
% 3.06/1.67 ! [A: $tType,A3: set @ A,A2: A] :
% 3.06/1.67 ( ( A3
% 3.06/1.67 = ( bot_bot @ ( set @ A ) ) )
% 3.06/1.67 => ~ ( member @ A @ A2 @ A3 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_103_equals0I,axiom,
% 3.06/1.67 ! [A: $tType,A3: set @ A] :
% 3.06/1.67 ( ! [Y3: A] :
% 3.06/1.67 ~ ( member @ A @ Y3 @ A3 )
% 3.06/1.67 => ( A3
% 3.06/1.67 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_104_ex__in__conv,axiom,
% 3.06/1.67 ! [A: $tType,A3: set @ A] :
% 3.06/1.67 ( ( ? [X: A] : ( member @ A @ X @ A3 ) )
% 3.06/1.67 = ( A3
% 3.06/1.67 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_105_bot__set__def,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( bot_bot @ ( set @ A ) )
% 3.06/1.67 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_106_IntE,axiom,
% 3.06/1.67 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 3.06/1.67 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 3.06/1.67 => ~ ( ( member @ A @ C2 @ A3 )
% 3.06/1.67 => ~ ( member @ A @ C2 @ B4 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_107_IntD1,axiom,
% 3.06/1.67 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 3.06/1.67 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 3.06/1.67 => ( member @ A @ C2 @ A3 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_108_IntD2,axiom,
% 3.06/1.67 ! [A: $tType,C2: A,A3: set @ A,B4: set @ A] :
% 3.06/1.67 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 3.06/1.67 => ( member @ A @ C2 @ B4 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_109_Int__assoc,axiom,
% 3.06/1.67 ! [A: $tType,A3: set @ A,B4: set @ A,C3: set @ A] :
% 3.06/1.67 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) @ C3 )
% 3.06/1.67 = ( inf_inf @ ( set @ A ) @ A3 @ ( inf_inf @ ( set @ A ) @ B4 @ C3 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_110_Int__absorb,axiom,
% 3.06/1.67 ! [A: $tType,A3: set @ A] :
% 3.06/1.67 ( ( inf_inf @ ( set @ A ) @ A3 @ A3 )
% 3.06/1.67 = A3 ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_111_Int__commute,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( inf_inf @ ( set @ A ) )
% 3.06/1.67 = ( ^ [A6: set @ A,B6: set @ A] : ( inf_inf @ ( set @ A ) @ B6 @ A6 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_112_Int__left__absorb,axiom,
% 3.06/1.67 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 3.06/1.67 ( ( inf_inf @ ( set @ A ) @ A3 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 3.06/1.67 = ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_113_Int__left__commute,axiom,
% 3.06/1.67 ! [A: $tType,A3: set @ A,B4: set @ A,C3: set @ A] :
% 3.06/1.67 ( ( inf_inf @ ( set @ A ) @ A3 @ ( inf_inf @ ( set @ A ) @ B4 @ C3 ) )
% 3.06/1.67 = ( inf_inf @ ( set @ A ) @ B4 @ ( inf_inf @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_114_empty__def,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( bot_bot @ ( set @ A ) )
% 3.06/1.67 = ( collect @ A
% 3.06/1.67 @ ^ [X: A] : $false ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_115_Collect__conj__eq,axiom,
% 3.06/1.67 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 3.06/1.67 ( ( collect @ A
% 3.06/1.67 @ ^ [X: A] :
% 3.06/1.67 ( ( P2 @ X )
% 3.06/1.67 & ( Q @ X ) ) )
% 3.06/1.67 = ( inf_inf @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_116_Int__Collect,axiom,
% 3.06/1.67 ! [A: $tType,X2: A,A3: set @ A,P2: A > $o] :
% 3.06/1.67 ( ( member @ A @ X2 @ ( inf_inf @ ( set @ A ) @ A3 @ ( collect @ A @ P2 ) ) )
% 3.06/1.67 = ( ( member @ A @ X2 @ A3 )
% 3.06/1.67 & ( P2 @ X2 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_117_Int__def,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( inf_inf @ ( set @ A ) )
% 3.06/1.67 = ( ^ [A6: set @ A,B6: set @ A] :
% 3.06/1.67 ( collect @ A
% 3.06/1.67 @ ^ [X: A] :
% 3.06/1.67 ( ( member @ A @ X @ A6 )
% 3.06/1.67 & ( member @ A @ X @ B6 ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_118_inf__set__def,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( inf_inf @ ( set @ A ) )
% 3.06/1.67 = ( ^ [A6: set @ A,B6: set @ A] :
% 3.06/1.67 ( collect @ A
% 3.06/1.67 @ ( inf_inf @ ( A > $o )
% 3.06/1.67 @ ^ [X: A] : ( member @ A @ X @ A6 )
% 3.06/1.67 @ ^ [X: A] : ( member @ A @ X @ B6 ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_119_Int__emptyI,axiom,
% 3.06/1.67 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 3.06/1.67 ( ! [X3: A] :
% 3.06/1.67 ( ( member @ A @ X3 @ A3 )
% 3.06/1.67 => ~ ( member @ A @ X3 @ B4 ) )
% 3.06/1.67 => ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 3.06/1.67 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_120_disjoint__iff,axiom,
% 3.06/1.67 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 3.06/1.67 ( ( ( inf_inf @ ( set @ A ) @ A3 @ B4 )
% 3.06/1.67 = ( bot_bot @ ( set @ A ) ) )
% 3.06/1.67 = ( ! [X: A] :
% 3.06/1.67 ( ( member @ A @ X @ A3 )
% 3.06/1.67 => ~ ( member @ A @ X @ B4 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_121_Int__empty__left,axiom,
% 3.06/1.67 ! [A: $tType,B4: set @ A] :
% 3.06/1.67 ( ( inf_inf @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B4 )
% 3.06/1.67 = ( bot_bot @ ( set @ A ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_122_Int__empty__right,axiom,
% 3.06/1.67 ! [A: $tType,A3: set @ A] :
% 3.06/1.67 ( ( inf_inf @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 3.06/1.67 = ( bot_bot @ ( set @ A ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_123_disjE__realizer2,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType,P2: $o,Q: A > $o,X2: option @ A,R4: B > $o,F3: B,G2: A > B] :
% 3.06/1.67 ( ( case_option @ $o @ A @ P2 @ Q @ X2 )
% 3.06/1.67 => ( ( P2
% 3.06/1.67 => ( R4 @ F3 ) )
% 3.06/1.67 => ( ! [Q2: A] :
% 3.06/1.67 ( ( Q @ Q2 )
% 3.06/1.67 => ( R4 @ ( G2 @ Q2 ) ) )
% 3.06/1.67 => ( R4 @ ( case_option @ B @ A @ F3 @ G2 @ X2 ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_124_usubstappf__geqr,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,Eta2: trm] :
% 3.06/1.67 ( ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 3.06/1.67 != ( none @ fml ) )
% 3.06/1.67 => ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 3.06/1.67 = ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Eta2 ) ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_125_usubstappf__geq,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,Eta2: trm] :
% 3.06/1.67 ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 3.06/1.67 != ( none @ trm ) )
% 3.06/1.67 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Eta2 )
% 3.06/1.67 != ( none @ trm ) )
% 3.06/1.67 => ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 3.06/1.67 = ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) @ ( the @ trm @ ( uSubst95898992stappt @ Sigma @ U @ Eta2 ) ) ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_126_Geqo_Osimps_I3_J,axiom,
% 3.06/1.67 ! [V3: trm] :
% 3.06/1.67 ( ( uSubst1556497037e_Geqo @ ( some @ trm @ V3 ) @ ( none @ trm ) )
% 3.06/1.67 = ( none @ fml ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_127_Set_Ois__empty__def,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( is_empty @ A )
% 3.06/1.67 = ( ^ [A6: set @ A] :
% 3.06/1.67 ( A6
% 3.06/1.67 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_128_usubstappf__geq__conv,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,Eta2: trm] :
% 3.06/1.67 ( ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 3.06/1.67 != ( none @ fml ) )
% 3.06/1.67 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 3.06/1.67 != ( none @ trm ) )
% 3.06/1.67 & ( ( uSubst95898992stappt @ Sigma @ U @ Eta2 )
% 3.06/1.67 != ( none @ trm ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_129_fml_Oinject_I2_J,axiom,
% 3.06/1.67 ! [X21: trm,X222: trm,Y21: trm,Y222: trm] :
% 3.06/1.67 ( ( ( geq @ X21 @ X222 )
% 3.06/1.67 = ( geq @ Y21 @ Y222 ) )
% 3.06/1.67 = ( ( X21 = Y21 )
% 3.06/1.67 & ( X222 = Y222 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_130_inf1I,axiom,
% 3.06/1.67 ! [A: $tType,A3: A > $o,X2: A,B4: A > $o] :
% 3.06/1.67 ( ( A3 @ X2 )
% 3.06/1.67 => ( ( B4 @ X2 )
% 3.06/1.67 => ( inf_inf @ ( A > $o ) @ A3 @ B4 @ X2 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_131_inf1E,axiom,
% 3.06/1.67 ! [A: $tType,A3: A > $o,B4: A > $o,X2: A] :
% 3.06/1.67 ( ( inf_inf @ ( A > $o ) @ A3 @ B4 @ X2 )
% 3.06/1.67 => ~ ( ( A3 @ X2 )
% 3.06/1.67 => ~ ( B4 @ X2 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_132_inf1D1,axiom,
% 3.06/1.67 ! [A: $tType,A3: A > $o,B4: A > $o,X2: A] :
% 3.06/1.67 ( ( inf_inf @ ( A > $o ) @ A3 @ B4 @ X2 )
% 3.06/1.67 => ( A3 @ X2 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_133_inf1D2,axiom,
% 3.06/1.67 ! [A: $tType,A3: A > $o,B4: A > $o,X2: A] :
% 3.06/1.67 ( ( inf_inf @ ( A > $o ) @ A3 @ B4 @ X2 )
% 3.06/1.67 => ( B4 @ X2 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_134_fml_Odistinct_I1_J,axiom,
% 3.06/1.67 ! [X11: char,X12: trm,X21: trm,X222: trm] :
% 3.06/1.67 ( ( pred @ X11 @ X12 )
% 3.06/1.67 != ( geq @ X21 @ X222 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_135_usubstappf_Osimps_I2_J,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,Eta2: trm] :
% 3.06/1.67 ( ( uSubst95898978stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 3.06/1.67 = ( uSubst1556497037e_Geqo @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) @ ( uSubst95898992stappt @ Sigma @ U @ Eta2 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_136_Geqo_Osimps_I1_J,axiom,
% 3.06/1.67 ! [Theta: trm,Eta2: trm] :
% 3.06/1.67 ( ( uSubst1556497037e_Geqo @ ( some @ trm @ Theta ) @ ( some @ trm @ Eta2 ) )
% 3.06/1.67 = ( some @ fml @ ( geq @ Theta @ Eta2 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_137_Geqo_Oelims,axiom,
% 3.06/1.67 ! [X2: option @ trm,Xa: option @ trm,Y2: option @ fml] :
% 3.06/1.67 ( ( ( uSubst1556497037e_Geqo @ X2 @ Xa )
% 3.06/1.67 = Y2 )
% 3.06/1.67 => ( ! [Theta2: trm] :
% 3.06/1.67 ( ( X2
% 3.06/1.67 = ( some @ trm @ Theta2 ) )
% 3.06/1.67 => ! [Eta: trm] :
% 3.06/1.67 ( ( Xa
% 3.06/1.67 = ( some @ trm @ Eta ) )
% 3.06/1.67 => ( Y2
% 3.06/1.67 != ( some @ fml @ ( geq @ Theta2 @ Eta ) ) ) ) )
% 3.06/1.67 => ( ( ( X2
% 3.06/1.67 = ( none @ trm ) )
% 3.06/1.67 => ( Y2
% 3.06/1.67 != ( none @ fml ) ) )
% 3.06/1.67 => ~ ( ? [V: trm] :
% 3.06/1.67 ( X2
% 3.06/1.67 = ( some @ trm @ V ) )
% 3.06/1.67 => ( ( Xa
% 3.06/1.67 = ( none @ trm ) )
% 3.06/1.67 => ( Y2
% 3.06/1.67 != ( none @ fml ) ) ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_138_Geqo_Osimps_I2_J,axiom,
% 3.06/1.67 ! [Eta2: option @ trm] :
% 3.06/1.67 ( ( uSubst1556497037e_Geqo @ ( none @ trm ) @ Eta2 )
% 3.06/1.67 = ( none @ fml ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_139_Geqo__undef,axiom,
% 3.06/1.67 ! [Theta: option @ trm,Eta2: option @ trm] :
% 3.06/1.67 ( ( ( uSubst1556497037e_Geqo @ Theta @ Eta2 )
% 3.06/1.67 = ( none @ fml ) )
% 3.06/1.67 = ( ( Theta
% 3.06/1.67 = ( none @ trm ) )
% 3.06/1.67 | ( Eta2
% 3.06/1.67 = ( none @ trm ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_140_inf__Int__eq,axiom,
% 3.06/1.67 ! [A: $tType,R4: set @ A,S: set @ A] :
% 3.06/1.67 ( ( inf_inf @ ( A > $o )
% 3.06/1.67 @ ^ [X: A] : ( member @ A @ X @ R4 )
% 3.06/1.67 @ ^ [X: A] : ( member @ A @ X @ S ) )
% 3.06/1.67 = ( ^ [X: A] : ( member @ A @ X @ ( inf_inf @ ( set @ A ) @ R4 @ S ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_141_Collect__empty__eq__bot,axiom,
% 3.06/1.67 ! [A: $tType,P2: A > $o] :
% 3.06/1.67 ( ( ( collect @ A @ P2 )
% 3.06/1.67 = ( bot_bot @ ( set @ A ) ) )
% 3.06/1.67 = ( P2
% 3.06/1.67 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_142_bot__empty__eq,axiom,
% 3.06/1.67 ! [A: $tType] :
% 3.06/1.67 ( ( bot_bot @ ( A > $o ) )
% 3.06/1.67 = ( ^ [X: A] : ( member @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_143_internal__case__prod__def,axiom,
% 3.06/1.67 ! [C: $tType,B: $tType,A: $tType] :
% 3.06/1.67 ( ( produc2004651681e_prod @ A @ B @ C )
% 3.06/1.67 = ( product_case_prod @ A @ B @ C ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_144_usubstappt_Osimps_I4_J,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F3: char,Theta: trm] :
% 3.06/1.67 ( ( uSubst95898992stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 3.06/1.67 = ( case_option @ ( option @ trm ) @ trm @ ( none @ trm )
% 3.06/1.67 @ ^ [Sigma_theta: trm] :
% 3.06/1.67 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( func @ F3 @ Sigma_theta ) )
% 3.06/1.67 @ ^ [R: trm] :
% 3.06/1.67 ( if @ ( option @ trm )
% 3.06/1.67 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R ) @ U )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 @ ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta ) @ ( bot_bot @ ( set @ variable ) ) @ R )
% 3.06/1.67 @ ( none @ trm ) )
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [F4: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 3.06/1.67 @ Sigma
% 3.06/1.67 @ F3 ) )
% 3.06/1.67 @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_145_Diamondo_Ocases,axiom,
% 3.06/1.67 ! [X2: product_prod @ ( option @ game ) @ ( option @ fml )] :
% 3.06/1.67 ( ! [Alpha: game,Phi: fml] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ Alpha ) @ ( some @ fml @ Phi ) ) )
% 3.06/1.67 => ( ! [Phi: option @ fml] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( none @ game ) @ Phi ) )
% 3.06/1.67 => ~ ! [V: game] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ V ) @ ( none @ fml ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_146_Testo__undef,axiom,
% 3.06/1.67 ! [Phi2: option @ fml] :
% 3.06/1.67 ( ( ( uSubst190403692_Testo @ Phi2 )
% 3.06/1.67 = ( none @ game ) )
% 3.06/1.67 = ( Phi2
% 3.06/1.67 = ( none @ fml ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_147_prod_Oinject,axiom,
% 3.06/1.67 ! [A: $tType,B: $tType,X13: A,X23: B,Y1: A,Y22: B] :
% 3.06/1.67 ( ( ( product_Pair @ A @ B @ X13 @ X23 )
% 3.06/1.67 = ( product_Pair @ A @ B @ Y1 @ Y22 ) )
% 3.06/1.67 = ( ( X13 = Y1 )
% 3.06/1.67 & ( X23 = Y22 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_148_old_Oprod_Oinject,axiom,
% 3.06/1.67 ! [A: $tType,B: $tType,A2: A,B2: B,A7: A,B7: B] :
% 3.06/1.67 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 3.06/1.67 = ( product_Pair @ A @ B @ A7 @ B7 ) )
% 3.06/1.67 = ( ( A2 = A7 )
% 3.06/1.67 & ( B2 = B7 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_149_trm_Oinject_I4_J,axiom,
% 3.06/1.67 ! [X41: char,X42: trm,Y41: char,Y42: trm] :
% 3.06/1.67 ( ( ( func @ X41 @ X42 )
% 3.06/1.67 = ( func @ Y41 @ Y42 ) )
% 3.06/1.67 = ( ( X41 = Y41 )
% 3.06/1.67 & ( X42 = Y42 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_150_case__prodI,axiom,
% 3.06/1.67 ! [A: $tType,B: $tType,F3: A > B > $o,A2: A,B2: B] :
% 3.06/1.67 ( ( F3 @ A2 @ B2 )
% 3.06/1.67 => ( product_case_prod @ A @ B @ $o @ F3 @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_151_case__prodI2,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType,P3: product_prod @ A @ B,C2: A > B > $o] :
% 3.06/1.67 ( ! [A5: A,B5: B] :
% 3.06/1.67 ( ( P3
% 3.06/1.67 = ( product_Pair @ A @ B @ A5 @ B5 ) )
% 3.06/1.67 => ( C2 @ A5 @ B5 ) )
% 3.06/1.67 => ( product_case_prod @ A @ B @ $o @ C2 @ P3 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_152_case__prodI2_H,axiom,
% 3.06/1.67 ! [A: $tType,B: $tType,C: $tType,P3: product_prod @ A @ B,C2: A > B > C > $o,X2: C] :
% 3.06/1.67 ( ! [A5: A,B5: B] :
% 3.06/1.67 ( ( ( product_Pair @ A @ B @ A5 @ B5 )
% 3.06/1.67 = P3 )
% 3.06/1.67 => ( C2 @ A5 @ B5 @ X2 ) )
% 3.06/1.67 => ( product_case_prod @ A @ B @ ( C > $o ) @ C2 @ P3 @ X2 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_153_mem__case__prodI,axiom,
% 3.06/1.67 ! [A: $tType,B: $tType,C: $tType,Z2: A,C2: B > C > ( set @ A ),A2: B,B2: C] :
% 3.06/1.67 ( ( member @ A @ Z2 @ ( C2 @ A2 @ B2 ) )
% 3.06/1.67 => ( member @ A @ Z2 @ ( product_case_prod @ B @ C @ ( set @ A ) @ C2 @ ( product_Pair @ B @ C @ A2 @ B2 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_154_mem__case__prodI2,axiom,
% 3.06/1.67 ! [C: $tType,B: $tType,A: $tType,P3: product_prod @ A @ B,Z2: C,C2: A > B > ( set @ C )] :
% 3.06/1.67 ( ! [A5: A,B5: B] :
% 3.06/1.67 ( ( P3
% 3.06/1.67 = ( product_Pair @ A @ B @ A5 @ B5 ) )
% 3.06/1.67 => ( member @ C @ Z2 @ ( C2 @ A5 @ B5 ) ) )
% 3.06/1.67 => ( member @ C @ Z2 @ ( product_case_prod @ A @ B @ ( set @ C ) @ C2 @ P3 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_155_case__prod__conv,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType,C: $tType,F3: B > C > A,A2: B,B2: C] :
% 3.06/1.67 ( ( product_case_prod @ B @ C @ A @ F3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 3.06/1.67 = ( F3 @ A2 @ B2 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_156_usubstappt__func2,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F3: char,R2: trm,U: set @ variable,Theta: trm] :
% 3.06/1.67 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [F4: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 3.06/1.67 @ Sigma
% 3.06/1.67 @ F3 )
% 3.06/1.67 = ( some @ trm @ R2 ) )
% 3.06/1.67 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U )
% 3.06/1.67 != ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 => ( ( uSubst95898992stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 3.06/1.67 = ( none @ trm ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_157_usubstappt__func,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F3: char,R2: trm,U: set @ variable,Theta: trm,Sigma_theta2: trm] :
% 3.06/1.67 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [F4: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 3.06/1.67 @ Sigma
% 3.06/1.67 @ F3 )
% 3.06/1.67 = ( some @ trm @ R2 ) )
% 3.06/1.67 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 3.06/1.67 = ( some @ trm @ Sigma_theta2 ) )
% 3.06/1.67 => ( ( uSubst95898992stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 3.06/1.67 = ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta2 ) @ ( bot_bot @ ( set @ variable ) ) @ R2 ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_158_inf__Int__eq2,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType,R4: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 3.06/1.67 ( ( inf_inf @ ( A > B > $o )
% 3.06/1.67 @ ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ R4 )
% 3.06/1.67 @ ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ S ) )
% 3.06/1.67 = ( ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ ( inf_inf @ ( set @ ( product_prod @ A @ B ) ) @ R4 @ S ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_159_bot__empty__eq2,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType] :
% 3.06/1.67 ( ( bot_bot @ ( A > B > $o ) )
% 3.06/1.67 = ( ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ ( bot_bot @ ( set @ ( product_prod @ A @ B ) ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_160_pred__equals__eq2,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType,R4: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 3.06/1.67 ( ( ( ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ R4 ) )
% 3.06/1.67 = ( ^ [X: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ S ) ) )
% 3.06/1.67 = ( R4 = S ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_161_cond__case__prod__eta,axiom,
% 3.06/1.67 ! [C: $tType,B: $tType,A: $tType,F3: A > B > C,G2: ( product_prod @ A @ B ) > C] :
% 3.06/1.67 ( ! [X3: A,Y3: B] :
% 3.06/1.67 ( ( F3 @ X3 @ Y3 )
% 3.06/1.67 = ( G2 @ ( product_Pair @ A @ B @ X3 @ Y3 ) ) )
% 3.06/1.67 => ( ( product_case_prod @ A @ B @ C @ F3 )
% 3.06/1.67 = G2 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_162_case__prod__eta,axiom,
% 3.06/1.67 ! [C: $tType,B: $tType,A: $tType,F3: ( product_prod @ A @ B ) > C] :
% 3.06/1.67 ( ( product_case_prod @ A @ B @ C
% 3.06/1.67 @ ^ [X: A,Y: B] : ( F3 @ ( product_Pair @ A @ B @ X @ Y ) ) )
% 3.06/1.67 = F3 ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_163_case__prodE2,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType,C: $tType,Q: A > $o,P2: B > C > A,Z2: product_prod @ B @ C] :
% 3.06/1.67 ( ( Q @ ( product_case_prod @ B @ C @ A @ P2 @ Z2 ) )
% 3.06/1.67 => ~ ! [X3: B,Y3: C] :
% 3.06/1.67 ( ( Z2
% 3.06/1.67 = ( product_Pair @ B @ C @ X3 @ Y3 ) )
% 3.06/1.67 => ~ ( Q @ ( P2 @ X3 @ Y3 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_164_surj__pair,axiom,
% 3.06/1.67 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 3.06/1.67 ? [X3: A,Y3: B] :
% 3.06/1.67 ( P3
% 3.06/1.67 = ( product_Pair @ A @ B @ X3 @ Y3 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_165_prod__cases,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 3.06/1.67 ( ! [A5: A,B5: B] : ( P2 @ ( product_Pair @ A @ B @ A5 @ B5 ) )
% 3.06/1.67 => ( P2 @ P3 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_166_Pair__inject,axiom,
% 3.06/1.67 ! [A: $tType,B: $tType,A2: A,B2: B,A7: A,B7: B] :
% 3.06/1.67 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 3.06/1.67 = ( product_Pair @ A @ B @ A7 @ B7 ) )
% 3.06/1.67 => ~ ( ( A2 = A7 )
% 3.06/1.67 => ( B2 != B7 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_167_prod__cases3,axiom,
% 3.06/1.67 ! [A: $tType,B: $tType,C: $tType,Y2: product_prod @ A @ ( product_prod @ B @ C )] :
% 3.06/1.67 ~ ! [A5: A,B5: B,C4: C] :
% 3.06/1.67 ( Y2
% 3.06/1.67 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B5 @ C4 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_168_prod__cases4,axiom,
% 3.06/1.67 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 3.06/1.67 ~ ! [A5: A,B5: B,C4: C,D2: D] :
% 3.06/1.67 ( Y2
% 3.06/1.67 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C4 @ D2 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_169_prod__cases5,axiom,
% 3.06/1.67 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 3.06/1.67 ~ ! [A5: A,B5: B,C4: C,D2: D,E2: E] :
% 3.06/1.67 ( Y2
% 3.06/1.67 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C4 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_170_prod__cases6,axiom,
% 3.06/1.67 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F5: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) )] :
% 3.06/1.67 ~ ! [A5: A,B5: B,C4: C,D2: D,E2: E,F6: F5] :
% 3.06/1.67 ( Y2
% 3.06/1.67 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ F5 ) @ D2 @ ( product_Pair @ E @ F5 @ E2 @ F6 ) ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_171_prod__cases7,axiom,
% 3.06/1.67 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F5: $tType,G3: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) )] :
% 3.06/1.67 ~ ! [A5: A,B5: B,C4: C,D2: D,E2: E,F6: F5,G4: G3] :
% 3.06/1.67 ( Y2
% 3.06/1.67 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F5 @ G3 ) @ E2 @ ( product_Pair @ F5 @ G3 @ F6 @ G4 ) ) ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_172_prod__induct3,axiom,
% 3.06/1.67 ! [C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ C )] :
% 3.06/1.67 ( ! [A5: A,B5: B,C4: C] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B5 @ C4 ) ) )
% 3.06/1.67 => ( P2 @ X2 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_173_prod__induct4,axiom,
% 3.06/1.67 ! [D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 3.06/1.67 ( ! [A5: A,B5: B,C4: C,D2: D] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C4 @ D2 ) ) ) )
% 3.06/1.67 => ( P2 @ X2 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_174_prod__induct5,axiom,
% 3.06/1.67 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 3.06/1.67 ( ! [A5: A,B5: B,C4: C,D2: D,E2: E] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C4 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 3.06/1.67 => ( P2 @ X2 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_175_prod__induct6,axiom,
% 3.06/1.67 ! [F5: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) )] :
% 3.06/1.67 ( ! [A5: A,B5: B,C4: C,D2: D,E2: E,F6: F5] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ F5 ) @ D2 @ ( product_Pair @ E @ F5 @ E2 @ F6 ) ) ) ) ) )
% 3.06/1.67 => ( P2 @ X2 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_176_prod__induct7,axiom,
% 3.06/1.67 ! [G3: $tType,F5: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) )] :
% 3.06/1.67 ( ! [A5: A,B5: B,C4: C,D2: D,E2: E,F6: F5,G4: G3] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F5 @ G3 ) @ E2 @ ( product_Pair @ F5 @ G3 @ F6 @ G4 ) ) ) ) ) ) )
% 3.06/1.67 => ( P2 @ X2 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_177_mem__case__prodE,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType,C: $tType,Z2: A,C2: B > C > ( set @ A ),P3: product_prod @ B @ C] :
% 3.06/1.67 ( ( member @ A @ Z2 @ ( product_case_prod @ B @ C @ ( set @ A ) @ C2 @ P3 ) )
% 3.06/1.67 => ~ ! [X3: B,Y3: C] :
% 3.06/1.67 ( ( P3
% 3.06/1.67 = ( product_Pair @ B @ C @ X3 @ Y3 ) )
% 3.06/1.67 => ~ ( member @ A @ Z2 @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_178_old_Oprod_Oexhaust,axiom,
% 3.06/1.67 ! [A: $tType,B: $tType,Y2: product_prod @ A @ B] :
% 3.06/1.67 ~ ! [A5: A,B5: B] :
% 3.06/1.67 ( Y2
% 3.06/1.67 != ( product_Pair @ A @ B @ A5 @ B5 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_179_old_Oprod_Oinducts,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 3.06/1.67 ( ! [A5: A,B5: B] : ( P2 @ ( product_Pair @ A @ B @ A5 @ B5 ) )
% 3.06/1.67 => ( P2 @ Prod ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_180_case__prodD,axiom,
% 3.06/1.67 ! [A: $tType,B: $tType,F3: A > B > $o,A2: A,B2: B] :
% 3.06/1.67 ( ( product_case_prod @ A @ B @ $o @ F3 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 3.06/1.67 => ( F3 @ A2 @ B2 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_181_case__prodE,axiom,
% 3.06/1.67 ! [A: $tType,B: $tType,C2: A > B > $o,P3: product_prod @ A @ B] :
% 3.06/1.67 ( ( product_case_prod @ A @ B @ $o @ C2 @ P3 )
% 3.06/1.67 => ~ ! [X3: A,Y3: B] :
% 3.06/1.67 ( ( P3
% 3.06/1.67 = ( product_Pair @ A @ B @ X3 @ Y3 ) )
% 3.06/1.67 => ~ ( C2 @ X3 @ Y3 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_182_case__prodD_H,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType,C: $tType,R4: A > B > C > $o,A2: A,B2: B,C2: C] :
% 3.06/1.67 ( ( product_case_prod @ A @ B @ ( C > $o ) @ R4 @ ( product_Pair @ A @ B @ A2 @ B2 ) @ C2 )
% 3.06/1.67 => ( R4 @ A2 @ B2 @ C2 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_183_case__prodE_H,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType,C: $tType,C2: A > B > C > $o,P3: product_prod @ A @ B,Z2: C] :
% 3.06/1.67 ( ( product_case_prod @ A @ B @ ( C > $o ) @ C2 @ P3 @ Z2 )
% 3.06/1.67 => ~ ! [X3: A,Y3: B] :
% 3.06/1.67 ( ( P3
% 3.06/1.67 = ( product_Pair @ A @ B @ X3 @ Y3 ) )
% 3.06/1.67 => ~ ( C2 @ X3 @ Y3 @ Z2 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_184_case__prod__Pair__iden,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType,P3: product_prod @ A @ B] :
% 3.06/1.67 ( ( product_case_prod @ A @ B @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B ) @ P3 )
% 3.06/1.67 = P3 ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_185_old_Oprod_Ocase,axiom,
% 3.06/1.67 ! [A: $tType,C: $tType,B: $tType,F3: A > B > C,X13: A,X23: B] :
% 3.06/1.67 ( ( product_case_prod @ A @ B @ C @ F3 @ ( product_Pair @ A @ B @ X13 @ X23 ) )
% 3.06/1.67 = ( F3 @ X13 @ X23 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_186_internal__case__prod__conv,axiom,
% 3.06/1.67 ! [B: $tType,A: $tType,C: $tType,C2: B > C > A,A2: B,B2: C] :
% 3.06/1.67 ( ( produc2004651681e_prod @ B @ C @ A @ C2 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 3.06/1.67 = ( C2 @ A2 @ B2 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_187_usubstappt__func__conv,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F3: char,Theta: trm] :
% 3.06/1.67 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 3.06/1.67 != ( none @ trm ) )
% 3.06/1.67 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 3.06/1.67 != ( none @ trm ) )
% 3.06/1.67 & ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [F4: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 3.06/1.67 @ Sigma
% 3.06/1.67 @ F3 )
% 3.06/1.67 = ( none @ trm ) )
% 3.06/1.67 | ? [R3: trm] :
% 3.06/1.67 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [F4: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 3.06/1.67 @ Sigma
% 3.06/1.67 @ F3 )
% 3.06/1.67 = ( some @ trm @ R3 ) )
% 3.06/1.67 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R3 ) @ U )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_188_Testo_Osimps_I2_J,axiom,
% 3.06/1.67 ( ( uSubst190403692_Testo @ ( none @ fml ) )
% 3.06/1.67 = ( none @ game ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_189_usappconst__simp,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F3: char,R2: trm,U: set @ variable] :
% 3.06/1.67 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [F0: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 3.06/1.67 @ Sigma
% 3.06/1.67 @ F3 )
% 3.06/1.67 = ( some @ trm @ R2 ) )
% 3.06/1.67 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 => ( ( uSubst1138577137pconst @ Sigma @ U @ F3 )
% 3.06/1.67 = ( some @ trm @ R2 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_190_usappconst__conv,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F3: char] :
% 3.06/1.67 ( ( ( uSubst1138577137pconst @ Sigma @ U @ F3 )
% 3.06/1.67 != ( none @ trm ) )
% 3.06/1.67 => ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [F0: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 3.06/1.67 @ Sigma
% 3.06/1.67 @ F3 )
% 3.06/1.67 = ( none @ trm ) )
% 3.06/1.67 | ? [R3: trm] :
% 3.06/1.67 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [F0: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 3.06/1.67 @ Sigma
% 3.06/1.67 @ F3 )
% 3.06/1.67 = ( some @ trm @ R3 ) )
% 3.06/1.67 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R3 ) @ U )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_191_usubstappt__const,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),F3: char,R2: trm,U: set @ variable] :
% 3.06/1.67 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [F0: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 3.06/1.67 @ Sigma
% 3.06/1.67 @ F3 )
% 3.06/1.67 = ( some @ trm @ R2 ) )
% 3.06/1.67 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R2 ) @ U )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 => ( ( uSubst95898992stappt @ Sigma @ U @ ( const @ F3 ) )
% 3.06/1.67 = ( some @ trm @ R2 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_192_trm_Oinject_I3_J,axiom,
% 3.06/1.67 ! [X32: char,Y32: char] :
% 3.06/1.67 ( ( ( const @ X32 )
% 3.06/1.67 = ( const @ Y32 ) )
% 3.06/1.67 = ( X32 = Y32 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_193_trm_Odistinct_I23_J,axiom,
% 3.06/1.67 ! [X32: char,X41: char,X42: trm] :
% 3.06/1.67 ( ( const @ X32 )
% 3.06/1.67 != ( func @ X41 @ X42 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_194_usubstappt_Osimps_I3_J,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F3: char] :
% 3.06/1.67 ( ( uSubst95898992stappt @ Sigma @ U @ ( const @ F3 ) )
% 3.06/1.67 = ( uSubst1138577137pconst @ Sigma @ U @ F3 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_195_ODEo_Ocases,axiom,
% 3.06/1.67 ! [X2: product_prod @ char @ ( option @ trm )] :
% 3.06/1.67 ( ! [X3: char,Theta2: trm] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ char @ ( option @ trm ) @ X3 @ ( some @ trm @ Theta2 ) ) )
% 3.06/1.67 => ~ ! [X3: char] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ char @ ( option @ trm ) @ X3 @ ( none @ trm ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_196_Assigno_Ocases,axiom,
% 3.06/1.67 ! [X2: product_prod @ variable @ ( option @ trm )] :
% 3.06/1.67 ( ! [X3: variable,Theta2: trm] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ variable @ ( option @ trm ) @ X3 @ ( some @ trm @ Theta2 ) ) )
% 3.06/1.67 => ~ ! [X3: variable] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ variable @ ( option @ trm ) @ X3 @ ( none @ trm ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_197_Timeso_Ocases,axiom,
% 3.06/1.67 ! [X2: product_prod @ ( option @ trm ) @ ( option @ trm )] :
% 3.06/1.67 ( ! [Theta2: trm,Eta: trm] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ Theta2 ) @ ( some @ trm @ Eta ) ) )
% 3.06/1.67 => ( ! [Eta: option @ trm] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( none @ trm ) @ Eta ) )
% 3.06/1.67 => ~ ! [V: trm] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ ( option @ trm ) @ ( option @ trm ) @ ( some @ trm @ V ) @ ( none @ trm ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_198_Existso_Ocases,axiom,
% 3.06/1.67 ! [X2: product_prod @ variable @ ( option @ fml )] :
% 3.06/1.67 ( ! [X3: variable,Phi: fml] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ variable @ ( option @ fml ) @ X3 @ ( some @ fml @ Phi ) ) )
% 3.06/1.67 => ~ ! [X3: variable] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ variable @ ( option @ fml ) @ X3 @ ( none @ fml ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_199_Ando_Ocases,axiom,
% 3.06/1.67 ! [X2: product_prod @ ( option @ fml ) @ ( option @ fml )] :
% 3.06/1.67 ( ! [Phi: fml,Psi: fml] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ ( option @ fml ) @ ( option @ fml ) @ ( some @ fml @ Phi ) @ ( some @ fml @ Psi ) ) )
% 3.06/1.67 => ( ! [Psi: option @ fml] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ ( option @ fml ) @ ( option @ fml ) @ ( none @ fml ) @ Psi ) )
% 3.06/1.67 => ~ ! [V: fml] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ ( option @ fml ) @ ( option @ fml ) @ ( some @ fml @ V ) @ ( none @ fml ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_200_Composeo_Ocases,axiom,
% 3.06/1.67 ! [X2: product_prod @ ( option @ game ) @ ( option @ game )] :
% 3.06/1.67 ( ! [Alpha: game,Beta: game] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ ( some @ game @ Alpha ) @ ( some @ game @ Beta ) ) )
% 3.06/1.67 => ( ! [Alpha: option @ game] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ Alpha @ ( none @ game ) ) )
% 3.06/1.67 => ~ ! [V: game] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ ( option @ game ) @ ( option @ game ) @ ( none @ game ) @ ( some @ game @ V ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_201_usappconst__def,axiom,
% 3.06/1.67 ( uSubst1138577137pconst
% 3.06/1.67 = ( ^ [Sigma2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U2: set @ variable,F2: char] :
% 3.06/1.67 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( const @ F2 ) )
% 3.06/1.67 @ ^ [R: trm] :
% 3.06/1.67 ( if @ ( option @ trm )
% 3.06/1.67 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R ) @ U2 )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 @ ( some @ trm @ R )
% 3.06/1.67 @ ( none @ trm ) )
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [F0: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 3.06/1.67 @ Sigma2
% 3.06/1.67 @ F2 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_202_usubstappt__const__conv,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F3: char] :
% 3.06/1.67 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( const @ F3 ) )
% 3.06/1.67 != ( none @ trm ) )
% 3.06/1.67 => ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [F0: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 3.06/1.67 @ Sigma
% 3.06/1.67 @ F3 )
% 3.06/1.67 = ( none @ trm ) )
% 3.06/1.67 | ? [R3: trm] :
% 3.06/1.67 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [F0: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F0 ) )
% 3.06/1.67 @ Sigma
% 3.06/1.67 @ F3 )
% 3.06/1.67 = ( some @ trm @ R3 ) )
% 3.06/1.67 & ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R3 ) @ U )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_203_old_Oprod_Orec,axiom,
% 3.06/1.67 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 3.06/1.67 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 3.06/1.67 = ( F1 @ A2 @ B2 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_204_usubstappt_Opsimps_I4_J,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F3: char,Theta: trm] :
% 3.06/1.67 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( func @ F3 @ Theta ) ) ) )
% 3.06/1.67 => ( ( uSubst95898992stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 3.06/1.67 = ( case_option @ ( option @ trm ) @ trm @ ( none @ trm )
% 3.06/1.67 @ ^ [Sigma_theta: trm] :
% 3.06/1.67 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( func @ F3 @ Sigma_theta ) )
% 3.06/1.67 @ ^ [R: trm] :
% 3.06/1.67 ( if @ ( option @ trm )
% 3.06/1.67 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R ) @ U )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 @ ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta ) @ ( bot_bot @ ( set @ variable ) ) @ R )
% 3.06/1.67 @ ( none @ trm ) )
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [F4: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 3.06/1.67 @ Sigma
% 3.06/1.67 @ F3 ) )
% 3.06/1.67 @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_205_usubstappt_Opsimps_I3_J,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,F3: char] :
% 3.06/1.67 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( const @ F3 ) ) ) )
% 3.06/1.67 => ( ( uSubst95898992stappt @ Sigma @ U @ ( const @ F3 ) )
% 3.06/1.67 = ( uSubst1138577137pconst @ Sigma @ U @ F3 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_206_usubstappt_Opsimps_I1_J,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,X2: variable] :
% 3.06/1.67 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( var @ X2 ) ) ) )
% 3.06/1.67 => ( ( uSubst95898992stappt @ Sigma @ U @ ( var @ X2 ) )
% 3.06/1.67 = ( some @ trm @ ( var @ X2 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_207_usubstappt_Opsimps_I2_J,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,R2: real] :
% 3.06/1.67 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma @ ( product_Pair @ ( set @ variable ) @ trm @ U @ ( number @ R2 ) ) ) )
% 3.06/1.67 => ( ( uSubst95898992stappt @ Sigma @ U @ ( number @ R2 ) )
% 3.06/1.67 = ( some @ trm @ ( number @ R2 ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_208_trm_Oinject_I2_J,axiom,
% 3.06/1.67 ! [X23: real,Y22: real] :
% 3.06/1.67 ( ( ( number @ X23 )
% 3.06/1.67 = ( number @ Y22 ) )
% 3.06/1.67 = ( X23 = Y22 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_209_trm_Oinject_I1_J,axiom,
% 3.06/1.67 ! [X13: variable,Y1: variable] :
% 3.06/1.67 ( ( ( var @ X13 )
% 3.06/1.67 = ( var @ Y1 ) )
% 3.06/1.67 = ( X13 = Y1 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_210_trm_Odistinct_I15_J,axiom,
% 3.06/1.67 ! [X23: real,X41: char,X42: trm] :
% 3.06/1.67 ( ( number @ X23 )
% 3.06/1.67 != ( func @ X41 @ X42 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_211_trm_Odistinct_I5_J,axiom,
% 3.06/1.67 ! [X13: variable,X41: char,X42: trm] :
% 3.06/1.67 ( ( var @ X13 )
% 3.06/1.67 != ( func @ X41 @ X42 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_212_trm_Odistinct_I1_J,axiom,
% 3.06/1.67 ! [X13: variable,X23: real] :
% 3.06/1.67 ( ( var @ X13 )
% 3.06/1.67 != ( number @ X23 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_213_trm_Odistinct_I13_J,axiom,
% 3.06/1.67 ! [X23: real,X32: char] :
% 3.06/1.67 ( ( number @ X23 )
% 3.06/1.67 != ( const @ X32 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_214_trm_Odistinct_I3_J,axiom,
% 3.06/1.67 ! [X13: variable,X32: char] :
% 3.06/1.67 ( ( var @ X13 )
% 3.06/1.67 != ( const @ X32 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_215_usubstappt_Osimps_I2_J,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,R2: real] :
% 3.06/1.67 ( ( uSubst95898992stappt @ Sigma @ U @ ( number @ R2 ) )
% 3.06/1.67 = ( some @ trm @ ( number @ R2 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_216_usubstappt_Osimps_I1_J,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,X2: variable] :
% 3.06/1.67 ( ( uSubst95898992stappt @ Sigma @ U @ ( var @ X2 ) )
% 3.06/1.67 = ( some @ trm @ ( var @ X2 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_217_usubstappt_Opinduct,axiom,
% 3.06/1.67 ! [A0: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),A1: set @ variable,A22: trm,P2: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > trm > $o] :
% 3.06/1.67 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ A0 @ ( product_Pair @ ( set @ variable ) @ trm @ A1 @ A22 ) ) )
% 3.06/1.67 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,X3: variable] :
% 3.06/1.67 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( var @ X3 ) ) ) )
% 3.06/1.67 => ( P2 @ Sigma3 @ U3 @ ( var @ X3 ) ) )
% 3.06/1.67 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,R3: real] :
% 3.06/1.67 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( number @ R3 ) ) ) )
% 3.06/1.67 => ( P2 @ Sigma3 @ U3 @ ( number @ R3 ) ) )
% 3.06/1.67 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F6: char] :
% 3.06/1.67 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( const @ F6 ) ) ) )
% 3.06/1.67 => ( P2 @ Sigma3 @ U3 @ ( const @ F6 ) ) )
% 3.06/1.67 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F6: char,Theta2: trm] :
% 3.06/1.67 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( func @ F6 @ Theta2 ) ) ) )
% 3.06/1.67 => ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 3.06/1.67 => ( ! [X25: trm] :
% 3.06/1.67 ( ( ( uSubst95898992stappt @ Sigma3 @ U3 @ Theta2 )
% 3.06/1.67 = ( some @ trm @ X25 ) )
% 3.06/1.67 => ! [X2a: trm] :
% 3.06/1.67 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [F4: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 3.06/1.67 @ Sigma3
% 3.06/1.67 @ F6 )
% 3.06/1.67 = ( some @ trm @ X2a ) )
% 3.06/1.67 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ X2a ) @ U3 )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 => ( P2 @ ( uSubst969145931substt @ X25 ) @ ( bot_bot @ ( set @ variable ) ) @ X2a ) ) ) )
% 3.06/1.67 => ( P2 @ Sigma3 @ U3 @ ( func @ F6 @ Theta2 ) ) ) ) )
% 3.06/1.67 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm,Eta: trm] :
% 3.06/1.67 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( plus @ Theta2 @ Eta ) ) ) )
% 3.06/1.67 => ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 3.06/1.67 => ( ( P2 @ Sigma3 @ U3 @ Eta )
% 3.06/1.67 => ( P2 @ Sigma3 @ U3 @ ( plus @ Theta2 @ Eta ) ) ) ) )
% 3.06/1.67 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm,Eta: trm] :
% 3.06/1.67 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( times @ Theta2 @ Eta ) ) ) )
% 3.06/1.67 => ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 3.06/1.67 => ( ( P2 @ Sigma3 @ U3 @ Eta )
% 3.06/1.67 => ( P2 @ Sigma3 @ U3 @ ( times @ Theta2 @ Eta ) ) ) ) )
% 3.06/1.67 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm] :
% 3.06/1.67 ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( differential @ Theta2 ) ) ) )
% 3.06/1.67 => ( ( P2 @ Sigma3
% 3.06/1.67 @ ( collect @ variable
% 3.06/1.67 @ ^ [X: variable] : $true )
% 3.06/1.67 @ Theta2 )
% 3.06/1.67 => ( P2 @ Sigma3 @ U3 @ ( differential @ Theta2 ) ) ) )
% 3.06/1.67 => ( P2 @ A0 @ A1 @ A22 ) ) ) ) ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_218_dotsubstt__def,axiom,
% 3.06/1.67 ( uSubst969145931substt
% 3.06/1.67 = ( ^ [Theta3: trm] :
% 3.06/1.67 ( product_Pair @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) )
% 3.06/1.67 @ ^ [F2: char] :
% 3.06/1.67 ( if @ ( option @ trm )
% 3.06/1.67 @ ( F2
% 3.06/1.67 = ( char2 @ $false @ $true @ $true @ $true @ $false @ $true @ $false @ $false ) )
% 3.06/1.67 @ ( some @ trm @ Theta3 )
% 3.06/1.67 @ ( none @ trm ) )
% 3.06/1.67 @ ( product_Pair @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) )
% 3.06/1.67 @ ^ [Uu: char] : ( none @ trm )
% 3.06/1.67 @ ( product_Pair @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) )
% 3.06/1.67 @ ^ [Uu: char] : ( none @ fml )
% 3.06/1.67 @ ^ [Uu: char] : ( none @ game ) ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_219_trm_Oinject_I6_J,axiom,
% 3.06/1.67 ! [X61: trm,X62: trm,Y61: trm,Y62: trm] :
% 3.06/1.67 ( ( ( times @ X61 @ X62 )
% 3.06/1.67 = ( times @ Y61 @ Y62 ) )
% 3.06/1.67 = ( ( X61 = Y61 )
% 3.06/1.67 & ( X62 = Y62 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_220_trm_Oinject_I5_J,axiom,
% 3.06/1.67 ! [X51: trm,X52: trm,Y51: trm,Y52: trm] :
% 3.06/1.67 ( ( ( plus @ X51 @ X52 )
% 3.06/1.67 = ( plus @ Y51 @ Y52 ) )
% 3.06/1.67 = ( ( X51 = Y51 )
% 3.06/1.67 & ( X52 = Y52 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_221_trm_Oinject_I7_J,axiom,
% 3.06/1.67 ! [X7: trm,Y7: trm] :
% 3.06/1.67 ( ( ( differential @ X7 )
% 3.06/1.67 = ( differential @ Y7 ) )
% 3.06/1.67 = ( X7 = Y7 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_222_trm_Odistinct_I7_J,axiom,
% 3.06/1.67 ! [X13: variable,X51: trm,X52: trm] :
% 3.06/1.67 ( ( var @ X13 )
% 3.06/1.67 != ( plus @ X51 @ X52 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_223_trm_Odistinct_I9_J,axiom,
% 3.06/1.67 ! [X13: variable,X61: trm,X62: trm] :
% 3.06/1.67 ( ( var @ X13 )
% 3.06/1.67 != ( times @ X61 @ X62 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_224_trm_Odistinct_I11_J,axiom,
% 3.06/1.67 ! [X13: variable,X7: trm] :
% 3.06/1.67 ( ( var @ X13 )
% 3.06/1.67 != ( differential @ X7 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_225_trm_Odistinct_I17_J,axiom,
% 3.06/1.67 ! [X23: real,X51: trm,X52: trm] :
% 3.06/1.67 ( ( number @ X23 )
% 3.06/1.67 != ( plus @ X51 @ X52 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_226_trm_Odistinct_I19_J,axiom,
% 3.06/1.67 ! [X23: real,X61: trm,X62: trm] :
% 3.06/1.67 ( ( number @ X23 )
% 3.06/1.67 != ( times @ X61 @ X62 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_227_trm_Odistinct_I21_J,axiom,
% 3.06/1.67 ! [X23: real,X7: trm] :
% 3.06/1.67 ( ( number @ X23 )
% 3.06/1.67 != ( differential @ X7 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_228_trm_Oexhaust,axiom,
% 3.06/1.67 ! [Y2: trm] :
% 3.06/1.67 ( ! [X14: variable] :
% 3.06/1.67 ( Y2
% 3.06/1.67 != ( var @ X14 ) )
% 3.06/1.67 => ( ! [X24: real] :
% 3.06/1.67 ( Y2
% 3.06/1.67 != ( number @ X24 ) )
% 3.06/1.67 => ( ! [X33: char] :
% 3.06/1.67 ( Y2
% 3.06/1.67 != ( const @ X33 ) )
% 3.06/1.67 => ( ! [X412: char,X422: trm] :
% 3.06/1.67 ( Y2
% 3.06/1.67 != ( func @ X412 @ X422 ) )
% 3.06/1.67 => ( ! [X512: trm,X522: trm] :
% 3.06/1.67 ( Y2
% 3.06/1.67 != ( plus @ X512 @ X522 ) )
% 3.06/1.67 => ( ! [X612: trm,X622: trm] :
% 3.06/1.67 ( Y2
% 3.06/1.67 != ( times @ X612 @ X622 ) )
% 3.06/1.67 => ~ ! [X72: trm] :
% 3.06/1.67 ( Y2
% 3.06/1.67 != ( differential @ X72 ) ) ) ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_229_trm_Oinduct,axiom,
% 3.06/1.67 ! [P2: trm > $o,Trm: trm] :
% 3.06/1.67 ( ! [X3: variable] : ( P2 @ ( var @ X3 ) )
% 3.06/1.67 => ( ! [X3: real] : ( P2 @ ( number @ X3 ) )
% 3.06/1.67 => ( ! [X3: char] : ( P2 @ ( const @ X3 ) )
% 3.06/1.67 => ( ! [X1a: char,X2a2: trm] :
% 3.06/1.67 ( ( P2 @ X2a2 )
% 3.06/1.67 => ( P2 @ ( func @ X1a @ X2a2 ) ) )
% 3.06/1.67 => ( ! [X1a: trm,X2a2: trm] :
% 3.06/1.67 ( ( P2 @ X1a )
% 3.06/1.67 => ( ( P2 @ X2a2 )
% 3.06/1.67 => ( P2 @ ( plus @ X1a @ X2a2 ) ) ) )
% 3.06/1.67 => ( ! [X1a: trm,X2a2: trm] :
% 3.06/1.67 ( ( P2 @ X1a )
% 3.06/1.67 => ( ( P2 @ X2a2 )
% 3.06/1.67 => ( P2 @ ( times @ X1a @ X2a2 ) ) ) )
% 3.06/1.67 => ( ! [X3: trm] :
% 3.06/1.67 ( ( P2 @ X3 )
% 3.06/1.67 => ( P2 @ ( differential @ X3 ) ) )
% 3.06/1.67 => ( P2 @ Trm ) ) ) ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_230_trm_Odistinct_I25_J,axiom,
% 3.06/1.67 ! [X32: char,X51: trm,X52: trm] :
% 3.06/1.67 ( ( const @ X32 )
% 3.06/1.67 != ( plus @ X51 @ X52 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_231_trm_Odistinct_I27_J,axiom,
% 3.06/1.67 ! [X32: char,X61: trm,X62: trm] :
% 3.06/1.67 ( ( const @ X32 )
% 3.06/1.67 != ( times @ X61 @ X62 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_232_trm_Odistinct_I29_J,axiom,
% 3.06/1.67 ! [X32: char,X7: trm] :
% 3.06/1.67 ( ( const @ X32 )
% 3.06/1.67 != ( differential @ X7 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_233_trm_Odistinct_I41_J,axiom,
% 3.06/1.67 ! [X61: trm,X62: trm,X7: trm] :
% 3.06/1.67 ( ( times @ X61 @ X62 )
% 3.06/1.67 != ( differential @ X7 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_234_trm_Odistinct_I39_J,axiom,
% 3.06/1.67 ! [X51: trm,X52: trm,X7: trm] :
% 3.06/1.67 ( ( plus @ X51 @ X52 )
% 3.06/1.67 != ( differential @ X7 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_235_trm_Odistinct_I37_J,axiom,
% 3.06/1.67 ! [X51: trm,X52: trm,X61: trm,X62: trm] :
% 3.06/1.67 ( ( plus @ X51 @ X52 )
% 3.06/1.67 != ( times @ X61 @ X62 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_236_trm_Odistinct_I31_J,axiom,
% 3.06/1.67 ! [X41: char,X42: trm,X51: trm,X52: trm] :
% 3.06/1.67 ( ( func @ X41 @ X42 )
% 3.06/1.67 != ( plus @ X51 @ X52 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_237_trm_Odistinct_I33_J,axiom,
% 3.06/1.67 ! [X41: char,X42: trm,X61: trm,X62: trm] :
% 3.06/1.67 ( ( func @ X41 @ X42 )
% 3.06/1.67 != ( times @ X61 @ X62 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_238_trm_Odistinct_I35_J,axiom,
% 3.06/1.67 ! [X41: char,X42: trm,X7: trm] :
% 3.06/1.67 ( ( func @ X41 @ X42 )
% 3.06/1.67 != ( differential @ X7 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_239_usubstappt_Ocases,axiom,
% 3.06/1.67 ! [X2: product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm )] :
% 3.06/1.67 ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,X3: variable] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( var @ X3 ) ) ) )
% 3.06/1.67 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,R3: real] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( number @ R3 ) ) ) )
% 3.06/1.67 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F6: char] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( const @ F6 ) ) ) )
% 3.06/1.67 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F6: char,Theta2: trm] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( func @ F6 @ Theta2 ) ) ) )
% 3.06/1.67 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm,Eta: trm] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( plus @ Theta2 @ Eta ) ) ) )
% 3.06/1.67 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm,Eta: trm] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( times @ Theta2 @ Eta ) ) ) )
% 3.06/1.67 => ~ ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm] :
% 3.06/1.67 ( X2
% 3.06/1.67 != ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ Sigma3 @ ( product_Pair @ ( set @ variable ) @ trm @ U3 @ ( differential @ Theta2 ) ) ) ) ) ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_240_usubstappt__times__conv,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,Eta2: trm] :
% 3.06/1.67 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( times @ Theta @ Eta2 ) )
% 3.06/1.67 != ( none @ trm ) )
% 3.06/1.67 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 3.06/1.67 != ( none @ trm ) )
% 3.06/1.67 & ( ( uSubst95898992stappt @ Sigma @ U @ Eta2 )
% 3.06/1.67 != ( none @ trm ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_241_usubstappt__plus__conv,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,Eta2: trm] :
% 3.06/1.67 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( plus @ Theta @ Eta2 ) )
% 3.06/1.67 != ( none @ trm ) )
% 3.06/1.67 => ( ( ( uSubst95898992stappt @ Sigma @ U @ Theta )
% 3.06/1.67 != ( none @ trm ) )
% 3.06/1.67 & ( ( uSubst95898992stappt @ Sigma @ U @ Eta2 )
% 3.06/1.67 != ( none @ trm ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_242_usubstappt__differential__conv,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm] :
% 3.06/1.67 ( ( ( uSubst95898992stappt @ Sigma @ U @ ( differential @ Theta ) )
% 3.06/1.67 != ( none @ trm ) )
% 3.06/1.67 => ( ( uSubst95898992stappt @ Sigma
% 3.06/1.67 @ ( collect @ variable
% 3.06/1.67 @ ^ [X: variable] : $true )
% 3.06/1.67 @ Theta )
% 3.06/1.67 != ( none @ trm ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_243_usubstappt__induct,axiom,
% 3.06/1.67 ! [P2: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > trm > $o,A0: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),A1: set @ variable,A22: trm] :
% 3.06/1.67 ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,X3: variable] : ( P2 @ Sigma3 @ U3 @ ( var @ X3 ) )
% 3.06/1.67 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,R3: real] : ( P2 @ Sigma3 @ U3 @ ( number @ R3 ) )
% 3.06/1.67 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F6: char] : ( P2 @ Sigma3 @ U3 @ ( const @ F6 ) )
% 3.06/1.67 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,F6: char,Theta2: trm] :
% 3.06/1.67 ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 3.06/1.67 => ( ! [X25: trm] :
% 3.06/1.67 ( ( ( uSubst95898992stappt @ Sigma3 @ U3 @ Theta2 )
% 3.06/1.67 = ( some @ trm @ X25 ) )
% 3.06/1.67 => ! [X2a: trm] :
% 3.06/1.67 ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [F4: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 3.06/1.67 @ Sigma3
% 3.06/1.67 @ F6 )
% 3.06/1.67 = ( some @ trm @ X2a ) )
% 3.06/1.67 => ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ X2a ) @ U3 )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 => ( P2 @ ( uSubst969145931substt @ X25 ) @ ( bot_bot @ ( set @ variable ) ) @ X2a ) ) ) )
% 3.06/1.67 => ( P2 @ Sigma3 @ U3 @ ( func @ F6 @ Theta2 ) ) ) )
% 3.06/1.67 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm] :
% 3.06/1.67 ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 3.06/1.67 => ! [Eta: trm] :
% 3.06/1.67 ( ( P2 @ Sigma3 @ U3 @ Eta )
% 3.06/1.67 => ( P2 @ Sigma3 @ U3 @ ( plus @ Theta2 @ Eta ) ) ) )
% 3.06/1.67 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm] :
% 3.06/1.67 ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 3.06/1.67 => ! [Eta: trm] :
% 3.06/1.67 ( ( P2 @ Sigma3 @ U3 @ Eta )
% 3.06/1.67 => ( P2 @ Sigma3 @ U3 @ ( times @ Theta2 @ Eta ) ) ) )
% 3.06/1.67 => ( ! [Sigma3: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U3: set @ variable,Theta2: trm] :
% 3.06/1.67 ( ( P2 @ Sigma3
% 3.06/1.67 @ ( collect @ variable
% 3.06/1.67 @ ^ [X: variable] : $true )
% 3.06/1.67 @ Theta2 )
% 3.06/1.67 => ( P2 @ Sigma3 @ U3 @ ( differential @ Theta2 ) ) )
% 3.06/1.67 => ( P2 @ A0 @ A1 @ A22 ) ) ) ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_244_dot__def,axiom,
% 3.06/1.67 ( uSubst_Mirabelle_dot
% 3.06/1.67 = ( const @ ( char2 @ $false @ $true @ $true @ $true @ $false @ $true @ $false @ $false ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_245_usubstappt_Opelims,axiom,
% 3.06/1.67 ! [X2: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),Xa: set @ variable,Xb: trm,Y2: option @ trm] :
% 3.06/1.67 ( ( ( uSubst95898992stappt @ X2 @ Xa @ Xb )
% 3.06/1.67 = Y2 )
% 3.06/1.67 => ( ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ X2 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ Xb ) ) )
% 3.06/1.67 => ( ! [X3: variable] :
% 3.06/1.67 ( ( Xb
% 3.06/1.67 = ( var @ X3 ) )
% 3.06/1.67 => ( ( Y2
% 3.06/1.67 = ( some @ trm @ ( var @ X3 ) ) )
% 3.06/1.67 => ~ ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ X2 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( var @ X3 ) ) ) ) ) )
% 3.06/1.67 => ( ! [R3: real] :
% 3.06/1.67 ( ( Xb
% 3.06/1.67 = ( number @ R3 ) )
% 3.06/1.67 => ( ( Y2
% 3.06/1.67 = ( some @ trm @ ( number @ R3 ) ) )
% 3.06/1.67 => ~ ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ X2 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( number @ R3 ) ) ) ) ) )
% 3.06/1.67 => ( ! [F6: char] :
% 3.06/1.67 ( ( Xb
% 3.06/1.67 = ( const @ F6 ) )
% 3.06/1.67 => ( ( Y2
% 3.06/1.67 = ( uSubst1138577137pconst @ X2 @ Xa @ F6 ) )
% 3.06/1.67 => ~ ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ X2 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( const @ F6 ) ) ) ) ) )
% 3.06/1.67 => ( ! [F6: char,Theta2: trm] :
% 3.06/1.67 ( ( Xb
% 3.06/1.67 = ( func @ F6 @ Theta2 ) )
% 3.06/1.67 => ( ( Y2
% 3.06/1.67 = ( case_option @ ( option @ trm ) @ trm @ ( none @ trm )
% 3.06/1.67 @ ^ [Sigma_theta: trm] :
% 3.06/1.67 ( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( func @ F6 @ Sigma_theta ) )
% 3.06/1.67 @ ^ [R: trm] :
% 3.06/1.67 ( if @ ( option @ trm )
% 3.06/1.67 @ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ R ) @ Xa )
% 3.06/1.67 = ( bot_bot @ ( set @ variable ) ) )
% 3.06/1.67 @ ( uSubst95898992stappt @ ( uSubst969145931substt @ Sigma_theta ) @ ( bot_bot @ ( set @ variable ) ) @ R )
% 3.06/1.67 @ ( none @ trm ) )
% 3.06/1.67 @ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [F4: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ fml ),Uw: char > ( option @ game )] : F4 ) )
% 3.06/1.67 @ X2
% 3.06/1.67 @ F6 ) )
% 3.06/1.67 @ ( uSubst95898992stappt @ X2 @ Xa @ Theta2 ) ) )
% 3.06/1.67 => ~ ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ X2 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( func @ F6 @ Theta2 ) ) ) ) ) )
% 3.06/1.67 => ( ! [Theta2: trm,Eta: trm] :
% 3.06/1.67 ( ( Xb
% 3.06/1.67 = ( plus @ Theta2 @ Eta ) )
% 3.06/1.67 => ( ( Y2
% 3.06/1.67 = ( uSubst1112714340_Pluso @ ( uSubst95898992stappt @ X2 @ Xa @ Theta2 ) @ ( uSubst95898992stappt @ X2 @ Xa @ Eta ) ) )
% 3.06/1.67 => ~ ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ X2 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( plus @ Theta2 @ Eta ) ) ) ) ) )
% 3.06/1.67 => ( ! [Theta2: trm,Eta: trm] :
% 3.06/1.67 ( ( Xb
% 3.06/1.67 = ( times @ Theta2 @ Eta ) )
% 3.06/1.67 => ( ( Y2
% 3.06/1.67 = ( uSubst277968634Timeso @ ( uSubst95898992stappt @ X2 @ Xa @ Theta2 ) @ ( uSubst95898992stappt @ X2 @ Xa @ Eta ) ) )
% 3.06/1.67 => ~ ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ X2 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( times @ Theta2 @ Eta ) ) ) ) ) )
% 3.06/1.67 => ~ ! [Theta2: trm] :
% 3.06/1.67 ( ( Xb
% 3.06/1.67 = ( differential @ Theta2 ) )
% 3.06/1.67 => ( ( Y2
% 3.06/1.67 = ( uSubst259074819ntialo
% 3.06/1.67 @ ( uSubst95898992stappt @ X2
% 3.06/1.67 @ ( collect @ variable
% 3.06/1.67 @ ^ [X: variable] : $true )
% 3.06/1.67 @ Theta2 ) ) )
% 3.06/1.67 => ~ ( accp @ ( product_prod @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) ) @ uSubst2096773001pt_rel @ ( product_Pair @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) @ ( product_prod @ ( set @ variable ) @ trm ) @ X2 @ ( product_Pair @ ( set @ variable ) @ trm @ Xa @ ( differential @ Theta2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_246_Differentialo_Osimps_I2_J,axiom,
% 3.06/1.67 ( ( uSubst259074819ntialo @ ( none @ trm ) )
% 3.06/1.67 = ( none @ trm ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_247_Differentialo__undef,axiom,
% 3.06/1.67 ! [Theta: option @ trm] :
% 3.06/1.67 ( ( ( uSubst259074819ntialo @ Theta )
% 3.06/1.67 = ( none @ trm ) )
% 3.06/1.67 = ( Theta
% 3.06/1.67 = ( none @ trm ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_248_Pluso_Osimps_I2_J,axiom,
% 3.06/1.67 ! [Eta2: option @ trm] :
% 3.06/1.67 ( ( uSubst1112714340_Pluso @ ( none @ trm ) @ Eta2 )
% 3.06/1.67 = ( none @ trm ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_249_Timeso_Osimps_I2_J,axiom,
% 3.06/1.67 ! [Eta2: option @ trm] :
% 3.06/1.67 ( ( uSubst277968634Timeso @ ( none @ trm ) @ Eta2 )
% 3.06/1.67 = ( none @ trm ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_250_Pluso__undef,axiom,
% 3.06/1.67 ! [Theta: option @ trm,Eta2: option @ trm] :
% 3.06/1.67 ( ( ( uSubst1112714340_Pluso @ Theta @ Eta2 )
% 3.06/1.67 = ( none @ trm ) )
% 3.06/1.67 = ( ( Theta
% 3.06/1.67 = ( none @ trm ) )
% 3.06/1.67 | ( Eta2
% 3.06/1.67 = ( none @ trm ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_251_Timeso__undef,axiom,
% 3.06/1.67 ! [Theta: option @ trm,Eta2: option @ trm] :
% 3.06/1.67 ( ( ( uSubst277968634Timeso @ Theta @ Eta2 )
% 3.06/1.67 = ( none @ trm ) )
% 3.06/1.67 = ( ( Theta
% 3.06/1.67 = ( none @ trm ) )
% 3.06/1.67 | ( Eta2
% 3.06/1.67 = ( none @ trm ) ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_252_Pluso_Osimps_I3_J,axiom,
% 3.06/1.67 ! [V3: trm] :
% 3.06/1.67 ( ( uSubst1112714340_Pluso @ ( some @ trm @ V3 ) @ ( none @ trm ) )
% 3.06/1.67 = ( none @ trm ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_253_Timeso_Osimps_I3_J,axiom,
% 3.06/1.67 ! [V3: trm] :
% 3.06/1.67 ( ( uSubst277968634Timeso @ ( some @ trm @ V3 ) @ ( none @ trm ) )
% 3.06/1.67 = ( none @ trm ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(fact_254_usubstappt_Osimps_I5_J,axiom,
% 3.06/1.67 ! [Sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),U: set @ variable,Theta: trm,Eta2: trm] :
% 3.06/1.67 ( ( uSubst95898992stappt @ Sigma @ U @ ( plus @ Theta @ Eta2 ) )
% 3.06/1.67 = ( uSubst1112714340_Pluso @ ( uSubst95898992stappt @ Sigma @ U @ Theta ) @ ( uSubst95898992stappt @ Sigma @ U @ Eta2 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 3.06/1.67 bounded_lattice @ $o ).
% 3.06/1.67
% 3.06/1.67 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 3.06/1.67 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 3.06/1.67 ! [A8: $tType,A9: $tType] :
% 3.06/1.67 ( ( bounded_lattice @ A9 )
% 3.06/1.67 => ( bounded_lattice @ ( A8 > A9 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 3.06/1.67 ! [A8: $tType,A9: $tType] :
% 3.06/1.67 ( ( bounded_lattice @ A9 )
% 3.06/1.67 => ( bounded_lattice_bot @ ( A8 > A9 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 3.06/1.67 ! [A8: $tType,A9: $tType] :
% 3.06/1.67 ( ( semilattice_inf @ A9 )
% 3.06/1.67 => ( semilattice_inf @ ( A8 > A9 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(tcon_fun___Lattices_Olattice,axiom,
% 3.06/1.67 ! [A8: $tType,A9: $tType] :
% 3.06/1.67 ( ( lattice @ A9 )
% 3.06/1.67 => ( lattice @ ( A8 > A9 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(tcon_fun___Orderings_Obot,axiom,
% 3.06/1.67 ! [A8: $tType,A9: $tType] :
% 3.06/1.67 ( ( bot @ A9 )
% 3.06/1.67 => ( bot @ ( A8 > A9 ) ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_3,axiom,
% 3.06/1.67 ! [A8: $tType] : ( bounded_lattice_bot @ ( set @ A8 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_4,axiom,
% 3.06/1.67 ! [A8: $tType] : ( semilattice_inf @ ( set @ A8 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(tcon_Set_Oset___Lattices_Olattice_5,axiom,
% 3.06/1.67 ! [A8: $tType] : ( lattice @ ( set @ A8 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(tcon_Set_Oset___Orderings_Obot_6,axiom,
% 3.06/1.67 ! [A8: $tType] : ( bot @ ( set @ A8 ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_7,axiom,
% 3.06/1.67 bounded_lattice_bot @ $o ).
% 3.06/1.67
% 3.06/1.67 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_8,axiom,
% 3.06/1.67 semilattice_inf @ $o ).
% 3.06/1.67
% 3.06/1.67 thf(tcon_HOL_Obool___Lattices_Olattice_9,axiom,
% 3.06/1.67 lattice @ $o ).
% 3.06/1.67
% 3.06/1.67 thf(tcon_HOL_Obool___Orderings_Obot_10,axiom,
% 3.06/1.67 bot @ $o ).
% 3.06/1.67
% 3.06/1.67 thf(tcon_Real_Oreal___Lattices_Osemilattice__inf_11,axiom,
% 3.06/1.67 semilattice_inf @ real ).
% 3.06/1.67
% 3.06/1.67 thf(tcon_Real_Oreal___Lattices_Olattice_12,axiom,
% 3.06/1.67 lattice @ real ).
% 3.06/1.67
% 3.06/1.67 thf(help_If_3_1_T,axiom,
% 3.06/1.67 ! [P2: $o] :
% 3.06/1.67 ( ( P2 = $true )
% 3.06/1.67 | ( P2 = $false ) ) ).
% 3.06/1.67
% 3.06/1.67 thf(help_If_2_1_T,axiom,
% 3.06/1.67 ! [A: $tType,X2: A,Y2: A] :
% 3.06/1.67 ( ( if @ A @ $false @ X2 @ Y2 )
% 3.06/1.67 = Y2 ) ).
% 3.06/1.67
% 3.06/1.67 thf(help_If_1_1_T,axiom,
% 3.06/1.67 ! [A: $tType,X2: A,Y2: A] :
% 3.06/1.67 ( ( if @ A @ $true @ X2 @ Y2 )
% 3.06/1.67 = X2 ) ).
% 3.06/1.67
% 3.06/1.67 thf(conj_0,conjecture,
% 3.06/1.67 ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uu: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [Uv: char > ( option @ trm )] :
% 3.06/1.67 ( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
% 3.06/1.67 @ ^ [P: char > ( option @ fml ),Uw: char > ( option @ game )] : P ) )
% 3.06/1.67 @ sigma
% 3.06/1.67 @ p )
% 3.06/1.67 = ( none @ fml ) ) ).
% 3.06/1.67 ------------------------
% 3.15/1.70 % (3666)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_3332 for (2999ds/2Mi)
% 3.15/1.70 % (3666)Instruction limit reached!
% 3.15/1.70 % (3666)------------------------------
% 3.15/1.70 % (3666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.70 % (3666)Termination reason: Unknown
% 3.15/1.70 % (3666)Termination phase: shuffling
% 3.15/1.70
% 3.15/1.70 % (3666)Memory used [KB]: 1407
% 3.15/1.70 % (3666)Time elapsed: 0.002 s
% 3.15/1.70 % (3666)Instructions burned: 2 (million)
% 3.15/1.70 % (3666)------------------------------
% 3.15/1.70 % (3666)------------------------------
% 3.15/1.70 % (3662)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3332 for (2999ds/183Mi)
% 3.15/1.70 % (3663)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_3332 for (2999ds/4Mi)
% 3.15/1.70 % (3664)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_3332 for (2999ds/27Mi)
% 3.15/1.70 % (3665)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3332 for (2999ds/2Mi)
% 3.15/1.70 % (3667)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_3332 for (2999ds/275Mi)
% 3.15/1.70 % (3668)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3332 for (2999ds/18Mi)
% 3.15/1.71 % (3665)Instruction limit reached!
% 3.15/1.71 % (3665)------------------------------
% 3.15/1.71 % (3665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.71 % (3665)Termination reason: Unknown
% 3.15/1.71 % (3665)Termination phase: shuffling
% 3.15/1.71
% 3.15/1.71 % (3665)Memory used [KB]: 1407
% 3.15/1.71 % (3665)Time elapsed: 0.004 s
% 3.15/1.71 % (3665)Instructions burned: 3 (million)
% 3.15/1.71 % (3665)------------------------------
% 3.15/1.71 % (3665)------------------------------
% 3.15/1.71 % (3663)Instruction limit reached!
% 3.15/1.71 % (3663)------------------------------
% 3.15/1.71 % (3663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.71 % (3663)Termination reason: Unknown
% 3.15/1.71 % (3663)Termination phase: shuffling
% 3.15/1.71
% 3.15/1.71 % (3663)Memory used [KB]: 1535
% 3.15/1.71 % (3663)Time elapsed: 0.005 s
% 3.15/1.71 % (3663)Instructions burned: 5 (million)
% 3.15/1.71 % (3663)------------------------------
% 3.15/1.71 % (3663)------------------------------
% 3.15/1.71 % (3669)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3332 for (2999ds/3Mi)
% 3.15/1.71 % (3669)Instruction limit reached!
% 3.15/1.71 % (3669)------------------------------
% 3.15/1.71 % (3669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.71 % (3669)Termination reason: Unknown
% 3.15/1.71 % (3669)Termination phase: shuffling
% 3.15/1.71
% 3.15/1.71 % (3669)Memory used [KB]: 1407
% 3.15/1.71 % (3669)Time elapsed: 0.003 s
% 3.15/1.71 % (3669)Instructions burned: 5 (million)
% 3.15/1.71 % (3669)------------------------------
% 3.15/1.71 % (3669)------------------------------
% 3.15/1.72 % (3668)Instruction limit reached!
% 3.15/1.72 % (3668)------------------------------
% 3.15/1.72 % (3668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.72 % (3668)Termination reason: Unknown
% 3.15/1.72 % (3668)Termination phase: shuffling
% 3.15/1.72
% 3.15/1.72 % (3668)Memory used [KB]: 1535
% 3.15/1.72 % (3668)Time elapsed: 0.013 s
% 3.15/1.72 % (3668)Instructions burned: 18 (million)
% 3.15/1.72 % (3668)------------------------------
% 3.15/1.72 % (3668)------------------------------
% 3.15/1.72 % (3664)Instruction limit reached!
% 3.15/1.72 % (3664)------------------------------
% 3.15/1.72 % (3664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.72 % (3664)Termination reason: Unknown
% 3.15/1.72 % (3664)Termination phase: shuffling
% 3.15/1.72
% 3.15/1.72 % (3664)Memory used [KB]: 1791
% 3.15/1.72 % (3664)Time elapsed: 0.018 s
% 3.15/1.72 % (3664)Instructions burned: 27 (million)
% 3.15/1.72 % (3664)------------------------------
% 3.15/1.72 % (3664)------------------------------
% 3.15/1.72 % (3672)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_3332 for (2999ds/3Mi)
% 3.15/1.72 % (3670)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_3332 for (2999ds/37Mi)
% 3.15/1.72 % (3672)Instruction limit reached!
% 3.15/1.72 % (3672)------------------------------
% 3.15/1.72 % (3672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.72 % (3672)Termination reason: Unknown
% 3.15/1.72 % (3672)Termination phase: shuffling
% 3.15/1.72
% 3.15/1.72 % (3672)Memory used [KB]: 1407
% 3.15/1.72 % (3672)Time elapsed: 0.003 s
% 3.15/1.72 % (3672)Instructions burned: 5 (million)
% 3.15/1.72 % (3672)------------------------------
% 3.15/1.72 % (3672)------------------------------
% 3.15/1.72 % (3671)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_3332 for (2999ds/15Mi)
% 3.15/1.73 % (3671)Instruction limit reached!
% 3.15/1.73 % (3671)------------------------------
% 3.15/1.73 % (3671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.73 % (3671)Termination reason: Unknown
% 3.15/1.73 % (3671)Termination phase: shuffling
% 3.15/1.73
% 3.15/1.73 % (3671)Memory used [KB]: 1535
% 3.15/1.73 % (3671)Time elapsed: 0.010 s
% 3.15/1.73 % (3671)Instructions burned: 16 (million)
% 3.15/1.73 % (3671)------------------------------
% 3.15/1.73 % (3671)------------------------------
% 3.15/1.73 % (3673)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_3332 for (2999ds/1041Mi)
% 3.15/1.73 % (3675)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3332 for (2999ds/16Mi)
% 3.15/1.74 % (3674)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3332 for (2999ds/7Mi)
% 3.15/1.74 % (3675)Instruction limit reached!
% 3.15/1.74 % (3675)------------------------------
% 3.15/1.74 % (3675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.74 % (3675)Termination reason: Unknown
% 3.15/1.74 % (3675)Termination phase: shuffling
% 3.15/1.74
% 3.15/1.74 % (3675)Memory used [KB]: 1663
% 3.15/1.74 % (3675)Time elapsed: 0.007 s
% 3.15/1.74 % (3675)Instructions burned: 18 (million)
% 3.15/1.74 % (3675)------------------------------
% 3.15/1.74 % (3675)------------------------------
% 3.15/1.74 % (3674)Instruction limit reached!
% 3.15/1.74 % (3674)------------------------------
% 3.15/1.74 % (3674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.74 % (3674)Termination reason: Unknown
% 3.15/1.74 % (3674)Termination phase: shuffling
% 3.15/1.74
% 3.15/1.74 % (3674)Memory used [KB]: 1535
% 3.15/1.74 % (3674)Time elapsed: 0.006 s
% 3.15/1.74 % (3674)Instructions burned: 7 (million)
% 3.15/1.74 % (3674)------------------------------
% 3.15/1.74 % (3674)------------------------------
% 3.15/1.74 % (3670)Instruction limit reached!
% 3.15/1.74 % (3670)------------------------------
% 3.15/1.74 % (3670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.74 % (3670)Termination reason: Unknown
% 3.15/1.74 % (3670)Termination phase: shuffling
% 3.15/1.74
% 3.15/1.74 % (3670)Memory used [KB]: 2174
% 3.15/1.74 % (3670)Time elapsed: 0.021 s
% 3.15/1.74 % (3670)Instructions burned: 37 (million)
% 3.15/1.74 % (3670)------------------------------
% 3.15/1.74 % (3670)------------------------------
% 3.15/1.74 % (3676)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_3332 for (2999ds/3Mi)
% 3.15/1.75 % (3676)Instruction limit reached!
% 3.15/1.75 % (3676)------------------------------
% 3.15/1.75 % (3676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.75 % (3676)Termination reason: Unknown
% 3.15/1.75 % (3676)Termination phase: shuffling
% 3.15/1.75
% 3.15/1.75 % (3676)Memory used [KB]: 1407
% 3.15/1.75 % (3676)Time elapsed: 0.003 s
% 3.15/1.75 % (3676)Instructions burned: 3 (million)
% 3.15/1.75 % (3676)------------------------------
% 3.15/1.75 % (3676)------------------------------
% 3.15/1.75 % (3677)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_3332 for (2999ds/3Mi)
% 3.15/1.75 % (3677)Instruction limit reached!
% 3.15/1.75 % (3677)------------------------------
% 3.15/1.75 % (3677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.75 % (3677)Termination reason: Unknown
% 3.15/1.75 % (3677)Termination phase: shuffling
% 3.15/1.75
% 3.15/1.75 % (3677)Memory used [KB]: 1407
% 3.15/1.75 % (3677)Time elapsed: 0.002 s
% 3.15/1.75 % (3677)Instructions burned: 3 (million)
% 3.15/1.75 % (3677)------------------------------
% 3.15/1.75 % (3677)------------------------------
% 3.15/1.76 % (3680)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3332 for (2999ds/4Mi)
% 3.15/1.76 % (3680)Instruction limit reached!
% 3.15/1.76 % (3680)------------------------------
% 3.15/1.76 % (3680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.76 % (3680)Termination reason: Unknown
% 3.15/1.76 % (3680)Termination phase: shuffling
% 3.15/1.76
% 3.15/1.76 % (3680)Memory used [KB]: 1535
% 3.15/1.76 % (3680)Time elapsed: 0.003 s
% 3.15/1.76 % (3680)Instructions burned: 6 (million)
% 3.15/1.76 % (3680)------------------------------
% 3.15/1.76 % (3680)------------------------------
% 3.15/1.76 % (3678)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3332 for (2999ds/7Mi)
% 3.15/1.76 % (3681)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3332 for (2999ds/18Mi)
% 3.15/1.76 % (3679)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3332 for (2999ds/3Mi)
% 3.15/1.76 % (3678)Instruction limit reached!
% 3.15/1.76 % (3678)------------------------------
% 3.15/1.76 % (3678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.76 % (3678)Termination reason: Unknown
% 3.15/1.76 % (3678)Termination phase: shuffling
% 3.15/1.76
% 3.15/1.76 % (3678)Memory used [KB]: 1535
% 3.15/1.76 % (3678)Time elapsed: 0.005 s
% 3.15/1.76 % (3678)Instructions burned: 7 (million)
% 3.15/1.76 % (3678)------------------------------
% 3.15/1.76 % (3678)------------------------------
% 3.15/1.76 % (3667)Refutation not found, incomplete strategy
% 3.15/1.76 % (3667)------------------------------
% 3.15/1.76 % (3667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.76 % (3667)Termination reason: Refutation not found, incomplete strategy
% 3.15/1.76
% 3.15/1.76
% 3.15/1.76 % (3667)Memory used [KB]: 7164
% 3.15/1.76 % (3667)Time elapsed: 0.059 s
% 3.15/1.76 % (3667)Instructions burned: 100 (million)
% 3.15/1.76 % (3667)------------------------------
% 3.15/1.76 % (3667)------------------------------
% 3.15/1.76 % (3679)Instruction limit reached!
% 3.15/1.76 % (3679)------------------------------
% 3.15/1.76 % (3679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.76 % (3679)Termination reason: Unknown
% 3.15/1.76 % (3679)Termination phase: shuffling
% 3.15/1.76
% 3.15/1.76 % (3679)Memory used [KB]: 1407
% 3.15/1.76 % (3679)Time elapsed: 0.004 s
% 3.15/1.76 % (3679)Instructions burned: 4 (million)
% 3.15/1.76 % (3679)------------------------------
% 3.15/1.76 % (3679)------------------------------
% 3.15/1.76 % (3681)Instruction limit reached!
% 3.15/1.76 % (3681)------------------------------
% 3.15/1.76 % (3681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.76 % (3681)Termination reason: Unknown
% 3.15/1.77 % (3681)Termination phase: shuffling
% 3.15/1.77
% 3.15/1.77 % (3681)Memory used [KB]: 1663
% 3.15/1.77 % (3681)Time elapsed: 0.007 s
% 3.15/1.77 % (3681)Instructions burned: 19 (million)
% 3.15/1.77 % (3681)------------------------------
% 3.15/1.77 % (3681)------------------------------
% 3.15/1.77 % (3682)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3332 for (2999ds/710Mi)
% 3.15/1.77 % (3683)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3332 for (2999ds/6Mi)
% 3.15/1.77 % (3686)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3332 for (2999ds/5Mi)
% 3.15/1.78 % (3686)Instruction limit reached!
% 3.15/1.78 % (3686)------------------------------
% 3.15/1.78 % (3686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.78 % (3686)Termination reason: Unknown
% 3.15/1.78 % (3686)Termination phase: shuffling
% 3.15/1.78
% 3.15/1.78 % (3686)Memory used [KB]: 1535
% 3.15/1.78 % (3686)Time elapsed: 0.003 s
% 3.15/1.78 % (3686)Instructions burned: 6 (million)
% 3.15/1.78 % (3686)------------------------------
% 3.15/1.78 % (3686)------------------------------
% 3.15/1.78 % (3683)Instruction limit reached!
% 3.15/1.78 % (3683)------------------------------
% 3.15/1.78 % (3683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.78 % (3683)Termination reason: Unknown
% 3.15/1.78 % (3683)Termination phase: shuffling
% 3.15/1.78
% 3.15/1.78 % (3683)Memory used [KB]: 1535
% 3.15/1.78 % (3683)Time elapsed: 0.004 s
% 3.15/1.78 % (3683)Instructions burned: 8 (million)
% 3.15/1.78 % (3683)------------------------------
% 3.15/1.78 % (3683)------------------------------
% 3.15/1.78 % (3684)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_3332 for (2999ds/902Mi)
% 3.15/1.78 % (3685)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_3332 for (2999ds/21Mi)
% 3.15/1.78 % (3662)Instruction limit reached!
% 3.15/1.78 % (3662)------------------------------
% 3.15/1.78 % (3662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.78 % (3662)Termination reason: Unknown
% 3.15/1.78 % (3662)Termination phase: Saturation
% 3.15/1.78
% 3.15/1.78 % (3662)Memory used [KB]: 7291
% 3.15/1.78 % (3662)Time elapsed: 0.082 s
% 3.15/1.78 % (3662)Instructions burned: 183 (million)
% 3.15/1.78 % (3662)------------------------------
% 3.15/1.78 % (3662)------------------------------
% 3.15/1.79 % (3687)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_3332 for (2999ds/6Mi)
% 3.15/1.79 % (3688)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3332 for (2999ds/377Mi)
% 3.15/1.79 % (3687)Instruction limit reached!
% 3.15/1.79 % (3687)------------------------------
% 3.15/1.79 % (3687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.79 % (3687)Termination reason: Unknown
% 3.15/1.79 % (3687)Termination phase: shuffling
% 3.15/1.79
% 3.15/1.79 % (3687)Memory used [KB]: 1535
% 3.15/1.79 % (3687)Time elapsed: 0.003 s
% 3.15/1.79 % (3687)Instructions burned: 7 (million)
% 3.15/1.79 % (3687)------------------------------
% 3.15/1.79 % (3687)------------------------------
% 3.15/1.79 % (3685)Instruction limit reached!
% 3.15/1.79 % (3685)------------------------------
% 3.15/1.79 % (3685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.79 % (3685)Termination reason: Unknown
% 3.15/1.79 % (3685)Termination phase: shuffling
% 3.15/1.79
% 3.15/1.79 % (3685)Memory used [KB]: 1663
% 3.15/1.79 % (3685)Time elapsed: 0.014 s
% 3.15/1.79 % (3685)Instructions burned: 21 (million)
% 3.15/1.79 % (3685)------------------------------
% 3.15/1.79 % (3685)------------------------------
% 3.15/1.79 % (3689)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_3332 for (2998ds/779Mi)
% 3.15/1.80 % (3690)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_3332 for (2998ds/19Mi)
% 3.15/1.80 % (3690)Instruction limit reached!
% 3.15/1.80 % (3690)------------------------------
% 3.15/1.80 % (3690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.80 % (3690)Termination reason: Unknown
% 3.15/1.80 % (3690)Termination phase: shuffling
% 3.15/1.80
% 3.15/1.80 % (3690)Memory used [KB]: 1791
% 3.15/1.80 % (3690)Time elapsed: 0.007 s
% 3.15/1.80 % (3690)Instructions burned: 21 (million)
% 3.15/1.80 % (3690)------------------------------
% 3.15/1.80 % (3690)------------------------------
% 3.15/1.81 % (3691)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3332 for (2998ds/879Mi)
% 3.15/1.81 % (3692)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3332 for (2998ds/17Mi)
% 3.15/1.82 % (3692)Instruction limit reached!
% 3.15/1.82 % (3692)------------------------------
% 3.15/1.82 % (3692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.82 % (3692)Termination reason: Unknown
% 3.15/1.82 % (3692)Termination phase: shuffling
% 3.15/1.82
% 3.15/1.82 % (3692)Memory used [KB]: 1663
% 3.15/1.82 % (3692)Time elapsed: 0.007 s
% 3.15/1.82 % (3692)Instructions burned: 18 (million)
% 3.15/1.82 % (3692)------------------------------
% 3.15/1.82 % (3692)------------------------------
% 3.15/1.83 % (3693)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3332 for (2998ds/3Mi)
% 3.15/1.83 % (3693)Instruction limit reached!
% 3.15/1.83 % (3693)------------------------------
% 3.15/1.83 % (3693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.83 % (3693)Termination reason: Unknown
% 3.15/1.83 % (3693)Termination phase: shuffling
% 3.15/1.83
% 3.15/1.83 % (3693)Memory used [KB]: 1407
% 3.15/1.83 % (3693)Time elapsed: 0.002 s
% 3.15/1.83 % (3693)Instructions burned: 4 (million)
% 3.15/1.83 % (3693)------------------------------
% 3.15/1.83 % (3693)------------------------------
% 3.15/1.84 % (3694)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3332 for (2998ds/30Mi)
% 3.15/1.85 % (3694)Instruction limit reached!
% 3.15/1.85 % (3694)------------------------------
% 3.15/1.85 % (3694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.85 % (3694)Termination reason: Unknown
% 3.15/1.85 % (3694)Termination phase: shuffling
% 3.15/1.85
% 3.15/1.85 % (3694)Memory used [KB]: 1918
% 3.15/1.85 % (3694)Time elapsed: 0.011 s
% 3.15/1.85 % (3694)Instructions burned: 32 (million)
% 3.15/1.85 % (3694)------------------------------
% 3.15/1.85 % (3694)------------------------------
% 3.15/1.86 % (3695)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_3332 for (2998ds/127Mi)
% 3.15/1.89 % (3695)Instruction limit reached!
% 3.15/1.89 % (3695)------------------------------
% 3.15/1.89 % (3695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.89 % (3695)Termination reason: Unknown
% 3.15/1.89 % (3695)Termination phase: Function definition elimination
% 3.15/1.89
% 3.15/1.89 % (3695)Memory used [KB]: 2686
% 3.15/1.89 % (3695)Time elapsed: 0.037 s
% 3.15/1.89 % (3695)Instructions burned: 127 (million)
% 3.15/1.89 % (3695)------------------------------
% 3.15/1.89 % (3695)------------------------------
% 3.15/1.90 % (3696)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_3332 for (2997ds/100Mi)
% 3.15/1.91 % (3688)Instruction limit reached!
% 3.15/1.91 % (3688)------------------------------
% 3.15/1.91 % (3688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.91 % (3688)Termination reason: Unknown
% 3.15/1.91 % (3688)Termination phase: Saturation
% 3.15/1.91
% 3.15/1.91 % (3688)Memory used [KB]: 8699
% 3.15/1.91 % (3688)Time elapsed: 0.122 s
% 3.15/1.91 % (3688)Instructions burned: 377 (million)
% 3.15/1.91 % (3688)------------------------------
% 3.15/1.91 % (3688)------------------------------
% 3.15/1.92 % (3697)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_3332 for (2997ds/3Mi)
% 3.15/1.92 % (3697)Instruction limit reached!
% 3.15/1.92 % (3697)------------------------------
% 3.15/1.92 % (3697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.92 % (3697)Termination reason: Unknown
% 3.15/1.92 % (3697)Termination phase: shuffling
% 3.15/1.92
% 3.15/1.92 % (3697)Memory used [KB]: 1407
% 3.15/1.92 % (3697)Time elapsed: 0.003 s
% 3.15/1.92 % (3697)Instructions burned: 4 (million)
% 3.15/1.92 % (3697)------------------------------
% 3.15/1.92 % (3697)------------------------------
% 3.15/1.93 % (3698)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_3332 for (2997ds/20Mi)
% 3.15/1.93 % (3696)Instruction limit reached!
% 3.15/1.93 % (3696)------------------------------
% 3.15/1.93 % (3696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.93 % (3696)Termination reason: Unknown
% 3.15/1.93 % (3696)Termination phase: Preprocessing 3
% 3.15/1.93
% 3.15/1.93 % (3696)Memory used [KB]: 2814
% 3.15/1.93 % (3696)Time elapsed: 0.028 s
% 3.15/1.93 % (3696)Instructions burned: 100 (million)
% 3.15/1.93 % (3696)------------------------------
% 3.15/1.93 % (3696)------------------------------
% 3.15/1.94 % (3698)Instruction limit reached!
% 3.15/1.94 % (3698)------------------------------
% 3.15/1.94 % (3698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.94 % (3698)Termination reason: Unknown
% 3.15/1.94 % (3698)Termination phase: shuffling
% 3.15/1.94
% 3.15/1.94 % (3698)Memory used [KB]: 1663
% 3.15/1.94 % (3698)Time elapsed: 0.009 s
% 3.15/1.94 % (3698)Instructions burned: 22 (million)
% 3.15/1.94 % (3698)------------------------------
% 3.15/1.94 % (3698)------------------------------
% 3.15/1.94 % (3699)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_3332 for (2997ds/86Mi)
% 3.15/1.95 % (3700)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_3332 for (2997ds/107Mi)
% 3.15/1.97 % (3699)Instruction limit reached!
% 3.15/1.97 % (3699)------------------------------
% 3.15/1.97 % (3699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.97 % (3699)Termination reason: Unknown
% 3.15/1.97 % (3699)Termination phase: Clausification
% 3.15/1.97
% 3.15/1.97 % (3699)Memory used [KB]: 2558
% 3.15/1.97 % (3699)Time elapsed: 0.027 s
% 3.15/1.97 % (3699)Instructions burned: 88 (million)
% 3.15/1.97 % (3699)------------------------------
% 3.15/1.97 % (3699)------------------------------
% 3.15/1.97 % (3701)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_3332 for (2997ds/39Mi)
% 3.15/1.98 % (3700)Instruction limit reached!
% 3.15/1.98 % (3700)------------------------------
% 3.15/1.98 % (3700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.98 % (3700)Termination reason: Unknown
% 3.15/1.98 % (3700)Termination phase: Property scanning
% 3.15/1.98
% 3.15/1.98 % (3700)Memory used [KB]: 2558
% 3.15/1.98 % (3700)Time elapsed: 0.035 s
% 3.15/1.98 % (3700)Instructions burned: 107 (million)
% 3.15/1.98 % (3700)------------------------------
% 3.15/1.98 % (3700)------------------------------
% 3.15/1.99 % (3701)Instruction limit reached!
% 3.15/1.99 % (3701)------------------------------
% 3.15/1.99 % (3701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.99 % (3701)Termination reason: Unknown
% 3.15/1.99 % (3701)Termination phase: shuffling
% 3.15/1.99
% 3.15/1.99 % (3701)Memory used [KB]: 2302
% 3.15/1.99 % (3701)Time elapsed: 0.012 s
% 3.15/1.99 % (3701)Instructions burned: 41 (million)
% 3.15/1.99 % (3701)------------------------------
% 3.15/1.99 % (3701)------------------------------
% 3.15/1.99 % (3682)Instruction limit reached!
% 3.15/1.99 % (3682)------------------------------
% 3.15/1.99 % (3682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.99 % (3682)Termination reason: Unknown
% 3.15/1.99 % (3682)Termination phase: Saturation
% 3.15/1.99
% 3.15/1.99 % (3682)Memory used [KB]: 8443
% 3.15/1.99 % (3682)Time elapsed: 0.220 s
% 3.15/1.99 % (3682)Instructions burned: 713 (million)
% 3.15/1.99 % (3682)------------------------------
% 3.15/1.99 % (3682)------------------------------
% 3.15/1.99 % (3702)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_3332 for (2997ds/448Mi)
% 3.15/2.00 % (3703)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_3332 for (2997ds/46Mi)
% 3.15/2.00 % (3704)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_3332 for (2997ds/98Mi)
% 3.15/2.01 % (3703)Instruction limit reached!
% 3.15/2.01 % (3703)------------------------------
% 3.15/2.01 % (3703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/2.01 % (3703)Termination reason: Unknown
% 3.15/2.01 % (3703)Termination phase: Property scanning
% 3.15/2.01
% 3.15/2.01 % (3703)Memory used [KB]: 1918
% 3.15/2.01 % (3703)Time elapsed: 0.016 s
% 3.15/2.01 % (3703)Instructions burned: 49 (million)
% 3.15/2.01 % (3703)------------------------------
% 3.15/2.01 % (3703)------------------------------
% 3.15/2.02 % (3705)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_3332 for (2996ds/507Mi)
% 3.15/2.02 % (3704)Instruction limit reached!
% 3.15/2.02 % (3704)------------------------------
% 3.15/2.02 % (3704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/2.02 % (3704)Termination reason: Unknown
% 3.15/2.02 % (3704)Termination phase: Preprocessing 3
% 3.15/2.02
% 3.15/2.02 % (3704)Memory used [KB]: 2814
% 3.15/2.02 % (3704)Time elapsed: 0.028 s
% 3.15/2.02 % (3704)Instructions burned: 101 (million)
% 3.15/2.02 % (3704)------------------------------
% 3.15/2.02 % (3704)------------------------------
% 5.40/2.03 % (3706)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_3332 for (2996ds/149Mi)
% 5.40/2.04 % (3689)Instruction limit reached!
% 5.40/2.04 % (3689)------------------------------
% 5.40/2.04 % (3689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.40/2.04 % (3689)Termination reason: Unknown
% 5.40/2.04 % (3689)Termination phase: Saturation
% 5.40/2.04
% 5.40/2.04 % (3689)Memory used [KB]: 9466
% 5.40/2.04 % (3689)Time elapsed: 0.246 s
% 5.40/2.04 % (3689)Instructions burned: 781 (million)
% 5.40/2.04 % (3689)------------------------------
% 5.40/2.04 % (3689)------------------------------
% 5.40/2.04 % (3684)Instruction limit reached!
% 5.40/2.04 % (3684)------------------------------
% 5.40/2.04 % (3684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.40/2.04 % (3684)Termination reason: Unknown
% 5.40/2.04 % (3684)Termination phase: Saturation
% 5.40/2.04
% 5.40/2.04 % (3684)Memory used [KB]: 8443
% 5.40/2.04 % (3684)Time elapsed: 0.265 s
% 5.40/2.04 % (3684)Instructions burned: 904 (million)
% 5.40/2.04 % (3684)------------------------------
% 5.40/2.04 % (3684)------------------------------
% 5.40/2.05 % (3707)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_3332 for (2996ds/39Mi)
% 5.40/2.05 % (3708)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_3332 for (2996ds/6Mi)
% 5.40/2.05 % (3708)Instruction limit reached!
% 5.40/2.05 % (3708)------------------------------
% 5.40/2.05 % (3708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.40/2.05 % (3708)Termination reason: Unknown
% 5.40/2.05 % (3708)Termination phase: shuffling
% 5.40/2.05
% 5.40/2.05 % (3708)Memory used [KB]: 1535
% 5.40/2.05 % (3708)Time elapsed: 0.003 s
% 5.40/2.05 % (3708)Instructions burned: 7 (million)
% 5.40/2.05 % (3708)------------------------------
% 5.40/2.05 % (3708)------------------------------
% 5.40/2.06 % (3707)Instruction limit reached!
% 5.40/2.06 % (3707)------------------------------
% 5.40/2.06 % (3707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.40/2.06 % (3707)Termination reason: Unknown
% 5.40/2.06 % (3707)Termination phase: shuffling
% 5.40/2.06
% 5.40/2.06 % (3707)Memory used [KB]: 1918
% 5.40/2.06 % (3707)Time elapsed: 0.015 s
% 5.40/2.06 % (3707)Instructions burned: 39 (million)
% 5.40/2.06 % (3707)------------------------------
% 5.40/2.06 % (3707)------------------------------
% 5.40/2.06 % (3709)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_3332 for (2996ds/1087Mi)
% 5.40/2.07 % (3706)Instruction limit reached!
% 5.40/2.07 % (3706)------------------------------
% 5.40/2.07 % (3706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.40/2.07 % (3706)Termination reason: Unknown
% 5.40/2.07 % (3706)Termination phase: Property scanning
% 5.40/2.07
% 5.40/2.07 % (3706)Memory used [KB]: 3326
% 5.40/2.07 % (3706)Time elapsed: 0.041 s
% 5.40/2.07 % (3706)Instructions burned: 151 (million)
% 5.40/2.07 % (3706)------------------------------
% 5.40/2.07 % (3706)------------------------------
% 5.40/2.07 % (3710)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_3332 for (2996ds/47Mi)
% 5.40/2.07 % (3673)Instruction limit reached!
% 5.40/2.07 % (3673)------------------------------
% 5.40/2.07 % (3673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.40/2.07 % (3673)Termination reason: Unknown
% 5.40/2.07 % (3673)Termination phase: Saturation
% 5.40/2.07
% 5.40/2.07 % (3673)Memory used [KB]: 10234
% 5.40/2.07 % (3673)Time elapsed: 0.342 s
% 5.40/2.07 % (3673)Instructions burned: 1042 (million)
% 5.40/2.07 % (3673)------------------------------
% 5.40/2.07 % (3673)------------------------------
% 5.40/2.08 % (3711)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_3332 for (2996ds/44Mi)
% 5.40/2.08 % (3712)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_3332 for (2996ds/432Mi)
% 5.40/2.09 % (3710)Instruction limit reached!
% 5.40/2.09 % (3710)------------------------------
% 5.40/2.09 % (3710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.40/2.09 % (3710)Termination reason: Unknown
% 5.40/2.09 % (3710)Termination phase: Property scanning
% 5.40/2.09
% 5.40/2.09 % (3710)Memory used [KB]: 1918
% 5.40/2.09 % (3710)Time elapsed: 0.018 s
% 5.40/2.09 % (3710)Instructions burned: 50 (million)
% 5.40/2.09 % (3710)------------------------------
% 5.40/2.09 % (3710)------------------------------
% 5.40/2.09 % (3711)Instruction limit reached!
% 5.40/2.09 % (3711)------------------------------
% 5.40/2.09 % (3711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.40/2.09 % (3711)Termination reason: Unknown
% 5.40/2.09 % (3711)Termination phase: shuffling
% 5.40/2.09
% 5.40/2.09 % (3711)Memory used [KB]: 2302
% 5.40/2.09 % (3711)Time elapsed: 0.013 s
% 5.40/2.09 % (3711)Instructions burned: 44 (million)
% 5.40/2.09 % (3711)------------------------------
% 5.40/2.09 % (3711)------------------------------
% 5.40/2.10 % (3713)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_3332 for (2995ds/62Mi)
% 5.40/2.10 % (3714)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_3332 for (2995ds/31Mi)
% 5.40/2.11 % (3714)Instruction limit reached!
% 5.40/2.11 % (3714)------------------------------
% 5.40/2.11 % (3714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.40/2.11 % (3714)Termination reason: Unknown
% 5.40/2.11 % (3714)Termination phase: shuffling
% 5.40/2.11
% 5.40/2.11 % (3714)Memory used [KB]: 1791
% 5.40/2.11 % (3714)Time elapsed: 0.011 s
% 5.40/2.11 % (3714)Instructions burned: 33 (million)
% 5.40/2.11 % (3714)------------------------------
% 5.40/2.11 % (3714)------------------------------
% 5.40/2.12 % (3713)Instruction limit reached!
% 5.40/2.12 % (3713)------------------------------
% 5.40/2.12 % (3713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.40/2.12 % (3713)Termination reason: Unknown
% 5.40/2.12 % (3713)Termination phase: Property scanning
% 5.40/2.12
% 5.40/2.12 % (3713)Memory used [KB]: 2430
% 5.40/2.12 % (3713)Time elapsed: 0.019 s
% 5.40/2.12 % (3713)Instructions burned: 63 (million)
% 5.40/2.12 % (3713)------------------------------
% 5.40/2.12 % (3713)------------------------------
% 5.40/2.12 % (3691)Instruction limit reached!
% 5.40/2.12 % (3691)------------------------------
% 5.40/2.12 % (3691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.40/2.12 % (3691)Termination reason: Unknown
% 5.40/2.12 % (3691)Termination phase: Saturation
% 5.40/2.12
% 5.40/2.12 % (3691)Memory used [KB]: 10106
% 5.40/2.12 % (3691)Time elapsed: 0.312 s
% 5.40/2.12 % (3691)Instructions burned: 881 (million)
% 5.40/2.12 % (3691)------------------------------
% 5.40/2.12 % (3691)------------------------------
% 5.40/2.12 % (3702)Instruction limit reached!
% 5.40/2.12 % (3702)------------------------------
% 5.40/2.12 % (3702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.40/2.12 % (3702)Termination reason: Unknown
% 5.40/2.12 % (3702)Termination phase: Saturation
% 5.40/2.12
% 5.40/2.12 % (3702)Memory used [KB]: 8827
% 5.40/2.12 % (3702)Time elapsed: 0.134 s
% 5.40/2.12 % (3702)Instructions burned: 449 (million)
% 5.40/2.12 % (3702)------------------------------
% 5.40/2.12 % (3702)------------------------------
% 5.40/2.12 % (3715)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_3332 for (2995ds/96Mi)
% 5.95/2.13 % (3716)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_3332 for (2995ds/453Mi)
% 5.95/2.13 % (3717)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_3332 for (2995ds/71Mi)
% 5.95/2.13 % (3718)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_3332 for (2995ds/83Mi)
% 5.95/2.15 % (3715)Instruction limit reached!
% 5.95/2.15 % (3715)------------------------------
% 5.95/2.15 % (3715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.15 % (3715)Termination reason: Unknown
% 5.95/2.15 % (3715)Termination phase: Property scanning
% 5.95/2.15
% 5.95/2.15 % (3715)Memory used [KB]: 2558
% 5.95/2.15 % (3715)Time elapsed: 0.029 s
% 5.95/2.15 % (3715)Instructions burned: 97 (million)
% 5.95/2.15 % (3715)------------------------------
% 5.95/2.15 % (3715)------------------------------
% 5.95/2.15 % (3717)Instruction limit reached!
% 5.95/2.15 % (3717)------------------------------
% 5.95/2.15 % (3717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.15 % (3717)Termination reason: Unknown
% 5.95/2.15 % (3717)Termination phase: Preprocessing 1
% 5.95/2.15
% 5.95/2.15 % (3717)Memory used [KB]: 2046
% 5.95/2.15 % (3717)Time elapsed: 0.025 s
% 5.95/2.15 % (3717)Instructions burned: 73 (million)
% 5.95/2.15 % (3717)------------------------------
% 5.95/2.15 % (3717)------------------------------
% 5.95/2.16 % (3718)Instruction limit reached!
% 5.95/2.16 % (3718)------------------------------
% 5.95/2.16 % (3718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.16 % (3718)Termination reason: Unknown
% 5.95/2.16 % (3718)Termination phase: Preprocessing 1
% 5.95/2.16
% 5.95/2.16 % (3718)Memory used [KB]: 2046
% 5.95/2.16 % (3718)Time elapsed: 0.025 s
% 5.95/2.16 % (3718)Instructions burned: 84 (million)
% 5.95/2.16 % (3718)------------------------------
% 5.95/2.16 % (3718)------------------------------
% 5.95/2.16 % (3719)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_3332 for (2995ds/11Mi)
% 5.95/2.16 % (3719)Instruction limit reached!
% 5.95/2.16 % (3719)------------------------------
% 5.95/2.16 % (3719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.16 % (3719)Termination reason: Unknown
% 5.95/2.16 % (3719)Termination phase: shuffling
% 5.95/2.16
% 5.95/2.16 % (3719)Memory used [KB]: 1663
% 5.95/2.16 % (3719)Time elapsed: 0.004 s
% 5.95/2.16 % (3719)Instructions burned: 11 (million)
% 5.95/2.16 % (3719)------------------------------
% 5.95/2.16 % (3719)------------------------------
% 5.95/2.16 % (3720)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_3332 for (2995ds/41Mi)
% 5.95/2.16 % (3721)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3332 for (2995ds/6Mi)
% 5.95/2.17 % (3705)Instruction limit reached!
% 5.95/2.17 % (3705)------------------------------
% 5.95/2.17 % (3705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.17 % (3705)Termination reason: Unknown
% 5.95/2.17 % (3705)Termination phase: Saturation
% 5.95/2.17
% 5.95/2.17 % (3705)Memory used [KB]: 8955
% 5.95/2.17 % (3705)Time elapsed: 0.147 s
% 5.95/2.17 % (3705)Instructions burned: 508 (million)
% 5.95/2.17 % (3705)------------------------------
% 5.95/2.17 % (3705)------------------------------
% 5.95/2.17 % (3721)Instruction limit reached!
% 5.95/2.17 % (3721)------------------------------
% 5.95/2.17 % (3721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.17 % (3721)Termination reason: Unknown
% 5.95/2.17 % (3721)Termination phase: shuffling
% 5.95/2.17
% 5.95/2.17 % (3721)Memory used [KB]: 1535
% 5.95/2.17 % (3721)Time elapsed: 0.003 s
% 5.95/2.17 % (3721)Instructions burned: 7 (million)
% 5.95/2.17 % (3721)------------------------------
% 5.95/2.17 % (3721)------------------------------
% 5.95/2.17 % (3722)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_3332 for (2995ds/150Mi)
% 5.95/2.17 % (3720)Instruction limit reached!
% 5.95/2.17 % (3720)------------------------------
% 5.95/2.17 % (3720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.17 % (3720)Termination reason: Unknown
% 5.95/2.17 % (3720)Termination phase: shuffling
% 5.95/2.17
% 5.95/2.17 % (3720)Memory used [KB]: 2302
% 5.95/2.17 % (3720)Time elapsed: 0.013 s
% 5.95/2.17 % (3720)Instructions burned: 41 (million)
% 5.95/2.17 % (3720)------------------------------
% 5.95/2.17 % (3720)------------------------------
% 5.95/2.18 % (3723)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_3332 for (2995ds/343Mi)
% 5.95/2.18 % (3724)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_3332 for (2995ds/109Mi)
% 5.95/2.18 % (3725)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_3332 for (2995ds/253Mi)
% 6.26/2.21 % (3724)Instruction limit reached!
% 6.26/2.21 % (3724)------------------------------
% 6.26/2.21 % (3724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.21 % (3724)Termination reason: Unknown
% 6.26/2.21 % (3724)Termination phase: Property scanning
% 6.26/2.21
% 6.26/2.21 % (3724)Memory used [KB]: 2558
% 6.26/2.21 % (3724)Time elapsed: 0.033 s
% 6.26/2.21 % (3724)Instructions burned: 110 (million)
% 6.26/2.21 % (3724)------------------------------
% 6.26/2.21 % (3724)------------------------------
% 6.26/2.21 % (3712)Instruction limit reached!
% 6.26/2.21 % (3712)------------------------------
% 6.26/2.21 % (3712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.21 % (3712)Termination reason: Unknown
% 6.26/2.21 % (3712)Termination phase: Saturation
% 6.26/2.21
% 6.26/2.21 % (3712)Memory used [KB]: 3837
% 6.26/2.21 % (3712)Time elapsed: 0.128 s
% 6.26/2.21 % (3712)Instructions burned: 432 (million)
% 6.26/2.21 % (3712)------------------------------
% 6.26/2.21 % (3712)------------------------------
% 6.26/2.21 % (3722)Instruction limit reached!
% 6.26/2.21 % (3722)------------------------------
% 6.26/2.21 % (3722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.21 % (3722)Termination reason: Unknown
% 6.26/2.21 % (3722)Termination phase: Function definition elimination
% 6.26/2.21
% 6.26/2.21 % (3722)Memory used [KB]: 2814
% 6.26/2.21 % (3722)Time elapsed: 0.043 s
% 6.26/2.21 % (3722)Instructions burned: 151 (million)
% 6.26/2.21 % (3722)------------------------------
% 6.26/2.21 % (3722)------------------------------
% 6.26/2.22 % (3726)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_3332 for (2994ds/140Mi)
% 6.26/2.22 % (3725)Refutation not found, incomplete strategy
% 6.26/2.22 % (3725)------------------------------
% 6.26/2.22 % (3725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.22 % (3725)Termination reason: Refutation not found, incomplete strategy
% 6.26/2.22
% 6.26/2.22
% 6.26/2.22 % (3725)Memory used [KB]: 7419
% 6.26/2.22 % (3727)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_3332 for (2994ds/614Mi)
% 6.26/2.22 % (3725)Time elapsed: 0.036 s
% 6.26/2.22 % (3725)Instructions burned: 114 (million)
% 6.26/2.22 % (3725)------------------------------
% 6.26/2.22 % (3725)------------------------------
% 6.26/2.22 % (3728)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_3332 for (2994ds/202Mi)
% 6.26/2.23 % (3729)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_3332 for (2994ds/339Mi)
% 6.26/2.25 % (3716)Instruction limit reached!
% 6.26/2.25 % (3716)------------------------------
% 6.26/2.25 % (3716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.25 % (3716)Termination reason: Unknown
% 6.26/2.25 % (3716)Termination phase: Saturation
% 6.26/2.25
% 6.26/2.25 % (3716)Memory used [KB]: 8059
% 6.26/2.25 % (3716)Time elapsed: 0.128 s
% 6.26/2.25 % (3716)Instructions burned: 454 (million)
% 6.26/2.25 % (3716)------------------------------
% 6.26/2.25 % (3716)------------------------------
% 6.26/2.26 % (3726)Instruction limit reached!
% 6.26/2.26 % (3726)------------------------------
% 6.26/2.26 % (3726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.26 % (3726)Termination reason: Unknown
% 6.26/2.26 % (3726)Termination phase: Saturation
% 6.26/2.26
% 6.26/2.26 % (3726)Memory used [KB]: 7164
% 6.26/2.26 % (3726)Time elapsed: 0.044 s
% 6.26/2.26 % (3726)Instructions burned: 142 (million)
% 6.26/2.26 % (3726)------------------------------
% 6.26/2.26 % (3726)------------------------------
% 6.26/2.26 % (3730)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_3332 for (2994ds/283Mi)
% 6.26/2.27 % (3728)Refutation not found, incomplete strategy
% 6.26/2.27 % (3728)------------------------------
% 6.26/2.27 % (3728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.27 % (3728)Termination reason: Refutation not found, incomplete strategy
% 6.26/2.27
% 6.26/2.27
% 6.26/2.27 % (3728)Memory used [KB]: 7803
% 6.26/2.27 % (3728)Time elapsed: 0.045 s
% 6.26/2.27 % (3728)Instructions burned: 147 (million)
% 6.26/2.27 % (3728)------------------------------
% 6.26/2.27 % (3728)------------------------------
% 6.26/2.27 % (3731)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_3332 for (2994ds/134Mi)
% 6.26/2.28 % (3732)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_3332 for (2994ds/298Mi)
% 6.26/2.28 % (3723)Instruction limit reached!
% 6.26/2.28 % (3723)------------------------------
% 6.26/2.28 % (3723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.28 % (3723)Termination reason: Unknown
% 6.26/2.28 % (3723)Termination phase: Saturation
% 6.26/2.28
% 6.26/2.28 % (3723)Memory used [KB]: 8315
% 6.26/2.28 % (3723)Time elapsed: 0.104 s
% 6.26/2.28 % (3723)Instructions burned: 343 (million)
% 6.26/2.28 % (3723)------------------------------
% 6.26/2.28 % (3723)------------------------------
% 6.26/2.29 % (3733)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_3332 for (2994ds/192Mi)
% 6.90/2.31 % (3731)Instruction limit reached!
% 6.90/2.31 % (3731)------------------------------
% 6.90/2.31 % (3731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.31 % (3731)Termination reason: Unknown
% 6.90/2.31 % (3731)Termination phase: Property scanning
% 6.90/2.31
% 6.90/2.31 % (3731)Memory used [KB]: 2686
% 6.90/2.31 % (3731)Time elapsed: 0.039 s
% 6.90/2.31 % (3731)Instructions burned: 137 (million)
% 6.90/2.31 % (3731)------------------------------
% 6.90/2.31 % (3731)------------------------------
% 6.90/2.32 % (3734)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_3332 for (2993ds/258Mi)
% 6.90/2.32 % (3729)Instruction limit reached!
% 6.90/2.32 % (3729)------------------------------
% 6.90/2.32 % (3729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.32 % (3729)Termination reason: Unknown
% 6.90/2.32 % (3729)Termination phase: Saturation
% 6.90/2.32
% 6.90/2.32 % (3729)Memory used [KB]: 7419
% 6.90/2.32 % (3729)Time elapsed: 0.093 s
% 6.90/2.32 % (3729)Instructions burned: 341 (million)
% 6.90/2.32 % (3729)------------------------------
% 6.90/2.32 % (3729)------------------------------
% 6.90/2.33 % (3735)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_3332 for (2993ds/90Mi)
% 6.90/2.34 % (3733)Instruction limit reached!
% 6.90/2.34 % (3733)------------------------------
% 6.90/2.34 % (3733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.34 % (3733)Termination reason: Unknown
% 6.90/2.34 % (3733)Termination phase: Saturation
% 6.90/2.34
% 6.90/2.34 % (3733)Memory used [KB]: 3326
% 6.90/2.34 % (3733)Time elapsed: 0.054 s
% 6.90/2.34 % (3733)Instructions burned: 192 (million)
% 6.90/2.34 % (3733)------------------------------
% 6.90/2.34 % (3733)------------------------------
% 6.90/2.34 % (3730)Instruction limit reached!
% 6.90/2.34 % (3730)------------------------------
% 6.90/2.34 % (3730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.34 % (3730)Termination reason: Unknown
% 6.90/2.34 % (3730)Termination phase: Saturation
% 6.90/2.34
% 6.90/2.34 % (3730)Memory used [KB]: 7675
% 6.90/2.34 % (3730)Time elapsed: 0.081 s
% 6.90/2.34 % (3730)Instructions burned: 284 (million)
% 6.90/2.34 % (3730)------------------------------
% 6.90/2.34 % (3730)------------------------------
% 6.90/2.35 % (3736)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_3332 for (2993ds/231Mi)
% 6.90/2.35 % (3737)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_3332 for (2993ds/458Mi)
% 6.90/2.36 % (3732)Instruction limit reached!
% 6.90/2.36 % (3732)------------------------------
% 6.90/2.36 % (3732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.36 % (3732)Termination reason: Unknown
% 6.90/2.36 % (3732)Termination phase: Saturation
% 6.90/2.36
% 6.90/2.36 % (3732)Memory used [KB]: 7931
% 6.90/2.36 % (3732)Time elapsed: 0.081 s
% 6.90/2.36 % (3732)Instructions burned: 300 (million)
% 6.90/2.36 % (3732)------------------------------
% 6.90/2.36 % (3732)------------------------------
% 6.90/2.36 % (3735)Instruction limit reached!
% 6.90/2.36 % (3735)------------------------------
% 6.90/2.36 % (3735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.36 % (3735)Termination reason: Unknown
% 6.90/2.36 % (3735)Termination phase: Property scanning
% 6.90/2.36
% 6.90/2.36 % (3735)Memory used [KB]: 2558
% 6.90/2.36 % (3735)Time elapsed: 0.028 s
% 6.90/2.36 % (3735)Instructions burned: 93 (million)
% 6.90/2.36 % (3735)------------------------------
% 6.90/2.36 % (3735)------------------------------
% 6.90/2.37 % (3739)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_3332 for (2993ds/297Mi)
% 6.90/2.38 % (3738)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_3332 for (2993ds/31Mi)
% 6.90/2.38 % (3734)Instruction limit reached!
% 6.90/2.38 % (3734)------------------------------
% 6.90/2.38 % (3734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.38 % (3734)Termination reason: Unknown
% 6.90/2.38 % (3734)Termination phase: Property scanning
% 6.90/2.38
% 6.90/2.38 % (3734)Memory used [KB]: 3198
% 6.90/2.38 % (3734)Time elapsed: 0.064 s
% 6.90/2.38 % (3734)Instructions burned: 260 (million)
% 6.90/2.38 % (3734)------------------------------
% 6.90/2.38 % (3734)------------------------------
% 6.90/2.39 % (3709)Instruction limit reached!
% 6.90/2.39 % (3709)------------------------------
% 6.90/2.39 % (3709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.39 % (3709)Termination reason: Unknown
% 6.90/2.39 % (3709)Termination phase: Saturation
% 6.90/2.39
% 6.90/2.39 % (3709)Memory used [KB]: 9210
% 6.90/2.39 % (3709)Time elapsed: 0.328 s
% 6.90/2.39 % (3709)Instructions burned: 1088 (million)
% 6.90/2.39 % (3709)------------------------------
% 6.90/2.39 % (3709)------------------------------
% 6.90/2.39 % (3740)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_3332 for (2992ds/987Mi)
% 6.90/2.39 % (3738)Instruction limit reached!
% 6.90/2.39 % (3738)------------------------------
% 6.90/2.39 % (3738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.39 % (3738)Termination reason: Unknown
% 6.90/2.39 % (3738)Termination phase: shuffling
% 6.90/2.39
% 6.90/2.39 % (3738)Memory used [KB]: 1918
% 6.90/2.39 % (3738)Time elapsed: 0.020 s
% 6.90/2.39 % (3738)Instructions burned: 31 (million)
% 6.90/2.39 % (3738)------------------------------
% 6.90/2.39 % (3738)------------------------------
% 6.90/2.39 % (3727)Instruction limit reached!
% 6.90/2.39 % (3727)------------------------------
% 6.90/2.39 % (3727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.39 % (3727)Termination reason: Unknown
% 6.90/2.39 % (3727)Termination phase: Saturation
% 6.90/2.39
% 6.90/2.39 % (3727)Memory used [KB]: 8827
% 6.90/2.39 % (3727)Time elapsed: 0.176 s
% 6.90/2.39 % (3727)Instructions burned: 614 (million)
% 6.90/2.39 % (3727)------------------------------
% 6.90/2.39 % (3727)------------------------------
% 7.96/2.40 % (3741)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_3332 for (2992ds/182Mi)
% 7.96/2.40 % (3743)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_3332 for (2992ds/154Mi)
% 7.96/2.41 % (3742)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_3332 for (2992ds/182Mi)
% 7.96/2.41 % (3736)Instruction limit reached!
% 7.96/2.41 % (3736)------------------------------
% 7.96/2.41 % (3736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.41 % (3736)Termination reason: Unknown
% 7.96/2.41 % (3736)Termination phase: Saturation
% 7.96/2.41
% 7.96/2.41 % (3736)Memory used [KB]: 7291
% 7.96/2.41 % (3736)Time elapsed: 0.063 s
% 7.96/2.41 % (3736)Instructions burned: 231 (million)
% 7.96/2.41 % (3736)------------------------------
% 7.96/2.41 % (3736)------------------------------
% 7.96/2.42 % (3744)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_3332 for (2992ds/79Mi)
% 7.96/2.44 % (3744)Instruction limit reached!
% 7.96/2.44 % (3744)------------------------------
% 7.96/2.44 % (3744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.44 % (3744)Termination reason: Unknown
% 7.96/2.44 % (3744)Termination phase: Preprocessing 3
% 7.96/2.44
% 7.96/2.44 % (3744)Memory used [KB]: 2302
% 7.96/2.44 % (3744)Time elapsed: 0.024 s
% 7.96/2.44 % (3744)Instructions burned: 79 (million)
% 7.96/2.44 % (3744)------------------------------
% 7.96/2.44 % (3744)------------------------------
% 7.96/2.45 % (3743)Instruction limit reached!
% 7.96/2.45 % (3743)------------------------------
% 7.96/2.45 % (3743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.45 % (3743)Termination reason: Unknown
% 7.96/2.45 % (3743)Termination phase: Property scanning
% 7.96/2.45
% 7.96/2.45 % (3743)Memory used [KB]: 2814
% 7.96/2.45 % (3743)Time elapsed: 0.042 s
% 7.96/2.45 % (3743)Instructions burned: 155 (million)
% 7.96/2.45 % (3743)------------------------------
% 7.96/2.45 % (3743)------------------------------
% 7.96/2.45 % (3741)Instruction limit reached!
% 7.96/2.45 % (3741)------------------------------
% 7.96/2.45 % (3741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.45 % (3741)Termination reason: Unknown
% 7.96/2.45 % (3741)Termination phase: Property scanning
% 7.96/2.45
% 7.96/2.45 % (3741)Memory used [KB]: 3326
% 7.96/2.45 % (3741)Time elapsed: 0.049 s
% 7.96/2.45 % (3741)Instructions burned: 186 (million)
% 7.96/2.45 % (3741)------------------------------
% 7.96/2.45 % (3741)------------------------------
% 7.96/2.45 % (3745)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_3332 for (2992ds/216Mi)
% 7.96/2.45 % (3739)Instruction limit reached!
% 7.96/2.45 % (3739)------------------------------
% 7.96/2.45 % (3739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.45 % (3739)Termination reason: Unknown
% 7.96/2.45 % (3739)Termination phase: Saturation
% 7.96/2.45
% 7.96/2.45 % (3739)Memory used [KB]: 7931
% 7.96/2.45 % (3739)Time elapsed: 0.088 s
% 7.96/2.45 % (3739)Instructions burned: 298 (million)
% 7.96/2.45 % (3739)------------------------------
% 7.96/2.45 % (3739)------------------------------
% 7.96/2.45 % (3746)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_3332 for (2992ds/114Mi)
% 7.96/2.46 % (3747)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_3332 for (2992ds/922Mi)
% 7.96/2.46 % (3748)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_3332 for (2992ds/182Mi)
% 7.96/2.48 % (3742)Instruction limit reached!
% 7.96/2.48 % (3742)------------------------------
% 7.96/2.48 % (3742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.48 % (3742)Termination reason: Unknown
% 7.96/2.48 % (3742)Termination phase: Saturation
% 7.96/2.48
% 7.96/2.48 % (3742)Memory used [KB]: 7291
% 7.96/2.48 % (3742)Time elapsed: 0.071 s
% 7.96/2.48 % (3742)Instructions burned: 184 (million)
% 7.96/2.48 % (3742)------------------------------
% 7.96/2.48 % (3742)------------------------------
% 7.96/2.49 % (3746)Instruction limit reached!
% 7.96/2.49 % (3746)------------------------------
% 7.96/2.49 % (3746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.49 % (3746)Termination reason: Unknown
% 7.96/2.49 % (3746)Termination phase: Function definition elimination
% 7.96/2.49
% 7.96/2.49 % (3746)Memory used [KB]: 2558
% 7.96/2.49 % (3746)Time elapsed: 0.034 s
% 7.96/2.49 % (3746)Instructions burned: 117 (million)
% 7.96/2.49 % (3746)------------------------------
% 7.96/2.49 % (3746)------------------------------
% 7.96/2.49 % (3737)Instruction limit reached!
% 7.96/2.49 % (3737)------------------------------
% 7.96/2.49 % (3737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.49 % (3737)Termination reason: Unknown
% 7.96/2.49 % (3737)Termination phase: Saturation
% 7.96/2.49
% 7.96/2.49 % (3737)Memory used [KB]: 8699
% 7.96/2.49 % (3737)Time elapsed: 0.137 s
% 7.96/2.49 % (3737)Instructions burned: 458 (million)
% 7.96/2.49 % (3737)------------------------------
% 7.96/2.49 % (3737)------------------------------
% 7.96/2.49 % (3749)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_3332 for (2991ds/164Mi)
% 8.53/2.50 % (3750)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_3332 for (2991ds/50Mi)
% 8.53/2.50 % (3751)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_3332 for (2991ds/368Mi)
% 8.53/2.51 % (3750)Instruction limit reached!
% 8.53/2.51 % (3750)------------------------------
% 8.53/2.51 % (3750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.53/2.51 % (3750)Termination reason: Unknown
% 8.53/2.51 % (3750)Termination phase: shuffling
% 8.53/2.51
% 8.53/2.51 % (3750)Memory used [KB]: 2430
% 8.53/2.51 % (3750)Time elapsed: 0.015 s
% 8.53/2.51 % (3750)Instructions burned: 51 (million)
% 8.53/2.51 % (3750)------------------------------
% 8.53/2.51 % (3750)------------------------------
% 8.53/2.51 % (3748)Instruction limit reached!
% 8.53/2.51 % (3748)------------------------------
% 8.53/2.51 % (3748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.53/2.51 % (3748)Termination reason: Unknown
% 8.53/2.51 % (3748)Termination phase: Saturation
% 8.53/2.51
% 8.53/2.51 % (3748)Memory used [KB]: 2814
% 8.53/2.51 % (3748)Time elapsed: 0.049 s
% 8.53/2.51 % (3748)Instructions burned: 185 (million)
% 8.53/2.51 % (3748)------------------------------
% 8.53/2.51 % (3748)------------------------------
% 8.53/2.51 % (3745)Instruction limit reached!
% 8.53/2.51 % (3745)------------------------------
% 8.53/2.51 % (3745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.53/2.51 % (3745)Termination reason: Unknown
% 8.53/2.51 % (3745)Termination phase: Saturation
% 8.53/2.51
% 8.53/2.51 % (3745)Memory used [KB]: 7419
% 8.53/2.51 % (3745)Time elapsed: 0.059 s
% 8.53/2.51 % (3745)Instructions burned: 217 (million)
% 8.53/2.51 % (3745)------------------------------
% 8.53/2.51 % (3745)------------------------------
% 8.53/2.52 % (3752)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_3332 for (2991ds/1021Mi)
% 8.53/2.52 % (3753)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_3332 for (2991ds/267Mi)
% 8.53/2.52 % (3754)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_3332 for (2991ds/204Mi)
% 8.53/2.54 % (3749)Instruction limit reached!
% 8.53/2.54 % (3749)------------------------------
% 8.53/2.54 % (3749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.53/2.54 % (3749)Termination reason: Unknown
% 8.53/2.54 % (3749)Termination phase: Saturation
% 8.53/2.54
% 8.53/2.54 % (3749)Memory used [KB]: 2814
% 8.53/2.54 % (3749)Time elapsed: 0.051 s
% 8.53/2.54 % (3749)Instructions burned: 166 (million)
% 8.53/2.54 % (3749)------------------------------
% 8.53/2.54 % (3749)------------------------------
% 8.53/2.55 % (3755)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_3332 for (2991ds/26Mi)
% 8.53/2.56 % (3755)Instruction limit reached!
% 8.53/2.56 % (3755)------------------------------
% 8.53/2.56 % (3755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.53/2.56 % (3755)Termination reason: Unknown
% 8.53/2.56 % (3755)Termination phase: shuffling
% 8.53/2.56
% 8.53/2.56 % (3755)Memory used [KB]: 2046
% 8.53/2.56 % (3755)Time elapsed: 0.010 s
% 8.53/2.56 % (3755)Instructions burned: 27 (million)
% 8.53/2.56 % (3755)------------------------------
% 8.53/2.56 % (3755)------------------------------
% 8.53/2.57 % (3756)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_3332 for (2991ds/53Mi)
% 8.53/2.58 % (3754)Instruction limit reached!
% 8.53/2.58 % (3754)------------------------------
% 8.53/2.58 % (3754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.53/2.58 % (3754)Termination reason: Unknown
% 8.53/2.58 % (3754)Termination phase: Saturation
% 8.53/2.58
% 8.53/2.58 % (3754)Memory used [KB]: 7164
% 8.53/2.58 % (3754)Time elapsed: 0.056 s
% 8.53/2.58 % (3754)Instructions burned: 204 (million)
% 8.53/2.58 % (3754)------------------------------
% 8.53/2.58 % (3754)------------------------------
% 8.53/2.58 % (3756)Instruction limit reached!
% 8.53/2.58 % (3756)------------------------------
% 8.53/2.58 % (3756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.53/2.58 % (3756)Termination reason: Unknown
% 8.53/2.58 % (3756)Termination phase: Property scanning
% 8.53/2.58
% 8.53/2.58 % (3756)Memory used [KB]: 2430
% 8.53/2.58 % (3756)Time elapsed: 0.018 s
% 8.53/2.58 % (3756)Instructions burned: 55 (million)
% 8.53/2.58 % (3756)------------------------------
% 8.53/2.58 % (3756)------------------------------
% 8.53/2.59 % (3757)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_3332 for (2991ds/4436Mi)
% 8.53/2.59 % (3758)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_3332 for (2990ds/1539Mi)
% 8.85/2.60 % (3753)Instruction limit reached!
% 8.85/2.60 % (3753)------------------------------
% 8.85/2.60 % (3753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.60 % (3753)Termination reason: Unknown
% 8.85/2.60 % (3753)Termination phase: Saturation
% 8.85/2.60
% 8.85/2.60 % (3753)Memory used [KB]: 7675
% 8.85/2.60 % (3753)Time elapsed: 0.076 s
% 8.85/2.60 % (3753)Instructions burned: 268 (million)
% 8.85/2.60 % (3753)------------------------------
% 8.85/2.60 % (3753)------------------------------
% 8.85/2.60 % (3751)Instruction limit reached!
% 8.85/2.60 % (3751)------------------------------
% 8.85/2.60 % (3751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.60 % (3751)Termination reason: Unknown
% 8.85/2.60 % (3751)Termination phase: Saturation
% 8.85/2.60
% 8.85/2.60 % (3751)Memory used [KB]: 8699
% 8.85/2.60 % (3751)Time elapsed: 0.108 s
% 8.85/2.60 % (3751)Instructions burned: 371 (million)
% 8.85/2.60 % (3751)------------------------------
% 8.85/2.60 % (3751)------------------------------
% 8.85/2.61 % (3759)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_3332 for (2990ds/408Mi)
% 8.85/2.61 % (3760)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_3332 for (2990ds/5205Mi)
% 8.85/2.69 % (3740)Instruction limit reached!
% 8.85/2.69 % (3740)------------------------------
% 8.85/2.69 % (3740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.69 % (3740)Termination reason: Unknown
% 8.85/2.69 % (3740)Termination phase: Saturation
% 8.85/2.69
% 8.85/2.69 % (3740)Memory used [KB]: 9850
% 8.85/2.69 % (3740)Time elapsed: 0.305 s
% 8.85/2.69 % (3740)Instructions burned: 988 (million)
% 8.85/2.69 % (3740)------------------------------
% 8.85/2.69 % (3740)------------------------------
% 9.38/2.70 % (3761)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_3332 for (2989ds/1913Mi)
% 9.38/2.73 % (3759)Instruction limit reached!
% 9.38/2.73 % (3759)------------------------------
% 9.38/2.73 % (3759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.38/2.73 % (3759)Termination reason: Unknown
% 9.38/2.73 % (3759)Termination phase: Saturation
% 9.38/2.73
% 9.38/2.73 % (3759)Memory used [KB]: 8699
% 9.38/2.73 % (3759)Time elapsed: 0.121 s
% 9.38/2.73 % (3759)Instructions burned: 410 (million)
% 9.38/2.73 % (3759)------------------------------
% 9.38/2.73 % (3759)------------------------------
% 9.38/2.73 % (3747)Instruction limit reached!
% 9.38/2.73 % (3747)------------------------------
% 9.38/2.73 % (3747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.38/2.73 % (3747)Termination reason: Unknown
% 9.38/2.73 % (3747)Termination phase: Saturation
% 9.38/2.73
% 9.38/2.73 % (3747)Memory used [KB]: 8827
% 9.38/2.73 % (3747)Time elapsed: 0.277 s
% 9.38/2.73 % (3747)Instructions burned: 925 (million)
% 9.38/2.73 % (3747)------------------------------
% 9.38/2.73 % (3747)------------------------------
% 9.38/2.74 % (3762)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_3332 for (2989ds/4350Mi)
% 9.38/2.74 % (3763)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_3332 for (2989ds/68Mi)
% 9.38/2.76 % (3763)Instruction limit reached!
% 9.38/2.76 % (3763)------------------------------
% 9.38/2.76 % (3763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.38/2.76 % (3763)Termination reason: Unknown
% 9.38/2.76 % (3763)Termination phase: SInE selection
% 9.38/2.76
% 9.38/2.76 % (3763)Memory used [KB]: 1918
% 9.38/2.76 % (3763)Time elapsed: 0.021 s
% 9.38/2.76 % (3763)Instructions burned: 69 (million)
% 9.38/2.76 % (3763)------------------------------
% 9.38/2.76 % (3763)------------------------------
% 9.38/2.77 % (3764)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_3332 for (2989ds/358Mi)
% 9.82/2.82 % (3752)Instruction limit reached!
% 9.82/2.82 % (3752)------------------------------
% 9.82/2.82 % (3752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.82/2.82 % (3752)Termination reason: Unknown
% 9.82/2.82 % (3752)Termination phase: Saturation
% 9.82/2.82
% 9.82/2.82 % (3752)Memory used [KB]: 10106
% 9.82/2.82 % (3752)Time elapsed: 0.302 s
% 9.82/2.82 % (3752)Instructions burned: 1021 (million)
% 9.82/2.82 % (3752)------------------------------
% 9.82/2.82 % (3752)------------------------------
% 9.82/2.83 % (3765)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_3332 for (2988ds/31Mi)
% 9.82/2.84 % (3765)Instruction limit reached!
% 9.82/2.84 % (3765)------------------------------
% 9.82/2.84 % (3765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.82/2.84 % (3765)Termination reason: Unknown
% 9.82/2.84 % (3765)Termination phase: shuffling
% 9.82/2.84
% 9.82/2.84 % (3765)Memory used [KB]: 1791
% 9.82/2.84 % (3765)Time elapsed: 0.012 s
% 9.82/2.84 % (3765)Instructions burned: 33 (million)
% 9.82/2.84 % (3765)------------------------------
% 9.82/2.84 % (3765)------------------------------
% 9.82/2.85 % (3766)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_3332 for (2988ds/279Mi)
% 9.82/2.88 % (3764)Instruction limit reached!
% 9.82/2.88 % (3764)------------------------------
% 9.82/2.88 % (3764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.82/2.88 % (3764)Termination reason: Unknown
% 9.82/2.88 % (3764)Termination phase: Saturation
% 9.82/2.88
% 9.82/2.88 % (3764)Memory used [KB]: 7803
% 9.82/2.88 % (3764)Time elapsed: 0.108 s
% 9.82/2.88 % (3764)Instructions burned: 360 (million)
% 9.82/2.88 % (3764)------------------------------
% 9.82/2.88 % (3764)------------------------------
% 9.82/2.89 % (3766)Refutation not found, incomplete strategy
% 9.82/2.89 % (3766)------------------------------
% 9.82/2.89 % (3766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.82/2.89 % (3766)Termination reason: Refutation not found, incomplete strategy
% 9.82/2.89
% 9.82/2.89
% 9.82/2.89 % (3766)Memory used [KB]: 7291
% 9.82/2.89 % (3766)Time elapsed: 0.035 s
% 9.82/2.89 % (3766)Instructions burned: 127 (million)
% 9.82/2.89 % (3766)------------------------------
% 9.82/2.89 % (3766)------------------------------
% 9.82/2.89 % (3767)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_3332 for (2988ds/258Mi)
% 9.82/2.90 % (3768)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_3332 for (2987ds/26Mi)
% 10.32/2.90 % (3768)Instruction limit reached!
% 10.32/2.90 % (3768)------------------------------
% 10.32/2.90 % (3768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.32/2.90 % (3768)Termination reason: Unknown
% 10.32/2.90 % (3768)Termination phase: shuffling
% 10.32/2.90
% 10.32/2.90 % (3768)Memory used [KB]: 2046
% 10.32/2.90 % (3768)Time elapsed: 0.008 s
% 10.32/2.90 % (3768)Instructions burned: 26 (million)
% 10.32/2.90 % (3768)------------------------------
% 10.32/2.90 % (3768)------------------------------
% 10.32/2.91 % (3769)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_3332 for (2987ds/995Mi)
% 10.32/2.97 % (3767)Instruction limit reached!
% 10.32/2.97 % (3767)------------------------------
% 10.32/2.97 % (3767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.32/2.97 % (3767)Termination reason: Unknown
% 10.32/2.97 % (3767)Termination phase: Saturation
% 10.32/2.97
% 10.32/2.97 % (3767)Memory used [KB]: 7803
% 10.32/2.97 % (3767)Time elapsed: 0.078 s
% 10.32/2.97 % (3767)Instructions burned: 260 (million)
% 10.32/2.97 % (3767)------------------------------
% 10.32/2.97 % (3767)------------------------------
% 10.32/2.98 % (3770)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_3332 for (2987ds/373Mi)
% 12.35/3.09 % (3770)Instruction limit reached!
% 12.35/3.09 % (3770)------------------------------
% 12.35/3.09 % (3770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.35/3.09 % (3770)Termination reason: Unknown
% 12.35/3.09 % (3770)Termination phase: Saturation
% 12.35/3.09
% 12.35/3.09 % (3770)Memory used [KB]: 8187
% 12.35/3.09 % (3770)Time elapsed: 0.114 s
% 12.35/3.09 % (3770)Instructions burned: 374 (million)
% 12.35/3.09 % (3770)------------------------------
% 12.35/3.09 % (3770)------------------------------
% 12.35/3.10 % (3771)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_3332 for (2985ds/253Mi)
% 13.06/3.12 % (3758)Instruction limit reached!
% 13.06/3.12 % (3758)------------------------------
% 13.06/3.12 % (3758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.06/3.12 % (3758)Termination reason: Unknown
% 13.06/3.12 % (3758)Termination phase: Saturation
% 13.06/3.12
% 13.06/3.12 % (3758)Memory used [KB]: 12281
% 13.06/3.12 % (3758)Time elapsed: 0.525 s
% 13.06/3.12 % (3758)Instructions burned: 1541 (million)
% 13.06/3.12 % (3758)------------------------------
% 13.06/3.12 % (3758)------------------------------
% 13.06/3.13 % (3772)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_3332 for (2985ds/832Mi)
% 13.06/3.17 % (3771)Instruction limit reached!
% 13.06/3.17 % (3771)------------------------------
% 13.06/3.17 % (3771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.06/3.17 % (3771)Termination reason: Unknown
% 13.06/3.17 % (3771)Termination phase: Saturation
% 13.06/3.17
% 13.06/3.17 % (3771)Memory used [KB]: 7547
% 13.06/3.17 % (3771)Time elapsed: 0.070 s
% 13.06/3.17 % (3771)Instructions burned: 253 (million)
% 13.06/3.17 % (3771)------------------------------
% 13.06/3.17 % (3771)------------------------------
% 13.06/3.18 % (3773)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_3332 for (2985ds/668Mi)
% 13.06/3.18 % (3769)Instruction limit reached!
% 13.06/3.18 % (3769)------------------------------
% 13.06/3.18 % (3769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.06/3.18 % (3769)Termination reason: Unknown
% 13.06/3.18 % (3769)Termination phase: Saturation
% 13.06/3.18
% 13.06/3.18 % (3769)Memory used [KB]: 8187
% 13.06/3.18 % (3769)Time elapsed: 0.269 s
% 13.06/3.18 % (3769)Instructions burned: 996 (million)
% 13.06/3.18 % (3769)------------------------------
% 13.06/3.18 % (3769)------------------------------
% 13.06/3.19 % (3774)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_3332 for (2984ds/40Mi)
% 13.56/3.20 % (3774)Instruction limit reached!
% 13.56/3.20 % (3774)------------------------------
% 13.56/3.20 % (3774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.56/3.20 % (3774)Termination reason: Unknown
% 13.56/3.20 % (3774)Termination phase: shuffling
% 13.56/3.20
% 13.56/3.20 % (3774)Memory used [KB]: 2302
% 13.56/3.20 % (3774)Time elapsed: 0.012 s
% 13.56/3.20 % (3774)Instructions burned: 40 (million)
% 13.56/3.20 % (3774)------------------------------
% 13.56/3.20 % (3774)------------------------------
% 13.56/3.21 % (3775)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_3332 for (2984ds/294Mi)
% 13.56/3.25 % (3775)Refutation not found, incomplete strategy
% 13.56/3.25 % (3775)------------------------------
% 13.56/3.25 % (3775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.56/3.25 % (3775)Termination reason: Refutation not found, incomplete strategy
% 13.56/3.25
% 13.56/3.25
% 13.56/3.25 % (3775)Memory used [KB]: 7419
% 13.56/3.25 % (3775)Time elapsed: 0.036 s
% 13.56/3.25 % (3775)Instructions burned: 125 (million)
% 13.56/3.25 % (3775)------------------------------
% 13.56/3.25 % (3775)------------------------------
% 13.56/3.26 % (3776)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_3332 for (2984ds/187Mi)
% 14.04/3.31 % (3776)Instruction limit reached!
% 14.04/3.31 % (3776)------------------------------
% 14.04/3.31 % (3776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.04/3.31 % (3776)Termination reason: Unknown
% 14.04/3.31 % (3776)Termination phase: Saturation
% 14.04/3.31
% 14.04/3.31 % (3776)Memory used [KB]: 7291
% 14.04/3.31 % (3776)Time elapsed: 0.053 s
% 14.04/3.31 % (3776)Instructions burned: 189 (million)
% 14.04/3.31 % (3776)------------------------------
% 14.04/3.31 % (3776)------------------------------
% 14.04/3.31 % (3761)Instruction limit reached!
% 14.04/3.31 % (3761)------------------------------
% 14.04/3.31 % (3761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.04/3.31 % (3761)Termination reason: Unknown
% 14.04/3.31 % (3761)Termination phase: Saturation
% 14.04/3.31
% 14.04/3.31 % (3761)Memory used [KB]: 5117
% 14.04/3.31 % (3761)Time elapsed: 0.606 s
% 14.04/3.31 % (3761)Instructions burned: 1915 (million)
% 14.04/3.31 % (3761)------------------------------
% 14.04/3.31 % (3761)------------------------------
% 14.04/3.32 % (3777)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_3332 for (2983ds/371Mi)
% 14.04/3.32 % (3778)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_3332 for (2983ds/1827Mi)
% 14.04/3.37 % (3773)Instruction limit reached!
% 14.04/3.37 % (3773)------------------------------
% 14.04/3.37 % (3773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.04/3.37 % (3773)Termination reason: Unknown
% 14.04/3.37 % (3773)Termination phase: Saturation
% 14.04/3.37
% 14.04/3.37 % (3773)Memory used [KB]: 13816
% 14.04/3.37 % (3773)Time elapsed: 0.198 s
% 14.04/3.37 % (3773)Instructions burned: 670 (million)
% 14.04/3.37 % (3773)------------------------------
% 14.04/3.37 % (3773)------------------------------
% 14.04/3.38 % (3772)Instruction limit reached!
% 14.04/3.38 % (3772)------------------------------
% 14.04/3.38 % (3772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.04/3.38 % (3772)Termination reason: Unknown
% 14.04/3.38 % (3772)Termination phase: Saturation
% 14.04/3.38
% 14.04/3.38 % (3772)Memory used [KB]: 9594
% 14.04/3.38 % (3772)Time elapsed: 0.252 s
% 14.04/3.38 % (3772)Instructions burned: 834 (million)
% 14.04/3.38 % (3772)------------------------------
% 14.04/3.38 % (3772)------------------------------
% 14.04/3.38 % (3779)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_3332 for (2982ds/70Mi)
% 14.04/3.39 % (3780)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_3332 for (2982ds/316Mi)
% 14.89/3.40 % (3779)Instruction limit reached!
% 14.89/3.40 % (3779)------------------------------
% 14.89/3.40 % (3779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.89/3.40 % (3779)Termination reason: Unknown
% 14.89/3.40 % (3779)Termination phase: Property scanning
% 14.89/3.40
% 14.89/3.40 % (3779)Memory used [KB]: 2430
% 14.89/3.40 % (3779)Time elapsed: 0.021 s
% 14.89/3.40 % (3779)Instructions burned: 72 (million)
% 14.89/3.40 % (3779)------------------------------
% 14.89/3.40 % (3779)------------------------------
% 14.89/3.41 % (3781)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_3332 for (2982ds/932Mi)
% 14.89/3.43 % (3777)Instruction limit reached!
% 14.89/3.43 % (3777)------------------------------
% 14.89/3.43 % (3777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.89/3.43 % (3777)Termination reason: Unknown
% 14.89/3.43 % (3777)Termination phase: Saturation
% 14.89/3.43
% 14.89/3.43 % (3777)Memory used [KB]: 8699
% 14.89/3.43 % (3777)Time elapsed: 0.113 s
% 14.89/3.43 % (3777)Instructions burned: 371 (million)
% 14.89/3.43 % (3777)------------------------------
% 14.89/3.43 % (3777)------------------------------
% 14.89/3.44 % (3782)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_3332 for (2982ds/4714Mi)
% 14.89/3.46 % (3780)Refutation not found, incomplete strategy
% 14.89/3.46 % (3780)------------------------------
% 14.89/3.46 % (3780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.89/3.46 % (3780)Termination reason: Refutation not found, incomplete strategy
% 14.89/3.46
% 14.89/3.46
% 14.89/3.46 % (3780)Memory used [KB]: 7931
% 14.89/3.46 % (3780)Time elapsed: 0.072 s
% 14.89/3.46 % (3780)Instructions burned: 258 (million)
% 14.89/3.46 % (3780)------------------------------
% 14.89/3.46 % (3780)------------------------------
% 14.89/3.47 % (3783)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_3332 for (2982ds/8250Mi)
% 15.43/3.52 % (3782)Refutation not found, incomplete strategy
% 15.43/3.52 % (3782)------------------------------
% 15.43/3.52 % (3782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.43/3.52 % (3782)Termination reason: Refutation not found, incomplete strategy
% 15.43/3.52
% 15.43/3.52
% 15.43/3.52 % (3782)Memory used [KB]: 8059
% 15.43/3.52 % (3782)Time elapsed: 0.078 s
% 15.43/3.52 % (3782)Instructions burned: 275 (million)
% 15.43/3.52 % (3782)------------------------------
% 15.43/3.52 % (3782)------------------------------
% 15.43/3.53 % (3784)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_3332 for (2981ds/770Mi)
% 15.82/3.69 % (3781)Instruction limit reached!
% 15.82/3.69 % (3781)------------------------------
% 15.82/3.69 % (3781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.82/3.69 % (3781)Termination reason: Unknown
% 15.82/3.69 % (3781)Termination phase: Saturation
% 15.82/3.69
% 15.82/3.69 % (3781)Memory used [KB]: 12025
% 15.82/3.69 % (3781)Time elapsed: 0.278 s
% 15.82/3.69 % (3781)Instructions burned: 933 (million)
% 15.82/3.69 % (3781)------------------------------
% 15.82/3.69 % (3781)------------------------------
% 16.40/3.70 % (3785)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_3332 for (2979ds/794Mi)
% 16.40/3.76 % (3784)Instruction limit reached!
% 16.40/3.76 % (3784)------------------------------
% 16.40/3.76 % (3784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.40/3.76 % (3784)Termination reason: Unknown
% 16.40/3.76 % (3784)Termination phase: Saturation
% 16.40/3.76
% 16.40/3.76 % (3784)Memory used [KB]: 9594
% 16.40/3.76 % (3784)Time elapsed: 0.236 s
% 16.40/3.76 % (3784)Instructions burned: 772 (million)
% 16.40/3.76 % (3784)------------------------------
% 16.40/3.76 % (3784)------------------------------
% 16.40/3.77 % (3786)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_3332 for (2979ds/464Mi)
% 16.96/3.89 % (3778)Instruction limit reached!
% 16.96/3.89 % (3778)------------------------------
% 16.96/3.89 % (3778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.96/3.89 % (3778)Termination reason: Unknown
% 16.96/3.89 % (3778)Termination phase: Saturation
% 16.96/3.89
% 16.96/3.89 % (3778)Memory used [KB]: 10874
% 16.96/3.89 % (3778)Time elapsed: 0.571 s
% 16.96/3.89 % (3778)Instructions burned: 1830 (million)
% 16.96/3.89 % (3778)------------------------------
% 16.96/3.89 % (3778)------------------------------
% 17.84/3.90 % (3787)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_3332 for (2977ds/1376Mi)
% 17.84/3.90 % (3757)Instruction limit reached!
% 17.84/3.90 % (3757)------------------------------
% 17.84/3.90 % (3757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.84/3.90 % (3757)Termination reason: Unknown
% 17.84/3.90 % (3757)Termination phase: Saturation
% 17.84/3.90
% 17.84/3.90 % (3757)Memory used [KB]: 13432
% 17.84/3.90 % (3757)Time elapsed: 1.315 s
% 17.84/3.90 % (3757)Instructions burned: 4438 (million)
% 17.84/3.90 % (3757)------------------------------
% 17.84/3.90 % (3757)------------------------------
% 17.84/3.91 % (3786)Instruction limit reached!
% 17.84/3.91 % (3786)------------------------------
% 17.84/3.91 % (3786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.84/3.91 % (3786)Termination reason: Unknown
% 17.84/3.91 % (3786)Termination phase: Saturation
% 17.84/3.91
% 17.84/3.91 % (3786)Memory used [KB]: 7803
% 17.84/3.91 % (3786)Time elapsed: 0.136 s
% 17.84/3.91 % (3786)Instructions burned: 466 (million)
% 17.84/3.91 % (3786)------------------------------
% 17.84/3.91 % (3786)------------------------------
% 17.84/3.91 % (3788)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_3332 for (2977ds/906Mi)
% 17.84/3.92 % (3789)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_3332 for (2977ds/434Mi)
% 17.84/3.95 % (3785)Instruction limit reached!
% 17.84/3.95 % (3785)------------------------------
% 17.84/3.95 % (3785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.84/3.95 % (3785)Termination reason: Unknown
% 17.84/3.95 % (3785)Termination phase: Saturation
% 17.84/3.95
% 17.84/3.95 % (3785)Memory used [KB]: 6524
% 17.84/3.95 % (3785)Time elapsed: 0.247 s
% 17.84/3.95 % (3785)Instructions burned: 796 (million)
% 17.84/3.95 % (3785)------------------------------
% 17.84/3.95 % (3785)------------------------------
% 17.84/3.96 % (3790)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_3332 for (2977ds/865Mi)
% 19.44/4.03 % (3762)Instruction limit reached!
% 19.44/4.03 % (3762)------------------------------
% 19.44/4.03 % (3762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.44/4.03 % (3762)Termination reason: Unknown
% 19.44/4.03 % (3762)Termination phase: Saturation
% 19.44/4.03
% 19.44/4.03 % (3762)Memory used [KB]: 16758
% 19.44/4.03 % (3762)Time elapsed: 1.291 s
% 19.44/4.03 % (3762)Instructions burned: 4351 (million)
% 19.44/4.03 % (3762)------------------------------
% 19.44/4.03 % (3762)------------------------------
% 19.44/4.04 % (3791)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_3332 for (2976ds/593Mi)
% 19.44/4.04 % (3789)Instruction limit reached!
% 19.44/4.04 % (3789)------------------------------
% 19.44/4.04 % (3789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.44/4.04 % (3789)Termination reason: Unknown
% 19.44/4.04 % (3789)Termination phase: Saturation
% 19.44/4.04
% 19.44/4.04 % (3789)Memory used [KB]: 7931
% 19.44/4.04 % (3789)Time elapsed: 0.130 s
% 19.44/4.04 % (3789)Instructions burned: 436 (million)
% 19.44/4.04 % (3789)------------------------------
% 19.44/4.04 % (3789)------------------------------
% 19.44/4.05 % (3792)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_3332 for (2976ds/443Mi)
% 20.00/4.17 % (3760)Instruction limit reached!
% 20.00/4.17 % (3760)------------------------------
% 20.00/4.17 % (3760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.00/4.17 % (3760)Termination reason: Unknown
% 20.00/4.17 % (3760)Termination phase: Saturation
% 20.00/4.17
% 20.00/4.17 % (3760)Memory used [KB]: 15095
% 20.00/4.17 % (3760)Time elapsed: 1.560 s
% 20.00/4.17 % (3760)Instructions burned: 5206 (million)
% 20.00/4.17 % (3760)------------------------------
% 20.00/4.17 % (3760)------------------------------
% 20.00/4.18 % (3793)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_3332 for (2974ds/594Mi)
% 20.00/4.19 % (3792)Instruction limit reached!
% 20.00/4.19 % (3792)------------------------------
% 20.00/4.19 % (3792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.00/4.19 % (3792)Termination reason: Unknown
% 20.00/4.19 % (3792)Termination phase: Saturation
% 20.00/4.19
% 20.00/4.19 % (3792)Memory used [KB]: 8059
% 20.00/4.19 % (3792)Time elapsed: 0.138 s
% 20.00/4.19 % (3792)Instructions burned: 443 (million)
% 20.00/4.19 % (3792)------------------------------
% 20.00/4.19 % (3792)------------------------------
% 20.52/4.20 % (3791)Instruction limit reached!
% 20.52/4.20 % (3791)------------------------------
% 20.52/4.20 % (3791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.52/4.20 % (3791)Termination reason: Unknown
% 20.52/4.20 % (3791)Termination phase: Saturation
% 20.52/4.20
% 20.52/4.20 % (3791)Memory used [KB]: 7675
% 20.52/4.20 % (3791)Time elapsed: 0.163 s
% 20.52/4.20 % (3791)Instructions burned: 596 (million)
% 20.52/4.20 % (3791)------------------------------
% 20.52/4.20 % (3791)------------------------------
% 20.52/4.20 % (3794)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_3332 for (2974ds/327Mi)
% 20.52/4.21 % (3795)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_3332 for (2974ds/5411Mi)
% 20.52/4.21 % (3790)Instruction limit reached!
% 20.52/4.21 % (3790)------------------------------
% 20.52/4.21 % (3790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.52/4.21 % (3790)Termination reason: Unknown
% 20.52/4.21 % (3790)Termination phase: Saturation
% 20.52/4.21
% 20.52/4.21 % (3790)Memory used [KB]: 12409
% 20.52/4.21 % (3790)Time elapsed: 0.256 s
% 20.52/4.21 % (3790)Instructions burned: 866 (million)
% 20.52/4.21 % (3790)------------------------------
% 20.52/4.21 % (3790)------------------------------
% 20.52/4.22 % (3796)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_3332 for (2974ds/1762Mi)
% 20.52/4.23 % (3788)Instruction limit reached!
% 20.52/4.23 % (3788)------------------------------
% 20.52/4.23 % (3788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.52/4.23 % (3788)Termination reason: Unknown
% 20.52/4.23 % (3788)Termination phase: Saturation
% 20.52/4.23
% 20.52/4.23 % (3788)Memory used [KB]: 11001
% 20.52/4.23 % (3788)Time elapsed: 0.316 s
% 20.52/4.23 % (3788)Instructions burned: 909 (million)
% 20.52/4.23 % (3788)------------------------------
% 20.52/4.23 % (3788)------------------------------
% 20.52/4.24 % (3797)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_3332 for (2974ds/96Mi)
% 20.52/4.24 % (3795)Refutation not found, incomplete strategy
% 20.52/4.24 % (3795)------------------------------
% 20.52/4.24 % (3795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.52/4.24 % (3795)Termination reason: Refutation not found, incomplete strategy
% 20.52/4.24
% 20.52/4.24
% 20.52/4.24 % (3795)Memory used [KB]: 7164
% 20.52/4.24 % (3795)Time elapsed: 0.031 s
% 20.52/4.24 % (3795)Instructions burned: 100 (million)
% 20.52/4.24 % (3795)------------------------------
% 20.52/4.24 % (3795)------------------------------
% 20.52/4.25 % (3798)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_3332 for (2974ds/503Mi)
% 20.52/4.26 % (3797)Instruction limit reached!
% 20.52/4.26 % (3797)------------------------------
% 20.52/4.26 % (3797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.52/4.26 % (3797)Termination reason: Unknown
% 20.52/4.26 % (3797)Termination phase: Preprocessing 3
% 20.52/4.26
% 20.52/4.26 % (3797)Memory used [KB]: 2814
% 20.52/4.26 % (3797)Time elapsed: 0.028 s
% 20.52/4.26 % (3797)Instructions burned: 97 (million)
% 20.52/4.26 % (3797)------------------------------
% 20.52/4.26 % (3797)------------------------------
% 20.52/4.27 % (3799)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_3332 for (2974ds/90Mi)
% 21.02/4.30 % (3799)Instruction limit reached!
% 21.02/4.30 % (3799)------------------------------
% 21.02/4.30 % (3799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.02/4.30 % (3799)Termination reason: Unknown
% 21.02/4.30 % (3799)Termination phase: Property scanning
% 21.02/4.30
% 21.02/4.30 % (3799)Memory used [KB]: 2558
% 21.02/4.30 % (3799)Time elapsed: 0.027 s
% 21.02/4.30 % (3799)Instructions burned: 90 (million)
% 21.02/4.30 % (3799)------------------------------
% 21.02/4.30 % (3799)------------------------------
% 21.02/4.30 % (3794)Instruction limit reached!
% 21.02/4.30 % (3794)------------------------------
% 21.02/4.30 % (3794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.02/4.30 % (3794)Termination reason: Unknown
% 21.02/4.30 % (3794)Termination phase: Saturation
% 21.02/4.30
% 21.02/4.30 % (3794)Memory used [KB]: 8187
% 21.02/4.30 % (3794)Time elapsed: 0.101 s
% 21.02/4.30 % (3794)Instructions burned: 329 (million)
% 21.02/4.30 % (3794)------------------------------
% 21.02/4.30 % (3794)------------------------------
% 21.02/4.31 % (3800)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_3332 for (2973ds/593Mi)
% 21.02/4.31 % (3787)Instruction limit reached!
% 21.02/4.31 % (3787)------------------------------
% 21.02/4.31 % (3787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.02/4.31 % (3787)Termination reason: Unknown
% 21.02/4.31 % (3787)Termination phase: Saturation
% 21.02/4.31
% 21.02/4.31 % (3787)Memory used [KB]: 12537
% 21.02/4.31 % (3787)Time elapsed: 0.411 s
% 21.02/4.31 % (3787)Instructions burned: 1377 (million)
% 21.02/4.31 % (3787)------------------------------
% 21.02/4.31 % (3787)------------------------------
% 21.02/4.31 % (3801)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_3332 for (2973ds/1512Mi)
% 21.02/4.32 % (3802)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_3332 for (2973ds/569Mi)
% 21.02/4.37 % (3793)Instruction limit reached!
% 21.02/4.37 % (3793)------------------------------
% 21.02/4.37 % (3793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.02/4.37 % (3793)Termination reason: Unknown
% 21.02/4.37 % (3793)Termination phase: Saturation
% 21.02/4.37
% 21.02/4.37 % (3793)Memory used [KB]: 8315
% 21.02/4.37 % (3793)Time elapsed: 0.183 s
% 21.02/4.37 % (3793)Instructions burned: 595 (million)
% 21.02/4.37 % (3793)------------------------------
% 21.02/4.37 % (3793)------------------------------
% 21.02/4.38 % (3803)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_3332 for (2973ds/501Mi)
% 21.02/4.40 % (3798)Instruction limit reached!
% 21.02/4.40 % (3798)------------------------------
% 21.02/4.40 % (3798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.02/4.40 % (3798)Termination reason: Unknown
% 21.02/4.40 % (3798)Termination phase: Saturation
% 21.02/4.40
% 21.02/4.40 % (3798)Memory used [KB]: 9594
% 21.02/4.40 % (3798)Time elapsed: 0.149 s
% 21.02/4.40 % (3798)Instructions burned: 505 (million)
% 21.02/4.40 % (3798)------------------------------
% 21.02/4.40 % (3798)------------------------------
% 21.49/4.41 % (3804)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_3332 for (2972ds/562Mi)
% 21.49/4.47 % (3802)Instruction limit reached!
% 21.49/4.47 % (3802)------------------------------
% 21.49/4.47 % (3802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.49/4.47 % (3802)Termination reason: Unknown
% 21.49/4.47 % (3802)Termination phase: Saturation
% 21.49/4.47
% 21.49/4.47 % (3802)Memory used [KB]: 7803
% 21.49/4.47 % (3802)Time elapsed: 0.149 s
% 21.49/4.47 % (3802)Instructions burned: 572 (million)
% 21.49/4.47 % (3802)------------------------------
% 21.49/4.47 % (3802)------------------------------
% 21.49/4.48 % (3805)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_3332 for (2972ds/406Mi)
% 21.49/4.49 % (3800)Instruction limit reached!
% 21.49/4.49 % (3800)------------------------------
% 21.49/4.49 % (3800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.49/4.49 % (3800)Termination reason: Unknown
% 21.49/4.49 % (3800)Termination phase: Saturation
% 21.49/4.49
% 21.49/4.49 % (3800)Memory used [KB]: 9083
% 21.49/4.49 % (3800)Time elapsed: 0.181 s
% 21.49/4.49 % (3800)Instructions burned: 595 (million)
% 21.49/4.49 % (3800)------------------------------
% 21.49/4.49 % (3800)------------------------------
% 22.09/4.50 % (3806)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_3332 for (2971ds/582Mi)
% 22.09/4.52 % (3803)Instruction limit reached!
% 22.09/4.52 % (3803)------------------------------
% 22.09/4.52 % (3803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.09/4.52 % (3803)Termination reason: Unknown
% 22.09/4.52 % (3803)Termination phase: Saturation
% 22.09/4.52
% 22.09/4.52 % (3803)Memory used [KB]: 9466
% 22.09/4.52 % (3803)Time elapsed: 0.150 s
% 22.09/4.52 % (3803)Instructions burned: 504 (million)
% 22.09/4.52 % (3803)------------------------------
% 22.09/4.52 % (3803)------------------------------
% 22.09/4.53 % (3807)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_3332 for (2971ds/456Mi)
% 22.09/4.58 % (3804)Instruction limit reached!
% 22.09/4.58 % (3804)------------------------------
% 22.09/4.58 % (3804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.09/4.58 % (3804)Termination reason: Unknown
% 22.09/4.58 % (3804)Termination phase: Saturation
% 22.09/4.58
% 22.09/4.58 % (3804)Memory used [KB]: 9210
% 22.09/4.58 % (3804)Time elapsed: 0.173 s
% 22.09/4.58 % (3804)Instructions burned: 562 (million)
% 22.09/4.58 % (3804)------------------------------
% 22.09/4.58 % (3804)------------------------------
% 22.09/4.59 % (3808)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_3332 for (2970ds/393Mi)
% 22.55/4.60 % (3805)Instruction limit reached!
% 22.55/4.60 % (3805)------------------------------
% 22.55/4.60 % (3805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.55/4.60 % (3805)Termination reason: Unknown
% 22.55/4.60 % (3805)Termination phase: Saturation
% 22.55/4.60
% 22.55/4.60 % (3805)Memory used [KB]: 8571
% 22.55/4.60 % (3805)Time elapsed: 0.124 s
% 22.55/4.60 % (3805)Instructions burned: 409 (million)
% 22.55/4.60 % (3805)------------------------------
% 22.55/4.60 % (3805)------------------------------
% 22.55/4.61 % (3809)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_3332 for (2970ds/1335Mi)
% 22.55/4.66 % (3807)Instruction limit reached!
% 22.55/4.66 % (3807)------------------------------
% 22.55/4.66 % (3807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.55/4.66 % (3807)Termination reason: Unknown
% 22.55/4.66 % (3807)Termination phase: Saturation
% 22.55/4.66
% 22.55/4.66 % (3807)Memory used [KB]: 8955
% 22.55/4.66 % (3807)Time elapsed: 0.131 s
% 22.55/4.66 % (3807)Instructions burned: 457 (million)
% 22.55/4.66 % (3807)------------------------------
% 22.55/4.66 % (3807)------------------------------
% 22.55/4.67 % (3806)Instruction limit reached!
% 22.55/4.67 % (3806)------------------------------
% 22.55/4.67 % (3806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.55/4.67 % (3806)Termination reason: Unknown
% 22.55/4.67 % (3806)Termination phase: Saturation
% 22.55/4.67
% 22.55/4.67 % (3806)Memory used [KB]: 8315
% 22.55/4.67 % (3806)Time elapsed: 0.177 s
% 22.55/4.67 % (3806)Instructions burned: 584 (million)
% 22.55/4.67 % (3806)------------------------------
% 22.55/4.67 % (3806)------------------------------
% 22.55/4.67 % (3810)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_3332 for (2970ds/3373Mi)
% 22.55/4.68 % (3811)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_3332 for (2970ds/474Mi)
% 23.11/4.70 % (3808)Instruction limit reached!
% 23.11/4.70 % (3808)------------------------------
% 23.11/4.70 % (3808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.11/4.70 % (3808)Termination reason: Unknown
% 23.11/4.70 % (3808)Termination phase: Saturation
% 23.11/4.70
% 23.11/4.70 % (3808)Memory used [KB]: 7931
% 23.11/4.70 % (3808)Time elapsed: 0.110 s
% 23.11/4.70 % (3808)Instructions burned: 394 (million)
% 23.11/4.70 % (3808)------------------------------
% 23.11/4.70 % (3808)------------------------------
% 23.11/4.71 % (3812)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_3332 for (2969ds/157Mi)
% 23.11/4.73 % (3796)Instruction limit reached!
% 23.11/4.73 % (3796)------------------------------
% 23.11/4.73 % (3796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.11/4.73 % (3796)Termination reason: Unknown
% 23.11/4.73 % (3796)Termination phase: Saturation
% 23.11/4.73
% 23.11/4.73 % (3796)Memory used [KB]: 10746
% 23.11/4.73 % (3796)Time elapsed: 0.507 s
% 23.11/4.73 % (3796)Instructions burned: 1762 (million)
% 23.11/4.73 % (3796)------------------------------
% 23.11/4.73 % (3796)------------------------------
% 23.11/4.74 % (3813)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_3332 for (2969ds/590Mi)
% 23.11/4.75 % (3812)Instruction limit reached!
% 23.11/4.75 % (3812)------------------------------
% 23.11/4.75 % (3812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.11/4.75 % (3812)Termination reason: Unknown
% 23.11/4.75 % (3812)Termination phase: Function definition elimination
% 23.11/4.75
% 23.11/4.75 % (3812)Memory used [KB]: 2814
% 23.11/4.75 % (3812)Time elapsed: 0.044 s
% 23.11/4.75 % (3812)Instructions burned: 160 (million)
% 23.11/4.75 % (3812)------------------------------
% 23.11/4.75 % (3812)------------------------------
% 23.11/4.76 % (3814)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_3332 for (2969ds/104Mi)
% 23.11/4.76 % (3801)Instruction limit reached!
% 23.11/4.76 % (3801)------------------------------
% 23.11/4.76 % (3801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.11/4.76 % (3801)Termination reason: Unknown
% 23.11/4.76 % (3801)Termination phase: Saturation
% 23.11/4.76
% 23.11/4.76 % (3801)Memory used [KB]: 10490
% 23.11/4.76 % (3801)Time elapsed: 0.454 s
% 23.11/4.76 % (3801)Instructions burned: 1512 (million)
% 23.11/4.76 % (3801)------------------------------
% 23.11/4.76 % (3801)------------------------------
% 23.11/4.77 % (3815)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_3332 for (2969ds/414Mi)
% 23.11/4.79 % (3814)Instruction limit reached!
% 23.11/4.79 % (3814)------------------------------
% 23.11/4.79 % (3814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.11/4.79 % (3814)Termination reason: Unknown
% 23.11/4.79 % (3814)Termination phase: Property scanning
% 23.11/4.79
% 23.11/4.79 % (3814)Memory used [KB]: 2686
% 23.11/4.79 % (3814)Time elapsed: 0.032 s
% 23.11/4.79 % (3814)Instructions burned: 107 (million)
% 23.11/4.79 % (3814)------------------------------
% 23.11/4.79 % (3814)------------------------------
% 24.39/4.80 % (3816)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_3332 for (2968ds/715Mi)
% 24.39/4.82 % (3811)Instruction limit reached!
% 24.39/4.82 % (3811)------------------------------
% 24.39/4.82 % (3811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.39/4.82 % (3811)Termination reason: Unknown
% 24.39/4.82 % (3811)Termination phase: Saturation
% 24.39/4.82
% 24.39/4.82 % (3811)Memory used [KB]: 8315
% 24.39/4.82 % (3811)Time elapsed: 0.140 s
% 24.39/4.82 % (3811)Instructions burned: 476 (million)
% 24.39/4.82 % (3811)------------------------------
% 24.39/4.82 % (3811)------------------------------
% 24.39/4.83 % (3817)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_3332 for (2968ds/961Mi)
% 24.39/4.89 % (3815)Instruction limit reached!
% 24.39/4.89 % (3815)------------------------------
% 24.39/4.89 % (3815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.39/4.89 % (3815)Termination reason: Unknown
% 24.39/4.89 % (3815)Termination phase: Saturation
% 24.39/4.89
% 24.39/4.89 % (3815)Memory used [KB]: 7931
% 24.39/4.89 % (3815)Time elapsed: 0.121 s
% 24.39/4.89 % (3815)Instructions burned: 414 (million)
% 24.39/4.89 % (3815)------------------------------
% 24.39/4.89 % (3815)------------------------------
% 24.78/4.90 % (3813)Instruction limit reached!
% 24.78/4.90 % (3813)------------------------------
% 24.78/4.90 % (3813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.78/4.90 % (3813)Termination reason: Unknown
% 24.78/4.90 % (3813)Termination phase: Saturation
% 24.78/4.90
% 24.78/4.90 % (3813)Memory used [KB]: 7547
% 24.78/4.90 % (3813)Time elapsed: 0.162 s
% 24.78/4.90 % (3813)Instructions burned: 590 (million)
% 24.78/4.90 % (3813)------------------------------
% 24.78/4.90 % (3813)------------------------------
% 24.78/4.90 % (3818)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_3332 for (2967ds/1213Mi)
% 24.78/4.91 % (3819)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_3332 for (2967ds/1979Mi)
% 24.78/5.00 % (3809)Instruction limit reached!
% 24.78/5.00 % (3809)------------------------------
% 24.78/5.00 % (3809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.78/5.00 % (3809)Termination reason: Unknown
% 24.78/5.00 % (3809)Termination phase: Saturation
% 24.78/5.00
% 24.78/5.00 % (3809)Memory used [KB]: 10106
% 24.78/5.00 % (3809)Time elapsed: 0.397 s
% 24.78/5.00 % (3809)Instructions burned: 1336 (million)
% 24.78/5.00 % (3809)------------------------------
% 24.78/5.00 % (3809)------------------------------
% 24.78/5.02 % (3820)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_3332 for (2966ds/481Mi)
% 24.78/5.02 % (3816)Instruction limit reached!
% 24.78/5.02 % (3816)------------------------------
% 24.78/5.02 % (3816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.78/5.02 % (3816)Termination reason: Unknown
% 24.78/5.02 % (3816)Termination phase: Saturation
% 24.78/5.02
% 24.78/5.02 % (3816)Memory used [KB]: 4989
% 24.78/5.02 % (3816)Time elapsed: 0.220 s
% 24.78/5.02 % (3816)Instructions burned: 715 (million)
% 24.78/5.02 % (3816)------------------------------
% 24.78/5.02 % (3816)------------------------------
% 26.47/5.03 % (3821)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_3332 for (2966ds/783Mi)
% 27.00/5.13 % (3817)Instruction limit reached!
% 27.00/5.13 % (3817)------------------------------
% 27.00/5.13 % (3817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.00/5.13 % (3817)Termination reason: Unknown
% 27.00/5.13 % (3817)Termination phase: Saturation
% 27.00/5.13
% 27.00/5.13 % (3817)Memory used [KB]: 8699
% 27.00/5.13 % (3817)Time elapsed: 0.295 s
% 27.00/5.13 % (3817)Instructions burned: 963 (million)
% 27.00/5.13 % (3817)------------------------------
% 27.00/5.13 % (3817)------------------------------
% 27.00/5.14 % (3822)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_3332 for (2965ds/432Mi)
% 27.00/5.16 % (3820)Instruction limit reached!
% 27.00/5.16 % (3820)------------------------------
% 27.00/5.16 % (3820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.00/5.16 % (3820)Termination reason: Unknown
% 27.00/5.16 % (3820)Termination phase: Saturation
% 27.00/5.16
% 27.00/5.16 % (3820)Memory used [KB]: 7931
% 27.00/5.16 % (3820)Time elapsed: 0.165 s
% 27.00/5.16 % (3820)Instructions burned: 483 (million)
% 27.00/5.16 % (3820)------------------------------
% 27.00/5.16 % (3820)------------------------------
% 27.00/5.17 % (3823)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_3332 for (2965ds/1670Mi)
% 27.45/5.26 % (3821)Instruction limit reached!
% 27.45/5.26 % (3821)------------------------------
% 27.45/5.26 % (3821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.45/5.26 % (3821)Termination reason: Unknown
% 27.45/5.26 % (3821)Termination phase: Saturation
% 27.45/5.26
% 27.45/5.26 % (3821)Memory used [KB]: 9722
% 27.45/5.26 % (3821)Time elapsed: 0.236 s
% 27.45/5.26 % (3821)Instructions burned: 785 (million)
% 27.45/5.26 % (3821)------------------------------
% 27.45/5.26 % (3821)------------------------------
% 27.45/5.27 % (3822)Instruction limit reached!
% 27.45/5.27 % (3822)------------------------------
% 27.45/5.27 % (3822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.45/5.27 % (3822)Termination reason: Unknown
% 27.45/5.27 % (3822)Termination phase: Saturation
% 27.45/5.27
% 27.45/5.27 % (3822)Memory used [KB]: 7675
% 27.45/5.27 % (3822)Time elapsed: 0.137 s
% 27.45/5.27 % (3822)Instructions burned: 433 (million)
% 27.45/5.27 % (3822)------------------------------
% 27.45/5.27 % (3822)------------------------------
% 27.45/5.27 % (3824)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_3332 for (2964ds/90Mi)
% 27.45/5.28 % (3818)Instruction limit reached!
% 27.45/5.28 % (3818)------------------------------
% 27.45/5.28 % (3818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.45/5.28 % (3818)Termination reason: Unknown
% 27.45/5.28 % (3818)Termination phase: Saturation
% 27.45/5.28
% 27.45/5.28 % (3818)Memory used [KB]: 9850
% 27.45/5.28 % (3818)Time elapsed: 0.375 s
% 27.45/5.28 % (3818)Instructions burned: 1214 (million)
% 27.45/5.28 % (3818)------------------------------
% 27.45/5.28 % (3818)------------------------------
% 27.45/5.28 % (3825)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_3332 for (2964ds/346Mi)
% 27.45/5.29 % (3826)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_3332 for (2963ds/401Mi)
% 28.24/5.30 % (3824)Instruction limit reached!
% 28.24/5.30 % (3824)------------------------------
% 28.24/5.30 % (3824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.24/5.30 % (3824)Termination reason: Unknown
% 28.24/5.30 % (3824)Termination phase: Property scanning
% 28.24/5.30
% 28.24/5.30 % (3824)Memory used [KB]: 2558
% 28.24/5.30 % (3824)Time elapsed: 0.028 s
% 28.24/5.30 % (3824)Instructions burned: 92 (million)
% 28.24/5.30 % (3824)------------------------------
% 28.24/5.30 % (3824)------------------------------
% 28.24/5.31 % (3827)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_3332 for (2963ds/6454Mi)
% 28.24/5.38 % (3825)Instruction limit reached!
% 28.24/5.38 % (3825)------------------------------
% 28.24/5.38 % (3825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.24/5.38 % (3825)Termination reason: Unknown
% 28.24/5.38 % (3825)Termination phase: Saturation
% 28.24/5.38
% 28.24/5.38 % (3825)Memory used [KB]: 7931
% 28.24/5.38 % (3825)Time elapsed: 0.103 s
% 28.24/5.38 % (3825)Instructions burned: 347 (million)
% 28.24/5.38 % (3825)------------------------------
% 28.24/5.38 % (3825)------------------------------
% 28.24/5.39 % (3828)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_3332 for (2962ds/283Mi)
% 28.24/5.40 % (3826)Instruction limit reached!
% 28.24/5.40 % (3826)------------------------------
% 28.24/5.40 % (3826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.24/5.40 % (3826)Termination reason: Unknown
% 28.24/5.40 % (3826)Termination phase: Saturation
% 28.24/5.40
% 28.24/5.40 % (3826)Memory used [KB]: 7803
% 28.24/5.40 % (3826)Time elapsed: 0.111 s
% 28.24/5.40 % (3826)Instructions burned: 402 (million)
% 28.24/5.40 % (3826)------------------------------
% 28.24/5.40 % (3826)------------------------------
% 28.69/5.41 % (3829)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_3332 for (2962ds/865Mi)
% 28.69/5.48 % (3828)Instruction limit reached!
% 28.69/5.48 % (3828)------------------------------
% 28.69/5.48 % (3828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.69/5.48 % (3828)Termination reason: Unknown
% 28.69/5.48 % (3828)Termination phase: Saturation
% 28.69/5.48
% 28.69/5.48 % (3828)Memory used [KB]: 7803
% 28.69/5.48 % (3828)Time elapsed: 0.089 s
% 28.69/5.48 % (3828)Instructions burned: 284 (million)
% 28.69/5.48 % (3828)------------------------------
% 28.69/5.48 % (3828)------------------------------
% 28.69/5.49 % (3830)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_3332 for (2961ds/4528Mi)
% 29.20/5.52 % (3830)Refutation not found, incomplete strategy
% 29.20/5.52 % (3830)------------------------------
% 29.20/5.52 % (3830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.20/5.52 % (3830)Termination reason: Refutation not found, incomplete strategy
% 29.20/5.52
% 29.20/5.52
% 29.20/5.52 % (3830)Memory used [KB]: 2302
% 29.20/5.52 % (3830)Time elapsed: 0.029 s
% 29.20/5.52 % (3830)Instructions burned: 95 (million)
% 29.20/5.52 % (3830)------------------------------
% 29.20/5.52 % (3830)------------------------------
% 29.20/5.52 % (3823)Instruction limit reached!
% 29.20/5.52 % (3823)------------------------------
% 29.20/5.52 % (3823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.20/5.52 % (3823)Termination reason: Unknown
% 29.20/5.52 % (3823)Termination phase: Saturation
% 29.20/5.52
% 29.20/5.52 % (3823)Memory used [KB]: 7931
% 29.20/5.52 % (3823)Time elapsed: 0.358 s
% 29.20/5.52 % (3823)Instructions burned: 1673 (million)
% 29.20/5.52 % (3823)------------------------------
% 29.20/5.52 % (3823)------------------------------
% 29.20/5.53 % (3819)Instruction limit reached!
% 29.20/5.53 % (3819)------------------------------
% 29.20/5.53 % (3819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.20/5.53 % (3819)Termination reason: Unknown
% 29.20/5.53 % (3819)Termination phase: Saturation
% 29.20/5.53
% 29.20/5.53 % (3819)Memory used [KB]: 9083
% 29.20/5.53 % (3819)Time elapsed: 0.620 s
% 29.20/5.53 % (3819)Instructions burned: 1979 (million)
% 29.20/5.53 % (3819)------------------------------
% 29.20/5.53 % (3819)------------------------------
% 29.20/5.53 % (3831)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_3332 for (2961ds/1001Mi)
% 29.20/5.53 % (3832)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_3332 for (2961ds/102Mi)
% 29.20/5.54 % (3833)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_3332 for (2961ds/952Mi)
% 29.20/5.56 % (3832)Instruction limit reached!
% 29.20/5.56 % (3832)------------------------------
% 29.20/5.56 % (3832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.20/5.56 % (3832)Termination reason: Unknown
% 29.20/5.56 % (3832)Termination phase: Property scanning
% 29.20/5.56
% 29.20/5.56 % (3832)Memory used [KB]: 2814
% 29.20/5.56 % (3832)Time elapsed: 0.029 s
% 29.20/5.56 % (3832)Instructions burned: 104 (million)
% 29.20/5.56 % (3832)------------------------------
% 29.20/5.56 % (3832)------------------------------
% 29.20/5.57 % (3834)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_3332 for (2961ds/578Mi)
% 29.89/5.66 % (3810)Instruction limit reached!
% 29.89/5.66 % (3810)------------------------------
% 29.89/5.66 % (3810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.89/5.66 % (3810)Termination reason: Unknown
% 29.89/5.66 % (3810)Termination phase: Saturation
% 29.89/5.66
% 29.89/5.66 % (3810)Memory used [KB]: 12025
% 29.89/5.66 % (3810)Time elapsed: 0.990 s
% 29.89/5.66 % (3810)Instructions burned: 3373 (million)
% 29.89/5.66 % (3810)------------------------------
% 29.89/5.66 % (3810)------------------------------
% 29.89/5.67 % (3829)Instruction limit reached!
% 29.89/5.67 % (3829)------------------------------
% 29.89/5.67 % (3829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.89/5.67 % (3829)Termination reason: Unknown
% 29.89/5.67 % (3829)Termination phase: Saturation
% 29.89/5.67
% 29.89/5.67 % (3829)Memory used [KB]: 11001
% 29.89/5.67 % (3829)Time elapsed: 0.263 s
% 29.89/5.67 % (3829)Instructions burned: 867 (million)
% 29.89/5.67 % (3829)------------------------------
% 29.89/5.67 % (3829)------------------------------
% 29.89/5.67 % (3835)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_3332 for (2960ds/643Mi)
% 29.89/5.68 % (3836)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_3332 for (2960ds/865Mi)
% 30.35/5.74 % (3834)Instruction limit reached!
% 30.35/5.74 % (3834)------------------------------
% 30.35/5.74 % (3834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.35/5.74 % (3834)Termination reason: Unknown
% 30.35/5.74 % (3834)Termination phase: Saturation
% 30.35/5.74
% 30.35/5.74 % (3834)Memory used [KB]: 9210
% 30.35/5.74 % (3834)Time elapsed: 0.171 s
% 30.35/5.74 % (3834)Instructions burned: 578 (million)
% 30.35/5.74 % (3834)------------------------------
% 30.35/5.74 % (3834)------------------------------
% 30.35/5.75 % (3837)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_3332 for (2959ds/1174Mi)
% 30.63/5.82 % (3833)Instruction limit reached!
% 30.63/5.82 % (3833)------------------------------
% 30.63/5.82 % (3833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.63/5.82 % (3833)Termination reason: Unknown
% 30.63/5.82 % (3833)Termination phase: Saturation
% 30.63/5.82
% 30.63/5.82 % (3833)Memory used [KB]: 9594
% 30.63/5.82 % (3833)Time elapsed: 0.288 s
% 30.63/5.82 % (3833)Instructions burned: 953 (million)
% 30.63/5.82 % (3833)------------------------------
% 30.63/5.82 % (3833)------------------------------
% 30.63/5.82 % (3831)Instruction limit reached!
% 30.63/5.82 % (3831)------------------------------
% 30.63/5.82 % (3831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.63/5.82 % (3831)Termination reason: Unknown
% 30.63/5.82 % (3831)Termination phase: Saturation
% 30.63/5.82
% 30.63/5.82 % (3831)Memory used [KB]: 9722
% 30.63/5.82 % (3831)Time elapsed: 0.296 s
% 30.63/5.82 % (3831)Instructions burned: 1002 (million)
% 30.63/5.82 % (3831)------------------------------
% 30.63/5.82 % (3831)------------------------------
% 30.63/5.83 % (3838)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_3332 for (2958ds/644Mi)
% 30.63/5.83 % (3839)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_3332 for (2958ds/1201Mi)
% 30.63/5.85 % (3835)Instruction limit reached!
% 30.63/5.85 % (3835)------------------------------
% 30.63/5.85 % (3835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.63/5.85 % (3835)Termination reason: Unknown
% 30.63/5.85 % (3835)Termination phase: Saturation
% 30.63/5.85
% 30.63/5.85 % (3835)Memory used [KB]: 8699
% 30.63/5.85 % (3835)Time elapsed: 0.181 s
% 30.63/5.85 % (3835)Instructions burned: 646 (million)
% 30.63/5.85 % (3835)------------------------------
% 30.63/5.85 % (3835)------------------------------
% 30.63/5.86 % (3840)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_3332 for (2958ds/1046Mi)
% 31.52/5.92 % (3836)Refutation not found, non-redundant clauses discarded% (3836)------------------------------
% 31.52/5.92 % (3836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.52/5.92 % (3836)Termination reason: Refutation not found, non-redundant clauses discarded
% 31.52/5.92
% 31.52/5.92 % (3836)Memory used [KB]: 10490
% 31.52/5.92 % (3836)Time elapsed: 0.238 s
% 31.52/5.92 % (3836)Instructions burned: 767 (million)
% 31.52/5.92 % (3836)------------------------------
% 31.52/5.92 % (3836)------------------------------
% 31.52/5.93 % (3841)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_3332 for (2957ds/222Mi)
% 31.52/5.98 % (3841)Instruction limit reached!
% 31.52/5.98 % (3841)------------------------------
% 31.52/5.98 % (3841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.52/5.98 % (3841)Termination reason: Unknown
% 31.52/5.98 % (3841)Termination phase: Saturation
% 31.52/5.98
% 31.52/5.98 % (3841)Memory used [KB]: 7419
% 31.52/5.98 % (3841)Time elapsed: 0.059 s
% 31.52/5.98 % (3841)Instructions burned: 224 (million)
% 31.52/5.98 % (3841)------------------------------
% 31.52/5.98 % (3841)------------------------------
% 31.52/5.99 % (3842)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_3332 for (2956ds/68Mi)
% 31.52/6.01 % (3783)Instruction limit reached!
% 31.52/6.01 % (3783)------------------------------
% 31.52/6.01 % (3783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.52/6.01 % (3783)Termination reason: Unknown
% 31.52/6.01 % (3783)Termination phase: Saturation
% 31.52/6.01
% 31.52/6.01 % (3783)Memory used [KB]: 15991
% 31.52/6.01 % (3783)Time elapsed: 2.542 s
% 31.52/6.01 % (3783)Instructions burned: 8252 (million)
% 31.52/6.01 % (3783)------------------------------
% 31.52/6.01 % (3783)------------------------------
% 31.52/6.01 % (3842)Instruction limit reached!
% 31.52/6.01 % (3842)------------------------------
% 31.52/6.01 % (3842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.52/6.01 % (3842)Termination reason: Unknown
% 31.52/6.01 % (3842)Termination phase: SInE selection
% 31.52/6.01
% 31.52/6.01 % (3842)Memory used [KB]: 1918
% 31.52/6.01 % (3842)Time elapsed: 0.021 s
% 31.52/6.01 % (3842)Instructions burned: 68 (million)
% 31.52/6.01 % (3842)------------------------------
% 31.52/6.01 % (3842)------------------------------
% 31.52/6.02 % (3843)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=454:si=on:rtra=on_0 on DTF2THF_3332 for (2956ds/454Mi)
% 31.52/6.02 % (3844)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_3332 for (2956ds/360Mi)
% 33.51/6.03 % (3838)Instruction limit reached!
% 33.51/6.03 % (3838)------------------------------
% 33.51/6.03 % (3838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.51/6.03 % (3838)Termination reason: Unknown
% 33.51/6.03 % (3838)Termination phase: Saturation
% 33.51/6.03
% 33.51/6.03 % (3838)Memory used [KB]: 11001
% 33.51/6.03 % (3838)Time elapsed: 0.196 s
% 33.51/6.03 % (3838)Instructions burned: 646 (million)
% 33.51/6.03 % (3838)------------------------------
% 33.51/6.03 % (3838)------------------------------
% 33.51/6.04 % (3845)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_3332 for (2956ds/157Mi)
% 33.51/6.08 % (3845)Instruction limit reached!
% 33.51/6.08 % (3845)------------------------------
% 33.51/6.08 % (3845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.51/6.08 % (3845)Termination reason: Unknown
% 33.51/6.08 % (3845)Termination phase: Function definition elimination
% 33.51/6.08
% 33.51/6.08 % (3845)Memory used [KB]: 2814
% 33.51/6.08 % (3845)Time elapsed: 0.044 s
% 33.51/6.08 % (3845)Instructions burned: 158 (million)
% 33.51/6.08 % (3845)------------------------------
% 33.51/6.08 % (3845)------------------------------
% 33.51/6.09 % (3846)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_3332 for (2955ds/5061Mi)
% 33.51/6.10 % (3837)Instruction limit reached!
% 33.51/6.10 % (3837)------------------------------
% 33.51/6.10 % (3837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.51/6.10 % (3837)Termination reason: Unknown
% 33.51/6.10 % (3837)Termination phase: Saturation
% 33.51/6.10
% 33.51/6.10 % (3837)Memory used [KB]: 10106
% 33.51/6.10 % (3837)Time elapsed: 0.352 s
% 33.51/6.10 % (3837)Instructions burned: 1174 (million)
% 33.51/6.10 % (3837)------------------------------
% 33.51/6.10 % (3837)------------------------------
% 33.51/6.11 % (3847)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_3332 for (2955ds/2401Mi)
% 33.51/6.12 % (3844)Instruction limit reached!
% 33.51/6.12 % (3844)------------------------------
% 33.51/6.12 % (3844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.51/6.12 % (3844)Termination reason: Unknown
% 33.51/6.12 % (3844)Termination phase: Saturation
% 33.51/6.12
% 33.51/6.12 % (3844)Memory used [KB]: 7675
% 33.51/6.12 % (3844)Time elapsed: 0.098 s
% 33.51/6.12 % (3844)Instructions burned: 360 (million)
% 33.51/6.12 % (3844)------------------------------
% 33.51/6.12 % (3844)------------------------------
% 34.08/6.13 % (3848)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_3332 for (2955ds/5798Mi)
% 34.08/6.15 % (3843)Instruction limit reached!
% 34.08/6.15 % (3843)------------------------------
% 34.08/6.15 % (3843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.08/6.15 % (3843)Termination reason: Unknown
% 34.08/6.15 % (3843)Termination phase: Saturation
% 34.08/6.15
% 34.08/6.15 % (3843)Memory used [KB]: 12409
% 34.08/6.15 % (3843)Time elapsed: 0.128 s
% 34.08/6.15 % (3843)Instructions burned: 457 (million)
% 34.08/6.15 % (3843)------------------------------
% 34.08/6.15 % (3843)------------------------------
% 34.08/6.16 % (3840)Instruction limit reached!
% 34.08/6.16 % (3840)------------------------------
% 34.08/6.16 % (3840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.08/6.16 % (3840)Termination reason: Unknown
% 34.08/6.16 % (3840)Termination phase: Saturation
% 34.08/6.16
% 34.08/6.16 % (3840)Memory used [KB]: 9083
% 34.08/6.16 % (3840)Time elapsed: 0.296 s
% 34.08/6.16 % (3840)Instructions burned: 1048 (million)
% 34.08/6.16 % (3840)------------------------------
% 34.08/6.16 % (3840)------------------------------
% 34.08/6.16 % (3849)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_3332 for (2955ds/346Mi)
% 34.08/6.17 % (3850)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_3332 for (2955ds/1321Mi)
% 34.08/6.18 % (3839)Instruction limit reached!
% 34.08/6.18 % (3839)------------------------------
% 34.08/6.18 % (3839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.08/6.18 % (3839)Termination reason: Unknown
% 34.08/6.18 % (3839)Termination phase: Saturation
% 34.08/6.18
% 34.08/6.18 % (3839)Memory used [KB]: 9466
% 34.08/6.18 % (3839)Time elapsed: 0.350 s
% 34.08/6.18 % (3839)Instructions burned: 1204 (million)
% 34.08/6.18 % (3839)------------------------------
% 34.08/6.18 % (3839)------------------------------
% 34.08/6.19 % (3851)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_3332 for (2954ds/1312Mi)
% 34.41/6.26 % (3849)Instruction limit reached!
% 34.41/6.26 % (3849)------------------------------
% 34.41/6.26 % (3849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.41/6.26 % (3849)Termination reason: Unknown
% 34.41/6.26 % (3849)Termination phase: Saturation
% 34.41/6.26
% 34.41/6.26 % (3849)Memory used [KB]: 7931
% 34.41/6.26 % (3849)Time elapsed: 0.101 s
% 34.41/6.26 % (3849)Instructions burned: 347 (million)
% 34.41/6.26 % (3849)------------------------------
% 34.41/6.26 % (3849)------------------------------
% 34.41/6.27 % (3852)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_3332 for (2954ds/672Mi)
% 34.72/6.47 % (3852)Instruction limit reached!
% 34.72/6.47 % (3852)------------------------------
% 34.72/6.47 % (3852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.72/6.47 % (3852)Termination reason: Unknown
% 34.72/6.47 % (3852)Termination phase: Saturation
% 34.72/6.47
% 34.72/6.47 % (3852)Memory used [KB]: 9978
% 34.72/6.47 % (3852)Time elapsed: 0.203 s
% 34.72/6.47 % (3852)Instructions burned: 672 (million)
% 34.72/6.47 % (3852)------------------------------
% 34.72/6.47 % (3852)------------------------------
% 34.72/6.48 % (3853)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_3332 for (2952ds/1897Mi)
% 35.04/6.51 % (3853)Refutation not found, incomplete strategy
% 35.04/6.51 % (3853)------------------------------
% 35.04/6.51 % (3853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.04/6.51 % (3853)Termination reason: Refutation not found, incomplete strategy
% 35.04/6.51
% 35.04/6.51
% 35.04/6.51 % (3853)Memory used [KB]: 7419
% 35.04/6.51 % (3853)Time elapsed: 0.036 s
% 35.04/6.51 % (3853)Instructions burned: 115 (million)
% 35.04/6.51 % (3853)------------------------------
% 35.04/6.51 % (3853)------------------------------
% 35.04/6.52 % (3854)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_3332 for (2951ds/1202Mi)
% 35.04/6.55 % (3850)Instruction limit reached!
% 35.04/6.55 % (3850)------------------------------
% 35.04/6.55 % (3850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.04/6.55 % (3850)Termination reason: Unknown
% 35.04/6.55 % (3850)Termination phase: Saturation
% 35.04/6.55
% 35.04/6.55 % (3850)Memory used [KB]: 4477
% 35.04/6.55 % (3850)Time elapsed: 0.386 s
% 35.04/6.55 % (3850)Instructions burned: 1322 (million)
% 35.04/6.55 % (3850)------------------------------
% 35.04/6.55 % (3850)------------------------------
% 35.04/6.56 % (3855)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_3332 for (2951ds/1493Mi)
% 35.04/6.58 % (3851)Instruction limit reached!
% 35.04/6.58 % (3851)------------------------------
% 35.04/6.58 % (3851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.04/6.58 % (3851)Termination reason: Unknown
% 35.04/6.58 % (3851)Termination phase: Saturation
% 35.04/6.58
% 35.04/6.58 % (3851)Memory used [KB]: 9594
% 35.04/6.58 % (3851)Time elapsed: 0.387 s
% 35.04/6.58 % (3851)Instructions burned: 1313 (million)
% 35.04/6.58 % (3851)------------------------------
% 35.04/6.58 % (3851)------------------------------
% 35.04/6.59 % (3856)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_3332 for (2951ds/7679Mi)
% 35.04/6.60 % (3855)Refutation not found, incomplete strategy
% 35.04/6.60 % (3855)------------------------------
% 35.04/6.60 % (3855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.04/6.60 % (3855)Termination reason: Refutation not found, incomplete strategy
% 35.04/6.60
% 35.04/6.60
% 35.04/6.60 % (3855)Memory used [KB]: 7291
% 35.04/6.60 % (3855)Time elapsed: 0.035 s
% 35.04/6.60 % (3855)Instructions burned: 127 (million)
% 35.04/6.60 % (3855)------------------------------
% 35.04/6.60 % (3855)------------------------------
% 35.97/6.61 % (3857)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_3332 for (2950ds/340Mi)
% 35.97/6.70 % (3857)Instruction limit reached!
% 35.97/6.70 % (3857)------------------------------
% 35.97/6.70 % (3857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.97/6.70 % (3857)Termination reason: Unknown
% 35.97/6.70 % (3857)Termination phase: Saturation
% 35.97/6.70
% 35.97/6.70 % (3857)Memory used [KB]: 7547
% 35.97/6.70 % (3857)Time elapsed: 0.091 s
% 35.97/6.70 % (3857)Instructions burned: 341 (million)
% 35.97/6.70 % (3857)------------------------------
% 35.97/6.70 % (3857)------------------------------
% 36.22/6.71 % (3858)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_3332 for (2949ds/3672Mi)
% 36.32/6.86 % (3847)Instruction limit reached!
% 36.32/6.86 % (3847)------------------------------
% 36.32/6.86 % (3847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.32/6.86 % (3847)Termination reason: Unknown
% 36.32/6.86 % (3847)Termination phase: Saturation
% 36.32/6.86
% 36.32/6.86 % (3847)Memory used [KB]: 10618
% 36.32/6.86 % (3847)Time elapsed: 0.751 s
% 36.32/6.86 % (3847)Instructions burned: 2403 (million)
% 36.32/6.86 % (3847)------------------------------
% 36.32/6.86 % (3847)------------------------------
% 36.32/6.87 % (3859)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_3332 for (2948ds/1535Mi)
% 36.32/6.90 % (3854)Instruction limit reached!
% 36.32/6.90 % (3854)------------------------------
% 36.32/6.90 % (3854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.32/6.90 % (3854)Termination reason: Unknown
% 36.32/6.90 % (3854)Termination phase: Saturation
% 36.32/6.90
% 36.32/6.90 % (3854)Memory used [KB]: 5245
% 36.32/6.90 % (3854)Time elapsed: 0.373 s
% 36.32/6.90 % (3854)Instructions burned: 1203 (million)
% 36.32/6.90 % (3854)------------------------------
% 36.32/6.90 % (3854)------------------------------
% 37.19/6.91 % (3860)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_3332 for (2947ds/4637Mi)
% 41.77/7.27 % (3859)Instruction limit reached!
% 41.77/7.27 % (3859)------------------------------
% 41.77/7.27 % (3859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.77/7.27 % (3859)Termination reason: Unknown
% 41.77/7.27 % (3859)Termination phase: Saturation
% 41.77/7.27
% 41.77/7.27 % (3859)Memory used [KB]: 9594
% 41.77/7.27 % (3859)Time elapsed: 0.403 s
% 41.77/7.27 % (3859)Instructions burned: 1535 (million)
% 41.77/7.27 % (3859)------------------------------
% 41.77/7.27 % (3859)------------------------------
% 41.77/7.28 % (3861)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_3332 for (2944ds/3174Mi)
% 42.46/7.31 % (3846)Instruction limit reached!
% 42.46/7.31 % (3846)------------------------------
% 42.46/7.31 % (3846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.46/7.31 % (3846)Termination reason: Unknown
% 42.46/7.31 % (3846)Termination phase: Saturation
% 42.46/7.31
% 42.46/7.31 % (3846)Memory used [KB]: 8443
% 42.46/7.31 % (3846)Time elapsed: 1.219 s
% 42.46/7.31 % (3846)Instructions burned: 5062 (million)
% 42.46/7.31 % (3846)------------------------------
% 42.46/7.31 % (3846)------------------------------
% 42.46/7.32 % (3827)Instruction limit reached!
% 42.46/7.32 % (3827)------------------------------
% 42.46/7.32 % (3827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.46/7.32 % (3827)Termination reason: Unknown
% 42.46/7.32 % (3827)Termination phase: Saturation
% 42.46/7.32
% 42.46/7.32 % (3827)Memory used [KB]: 18293
% 42.46/7.32 % (3827)Time elapsed: 2.007 s
% 42.46/7.32 % (3827)Instructions burned: 6456 (million)
% 42.46/7.32 % (3827)------------------------------
% 42.46/7.32 % (3827)------------------------------
% 42.46/7.32 % (3862)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_3332 for (2943ds/307Mi)
% 42.46/7.33 % (3863)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_3332 for (2943ds/3619Mi)
% 42.90/7.40 % (3862)Instruction limit reached!
% 42.90/7.40 % (3862)------------------------------
% 42.90/7.40 % (3862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.90/7.40 % (3862)Termination reason: Unknown
% 42.90/7.40 % (3862)Termination phase: Saturation
% 42.90/7.40
% 42.90/7.40 % (3862)Memory used [KB]: 7803
% 42.90/7.40 % (3862)Time elapsed: 0.084 s
% 42.90/7.40 % (3862)Instructions burned: 307 (million)
% 42.90/7.40 % (3862)------------------------------
% 42.90/7.40 % (3862)------------------------------
% 42.90/7.41 % (3864)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_3332 for (2942ds/2325Mi)
% 44.60/7.86 % (3848)Instruction limit reached!
% 44.60/7.86 % (3848)------------------------------
% 44.60/7.86 % (3848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.60/7.86 % (3848)Termination reason: Unknown
% 44.60/7.86 % (3848)Termination phase: Saturation
% 44.60/7.86
% 44.60/7.86 % (3848)Memory used [KB]: 16119
% 44.60/7.86 % (3848)Time elapsed: 1.728 s
% 44.60/7.86 % (3848)Instructions burned: 5798 (million)
% 44.60/7.86 % (3848)------------------------------
% 44.60/7.86 % (3848)------------------------------
% 44.60/7.86 % (3858)Instruction limit reached!
% 44.60/7.86 % (3858)------------------------------
% 44.60/7.86 % (3858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.60/7.86 % (3858)Termination reason: Unknown
% 44.60/7.86 % (3858)Termination phase: Saturation
% 44.60/7.86
% 44.60/7.86 % (3858)Memory used [KB]: 11897
% 44.60/7.86 % (3858)Time elapsed: 1.153 s
% 44.60/7.86 % (3858)Instructions burned: 3673 (million)
% 44.60/7.86 % (3858)------------------------------
% 44.60/7.86 % (3858)------------------------------
% 44.60/7.87 % (3865)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_3332 for (2938ds/2341Mi)
% 44.60/7.87 % (3866)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_3332 for (2938ds/7257Mi)
% 47.53/8.12 % (3864)Instruction limit reached!
% 47.53/8.12 % (3864)------------------------------
% 47.53/8.12 % (3864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.53/8.12 % (3864)Termination reason: Unknown
% 47.53/8.12 % (3864)Termination phase: Saturation
% 47.53/8.12
% 47.53/8.12 % (3864)Memory used [KB]: 10746
% 47.53/8.12 % (3864)Time elapsed: 0.709 s
% 47.53/8.12 % (3864)Instructions burned: 2325 (million)
% 47.53/8.12 % (3864)------------------------------
% 47.53/8.12 % (3864)------------------------------
% 48.30/8.13 % (3867)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_3332 for (2935ds/3710Mi)
% 48.72/8.25 % (3861)Instruction limit reached!
% 48.72/8.25 % (3861)------------------------------
% 48.72/8.25 % (3861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.72/8.25 % (3861)Termination reason: Unknown
% 48.72/8.25 % (3861)Termination phase: Saturation
% 48.72/8.25
% 48.72/8.25 % (3861)Memory used [KB]: 14711
% 48.72/8.25 % (3861)Time elapsed: 0.962 s
% 48.72/8.25 % (3861)Instructions burned: 3174 (million)
% 48.72/8.25 % (3861)------------------------------
% 48.72/8.25 % (3861)------------------------------
% 48.72/8.26 % (3868)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_3332 for (2934ds/326Mi)
% 48.72/8.29 % (3860)Instruction limit reached!
% 48.72/8.29 % (3860)------------------------------
% 48.72/8.29 % (3860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.72/8.29 % (3860)Termination reason: Unknown
% 48.72/8.29 % (3860)Termination phase: Saturation
% 48.72/8.29
% 48.72/8.29 % (3860)Memory used [KB]: 17910
% 48.72/8.29 % (3860)Time elapsed: 1.385 s
% 48.72/8.29 % (3860)Instructions burned: 4639 (million)
% 48.72/8.29 % (3860)------------------------------
% 48.72/8.29 % (3860)------------------------------
% 49.28/8.30 % (3869)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_3332 for (2933ds/1100Mi)
% 49.28/8.35 % (3863)Instruction limit reached!
% 49.28/8.35 % (3863)------------------------------
% 49.28/8.35 % (3863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.28/8.35 % (3863)Termination reason: Unknown
% 49.28/8.35 % (3863)Termination phase: Saturation
% 49.28/8.35
% 49.28/8.35 % (3863)Memory used [KB]: 9466
% 49.28/8.35 % (3863)Time elapsed: 1.023 s
% 49.28/8.35 % (3863)Instructions burned: 3622 (million)
% 49.28/8.35 % (3863)------------------------------
% 49.28/8.35 % (3863)------------------------------
% 49.28/8.36 % (3870)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_3332 for (2933ds/406Mi)
% 49.28/8.36 % (3868)Instruction limit reached!
% 49.28/8.36 % (3868)------------------------------
% 49.28/8.36 % (3868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.28/8.36 % (3868)Termination reason: Unknown
% 49.28/8.36 % (3868)Termination phase: Saturation
% 49.28/8.36
% 49.28/8.36 % (3868)Memory used [KB]: 7675
% 49.28/8.36 % (3868)Time elapsed: 0.104 s
% 49.28/8.36 % (3868)Instructions burned: 328 (million)
% 49.28/8.36 % (3868)------------------------------
% 49.28/8.36 % (3868)------------------------------
% 49.28/8.37 % (3871)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_3332 for (2933ds/1871Mi)
% 49.76/8.48 % (3870)Instruction limit reached!
% 49.76/8.48 % (3870)------------------------------
% 49.76/8.48 % (3870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.76/8.48 % (3870)Termination reason: Unknown
% 49.76/8.48 % (3870)Termination phase: Saturation
% 49.76/8.48
% 49.76/8.48 % (3870)Memory used [KB]: 8571
% 49.76/8.48 % (3870)Time elapsed: 0.127 s
% 49.76/8.48 % (3870)Instructions burned: 406 (million)
% 49.76/8.48 % (3870)------------------------------
% 49.76/8.48 % (3870)------------------------------
% 49.76/8.49 % (3872)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_3332 for (2931ds/1194Mi)
% 50.50/8.60 % (3865)Instruction limit reached!
% 50.50/8.60 % (3865)------------------------------
% 50.50/8.60 % (3865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.50/8.60 % (3865)Termination reason: Unknown
% 50.50/8.60 % (3865)Termination phase: Saturation
% 50.50/8.60
% 50.50/8.60 % (3865)Memory used [KB]: 10234
% 50.50/8.60 % (3865)Time elapsed: 0.735 s
% 50.50/8.60 % (3865)Instructions burned: 2341 (million)
% 50.50/8.60 % (3865)------------------------------
% 50.50/8.60 % (3865)------------------------------
% 50.50/8.61 % (3873)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_3332 for (2930ds/474Mi)
% 50.50/8.64 % (3869)Instruction limit reached!
% 50.50/8.64 % (3869)------------------------------
% 50.50/8.64 % (3869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.50/8.64 % (3869)Termination reason: Unknown
% 50.50/8.64 % (3869)Termination phase: Saturation
% 50.50/8.64
% 50.50/8.64 % (3869)Memory used [KB]: 10618
% 50.50/8.64 % (3869)Time elapsed: 0.345 s
% 50.50/8.64 % (3869)Instructions burned: 1100 (million)
% 50.50/8.64 % (3869)------------------------------
% 50.50/8.64 % (3869)------------------------------
% 50.50/8.65 % (3874)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_3332 for (2930ds/3115Mi)
% 51.07/8.75 % (3873)Instruction limit reached!
% 51.07/8.75 % (3873)------------------------------
% 51.07/8.75 % (3873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.07/8.75 % (3873)Termination reason: Unknown
% 51.07/8.75 % (3873)Termination phase: Saturation
% 51.07/8.75
% 51.07/8.75 % (3873)Memory used [KB]: 8187
% 51.07/8.75 % (3873)Time elapsed: 0.138 s
% 51.07/8.75 % (3873)Instructions burned: 474 (million)
% 51.07/8.75 % (3873)------------------------------
% 51.07/8.75 % (3873)------------------------------
% 51.07/8.76 % (3875)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_3332 for (2929ds/831Mi)
% 51.42/8.84 % (3872)Instruction limit reached!
% 51.42/8.84 % (3872)------------------------------
% 51.42/8.84 % (3872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.42/8.84 % (3872)Termination reason: Unknown
% 51.42/8.84 % (3872)Termination phase: Saturation
% 51.42/8.84
% 51.42/8.84 % (3872)Memory used [KB]: 10490
% 51.42/8.84 % (3872)Time elapsed: 0.352 s
% 51.42/8.84 % (3872)Instructions burned: 1194 (million)
% 51.42/8.84 % (3872)------------------------------
% 51.42/8.84 % (3872)------------------------------
% 51.42/8.85 % (3876)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_3332 for (2928ds/1188Mi)
% 51.98/8.91 % (3856)Instruction limit reached!
% 51.98/8.91 % (3856)------------------------------
% 51.98/8.91 % (3856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.98/8.91 % (3856)Termination reason: Unknown
% 51.98/8.91 % (3856)Termination phase: Saturation
% 51.98/8.91
% 51.98/8.91 % (3856)Memory used [KB]: 23666
% 51.98/8.91 % (3856)Time elapsed: 2.323 s
% 51.98/8.91 % (3856)Instructions burned: 7679 (million)
% 51.98/8.91 % (3856)------------------------------
% 51.98/8.91 % (3856)------------------------------
% 51.98/8.93 % (3877)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_3332 for (2927ds/2868Mi)
% 51.98/8.94 % (3871)Instruction limit reached!
% 51.98/8.94 % (3871)------------------------------
% 51.98/8.94 % (3871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.98/8.94 % (3871)Termination reason: Unknown
% 51.98/8.94 % (3871)Termination phase: Saturation
% 51.98/8.94
% 51.98/8.94 % (3871)Memory used [KB]: 12665
% 51.98/8.94 % (3871)Time elapsed: 0.577 s
% 51.98/8.94 % (3871)Instructions burned: 1871 (million)
% 51.98/8.94 % (3871)------------------------------
% 51.98/8.94 % (3871)------------------------------
% 51.98/8.95 % (3878)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_3332 for (2927ds/1516Mi)
% 51.98/9.00 % (3875)Instruction limit reached!
% 51.98/9.00 % (3875)------------------------------
% 51.98/9.00 % (3875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.98/9.00 % (3875)Termination reason: Unknown
% 51.98/9.00 % (3875)Termination phase: Saturation
% 51.98/9.00
% 51.98/9.00 % (3875)Memory used [KB]: 11129
% 51.98/9.00 % (3875)Time elapsed: 0.243 s
% 51.98/9.00 % (3875)Instructions burned: 831 (million)
% 51.98/9.00 % (3875)------------------------------
% 51.98/9.00 % (3875)------------------------------
% 51.98/9.01 % (3879)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_3332 for (2926ds/2321Mi)
% 54.55/9.04 % (3877)Refutation not found, incomplete strategy
% 54.55/9.04 % (3877)------------------------------
% 54.55/9.04 % (3877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.55/9.04 % (3877)Termination reason: Refutation not found, incomplete strategy
% 54.55/9.04
% 54.55/9.04
% 54.55/9.04 % (3877)Memory used [KB]: 8187
% 54.55/9.04 % (3877)Time elapsed: 0.110 s
% 54.55/9.04 % (3877)Instructions burned: 274 (million)
% 54.55/9.04 % (3877)------------------------------
% 54.55/9.04 % (3877)------------------------------
% 54.55/9.05 % (3880)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_3332 for (2926ds/2812Mi)
% 54.55/9.09 % (3879)Refutation not found, incomplete strategy
% 54.55/9.09 % (3879)------------------------------
% 54.55/9.09 % (3879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.55/9.09 % (3879)Termination reason: Refutation not found, incomplete strategy
% 54.55/9.09
% 54.55/9.09
% 54.55/9.09 % (3879)Memory used [KB]: 8187
% 54.55/9.09 % (3879)Time elapsed: 0.077 s
% 54.55/9.09 % (3879)Instructions burned: 283 (million)
% 54.55/9.09 % (3879)------------------------------
% 54.55/9.09 % (3879)------------------------------
% 54.55/9.10 % (3881)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_3332 for (2925ds/4604Mi)
% 55.55/9.22 % (3876)Instruction limit reached!
% 55.55/9.22 % (3876)------------------------------
% 55.55/9.22 % (3876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.55/9.22 % (3876)Termination reason: Unknown
% 55.55/9.22 % (3876)Termination phase: Saturation
% 55.55/9.22
% 55.55/9.22 % (3876)Memory used [KB]: 11513
% 55.55/9.22 % (3876)Time elapsed: 0.365 s
% 55.55/9.22 % (3876)Instructions burned: 1190 (million)
% 55.55/9.22 % (3876)------------------------------
% 55.55/9.22 % (3876)------------------------------
% 55.55/9.23 % (3882)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_3332 for (2924ds/2678Mi)
% 55.55/9.24 % (3867)Instruction limit reached!
% 55.55/9.24 % (3867)------------------------------
% 55.55/9.24 % (3867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.55/9.24 % (3867)Termination reason: Unknown
% 55.55/9.24 % (3867)Termination phase: Saturation
% 55.55/9.24
% 55.55/9.24 % (3867)Memory used [KB]: 28912
% 55.55/9.24 % (3867)Time elapsed: 1.114 s
% 55.55/9.24 % (3867)Instructions burned: 3712 (million)
% 55.55/9.24 % (3867)------------------------------
% 55.55/9.24 % (3867)------------------------------
% 55.55/9.25 % (3883)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_3332 for (2924ds/643Mi)
% 56.25/9.41 % (3878)Instruction limit reached!
% 56.25/9.41 % (3878)------------------------------
% 56.25/9.41 % (3878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.25/9.41 % (3878)Termination reason: Unknown
% 56.25/9.41 % (3878)Termination phase: Saturation
% 56.25/9.41
% 56.25/9.41 % (3878)Memory used [KB]: 9722
% 56.25/9.41 % (3878)Time elapsed: 0.454 s
% 56.25/9.41 % (3878)Instructions burned: 1518 (million)
% 56.25/9.41 % (3878)------------------------------
% 56.25/9.41 % (3878)------------------------------
% 56.25/9.42 % (3884)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_3332 for (2922ds/458Mi)
% 56.25/9.43 % (3883)Instruction limit reached!
% 56.25/9.43 % (3883)------------------------------
% 56.25/9.43 % (3883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.25/9.43 % (3883)Termination reason: Unknown
% 56.25/9.43 % (3883)Termination phase: Saturation
% 56.25/9.43
% 56.25/9.43 % (3883)Memory used [KB]: 7803
% 56.25/9.43 % (3883)Time elapsed: 0.177 s
% 56.25/9.43 % (3883)Instructions burned: 646 (million)
% 56.25/9.43 % (3883)------------------------------
% 56.25/9.43 % (3883)------------------------------
% 56.25/9.44 % (3885)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_3332 for (2922ds/2546Mi)
% 56.66/9.54 % (3884)Instruction limit reached!
% 56.66/9.54 % (3884)------------------------------
% 56.66/9.54 % (3884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.66/9.54 % (3884)Termination reason: Unknown
% 56.66/9.54 % (3884)Termination phase: Saturation
% 56.66/9.54
% 56.66/9.54 % (3884)Memory used [KB]: 8059
% 56.66/9.54 % (3884)Time elapsed: 0.128 s
% 56.66/9.54 % (3884)Instructions burned: 460 (million)
% 56.66/9.54 % (3884)------------------------------
% 56.66/9.54 % (3884)------------------------------
% 56.66/9.55 % (3886)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_3332 for (2921ds/1432Mi)
% 56.66/9.58 % (3874)Instruction limit reached!
% 56.66/9.58 % (3874)------------------------------
% 56.66/9.58 % (3874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.66/9.58 % (3874)Termination reason: Unknown
% 56.66/9.58 % (3874)Termination phase: Saturation
% 56.66/9.58
% 56.66/9.58 % (3874)Memory used [KB]: 13432
% 56.66/9.58 % (3874)Time elapsed: 0.930 s
% 56.66/9.58 % (3874)Instructions burned: 3115 (million)
% 56.66/9.58 % (3874)------------------------------
% 56.66/9.58 % (3874)------------------------------
% 56.66/9.59 % (3887)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_3332 for (2921ds/386Mi)
% 57.09/9.70 % (3887)Instruction limit reached!
% 57.09/9.70 % (3887)------------------------------
% 57.09/9.70 % (3887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.09/9.70 % (3887)Termination reason: Unknown
% 57.09/9.70 % (3887)Termination phase: Saturation
% 57.09/9.70
% 57.09/9.70 % (3887)Memory used [KB]: 7803
% 57.09/9.70 % (3887)Time elapsed: 0.108 s
% 57.09/9.70 % (3887)Instructions burned: 387 (million)
% 57.09/9.70 % (3887)------------------------------
% 57.09/9.70 % (3887)------------------------------
% 57.09/9.71 % (3888)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_3332 for (2919ds/360Mi)
% 57.32/9.81 % (3888)Instruction limit reached!
% 57.32/9.81 % (3888)------------------------------
% 57.32/9.81 % (3888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.32/9.81 % (3888)Termination reason: Unknown
% 57.32/9.81 % (3888)Termination phase: Saturation
% 57.32/9.81
% 57.32/9.81 % (3888)Memory used [KB]: 8571
% 57.32/9.81 % (3888)Time elapsed: 0.098 s
% 57.32/9.81 % (3888)Instructions burned: 363 (million)
% 57.32/9.81 % (3888)------------------------------
% 57.32/9.81 % (3888)------------------------------
% 57.32/9.82 % (3889)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_3332 for (2918ds/5446Mi)
% 57.52/9.92 % (3886)Instruction limit reached!
% 57.52/9.92 % (3886)------------------------------
% 57.52/9.92 % (3886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.52/9.92 % (3886)Termination reason: Unknown
% 57.52/9.92 % (3886)Termination phase: Saturation
% 57.52/9.92
% 57.52/9.92 % (3886)Memory used [KB]: 11897
% 57.52/9.92 % (3886)Time elapsed: 0.363 s
% 57.52/9.92 % (3886)Instructions burned: 1434 (million)
% 57.52/9.92 % (3886)------------------------------
% 57.52/9.92 % (3886)------------------------------
% 57.52/9.92 % (3880)Instruction limit reached!
% 57.52/9.92 % (3880)------------------------------
% 57.52/9.92 % (3880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.52/9.92 % (3880)Termination reason: Unknown
% 57.52/9.92 % (3880)Termination phase: Saturation
% 57.52/9.92
% 57.52/9.92 % (3880)Memory used [KB]: 12409
% 57.52/9.92 % (3880)Time elapsed: 0.876 s
% 57.52/9.92 % (3880)Instructions burned: 2813 (million)
% 57.52/9.92 % (3880)------------------------------
% 57.52/9.92 % (3880)------------------------------
% 57.52/9.93 % (3890)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_3332 for (2917ds/2573Mi)
% 57.52/9.93 % (3891)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=2655:si=on:rtra=on_0 on DTF2THF_3332 for (2917ds/2655Mi)
% 57.52/9.96 % (3882)Instruction limit reached!
% 57.52/9.96 % (3882)------------------------------
% 57.52/9.96 % (3882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.52/9.96 % (3882)Termination reason: Unknown
% 57.52/9.96 % (3882)Termination phase: Saturation
% 57.52/9.96
% 57.52/9.96 % (3882)Memory used [KB]: 9210
% 57.52/9.96 % (3882)Time elapsed: 0.729 s
% 57.52/9.96 % (3882)Instructions burned: 2680 (million)
% 57.52/9.96 % (3882)------------------------------
% 57.52/9.96 % (3882)------------------------------
% 57.52/9.97 % (3892)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_3332 for (2917ds/2781Mi)
% 57.52/9.99 % (3866)Instruction limit reached!
% 57.52/9.99 % (3866)------------------------------
% 57.52/9.99 % (3866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.52/9.99 % (3866)Termination reason: Unknown
% 57.52/9.99 % (3866)Termination phase: Saturation
% 57.52/9.99
% 57.52/9.99 % (3866)Memory used [KB]: 27249
% 57.52/9.99 % (3866)Time elapsed: 2.126 s
% 57.52/9.99 % (3866)Instructions burned: 7259 (million)
% 57.52/9.99 % (3866)------------------------------
% 57.52/9.99 % (3866)------------------------------
% 57.52/10.00 % (3893)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_3332 for (2916ds/307Mi)
% 61.61/10.09 % (3893)Instruction limit reached!
% 61.61/10.09 % (3893)------------------------------
% 61.61/10.09 % (3893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.61/10.09 % (3893)Termination reason: Unknown
% 61.61/10.09 % (3893)Termination phase: Saturation
% 61.61/10.09
% 61.61/10.09 % (3893)Memory used [KB]: 7675
% 61.61/10.09 % (3893)Time elapsed: 0.084 s
% 61.61/10.09 % (3893)Instructions burned: 307 (million)
% 61.61/10.09 % (3893)------------------------------
% 61.61/10.09 % (3893)------------------------------
% 61.61/10.10 % (3894)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_3332 for (2915ds/1548Mi)
% 62.73/10.23 % (3885)Instruction limit reached!
% 62.73/10.23 % (3885)------------------------------
% 62.73/10.23 % (3885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.73/10.23 % (3885)Termination reason: Unknown
% 62.73/10.23 % (3885)Termination phase: Saturation
% 62.73/10.23
% 62.73/10.23 % (3885)Memory used [KB]: 13560
% 62.73/10.23 % (3885)Time elapsed: 0.795 s
% 62.73/10.23 % (3885)Instructions burned: 2548 (million)
% 62.73/10.23 % (3885)------------------------------
% 62.73/10.23 % (3885)------------------------------
% 62.73/10.24 % (3895)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_3332 for (2914ds/5214Mi)
% 63.78/10.46 % (3881)Instruction limit reached!
% 63.78/10.46 % (3881)------------------------------
% 63.78/10.46 % (3881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.78/10.46 % (3881)Termination reason: Unknown
% 63.78/10.46 % (3881)Termination phase: Saturation
% 63.78/10.46
% 63.78/10.46 % (3881)Memory used [KB]: 18166
% 63.78/10.46 % (3881)Time elapsed: 1.369 s
% 63.78/10.46 % (3881)Instructions burned: 4604 (million)
% 63.78/10.46 % (3881)------------------------------
% 63.78/10.46 % (3881)------------------------------
% 63.78/10.48 % (3896)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_3332 for (2912ds/3201Mi)
% 64.27/10.57 % (3894)Instruction limit reached!
% 64.27/10.57 % (3894)------------------------------
% 64.27/10.57 % (3894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.27/10.57 % (3894)Termination reason: Unknown
% 64.27/10.57 % (3894)Termination phase: Saturation
% 64.27/10.57
% 64.27/10.57 % (3894)Memory used [KB]: 9850
% 64.27/10.57 % (3894)Time elapsed: 0.476 s
% 64.27/10.57 % (3894)Instructions burned: 1548 (million)
% 64.27/10.57 % (3894)------------------------------
% 64.27/10.57 % (3894)------------------------------
% 64.27/10.58 % (3897)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=454:si=on:rtra=on_0 on DTF2THF_3332 for (2910ds/454Mi)
% 64.27/10.58 % (3892)Instruction limit reached!
% 64.27/10.58 % (3892)------------------------------
% 64.27/10.58 % (3892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.27/10.58 % (3892)Termination reason: Unknown
% 64.27/10.58 % (3892)Termination phase: Function definition elimination
% 64.27/10.58
% 64.27/10.58 % (3892)Memory used [KB]: 3837
% 64.27/10.58 % (3892)Time elapsed: 0.617 s
% 64.27/10.58 % (3892)Instructions burned: 2782 (million)
% 64.27/10.58 % (3892)------------------------------
% 64.27/10.58 % (3892)------------------------------
% 64.27/10.59 % (3898)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_3332 for (2910ds/3049Mi)
% 65.44/10.71 % (3897)Instruction limit reached!
% 65.44/10.71 % (3897)------------------------------
% 65.44/10.71 % (3897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.44/10.71 % (3897)Termination reason: Unknown
% 65.44/10.71 % (3897)Termination phase: Saturation
% 65.44/10.71
% 65.44/10.71 % (3897)Memory used [KB]: 12537
% 65.44/10.71 % (3897)Time elapsed: 0.126 s
% 65.44/10.71 % (3897)Instructions burned: 457 (million)
% 65.44/10.71 % (3897)------------------------------
% 65.44/10.71 % (3897)------------------------------
% 65.44/10.71 % (3890)Instruction limit reached!
% 65.44/10.71 % (3890)------------------------------
% 65.44/10.71 % (3890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.44/10.71 % (3890)Termination reason: Unknown
% 65.44/10.71 % (3890)Termination phase: Saturation
% 65.44/10.71
% 65.44/10.71 % (3890)Memory used [KB]: 12665
% 65.44/10.71 % (3890)Time elapsed: 0.787 s
% 65.44/10.71 % (3890)Instructions burned: 2575 (million)
% 65.44/10.71 % (3890)------------------------------
% 65.44/10.71 % (3890)------------------------------
% 65.44/10.72 % (3899)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_3332 for (2909ds/7311Mi)
% 65.44/10.72 % (3900)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_3332 for (2909ds/6804Mi)
% 65.44/10.73 % (3891)Instruction limit reached!
% 65.44/10.73 % (3891)------------------------------
% 65.44/10.73 % (3891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.44/10.73 % (3891)Termination reason: Unknown
% 65.44/10.73 % (3891)Termination phase: Saturation
% 65.44/10.73
% 65.44/10.73 % (3891)Memory used [KB]: 14072
% 65.44/10.73 % (3891)Time elapsed: 0.797 s
% 65.44/10.73 % (3891)Instructions burned: 2657 (million)
% 65.44/10.73 % (3891)------------------------------
% 65.44/10.73 % (3891)------------------------------
% 65.44/10.74 % (3901)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_3332 for (2909ds/1683Mi)
% 69.86/11.27 % (3901)Instruction limit reached!
% 69.86/11.27 % (3901)------------------------------
% 69.86/11.27 % (3901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.86/11.27 % (3901)Termination reason: Unknown
% 69.86/11.27 % (3901)Termination phase: Saturation
% 69.86/11.27
% 69.86/11.27 % (3901)Memory used [KB]: 10618
% 69.86/11.27 % (3901)Time elapsed: 0.533 s
% 69.86/11.27 % (3901)Instructions burned: 1684 (million)
% 69.86/11.27 % (3901)------------------------------
% 69.86/11.27 % (3901)------------------------------
% 69.86/11.28 % (3902)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_3332 for (2904ds/4688Mi)
% 71.15/11.46 % (3896)Instruction limit reached!
% 71.15/11.46 % (3896)------------------------------
% 71.15/11.46 % (3896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.15/11.46 % (3896)Termination reason: Unknown
% 71.15/11.46 % (3896)Termination phase: Saturation
% 71.15/11.46
% 71.15/11.46 % (3896)Memory used [KB]: 13560
% 71.15/11.46 % (3896)Time elapsed: 0.983 s
% 71.15/11.46 % (3896)Instructions burned: 3203 (million)
% 71.15/11.46 % (3896)------------------------------
% 71.15/11.46 % (3896)------------------------------
% 71.15/11.47 % (3903)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_3332 for (2902ds/2207Mi)
% 71.72/11.54 % (3889)Instruction limit reached!
% 71.72/11.54 % (3889)------------------------------
% 71.72/11.54 % (3889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.72/11.54 % (3889)Termination reason: Unknown
% 71.72/11.54 % (3889)Termination phase: Saturation
% 71.72/11.54
% 71.72/11.54 % (3889)Memory used [KB]: 16502
% 71.72/11.54 % (3889)Time elapsed: 1.724 s
% 71.72/11.54 % (3889)Instructions burned: 5448 (million)
% 71.72/11.54 % (3889)------------------------------
% 71.72/11.54 % (3889)------------------------------
% 71.72/11.55 % (3904)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=8216:si=on:rtra=on_0 on DTF2THF_3332 for (2901ds/8216Mi)
% 71.72/11.57 % (3898)Instruction limit reached!
% 71.72/11.57 % (3898)------------------------------
% 71.72/11.57 % (3898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.72/11.57 % (3898)Termination reason: Unknown
% 71.72/11.57 % (3898)Termination phase: Saturation
% 71.72/11.57
% 71.72/11.57 % (3898)Memory used [KB]: 11129
% 71.72/11.57 % (3898)Time elapsed: 0.980 s
% 71.72/11.57 % (3898)Instructions burned: 3052 (million)
% 71.72/11.57 % (3898)------------------------------
% 71.72/11.57 % (3898)------------------------------
% 71.72/11.58 % (3905)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_3332 for (2901ds/430Mi)
% 72.45/11.70 % (3905)Instruction limit reached!
% 72.45/11.70 % (3905)------------------------------
% 72.45/11.70 % (3905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.45/11.70 % (3905)Termination reason: Unknown
% 72.45/11.70 % (3905)Termination phase: Saturation
% 72.45/11.70
% 72.45/11.70 % (3905)Memory used [KB]: 8699
% 72.45/11.70 % (3905)Time elapsed: 0.120 s
% 72.45/11.70 % (3905)Instructions burned: 433 (million)
% 72.45/11.70 % (3905)------------------------------
% 72.45/11.70 % (3905)------------------------------
% 72.45/11.71 % (3906)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_3332 for (2899ds/2012Mi)
% 72.89/11.87 % (3895)Instruction limit reached!
% 72.89/11.87 % (3895)------------------------------
% 72.89/11.87 % (3895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.89/11.87 % (3895)Termination reason: Unknown
% 72.89/11.87 % (3895)Termination phase: Saturation
% 72.89/11.87
% 72.89/11.87 % (3895)Memory used [KB]: 20980
% 72.89/11.87 % (3895)Time elapsed: 1.631 s
% 72.89/11.87 % (3895)Instructions burned: 5215 (million)
% 72.89/11.87 % (3895)------------------------------
% 72.89/11.87 % (3895)------------------------------
% 72.89/11.88 % (3907)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_3332 for (2898ds/631Mi)
% 75.64/12.07 % (3907)Instruction limit reached!
% 75.64/12.07 % (3907)------------------------------
% 75.64/12.07 % (3907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.64/12.07 % (3907)Termination reason: Unknown
% 75.64/12.07 % (3907)Termination phase: Saturation
% 75.64/12.07
% 75.64/12.07 % (3907)Memory used [KB]: 11001
% 75.64/12.07 % (3907)Time elapsed: 0.191 s
% 75.64/12.07 % (3907)Instructions burned: 634 (million)
% 75.64/12.07 % (3907)------------------------------
% 75.64/12.07 % (3907)------------------------------
% 75.64/12.08 % (3908)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_3332 for (2896ds/8785Mi)
% 76.30/12.14 % (3903)Instruction limit reached!
% 76.30/12.14 % (3903)------------------------------
% 76.30/12.14 % (3903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.30/12.14 % (3903)Termination reason: Unknown
% 76.30/12.14 % (3903)Termination phase: Saturation
% 76.30/12.14
% 76.30/12.14 % (3903)Memory used [KB]: 10874
% 76.30/12.14 % (3903)Time elapsed: 0.670 s
% 76.30/12.14 % (3903)Instructions burned: 2208 (million)
% 76.30/12.14 % (3903)------------------------------
% 76.30/12.14 % (3903)------------------------------
% 76.30/12.15 % (3909)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_3332 for (2895ds/739Mi)
% 77.22/12.32 % (3902)Instruction limit reached!
% 77.22/12.32 % (3902)------------------------------
% 77.22/12.32 % (3902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.22/12.32 % (3902)Termination reason: Unknown
% 77.22/12.32 % (3902)Termination phase: Property scanning
% 77.22/12.32
% 77.22/12.32 % (3902)Memory used [KB]: 4477
% 77.22/12.32 % (3902)Time elapsed: 1.037 s
% 77.22/12.32 % (3902)Instructions burned: 4689 (million)
% 77.22/12.32 % (3902)------------------------------
% 77.22/12.32 % (3902)------------------------------
% 77.22/12.33 % (3910)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_3332 for (2893ds/5473Mi)
% 77.22/12.33 % (3906)Instruction limit reached!
% 77.22/12.33 % (3906)------------------------------
% 77.22/12.33 % (3906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.22/12.33 % (3906)Termination reason: Unknown
% 77.22/12.33 % (3906)Termination phase: Saturation
% 77.22/12.33
% 77.22/12.33 % (3906)Memory used [KB]: 18166
% 77.22/12.33 % (3906)Time elapsed: 0.623 s
% 77.22/12.33 % (3906)Instructions burned: 2014 (million)
% 77.22/12.33 % (3906)------------------------------
% 77.22/12.33 % (3906)------------------------------
% 77.22/12.34 % (3911)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_3332 for (2893ds/43570Mi)
% 77.22/12.37 % (3911)Refutation not found, incomplete strategy
% 77.22/12.37 % (3911)------------------------------
% 77.22/12.37 % (3911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.22/12.37 % (3911)Termination reason: Refutation not found, incomplete strategy
% 77.22/12.37
% 77.22/12.37
% 77.22/12.37 % (3911)Memory used [KB]: 7036
% 77.22/12.37 % (3911)Time elapsed: 0.030 s
% 77.22/12.37 % (3911)Instructions burned: 99 (million)
% 77.22/12.37 % (3911)------------------------------
% 77.22/12.37 % (3911)------------------------------
% 77.22/12.37 % (3909)Instruction limit reached!
% 77.22/12.37 % (3909)------------------------------
% 77.22/12.37 % (3909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.22/12.37 % (3909)Termination reason: Unknown
% 77.22/12.37 % (3909)Termination phase: Saturation
% 77.22/12.37
% 77.22/12.37 % (3909)Memory used [KB]: 9466
% 77.22/12.37 % (3909)Time elapsed: 0.228 s
% 77.22/12.37 % (3909)Instructions burned: 741 (million)
% 77.22/12.37 % (3909)------------------------------
% 77.22/12.37 % (3909)------------------------------
% 77.22/12.38 % (3912)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_3332 for (2893ds/8382Mi)
% 77.22/12.38 % (3913)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_3332 for (2893ds/407Mi)
% 78.15/12.51 % (3913)Instruction limit reached!
% 78.15/12.51 % (3913)------------------------------
% 78.15/12.51 % (3913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.15/12.51 % (3913)Termination reason: Unknown
% 78.15/12.51 % (3913)Termination phase: Saturation
% 78.15/12.51
% 78.15/12.51 % (3913)Memory used [KB]: 8827
% 78.15/12.51 % (3913)Time elapsed: 0.123 s
% 78.15/12.51 % (3913)Instructions burned: 408 (million)
% 78.15/12.51 % (3913)------------------------------
% 78.15/12.51 % (3913)------------------------------
% 78.15/12.52 % (3914)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_3332 for (2891ds/2971Mi)
% 78.15/12.59 % (3914)Refutation not found, incomplete strategy
% 78.15/12.59 % (3914)------------------------------
% 78.15/12.59 % (3914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.15/12.59 % (3914)Termination reason: Refutation not found, incomplete strategy
% 78.15/12.59
% 78.15/12.59
% 78.15/12.59 % (3914)Memory used [KB]: 8059
% 78.15/12.59 % (3914)Time elapsed: 0.076 s
% 78.15/12.59 % (3914)Instructions burned: 277 (million)
% 78.15/12.59 % (3914)------------------------------
% 78.15/12.59 % (3914)------------------------------
% 78.67/12.60 % (3915)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_3332 for (2890ds/9822Mi)
% 78.97/12.78 % (3900)Instruction limit reached!
% 78.97/12.78 % (3900)------------------------------
% 78.97/12.78 % (3900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.97/12.78 % (3900)Termination reason: Unknown
% 78.97/12.78 % (3900)Termination phase: Saturation
% 78.97/12.78
% 78.97/12.78 % (3900)Memory used [KB]: 13944
% 78.97/12.78 % (3900)Time elapsed: 2.062 s
% 78.97/12.78 % (3900)Instructions burned: 6805 (million)
% 78.97/12.78 % (3900)------------------------------
% 78.97/12.78 % (3900)------------------------------
% 78.97/12.79 % (3916)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_3332 for (2888ds/8425Mi)
% 79.50/12.96 % (3899)Instruction limit reached!
% 79.50/12.96 % (3899)------------------------------
% 79.50/12.96 % (3899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.50/12.96 % (3899)Termination reason: Unknown
% 79.50/12.96 % (3899)Termination phase: Saturation
% 79.50/12.96
% 79.50/12.96 % (3899)Memory used [KB]: 21108
% 79.50/12.96 % (3899)Time elapsed: 2.241 s
% 79.50/12.96 % (3899)Instructions burned: 7311 (million)
% 79.50/12.96 % (3899)------------------------------
% 79.50/12.96 % (3899)------------------------------
% 79.50/12.97 % (3917)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_3332 for (2887ds/3107Mi)
% 82.64/13.05 % (3917)Refutation not found, incomplete strategy
% 82.64/13.05 % (3917)------------------------------
% 82.64/13.05 % (3917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.64/13.05 % (3917)Termination reason: Refutation not found, incomplete strategy
% 82.64/13.05
% 82.64/13.05
% 82.64/13.05 % (3917)Memory used [KB]: 9338
% 82.64/13.05 % (3917)Time elapsed: 0.082 s
% 82.64/13.05 % (3917)Instructions burned: 270 (million)
% 82.64/13.05 % (3917)------------------------------
% 82.64/13.05 % (3917)------------------------------
% 82.64/13.06 % (3918)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_3332 for (2886ds/7967Mi)
% 83.32/13.14 % (3918)Refutation not found, incomplete strategy
% 83.32/13.14 % (3918)------------------------------
% 83.32/13.14 % (3918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.32/13.14 % (3918)Termination reason: Refutation not found, incomplete strategy
% 83.32/13.14
% 83.32/13.14
% 83.32/13.14 % (3918)Memory used [KB]: 8059
% 83.32/13.14 % (3918)Time elapsed: 0.078 s
% 83.32/13.14 % (3918)Instructions burned: 274 (million)
% 83.32/13.14 % (3918)------------------------------
% 83.32/13.14 % (3918)------------------------------
% 83.32/13.15 % (3919)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on DTF2THF_3332 for (2885ds/3629Mi)
% 88.08/13.98 % (3919)Instruction limit reached!
% 88.08/13.98 % (3919)------------------------------
% 88.08/13.98 % (3919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 88.08/13.98 % (3919)Termination reason: Unknown
% 88.08/13.98 % (3919)Termination phase: Saturation
% 88.08/13.98
% 88.08/13.98 % (3919)Memory used [KB]: 7675
% 88.08/13.98 % (3919)Time elapsed: 0.834 s
% 88.08/13.98 % (3919)Instructions burned: 3632 (million)
% 88.08/13.98 % (3919)------------------------------
% 88.08/13.98 % (3919)------------------------------
% 88.08/13.99 % (3922)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on DTF2THF_3332 for (2876ds/939Mi)
% 89.68/14.05 % (3904)Instruction limit reached!
% 89.68/14.05 % (3904)------------------------------
% 89.68/14.05 % (3904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 89.68/14.05 % (3904)Termination reason: Unknown
% 89.68/14.05 % (3904)Termination phase: Saturation
% 89.68/14.05
% 89.68/14.05 % (3904)Memory used [KB]: 19573
% 89.68/14.05 % (3904)Time elapsed: 2.502 s
% 89.68/14.05 % (3904)Instructions burned: 8217 (million)
% 89.68/14.05 % (3904)------------------------------
% 89.68/14.05 % (3904)------------------------------
% 89.68/14.06 % (3910)Instruction limit reached!
% 89.68/14.06 % (3910)------------------------------
% 89.68/14.06 % (3910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 89.68/14.06 % (3910)Termination reason: Unknown
% 89.68/14.06 % (3910)Termination phase: Saturation
% 89.68/14.06
% 89.68/14.06 % (3910)Memory used [KB]: 10746
% 89.68/14.06 % (3910)Time elapsed: 1.734 s
% 89.68/14.06 % (3910)Instructions burned: 5474 (million)
% 89.68/14.06 % (3910)------------------------------
% 89.68/14.06 % (3910)------------------------------
% 89.68/14.06 % (3939)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_3332 for (2876ds/1188Mi)
% 89.68/14.07 % (3942)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on DTF2THF_3332 for (2876ds/3205Mi)
% 90.66/14.20 % (3922)Instruction limit reached!
% 90.66/14.20 % (3922)------------------------------
% 90.66/14.20 % (3922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.66/14.20 % (3922)Termination reason: Unknown
% 90.66/14.20 % (3922)Termination phase: Property scanning
% 90.66/14.20
% 90.66/14.20 % (3922)Memory used [KB]: 3326
% 90.66/14.20 % (3922)Time elapsed: 0.213 s
% 90.66/14.20 % (3922)Instructions burned: 940 (million)
% 90.66/14.20 % (3922)------------------------------
% 90.66/14.20 % (3922)------------------------------
% 90.66/14.21 % (4014)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_3332 for (2874ds/865Mi)
% 91.09/14.38 % (3912)Instruction limit reached!
% 91.09/14.38 % (3912)------------------------------
% 91.09/14.38 % (3912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.09/14.38 % (3912)Termination reason: Unknown
% 91.09/14.38 % (3912)Termination phase: Saturation
% 91.09/14.38
% 91.09/14.38 % (3912)Memory used [KB]: 11257
% 91.09/14.38 % (3912)Time elapsed: 2.003 s
% 91.09/14.38 % (3912)Instructions burned: 8384 (million)
% 91.09/14.38 % (3912)------------------------------
% 91.09/14.38 % (3912)------------------------------
% 91.09/14.39 % (4071)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on DTF2THF_3332 for (2873ds/7469Mi)
% 91.47/14.43 % (3939)Instruction limit reached!
% 91.47/14.43 % (3939)------------------------------
% 91.47/14.43 % (3939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.47/14.43 % (3939)Termination reason: Unknown
% 91.47/14.43 % (3939)Termination phase: Saturation
% 91.47/14.43
% 91.47/14.43 % (3939)Memory used [KB]: 11513
% 91.47/14.43 % (3939)Time elapsed: 0.369 s
% 91.47/14.43 % (3939)Instructions burned: 1189 (million)
% 91.47/14.43 % (3939)------------------------------
% 91.47/14.43 % (3939)------------------------------
% 91.47/14.44 % (4085)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on DTF2THF_3332 for (2872ds/4165Mi)
% 91.47/14.46 % (4014)Refutation not found, non-redundant clauses discarded% (4014)------------------------------
% 91.47/14.46 % (4014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.47/14.46 % (4014)Termination reason: Refutation not found, non-redundant clauses discarded
% 91.47/14.46
% 91.47/14.46 % (4014)Memory used [KB]: 10362
% 91.47/14.46 % (4014)Time elapsed: 0.249 s
% 91.47/14.46 % (4014)Instructions burned: 783 (million)
% 91.47/14.46 % (4014)------------------------------
% 91.47/14.46 % (4014)------------------------------
% 91.47/14.47 % (4096)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on DTF2THF_3332 for (2872ds/13468Mi)
% 93.32/14.80 % (3908)Instruction limit reached!
% 93.32/14.80 % (3908)------------------------------
% 93.32/14.80 % (3908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.32/14.80 % (3908)Termination reason: Unknown
% 93.32/14.80 % (3908)Termination phase: Saturation
% 93.32/14.80
% 93.32/14.80 % (3908)Memory used [KB]: 22259
% 93.32/14.80 % (3908)Time elapsed: 2.715 s
% 93.32/14.80 % (3908)Instructions burned: 8786 (million)
% 93.32/14.80 % (3908)------------------------------
% 93.32/14.80 % (3908)------------------------------
% 93.32/14.81 % (4158)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on DTF2THF_3332 for (2868ds/2635Mi)
% 96.69/15.06 % (3942)Instruction limit reached!
% 96.69/15.06 % (3942)------------------------------
% 96.69/15.06 % (3942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 96.69/15.06 % (3942)Termination reason: Unknown
% 96.69/15.06 % (3942)Termination phase: Saturation
% 96.69/15.06
% 96.69/15.06 % (3942)Memory used [KB]: 12537
% 96.69/15.06 % (3942)Time elapsed: 0.996 s
% 96.69/15.06 % (3942)Instructions burned: 3207 (million)
% 96.69/15.06 % (3942)------------------------------
% 96.69/15.06 % (3942)------------------------------
% 96.69/15.08 % (4168)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=631:si=on:rtra=on_0 on DTF2THF_3332 for (2866ds/631Mi)
% 97.81/15.24 % (4168)Instruction limit reached!
% 97.81/15.24 % (4168)------------------------------
% 97.81/15.24 % (4168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.81/15.24 % (4168)Termination reason: Unknown
% 97.81/15.24 % (4168)Termination phase: Saturation
% 97.81/15.24
% 97.81/15.24 % (4168)Memory used [KB]: 8699
% 97.81/15.24 % (4168)Time elapsed: 0.171 s
% 97.81/15.24 % (4168)Instructions burned: 631 (million)
% 97.81/15.24 % (4168)------------------------------
% 97.81/15.24 % (4168)------------------------------
% 97.81/15.25 % (4238)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=15557:si=on:rtra=on_0 on DTF2THF_3332 for (2864ds/15557Mi)
% 97.81/15.30 % (3916)Instruction limit reached!
% 97.81/15.30 % (3916)------------------------------
% 97.81/15.30 % (3916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.81/15.30 % (3916)Termination reason: Unknown
% 97.81/15.30 % (3916)Termination phase: Saturation
% 97.81/15.30
% 97.81/15.30 % (3916)Memory used [KB]: 22259
% 97.81/15.30 % (3916)Time elapsed: 2.505 s
% 97.81/15.30 % (3916)Instructions burned: 8426 (million)
% 97.81/15.30 % (3916)------------------------------
% 97.81/15.30 % (3916)------------------------------
% 96.09/15.31 % (4283)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on DTF2THF_3332 for (2863ds/2142Mi)
% 99.61/15.55 % (3915)Instruction limit reached!
% 99.61/15.55 % (3915)------------------------------
% 99.61/15.55 % (3915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.61/15.55 % (3915)Termination reason: Unknown
% 99.61/15.55 % (3915)Termination phase: Saturation
% 99.61/15.55
% 99.61/15.55 % (3915)Memory used [KB]: 18293
% 99.61/15.55 % (3915)Time elapsed: 2.952 s
% 99.61/15.55 % (3915)Instructions burned: 9825 (million)
% 99.61/15.55 % (3915)------------------------------
% 99.61/15.55 % (3915)------------------------------
% 99.61/15.56 % (4322)dis+1002_1:1_aac=none:au=on:bd=off:cnfonf=conj_eager:nwc=5.0:sgt=5:sp=reverse_arity:ss=axioms:i=5624:si=on:rtra=on_0 on DTF2THF_3332 for (2861ds/5624Mi)
% 99.61/15.59 % (4158)Instruction limit reached!
% 99.61/15.59 % (4158)------------------------------
% 99.61/15.59 % (4158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.61/15.59 % (4158)Termination reason: Unknown
% 99.61/15.59 % (4158)Termination phase: Saturation
% 99.61/15.59
% 99.61/15.59 % (4158)Memory used [KB]: 11385
% 99.61/15.59 % (4158)Time elapsed: 0.780 s
% 99.61/15.59 % (4158)Instructions burned: 2636 (million)
% 99.61/15.59 % (4158)------------------------------
% 99.61/15.59 % (4158)------------------------------
% 99.61/15.60 % (4347)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=1665:si=on:rtra=on_0 on DTF2THF_3332 for (2860ds/1665Mi)
% 100.38/15.77 % (4085)Instruction limit reached!
% 100.38/15.77 % (4085)------------------------------
% 100.38/15.77 % (4085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.38/15.77 % (4085)Termination reason: Unknown
% 100.38/15.77 % (4085)Termination phase: Saturation
% 100.38/15.77
% 100.38/15.77 % (4085)Memory used [KB]: 13304
% 100.38/15.77 % (4085)Time elapsed: 1.332 s
% 100.38/15.77 % (4085)Instructions burned: 4165 (million)
% 100.38/15.77 % (4085)------------------------------
% 100.38/15.77 % (4085)------------------------------
% 100.38/15.78 % (4389)dis+1002_1:1_av=off:prag=on:sd=1:sos=on:sp=occurrence:ss=axioms:i=64912:si=on:rtra=on_0 on DTF2THF_3332 for (2859ds/64912Mi)
% 100.86/15.96 % (4347)Instruction limit reached!
% 100.86/15.96 % (4347)------------------------------
% 100.86/15.96 % (4347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.86/15.96 % (4347)Termination reason: Unknown
% 100.86/15.96 % (4347)Termination phase: Saturation
% 100.86/15.96
% 100.86/15.96 % (4347)Memory used [KB]: 7931
% 100.86/15.96 % (4347)Time elapsed: 0.367 s
% 100.86/15.96 % (4347)Instructions burned: 1667 (million)
% 100.86/15.96 % (4347)------------------------------
% 100.86/15.96 % (4347)------------------------------
% 100.86/15.98 % (4408)lrs+10_1:32_atotf=0.1:avsq=on:bsr=on:cnfonf=lazy_gen:fde=unused:i=7801:si=on:rtra=on_0 on DTF2THF_3332 for (2857ds/7801Mi)
% 100.86/15.98 % (4283)Instruction limit reached!
% 100.86/15.98 % (4283)------------------------------
% 100.86/15.98 % (4283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.86/15.98 % (4283)Termination reason: Unknown
% 100.86/15.98 % (4283)Termination phase: Saturation
% 100.86/15.98
% 100.86/15.98 % (4283)Memory used [KB]: 9850
% 100.86/15.98 % (4283)Time elapsed: 0.671 s
% 100.86/15.98 % (4283)Instructions burned: 2143 (million)
% 100.86/15.98 % (4283)------------------------------
% 100.86/15.98 % (4283)------------------------------
% 100.86/15.99 % (4409)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15194:si=on:rtra=on_0 on DTF2THF_3332 for (2857ds/15194Mi)
% 108.46/16.79 % (4071)Instruction limit reached!
% 108.46/16.79 % (4071)------------------------------
% 108.46/16.79 % (4071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 108.46/16.79 % (4071)Termination reason: Unknown
% 108.46/16.79 % (4071)Termination phase: Saturation
% 108.46/16.79
% 108.46/16.79 % (4071)Memory used [KB]: 12409
% 108.46/16.79 % (4071)Time elapsed: 2.401 s
% 108.46/16.79 % (4071)Instructions burned: 7471 (million)
% 108.46/16.79 % (4071)------------------------------
% 108.46/16.79 % (4071)------------------------------
% 109.17/16.80 % (4412)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=6753:si=on:rtra=on_0 on DTF2THF_3332 for (2848ds/6753Mi)
% 114.04/17.50 % (4322)Instruction limit reached!
% 114.04/17.50 % (4322)------------------------------
% 114.04/17.50 % (4322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 114.04/17.50 % (4322)Termination reason: Unknown
% 114.04/17.50 % (4322)Termination phase: Saturation
% 114.04/17.50
% 114.04/17.50 % (4322)Memory used [KB]: 12025
% 114.04/17.50 % (4322)Time elapsed: 1.938 s
% 114.04/17.50 % (4322)Instructions burned: 5624 (million)
% 114.04/17.50 % (4322)------------------------------
% 114.04/17.50 % (4322)------------------------------
% 114.04/17.52 % (4422)lrs+1002_1:28_bd=off:cnfonf=lazy_simp:plsq=on:plsqr=1,1:prag=on:i=1003:si=on:rtra=on_0 on DTF2THF_3332 for (2841ds/1003Mi)
% 115.85/17.89 % (4422)Instruction limit reached!
% 115.85/17.89 % (4422)------------------------------
% 115.85/17.89 % (4422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 115.85/17.89 % (4422)Termination reason: Unknown
% 115.85/17.89 % (4422)Termination phase: Saturation
% 115.85/17.89
% 115.85/17.89 % (4422)Memory used [KB]: 9083
% 115.85/17.89 % (4422)Time elapsed: 0.378 s
% 115.85/17.89 % (4422)Instructions burned: 1003 (million)
% 115.85/17.89 % (4422)------------------------------
% 115.85/17.89 % (4422)------------------------------
% 116.83/17.91 % (4423)ott-21_5:4_atotf=0.3:e2e=on:hud=15:ins=1:plsq=on:plsqc=1:plsqr=32,1:sp=unary_frequency:tnu=2:i=13018:si=on:rtra=on_0 on DTF2THF_3332 for (2837ds/13018Mi)
% 122.42/18.79 % (4408)Instruction limit reached!
% 122.42/18.79 % (4408)------------------------------
% 122.42/18.79 % (4408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 122.42/18.79 % (4408)Termination reason: Unknown
% 122.42/18.79 % (4408)Termination phase: Saturation
% 122.42/18.79
% 122.42/18.79 % (4408)Memory used [KB]: 12665
% 122.42/18.79 % (4408)Time elapsed: 2.811 s
% 122.42/18.79 % (4408)Instructions burned: 7802 (million)
% 122.42/18.79 % (4408)------------------------------
% 122.42/18.79 % (4408)------------------------------
% 122.42/18.80 % (4429)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1267:si=on:rtra=on_0 on DTF2THF_3332 for (2828ds/1267Mi)
% 124.58/19.07 % (4096)Instruction limit reached!
% 124.58/19.07 % (4096)------------------------------
% 124.58/19.07 % (4096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 124.58/19.07 % (4096)Termination reason: Unknown
% 124.58/19.07 % (4096)Termination phase: Saturation
% 124.58/19.07
% 124.58/19.07 % (4096)Memory used [KB]: 21108
% 124.58/19.07 % (4096)Time elapsed: 4.598 s
% 124.58/19.07 % (4096)Instructions burned: 13469 (million)
% 124.58/19.07 % (4096)------------------------------
% 124.58/19.07 % (4096)------------------------------
% 124.58/19.08 % (4430)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=2570:si=on:rtra=on_0 on DTF2THF_3332 for (2826ds/2570Mi)
% 125.26/19.13 % (4412)Instruction limit reached!
% 125.26/19.13 % (4412)------------------------------
% 125.26/19.13 % (4412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 125.26/19.13 % (4412)Termination reason: Unknown
% 125.26/19.13 % (4412)Termination phase: Saturation
% 125.26/19.13
% 125.26/19.13 % (4412)Memory used [KB]: 14200
% 125.26/19.13 % (4412)Time elapsed: 2.320 s
% 125.26/19.13 % (4412)Instructions burned: 6753 (million)
% 125.26/19.13 % (4412)------------------------------
% 125.26/19.13 % (4412)------------------------------
% 125.26/19.14 % (4431)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_3332 for (2825ds/13163Mi)
% 125.26/19.17 % (4429)Instruction limit reached!
% 125.26/19.17 % (4429)------------------------------
% 125.26/19.17 % (4429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 125.26/19.17 % (4429)Termination reason: Unknown
% 125.26/19.17 % (4429)Termination phase: Saturation
% 125.26/19.17
% 125.26/19.17 % (4429)Memory used [KB]: 8443
% 125.26/19.17 % (4429)Time elapsed: 0.380 s
% 125.26/19.17 % (4429)Instructions burned: 1269 (million)
% 125.26/19.17 % (4429)------------------------------
% 125.26/19.17 % (4429)------------------------------
% 125.26/19.18 % (4432)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_3332 for (2825ds/5087Mi)
% 128.11/19.80 % (4430)Instruction limit reached!
% 128.11/19.80 % (4430)------------------------------
% 128.11/19.80 % (4430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 128.11/19.81 % (4430)Termination reason: Unknown
% 128.11/19.81 % (4430)Termination phase: Saturation
% 128.11/19.81
% 128.11/19.81 % (4430)Memory used [KB]: 11257
% 128.11/19.81 % (4430)Time elapsed: 0.730 s
% 128.11/19.81 % (4430)Instructions burned: 2570 (million)
% 128.11/19.81 % (4430)------------------------------
% 128.11/19.81 % (4430)------------------------------
% 128.11/19.82 % (4433)lrs+1002_1:1_aac=none:au=on:bd=off:cnfonf=lazy_pi_sigma_gen:s2a=on:sac=on:sd=1:sgt=20:ss=axioms:i=10380:si=on:rtra=on_0 on DTF2THF_3332 for (2818ds/10380Mi)
% 131.57/20.08 % (4238)Instruction limit reached!
% 131.57/20.08 % (4238)------------------------------
% 131.57/20.08 % (4238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 131.57/20.08 % (4238)Termination reason: Unknown
% 131.57/20.08 % (4238)Termination phase: Saturation
% 131.57/20.08
% 131.57/20.08 % (4238)Memory used [KB]: 32366
% 131.57/20.08 % (4238)Time elapsed: 4.822 s
% 131.57/20.08 % (4238)Instructions burned: 15560 (million)
% 131.57/20.08 % (4238)------------------------------
% 131.57/20.08 % (4238)------------------------------
% 131.57/20.09 % (4434)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4218:si=on:rtra=on_0 on DTF2THF_3332 for (2816ds/4218Mi)
% 135.76/20.79 % (4432)Instruction limit reached!
% 135.76/20.79 % (4432)------------------------------
% 135.76/20.79 % (4432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 135.76/20.79 % (4432)Termination reason: Unknown
% 135.76/20.79 % (4432)Termination phase: Saturation
% 135.76/20.79
% 135.76/20.79 % (4432)Memory used [KB]: 15991
% 135.76/20.79 % (4432)Time elapsed: 1.608 s
% 135.76/20.79 % (4432)Instructions burned: 5090 (million)
% 135.76/20.79 % (4432)------------------------------
% 135.76/20.79 % (4432)------------------------------
% 136.38/20.80 % (4437)ott+1666_1:1_hfaw=0:hfsq=on:hfsql=off:hfsqr=1,16:hud=15:slsq=on:slsqr=1,2:tnu=2:i=3971:si=on:rtra=on_0 on DTF2THF_3332 for (2808ds/3971Mi)
% 140.54/21.33 % (4409)Instruction limit reached!
% 140.54/21.33 % (4409)------------------------------
% 140.54/21.33 % (4409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 140.54/21.33 % (4409)Termination reason: Unknown
% 140.54/21.33 % (4409)Termination phase: Saturation
% 140.54/21.33
% 140.54/21.33 % (4409)Memory used [KB]: 19829
% 140.54/21.33 % (4409)Time elapsed: 5.348 s
% 140.54/21.33 % (4409)Instructions burned: 15195 (million)
% 140.54/21.33 % (4409)------------------------------
% 140.54/21.33 % (4409)------------------------------
% 140.54/21.35 % (4481)dis+1010_1:1_anc=all_dependent:au=on:bs=on:sd=5:sp=occurrence:ss=axioms:st=2.0:i=14014:si=on:rtra=on_0 on DTF2THF_3332 for (2803ds/14014Mi)
% 142.41/21.60 % (4434)Instruction limit reached!
% 142.41/21.60 % (4434)------------------------------
% 142.41/21.60 % (4434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 142.41/21.60 % (4434)Termination reason: Unknown
% 142.41/21.60 % (4434)Termination phase: Saturation
% 142.41/21.60
% 142.41/21.60 % (4434)Memory used [KB]: 17142
% 142.41/21.60 % (4434)Time elapsed: 1.517 s
% 142.41/21.60 % (4434)Instructions burned: 4219 (million)
% 142.41/21.60 % (4434)------------------------------
% 142.41/21.60 % (4434)------------------------------
% 142.41/21.62 % (4502)lrs+10_1:1_ins=1:sgt=8:ss=axioms:i=8517:si=on:rtra=on_0 on DTF2THF_3332 for (2800ds/8517Mi)
% 148.25/22.47 % (4423)Instruction limit reached!
% 148.25/22.47 % (4423)------------------------------
% 148.25/22.47 % (4423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 148.25/22.47 % (4423)Termination reason: Unknown
% 148.25/22.47 % (4423)Termination phase: Saturation
% 148.25/22.47
% 148.25/22.47 % (4423)Memory used [KB]: 34796
% 148.25/22.47 % (4423)Time elapsed: 4.558 s
% 148.25/22.47 % (4423)Instructions burned: 13018 (million)
% 148.25/22.47 % (4423)------------------------------
% 148.25/22.47 % (4423)------------------------------
% 148.25/22.48 % (4437)Instruction limit reached!
% 148.25/22.48 % (4437)------------------------------
% 148.25/22.48 % (4437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 148.25/22.48 % (4437)Termination reason: Unknown
% 148.25/22.48 % (4437)Termination phase: Saturation
% 148.25/22.48
% 148.25/22.48 % (4437)Memory used [KB]: 19957
% 148.25/22.48 % (4437)Time elapsed: 1.679 s
% 148.25/22.48 % (4437)Instructions burned: 3972 (million)
% 148.25/22.48 % (4437)------------------------------
% 148.25/22.48 % (4437)------------------------------
% 148.25/22.48 % (4539)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=10148:si=on:rtra=on_0 on DTF2THF_3332 for (2792ds/10148Mi)
% 148.93/22.50 % (4540)lrs+10_1:2_ntd=on:nwc=10.0:plsq=on:plsqc=1:plsqr=2,1:ss=axioms:i=9078:si=on:rtra=on_0 on DTF2THF_3332 for (2791ds/9078Mi)
% 158.03/23.80 % (4433)Instruction limit reached!
% 158.03/23.80 % (4433)------------------------------
% 158.03/23.80 % (4433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 158.03/23.80 % (4433)Termination reason: Unknown
% 158.03/23.80 % (4433)Termination phase: Saturation
% 158.03/23.80
% 158.03/23.80 % (4433)Memory used [KB]: 19573
% 158.03/23.80 % (4433)Time elapsed: 3.996 s
% 158.03/23.80 % (4433)Instructions burned: 10381 (million)
% 158.03/23.80 % (4433)------------------------------
% 158.03/23.80 % (4433)------------------------------
% 158.03/23.81 % (4708)lrs+2_1:1_bet=on:bsr=on:cnfonf=lazy_pi_sigma_gen:er=filter:kws=inv_frequency:ntd=on:sd=3:ss=axioms:i=16164:si=on:rtra=on_0 on DTF2THF_3332 for (2778ds/16164Mi)
% 158.03/23.84 % (4431)Instruction limit reached!
% 158.03/23.84 % (4431)------------------------------
% 158.03/23.84 % (4431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 158.03/23.84 % (4431)Termination reason: Unknown
% 158.03/23.84 % (4431)Termination phase: Saturation
% 158.03/23.84
% 158.03/23.84 % (4431)Memory used [KB]: 18421
% 158.03/23.84 % (4431)Time elapsed: 4.717 s
% 158.03/23.84 % (4431)Instructions burned: 13163 (million)
% 158.03/23.84 % (4431)------------------------------
% 158.03/23.84 % (4431)------------------------------
% 158.03/23.85 % (4709)lrs+32_1:1_au=on:bet=on:cbe=off:cs=on:ins=3:i=6102:si=on:rtra=on_0 on DTF2THF_3332 for (2778ds/6102Mi)
% 164.36/24.72 % (4502)Instruction limit reached!
% 164.36/24.72 % (4502)------------------------------
% 164.36/24.72 % (4502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 164.36/24.72 % (4502)Termination reason: Unknown
% 164.36/24.72 % (4502)Termination phase: Saturation
% 164.36/24.72
% 164.36/24.72 % (4502)Memory used [KB]: 22643
% 164.36/24.72 % (4502)Time elapsed: 3.105 s
% 164.36/24.72 % (4502)Instructions burned: 8518 (million)
% 164.36/24.72 % (4502)------------------------------
% 164.36/24.72 % (4502)------------------------------
% 164.36/24.74 % (4787)lrs+1010_1:1_au=on:bd=off:e2e=on:fde=unused:nm=4:s2a=on:sos=all:sp=const_frequency:i=10308:si=on:rtra=on_0 on DTF2THF_3332 for (2769ds/10308Mi)
% 165.61/24.94 % (4787)First to succeed.
% 165.61/24.94 % (4787)Refutation found. Thanks to Tanya!
% 165.61/24.94 % SZS status Theorem for DTF2THF_3332
% 165.61/24.94 % SZS output start Proof for DTF2THF_3332
% 165.61/24.94 thf(type_def_6, type, option: ($tType) > $tType).
% 165.61/24.94 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 165.61/24.94 thf(type_def_8, type, set: ($tType) > $tType).
% 165.61/24.94 thf(type_def_9, type, fml: $tType).
% 165.61/24.94 thf(type_def_10, type, variable: $tType).
% 165.61/24.94 thf(type_def_11, type, trm: $tType).
% 165.61/24.94 thf(type_def_12, type, char: $tType).
% 165.61/24.94 thf(type_def_13, type, real: $tType).
% 165.61/24.94 thf(type_def_14, type, game: $tType).
% 165.61/24.94 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 165.61/24.94 thf(func_def_1, type, variable: $tType).
% 165.61/24.94 thf(func_def_2, type, option: ($tType) > $tType).
% 165.61/24.94 thf(func_def_3, type, game: $tType).
% 165.61/24.94 thf(func_def_4, type, char: $tType).
% 165.61/24.94 thf(func_def_5, type, trm: $tType).
% 165.61/24.94 thf(func_def_6, type, fml: $tType).
% 165.61/24.94 thf(func_def_7, type, real: $tType).
% 165.61/24.94 thf(func_def_8, type, set: ($tType) > $tType).
% 165.61/24.94 thf(func_def_9, type, bounded_lattice: !>[X0: $tType]:($o)).
% 165.61/24.94 thf(func_def_10, type, type: !>[X0: $tType]:($o)).
% 165.61/24.94 thf(func_def_11, type, bot: !>[X0: $tType]:($o)).
% 165.61/24.94 thf(func_def_12, type, lattice: !>[X0: $tType]:($o)).
% 165.61/24.94 thf(func_def_13, type, semilattice_inf: !>[X0: $tType]:($o)).
% 165.61/24.94 thf(func_def_14, type, bounded_lattice_bot: !>[X0: $tType]:($o)).
% 165.61/24.94 thf(func_def_15, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 165.61/24.94 thf(func_def_16, type, inf_inf: !>[X0: $tType]:(X0 > X0 > X0)).
% 165.61/24.94 thf(func_def_17, type, none: !>[X0: $tType]:(option @ X0)).
% 165.61/24.94 thf(func_def_18, type, some: !>[X0: $tType]:(X0 > option @ X0)).
% 165.61/24.94 thf(func_def_19, type, case_option: !>[X0: $tType, X1: $tType]:(X0 > (X1 > X0) > option @ X1 > X0)).
% 165.61/24.94 thf(func_def_20, type, the: !>[X0: $tType]:(option @ X0 > X0)).
% 165.61/24.94 thf(func_def_21, type, bot_bot: !>[X0: $tType]:(X0)).
% 165.61/24.94 thf(func_def_22, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 165.61/24.94 thf(func_def_23, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 165.61/24.94 thf(func_def_24, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 165.61/24.94 thf(func_def_25, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 165.61/24.94 thf(func_def_26, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 165.61/24.94 thf(func_def_27, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 165.61/24.94 thf(func_def_28, type, static_FVF: fml > set @ variable).
% 165.61/24.94 thf(func_def_29, type, static_FVT: trm > set @ variable).
% 165.61/24.94 thf(func_def_30, type, char2: $o > $o > $o > $o > $o > $o > $o > $o > char).
% 165.61/24.94 thf(func_def_31, type, geq: trm > trm > fml).
% 165.61/24.94 thf(func_def_32, type, pred: char > trm > fml).
% 165.61/24.94 thf(func_def_33, type, const: char > trm).
% 165.61/24.94 thf(func_def_34, type, differential: trm > trm).
% 165.61/24.94 thf(func_def_35, type, func: char > trm > trm).
% 165.61/24.94 thf(func_def_36, type, number: real > trm).
% 165.61/24.94 thf(func_def_37, type, plus: trm > trm > trm).
% 165.61/24.94 thf(func_def_38, type, times: trm > trm > trm).
% 165.61/24.94 thf(func_def_39, type, var: variable > trm).
% 165.61/24.94 thf(func_def_40, type, uSubst259074819ntialo: option @ trm > option @ trm).
% 165.61/24.94 thf(func_def_41, type, uSubst1556497037e_Geqo: option @ trm > option @ trm > option @ fml).
% 165.61/24.94 thf(func_def_42, type, uSubst1112714340_Pluso: option @ trm > option @ trm > option @ trm).
% 165.61/24.94 thf(func_def_43, type, uSubst190403692_Testo: option @ fml > option @ game).
% 165.61/24.94 thf(func_def_44, type, uSubst277968634Timeso: option @ trm > option @ trm > option @ trm).
% 165.61/24.94 thf(func_def_45, type, uSubst_Mirabelle_dot: trm).
% 165.61/24.94 thf(func_def_46, type, uSubst969145931substt: trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_47, type, uSubst1138577137pconst: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > char > option @ trm).
% 165.61/24.94 thf(func_def_48, type, uSubst95898978stappf: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > fml > option @ fml).
% 165.61/24.94 thf(func_def_49, type, uSubst95898992stappt: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > option @ trm).
% 165.61/24.94 thf(func_def_50, type, uSubst2096773001pt_rel: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > $o).
% 165.61/24.94 thf(func_def_51, type, accp: !>[X0: $tType]:((X0 > X0 > $o) > X0 > $o)).
% 165.61/24.94 thf(func_def_52, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 165.61/24.94 thf(func_def_53, type, ua: set @ variable).
% 165.61/24.94 thf(func_def_54, type, va: set @ variable).
% 165.61/24.94 thf(func_def_55, type, sigma: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_56, type, theta: trm).
% 165.61/24.94 thf(func_def_57, type, p: char).
% 165.61/24.94 thf(func_def_72, type, sP0: !>[X0: $tType]:(option @ X0 > option @ X0 > $o)).
% 165.61/24.94 thf(func_def_73, type, sP1: option @ trm > option @ trm > option @ fml > $o).
% 165.61/24.94 thf(func_def_74, type, sP2: option @ fml > option @ trm > option @ trm > $o).
% 165.61/24.94 thf(func_def_75, type, sP3: (trm > $o) > $o).
% 165.61/24.94 thf(func_def_76, type, sP4: (trm > $o) > $o).
% 165.61/24.94 thf(func_def_77, type, sP5: !>[X0: $tType, X1: $tType]:((option @ X0 > option @ X1 > $o) > option @ X1 > option @ X0 > $o)).
% 165.61/24.94 thf(func_def_78, type, sP6: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X1 > $o) > X1 > option @ X0 > $o)).
% 165.61/24.94 thf(func_def_79, type, sP7: option @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o).
% 165.61/24.94 thf(func_def_80, type, sP8: option @ trm > trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > $o).
% 165.61/24.94 thf(func_def_81, type, sP9: option @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o).
% 165.61/24.94 thf(func_def_82, type, sP10: trm > option @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > $o).
% 165.61/24.94 thf(func_def_83, type, sP11: trm > option @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > $o).
% 165.61/24.94 thf(func_def_84, type, sP12: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > trm > $o).
% 165.61/24.94 thf(func_def_85, type, sP13: !>[X0: $tType, X1: $tType]:(X1 > (X1 > $o) > (X0 > X1) > option @ X0 > $o)).
% 165.61/24.94 thf(func_def_86, type, sP14: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > $o).
% 165.61/24.94 thf(func_def_87, type, sP15: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > $o).
% 165.61/24.94 thf(func_def_88, type, sP16: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > $o).
% 165.61/24.94 thf(func_def_89, type, sP17: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > $o).
% 165.61/24.94 thf(func_def_90, type, sP18: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > $o).
% 165.61/24.94 thf(func_def_91, type, sP19: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > $o).
% 165.61/24.94 thf(func_def_92, type, sP20: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > $o).
% 165.61/24.94 thf(func_def_93, type, sP21: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > $o).
% 165.61/24.94 thf(func_def_94, type, sK22: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 165.61/24.94 thf(func_def_95, type, sK23: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 165.61/24.94 thf(func_def_96, type, sK24: char > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > trm).
% 165.61/24.94 thf(func_def_97, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1 > set @ X0) > X0 > product_prod @ X2 @ X1 > X2)).
% 165.61/24.94 thf(func_def_98, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1 > set @ X0) > X0 > product_prod @ X2 @ X1 > X1)).
% 165.61/24.94 thf(func_def_99, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > product_prod @ X1 @ X0 > (X1 > X0 > X2 > $o) > X1)).
% 165.61/24.94 thf(func_def_100, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > product_prod @ X1 @ X0 > (X1 > X0 > X2 > $o) > X0)).
% 165.61/24.94 thf(func_def_101, type, sK29: char > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > trm).
% 165.61/24.94 thf(func_def_102, type, sK30: option @ game > game).
% 165.61/24.94 thf(func_def_103, type, sK31: !>[X0: $tType]:(option @ X0 > (X0 > $o) > X0)).
% 165.61/24.94 thf(func_def_104, type, sK32: (option @ trm > $o) > trm).
% 165.61/24.94 thf(func_def_105, type, sK33: product_prod @ option @ game @ option @ game > option @ game).
% 165.61/24.94 thf(func_def_106, type, sK34: product_prod @ option @ game @ option @ game > game).
% 165.61/24.94 thf(func_def_107, type, sK35: product_prod @ option @ game @ option @ game > game).
% 165.61/24.94 thf(func_def_108, type, sK36: product_prod @ option @ game @ option @ game > game).
% 165.61/24.94 thf(func_def_109, type, sK37: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 165.61/24.94 thf(func_def_110, type, sK38: product_prod @ char @ option @ trm > char).
% 165.61/24.94 thf(func_def_111, type, sK39: product_prod @ char @ option @ trm > char).
% 165.61/24.94 thf(func_def_112, type, sK40: product_prod @ char @ option @ trm > trm).
% 165.61/24.94 thf(func_def_113, type, sK41: trm > trm).
% 165.61/24.94 thf(func_def_114, type, sK42: trm > trm).
% 165.61/24.94 thf(func_def_115, type, sK43: trm > char).
% 165.61/24.94 thf(func_def_116, type, sK44: trm > variable).
% 165.61/24.94 thf(func_def_117, type, sK45: trm > trm).
% 165.61/24.94 thf(func_def_118, type, sK46: trm > trm).
% 165.61/24.94 thf(func_def_119, type, sK47: trm > trm).
% 165.61/24.94 thf(func_def_120, type, sK48: trm > char).
% 165.61/24.94 thf(func_def_121, type, sK49: trm > trm).
% 165.61/24.94 thf(func_def_122, type, sK50: trm > real).
% 165.61/24.94 thf(func_def_123, type, sK51: option @ trm > trm).
% 165.61/24.94 thf(func_def_124, type, sK52: option @ trm > option @ trm > option @ fml > trm).
% 165.61/24.94 thf(func_def_125, type, sK53: option @ trm > option @ trm > option @ fml > trm).
% 165.61/24.94 thf(func_def_126, type, sK54: !>[X0: $tType]:((X0 > $o) > X0)).
% 165.61/24.94 thf(func_def_127, type, sK55: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 165.61/24.94 thf(func_def_128, type, sK56: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 165.61/24.94 thf(func_def_129, type, sK57: (option @ game > option @ game > $o) > option @ game).
% 165.61/24.94 thf(func_def_130, type, sK58: (option @ game > option @ game > $o) > game).
% 165.61/24.94 thf(func_def_131, type, sK59: (option @ game > option @ game > $o) > game).
% 165.61/24.94 thf(func_def_132, type, sK60: (option @ game > option @ game > $o) > game).
% 165.61/24.94 thf(func_def_133, type, sK61: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 165.61/24.94 thf(func_def_134, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X1 > $o) > X0)).
% 165.61/24.94 thf(func_def_135, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X1 > $o) > X2)).
% 165.61/24.94 thf(func_def_136, type, sK64: (trm > $o) > trm).
% 165.61/24.94 thf(func_def_137, type, sK65: (trm > $o) > trm).
% 165.61/24.94 thf(func_def_138, type, sK66: (trm > $o) > trm).
% 165.61/24.94 thf(func_def_139, type, sK67: (trm > $o) > trm).
% 165.61/24.94 thf(func_def_140, type, sK68: (trm > $o) > trm).
% 165.61/24.94 thf(func_def_141, type, sK69: (trm > $o) > real).
% 165.61/24.94 thf(func_def_142, type, sK70: (trm > $o) > char).
% 165.61/24.94 thf(func_def_143, type, sK71: (trm > $o) > trm).
% 165.61/24.94 thf(func_def_144, type, sK72: (trm > $o) > variable).
% 165.61/24.94 thf(func_def_145, type, sK73: (trm > $o) > char).
% 165.61/24.94 thf(func_def_146, type, sK74: !>[X0: $tType, X1: $tType]:((option @ X0 > option @ X1 > $o) > option @ X1 > option @ X0 > X0)).
% 165.61/24.94 thf(func_def_147, type, sK75: !>[X0: $tType, X1: $tType]:((option @ X0 > option @ X1 > $o) > option @ X1 > option @ X0 > X1)).
% 165.61/24.94 thf(func_def_148, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 165.61/24.94 thf(func_def_149, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 165.61/24.94 thf(func_def_150, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 165.61/24.94 thf(func_def_151, type, sK79: !>[X0: $tType]:(option @ X0 > X0)).
% 165.61/24.94 thf(func_def_152, type, sK80: option @ fml > fml).
% 165.61/24.94 thf(func_def_153, type, sK81: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_154, type, sK82: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable).
% 165.61/24.94 thf(func_def_155, type, sK83: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > variable).
% 165.61/24.94 thf(func_def_156, type, sK84: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_157, type, sK85: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable).
% 165.61/24.94 thf(func_def_158, type, sK86: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > trm).
% 165.61/24.94 thf(func_def_159, type, sK87: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_160, type, sK88: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable).
% 165.61/24.94 thf(func_def_161, type, sK89: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > trm).
% 165.61/24.94 thf(func_def_162, type, sK90: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > trm).
% 165.61/24.94 thf(func_def_163, type, sK91: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_164, type, sK92: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable).
% 165.61/24.94 thf(func_def_165, type, sK93: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > real).
% 165.61/24.94 thf(func_def_166, type, sK94: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_167, type, sK95: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable).
% 165.61/24.94 thf(func_def_168, type, sK96: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > char).
% 165.61/24.94 thf(func_def_169, type, sK97: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_170, type, sK98: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable).
% 165.61/24.94 thf(func_def_171, type, sK99: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > trm).
% 165.61/24.94 thf(func_def_172, type, sK100: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > trm).
% 165.61/24.94 thf(func_def_173, type, sK101: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_174, type, sK102: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable).
% 165.61/24.94 thf(func_def_175, type, sK103: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > char).
% 165.61/24.94 thf(func_def_176, type, sK104: product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > trm).
% 165.61/24.94 thf(func_def_177, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X0)).
% 165.61/24.94 thf(func_def_178, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X1)).
% 165.61/24.94 thf(func_def_179, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X2)).
% 165.61/24.94 thf(func_def_180, type, sK108: !>[X0: $tType]:(option @ X0 > X0)).
% 165.61/24.94 thf(func_def_181, type, sK109: (option @ game > option @ fml > $o) > game).
% 165.61/24.94 thf(func_def_182, type, sK110: (option @ game > option @ fml > $o) > game).
% 165.61/24.94 thf(func_def_183, type, sK111: (option @ game > option @ fml > $o) > fml).
% 165.61/24.94 thf(func_def_184, type, sK112: (option @ game > option @ fml > $o) > option @ fml).
% 165.61/24.94 thf(func_def_185, type, sK113: product_prod @ option @ fml @ option @ fml > fml).
% 165.61/24.94 thf(func_def_186, type, sK114: product_prod @ option @ fml @ option @ fml > fml).
% 165.61/24.94 thf(func_def_187, type, sK115: product_prod @ option @ fml @ option @ fml > fml).
% 165.61/24.94 thf(func_def_188, type, sK116: product_prod @ option @ fml @ option @ fml > option @ fml).
% 165.61/24.94 thf(func_def_189, type, sK117: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 165.61/24.94 thf(func_def_190, type, sK118: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 165.61/24.94 thf(func_def_191, type, sK119: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0)).
% 165.61/24.94 thf(func_def_192, type, sK120: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1)).
% 165.61/24.94 thf(func_def_193, type, sK121: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2)).
% 165.61/24.94 thf(func_def_194, type, sK122: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3)).
% 165.61/24.94 thf(func_def_195, type, sK123: (option @ trm > option @ trm > $o) > trm).
% 165.61/24.94 thf(func_def_196, type, sK124: (option @ trm > option @ trm > $o) > trm).
% 165.61/24.94 thf(func_def_197, type, sK125: (option @ trm > option @ trm > $o) > option @ trm).
% 165.61/24.94 thf(func_def_198, type, sK126: (option @ trm > option @ trm > $o) > trm).
% 165.61/24.94 thf(func_def_199, type, sK127: (option @ fml > option @ fml > $o) > fml).
% 165.61/24.94 thf(func_def_200, type, sK128: (option @ fml > option @ fml > $o) > fml).
% 165.61/24.94 thf(func_def_201, type, sK129: (option @ fml > option @ fml > $o) > fml).
% 165.61/24.94 thf(func_def_202, type, sK130: (option @ fml > option @ fml > $o) > option @ fml).
% 165.61/24.94 thf(func_def_203, type, sK131: !>[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)).
% 165.61/24.94 thf(func_def_204, type, sK132: !>[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)).
% 165.61/24.94 thf(func_def_205, type, sK133: !>[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)).
% 165.61/24.94 thf(func_def_206, type, sK134: !>[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)).
% 165.61/24.94 thf(func_def_207, type, sK135: !>[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)).
% 165.61/24.94 thf(func_def_208, type, sK136: !>[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)).
% 165.61/24.94 thf(func_def_209, type, sK137: product_prod @ variable @ option @ trm > variable).
% 165.61/24.94 thf(func_def_210, type, sK138: product_prod @ variable @ option @ trm > variable).
% 165.61/24.94 thf(func_def_211, type, sK139: product_prod @ variable @ option @ trm > trm).
% 165.61/24.94 thf(func_def_212, type, sK140: !>[X0: $tType]:((X0 > $o) > X0)).
% 165.61/24.94 thf(func_def_213, type, sK141: !>[X0: $tType]:(option @ X0 > X0)).
% 165.61/24.94 thf(func_def_214, type, sK142: (variable > option @ fml > $o) > variable).
% 165.61/24.94 thf(func_def_215, type, sK143: (variable > option @ fml > $o) > variable).
% 165.61/24.94 thf(func_def_216, type, sK144: (variable > option @ fml > $o) > fml).
% 165.61/24.94 thf(func_def_217, type, sK145: (variable > option @ trm > $o) > variable).
% 165.61/24.94 thf(func_def_218, type, sK146: (variable > option @ trm > $o) > variable).
% 165.61/24.94 thf(func_def_219, type, sK147: (variable > option @ trm > $o) > trm).
% 165.61/24.94 thf(func_def_220, type, sK148: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ X1 > X0) > (X2 > X1 > X0) > X2)).
% 165.61/24.94 thf(func_def_221, type, sK149: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ X1 > X0) > (X2 > X1 > X0) > X1)).
% 165.61/24.94 thf(func_def_222, type, sK150: !>[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)).
% 165.61/24.94 thf(func_def_223, type, sK151: !>[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)).
% 165.61/24.94 thf(func_def_224, type, sK152: !>[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)).
% 165.61/24.94 thf(func_def_225, type, sK153: !>[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)).
% 165.61/24.94 thf(func_def_226, type, sK154: !>[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)).
% 165.61/24.94 thf(func_def_227, type, sK155: !>[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)).
% 165.61/24.94 thf(func_def_228, type, sK156: !>[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)).
% 165.61/24.94 thf(func_def_229, type, sK157: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > trm > real).
% 165.61/24.94 thf(func_def_230, type, sK158: trm > option @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm).
% 165.61/24.94 thf(func_def_231, type, sK159: trm > option @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm).
% 165.61/24.94 thf(func_def_232, type, sK160: trm > option @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm).
% 165.61/24.94 thf(func_def_233, type, sK161: option @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > char).
% 165.61/24.94 thf(func_def_234, type, sK162: option @ trm > trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > variable).
% 165.61/24.94 thf(func_def_235, type, sK163: option @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > trm).
% 165.61/24.94 thf(func_def_236, type, sK164: option @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > trm).
% 165.61/24.94 thf(func_def_237, type, sK165: option @ trm > trm > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > char).
% 165.61/24.94 thf(func_def_238, type, sK166: option @ trm > trm > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > trm).
% 165.61/24.94 thf(func_def_239, type, sK167: !>[X0: $tType]:(set @ X0 > X0)).
% 165.61/24.94 thf(func_def_240, type, sK168: (option @ game > $o) > game).
% 165.61/24.94 thf(func_def_241, type, sK169: option @ trm > trm).
% 165.61/24.94 thf(func_def_242, type, sK170: !>[X0: $tType]:((option @ X0 > $o) > X0)).
% 165.61/24.94 thf(func_def_243, type, sK171: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_244, type, sK172: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable).
% 165.61/24.94 thf(func_def_245, type, sK173: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > variable).
% 165.61/24.94 thf(func_def_246, type, sK174: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_247, type, sK175: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable).
% 165.61/24.94 thf(func_def_248, type, sK176: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm).
% 165.61/24.94 thf(func_def_249, type, sK177: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_250, type, sK178: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable).
% 165.61/24.94 thf(func_def_251, type, sK179: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm).
% 165.61/24.94 thf(func_def_252, type, sK180: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm).
% 165.61/24.94 thf(func_def_253, type, sK181: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_254, type, sK182: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable).
% 165.61/24.94 thf(func_def_255, type, sK183: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm).
% 165.61/24.94 thf(func_def_256, type, sK184: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm).
% 165.61/24.94 thf(func_def_257, type, sK185: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_258, type, sK186: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable).
% 165.61/24.94 thf(func_def_259, type, sK187: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > char).
% 165.61/24.94 thf(func_def_260, type, sK188: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm).
% 165.61/24.94 thf(func_def_261, type, sK189: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_262, type, sK190: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable).
% 165.61/24.94 thf(func_def_263, type, sK191: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > char).
% 165.61/24.94 thf(func_def_264, type, sK192: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_265, type, sK193: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable).
% 165.61/24.94 thf(func_def_266, type, sK194: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > real).
% 165.61/24.94 thf(func_def_267, type, sK195: product_prod @ option @ trm @ option @ trm > trm).
% 165.61/24.94 thf(func_def_268, type, sK196: product_prod @ option @ trm @ option @ trm > trm).
% 165.61/24.94 thf(func_def_269, type, sK197: product_prod @ option @ trm @ option @ trm > trm).
% 165.61/24.94 thf(func_def_270, type, sK198: product_prod @ option @ trm @ option @ trm > option @ trm).
% 165.61/24.94 thf(func_def_271, type, sK199: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 165.61/24.94 thf(func_def_272, type, sK200: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 165.61/24.94 thf(func_def_273, type, sK201: char > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > fml).
% 165.61/24.94 thf(func_def_274, type, sK202: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X0 > $o) > (X1 > $o) > X1)).
% 165.61/24.94 thf(func_def_275, type, sK203: (char > option @ trm > $o) > char).
% 165.61/24.94 thf(func_def_276, type, sK204: (char > option @ trm > $o) > char).
% 165.61/24.94 thf(func_def_277, type, sK205: (char > option @ trm > $o) > trm).
% 165.61/24.94 thf(func_def_278, type, sK206: option @ trm > trm).
% 165.61/24.94 thf(func_def_279, type, sK207: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > product_prod @ X1 @ X0 > X1)).
% 165.61/24.94 thf(func_def_280, type, sK208: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > product_prod @ X1 @ X0 > X0)).
% 165.61/24.94 thf(func_def_281, type, sK209: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 165.61/24.94 thf(func_def_282, type, sK210: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 165.61/24.94 thf(func_def_283, type, sK211: !>[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)).
% 165.61/24.94 thf(func_def_284, type, sK212: !>[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)).
% 165.61/24.94 thf(func_def_285, type, sK213: !>[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)).
% 165.61/24.94 thf(func_def_286, type, sK214: !>[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)).
% 165.61/24.94 thf(func_def_287, type, sK215: !>[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)).
% 165.61/24.94 thf(func_def_288, type, sK216: !>[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)).
% 165.61/24.94 thf(func_def_289, type, sK217: !>[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)).
% 165.61/24.94 thf(func_def_290, type, sK218: option @ game > game).
% 165.61/24.94 thf(func_def_291, type, sK219: !>[X0: $tType]:(set @ X0 > X0)).
% 165.61/24.94 thf(func_def_292, type, sK220: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 165.61/24.94 thf(func_def_293, type, sK221: product_prod @ variable @ option @ fml > variable).
% 165.61/24.94 thf(func_def_294, type, sK222: product_prod @ variable @ option @ fml > variable).
% 165.61/24.94 thf(func_def_295, type, sK223: product_prod @ variable @ option @ fml > fml).
% 165.61/24.94 thf(func_def_296, type, sK224: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_297, type, sK225: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable).
% 165.61/24.94 thf(func_def_298, type, sK226: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm).
% 165.61/24.94 thf(func_def_299, type, sK227: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm).
% 165.61/24.94 thf(func_def_300, type, sK228: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_301, type, sK229: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable).
% 165.61/24.94 thf(func_def_302, type, sK230: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm).
% 165.61/24.94 thf(func_def_303, type, sK231: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm).
% 165.61/24.94 thf(func_def_304, type, sK232: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_305, type, sK233: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable).
% 165.61/24.94 thf(func_def_306, type, sK234: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > char).
% 165.61/24.94 thf(func_def_307, type, sK235: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm).
% 165.61/24.94 thf(func_def_308, type, sK236: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_309, type, sK237: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable).
% 165.61/24.94 thf(func_def_310, type, sK238: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > real).
% 165.61/24.94 thf(func_def_311, type, sK239: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_312, type, sK240: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable).
% 165.61/24.94 thf(func_def_313, type, sK241: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > variable).
% 165.61/24.94 thf(func_def_314, type, sK242: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_315, type, sK243: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable).
% 165.61/24.94 thf(func_def_316, type, sK244: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm).
% 165.61/24.94 thf(func_def_317, type, sK245: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 165.61/24.94 thf(func_def_318, type, sK246: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable).
% 165.61/24.94 thf(func_def_319, type, sK247: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > char).
% 165.61/24.94 thf(func_def_320, type, sK248: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > (X0 > X1 > $o) > X0)).
% 165.61/24.94 thf(func_def_321, type, sK249: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > (X0 > X1 > $o) > X1)).
% 165.61/24.94 thf(func_def_322, type, sK250: char > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > trm).
% 165.61/24.94 thf(func_def_323, type, sK251: !>[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)).
% 165.61/24.94 thf(func_def_324, type, sK252: !>[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)).
% 165.61/24.94 thf(func_def_325, type, sK253: !>[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)).
% 165.61/24.94 thf(func_def_326, type, sK254: !>[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)).
% 165.61/24.94 thf(func_def_327, type, sK255: !>[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)).
% 165.61/24.94 thf(func_def_328, type, sK256: !>[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)).
% 165.61/24.94 thf(func_def_329, type, sK257: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 165.61/24.94 thf(func_def_330, type, sK258: !>[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)).
% 165.61/24.94 thf(func_def_331, type, sK259: !>[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)).
% 165.61/24.94 thf(func_def_332, type, sK260: !>[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)).
% 165.61/24.94 thf(func_def_333, type, sK261: !>[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)).
% 165.61/24.94 thf(func_def_334, type, sK262: !>[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)).
% 165.61/24.94 thf(func_def_335, type, sK263: product_prod @ option @ game @ option @ fml > game).
% 165.61/24.94 thf(func_def_336, type, sK264: product_prod @ option @ game @ option @ fml > option @ fml).
% 165.61/24.94 thf(func_def_337, type, sK265: product_prod @ option @ game @ option @ fml > game).
% 165.61/24.94 thf(func_def_338, type, sK266: product_prod @ option @ game @ option @ fml > fml).
% 165.61/24.94 thf(func_def_339, type, sK267: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 165.61/24.94 thf(func_def_340, type, sK268: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 165.61/24.94 thf(func_def_341, type, sK269: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 165.61/24.94 thf(func_def_342, type, sK270: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 165.61/24.94 thf(func_def_343, type, sK271: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > (X0 > X1 > X2 > $o) > product_prod @ X0 @ X1 > X0)).
% 165.61/24.94 thf(func_def_344, type, sK272: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > (X0 > X1 > X2 > $o) > product_prod @ X0 @ X1 > X1)).
% 165.61/24.94 thf(func_def_345, type, sK273: !>[X0: $tType]:(set @ X0 > X0)).
% 165.61/24.94 thf(func_def_346, type, sK274: (option @ fml > $o) > fml).
% 165.61/24.94 thf(func_def_347, type, sK275: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X0)).
% 165.61/24.94 thf(func_def_348, type, sK276: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X2)).
% 165.61/24.94 thf(func_def_349, type, sK277: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0)).
% 165.61/24.94 thf(func_def_350, type, sK278: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1)).
% 165.61/24.94 thf(func_def_351, type, sK279: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2)).
% 165.61/24.94 thf(func_def_352, type, sK280: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3)).
% 165.61/24.94 thf(func_def_353, type, sK281: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4)).
% 165.61/24.94 thf(func_def_354, type, sK282: option @ fml > fml).
% 165.61/24.94 thf(func_def_356, type, ph284: !>[X0: $tType]:(X0)).
% 165.61/24.94 thf(f2292,plain,(
% 165.61/24.94 $false),
% 165.61/24.94 inference(avatar_sat_refutation,[status(thm)],[f2056,f2291])).
% 165.61/24.94 thf(f2291,plain,(
% 165.61/24.94 ~spl283_1),
% 165.61/24.94 inference(avatar_contradiction_clause,[status(thm)],[f2290])).
% 165.61/24.94 thf(f2290,plain,(
% 165.61/24.94 $false | ~spl283_1),
% 165.61/24.94 inference(trivial_inequality_removal,[status(thm)],[f2287])).
% 165.61/24.94 thf(f2287,plain,(
% 165.61/24.94 (none @ fml != none @ fml) | ~spl283_1),
% 165.61/24.94 inference(superposition,[status(thm)],[f1488,f2054])).
% 165.61/24.94 thf(f2054,plain,(
% 165.61/24.94 ( ! [X1 : trm] : ((none @ fml = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ X1)))) ) | ~spl283_1),
% 165.61/24.94 inference(avatar_component_clause,[status(thm)],[f2053])).
% 165.61/24.94 thf(f2053,definition,(
% 165.61/24.94 spl283_1 <=> ! [X1 : trm] : (none @ fml = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ X1)))),
% 165.61/24.94 introduced(definition,[new_symbols(naming,[spl283_1])],[avatar_definition])).
% 165.61/24.94 thf(f1488,plain,(
% 165.61/24.94 (none @ fml != (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)))),
% 165.61/24.94 inference(cnf_transformation,[status(thm)],[f2])).
% 165.61/24.94 thf(f2,axiom,(
% 165.61/24.94 (none @ fml != (uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)))),
% 165.61/24.94 file('/export/starexec/sandbox/tmp/tmp.oidpnoGwex/DTF2THF_3332.p',fact_1_Pred_Oprems_I2_J)).
% 165.61/24.94 thf(f2056,plain,(
% 165.61/24.94 spl283_1 | spl283_1),
% 165.61/24.94 inference(avatar_split_clause,[status(thm)],[f2042,f2053,f2053])).
% 165.61/24.94 thf(f2042,plain,(
% 165.61/24.94 ( ! [X0 : trm,X1 : trm] : ((none @ fml = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ X1))) | (none @ fml = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ X0)))) )),
% 165.61/24.94 inference(trivial_inequality_removal,[status(thm)],[f2033])).
% 165.61/24.94 thf(f2033,plain,(
% 165.61/24.94 ( ! [X0 : trm,X1 : trm] : ((none @ fml = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ X1))) | (none @ fml = (uSubst95898978stappf @ sigma @ va @ (pred @ p @ X0))) | (bot_bot @ set @ variable != bot_bot @ set @ variable)) )),
% 165.61/24.94 inference(superposition,[status(thm)],[f2015,f1821])).
% 165.61/24.94 thf(f1821,plain,(
% 165.61/24.94 ( ! [X0 : set @ variable,X1 : trm] : ((bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVF @ (sK201 @ p @ X0 @ sigma)) @ X0)) | (none @ fml = (uSubst95898978stappf @ sigma @ X0 @ (pred @ p @ X1)))) )),
% 165.61/24.94 inference(trivial_inequality_removal,[status(thm)],[f1820])).
% 165.61/24.94 thf(f1820,plain,(
% 165.61/24.94 ( ! [X0 : set @ variable,X1 : trm] : ((bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVF @ (sK201 @ p @ X0 @ sigma)) @ X0)) | (none @ fml != none @ fml) | (none @ fml = (uSubst95898978stappf @ sigma @ X0 @ (pred @ p @ X1)))) )),
% 165.61/24.94 inference(superposition,[status(thm)],[f1358,f1633])).
% 165.61/24.94 thf(f1633,plain,(
% 165.61/24.94 ( ! [X2 : char,X3 : trm,X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X1 : set @ variable] : ((none @ fml = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ X0 @ X2)) | (none @ fml = (uSubst95898978stappf @ X0 @ X1 @ (pred @ X2 @ X3))) | (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVF @ (sK201 @ X2 @ X1 @ X0)) @ X1))) )),
% 165.61/24.94 inference(cnf_transformation,[status(thm)],[f1212])).
% 165.61/24.94 thf(f1212,plain,(
% 165.61/24.94 ! [X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X1 : set @ variable,X2 : char,X3 : trm] : (((none @ trm != (uSubst95898992stappt @ X0 @ X1 @ X3)) & (((bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVF @ (sK201 @ X2 @ X1 @ X0)) @ X1)) & ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ X0 @ X2) = (some @ fml @ (sK201 @ X2 @ X1 @ X0)))) | (none @ fml = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ X0 @ X2)))) | (none @ fml = (uSubst95898978stappf @ X0 @ X1 @ (pred @ X2 @ X3))))),
% 165.61/24.94 inference(skolemisation,[status(esa),new_symbols(skolem,[sK201])],[f823,f1211])).
% 165.61/24.94 thf(f1211,plain,(
% 165.61/24.94 ! [X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X1 : set @ variable,X2 : char] : (? [X4 : fml] : ((bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVF @ X4) @ X1)) & ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ X0 @ X2) = (some @ fml @ X4))) => ((bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVF @ (sK201 @ X2 @ X1 @ X0)) @ X1)) & ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ X0 @ X2) = (some @ fml @ (sK201 @ X2 @ X1 @ X0)))))),
% 165.61/24.94 introduced(definition,[],[choice_axiom])).
% 165.61/24.94 thf(f823,plain,(
% 165.61/24.94 ! [X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X1 : set @ variable,X2 : char,X3 : trm] : (((none @ trm != (uSubst95898992stappt @ X0 @ X1 @ X3)) & (? [X4 : fml] : ((bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVF @ X4) @ X1)) & ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ X0 @ X2) = (some @ fml @ X4))) | (none @ fml = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ X0 @ X2)))) | (none @ fml = (uSubst95898978stappf @ X0 @ X1 @ (pred @ X2 @ X3))))),
% 165.61/24.94 inference(ennf_transformation,[status(thm)],[f683])).
% 165.61/24.94 thf(f683,plain,(
% 165.61/24.94 ! [X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X1 : set @ variable,X2 : char,X3 : trm] : ((none @ fml != (uSubst95898978stappf @ X0 @ X1 @ (pred @ X2 @ X3))) => ((none @ trm != (uSubst95898992stappt @ X0 @ X1 @ X3)) & (? [X4 : fml] : ((bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVF @ X4) @ X1)) & ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ X0 @ X2) = (some @ fml @ X4))) | (none @ fml = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ X0 @ X2)))))),
% 165.61/24.94 inference(rectify,[status(thm)],[f439])).
% 165.61/24.94 thf(f439,plain,(
% 165.61/24.94 ! [X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X1 : set @ variable,X2 : char,X3 : trm] : ((none @ fml != (uSubst95898978stappf @ X0 @ X1 @ (pred @ X2 @ X3))) => (((none @ fml = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ X0 @ X2)) | ? [X8 : fml] : ((bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVF @ X8) @ X1)) & ((some @ fml @ X8) = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ X0 @ X2)))) & (none @ trm != (uSubst95898992stappt @ X0 @ X1 @ X3))))),
% 165.61/24.94 inference(fool_elimination,[status(thm)],[f438])).
% 165.61/24.94 thf(f438,plain,(
% 165.61/24.94 ! [X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X1 : set @ variable,X2 : char,X3 : trm] : ((none @ fml != (uSubst95898978stappf @ X0 @ X1 @ (pred @ X2 @ X3))) => (((none @ fml = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X4 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X5 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X6 : char > option @ fml, X7 : char > option @ game] : (X6)))))) @ X0 @ X2)) | ? [X8 : fml] : ((bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVF @ X8) @ X1)) & ((some @ fml @ X8) = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X9 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X10 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X11 : char > option @ fml, X12 : char > option @ game] : (X11)))))) @ X0 @ X2)))) & (none @ trm != (uSubst95898992stappt @ X0 @ X1 @ X3))))),
% 165.61/24.94 inference(rectify,[status(thm)],[f78])).
% 165.61/24.94 thf(f78,axiom,(
% 165.61/24.94 ! [X32 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X35 : set @ variable,X33 : char,X36 : trm] : ((none @ fml != (uSubst95898978stappf @ X32 @ X35 @ (pred @ X33 @ X36))) => (((none @ fml = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X13 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X14 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X15 : char > option @ fml, X16 : char > option @ game] : (X15)))))) @ X32 @ X33)) | ? [X70 : fml] : ((bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVF @ X70) @ X35)) & ((some @ fml @ X70) = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X13 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X14 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X15 : char > option @ fml, X16 : char > option @ game] : (X15)))))) @ X32 @ X33)))) & ((uSubst95898992stappt @ X32 @ X35 @ X36) != none @ trm)))),
% 165.61/24.94 file('/export/starexec/sandbox/tmp/tmp.oidpnoGwex/DTF2THF_3332.p',fact_77_usubstappf__pred__conv)).
% 165.61/24.94 thf(f1358,plain,(
% 165.61/24.94 (none @ fml != (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))),
% 165.61/24.94 inference(cnf_transformation,[status(thm)],[f642])).
% 165.61/24.94 thf(f642,plain,(
% 165.61/24.94 (none @ fml != (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))),
% 165.61/24.94 inference(flattening,[status(thm)],[f298])).
% 165.61/24.94 thf(f298,plain,(
% 165.61/24.94 ~(none @ fml = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))),
% 165.61/24.94 inference(fool_elimination,[status(thm)],[f297])).
% 165.61/24.94 thf(f297,plain,(
% 165.61/24.94 ~((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : char > option @ fml, X3 : char > option @ game] : (X2)))))) @ sigma @ p) = none @ fml)),
% 165.61/24.94 inference(rectify,[status(thm)],[f277])).
% 165.61/24.94 thf(f277,negated_conjecture,(
% 165.61/24.94 ~((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X13 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X14 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X15 : char > option @ fml, X16 : char > option @ game] : (X15)))))) @ sigma @ p) = none @ fml)),
% 165.61/24.94 inference(negated_conjecture,[status(cth)],[f276])).
% 165.61/24.94 thf(f276,conjecture,(
% 165.61/24.94 ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X13 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X14 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X15 : char > option @ fml, X16 : char > option @ game] : (X15)))))) @ sigma @ p) = none @ fml)),
% 165.61/24.94 file('/export/starexec/sandbox/tmp/tmp.oidpnoGwex/DTF2THF_3332.p',conj_0)).
% 165.61/24.94 thf(f2015,plain,(
% 165.61/24.94 ( ! [X0 : set @ variable,X1 : trm] : ((bot_bot @ set @ variable != (inf_inf @ set @ variable @ (static_FVF @ (sK201 @ p @ X0 @ sigma)) @ va)) | (none @ fml = (uSubst95898978stappf @ sigma @ X0 @ (pred @ p @ X1)))) )),
% 165.61/24.94 inference(forward_demodulation,[status(thm)],[f1987,f1590])).
% 165.61/24.94 thf(f1590,plain,(
% 165.61/24.94 ( ! [X0 : $tType,X1 : X0] : (((the @ X0 @ (some @ X0 @ X1)) = X1)) )),
% 165.61/24.94 inference(cnf_transformation,[status(thm)],[f733])).
% 165.61/24.94 thf(f733,plain,(
% 165.61/24.94 ! [X0 : $tType,X1 : X0] : ((the @ X0 @ (some @ X0 @ X1)) = X1)),
% 165.61/24.94 inference(rectify,[status(thm)],[f75])).
% 165.61/24.94 thf(f75,axiom,(
% 165.61/24.94 ! [X0 : $tType,X46 : X0] : ((the @ X0 @ (some @ X0 @ X46)) = X46)),
% 165.61/24.94 file('/export/starexec/sandbox/tmp/tmp.oidpnoGwex/DTF2THF_3332.p',fact_74_option_Osel)).
% 165.61/24.94 thf(f1987,plain,(
% 165.61/24.94 ( ! [X0 : set @ variable,X1 : trm] : ((none @ fml = (uSubst95898978stappf @ sigma @ X0 @ (pred @ p @ X1))) | (bot_bot @ set @ variable != (inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (some @ fml @ (sK201 @ p @ X0 @ sigma)))) @ va))) )),
% 165.61/24.94 inference(superposition,[status(thm)],[f1629,f1823])).
% 165.61/24.94 thf(f1823,plain,(
% 165.61/24.94 ( ! [X0 : set @ variable,X1 : trm] : (((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p) = (some @ fml @ (sK201 @ p @ X0 @ sigma))) | (none @ fml = (uSubst95898978stappf @ sigma @ X0 @ (pred @ p @ X1)))) )),
% 165.61/24.94 inference(trivial_inequality_removal,[status(thm)],[f1818])).
% 165.61/24.94 thf(f1818,plain,(
% 165.61/24.94 ( ! [X0 : set @ variable,X1 : trm] : (((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p) = (some @ fml @ (sK201 @ p @ X0 @ sigma))) | (none @ fml != none @ fml) | (none @ fml = (uSubst95898978stappf @ sigma @ X0 @ (pred @ p @ X1)))) )),
% 165.61/24.94 inference(superposition,[status(thm)],[f1358,f1632])).
% 165.61/24.94 thf(f1632,plain,(
% 165.61/24.94 ( ! [X2 : char,X3 : trm,X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X1 : set @ variable] : (((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ X0 @ X2) = (some @ fml @ (sK201 @ X2 @ X1 @ X0))) | (none @ fml = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ X0 @ X2)) | (none @ fml = (uSubst95898978stappf @ X0 @ X1 @ (pred @ X2 @ X3)))) )),
% 165.61/24.94 inference(cnf_transformation,[status(thm)],[f1212])).
% 165.61/24.94 thf(f1629,plain,(
% 165.61/24.94 (bot_bot @ set @ variable != (inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va))),
% 165.61/24.94 inference(cnf_transformation,[status(thm)],[f884])).
% 165.61/24.94 thf(f884,plain,(
% 165.61/24.94 (none @ fml != (uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) & (bot_bot @ set @ variable != (inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va))),
% 165.61/24.94 inference(ennf_transformation,[status(thm)],[f479])).
% 165.61/24.94 thf(f479,plain,(
% 165.61/24.94 ~((bot_bot @ set @ variable != (inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va)) => (none @ fml = (uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))))),
% 165.61/24.94 inference(fool_elimination,[status(thm)],[f478])).
% 165.61/24.94 thf(f478,plain,(
% 165.61/24.94 ~(((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : char > option @ fml, X3 : char > option @ game] : (X2)))))) @ sigma @ p))) @ va) != bot_bot @ set @ variable) => (none @ fml = (uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X4 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X5 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X6 : char > option @ fml, X7 : char > option @ game] : (X6)))))) @ sigma @ p)))))),
% 165.61/24.94 inference(rectify,[status(thm)],[f5])).
% 165.61/24.94 thf(f5,axiom,(
% 165.61/24.94 ~(((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X13 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X14 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X15 : char > option @ fml, X16 : char > option @ game] : (X15)))))) @ sigma @ p))) @ va) != bot_bot @ set @ variable) => (none @ fml = (uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X13 : char > option @ trm] : (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X14 : char > option @ trm] : (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X15 : char > option @ fml, X16 : char > option @ game] : (X15)))))) @ sigma @ p)))))),
% 165.61/24.94 file('/export/starexec/sandbox/tmp/tmp.oidpnoGwex/DTF2THF_3332.p',fact_4__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_092_060close_062)).
% 165.61/24.94 % SZS output end Proof for DTF2THF_3332
% 165.61/24.94 % (4787)------------------------------
% 165.61/24.94 % (4787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 165.61/24.94 % (4787)Termination reason: Refutation
% 165.61/24.94
% 165.61/24.94 % (4787)Memory used [KB]: 8955
% 165.61/24.94 % (4787)Time elapsed: 0.203 s
% 165.61/24.94 % (4787)Instructions burned: 679 (million)
% 165.61/24.94 % (4787)------------------------------
% 165.61/24.94 % (4787)------------------------------
% 165.61/24.94 % (3661)Success in time 23.263 s
%------------------------------------------------------------------------------