TSTP Solution File: ITP200^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP200^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n011.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 : Thu Aug 31 03:19:07 EDT 2023
% Result : Theorem 0.53s 1.14s
% Output : Proof 0.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.18 % Problem : ITP200^1 : TPTP v8.1.2. Released v7.5.0.
% 0.18/0.20 % Command : do_cvc5 %s %d
% 0.19/0.40 % Computer : n011.cluster.edu
% 0.19/0.40 % Model : x86_64 x86_64
% 0.19/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.40 % Memory : 8042.1875MB
% 0.19/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.40 % CPULimit : 300
% 0.19/0.40 % WCLimit : 300
% 0.19/0.40 % DateTime : Sun Aug 27 15:45:10 EDT 2023
% 0.19/0.41 % CPUTime :
% 0.26/0.58 %----Proving TH0
% 0.26/0.59 %------------------------------------------------------------------------------
% 0.26/0.59 % File : ITP200^1 : TPTP v8.1.2. Released v7.5.0.
% 0.26/0.59 % Domain : Interactive Theorem Proving
% 0.26/0.59 % Problem : Sledgehammer USubst problem prob_1407__6352118_1
% 0.26/0.59 % Version : Especial.
% 0.26/0.59 % English :
% 0.26/0.59
% 0.26/0.59 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.26/0.59 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.26/0.59 % Source : [Des21]
% 0.26/0.59 % Names : USubst/prob_1407__6352118_1 [Des21]
% 0.26/0.59
% 0.26/0.59 % Status : Theorem
% 0.26/0.59 % Rating : 0.23 v8.1.0, 0.27 v7.5.0
% 0.26/0.59 % Syntax : Number of formulae : 549 ( 161 unt; 196 typ; 0 def)
% 0.26/0.59 % Number of atoms : 1044 ( 570 equ; 0 cnn)
% 0.26/0.59 % Maximal formula atoms : 17 ( 2 avg)
% 0.26/0.59 % Number of connectives : 3358 ( 206 ~; 13 |; 55 &;2450 @)
% 0.26/0.59 % ( 0 <=>; 634 =>; 0 <=; 0 <~>)
% 0.26/0.59 % Maximal formula depth : 19 ( 7 avg)
% 0.26/0.59 % Number of types : 52 ( 51 usr)
% 0.26/0.59 % Number of type conns : 638 ( 638 >; 0 *; 0 +; 0 <<)
% 0.26/0.59 % Number of symbols : 148 ( 145 usr; 10 con; 0-3 aty)
% 0.26/0.59 % Number of variables : 1316 ( 173 ^;1110 !; 33 ?;1316 :)
% 0.26/0.59 % SPC : TH0_THM_EQU_NAR
% 0.26/0.59
% 0.26/0.59 % Comments : This file was generated by Sledgehammer 2021-02-23 15:38:23.912
% 0.26/0.59 %------------------------------------------------------------------------------
% 0.26/0.59 % Could-be-implicit typings (51)
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 0.26/0.59 produc1699626005le_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J_J,type,
% 0.26/0.59 produc1418842292n_game: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J_J,type,
% 0.26/0.59 set_Pr1918373977on_fml: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J_J,type,
% 0.26/0.59 set_Pr1062384839on_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J_J,type,
% 0.26/0.59 set_Pr519625031on_fml: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J_J,type,
% 0.26/0.59 set_Pr1588097095on_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J_J,type,
% 0.26/0.59 set_Pr1045337287on_fml: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.26/0.59 produc1928189433on_fml: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.26/0.59 produc2024965863on_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.26/0.59 produc591588199on_fml: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.26/0.59 produc1158546023on_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.26/0.59 produc1872652007on_fml: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J_J,type,
% 0.26/0.59 set_Pr1481565921on_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J_J,type,
% 0.26/0.59 set_Pr1969262145le_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.26/0.59 produc2018724225on_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 0.26/0.59 produc1279577057le_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J,type,
% 0.26/0.59 set_Pr1625152599n_game: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.26/0.59 set_Pr622314946on_fml: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.26/0.59 set_Pr1471344007on_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.26/0.59 set_Pr927595527on_fml: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J_J,type,
% 0.26/0.59 set_Pr181266295riable: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 0.26/0.59 produc1016592119n_game: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.26/0.59 produc1739631244on_fml: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.26/0.59 produc1072747943on_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.26/0.59 produc1456309597on_fml: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.26/0.59 produc1810527345on_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.26/0.59 produc46605351on_fml: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J,type,
% 0.26/0.59 produc432717079riable: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.26/0.59 set_Pr943832262on_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 0.26/0.59 set_Pr1235432374le_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.26/0.59 produc1024976764on_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.26/0.59 produc1408538418on_fml: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.26/0.59 produc464795408on_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp_Mt__Syntax__Otrm_J,type,
% 0.26/0.59 produc833882726rp_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 0.26/0.59 produc1367888000le_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__String__Ochar_Mt__String__Ochar_J_J,type,
% 0.26/0.59 set_Pr604539619r_char: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Syntax__Otrm_Mt__Syntax__Otrm_J_J,type,
% 0.26/0.59 set_Pr491793543rm_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__String__Ochar_Mt__String__Ochar_J,type,
% 0.26/0.59 produc1593312387r_char: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Product____Type__Oprod_It__Syntax__Otrm_Mt__Syntax__Otrm_J,type,
% 0.26/0.59 product_prod_trm_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.26/0.59 option_game: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.26/0.59 option_trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.26/0.59 option_fml: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Denotational____Semantics__Ointerp,type,
% 0.26/0.59 denotational_interp: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.26/0.59 set_variable: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Set__Oset_It__String__Ochar_J,type,
% 0.26/0.59 set_char: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Syntax__Ovariable,type,
% 0.26/0.59 variable: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Syntax__Ogame,type,
% 0.26/0.59 game: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__String__Ochar,type,
% 0.26/0.59 char: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Syntax__Otrm,type,
% 0.26/0.59 trm: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Syntax__Ofml,type,
% 0.26/0.59 fml: $tType ).
% 0.26/0.59
% 0.26/0.59 thf(ty_n_t__Real__Oreal,type,
% 0.26/0.59 real: $tType ).
% 0.26/0.59
% 0.26/0.59 % Explicit typings (145)
% 0.26/0.59 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.26/0.59 bNF_Gr1866170027on_fml: set_char > ( char > option_fml ) > ( char > option_fml ) > set_Pr927595527on_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.26/0.59 bNF_Gr756940202on_fml: set_char > ( char > option_game ) > ( char > option_fml ) > set_Pr622314946on_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.26/0.59 bNF_Gr1666135339on_trm: set_char > ( char > option_trm ) > ( char > option_trm ) > set_Pr1471344007on_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__String__Ochar_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm,type,
% 0.26/0.59 bNF_Gr852774302le_trm: set_char > ( char > set_variable ) > ( char > trm ) > set_Pr1235432374le_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__String__Ochar_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.26/0.59 bNF_Gr951178926on_trm: set_char > ( char > char ) > ( char > option_trm ) > set_Pr943832262on_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.26/0.59 bNF_Gr600956991on_fml: set_variable > ( variable > option_fml ) > ( variable > option_fml ) > set_Pr927595527on_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.26/0.59 bNF_Gr2142503190on_fml: set_variable > ( variable > option_game ) > ( variable > option_fml ) > set_Pr622314946on_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.26/0.59 bNF_Gr400922303on_trm: set_variable > ( variable > option_trm ) > ( variable > option_trm ) > set_Pr1471344007on_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Syntax__Ovariable_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm,type,
% 0.26/0.59 bNF_Gr1330108682le_trm: set_variable > ( variable > set_variable ) > ( variable > trm ) > set_Pr1235432374le_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Syntax__Ovariable_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.26/0.59 bNF_Gr1933470746on_trm: set_variable > ( variable > char ) > ( variable > option_trm ) > set_Pr943832262on_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_BNF__Greatest__Fixpoint_OrelImage_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.26/0.59 bNF_Gr806120164on_fml: set_Pr927595527on_fml > ( option_fml > option_fml ) > set_Pr927595527on_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Denotational__Semantics_OUvariation,type,
% 0.26/0.59 denota1419872369iation: ( variable > real ) > ( variable > real ) > set_variable > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ofml,type,
% 0.26/0.59 none_fml: option_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ogame,type,
% 0.26/0.59 none_game: option_game ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Otrm,type,
% 0.26/0.59 none_trm: option_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ofml,type,
% 0.26/0.59 some_fml: fml > option_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ogame,type,
% 0.26/0.59 some_game: game > option_game ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Otrm,type,
% 0.26/0.59 some_trm: trm > option_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Ofml,type,
% 0.26/0.59 case_option_o_fml: $o > ( fml > $o ) > option_fml > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Ogame,type,
% 0.26/0.59 case_option_o_game: $o > ( game > $o ) > option_game > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Otrm,type,
% 0.26/0.59 case_option_o_trm: $o > ( trm > $o ) > option_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ofml,type,
% 0.26/0.59 the_fml: option_fml > fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ogame,type,
% 0.26/0.59 the_game: option_game > game ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Otrm,type,
% 0.26/0.59 the_trm: option_trm > trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_It__Syntax__Ofml_J_M_062_It__Option__Ooption_It__Syntax__Ofml_J_M_Eo_J_J,type,
% 0.26/0.59 ord_le802833166_fml_o: ( option_fml > option_fml > $o ) > ( option_fml > option_fml > $o ) > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_It__Syntax__Ofml_J_M_Eo_J,type,
% 0.26/0.59 ord_le181580155_fml_o: ( option_fml > $o ) > ( option_fml > $o ) > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_It__Syntax__Ogame_J_M_062_It__Option__Ooption_It__Syntax__Ofml_J_M_Eo_J_J,type,
% 0.26/0.59 ord_le1588489637_fml_o: ( option_game > option_fml > $o ) > ( option_game > option_fml > $o ) > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_It__Syntax__Otrm_J_M_062_It__Option__Ooption_It__Syntax__Otrm_J_M_Eo_J_J,type,
% 0.26/0.59 ord_le847028878_trm_o: ( option_trm > option_trm > $o ) > ( option_trm > option_trm > $o ) > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_It__Syntax__Otrm_J_M_Eo_J,type,
% 0.26/0.59 ord_le1957133745_trm_o: ( option_trm > $o ) > ( option_trm > $o ) > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_Eo_J_J,type,
% 0.26/0.59 ord_le90123726_trm_o: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > ( produc1072747943on_trm > produc1072747943on_trm > $o ) > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_Eo_J,type,
% 0.26/0.59 ord_le1721128566_trm_o: ( produc1072747943on_trm > $o ) > ( produc1072747943on_trm > $o ) > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_Eo_J_J,type,
% 0.26/0.59 ord_le157637894_trm_o: ( produc464795408on_trm > produc464795408on_trm > $o ) > ( produc464795408on_trm > produc464795408on_trm > $o ) > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_Eo_J,type,
% 0.26/0.59 ord_le1222882015_trm_o: ( produc464795408on_trm > $o ) > ( produc464795408on_trm > $o ) > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_Eo_J_J,type,
% 0.26/0.59 ord_le370603054_trm_o: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > ( produc1024976764on_trm > produc1024976764on_trm > $o ) > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_Eo_J,type,
% 0.26/0.59 ord_le373274227_trm_o: ( produc1024976764on_trm > $o ) > ( produc1024976764on_trm > $o ) > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Set__Oset_It__Syntax__Ovariable_J_M_062_It__Syntax__Otrm_M_Eo_J_J,type,
% 0.26/0.59 ord_le691957041_trm_o: ( set_variable > trm > $o ) > ( set_variable > trm > $o ) > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__String__Ochar_M_062_It__Option__Ooption_It__Syntax__Otrm_J_M_Eo_J_J,type,
% 0.26/0.59 ord_le1890124833_trm_o: ( char > option_trm > $o ) > ( char > option_trm > $o ) > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__String__Ochar_M_Eo_J,type,
% 0.26/0.59 ord_less_eq_char_o: ( char > $o ) > ( char > $o ) > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 0.26/0.59 ord_le1407353162able_o: ( variable > $o ) > ( variable > $o ) > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.26/0.59 ord_le778974119on_fml: set_Pr927595527on_fml > set_Pr927595527on_fml > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.26/0.59 ord_le782333474on_fml: set_Pr622314946on_fml > set_Pr622314946on_fml > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.26/0.59 ord_le1322722599on_trm: set_Pr1471344007on_trm > set_Pr1471344007on_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 0.26/0.59 ord_le2102862870le_trm: set_Pr1235432374le_trm > set_Pr1235432374le_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.26/0.59 ord_le541293862on_trm: set_Pr943832262on_trm > set_Pr943832262on_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__String__Ochar_J,type,
% 0.26/0.59 ord_less_eq_set_char: set_char > set_char > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.26/0.59 ord_le282106107riable: set_variable > set_variable > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.26/0.59 order_272405634riable: ( set_variable > $o ) > set_variable ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Denotational____Semantics__Ointerp_001t__Syntax__Otrm,type,
% 0.26/0.59 produc1132922070rp_trm: denotational_interp > trm > produc833882726rp_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.26/0.59 produc909629463on_fml: option_fml > option_fml > produc46605351on_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.26/0.59 produc1447374177on_trm: option_fml > option_trm > produc1810527345on_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.26/0.59 produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.26/0.59 produc1111617711n_game: option_game > option_game > produc1016592119n_game ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.26/0.59 produc171850061on_fml: option_trm > option_fml > produc1456309597on_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.26/0.59 produc709594775on_trm: option_trm > option_trm > produc1072747943on_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 0.26/0.59 produc2015636557le_trm: produc1418842292n_game > produc1367888000le_trm > produc1699626005le_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.26/0.59 produc1367044951on_fml: produc46605351on_fml > produc46605351on_fml > produc1872652007on_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.26/0.59 produc2132972503on_trm: produc1810527345on_trm > produc1810527345on_trm > produc1158546023on_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.26/0.59 produc556056113on_fml: produc1739631244on_fml > produc1739631244on_fml > produc1928189433on_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.26/0.59 produc1235825367on_fml: produc1456309597on_fml > produc1456309597on_fml > produc591588199on_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.26/0.59 produc2001752919on_trm: produc1072747943on_trm > produc1072747943on_trm > produc2024965863on_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 0.26/0.59 produc1056455193le_trm: produc1367888000le_trm > produc1367888000le_trm > produc1279577057le_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.26/0.59 produc444919481on_trm: produc464795408on_trm > produc464795408on_trm > produc2018724225on_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.26/0.59 produc1766592463riable: set_variable > set_variable > produc432717079riable ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm,type,
% 0.26/0.59 produc1482344242le_trm: set_variable > trm > produc1367888000le_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.26/0.59 produc1500300866on_trm: char > option_trm > produc464795408on_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__String__Ochar_001t__String__Ochar,type,
% 0.26/0.59 produc19545147r_char: char > char > produc1593312387r_char ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Syntax__Otrm_001t__Syntax__Otrm,type,
% 0.26/0.59 product_Pair_trm_trm: trm > trm > product_prod_trm_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.26/0.59 produc1205977188on_fml: variable > option_fml > produc1408538418on_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Product__Type_OPair_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.26/0.59 produc1743721902on_trm: variable > option_trm > produc1024976764on_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.26/0.59 collec670974098on_fml: ( produc46605351on_fml > $o ) > set_Pr927595527on_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.26/0.59 collec749447393on_fml: ( produc1739631244on_fml > $o ) > set_Pr622314946on_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.26/0.59 collec1697116690on_trm: ( produc1072747943on_trm > $o ) > set_Pr1471344007on_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 0.26/0.59 collec575343829le_trm: ( produc1367888000le_trm > $o ) > set_Pr1235432374le_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.26/0.59 collec1756633317on_trm: ( produc464795408on_trm > $o ) > set_Pr943832262on_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Set_OCollect_001t__String__Ochar,type,
% 0.26/0.59 collect_char: ( char > $o ) > set_char ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Set_OCollect_001t__Syntax__Ovariable,type,
% 0.26/0.59 collect_variable: ( variable > $o ) > set_variable ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Syntax_Ofml_OGeq,type,
% 0.26/0.59 geq: trm > trm > fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Syntax_Ogame_OAssign,type,
% 0.26/0.59 assign: variable > trm > game ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Syntax_Ogame_OODE,type,
% 0.26/0.59 ode: char > trm > game ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Syntax_Ogame_OTest,type,
% 0.26/0.59 test: fml > game ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Syntax_Otrm_OConst,type,
% 0.26/0.59 const: char > trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Syntax_Otrm_ODifferential,type,
% 0.26/0.59 differential: trm > trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Syntax_Otrm_OFunc,type,
% 0.26/0.59 func: char > trm > trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Syntax_Otrm_ONumber,type,
% 0.26/0.59 number: real > trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Syntax_Otrm_OPlus,type,
% 0.26/0.59 plus: trm > trm > trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Syntax_Otrm_OTimes,type,
% 0.26/0.59 times: trm > trm > trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Syntax_Otrm_OVar,type,
% 0.26/0.59 var: variable > trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OAssigno,type,
% 0.26/0.59 uSubst834381837ssigno: variable > option_trm > option_game ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OAssigno__rel,type,
% 0.26/0.59 uSubst157155628no_rel: produc1024976764on_trm > produc1024976764on_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_ODifferentialo,type,
% 0.26/0.59 uSubst716837505ntialo: option_trm > option_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_ODifferentialo__rel,type,
% 0.26/0.59 uSubst2051024824lo_rel: option_trm > option_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OGeqo,type,
% 0.26/0.59 uSubst152838031e_Geqo: option_trm > option_trm > option_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OGeqo__rel,type,
% 0.26/0.59 uSubst1304144938qo_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OODEo,type,
% 0.26/0.59 uSubst1827052306e_ODEo: char > option_trm > option_game ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OODEo__rel,type,
% 0.26/0.59 uSubst299938919Eo_rel: produc464795408on_trm > produc464795408on_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OPluso,type,
% 0.26/0.59 uSubst141955042_Pluso: option_trm > option_trm > option_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OPluso__rel,type,
% 0.26/0.59 uSubst691094423so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTesto,type,
% 0.26/0.59 uSubst1367128042_Testo: option_fml > option_game ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTesto__rel,type,
% 0.26/0.59 uSubst954181007to_rel: option_fml > option_fml > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTimeso,type,
% 0.26/0.59 uSubst918876924Timeso: option_trm > option_trm > option_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTimeso__rel,type,
% 0.26/0.59 uSubst924844285so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousappconst,type,
% 0.26/0.59 uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappf,type,
% 0.26/0.59 uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappt,type,
% 0.26/0.59 uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappt__rel,type,
% 0.26/0.59 uSubst1917534215pt_rel: produc1699626005le_trm > produc1699626005le_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Wellfounded_Oaccp_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.26/0.59 accp_option_fml: ( option_fml > option_fml > $o ) > option_fml > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Wellfounded_Oaccp_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.26/0.59 accp_option_trm: ( option_trm > option_trm > $o ) > option_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.26/0.59 accp_P758790320on_trm: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 0.26/0.59 accp_P1877119646le_trm: ( produc1699626005le_trm > produc1699626005le_trm > $o ) > produc1699626005le_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.26/0.59 accp_P419951815on_trm: ( produc464795408on_trm > produc464795408on_trm > $o ) > produc464795408on_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.26/0.59 accp_P394694195on_trm: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > produc1024976764on_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Wellfounded_Olex__prod_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.26/0.59 lex_pr314879023on_fml: set_Pr927595527on_fml > set_Pr927595527on_fml > set_Pr1045337287on_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Wellfounded_Olex__prod_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.26/0.59 lex_pr852623737on_trm: set_Pr927595527on_fml > set_Pr1471344007on_trm > set_Pr1588097095on_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Wellfounded_Olex__prod_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.26/0.59 lex_pr425996582on_fml: set_Pr1625152599n_game > set_Pr927595527on_fml > set_Pr1918373977on_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Wellfounded_Olex__prod_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.26/0.59 lex_pr1724583269on_fml: set_Pr1471344007on_trm > set_Pr927595527on_fml > set_Pr519625031on_fml ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Wellfounded_Olex__prod_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.26/0.59 lex_pr114844335on_trm: set_Pr1471344007on_trm > set_Pr1471344007on_trm > set_Pr1062384839on_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Wellfounded_Olex__prod_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm,type,
% 0.26/0.59 lex_pr1522821402le_trm: set_Pr181266295riable > set_Pr491793543rm_trm > set_Pr1969262145le_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_Wellfounded_Olex__prod_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.26/0.59 lex_pr1901327402on_trm: set_Pr604539619r_char > set_Pr1471344007on_trm > set_Pr1481565921on_trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.26/0.59 member1287158352on_fml: produc46605351on_fml > set_Pr927595527on_fml > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.26/0.59 member1883102883on_fml: produc1739631244on_fml > set_Pr622314946on_fml > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 0.26/0.59 member191809696n_game: produc1016592119n_game > set_Pr1625152599n_game > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.26/0.59 member165817296on_trm: produc1072747943on_trm > set_Pr1471344007on_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.26/0.59 member450497296on_fml: produc1872652007on_fml > set_Pr1045337287on_fml > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.26/0.59 member1883874960on_trm: produc1158546023on_trm > set_Pr1588097095on_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.26/0.59 member113767842on_fml: produc1928189433on_fml > set_Pr1918373977on_fml > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.26/0.59 member1316917136on_fml: produc591588199on_fml > set_Pr519625031on_fml > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.26/0.59 member602811152on_trm: produc2024965863on_trm > set_Pr1062384839on_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 0.26/0.59 member1150310282le_trm: produc1279577057le_trm > set_Pr1969262145le_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.26/0.59 member1950256170on_trm: produc2018724225on_trm > set_Pr1481565921on_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J,type,
% 0.26/0.59 member1978718144riable: produc432717079riable > set_Pr181266295riable > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 0.26/0.59 member2122665623le_trm: produc1367888000le_trm > set_Pr1235432374le_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.26/0.59 member694524327on_trm: produc464795408on_trm > set_Pr943832262on_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Product____Type__Oprod_It__String__Ochar_Mt__String__Ochar_J,type,
% 0.26/0.59 member1866856748r_char: produc1593312387r_char > set_Pr604539619r_char > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Product____Type__Oprod_It__Syntax__Otrm_Mt__Syntax__Otrm_J,type,
% 0.26/0.59 member1735386832rm_trm: product_prod_trm_trm > set_Pr491793543rm_trm > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__String__Ochar,type,
% 0.26/0.59 member_char: char > set_char > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_c_member_001t__Syntax__Ovariable,type,
% 0.26/0.59 member_variable: variable > set_variable > $o ).
% 0.26/0.59
% 0.26/0.59 thf(sy_v_U,type,
% 0.26/0.59 u: set_variable ).
% 0.26/0.59
% 0.26/0.59 thf(sy_v_Ua____,type,
% 0.26/0.59 ua: set_variable ).
% 0.26/0.59
% 0.26/0.59 thf(sy_v__092_060eta_062____,type,
% 0.26/0.59 eta: trm ).
% 0.26/0.59
% 0.26/0.59 thf(sy_v__092_060nu_062,type,
% 0.26/0.59 nu: variable > real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_v__092_060nu_062_H____,type,
% 0.26/0.59 nu2: variable > real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_v__092_060omega_062,type,
% 0.26/0.59 omega: variable > real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_v__092_060omega_062_H____,type,
% 0.26/0.59 omega2: variable > real ).
% 0.26/0.59
% 0.26/0.59 thf(sy_v__092_060sigma_062_H_H____,type,
% 0.26/0.59 sigma: produc1418842292n_game ).
% 0.26/0.59
% 0.26/0.59 thf(sy_v__092_060theta_062____,type,
% 0.26/0.59 theta: trm ).
% 0.26/0.59
% 0.26/0.59 % Relevant facts (352)
% 0.26/0.59 thf(fact_0_vaouter,axiom,
% 0.26/0.59 denota1419872369iation @ nu @ omega @ u ).
% 0.26/0.59
% 0.26/0.59 % vaouter
% 0.26/0.59 thf(fact_1_usubstappf__geq__conv,axiom,
% 0.26/0.59 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.26/0.59 ( ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.26/0.59 != none_fml )
% 0.26/0.59 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.26/0.59 != none_trm )
% 0.26/0.59 & ( ( uSubst516392818stappt @ Sigma @ U @ Eta )
% 0.26/0.59 != none_trm ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % usubstappf_geq_conv
% 0.26/0.59 thf(fact_2_Geq_Oprems_I1_J,axiom,
% 0.26/0.59 ( ( uSubst516392804stappf @ sigma @ ua @ ( geq @ theta @ eta ) )
% 0.26/0.59 != none_fml ) ).
% 0.26/0.59
% 0.26/0.59 % Geq.prems(1)
% 0.26/0.59 thf(fact_3_undeft__None,axiom,
% 0.26/0.59 none_trm = none_trm ).
% 0.26/0.59
% 0.26/0.59 % undeft_None
% 0.26/0.59 thf(fact_4_usubstappt__det,axiom,
% 0.26/0.59 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,V: set_variable] :
% 0.26/0.59 ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.26/0.59 != none_trm )
% 0.26/0.59 => ( ( ( uSubst516392818stappt @ Sigma @ V @ Theta )
% 0.26/0.59 != none_trm )
% 0.26/0.59 => ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.26/0.59 = ( uSubst516392818stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % usubstappt_det
% 0.26/0.59 thf(fact_5_Geq_Oprems_I2_J,axiom,
% 0.26/0.59 denota1419872369iation @ nu2 @ omega2 @ ua ).
% 0.26/0.59
% 0.26/0.59 % Geq.prems(2)
% 0.26/0.59 thf(fact_6_usubstappt__plus__conv,axiom,
% 0.26/0.59 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.26/0.59 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( plus @ Theta @ Eta ) )
% 0.26/0.59 != none_trm )
% 0.26/0.59 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.26/0.59 != none_trm )
% 0.26/0.59 & ( ( uSubst516392818stappt @ Sigma @ U @ Eta )
% 0.26/0.59 != none_trm ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % usubstappt_plus_conv
% 0.26/0.59 thf(fact_7_usubstappt__times__conv,axiom,
% 0.26/0.59 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.26/0.59 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 0.26/0.59 != none_trm )
% 0.26/0.59 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.26/0.59 != none_trm )
% 0.26/0.59 & ( ( uSubst516392818stappt @ Sigma @ U @ Eta )
% 0.26/0.59 != none_trm ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % usubstappt_times_conv
% 0.26/0.59 thf(fact_8_usubstappt__antimon,axiom,
% 0.26/0.59 ! [V: set_variable,U: set_variable,Sigma: produc1418842292n_game,Theta: trm] :
% 0.26/0.59 ( ( ord_le282106107riable @ V @ U )
% 0.26/0.59 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.26/0.59 != none_trm )
% 0.26/0.59 => ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.26/0.59 = ( uSubst516392818stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % usubstappt_antimon
% 0.26/0.59 thf(fact_9_Differentialo_Osimps_I2_J,axiom,
% 0.26/0.59 ( ( uSubst716837505ntialo @ none_trm )
% 0.26/0.59 = none_trm ) ).
% 0.26/0.59
% 0.26/0.59 % Differentialo.simps(2)
% 0.26/0.59 thf(fact_10_Differentialo__undef,axiom,
% 0.26/0.59 ! [Theta: option_trm] :
% 0.26/0.59 ( ( ( uSubst716837505ntialo @ Theta )
% 0.26/0.59 = none_trm )
% 0.26/0.59 = ( Theta = none_trm ) ) ).
% 0.26/0.59
% 0.26/0.59 % Differentialo_undef
% 0.26/0.59 thf(fact_11_Pluso_Osimps_I2_J,axiom,
% 0.26/0.59 ! [Eta: option_trm] :
% 0.26/0.59 ( ( uSubst141955042_Pluso @ none_trm @ Eta )
% 0.26/0.59 = none_trm ) ).
% 0.26/0.59
% 0.26/0.59 % Pluso.simps(2)
% 0.26/0.59 thf(fact_12_Timeso_Osimps_I2_J,axiom,
% 0.26/0.59 ! [Eta: option_trm] :
% 0.26/0.59 ( ( uSubst918876924Timeso @ none_trm @ Eta )
% 0.26/0.59 = none_trm ) ).
% 0.26/0.59
% 0.26/0.59 % Timeso.simps(2)
% 0.26/0.59 thf(fact_13_Pluso__undef,axiom,
% 0.26/0.59 ! [Theta: option_trm,Eta: option_trm] :
% 0.26/0.59 ( ( ( uSubst141955042_Pluso @ Theta @ Eta )
% 0.26/0.59 = none_trm )
% 0.26/0.59 = ( ( Theta = none_trm )
% 0.26/0.59 | ( Eta = none_trm ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Pluso_undef
% 0.26/0.59 thf(fact_14_Timeso__undef,axiom,
% 0.26/0.59 ! [Theta: option_trm,Eta: option_trm] :
% 0.26/0.59 ( ( ( uSubst918876924Timeso @ Theta @ Eta )
% 0.26/0.59 = none_trm )
% 0.26/0.59 = ( ( Theta = none_trm )
% 0.26/0.59 | ( Eta = none_trm ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Timeso_undef
% 0.26/0.59 thf(fact_15_Geqo_Osimps_I2_J,axiom,
% 0.26/0.59 ! [Eta: option_trm] :
% 0.26/0.59 ( ( uSubst152838031e_Geqo @ none_trm @ Eta )
% 0.26/0.59 = none_fml ) ).
% 0.26/0.59
% 0.26/0.59 % Geqo.simps(2)
% 0.26/0.59 thf(fact_16_usubstappf__antimon,axiom,
% 0.26/0.59 ! [V: set_variable,U: set_variable,Sigma: produc1418842292n_game,Phi: fml] :
% 0.26/0.59 ( ( ord_le282106107riable @ V @ U )
% 0.26/0.59 => ( ( ( uSubst516392804stappf @ Sigma @ U @ Phi )
% 0.26/0.59 != none_fml )
% 0.26/0.59 => ( ( uSubst516392804stappf @ Sigma @ U @ Phi )
% 0.26/0.59 = ( uSubst516392804stappf @ Sigma @ V @ Phi ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % usubstappf_antimon
% 0.26/0.59 thf(fact_17_usubstappf__det,axiom,
% 0.26/0.59 ! [Sigma: produc1418842292n_game,U: set_variable,Phi: fml,V: set_variable] :
% 0.26/0.59 ( ( ( uSubst516392804stappf @ Sigma @ U @ Phi )
% 0.26/0.59 != none_fml )
% 0.26/0.59 => ( ( ( uSubst516392804stappf @ Sigma @ V @ Phi )
% 0.26/0.59 != none_fml )
% 0.26/0.59 => ( ( uSubst516392804stappf @ Sigma @ U @ Phi )
% 0.26/0.59 = ( uSubst516392804stappf @ Sigma @ V @ Phi ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % usubstappf_det
% 0.26/0.59 thf(fact_18_usubstappt_Osimps_I5_J,axiom,
% 0.26/0.59 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.26/0.59 ( ( uSubst516392818stappt @ Sigma @ U @ ( plus @ Theta @ Eta ) )
% 0.26/0.59 = ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % usubstappt.simps(5)
% 0.26/0.59 thf(fact_19_usubstappt_Osimps_I6_J,axiom,
% 0.26/0.59 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.26/0.59 ( ( uSubst516392818stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 0.26/0.59 = ( uSubst918876924Timeso @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % usubstappt.simps(6)
% 0.26/0.59 thf(fact_20_usubstappf_Osimps_I2_J,axiom,
% 0.26/0.59 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.26/0.59 ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.26/0.59 = ( uSubst152838031e_Geqo @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % usubstappf.simps(2)
% 0.26/0.59 thf(fact_21_Geqo__undef,axiom,
% 0.26/0.59 ! [Theta: option_trm,Eta: option_trm] :
% 0.26/0.59 ( ( ( uSubst152838031e_Geqo @ Theta @ Eta )
% 0.26/0.59 = none_fml )
% 0.26/0.59 = ( ( Theta = none_trm )
% 0.26/0.59 | ( Eta = none_trm ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Geqo_undef
% 0.26/0.59 thf(fact_22_trm_Oinject_I6_J,axiom,
% 0.26/0.59 ! [X61: trm,X62: trm,Y61: trm,Y62: trm] :
% 0.26/0.59 ( ( ( times @ X61 @ X62 )
% 0.26/0.59 = ( times @ Y61 @ Y62 ) )
% 0.26/0.59 = ( ( X61 = Y61 )
% 0.26/0.59 & ( X62 = Y62 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % trm.inject(6)
% 0.26/0.59 thf(fact_23_trm_Oinject_I5_J,axiom,
% 0.26/0.59 ! [X51: trm,X52: trm,Y51: trm,Y52: trm] :
% 0.26/0.59 ( ( ( plus @ X51 @ X52 )
% 0.26/0.59 = ( plus @ Y51 @ Y52 ) )
% 0.26/0.59 = ( ( X51 = Y51 )
% 0.26/0.59 & ( X52 = Y52 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % trm.inject(5)
% 0.26/0.59 thf(fact_24_fml_Oinject_I2_J,axiom,
% 0.26/0.59 ! [X21: trm,X22: trm,Y21: trm,Y22: trm] :
% 0.26/0.59 ( ( ( geq @ X21 @ X22 )
% 0.26/0.59 = ( geq @ Y21 @ Y22 ) )
% 0.26/0.59 = ( ( X21 = Y21 )
% 0.26/0.59 & ( X22 = Y22 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % fml.inject(2)
% 0.26/0.59 thf(fact_25_Uvariation__mon,axiom,
% 0.26/0.59 ! [U: set_variable,V: set_variable,Omega: variable > real,Nu: variable > real] :
% 0.26/0.59 ( ( ord_le282106107riable @ U @ V )
% 0.26/0.59 => ( ( denota1419872369iation @ Omega @ Nu @ U )
% 0.26/0.59 => ( denota1419872369iation @ Omega @ Nu @ V ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Uvariation_mon
% 0.26/0.59 thf(fact_26_subsetI,axiom,
% 0.26/0.59 ! [A: set_char,B: set_char] :
% 0.26/0.59 ( ! [X: char] :
% 0.26/0.59 ( ( member_char @ X @ A )
% 0.26/0.59 => ( member_char @ X @ B ) )
% 0.26/0.59 => ( ord_less_eq_set_char @ A @ B ) ) ).
% 0.26/0.59
% 0.26/0.59 % subsetI
% 0.26/0.59 thf(fact_27_subsetI,axiom,
% 0.26/0.59 ! [A: set_variable,B: set_variable] :
% 0.26/0.59 ( ! [X: variable] :
% 0.26/0.59 ( ( member_variable @ X @ A )
% 0.26/0.59 => ( member_variable @ X @ B ) )
% 0.26/0.59 => ( ord_le282106107riable @ A @ B ) ) ).
% 0.26/0.59
% 0.26/0.59 % subsetI
% 0.26/0.59 thf(fact_28_subset__antisym,axiom,
% 0.26/0.59 ! [A: set_variable,B: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ A @ B )
% 0.26/0.59 => ( ( ord_le282106107riable @ B @ A )
% 0.26/0.59 => ( A = B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_antisym
% 0.26/0.59 thf(fact_29_trm_Odistinct_I37_J,axiom,
% 0.26/0.59 ! [X51: trm,X52: trm,X61: trm,X62: trm] :
% 0.26/0.59 ( ( plus @ X51 @ X52 )
% 0.26/0.59 != ( times @ X61 @ X62 ) ) ).
% 0.26/0.59
% 0.26/0.59 % trm.distinct(37)
% 0.26/0.59 thf(fact_30_order__refl,axiom,
% 0.26/0.59 ! [X2: set_variable] : ( ord_le282106107riable @ X2 @ X2 ) ).
% 0.26/0.59
% 0.26/0.59 % order_refl
% 0.26/0.59 thf(fact_31_Uvariation__univ,axiom,
% 0.26/0.59 ! [Nu: variable > real,Nu2: variable > real] :
% 0.26/0.59 ( denota1419872369iation @ Nu @ Nu2
% 0.26/0.59 @ ( collect_variable
% 0.26/0.59 @ ^ [X3: variable] : $true ) ) ).
% 0.26/0.59
% 0.26/0.59 % Uvariation_univ
% 0.26/0.59 thf(fact_32_Collect__subset,axiom,
% 0.26/0.59 ! [A: set_char,P: char > $o] :
% 0.26/0.59 ( ord_less_eq_set_char
% 0.26/0.59 @ ( collect_char
% 0.26/0.59 @ ^ [X3: char] :
% 0.26/0.59 ( ( member_char @ X3 @ A )
% 0.26/0.59 & ( P @ X3 ) ) )
% 0.26/0.59 @ A ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_subset
% 0.26/0.59 thf(fact_33_Collect__subset,axiom,
% 0.26/0.59 ! [A: set_variable,P: variable > $o] :
% 0.26/0.59 ( ord_le282106107riable
% 0.26/0.59 @ ( collect_variable
% 0.26/0.59 @ ^ [X3: variable] :
% 0.26/0.59 ( ( member_variable @ X3 @ A )
% 0.26/0.59 & ( P @ X3 ) ) )
% 0.26/0.59 @ A ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_subset
% 0.26/0.59 thf(fact_34_less__eq__set__def,axiom,
% 0.26/0.59 ( ord_less_eq_set_char
% 0.26/0.59 = ( ^ [A2: set_char,B2: set_char] :
% 0.26/0.59 ( ord_less_eq_char_o
% 0.26/0.59 @ ^ [X3: char] : ( member_char @ X3 @ A2 )
% 0.26/0.59 @ ^ [X3: char] : ( member_char @ X3 @ B2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % less_eq_set_def
% 0.26/0.59 thf(fact_35_less__eq__set__def,axiom,
% 0.26/0.59 ( ord_le282106107riable
% 0.26/0.59 = ( ^ [A2: set_variable,B2: set_variable] :
% 0.26/0.59 ( ord_le1407353162able_o
% 0.26/0.59 @ ^ [X3: variable] : ( member_variable @ X3 @ A2 )
% 0.26/0.59 @ ^ [X3: variable] : ( member_variable @ X3 @ B2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % less_eq_set_def
% 0.26/0.59 thf(fact_36_dual__order_Oantisym,axiom,
% 0.26/0.59 ! [B3: set_variable,A3: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ B3 @ A3 )
% 0.26/0.59 => ( ( ord_le282106107riable @ A3 @ B3 )
% 0.26/0.59 => ( A3 = B3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.antisym
% 0.26/0.59 thf(fact_37_dual__order_Oeq__iff,axiom,
% 0.26/0.59 ( ( ^ [Y: set_variable,Z: set_variable] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [A4: set_variable,B4: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ B4 @ A4 )
% 0.26/0.59 & ( ord_le282106107riable @ A4 @ B4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.eq_iff
% 0.26/0.59 thf(fact_38_dual__order_Otrans,axiom,
% 0.26/0.59 ! [B3: set_variable,A3: set_variable,C: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ B3 @ A3 )
% 0.26/0.59 => ( ( ord_le282106107riable @ C @ B3 )
% 0.26/0.59 => ( ord_le282106107riable @ C @ A3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.trans
% 0.26/0.59 thf(fact_39_dual__order_Orefl,axiom,
% 0.26/0.59 ! [A3: set_variable] : ( ord_le282106107riable @ A3 @ A3 ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.refl
% 0.26/0.59 thf(fact_40_order__trans,axiom,
% 0.26/0.59 ! [X2: set_variable,Y2: set_variable,Z2: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ X2 @ Y2 )
% 0.26/0.59 => ( ( ord_le282106107riable @ Y2 @ Z2 )
% 0.26/0.59 => ( ord_le282106107riable @ X2 @ Z2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_trans
% 0.26/0.59 thf(fact_41_order__class_Oorder_Oantisym,axiom,
% 0.26/0.59 ! [A3: set_variable,B3: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ A3 @ B3 )
% 0.26/0.59 => ( ( ord_le282106107riable @ B3 @ A3 )
% 0.26/0.59 => ( A3 = B3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_class.order.antisym
% 0.26/0.59 thf(fact_42_ord__le__eq__trans,axiom,
% 0.26/0.59 ! [A3: set_variable,B3: set_variable,C: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ A3 @ B3 )
% 0.26/0.59 => ( ( B3 = C )
% 0.26/0.59 => ( ord_le282106107riable @ A3 @ C ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_le_eq_trans
% 0.26/0.59 thf(fact_43_ord__eq__le__trans,axiom,
% 0.26/0.59 ! [A3: set_variable,B3: set_variable,C: set_variable] :
% 0.26/0.59 ( ( A3 = B3 )
% 0.26/0.59 => ( ( ord_le282106107riable @ B3 @ C )
% 0.26/0.59 => ( ord_le282106107riable @ A3 @ C ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_eq_le_trans
% 0.26/0.59 thf(fact_44_order__class_Oorder_Oeq__iff,axiom,
% 0.26/0.59 ( ( ^ [Y: set_variable,Z: set_variable] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [A4: set_variable,B4: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ A4 @ B4 )
% 0.26/0.59 & ( ord_le282106107riable @ B4 @ A4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_class.order.eq_iff
% 0.26/0.59 thf(fact_45_antisym__conv,axiom,
% 0.26/0.59 ! [Y2: set_variable,X2: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ Y2 @ X2 )
% 0.26/0.59 => ( ( ord_le282106107riable @ X2 @ Y2 )
% 0.26/0.59 = ( X2 = Y2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antisym_conv
% 0.26/0.59 thf(fact_46_mem__Collect__eq,axiom,
% 0.26/0.59 ! [A3: variable,P: variable > $o] :
% 0.26/0.59 ( ( member_variable @ A3 @ ( collect_variable @ P ) )
% 0.26/0.59 = ( P @ A3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % mem_Collect_eq
% 0.26/0.59 thf(fact_47_mem__Collect__eq,axiom,
% 0.26/0.59 ! [A3: char,P: char > $o] :
% 0.26/0.59 ( ( member_char @ A3 @ ( collect_char @ P ) )
% 0.26/0.59 = ( P @ A3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % mem_Collect_eq
% 0.26/0.59 thf(fact_48_Collect__mem__eq,axiom,
% 0.26/0.59 ! [A: set_variable] :
% 0.26/0.59 ( ( collect_variable
% 0.26/0.59 @ ^ [X3: variable] : ( member_variable @ X3 @ A ) )
% 0.26/0.59 = A ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_mem_eq
% 0.26/0.59 thf(fact_49_Collect__mem__eq,axiom,
% 0.26/0.59 ! [A: set_char] :
% 0.26/0.59 ( ( collect_char
% 0.26/0.59 @ ^ [X3: char] : ( member_char @ X3 @ A ) )
% 0.26/0.59 = A ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_mem_eq
% 0.26/0.59 thf(fact_50_Collect__cong,axiom,
% 0.26/0.59 ! [P: variable > $o,Q: variable > $o] :
% 0.26/0.59 ( ! [X: variable] :
% 0.26/0.59 ( ( P @ X )
% 0.26/0.59 = ( Q @ X ) )
% 0.26/0.59 => ( ( collect_variable @ P )
% 0.26/0.59 = ( collect_variable @ Q ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_cong
% 0.26/0.59 thf(fact_51_Collect__cong,axiom,
% 0.26/0.59 ! [P: char > $o,Q: char > $o] :
% 0.26/0.59 ( ! [X: char] :
% 0.26/0.59 ( ( P @ X )
% 0.26/0.59 = ( Q @ X ) )
% 0.26/0.59 => ( ( collect_char @ P )
% 0.26/0.59 = ( collect_char @ Q ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_cong
% 0.26/0.59 thf(fact_52_order_Otrans,axiom,
% 0.26/0.59 ! [A3: set_variable,B3: set_variable,C: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ A3 @ B3 )
% 0.26/0.59 => ( ( ord_le282106107riable @ B3 @ C )
% 0.26/0.59 => ( ord_le282106107riable @ A3 @ C ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order.trans
% 0.26/0.59 thf(fact_53_eq__refl,axiom,
% 0.26/0.59 ! [X2: set_variable,Y2: set_variable] :
% 0.26/0.59 ( ( X2 = Y2 )
% 0.26/0.59 => ( ord_le282106107riable @ X2 @ Y2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % eq_refl
% 0.26/0.59 thf(fact_54_antisym,axiom,
% 0.26/0.59 ! [X2: set_variable,Y2: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ X2 @ Y2 )
% 0.26/0.59 => ( ( ord_le282106107riable @ Y2 @ X2 )
% 0.26/0.59 => ( X2 = Y2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antisym
% 0.26/0.59 thf(fact_55_eq__iff,axiom,
% 0.26/0.59 ( ( ^ [Y: set_variable,Z: set_variable] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [X3: set_variable,Y3: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ X3 @ Y3 )
% 0.26/0.59 & ( ord_le282106107riable @ Y3 @ X3 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % eq_iff
% 0.26/0.59 thf(fact_56_ord__le__eq__subst,axiom,
% 0.26/0.59 ! [A3: set_variable,B3: set_variable,F: set_variable > set_variable,C: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ A3 @ B3 )
% 0.26/0.59 => ( ( ( F @ B3 )
% 0.26/0.59 = C )
% 0.26/0.59 => ( ! [X: set_variable,Y4: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ X @ Y4 )
% 0.26/0.59 => ( ord_le282106107riable @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_le282106107riable @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_le_eq_subst
% 0.26/0.59 thf(fact_57_ord__eq__le__subst,axiom,
% 0.26/0.59 ! [A3: set_variable,F: set_variable > set_variable,B3: set_variable,C: set_variable] :
% 0.26/0.59 ( ( A3
% 0.26/0.59 = ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_le282106107riable @ B3 @ C )
% 0.26/0.59 => ( ! [X: set_variable,Y4: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ X @ Y4 )
% 0.26/0.59 => ( ord_le282106107riable @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_le282106107riable @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_eq_le_subst
% 0.26/0.59 thf(fact_58_order__subst2,axiom,
% 0.26/0.59 ! [A3: set_variable,B3: set_variable,F: set_variable > set_variable,C: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ A3 @ B3 )
% 0.26/0.59 => ( ( ord_le282106107riable @ ( F @ B3 ) @ C )
% 0.26/0.59 => ( ! [X: set_variable,Y4: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ X @ Y4 )
% 0.26/0.59 => ( ord_le282106107riable @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_le282106107riable @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst2
% 0.26/0.59 thf(fact_59_order__subst1,axiom,
% 0.26/0.59 ! [A3: set_variable,F: set_variable > set_variable,B3: set_variable,C: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ A3 @ ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_le282106107riable @ B3 @ C )
% 0.26/0.59 => ( ! [X: set_variable,Y4: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ X @ Y4 )
% 0.26/0.59 => ( ord_le282106107riable @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_le282106107riable @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst1
% 0.26/0.59 thf(fact_60_Collect__mono__iff,axiom,
% 0.26/0.59 ! [P: char > $o,Q: char > $o] :
% 0.26/0.59 ( ( ord_less_eq_set_char @ ( collect_char @ P ) @ ( collect_char @ Q ) )
% 0.26/0.59 = ( ! [X3: char] :
% 0.26/0.59 ( ( P @ X3 )
% 0.26/0.59 => ( Q @ X3 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_mono_iff
% 0.26/0.59 thf(fact_61_Collect__mono__iff,axiom,
% 0.26/0.59 ! [P: variable > $o,Q: variable > $o] :
% 0.26/0.59 ( ( ord_le282106107riable @ ( collect_variable @ P ) @ ( collect_variable @ Q ) )
% 0.26/0.59 = ( ! [X3: variable] :
% 0.26/0.59 ( ( P @ X3 )
% 0.26/0.59 => ( Q @ X3 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_mono_iff
% 0.26/0.59 thf(fact_62_set__eq__subset,axiom,
% 0.26/0.59 ( ( ^ [Y: set_variable,Z: set_variable] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [A2: set_variable,B2: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ A2 @ B2 )
% 0.26/0.59 & ( ord_le282106107riable @ B2 @ A2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % set_eq_subset
% 0.26/0.59 thf(fact_63_subset__trans,axiom,
% 0.26/0.59 ! [A: set_variable,B: set_variable,C2: set_variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ A @ B )
% 0.26/0.59 => ( ( ord_le282106107riable @ B @ C2 )
% 0.26/0.59 => ( ord_le282106107riable @ A @ C2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_trans
% 0.26/0.59 thf(fact_64_Collect__mono,axiom,
% 0.26/0.59 ! [P: char > $o,Q: char > $o] :
% 0.26/0.59 ( ! [X: char] :
% 0.26/0.59 ( ( P @ X )
% 0.26/0.59 => ( Q @ X ) )
% 0.26/0.59 => ( ord_less_eq_set_char @ ( collect_char @ P ) @ ( collect_char @ Q ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_mono
% 0.26/0.59 thf(fact_65_Collect__mono,axiom,
% 0.26/0.59 ! [P: variable > $o,Q: variable > $o] :
% 0.26/0.59 ( ! [X: variable] :
% 0.26/0.59 ( ( P @ X )
% 0.26/0.59 => ( Q @ X ) )
% 0.26/0.59 => ( ord_le282106107riable @ ( collect_variable @ P ) @ ( collect_variable @ Q ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_mono
% 0.26/0.59 thf(fact_66_subset__refl,axiom,
% 0.26/0.59 ! [A: set_variable] : ( ord_le282106107riable @ A @ A ) ).
% 0.26/0.59
% 0.26/0.59 % subset_refl
% 0.26/0.59 thf(fact_67_subset__iff,axiom,
% 0.26/0.59 ( ord_less_eq_set_char
% 0.26/0.59 = ( ^ [A2: set_char,B2: set_char] :
% 0.26/0.59 ! [T: char] :
% 0.26/0.59 ( ( member_char @ T @ A2 )
% 0.26/0.59 => ( member_char @ T @ B2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_iff
% 0.26/0.59 thf(fact_68_subset__iff,axiom,
% 0.26/0.59 ( ord_le282106107riable
% 0.26/0.59 = ( ^ [A2: set_variable,B2: set_variable] :
% 0.26/0.59 ! [T: variable] :
% 0.26/0.59 ( ( member_variable @ T @ A2 )
% 0.26/0.59 => ( member_variable @ T @ B2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_iff
% 0.26/0.59 thf(fact_69_equalityD2,axiom,
% 0.26/0.59 ! [A: set_variable,B: set_variable] :
% 0.26/0.59 ( ( A = B )
% 0.26/0.59 => ( ord_le282106107riable @ B @ A ) ) ).
% 0.26/0.59
% 0.26/0.59 % equalityD2
% 0.26/0.59 thf(fact_70_equalityD1,axiom,
% 0.26/0.59 ! [A: set_variable,B: set_variable] :
% 0.26/0.59 ( ( A = B )
% 0.26/0.59 => ( ord_le282106107riable @ A @ B ) ) ).
% 0.26/0.59
% 0.26/0.59 % equalityD1
% 0.26/0.59 thf(fact_71_subset__eq,axiom,
% 0.26/0.59 ( ord_less_eq_set_char
% 0.26/0.59 = ( ^ [A2: set_char,B2: set_char] :
% 0.26/0.59 ! [X3: char] :
% 0.26/0.59 ( ( member_char @ X3 @ A2 )
% 0.26/0.59 => ( member_char @ X3 @ B2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_eq
% 0.26/0.59 thf(fact_72_subset__eq,axiom,
% 0.26/0.59 ( ord_le282106107riable
% 0.26/0.59 = ( ^ [A2: set_variable,B2: set_variable] :
% 0.26/0.59 ! [X3: variable] :
% 0.26/0.59 ( ( member_variable @ X3 @ A2 )
% 0.26/0.59 => ( member_variable @ X3 @ B2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_eq
% 0.26/0.59 thf(fact_73_equalityE,axiom,
% 0.26/0.59 ! [A: set_variable,B: set_variable] :
% 0.26/0.59 ( ( A = B )
% 0.26/0.59 => ~ ( ( ord_le282106107riable @ A @ B )
% 0.26/0.59 => ~ ( ord_le282106107riable @ B @ A ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % equalityE
% 0.26/0.59 thf(fact_74_subsetD,axiom,
% 0.26/0.59 ! [A: set_char,B: set_char,C: char] :
% 0.26/0.59 ( ( ord_less_eq_set_char @ A @ B )
% 0.26/0.59 => ( ( member_char @ C @ A )
% 0.26/0.59 => ( member_char @ C @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subsetD
% 0.26/0.59 thf(fact_75_subsetD,axiom,
% 0.26/0.59 ! [A: set_variable,B: set_variable,C: variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ A @ B )
% 0.26/0.59 => ( ( member_variable @ C @ A )
% 0.26/0.59 => ( member_variable @ C @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subsetD
% 0.26/0.59 thf(fact_76_in__mono,axiom,
% 0.26/0.59 ! [A: set_char,B: set_char,X2: char] :
% 0.26/0.59 ( ( ord_less_eq_set_char @ A @ B )
% 0.26/0.59 => ( ( member_char @ X2 @ A )
% 0.26/0.59 => ( member_char @ X2 @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % in_mono
% 0.26/0.59 thf(fact_77_in__mono,axiom,
% 0.26/0.59 ! [A: set_variable,B: set_variable,X2: variable] :
% 0.26/0.59 ( ( ord_le282106107riable @ A @ B )
% 0.26/0.59 => ( ( member_variable @ X2 @ A )
% 0.26/0.59 => ( member_variable @ X2 @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % in_mono
% 0.26/0.59 thf(fact_78_Uvariation__sym__rel,axiom,
% 0.26/0.59 ! [Omega: variable > real,Nu: variable > real,U: set_variable] :
% 0.26/0.59 ( ( denota1419872369iation @ Omega @ Nu @ U )
% 0.26/0.59 => ( denota1419872369iation @ Nu @ Omega @ U ) ) ).
% 0.26/0.59
% 0.26/0.59 % Uvariation_sym_rel
% 0.26/0.59 thf(fact_79_Uvariation__refl,axiom,
% 0.26/0.59 ! [Nu: variable > real,V: set_variable] : ( denota1419872369iation @ Nu @ Nu @ V ) ).
% 0.26/0.59
% 0.26/0.59 % Uvariation_refl
% 0.26/0.59 thf(fact_80_Uvariation__sym,axiom,
% 0.26/0.59 ( denota1419872369iation
% 0.26/0.59 = ( ^ [Omega2: variable > real,Nu3: variable > real] : ( denota1419872369iation @ Nu3 @ Omega2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Uvariation_sym
% 0.26/0.59 thf(fact_81_Uvariation__def,axiom,
% 0.26/0.59 ( denota1419872369iation
% 0.26/0.59 = ( ^ [Nu3: variable > real,Nu4: variable > real,U2: set_variable] :
% 0.26/0.59 ! [I: variable] :
% 0.26/0.59 ( ~ ( member_variable @ I @ U2 )
% 0.26/0.59 => ( ( Nu3 @ I )
% 0.26/0.59 = ( Nu4 @ I ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Uvariation_def
% 0.26/0.59 thf(fact_82_pred__subset__eq,axiom,
% 0.26/0.59 ! [R: set_char,S: set_char] :
% 0.26/0.59 ( ( ord_less_eq_char_o
% 0.26/0.59 @ ^ [X3: char] : ( member_char @ X3 @ R )
% 0.26/0.59 @ ^ [X3: char] : ( member_char @ X3 @ S ) )
% 0.26/0.59 = ( ord_less_eq_set_char @ R @ S ) ) ).
% 0.26/0.59
% 0.26/0.59 % pred_subset_eq
% 0.26/0.59 thf(fact_83_pred__subset__eq,axiom,
% 0.26/0.59 ! [R: set_variable,S: set_variable] :
% 0.26/0.59 ( ( ord_le1407353162able_o
% 0.26/0.59 @ ^ [X3: variable] : ( member_variable @ X3 @ R )
% 0.26/0.59 @ ^ [X3: variable] : ( member_variable @ X3 @ S ) )
% 0.26/0.59 = ( ord_le282106107riable @ R @ S ) ) ).
% 0.26/0.59
% 0.26/0.59 % pred_subset_eq
% 0.26/0.59 thf(fact_84_subset__Collect__iff,axiom,
% 0.26/0.59 ! [B: set_char,A: set_char,P: char > $o] :
% 0.26/0.59 ( ( ord_less_eq_set_char @ B @ A )
% 0.26/0.59 => ( ( ord_less_eq_set_char @ B
% 0.26/0.59 @ ( collect_char
% 0.26/0.59 @ ^ [X3: char] :
% 0.26/0.59 ( ( member_char @ X3 @ A )
% 0.26/0.59 & ( P @ X3 ) ) ) )
% 0.26/0.59 = ( ! [X3: char] :
% 0.26/0.59 ( ( member_char @ X3 @ B )
% 0.26/0.59 => ( P @ X3 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_Collect_iff
% 0.26/0.59 thf(fact_85_subset__Collect__iff,axiom,
% 0.26/0.59 ! [B: set_variable,A: set_variable,P: variable > $o] :
% 0.26/0.59 ( ( ord_le282106107riable @ B @ A )
% 0.26/0.59 => ( ( ord_le282106107riable @ B
% 0.26/0.59 @ ( collect_variable
% 0.26/0.59 @ ^ [X3: variable] :
% 0.26/0.59 ( ( member_variable @ X3 @ A )
% 0.26/0.59 & ( P @ X3 ) ) ) )
% 0.26/0.59 = ( ! [X3: variable] :
% 0.26/0.59 ( ( member_variable @ X3 @ B )
% 0.26/0.59 => ( P @ X3 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_Collect_iff
% 0.26/0.59 thf(fact_86_subset__CollectI,axiom,
% 0.26/0.59 ! [B: set_char,A: set_char,Q: char > $o,P: char > $o] :
% 0.26/0.59 ( ( ord_less_eq_set_char @ B @ A )
% 0.26/0.59 => ( ! [X: char] :
% 0.26/0.59 ( ( member_char @ X @ B )
% 0.26/0.59 => ( ( Q @ X )
% 0.26/0.59 => ( P @ X ) ) )
% 0.26/0.59 => ( ord_less_eq_set_char
% 0.26/0.59 @ ( collect_char
% 0.26/0.59 @ ^ [X3: char] :
% 0.26/0.59 ( ( member_char @ X3 @ B )
% 0.26/0.59 & ( Q @ X3 ) ) )
% 0.26/0.59 @ ( collect_char
% 0.26/0.59 @ ^ [X3: char] :
% 0.26/0.59 ( ( member_char @ X3 @ A )
% 0.26/0.59 & ( P @ X3 ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_CollectI
% 0.26/0.59 thf(fact_87_subset__CollectI,axiom,
% 0.26/0.59 ! [B: set_variable,A: set_variable,Q: variable > $o,P: variable > $o] :
% 0.26/0.59 ( ( ord_le282106107riable @ B @ A )
% 0.26/0.59 => ( ! [X: variable] :
% 0.26/0.59 ( ( member_variable @ X @ B )
% 0.26/0.59 => ( ( Q @ X )
% 0.26/0.59 => ( P @ X ) ) )
% 0.26/0.59 => ( ord_le282106107riable
% 0.26/0.59 @ ( collect_variable
% 0.26/0.59 @ ^ [X3: variable] :
% 0.26/0.59 ( ( member_variable @ X3 @ B )
% 0.26/0.59 & ( Q @ X3 ) ) )
% 0.26/0.59 @ ( collect_variable
% 0.26/0.59 @ ^ [X3: variable] :
% 0.26/0.59 ( ( member_variable @ X3 @ A )
% 0.26/0.59 & ( P @ X3 ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_CollectI
% 0.26/0.59 thf(fact_88_Collect__restrict,axiom,
% 0.26/0.59 ! [X4: set_char,P: char > $o] :
% 0.26/0.59 ( ord_less_eq_set_char
% 0.26/0.59 @ ( collect_char
% 0.26/0.59 @ ^ [X3: char] :
% 0.26/0.59 ( ( member_char @ X3 @ X4 )
% 0.26/0.59 & ( P @ X3 ) ) )
% 0.26/0.59 @ X4 ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_restrict
% 0.26/0.59 thf(fact_89_Collect__restrict,axiom,
% 0.26/0.59 ! [X4: set_variable,P: variable > $o] :
% 0.26/0.59 ( ord_le282106107riable
% 0.26/0.59 @ ( collect_variable
% 0.26/0.59 @ ^ [X3: variable] :
% 0.26/0.59 ( ( member_variable @ X3 @ X4 )
% 0.26/0.59 & ( P @ X3 ) ) )
% 0.26/0.59 @ X4 ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_restrict
% 0.26/0.59 thf(fact_90_prop__restrict,axiom,
% 0.26/0.59 ! [X2: char,Z3: set_char,X4: set_char,P: char > $o] :
% 0.26/0.59 ( ( member_char @ X2 @ Z3 )
% 0.26/0.59 => ( ( ord_less_eq_set_char @ Z3
% 0.26/0.59 @ ( collect_char
% 0.26/0.59 @ ^ [X3: char] :
% 0.26/0.59 ( ( member_char @ X3 @ X4 )
% 0.26/0.59 & ( P @ X3 ) ) ) )
% 0.26/0.59 => ( P @ X2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % prop_restrict
% 0.26/0.59 thf(fact_91_prop__restrict,axiom,
% 0.26/0.59 ! [X2: variable,Z3: set_variable,X4: set_variable,P: variable > $o] :
% 0.26/0.59 ( ( member_variable @ X2 @ Z3 )
% 0.26/0.59 => ( ( ord_le282106107riable @ Z3
% 0.26/0.59 @ ( collect_variable
% 0.26/0.59 @ ^ [X3: variable] :
% 0.26/0.59 ( ( member_variable @ X3 @ X4 )
% 0.26/0.59 & ( P @ X3 ) ) ) )
% 0.26/0.59 => ( P @ X2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % prop_restrict
% 0.26/0.59 thf(fact_92_conj__subset__def,axiom,
% 0.26/0.59 ! [A: set_char,P: char > $o,Q: char > $o] :
% 0.26/0.59 ( ( ord_less_eq_set_char @ A
% 0.26/0.59 @ ( collect_char
% 0.26/0.59 @ ^ [X3: char] :
% 0.26/0.59 ( ( P @ X3 )
% 0.26/0.59 & ( Q @ X3 ) ) ) )
% 0.26/0.59 = ( ( ord_less_eq_set_char @ A @ ( collect_char @ P ) )
% 0.26/0.59 & ( ord_less_eq_set_char @ A @ ( collect_char @ Q ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % conj_subset_def
% 0.26/0.59 thf(fact_93_conj__subset__def,axiom,
% 0.26/0.59 ! [A: set_variable,P: variable > $o,Q: variable > $o] :
% 0.26/0.59 ( ( ord_le282106107riable @ A
% 0.26/0.59 @ ( collect_variable
% 0.26/0.59 @ ^ [X3: variable] :
% 0.26/0.59 ( ( P @ X3 )
% 0.26/0.59 & ( Q @ X3 ) ) ) )
% 0.26/0.59 = ( ( ord_le282106107riable @ A @ ( collect_variable @ P ) )
% 0.26/0.59 & ( ord_le282106107riable @ A @ ( collect_variable @ Q ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % conj_subset_def
% 0.26/0.59 thf(fact_94_Pluso_Oelims,axiom,
% 0.26/0.59 ! [X2: option_trm,Xa: option_trm,Y2: option_trm] :
% 0.26/0.59 ( ( ( uSubst141955042_Pluso @ X2 @ Xa )
% 0.26/0.59 = Y2 )
% 0.26/0.59 => ( ! [Theta2: trm] :
% 0.26/0.59 ( ( X2
% 0.26/0.59 = ( some_trm @ Theta2 ) )
% 0.26/0.59 => ! [Eta2: trm] :
% 0.26/0.59 ( ( Xa
% 0.26/0.59 = ( some_trm @ Eta2 ) )
% 0.26/0.59 => ( Y2
% 0.26/0.59 != ( some_trm @ ( plus @ Theta2 @ Eta2 ) ) ) ) )
% 0.26/0.59 => ( ( ( X2 = none_trm )
% 0.26/0.59 => ( Y2 != none_trm ) )
% 0.26/0.59 => ~ ( ? [V2: trm] :
% 0.26/0.59 ( X2
% 0.26/0.59 = ( some_trm @ V2 ) )
% 0.26/0.59 => ( ( Xa = none_trm )
% 0.26/0.59 => ( Y2 != none_trm ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Pluso.elims
% 0.26/0.59 thf(fact_95_Timeso_Oelims,axiom,
% 0.26/0.59 ! [X2: option_trm,Xa: option_trm,Y2: option_trm] :
% 0.26/0.59 ( ( ( uSubst918876924Timeso @ X2 @ Xa )
% 0.26/0.59 = Y2 )
% 0.26/0.59 => ( ! [Theta2: trm] :
% 0.26/0.59 ( ( X2
% 0.26/0.59 = ( some_trm @ Theta2 ) )
% 0.26/0.59 => ! [Eta2: trm] :
% 0.26/0.59 ( ( Xa
% 0.26/0.59 = ( some_trm @ Eta2 ) )
% 0.26/0.59 => ( Y2
% 0.26/0.59 != ( some_trm @ ( times @ Theta2 @ Eta2 ) ) ) ) )
% 0.26/0.59 => ( ( ( X2 = none_trm )
% 0.26/0.59 => ( Y2 != none_trm ) )
% 0.26/0.59 => ~ ( ? [V2: trm] :
% 0.26/0.59 ( X2
% 0.26/0.59 = ( some_trm @ V2 ) )
% 0.26/0.59 => ( ( Xa = none_trm )
% 0.26/0.59 => ( Y2 != none_trm ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Timeso.elims
% 0.26/0.59 thf(fact_96_usubstappt_Osimps_I7_J,axiom,
% 0.26/0.59 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm] :
% 0.26/0.59 ( ( uSubst516392818stappt @ Sigma @ U @ ( differential @ Theta ) )
% 0.26/0.59 = ( uSubst716837505ntialo
% 0.26/0.59 @ ( uSubst516392818stappt @ Sigma
% 0.26/0.59 @ ( collect_variable
% 0.26/0.59 @ ^ [X3: variable] : $true )
% 0.26/0.59 @ Theta ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % usubstappt.simps(7)
% 0.26/0.59 thf(fact_97_option_Oinject,axiom,
% 0.26/0.59 ! [X23: trm,Y23: trm] :
% 0.26/0.59 ( ( ( some_trm @ X23 )
% 0.26/0.59 = ( some_trm @ Y23 ) )
% 0.26/0.59 = ( X23 = Y23 ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.inject
% 0.26/0.59 thf(fact_98_option_Oinject,axiom,
% 0.26/0.59 ! [X23: fml,Y23: fml] :
% 0.26/0.59 ( ( ( some_fml @ X23 )
% 0.26/0.59 = ( some_fml @ Y23 ) )
% 0.26/0.59 = ( X23 = Y23 ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.inject
% 0.26/0.59 thf(fact_99_option_Oinject,axiom,
% 0.26/0.59 ! [X23: game,Y23: game] :
% 0.26/0.59 ( ( ( some_game @ X23 )
% 0.26/0.59 = ( some_game @ Y23 ) )
% 0.26/0.59 = ( X23 = Y23 ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.inject
% 0.26/0.59 thf(fact_100_trm_Oinject_I7_J,axiom,
% 0.26/0.59 ! [X7: trm,Y7: trm] :
% 0.26/0.59 ( ( ( differential @ X7 )
% 0.26/0.59 = ( differential @ Y7 ) )
% 0.26/0.59 = ( X7 = Y7 ) ) ).
% 0.26/0.59
% 0.26/0.59 % trm.inject(7)
% 0.26/0.59 thf(fact_101_not__Some__eq,axiom,
% 0.26/0.59 ! [X2: option_trm] :
% 0.26/0.59 ( ( ! [Y3: trm] :
% 0.26/0.59 ( X2
% 0.26/0.59 != ( some_trm @ Y3 ) ) )
% 0.26/0.59 = ( X2 = none_trm ) ) ).
% 0.26/0.59
% 0.26/0.59 % not_Some_eq
% 0.26/0.59 thf(fact_102_not__Some__eq,axiom,
% 0.26/0.59 ! [X2: option_fml] :
% 0.26/0.59 ( ( ! [Y3: fml] :
% 0.26/0.59 ( X2
% 0.26/0.59 != ( some_fml @ Y3 ) ) )
% 0.26/0.59 = ( X2 = none_fml ) ) ).
% 0.26/0.59
% 0.26/0.59 % not_Some_eq
% 0.26/0.59 thf(fact_103_not__Some__eq,axiom,
% 0.26/0.59 ! [X2: option_game] :
% 0.26/0.59 ( ( ! [Y3: game] :
% 0.26/0.59 ( X2
% 0.26/0.59 != ( some_game @ Y3 ) ) )
% 0.26/0.59 = ( X2 = none_game ) ) ).
% 0.26/0.59
% 0.26/0.59 % not_Some_eq
% 0.26/0.59 thf(fact_104_not__None__eq,axiom,
% 0.26/0.59 ! [X2: option_trm] :
% 0.26/0.59 ( ( X2 != none_trm )
% 0.26/0.59 = ( ? [Y3: trm] :
% 0.26/0.59 ( X2
% 0.26/0.59 = ( some_trm @ Y3 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % not_None_eq
% 0.26/0.59 thf(fact_105_not__None__eq,axiom,
% 0.26/0.59 ! [X2: option_fml] :
% 0.26/0.59 ( ( X2 != none_fml )
% 0.26/0.59 = ( ? [Y3: fml] :
% 0.26/0.59 ( X2
% 0.26/0.59 = ( some_fml @ Y3 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % not_None_eq
% 0.26/0.59 thf(fact_106_not__None__eq,axiom,
% 0.26/0.59 ! [X2: option_game] :
% 0.26/0.59 ( ( X2 != none_game )
% 0.26/0.59 = ( ? [Y3: game] :
% 0.26/0.59 ( X2
% 0.26/0.59 = ( some_game @ Y3 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % not_None_eq
% 0.26/0.59 thf(fact_107_Aterm__Some,axiom,
% 0.26/0.59 some_trm = some_trm ).
% 0.26/0.59
% 0.26/0.59 % Aterm_Some
% 0.26/0.59 thf(fact_108_Differentialo_Osimps_I1_J,axiom,
% 0.26/0.59 ! [Theta: trm] :
% 0.26/0.59 ( ( uSubst716837505ntialo @ ( some_trm @ Theta ) )
% 0.26/0.59 = ( some_trm @ ( differential @ Theta ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Differentialo.simps(1)
% 0.26/0.59 thf(fact_109_combine__options__cases,axiom,
% 0.26/0.59 ! [X2: option_trm,P: option_trm > option_trm > $o,Y2: option_trm] :
% 0.26/0.59 ( ( ( X2 = none_trm )
% 0.26/0.59 => ( P @ X2 @ Y2 ) )
% 0.26/0.59 => ( ( ( Y2 = none_trm )
% 0.26/0.59 => ( P @ X2 @ Y2 ) )
% 0.26/0.59 => ( ! [A5: trm,B5: trm] :
% 0.26/0.59 ( ( X2
% 0.26/0.59 = ( some_trm @ A5 ) )
% 0.26/0.59 => ( ( Y2
% 0.26/0.59 = ( some_trm @ B5 ) )
% 0.26/0.59 => ( P @ X2 @ Y2 ) ) )
% 0.26/0.59 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % combine_options_cases
% 0.26/0.59 thf(fact_110_combine__options__cases,axiom,
% 0.26/0.59 ! [X2: option_trm,P: option_trm > option_fml > $o,Y2: option_fml] :
% 0.26/0.59 ( ( ( X2 = none_trm )
% 0.26/0.59 => ( P @ X2 @ Y2 ) )
% 0.26/0.59 => ( ( ( Y2 = none_fml )
% 0.26/0.59 => ( P @ X2 @ Y2 ) )
% 0.26/0.59 => ( ! [A5: trm,B5: fml] :
% 0.26/0.59 ( ( X2
% 0.26/0.59 = ( some_trm @ A5 ) )
% 0.26/0.59 => ( ( Y2
% 0.26/0.59 = ( some_fml @ B5 ) )
% 0.26/0.59 => ( P @ X2 @ Y2 ) ) )
% 0.26/0.59 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % combine_options_cases
% 0.26/0.59 thf(fact_111_combine__options__cases,axiom,
% 0.26/0.59 ! [X2: option_trm,P: option_trm > option_game > $o,Y2: option_game] :
% 0.26/0.59 ( ( ( X2 = none_trm )
% 0.26/0.59 => ( P @ X2 @ Y2 ) )
% 0.26/0.59 => ( ( ( Y2 = none_game )
% 0.26/0.59 => ( P @ X2 @ Y2 ) )
% 0.26/0.59 => ( ! [A5: trm,B5: game] :
% 0.26/0.59 ( ( X2
% 0.26/0.59 = ( some_trm @ A5 ) )
% 0.26/0.59 => ( ( Y2
% 0.26/0.59 = ( some_game @ B5 ) )
% 0.26/0.59 => ( P @ X2 @ Y2 ) ) )
% 0.26/0.59 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % combine_options_cases
% 0.26/0.59 thf(fact_112_combine__options__cases,axiom,
% 0.26/0.59 ! [X2: option_fml,P: option_fml > option_trm > $o,Y2: option_trm] :
% 0.26/0.59 ( ( ( X2 = none_fml )
% 0.26/0.59 => ( P @ X2 @ Y2 ) )
% 0.26/0.59 => ( ( ( Y2 = none_trm )
% 0.26/0.59 => ( P @ X2 @ Y2 ) )
% 0.26/0.59 => ( ! [A5: fml,B5: trm] :
% 0.26/0.59 ( ( X2
% 0.26/0.59 = ( some_fml @ A5 ) )
% 0.26/0.59 => ( ( Y2
% 0.26/0.59 = ( some_trm @ B5 ) )
% 0.26/0.59 => ( P @ X2 @ Y2 ) ) )
% 0.26/0.59 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % combine_options_cases
% 0.26/0.59 thf(fact_113_combine__options__cases,axiom,
% 0.26/0.59 ! [X2: option_fml,P: option_fml > option_fml > $o,Y2: option_fml] :
% 0.26/0.59 ( ( ( X2 = none_fml )
% 0.26/0.59 => ( P @ X2 @ Y2 ) )
% 0.26/0.59 => ( ( ( Y2 = none_fml )
% 0.26/0.59 => ( P @ X2 @ Y2 ) )
% 0.26/0.59 => ( ! [A5: fml,B5: fml] :
% 0.26/0.59 ( ( X2
% 0.26/0.59 = ( some_fml @ A5 ) )
% 0.26/0.59 => ( ( Y2
% 0.26/0.59 = ( some_fml @ B5 ) )
% 0.26/0.59 => ( P @ X2 @ Y2 ) ) )
% 0.26/0.59 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % combine_options_cases
% 0.26/0.59 thf(fact_114_combine__options__cases,axiom,
% 0.26/0.59 ! [X2: option_fml,P: option_fml > option_game > $o,Y2: option_game] :
% 0.26/0.59 ( ( ( X2 = none_fml )
% 0.26/0.59 => ( P @ X2 @ Y2 ) )
% 0.26/0.59 => ( ( ( Y2 = none_game )
% 0.26/0.59 => ( P @ X2 @ Y2 ) )
% 0.26/0.59 => ( ! [A5: fml,B5: game] :
% 0.26/0.59 ( ( X2
% 0.26/0.59 = ( some_fml @ A5 ) )
% 0.26/0.59 => ( ( Y2
% 0.26/0.59 = ( some_game @ B5 ) )
% 0.26/0.59 => ( P @ X2 @ Y2 ) ) )
% 0.26/0.59 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % combine_options_cases
% 0.26/0.59 thf(fact_115_combine__options__cases,axiom,
% 0.26/0.59 ! [X2: option_game,P: option_game > option_trm > $o,Y2: option_trm] :
% 0.26/0.59 ( ( ( X2 = none_game )
% 0.26/0.59 => ( P @ X2 @ Y2 ) )
% 0.26/0.59 => ( ( ( Y2 = none_trm )
% 0.26/0.59 => ( P @ X2 @ Y2 ) )
% 0.26/0.59 => ( ! [A5: game,B5: trm] :
% 0.26/0.59 ( ( X2
% 0.26/0.59 = ( some_game @ A5 ) )
% 0.26/0.59 => ( ( Y2
% 0.26/0.59 = ( some_trm @ B5 ) )
% 0.26/0.59 => ( P @ X2 @ Y2 ) ) )
% 0.26/0.59 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % combine_options_cases
% 0.26/0.59 thf(fact_116_combine__options__cases,axiom,
% 0.26/0.59 ! [X2: option_game,P: option_game > option_fml > $o,Y2: option_fml] :
% 0.26/0.59 ( ( ( X2 = none_game )
% 0.26/0.59 => ( P @ X2 @ Y2 ) )
% 0.26/0.59 => ( ( ( Y2 = none_fml )
% 0.26/0.59 => ( P @ X2 @ Y2 ) )
% 0.26/0.59 => ( ! [A5: game,B5: fml] :
% 0.26/0.59 ( ( X2
% 0.26/0.59 = ( some_game @ A5 ) )
% 0.26/0.59 => ( ( Y2
% 0.26/0.59 = ( some_fml @ B5 ) )
% 0.26/0.59 => ( P @ X2 @ Y2 ) ) )
% 0.26/0.59 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % combine_options_cases
% 0.26/0.59 thf(fact_117_combine__options__cases,axiom,
% 0.26/0.59 ! [X2: option_game,P: option_game > option_game > $o,Y2: option_game] :
% 0.26/0.59 ( ( ( X2 = none_game )
% 0.26/0.59 => ( P @ X2 @ Y2 ) )
% 0.26/0.59 => ( ( ( Y2 = none_game )
% 0.26/0.59 => ( P @ X2 @ Y2 ) )
% 0.26/0.59 => ( ! [A5: game,B5: game] :
% 0.26/0.59 ( ( X2
% 0.26/0.59 = ( some_game @ A5 ) )
% 0.26/0.59 => ( ( Y2
% 0.26/0.59 = ( some_game @ B5 ) )
% 0.26/0.59 => ( P @ X2 @ Y2 ) ) )
% 0.26/0.59 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % combine_options_cases
% 0.26/0.59 thf(fact_118_split__option__all,axiom,
% 0.26/0.59 ( ( ^ [P2: option_trm > $o] :
% 0.26/0.59 ! [X5: option_trm] : ( P2 @ X5 ) )
% 0.26/0.59 = ( ^ [P3: option_trm > $o] :
% 0.26/0.59 ( ( P3 @ none_trm )
% 0.26/0.59 & ! [X3: trm] : ( P3 @ ( some_trm @ X3 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % split_option_all
% 0.26/0.59 thf(fact_119_split__option__all,axiom,
% 0.26/0.59 ( ( ^ [P2: option_fml > $o] :
% 0.26/0.59 ! [X5: option_fml] : ( P2 @ X5 ) )
% 0.26/0.59 = ( ^ [P3: option_fml > $o] :
% 0.26/0.59 ( ( P3 @ none_fml )
% 0.26/0.59 & ! [X3: fml] : ( P3 @ ( some_fml @ X3 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % split_option_all
% 0.26/0.59 thf(fact_120_split__option__all,axiom,
% 0.26/0.59 ( ( ^ [P2: option_game > $o] :
% 0.26/0.59 ! [X5: option_game] : ( P2 @ X5 ) )
% 0.26/0.59 = ( ^ [P3: option_game > $o] :
% 0.26/0.59 ( ( P3 @ none_game )
% 0.26/0.59 & ! [X3: game] : ( P3 @ ( some_game @ X3 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % split_option_all
% 0.26/0.59 thf(fact_121_split__option__ex,axiom,
% 0.26/0.59 ( ( ^ [P2: option_trm > $o] :
% 0.26/0.59 ? [X5: option_trm] : ( P2 @ X5 ) )
% 0.26/0.59 = ( ^ [P3: option_trm > $o] :
% 0.26/0.59 ( ( P3 @ none_trm )
% 0.26/0.59 | ? [X3: trm] : ( P3 @ ( some_trm @ X3 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % split_option_ex
% 0.26/0.59 thf(fact_122_split__option__ex,axiom,
% 0.26/0.59 ( ( ^ [P2: option_fml > $o] :
% 0.26/0.59 ? [X5: option_fml] : ( P2 @ X5 ) )
% 0.26/0.59 = ( ^ [P3: option_fml > $o] :
% 0.26/0.59 ( ( P3 @ none_fml )
% 0.26/0.59 | ? [X3: fml] : ( P3 @ ( some_fml @ X3 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % split_option_ex
% 0.26/0.59 thf(fact_123_split__option__ex,axiom,
% 0.26/0.59 ( ( ^ [P2: option_game > $o] :
% 0.26/0.59 ? [X5: option_game] : ( P2 @ X5 ) )
% 0.26/0.59 = ( ^ [P3: option_game > $o] :
% 0.26/0.59 ( ( P3 @ none_game )
% 0.26/0.59 | ? [X3: game] : ( P3 @ ( some_game @ X3 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % split_option_ex
% 0.26/0.59 thf(fact_124_option_Oinducts,axiom,
% 0.26/0.59 ! [P: option_trm > $o,Option: option_trm] :
% 0.26/0.59 ( ( P @ none_trm )
% 0.26/0.59 => ( ! [X: trm] : ( P @ ( some_trm @ X ) )
% 0.26/0.59 => ( P @ Option ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.inducts
% 0.26/0.59 thf(fact_125_option_Oinducts,axiom,
% 0.26/0.59 ! [P: option_fml > $o,Option: option_fml] :
% 0.26/0.59 ( ( P @ none_fml )
% 0.26/0.59 => ( ! [X: fml] : ( P @ ( some_fml @ X ) )
% 0.26/0.59 => ( P @ Option ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.inducts
% 0.26/0.59 thf(fact_126_option_Oinducts,axiom,
% 0.26/0.59 ! [P: option_game > $o,Option: option_game] :
% 0.26/0.59 ( ( P @ none_game )
% 0.26/0.59 => ( ! [X: game] : ( P @ ( some_game @ X ) )
% 0.26/0.59 => ( P @ Option ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.inducts
% 0.26/0.59 thf(fact_127_option_Oexhaust,axiom,
% 0.26/0.59 ! [Y2: option_trm] :
% 0.26/0.59 ( ( Y2 != none_trm )
% 0.26/0.59 => ~ ! [X24: trm] :
% 0.26/0.59 ( Y2
% 0.26/0.59 != ( some_trm @ X24 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.exhaust
% 0.26/0.59 thf(fact_128_option_Oexhaust,axiom,
% 0.26/0.59 ! [Y2: option_fml] :
% 0.26/0.59 ( ( Y2 != none_fml )
% 0.26/0.59 => ~ ! [X24: fml] :
% 0.26/0.59 ( Y2
% 0.26/0.59 != ( some_fml @ X24 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.exhaust
% 0.26/0.59 thf(fact_129_option_Oexhaust,axiom,
% 0.26/0.59 ! [Y2: option_game] :
% 0.26/0.59 ( ( Y2 != none_game )
% 0.26/0.59 => ~ ! [X24: game] :
% 0.26/0.59 ( Y2
% 0.26/0.59 != ( some_game @ X24 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.exhaust
% 0.26/0.59 thf(fact_130_option_OdiscI,axiom,
% 0.26/0.59 ! [Option: option_trm,X23: trm] :
% 0.26/0.59 ( ( Option
% 0.26/0.59 = ( some_trm @ X23 ) )
% 0.26/0.59 => ( Option != none_trm ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.discI
% 0.26/0.59 thf(fact_131_option_OdiscI,axiom,
% 0.26/0.59 ! [Option: option_fml,X23: fml] :
% 0.26/0.59 ( ( Option
% 0.26/0.59 = ( some_fml @ X23 ) )
% 0.26/0.59 => ( Option != none_fml ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.discI
% 0.26/0.59 thf(fact_132_option_OdiscI,axiom,
% 0.26/0.59 ! [Option: option_game,X23: game] :
% 0.26/0.59 ( ( Option
% 0.26/0.59 = ( some_game @ X23 ) )
% 0.26/0.59 => ( Option != none_game ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.discI
% 0.26/0.59 thf(fact_133_option_Odistinct_I1_J,axiom,
% 0.26/0.59 ! [X23: trm] :
% 0.26/0.59 ( none_trm
% 0.26/0.59 != ( some_trm @ X23 ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.distinct(1)
% 0.26/0.59 thf(fact_134_option_Odistinct_I1_J,axiom,
% 0.26/0.59 ! [X23: fml] :
% 0.26/0.59 ( none_fml
% 0.26/0.59 != ( some_fml @ X23 ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.distinct(1)
% 0.26/0.59 thf(fact_135_option_Odistinct_I1_J,axiom,
% 0.26/0.59 ! [X23: game] :
% 0.26/0.59 ( none_game
% 0.26/0.59 != ( some_game @ X23 ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.distinct(1)
% 0.26/0.59 thf(fact_136_Differentialo_Oinduct,axiom,
% 0.26/0.59 ! [P: option_trm > $o,A0: option_trm] :
% 0.26/0.59 ( ! [Theta2: trm] : ( P @ ( some_trm @ Theta2 ) )
% 0.26/0.59 => ( ( P @ none_trm )
% 0.26/0.59 => ( P @ A0 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Differentialo.induct
% 0.26/0.59 thf(fact_137_Differentialo_Ocases,axiom,
% 0.26/0.59 ! [X2: option_trm] :
% 0.26/0.59 ( ! [Theta2: trm] :
% 0.26/0.59 ( X2
% 0.26/0.59 != ( some_trm @ Theta2 ) )
% 0.26/0.59 => ( X2 = none_trm ) ) ).
% 0.26/0.59
% 0.26/0.59 % Differentialo.cases
% 0.26/0.59 thf(fact_138_Assigno_Oinduct,axiom,
% 0.26/0.59 ! [P: variable > option_trm > $o,A0: variable,A1: option_trm] :
% 0.26/0.59 ( ! [X: variable,Theta2: trm] : ( P @ X @ ( some_trm @ Theta2 ) )
% 0.26/0.59 => ( ! [X: variable] : ( P @ X @ none_trm )
% 0.26/0.59 => ( P @ A0 @ A1 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Assigno.induct
% 0.26/0.59 thf(fact_139_Timeso_Oinduct,axiom,
% 0.26/0.59 ! [P: option_trm > option_trm > $o,A0: option_trm,A1: option_trm] :
% 0.26/0.59 ( ! [Theta2: trm,Eta2: trm] : ( P @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) )
% 0.26/0.59 => ( ! [X_1: option_trm] : ( P @ none_trm @ X_1 )
% 0.26/0.59 => ( ! [V2: trm] : ( P @ ( some_trm @ V2 ) @ none_trm )
% 0.26/0.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Timeso.induct
% 0.26/0.59 thf(fact_140_undeft__equiv,axiom,
% 0.26/0.59 ! [Theta: option_trm] :
% 0.26/0.59 ( ( Theta != none_trm )
% 0.26/0.59 = ( ? [T: trm] :
% 0.26/0.59 ( Theta
% 0.26/0.59 = ( some_trm @ T ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % undeft_equiv
% 0.26/0.59 thf(fact_141_ODEo_Oinduct,axiom,
% 0.26/0.59 ! [P: char > option_trm > $o,A0: char,A1: option_trm] :
% 0.26/0.59 ( ! [X: char,Theta2: trm] : ( P @ X @ ( some_trm @ Theta2 ) )
% 0.26/0.59 => ( ! [X: char] : ( P @ X @ none_trm )
% 0.26/0.59 => ( P @ A0 @ A1 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ODEo.induct
% 0.26/0.59 thf(fact_142_Differentialo_Oelims,axiom,
% 0.26/0.59 ! [X2: option_trm,Y2: option_trm] :
% 0.26/0.59 ( ( ( uSubst716837505ntialo @ X2 )
% 0.26/0.59 = Y2 )
% 0.26/0.59 => ( ! [Theta2: trm] :
% 0.26/0.59 ( ( X2
% 0.26/0.59 = ( some_trm @ Theta2 ) )
% 0.26/0.59 => ( Y2
% 0.26/0.59 != ( some_trm @ ( differential @ Theta2 ) ) ) )
% 0.26/0.59 => ~ ( ( X2 = none_trm )
% 0.26/0.59 => ( Y2 != none_trm ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Differentialo.elims
% 0.26/0.59 thf(fact_143_trm_Odistinct_I41_J,axiom,
% 0.26/0.59 ! [X61: trm,X62: trm,X7: trm] :
% 0.26/0.59 ( ( times @ X61 @ X62 )
% 0.26/0.59 != ( differential @ X7 ) ) ).
% 0.26/0.59
% 0.26/0.59 % trm.distinct(41)
% 0.26/0.59 thf(fact_144_trm_Odistinct_I39_J,axiom,
% 0.26/0.59 ! [X51: trm,X52: trm,X7: trm] :
% 0.26/0.59 ( ( plus @ X51 @ X52 )
% 0.26/0.59 != ( differential @ X7 ) ) ).
% 0.26/0.59
% 0.26/0.59 % trm.distinct(39)
% 0.26/0.59 thf(fact_145_Timeso_Osimps_I3_J,axiom,
% 0.26/0.59 ! [V3: trm] :
% 0.26/0.59 ( ( uSubst918876924Timeso @ ( some_trm @ V3 ) @ none_trm )
% 0.26/0.59 = none_trm ) ).
% 0.26/0.59
% 0.26/0.59 % Timeso.simps(3)
% 0.26/0.59 thf(fact_146_Pluso_Osimps_I3_J,axiom,
% 0.26/0.59 ! [V3: trm] :
% 0.26/0.59 ( ( uSubst141955042_Pluso @ ( some_trm @ V3 ) @ none_trm )
% 0.26/0.59 = none_trm ) ).
% 0.26/0.59
% 0.26/0.59 % Pluso.simps(3)
% 0.26/0.59 thf(fact_147_Pluso_Osimps_I1_J,axiom,
% 0.26/0.59 ! [Theta: trm,Eta: trm] :
% 0.26/0.59 ( ( uSubst141955042_Pluso @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) )
% 0.26/0.59 = ( some_trm @ ( plus @ Theta @ Eta ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Pluso.simps(1)
% 0.26/0.59 thf(fact_148_Timeso_Osimps_I1_J,axiom,
% 0.26/0.59 ! [Theta: trm,Eta: trm] :
% 0.26/0.59 ( ( uSubst918876924Timeso @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) )
% 0.26/0.59 = ( some_trm @ ( times @ Theta @ Eta ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Timeso.simps(1)
% 0.26/0.59 thf(fact_149_usubstappt__differential__conv,axiom,
% 0.26/0.59 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm] :
% 0.26/0.59 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( differential @ Theta ) )
% 0.26/0.59 != none_trm )
% 0.26/0.59 => ( ( uSubst516392818stappt @ Sigma
% 0.26/0.59 @ ( collect_variable
% 0.26/0.59 @ ^ [X3: variable] : $true )
% 0.26/0.59 @ Theta )
% 0.26/0.59 != none_trm ) ) ).
% 0.26/0.59
% 0.26/0.59 % usubstappt_differential_conv
% 0.26/0.59 thf(fact_150_Geqo_Osimps_I3_J,axiom,
% 0.26/0.59 ! [V3: trm] :
% 0.26/0.59 ( ( uSubst152838031e_Geqo @ ( some_trm @ V3 ) @ none_trm )
% 0.26/0.59 = none_fml ) ).
% 0.26/0.59
% 0.26/0.59 % Geqo.simps(3)
% 0.26/0.59 thf(fact_151_Geqo_Oelims,axiom,
% 0.26/0.59 ! [X2: option_trm,Xa: option_trm,Y2: option_fml] :
% 0.26/0.59 ( ( ( uSubst152838031e_Geqo @ X2 @ Xa )
% 0.26/0.59 = Y2 )
% 0.26/0.59 => ( ! [Theta2: trm] :
% 0.26/0.59 ( ( X2
% 0.26/0.59 = ( some_trm @ Theta2 ) )
% 0.26/0.59 => ! [Eta2: trm] :
% 0.26/0.59 ( ( Xa
% 0.26/0.59 = ( some_trm @ Eta2 ) )
% 0.26/0.59 => ( Y2
% 0.26/0.59 != ( some_fml @ ( geq @ Theta2 @ Eta2 ) ) ) ) )
% 0.26/0.59 => ( ( ( X2 = none_trm )
% 0.26/0.59 => ( Y2 != none_fml ) )
% 0.26/0.59 => ~ ( ? [V2: trm] :
% 0.26/0.59 ( X2
% 0.26/0.59 = ( some_trm @ V2 ) )
% 0.26/0.59 => ( ( Xa = none_trm )
% 0.26/0.59 => ( Y2 != none_fml ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Geqo.elims
% 0.26/0.59 thf(fact_152_Differentialo_Opelims,axiom,
% 0.26/0.59 ! [X2: option_trm,Y2: option_trm] :
% 0.26/0.59 ( ( ( uSubst716837505ntialo @ X2 )
% 0.26/0.59 = Y2 )
% 0.26/0.59 => ( ( accp_option_trm @ uSubst2051024824lo_rel @ X2 )
% 0.26/0.59 => ( ! [Theta2: trm] :
% 0.26/0.59 ( ( X2
% 0.26/0.59 = ( some_trm @ Theta2 ) )
% 0.26/0.59 => ( ( Y2
% 0.26/0.59 = ( some_trm @ ( differential @ Theta2 ) ) )
% 0.26/0.59 => ~ ( accp_option_trm @ uSubst2051024824lo_rel @ ( some_trm @ Theta2 ) ) ) )
% 0.26/0.59 => ~ ( ( X2 = none_trm )
% 0.26/0.59 => ( ( Y2 = none_trm )
% 0.26/0.59 => ~ ( accp_option_trm @ uSubst2051024824lo_rel @ none_trm ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Differentialo.pelims
% 0.26/0.59 thf(fact_153_Geqo_Osimps_I1_J,axiom,
% 0.26/0.59 ! [Theta: trm,Eta: trm] :
% 0.26/0.59 ( ( uSubst152838031e_Geqo @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) )
% 0.26/0.59 = ( some_fml @ ( geq @ Theta @ Eta ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Geqo.simps(1)
% 0.26/0.59 thf(fact_154_GreatestI2__order,axiom,
% 0.26/0.59 ! [P: set_variable > $o,X2: set_variable,Q: set_variable > $o] :
% 0.26/0.59 ( ( P @ X2 )
% 0.26/0.59 => ( ! [Y4: set_variable] :
% 0.26/0.59 ( ( P @ Y4 )
% 0.26/0.59 => ( ord_le282106107riable @ Y4 @ X2 ) )
% 0.26/0.59 => ( ! [X: set_variable] :
% 0.26/0.59 ( ( P @ X )
% 0.26/0.59 => ( ! [Y5: set_variable] :
% 0.26/0.59 ( ( P @ Y5 )
% 0.26/0.59 => ( ord_le282106107riable @ Y5 @ X ) )
% 0.26/0.59 => ( Q @ X ) ) )
% 0.26/0.59 => ( Q @ ( order_272405634riable @ P ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % GreatestI2_order
% 0.26/0.59 thf(fact_155_Greatest__equality,axiom,
% 0.26/0.59 ! [P: set_variable > $o,X2: set_variable] :
% 0.26/0.59 ( ( P @ X2 )
% 0.26/0.59 => ( ! [Y4: set_variable] :
% 0.26/0.59 ( ( P @ Y4 )
% 0.26/0.59 => ( ord_le282106107riable @ Y4 @ X2 ) )
% 0.26/0.59 => ( ( order_272405634riable @ P )
% 0.26/0.59 = X2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Greatest_equality
% 0.26/0.59 thf(fact_156_Diamondo_Oinduct,axiom,
% 0.26/0.59 ! [P: option_game > option_fml > $o,A0: option_game,A1: option_fml] :
% 0.26/0.59 ( ! [Alpha: game,Phi2: fml] : ( P @ ( some_game @ Alpha ) @ ( some_fml @ Phi2 ) )
% 0.26/0.59 => ( ! [X_1: option_fml] : ( P @ none_game @ X_1 )
% 0.26/0.59 => ( ! [V2: game] : ( P @ ( some_game @ V2 ) @ none_fml )
% 0.26/0.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Diamondo.induct
% 0.26/0.59 thf(fact_157_Existso_Oinduct,axiom,
% 0.26/0.59 ! [P: variable > option_fml > $o,A0: variable,A1: option_fml] :
% 0.26/0.59 ( ! [X: variable,Phi2: fml] : ( P @ X @ ( some_fml @ Phi2 ) )
% 0.26/0.59 => ( ! [X: variable] : ( P @ X @ none_fml )
% 0.26/0.59 => ( P @ A0 @ A1 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Existso.induct
% 0.26/0.59 thf(fact_158_undeff__equiv,axiom,
% 0.26/0.59 ! [Phi: option_fml] :
% 0.26/0.59 ( ( Phi != none_fml )
% 0.26/0.59 = ( ? [F2: fml] :
% 0.26/0.59 ( Phi
% 0.26/0.59 = ( some_fml @ F2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % undeff_equiv
% 0.26/0.59 thf(fact_159_Testo_Oinduct,axiom,
% 0.26/0.59 ! [P: option_fml > $o,A0: option_fml] :
% 0.26/0.59 ( ! [Phi2: fml] : ( P @ ( some_fml @ Phi2 ) )
% 0.26/0.59 => ( ( P @ none_fml )
% 0.26/0.59 => ( P @ A0 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Testo.induct
% 0.26/0.59 thf(fact_160_Testo_Ocases,axiom,
% 0.26/0.59 ! [X2: option_fml] :
% 0.26/0.59 ( ! [Phi2: fml] :
% 0.26/0.59 ( X2
% 0.26/0.59 != ( some_fml @ Phi2 ) )
% 0.26/0.59 => ( X2 = none_fml ) ) ).
% 0.26/0.59
% 0.26/0.59 % Testo.cases
% 0.26/0.59 thf(fact_161_Ando_Oinduct,axiom,
% 0.26/0.59 ! [P: option_fml > option_fml > $o,A0: option_fml,A1: option_fml] :
% 0.26/0.59 ( ! [Phi2: fml,Psi: fml] : ( P @ ( some_fml @ Phi2 ) @ ( some_fml @ Psi ) )
% 0.26/0.59 => ( ! [X_1: option_fml] : ( P @ none_fml @ X_1 )
% 0.26/0.59 => ( ! [V2: fml] : ( P @ ( some_fml @ V2 ) @ none_fml )
% 0.26/0.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Ando.induct
% 0.26/0.59 thf(fact_162_accp__subset,axiom,
% 0.26/0.59 ! [R1: produc1024976764on_trm > produc1024976764on_trm > $o,R2: produc1024976764on_trm > produc1024976764on_trm > $o] :
% 0.26/0.59 ( ( ord_le370603054_trm_o @ R1 @ R2 )
% 0.26/0.59 => ( ord_le373274227_trm_o @ ( accp_P394694195on_trm @ R2 ) @ ( accp_P394694195on_trm @ R1 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % accp_subset
% 0.26/0.59 thf(fact_163_accp__subset,axiom,
% 0.26/0.59 ! [R1: produc1072747943on_trm > produc1072747943on_trm > $o,R2: produc1072747943on_trm > produc1072747943on_trm > $o] :
% 0.26/0.59 ( ( ord_le90123726_trm_o @ R1 @ R2 )
% 0.26/0.59 => ( ord_le1721128566_trm_o @ ( accp_P758790320on_trm @ R2 ) @ ( accp_P758790320on_trm @ R1 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % accp_subset
% 0.26/0.59 thf(fact_164_accp__subset,axiom,
% 0.26/0.59 ! [R1: produc464795408on_trm > produc464795408on_trm > $o,R2: produc464795408on_trm > produc464795408on_trm > $o] :
% 0.26/0.59 ( ( ord_le157637894_trm_o @ R1 @ R2 )
% 0.26/0.59 => ( ord_le1222882015_trm_o @ ( accp_P419951815on_trm @ R2 ) @ ( accp_P419951815on_trm @ R1 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % accp_subset
% 0.26/0.59 thf(fact_165_accp__subset,axiom,
% 0.26/0.59 ! [R1: option_trm > option_trm > $o,R2: option_trm > option_trm > $o] :
% 0.26/0.59 ( ( ord_le847028878_trm_o @ R1 @ R2 )
% 0.26/0.59 => ( ord_le1957133745_trm_o @ ( accp_option_trm @ R2 ) @ ( accp_option_trm @ R1 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % accp_subset
% 0.26/0.59 thf(fact_166_accp__subset,axiom,
% 0.26/0.59 ! [R1: option_fml > option_fml > $o,R2: option_fml > option_fml > $o] :
% 0.26/0.59 ( ( ord_le802833166_fml_o @ R1 @ R2 )
% 0.26/0.59 => ( ord_le181580155_fml_o @ ( accp_option_fml @ R2 ) @ ( accp_option_fml @ R1 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % accp_subset
% 0.26/0.59 thf(fact_167_accp__subset__induct,axiom,
% 0.26/0.59 ! [D: produc1024976764on_trm > $o,R: produc1024976764on_trm > produc1024976764on_trm > $o,X2: produc1024976764on_trm,P: produc1024976764on_trm > $o] :
% 0.26/0.59 ( ( ord_le373274227_trm_o @ D @ ( accp_P394694195on_trm @ R ) )
% 0.26/0.59 => ( ! [X: produc1024976764on_trm,Z4: produc1024976764on_trm] :
% 0.26/0.59 ( ( D @ X )
% 0.26/0.59 => ( ( R @ Z4 @ X )
% 0.26/0.59 => ( D @ Z4 ) ) )
% 0.26/0.59 => ( ( D @ X2 )
% 0.26/0.59 => ( ! [X: produc1024976764on_trm] :
% 0.26/0.59 ( ( D @ X )
% 0.26/0.59 => ( ! [Z5: produc1024976764on_trm] :
% 0.26/0.59 ( ( R @ Z5 @ X )
% 0.26/0.59 => ( P @ Z5 ) )
% 0.26/0.59 => ( P @ X ) ) )
% 0.26/0.59 => ( P @ X2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % accp_subset_induct
% 0.26/0.59 thf(fact_168_accp__subset__induct,axiom,
% 0.26/0.59 ! [D: produc1072747943on_trm > $o,R: produc1072747943on_trm > produc1072747943on_trm > $o,X2: produc1072747943on_trm,P: produc1072747943on_trm > $o] :
% 0.26/0.59 ( ( ord_le1721128566_trm_o @ D @ ( accp_P758790320on_trm @ R ) )
% 0.26/0.59 => ( ! [X: produc1072747943on_trm,Z4: produc1072747943on_trm] :
% 0.26/0.59 ( ( D @ X )
% 0.26/0.59 => ( ( R @ Z4 @ X )
% 0.26/0.59 => ( D @ Z4 ) ) )
% 0.26/0.59 => ( ( D @ X2 )
% 0.26/0.59 => ( ! [X: produc1072747943on_trm] :
% 0.26/0.59 ( ( D @ X )
% 0.26/0.59 => ( ! [Z5: produc1072747943on_trm] :
% 0.26/0.59 ( ( R @ Z5 @ X )
% 0.26/0.59 => ( P @ Z5 ) )
% 0.26/0.59 => ( P @ X ) ) )
% 0.26/0.59 => ( P @ X2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % accp_subset_induct
% 0.26/0.59 thf(fact_169_accp__subset__induct,axiom,
% 0.26/0.59 ! [D: produc464795408on_trm > $o,R: produc464795408on_trm > produc464795408on_trm > $o,X2: produc464795408on_trm,P: produc464795408on_trm > $o] :
% 0.26/0.59 ( ( ord_le1222882015_trm_o @ D @ ( accp_P419951815on_trm @ R ) )
% 0.26/0.59 => ( ! [X: produc464795408on_trm,Z4: produc464795408on_trm] :
% 0.26/0.59 ( ( D @ X )
% 0.26/0.59 => ( ( R @ Z4 @ X )
% 0.26/0.59 => ( D @ Z4 ) ) )
% 0.26/0.59 => ( ( D @ X2 )
% 0.26/0.59 => ( ! [X: produc464795408on_trm] :
% 0.26/0.59 ( ( D @ X )
% 0.26/0.59 => ( ! [Z5: produc464795408on_trm] :
% 0.26/0.59 ( ( R @ Z5 @ X )
% 0.26/0.59 => ( P @ Z5 ) )
% 0.26/0.59 => ( P @ X ) ) )
% 0.26/0.59 => ( P @ X2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % accp_subset_induct
% 0.26/0.59 thf(fact_170_accp__subset__induct,axiom,
% 0.26/0.59 ! [D: option_trm > $o,R: option_trm > option_trm > $o,X2: option_trm,P: option_trm > $o] :
% 0.26/0.59 ( ( ord_le1957133745_trm_o @ D @ ( accp_option_trm @ R ) )
% 0.26/0.59 => ( ! [X: option_trm,Z4: option_trm] :
% 0.26/0.59 ( ( D @ X )
% 0.26/0.59 => ( ( R @ Z4 @ X )
% 0.26/0.59 => ( D @ Z4 ) ) )
% 0.26/0.59 => ( ( D @ X2 )
% 0.26/0.59 => ( ! [X: option_trm] :
% 0.26/0.59 ( ( D @ X )
% 0.26/0.59 => ( ! [Z5: option_trm] :
% 0.26/0.59 ( ( R @ Z5 @ X )
% 0.26/0.59 => ( P @ Z5 ) )
% 0.26/0.59 => ( P @ X ) ) )
% 0.26/0.59 => ( P @ X2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % accp_subset_induct
% 0.26/0.59 thf(fact_171_accp__subset__induct,axiom,
% 0.26/0.59 ! [D: option_fml > $o,R: option_fml > option_fml > $o,X2: option_fml,P: option_fml > $o] :
% 0.26/0.59 ( ( ord_le181580155_fml_o @ D @ ( accp_option_fml @ R ) )
% 0.26/0.59 => ( ! [X: option_fml,Z4: option_fml] :
% 0.26/0.59 ( ( D @ X )
% 0.26/0.59 => ( ( R @ Z4 @ X )
% 0.26/0.59 => ( D @ Z4 ) ) )
% 0.26/0.59 => ( ( D @ X2 )
% 0.26/0.59 => ( ! [X: option_fml] :
% 0.26/0.59 ( ( D @ X )
% 0.26/0.59 => ( ! [Z5: option_fml] :
% 0.26/0.59 ( ( R @ Z5 @ X )
% 0.26/0.59 => ( P @ Z5 ) )
% 0.26/0.59 => ( P @ X ) ) )
% 0.26/0.59 => ( P @ X2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % accp_subset_induct
% 0.26/0.59 thf(fact_172_usubstappf__geqr,axiom,
% 0.26/0.59 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.26/0.59 ( ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.26/0.59 != none_fml )
% 0.26/0.59 => ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.26/0.59 = ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % usubstappf_geqr
% 0.26/0.59 thf(fact_173_usubstappf__geq,axiom,
% 0.26/0.59 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.26/0.59 ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.26/0.59 != none_trm )
% 0.26/0.59 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Eta )
% 0.26/0.59 != none_trm )
% 0.26/0.59 => ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.26/0.59 = ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % usubstappf_geq
% 0.26/0.59 thf(fact_174_option_Ocollapse,axiom,
% 0.26/0.59 ! [Option: option_trm] :
% 0.26/0.59 ( ( Option != none_trm )
% 0.26/0.59 => ( ( some_trm @ ( the_trm @ Option ) )
% 0.26/0.59 = Option ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.collapse
% 0.26/0.59 thf(fact_175_option_Ocollapse,axiom,
% 0.26/0.59 ! [Option: option_fml] :
% 0.26/0.59 ( ( Option != none_fml )
% 0.26/0.59 => ( ( some_fml @ ( the_fml @ Option ) )
% 0.26/0.59 = Option ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.collapse
% 0.26/0.59 thf(fact_176_option_Ocollapse,axiom,
% 0.26/0.59 ! [Option: option_game] :
% 0.26/0.59 ( ( Option != none_game )
% 0.26/0.59 => ( ( some_game @ ( the_game @ Option ) )
% 0.26/0.59 = Option ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.collapse
% 0.26/0.59 thf(fact_177_Composeo_Oinduct,axiom,
% 0.26/0.59 ! [P: option_game > option_game > $o,A0: option_game,A1: option_game] :
% 0.26/0.59 ( ! [Alpha: game,Beta: game] : ( P @ ( some_game @ Alpha ) @ ( some_game @ Beta ) )
% 0.26/0.59 => ( ! [Alpha: option_game] : ( P @ Alpha @ none_game )
% 0.26/0.59 => ( ! [V2: game] : ( P @ none_game @ ( some_game @ V2 ) )
% 0.26/0.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Composeo.induct
% 0.26/0.59 thf(fact_178_undefg__equiv,axiom,
% 0.26/0.59 ! [Alpha2: option_game] :
% 0.26/0.59 ( ( Alpha2 != none_game )
% 0.26/0.59 = ( ? [G: game] :
% 0.26/0.59 ( Alpha2
% 0.26/0.59 = ( some_game @ G ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % undefg_equiv
% 0.26/0.59 thf(fact_179_Loopo_Oinduct,axiom,
% 0.26/0.59 ! [P: option_game > $o,A0: option_game] :
% 0.26/0.59 ( ! [Alpha: game] : ( P @ ( some_game @ Alpha ) )
% 0.26/0.59 => ( ( P @ none_game )
% 0.26/0.59 => ( P @ A0 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Loopo.induct
% 0.26/0.59 thf(fact_180_Loopo_Ocases,axiom,
% 0.26/0.59 ! [X2: option_game] :
% 0.26/0.59 ( ! [Alpha: game] :
% 0.26/0.59 ( X2
% 0.26/0.59 != ( some_game @ Alpha ) )
% 0.26/0.59 => ( X2 = none_game ) ) ).
% 0.26/0.59
% 0.26/0.59 % Loopo.cases
% 0.26/0.59 thf(fact_181_option_Oexpand,axiom,
% 0.26/0.59 ! [Option: option_trm,Option2: option_trm] :
% 0.26/0.59 ( ( ( Option = none_trm )
% 0.26/0.59 = ( Option2 = none_trm ) )
% 0.26/0.59 => ( ( ( Option != none_trm )
% 0.26/0.59 => ( ( Option2 != none_trm )
% 0.26/0.59 => ( ( the_trm @ Option )
% 0.26/0.59 = ( the_trm @ Option2 ) ) ) )
% 0.26/0.59 => ( Option = Option2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.expand
% 0.26/0.59 thf(fact_182_option_Oexpand,axiom,
% 0.26/0.59 ! [Option: option_fml,Option2: option_fml] :
% 0.26/0.59 ( ( ( Option = none_fml )
% 0.26/0.59 = ( Option2 = none_fml ) )
% 0.26/0.59 => ( ( ( Option != none_fml )
% 0.26/0.59 => ( ( Option2 != none_fml )
% 0.26/0.59 => ( ( the_fml @ Option )
% 0.26/0.59 = ( the_fml @ Option2 ) ) ) )
% 0.26/0.59 => ( Option = Option2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.expand
% 0.26/0.59 thf(fact_183_option_Oexpand,axiom,
% 0.26/0.59 ! [Option: option_game,Option2: option_game] :
% 0.26/0.59 ( ( ( Option = none_game )
% 0.26/0.59 = ( Option2 = none_game ) )
% 0.26/0.59 => ( ( ( Option != none_game )
% 0.26/0.59 => ( ( Option2 != none_game )
% 0.26/0.59 => ( ( the_game @ Option )
% 0.26/0.59 = ( the_game @ Option2 ) ) ) )
% 0.26/0.59 => ( Option = Option2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.expand
% 0.26/0.59 thf(fact_184_option_Osel,axiom,
% 0.26/0.59 ! [X23: trm] :
% 0.26/0.59 ( ( the_trm @ ( some_trm @ X23 ) )
% 0.26/0.59 = X23 ) ).
% 0.26/0.59
% 0.26/0.59 % option.sel
% 0.26/0.59 thf(fact_185_option_Osel,axiom,
% 0.26/0.59 ! [X23: fml] :
% 0.26/0.59 ( ( the_fml @ ( some_fml @ X23 ) )
% 0.26/0.59 = X23 ) ).
% 0.26/0.59
% 0.26/0.59 % option.sel
% 0.26/0.59 thf(fact_186_option_Osel,axiom,
% 0.26/0.59 ! [X23: game] :
% 0.26/0.59 ( ( the_game @ ( some_game @ X23 ) )
% 0.26/0.59 = X23 ) ).
% 0.26/0.59
% 0.26/0.59 % option.sel
% 0.26/0.59 thf(fact_187_option_Oexhaust__sel,axiom,
% 0.26/0.59 ! [Option: option_trm] :
% 0.26/0.59 ( ( Option != none_trm )
% 0.26/0.59 => ( Option
% 0.26/0.59 = ( some_trm @ ( the_trm @ Option ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.exhaust_sel
% 0.26/0.59 thf(fact_188_option_Oexhaust__sel,axiom,
% 0.26/0.59 ! [Option: option_fml] :
% 0.26/0.59 ( ( Option != none_fml )
% 0.26/0.59 => ( Option
% 0.26/0.59 = ( some_fml @ ( the_fml @ Option ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.exhaust_sel
% 0.26/0.59 thf(fact_189_option_Oexhaust__sel,axiom,
% 0.26/0.59 ! [Option: option_game] :
% 0.26/0.59 ( ( Option != none_game )
% 0.26/0.59 => ( Option
% 0.26/0.59 = ( some_game @ ( the_game @ Option ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % option.exhaust_sel
% 0.26/0.59 thf(fact_190_accp_Ocases,axiom,
% 0.26/0.59 ! [R3: produc1024976764on_trm > produc1024976764on_trm > $o,A3: produc1024976764on_trm] :
% 0.26/0.59 ( ( accp_P394694195on_trm @ R3 @ A3 )
% 0.26/0.59 => ! [Y5: produc1024976764on_trm] :
% 0.26/0.59 ( ( R3 @ Y5 @ A3 )
% 0.26/0.59 => ( accp_P394694195on_trm @ R3 @ Y5 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % accp.cases
% 0.26/0.59 thf(fact_191_accp_Ocases,axiom,
% 0.26/0.59 ! [R3: produc1072747943on_trm > produc1072747943on_trm > $o,A3: produc1072747943on_trm] :
% 0.26/0.59 ( ( accp_P758790320on_trm @ R3 @ A3 )
% 0.26/0.59 => ! [Y5: produc1072747943on_trm] :
% 0.26/0.59 ( ( R3 @ Y5 @ A3 )
% 0.26/0.59 => ( accp_P758790320on_trm @ R3 @ Y5 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % accp.cases
% 0.26/0.59 thf(fact_192_accp_Ocases,axiom,
% 0.26/0.59 ! [R3: produc464795408on_trm > produc464795408on_trm > $o,A3: produc464795408on_trm] :
% 0.26/0.59 ( ( accp_P419951815on_trm @ R3 @ A3 )
% 0.26/0.59 => ! [Y5: produc464795408on_trm] :
% 0.26/0.59 ( ( R3 @ Y5 @ A3 )
% 0.26/0.59 => ( accp_P419951815on_trm @ R3 @ Y5 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % accp.cases
% 0.26/0.59 thf(fact_193_accp_Ocases,axiom,
% 0.26/0.59 ! [R3: option_trm > option_trm > $o,A3: option_trm] :
% 0.26/0.59 ( ( accp_option_trm @ R3 @ A3 )
% 0.26/0.59 => ! [Y5: option_trm] :
% 0.26/0.59 ( ( R3 @ Y5 @ A3 )
% 0.26/0.59 => ( accp_option_trm @ R3 @ Y5 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % accp.cases
% 0.26/0.59 thf(fact_194_accp_Ocases,axiom,
% 0.26/0.59 ! [R3: option_fml > option_fml > $o,A3: option_fml] :
% 0.26/0.60 ( ( accp_option_fml @ R3 @ A3 )
% 0.26/0.60 => ! [Y5: option_fml] :
% 0.26/0.60 ( ( R3 @ Y5 @ A3 )
% 0.26/0.60 => ( accp_option_fml @ R3 @ Y5 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp.cases
% 0.26/0.60 thf(fact_195_accp_Osimps,axiom,
% 0.26/0.60 ( accp_P394694195on_trm
% 0.26/0.60 = ( ^ [R4: produc1024976764on_trm > produc1024976764on_trm > $o,A4: produc1024976764on_trm] :
% 0.26/0.60 ? [X3: produc1024976764on_trm] :
% 0.26/0.60 ( ( A4 = X3 )
% 0.26/0.60 & ! [Y3: produc1024976764on_trm] :
% 0.26/0.60 ( ( R4 @ Y3 @ X3 )
% 0.26/0.60 => ( accp_P394694195on_trm @ R4 @ Y3 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp.simps
% 0.26/0.60 thf(fact_196_accp_Osimps,axiom,
% 0.26/0.60 ( accp_P758790320on_trm
% 0.26/0.60 = ( ^ [R4: produc1072747943on_trm > produc1072747943on_trm > $o,A4: produc1072747943on_trm] :
% 0.26/0.60 ? [X3: produc1072747943on_trm] :
% 0.26/0.60 ( ( A4 = X3 )
% 0.26/0.60 & ! [Y3: produc1072747943on_trm] :
% 0.26/0.60 ( ( R4 @ Y3 @ X3 )
% 0.26/0.60 => ( accp_P758790320on_trm @ R4 @ Y3 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp.simps
% 0.26/0.60 thf(fact_197_accp_Osimps,axiom,
% 0.26/0.60 ( accp_P419951815on_trm
% 0.26/0.60 = ( ^ [R4: produc464795408on_trm > produc464795408on_trm > $o,A4: produc464795408on_trm] :
% 0.26/0.60 ? [X3: produc464795408on_trm] :
% 0.26/0.60 ( ( A4 = X3 )
% 0.26/0.60 & ! [Y3: produc464795408on_trm] :
% 0.26/0.60 ( ( R4 @ Y3 @ X3 )
% 0.26/0.60 => ( accp_P419951815on_trm @ R4 @ Y3 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp.simps
% 0.26/0.60 thf(fact_198_accp_Osimps,axiom,
% 0.26/0.60 ( accp_option_trm
% 0.26/0.60 = ( ^ [R4: option_trm > option_trm > $o,A4: option_trm] :
% 0.26/0.60 ? [X3: option_trm] :
% 0.26/0.60 ( ( A4 = X3 )
% 0.26/0.60 & ! [Y3: option_trm] :
% 0.26/0.60 ( ( R4 @ Y3 @ X3 )
% 0.26/0.60 => ( accp_option_trm @ R4 @ Y3 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp.simps
% 0.26/0.60 thf(fact_199_accp_Osimps,axiom,
% 0.26/0.60 ( accp_option_fml
% 0.26/0.60 = ( ^ [R4: option_fml > option_fml > $o,A4: option_fml] :
% 0.26/0.60 ? [X3: option_fml] :
% 0.26/0.60 ( ( A4 = X3 )
% 0.26/0.60 & ! [Y3: option_fml] :
% 0.26/0.60 ( ( R4 @ Y3 @ X3 )
% 0.26/0.60 => ( accp_option_fml @ R4 @ Y3 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp.simps
% 0.26/0.60 thf(fact_200_accp_Ointros,axiom,
% 0.26/0.60 ! [R3: produc1024976764on_trm > produc1024976764on_trm > $o,X2: produc1024976764on_trm] :
% 0.26/0.60 ( ! [Y4: produc1024976764on_trm] :
% 0.26/0.60 ( ( R3 @ Y4 @ X2 )
% 0.26/0.60 => ( accp_P394694195on_trm @ R3 @ Y4 ) )
% 0.26/0.60 => ( accp_P394694195on_trm @ R3 @ X2 ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp.intros
% 0.26/0.60 thf(fact_201_accp_Ointros,axiom,
% 0.26/0.60 ! [R3: produc1072747943on_trm > produc1072747943on_trm > $o,X2: produc1072747943on_trm] :
% 0.26/0.60 ( ! [Y4: produc1072747943on_trm] :
% 0.26/0.60 ( ( R3 @ Y4 @ X2 )
% 0.26/0.60 => ( accp_P758790320on_trm @ R3 @ Y4 ) )
% 0.26/0.60 => ( accp_P758790320on_trm @ R3 @ X2 ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp.intros
% 0.26/0.60 thf(fact_202_accp_Ointros,axiom,
% 0.26/0.60 ! [R3: produc464795408on_trm > produc464795408on_trm > $o,X2: produc464795408on_trm] :
% 0.26/0.60 ( ! [Y4: produc464795408on_trm] :
% 0.26/0.60 ( ( R3 @ Y4 @ X2 )
% 0.26/0.60 => ( accp_P419951815on_trm @ R3 @ Y4 ) )
% 0.26/0.60 => ( accp_P419951815on_trm @ R3 @ X2 ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp.intros
% 0.26/0.60 thf(fact_203_accp_Ointros,axiom,
% 0.26/0.60 ! [R3: option_trm > option_trm > $o,X2: option_trm] :
% 0.26/0.60 ( ! [Y4: option_trm] :
% 0.26/0.60 ( ( R3 @ Y4 @ X2 )
% 0.26/0.60 => ( accp_option_trm @ R3 @ Y4 ) )
% 0.26/0.60 => ( accp_option_trm @ R3 @ X2 ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp.intros
% 0.26/0.60 thf(fact_204_accp_Ointros,axiom,
% 0.26/0.60 ! [R3: option_fml > option_fml > $o,X2: option_fml] :
% 0.26/0.60 ( ! [Y4: option_fml] :
% 0.26/0.60 ( ( R3 @ Y4 @ X2 )
% 0.26/0.60 => ( accp_option_fml @ R3 @ Y4 ) )
% 0.26/0.60 => ( accp_option_fml @ R3 @ X2 ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp.intros
% 0.26/0.60 thf(fact_205_accp__induct,axiom,
% 0.26/0.60 ! [R3: produc1024976764on_trm > produc1024976764on_trm > $o,A3: produc1024976764on_trm,P: produc1024976764on_trm > $o] :
% 0.26/0.60 ( ( accp_P394694195on_trm @ R3 @ A3 )
% 0.26/0.60 => ( ! [X: produc1024976764on_trm] :
% 0.26/0.60 ( ( accp_P394694195on_trm @ R3 @ X )
% 0.26/0.60 => ( ! [Y5: produc1024976764on_trm] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( P @ Y5 ) )
% 0.26/0.60 => ( P @ X ) ) )
% 0.26/0.60 => ( P @ A3 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp_induct
% 0.26/0.60 thf(fact_206_accp__induct,axiom,
% 0.26/0.60 ! [R3: produc1072747943on_trm > produc1072747943on_trm > $o,A3: produc1072747943on_trm,P: produc1072747943on_trm > $o] :
% 0.26/0.60 ( ( accp_P758790320on_trm @ R3 @ A3 )
% 0.26/0.60 => ( ! [X: produc1072747943on_trm] :
% 0.26/0.60 ( ( accp_P758790320on_trm @ R3 @ X )
% 0.26/0.60 => ( ! [Y5: produc1072747943on_trm] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( P @ Y5 ) )
% 0.26/0.60 => ( P @ X ) ) )
% 0.26/0.60 => ( P @ A3 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp_induct
% 0.26/0.60 thf(fact_207_accp__induct,axiom,
% 0.26/0.60 ! [R3: produc464795408on_trm > produc464795408on_trm > $o,A3: produc464795408on_trm,P: produc464795408on_trm > $o] :
% 0.26/0.60 ( ( accp_P419951815on_trm @ R3 @ A3 )
% 0.26/0.60 => ( ! [X: produc464795408on_trm] :
% 0.26/0.60 ( ( accp_P419951815on_trm @ R3 @ X )
% 0.26/0.60 => ( ! [Y5: produc464795408on_trm] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( P @ Y5 ) )
% 0.26/0.60 => ( P @ X ) ) )
% 0.26/0.60 => ( P @ A3 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp_induct
% 0.26/0.60 thf(fact_208_accp__induct,axiom,
% 0.26/0.60 ! [R3: option_trm > option_trm > $o,A3: option_trm,P: option_trm > $o] :
% 0.26/0.60 ( ( accp_option_trm @ R3 @ A3 )
% 0.26/0.60 => ( ! [X: option_trm] :
% 0.26/0.60 ( ( accp_option_trm @ R3 @ X )
% 0.26/0.60 => ( ! [Y5: option_trm] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( P @ Y5 ) )
% 0.26/0.60 => ( P @ X ) ) )
% 0.26/0.60 => ( P @ A3 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp_induct
% 0.26/0.60 thf(fact_209_accp__induct,axiom,
% 0.26/0.60 ! [R3: option_fml > option_fml > $o,A3: option_fml,P: option_fml > $o] :
% 0.26/0.60 ( ( accp_option_fml @ R3 @ A3 )
% 0.26/0.60 => ( ! [X: option_fml] :
% 0.26/0.60 ( ( accp_option_fml @ R3 @ X )
% 0.26/0.60 => ( ! [Y5: option_fml] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( P @ Y5 ) )
% 0.26/0.60 => ( P @ X ) ) )
% 0.26/0.60 => ( P @ A3 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp_induct
% 0.26/0.60 thf(fact_210_accp_Oinducts,axiom,
% 0.26/0.60 ! [R3: produc1024976764on_trm > produc1024976764on_trm > $o,X2: produc1024976764on_trm,P: produc1024976764on_trm > $o] :
% 0.26/0.60 ( ( accp_P394694195on_trm @ R3 @ X2 )
% 0.26/0.60 => ( ! [X: produc1024976764on_trm] :
% 0.26/0.60 ( ! [Y5: produc1024976764on_trm] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( accp_P394694195on_trm @ R3 @ Y5 ) )
% 0.26/0.60 => ( ! [Y5: produc1024976764on_trm] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( P @ Y5 ) )
% 0.26/0.60 => ( P @ X ) ) )
% 0.26/0.60 => ( P @ X2 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp.inducts
% 0.26/0.60 thf(fact_211_accp_Oinducts,axiom,
% 0.26/0.60 ! [R3: produc1072747943on_trm > produc1072747943on_trm > $o,X2: produc1072747943on_trm,P: produc1072747943on_trm > $o] :
% 0.26/0.60 ( ( accp_P758790320on_trm @ R3 @ X2 )
% 0.26/0.60 => ( ! [X: produc1072747943on_trm] :
% 0.26/0.60 ( ! [Y5: produc1072747943on_trm] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( accp_P758790320on_trm @ R3 @ Y5 ) )
% 0.26/0.60 => ( ! [Y5: produc1072747943on_trm] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( P @ Y5 ) )
% 0.26/0.60 => ( P @ X ) ) )
% 0.26/0.60 => ( P @ X2 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp.inducts
% 0.26/0.60 thf(fact_212_accp_Oinducts,axiom,
% 0.26/0.60 ! [R3: produc464795408on_trm > produc464795408on_trm > $o,X2: produc464795408on_trm,P: produc464795408on_trm > $o] :
% 0.26/0.60 ( ( accp_P419951815on_trm @ R3 @ X2 )
% 0.26/0.60 => ( ! [X: produc464795408on_trm] :
% 0.26/0.60 ( ! [Y5: produc464795408on_trm] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( accp_P419951815on_trm @ R3 @ Y5 ) )
% 0.26/0.60 => ( ! [Y5: produc464795408on_trm] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( P @ Y5 ) )
% 0.26/0.60 => ( P @ X ) ) )
% 0.26/0.60 => ( P @ X2 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp.inducts
% 0.26/0.60 thf(fact_213_accp_Oinducts,axiom,
% 0.26/0.60 ! [R3: option_trm > option_trm > $o,X2: option_trm,P: option_trm > $o] :
% 0.26/0.60 ( ( accp_option_trm @ R3 @ X2 )
% 0.26/0.60 => ( ! [X: option_trm] :
% 0.26/0.60 ( ! [Y5: option_trm] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( accp_option_trm @ R3 @ Y5 ) )
% 0.26/0.60 => ( ! [Y5: option_trm] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( P @ Y5 ) )
% 0.26/0.60 => ( P @ X ) ) )
% 0.26/0.60 => ( P @ X2 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp.inducts
% 0.26/0.60 thf(fact_214_accp_Oinducts,axiom,
% 0.26/0.60 ! [R3: option_fml > option_fml > $o,X2: option_fml,P: option_fml > $o] :
% 0.26/0.60 ( ( accp_option_fml @ R3 @ X2 )
% 0.26/0.60 => ( ! [X: option_fml] :
% 0.26/0.60 ( ! [Y5: option_fml] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( accp_option_fml @ R3 @ Y5 ) )
% 0.26/0.60 => ( ! [Y5: option_fml] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( P @ Y5 ) )
% 0.26/0.60 => ( P @ X ) ) )
% 0.26/0.60 => ( P @ X2 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp.inducts
% 0.26/0.60 thf(fact_215_accp__downward,axiom,
% 0.26/0.60 ! [R3: produc1024976764on_trm > produc1024976764on_trm > $o,B3: produc1024976764on_trm,A3: produc1024976764on_trm] :
% 0.26/0.60 ( ( accp_P394694195on_trm @ R3 @ B3 )
% 0.26/0.60 => ( ( R3 @ A3 @ B3 )
% 0.26/0.60 => ( accp_P394694195on_trm @ R3 @ A3 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp_downward
% 0.26/0.60 thf(fact_216_accp__downward,axiom,
% 0.26/0.60 ! [R3: produc1072747943on_trm > produc1072747943on_trm > $o,B3: produc1072747943on_trm,A3: produc1072747943on_trm] :
% 0.26/0.60 ( ( accp_P758790320on_trm @ R3 @ B3 )
% 0.26/0.60 => ( ( R3 @ A3 @ B3 )
% 0.26/0.60 => ( accp_P758790320on_trm @ R3 @ A3 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp_downward
% 0.26/0.60 thf(fact_217_accp__downward,axiom,
% 0.26/0.60 ! [R3: produc464795408on_trm > produc464795408on_trm > $o,B3: produc464795408on_trm,A3: produc464795408on_trm] :
% 0.26/0.60 ( ( accp_P419951815on_trm @ R3 @ B3 )
% 0.26/0.60 => ( ( R3 @ A3 @ B3 )
% 0.26/0.60 => ( accp_P419951815on_trm @ R3 @ A3 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp_downward
% 0.26/0.60 thf(fact_218_accp__downward,axiom,
% 0.26/0.60 ! [R3: option_trm > option_trm > $o,B3: option_trm,A3: option_trm] :
% 0.26/0.60 ( ( accp_option_trm @ R3 @ B3 )
% 0.26/0.60 => ( ( R3 @ A3 @ B3 )
% 0.26/0.60 => ( accp_option_trm @ R3 @ A3 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp_downward
% 0.26/0.60 thf(fact_219_accp__downward,axiom,
% 0.26/0.60 ! [R3: option_fml > option_fml > $o,B3: option_fml,A3: option_fml] :
% 0.26/0.60 ( ( accp_option_fml @ R3 @ B3 )
% 0.26/0.60 => ( ( R3 @ A3 @ B3 )
% 0.26/0.60 => ( accp_option_fml @ R3 @ A3 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp_downward
% 0.26/0.60 thf(fact_220_not__accp__down,axiom,
% 0.26/0.60 ! [R: produc1024976764on_trm > produc1024976764on_trm > $o,X2: produc1024976764on_trm] :
% 0.26/0.60 ( ~ ( accp_P394694195on_trm @ R @ X2 )
% 0.26/0.60 => ~ ! [Z4: produc1024976764on_trm] :
% 0.26/0.60 ( ( R @ Z4 @ X2 )
% 0.26/0.60 => ( accp_P394694195on_trm @ R @ Z4 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % not_accp_down
% 0.26/0.60 thf(fact_221_not__accp__down,axiom,
% 0.26/0.60 ! [R: produc1072747943on_trm > produc1072747943on_trm > $o,X2: produc1072747943on_trm] :
% 0.26/0.60 ( ~ ( accp_P758790320on_trm @ R @ X2 )
% 0.26/0.60 => ~ ! [Z4: produc1072747943on_trm] :
% 0.26/0.60 ( ( R @ Z4 @ X2 )
% 0.26/0.60 => ( accp_P758790320on_trm @ R @ Z4 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % not_accp_down
% 0.26/0.60 thf(fact_222_not__accp__down,axiom,
% 0.26/0.60 ! [R: produc464795408on_trm > produc464795408on_trm > $o,X2: produc464795408on_trm] :
% 0.26/0.60 ( ~ ( accp_P419951815on_trm @ R @ X2 )
% 0.26/0.60 => ~ ! [Z4: produc464795408on_trm] :
% 0.26/0.60 ( ( R @ Z4 @ X2 )
% 0.26/0.60 => ( accp_P419951815on_trm @ R @ Z4 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % not_accp_down
% 0.26/0.60 thf(fact_223_not__accp__down,axiom,
% 0.26/0.60 ! [R: option_trm > option_trm > $o,X2: option_trm] :
% 0.26/0.60 ( ~ ( accp_option_trm @ R @ X2 )
% 0.26/0.60 => ~ ! [Z4: option_trm] :
% 0.26/0.60 ( ( R @ Z4 @ X2 )
% 0.26/0.60 => ( accp_option_trm @ R @ Z4 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % not_accp_down
% 0.26/0.60 thf(fact_224_not__accp__down,axiom,
% 0.26/0.60 ! [R: option_fml > option_fml > $o,X2: option_fml] :
% 0.26/0.60 ( ~ ( accp_option_fml @ R @ X2 )
% 0.26/0.60 => ~ ! [Z4: option_fml] :
% 0.26/0.60 ( ( R @ Z4 @ X2 )
% 0.26/0.60 => ( accp_option_fml @ R @ Z4 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % not_accp_down
% 0.26/0.60 thf(fact_225_accp__induct__rule,axiom,
% 0.26/0.60 ! [R3: produc1024976764on_trm > produc1024976764on_trm > $o,A3: produc1024976764on_trm,P: produc1024976764on_trm > $o] :
% 0.26/0.60 ( ( accp_P394694195on_trm @ R3 @ A3 )
% 0.26/0.60 => ( ! [X: produc1024976764on_trm] :
% 0.26/0.60 ( ( accp_P394694195on_trm @ R3 @ X )
% 0.26/0.60 => ( ! [Y5: produc1024976764on_trm] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( P @ Y5 ) )
% 0.26/0.60 => ( P @ X ) ) )
% 0.26/0.60 => ( P @ A3 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp_induct_rule
% 0.26/0.60 thf(fact_226_accp__induct__rule,axiom,
% 0.26/0.60 ! [R3: produc1072747943on_trm > produc1072747943on_trm > $o,A3: produc1072747943on_trm,P: produc1072747943on_trm > $o] :
% 0.26/0.60 ( ( accp_P758790320on_trm @ R3 @ A3 )
% 0.26/0.60 => ( ! [X: produc1072747943on_trm] :
% 0.26/0.60 ( ( accp_P758790320on_trm @ R3 @ X )
% 0.26/0.60 => ( ! [Y5: produc1072747943on_trm] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( P @ Y5 ) )
% 0.26/0.60 => ( P @ X ) ) )
% 0.26/0.60 => ( P @ A3 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp_induct_rule
% 0.26/0.60 thf(fact_227_accp__induct__rule,axiom,
% 0.26/0.60 ! [R3: produc464795408on_trm > produc464795408on_trm > $o,A3: produc464795408on_trm,P: produc464795408on_trm > $o] :
% 0.26/0.60 ( ( accp_P419951815on_trm @ R3 @ A3 )
% 0.26/0.60 => ( ! [X: produc464795408on_trm] :
% 0.26/0.60 ( ( accp_P419951815on_trm @ R3 @ X )
% 0.26/0.60 => ( ! [Y5: produc464795408on_trm] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( P @ Y5 ) )
% 0.26/0.60 => ( P @ X ) ) )
% 0.26/0.60 => ( P @ A3 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp_induct_rule
% 0.26/0.60 thf(fact_228_accp__induct__rule,axiom,
% 0.26/0.60 ! [R3: option_trm > option_trm > $o,A3: option_trm,P: option_trm > $o] :
% 0.26/0.60 ( ( accp_option_trm @ R3 @ A3 )
% 0.26/0.60 => ( ! [X: option_trm] :
% 0.26/0.60 ( ( accp_option_trm @ R3 @ X )
% 0.26/0.60 => ( ! [Y5: option_trm] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( P @ Y5 ) )
% 0.26/0.60 => ( P @ X ) ) )
% 0.26/0.60 => ( P @ A3 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp_induct_rule
% 0.26/0.60 thf(fact_229_accp__induct__rule,axiom,
% 0.26/0.60 ! [R3: option_fml > option_fml > $o,A3: option_fml,P: option_fml > $o] :
% 0.26/0.60 ( ( accp_option_fml @ R3 @ A3 )
% 0.26/0.60 => ( ! [X: option_fml] :
% 0.26/0.60 ( ( accp_option_fml @ R3 @ X )
% 0.26/0.60 => ( ! [Y5: option_fml] :
% 0.26/0.60 ( ( R3 @ Y5 @ X )
% 0.26/0.60 => ( P @ Y5 ) )
% 0.26/0.60 => ( P @ X ) ) )
% 0.26/0.60 => ( P @ A3 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % accp_induct_rule
% 0.26/0.60 thf(fact_230_Geqo_Opelims,axiom,
% 0.26/0.60 ! [X2: option_trm,Xa: option_trm,Y2: option_fml] :
% 0.26/0.60 ( ( ( uSubst152838031e_Geqo @ X2 @ Xa )
% 0.26/0.60 = Y2 )
% 0.26/0.60 => ( ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ X2 @ Xa ) )
% 0.26/0.60 => ( ! [Theta2: trm] :
% 0.26/0.60 ( ( X2
% 0.26/0.60 = ( some_trm @ Theta2 ) )
% 0.26/0.60 => ! [Eta2: trm] :
% 0.26/0.60 ( ( Xa
% 0.26/0.60 = ( some_trm @ Eta2 ) )
% 0.26/0.60 => ( ( Y2
% 0.26/0.60 = ( some_fml @ ( geq @ Theta2 @ Eta2 ) ) )
% 0.26/0.60 => ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) ) ) ) ) )
% 0.26/0.60 => ( ( ( X2 = none_trm )
% 0.26/0.60 => ( ( Y2 = none_fml )
% 0.26/0.60 => ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ none_trm @ Xa ) ) ) )
% 0.26/0.60 => ~ ! [V2: trm] :
% 0.26/0.60 ( ( X2
% 0.26/0.60 = ( some_trm @ V2 ) )
% 0.26/0.60 => ( ( Xa = none_trm )
% 0.26/0.60 => ( ( Y2 = none_fml )
% 0.26/0.60 => ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ ( some_trm @ V2 ) @ none_trm ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Geqo.pelims
% 0.26/0.60 thf(fact_231_Diamondo_Ocases,axiom,
% 0.26/0.60 ! [X2: produc1739631244on_fml] :
% 0.26/0.60 ( ! [Alpha: game,Phi2: fml] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc2124676926on_fml @ ( some_game @ Alpha ) @ ( some_fml @ Phi2 ) ) )
% 0.26/0.60 => ( ! [Phi2: option_fml] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc2124676926on_fml @ none_game @ Phi2 ) )
% 0.26/0.60 => ~ ! [V2: game] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc2124676926on_fml @ ( some_game @ V2 ) @ none_fml ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Diamondo.cases
% 0.26/0.60 thf(fact_232_subrelI,axiom,
% 0.26/0.60 ! [R3: set_Pr622314946on_fml,S2: set_Pr622314946on_fml] :
% 0.26/0.60 ( ! [X: option_game,Y4: option_fml] :
% 0.26/0.60 ( ( member1883102883on_fml @ ( produc2124676926on_fml @ X @ Y4 ) @ R3 )
% 0.26/0.60 => ( member1883102883on_fml @ ( produc2124676926on_fml @ X @ Y4 ) @ S2 ) )
% 0.26/0.60 => ( ord_le782333474on_fml @ R3 @ S2 ) ) ).
% 0.26/0.60
% 0.26/0.60 % subrelI
% 0.26/0.60 thf(fact_233_subrelI,axiom,
% 0.26/0.60 ! [R3: set_Pr1471344007on_trm,S2: set_Pr1471344007on_trm] :
% 0.26/0.60 ( ! [X: option_trm,Y4: option_trm] :
% 0.26/0.60 ( ( member165817296on_trm @ ( produc709594775on_trm @ X @ Y4 ) @ R3 )
% 0.26/0.60 => ( member165817296on_trm @ ( produc709594775on_trm @ X @ Y4 ) @ S2 ) )
% 0.26/0.60 => ( ord_le1322722599on_trm @ R3 @ S2 ) ) ).
% 0.26/0.60
% 0.26/0.60 % subrelI
% 0.26/0.60 thf(fact_234_subrelI,axiom,
% 0.26/0.60 ! [R3: set_Pr927595527on_fml,S2: set_Pr927595527on_fml] :
% 0.26/0.60 ( ! [X: option_fml,Y4: option_fml] :
% 0.26/0.60 ( ( member1287158352on_fml @ ( produc909629463on_fml @ X @ Y4 ) @ R3 )
% 0.26/0.60 => ( member1287158352on_fml @ ( produc909629463on_fml @ X @ Y4 ) @ S2 ) )
% 0.26/0.60 => ( ord_le778974119on_fml @ R3 @ S2 ) ) ).
% 0.26/0.60
% 0.26/0.60 % subrelI
% 0.26/0.60 thf(fact_235_subrelI,axiom,
% 0.26/0.60 ! [R3: set_Pr943832262on_trm,S2: set_Pr943832262on_trm] :
% 0.26/0.60 ( ! [X: char,Y4: option_trm] :
% 0.26/0.60 ( ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y4 ) @ R3 )
% 0.26/0.60 => ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y4 ) @ S2 ) )
% 0.26/0.60 => ( ord_le541293862on_trm @ R3 @ S2 ) ) ).
% 0.26/0.60
% 0.26/0.60 % subrelI
% 0.26/0.60 thf(fact_236_subrelI,axiom,
% 0.26/0.60 ! [R3: set_Pr1235432374le_trm,S2: set_Pr1235432374le_trm] :
% 0.26/0.60 ( ! [X: set_variable,Y4: trm] :
% 0.26/0.60 ( ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y4 ) @ R3 )
% 0.26/0.60 => ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y4 ) @ S2 ) )
% 0.26/0.60 => ( ord_le2102862870le_trm @ R3 @ S2 ) ) ).
% 0.26/0.60
% 0.26/0.60 % subrelI
% 0.26/0.60 thf(fact_237_ssubst__Pair__rhs,axiom,
% 0.26/0.60 ! [R3: option_game,S2: option_fml,R: set_Pr622314946on_fml,S3: option_fml] :
% 0.26/0.60 ( ( member1883102883on_fml @ ( produc2124676926on_fml @ R3 @ S2 ) @ R )
% 0.26/0.60 => ( ( S3 = S2 )
% 0.26/0.60 => ( member1883102883on_fml @ ( produc2124676926on_fml @ R3 @ S3 ) @ R ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % ssubst_Pair_rhs
% 0.26/0.60 thf(fact_238_ssubst__Pair__rhs,axiom,
% 0.26/0.60 ! [R3: option_trm,S2: option_trm,R: set_Pr1471344007on_trm,S3: option_trm] :
% 0.26/0.60 ( ( member165817296on_trm @ ( produc709594775on_trm @ R3 @ S2 ) @ R )
% 0.26/0.60 => ( ( S3 = S2 )
% 0.26/0.60 => ( member165817296on_trm @ ( produc709594775on_trm @ R3 @ S3 ) @ R ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % ssubst_Pair_rhs
% 0.26/0.60 thf(fact_239_ssubst__Pair__rhs,axiom,
% 0.26/0.60 ! [R3: option_fml,S2: option_fml,R: set_Pr927595527on_fml,S3: option_fml] :
% 0.26/0.60 ( ( member1287158352on_fml @ ( produc909629463on_fml @ R3 @ S2 ) @ R )
% 0.26/0.60 => ( ( S3 = S2 )
% 0.26/0.60 => ( member1287158352on_fml @ ( produc909629463on_fml @ R3 @ S3 ) @ R ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % ssubst_Pair_rhs
% 0.26/0.60 thf(fact_240_ssubst__Pair__rhs,axiom,
% 0.26/0.60 ! [R3: char,S2: option_trm,R: set_Pr943832262on_trm,S3: option_trm] :
% 0.26/0.60 ( ( member694524327on_trm @ ( produc1500300866on_trm @ R3 @ S2 ) @ R )
% 0.26/0.60 => ( ( S3 = S2 )
% 0.26/0.60 => ( member694524327on_trm @ ( produc1500300866on_trm @ R3 @ S3 ) @ R ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % ssubst_Pair_rhs
% 0.26/0.60 thf(fact_241_ssubst__Pair__rhs,axiom,
% 0.26/0.60 ! [R3: set_variable,S2: trm,R: set_Pr1235432374le_trm,S3: trm] :
% 0.26/0.60 ( ( member2122665623le_trm @ ( produc1482344242le_trm @ R3 @ S2 ) @ R )
% 0.26/0.60 => ( ( S3 = S2 )
% 0.26/0.60 => ( member2122665623le_trm @ ( produc1482344242le_trm @ R3 @ S3 ) @ R ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % ssubst_Pair_rhs
% 0.26/0.60 thf(fact_242_pred__equals__eq2,axiom,
% 0.26/0.60 ! [R: set_Pr622314946on_fml,S: set_Pr622314946on_fml] :
% 0.26/0.60 ( ( ( ^ [X3: option_game,Y3: option_fml] : ( member1883102883on_fml @ ( produc2124676926on_fml @ X3 @ Y3 ) @ R ) )
% 0.26/0.60 = ( ^ [X3: option_game,Y3: option_fml] : ( member1883102883on_fml @ ( produc2124676926on_fml @ X3 @ Y3 ) @ S ) ) )
% 0.26/0.60 = ( R = S ) ) ).
% 0.26/0.60
% 0.26/0.60 % pred_equals_eq2
% 0.26/0.60 thf(fact_243_pred__equals__eq2,axiom,
% 0.26/0.60 ! [R: set_Pr1471344007on_trm,S: set_Pr1471344007on_trm] :
% 0.26/0.60 ( ( ( ^ [X3: option_trm,Y3: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ X3 @ Y3 ) @ R ) )
% 0.26/0.60 = ( ^ [X3: option_trm,Y3: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ X3 @ Y3 ) @ S ) ) )
% 0.26/0.60 = ( R = S ) ) ).
% 0.26/0.60
% 0.26/0.60 % pred_equals_eq2
% 0.26/0.60 thf(fact_244_pred__equals__eq2,axiom,
% 0.26/0.60 ! [R: set_Pr927595527on_fml,S: set_Pr927595527on_fml] :
% 0.26/0.60 ( ( ( ^ [X3: option_fml,Y3: option_fml] : ( member1287158352on_fml @ ( produc909629463on_fml @ X3 @ Y3 ) @ R ) )
% 0.26/0.60 = ( ^ [X3: option_fml,Y3: option_fml] : ( member1287158352on_fml @ ( produc909629463on_fml @ X3 @ Y3 ) @ S ) ) )
% 0.26/0.60 = ( R = S ) ) ).
% 0.26/0.60
% 0.26/0.60 % pred_equals_eq2
% 0.26/0.60 thf(fact_245_pred__equals__eq2,axiom,
% 0.26/0.60 ! [R: set_Pr943832262on_trm,S: set_Pr943832262on_trm] :
% 0.26/0.60 ( ( ( ^ [X3: char,Y3: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X3 @ Y3 ) @ R ) )
% 0.26/0.60 = ( ^ [X3: char,Y3: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X3 @ Y3 ) @ S ) ) )
% 0.26/0.60 = ( R = S ) ) ).
% 0.26/0.60
% 0.26/0.60 % pred_equals_eq2
% 0.26/0.60 thf(fact_246_pred__equals__eq2,axiom,
% 0.26/0.60 ! [R: set_Pr1235432374le_trm,S: set_Pr1235432374le_trm] :
% 0.26/0.60 ( ( ( ^ [X3: set_variable,Y3: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X3 @ Y3 ) @ R ) )
% 0.26/0.60 = ( ^ [X3: set_variable,Y3: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X3 @ Y3 ) @ S ) ) )
% 0.26/0.60 = ( R = S ) ) ).
% 0.26/0.60
% 0.26/0.60 % pred_equals_eq2
% 0.26/0.60 thf(fact_247_pred__subset__eq2,axiom,
% 0.26/0.60 ! [R: set_Pr622314946on_fml,S: set_Pr622314946on_fml] :
% 0.26/0.60 ( ( ord_le1588489637_fml_o
% 0.26/0.60 @ ^ [X3: option_game,Y3: option_fml] : ( member1883102883on_fml @ ( produc2124676926on_fml @ X3 @ Y3 ) @ R )
% 0.26/0.60 @ ^ [X3: option_game,Y3: option_fml] : ( member1883102883on_fml @ ( produc2124676926on_fml @ X3 @ Y3 ) @ S ) )
% 0.26/0.60 = ( ord_le782333474on_fml @ R @ S ) ) ).
% 0.26/0.60
% 0.26/0.60 % pred_subset_eq2
% 0.26/0.60 thf(fact_248_pred__subset__eq2,axiom,
% 0.26/0.60 ! [R: set_Pr1471344007on_trm,S: set_Pr1471344007on_trm] :
% 0.26/0.60 ( ( ord_le847028878_trm_o
% 0.26/0.60 @ ^ [X3: option_trm,Y3: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ X3 @ Y3 ) @ R )
% 0.26/0.60 @ ^ [X3: option_trm,Y3: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ X3 @ Y3 ) @ S ) )
% 0.26/0.60 = ( ord_le1322722599on_trm @ R @ S ) ) ).
% 0.26/0.60
% 0.26/0.60 % pred_subset_eq2
% 0.26/0.60 thf(fact_249_pred__subset__eq2,axiom,
% 0.26/0.60 ! [R: set_Pr927595527on_fml,S: set_Pr927595527on_fml] :
% 0.26/0.60 ( ( ord_le802833166_fml_o
% 0.26/0.60 @ ^ [X3: option_fml,Y3: option_fml] : ( member1287158352on_fml @ ( produc909629463on_fml @ X3 @ Y3 ) @ R )
% 0.26/0.60 @ ^ [X3: option_fml,Y3: option_fml] : ( member1287158352on_fml @ ( produc909629463on_fml @ X3 @ Y3 ) @ S ) )
% 0.26/0.60 = ( ord_le778974119on_fml @ R @ S ) ) ).
% 0.26/0.60
% 0.26/0.60 % pred_subset_eq2
% 0.26/0.60 thf(fact_250_pred__subset__eq2,axiom,
% 0.26/0.60 ! [R: set_Pr943832262on_trm,S: set_Pr943832262on_trm] :
% 0.26/0.60 ( ( ord_le1890124833_trm_o
% 0.26/0.60 @ ^ [X3: char,Y3: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X3 @ Y3 ) @ R )
% 0.26/0.60 @ ^ [X3: char,Y3: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X3 @ Y3 ) @ S ) )
% 0.26/0.60 = ( ord_le541293862on_trm @ R @ S ) ) ).
% 0.26/0.60
% 0.26/0.60 % pred_subset_eq2
% 0.26/0.60 thf(fact_251_pred__subset__eq2,axiom,
% 0.26/0.60 ! [R: set_Pr1235432374le_trm,S: set_Pr1235432374le_trm] :
% 0.26/0.60 ( ( ord_le691957041_trm_o
% 0.26/0.60 @ ^ [X3: set_variable,Y3: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X3 @ Y3 ) @ R )
% 0.26/0.60 @ ^ [X3: set_variable,Y3: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X3 @ Y3 ) @ S ) )
% 0.26/0.60 = ( ord_le2102862870le_trm @ R @ S ) ) ).
% 0.26/0.60
% 0.26/0.60 % pred_subset_eq2
% 0.26/0.60 thf(fact_252_option_Odisc__eq__case_I1_J,axiom,
% 0.26/0.60 ! [Option: option_trm] :
% 0.26/0.60 ( ( Option = none_trm )
% 0.26/0.60 = ( case_option_o_trm @ $true
% 0.26/0.60 @ ^ [Uu: trm] : $false
% 0.26/0.60 @ Option ) ) ).
% 0.26/0.60
% 0.26/0.60 % option.disc_eq_case(1)
% 0.26/0.60 thf(fact_253_option_Odisc__eq__case_I1_J,axiom,
% 0.26/0.60 ! [Option: option_fml] :
% 0.26/0.60 ( ( Option = none_fml )
% 0.26/0.60 = ( case_option_o_fml @ $true
% 0.26/0.60 @ ^ [Uu: fml] : $false
% 0.26/0.60 @ Option ) ) ).
% 0.26/0.60
% 0.26/0.60 % option.disc_eq_case(1)
% 0.26/0.60 thf(fact_254_option_Odisc__eq__case_I1_J,axiom,
% 0.26/0.60 ! [Option: option_game] :
% 0.26/0.60 ( ( Option = none_game )
% 0.26/0.60 = ( case_option_o_game @ $true
% 0.26/0.60 @ ^ [Uu: game] : $false
% 0.26/0.60 @ Option ) ) ).
% 0.26/0.60
% 0.26/0.60 % option.disc_eq_case(1)
% 0.26/0.60 thf(fact_255_option_Odisc__eq__case_I2_J,axiom,
% 0.26/0.60 ! [Option: option_trm] :
% 0.26/0.60 ( ( Option != none_trm )
% 0.26/0.60 = ( case_option_o_trm @ $false
% 0.26/0.60 @ ^ [Uu: trm] : $true
% 0.26/0.60 @ Option ) ) ).
% 0.26/0.60
% 0.26/0.60 % option.disc_eq_case(2)
% 0.26/0.60 thf(fact_256_option_Odisc__eq__case_I2_J,axiom,
% 0.26/0.60 ! [Option: option_fml] :
% 0.26/0.60 ( ( Option != none_fml )
% 0.26/0.60 = ( case_option_o_fml @ $false
% 0.26/0.60 @ ^ [Uu: fml] : $true
% 0.26/0.60 @ Option ) ) ).
% 0.26/0.60
% 0.26/0.60 % option.disc_eq_case(2)
% 0.26/0.60 thf(fact_257_option_Odisc__eq__case_I2_J,axiom,
% 0.26/0.60 ! [Option: option_game] :
% 0.26/0.60 ( ( Option != none_game )
% 0.26/0.60 = ( case_option_o_game @ $false
% 0.26/0.60 @ ^ [Uu: game] : $true
% 0.26/0.60 @ Option ) ) ).
% 0.26/0.60
% 0.26/0.60 % option.disc_eq_case(2)
% 0.26/0.60 thf(fact_258_Timeso_Ocases,axiom,
% 0.26/0.60 ! [X2: produc1072747943on_trm] :
% 0.26/0.60 ( ! [Theta2: trm,Eta2: trm] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc709594775on_trm @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) ) )
% 0.26/0.60 => ( ! [Eta2: option_trm] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc709594775on_trm @ none_trm @ Eta2 ) )
% 0.26/0.60 => ~ ! [V2: trm] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc709594775on_trm @ ( some_trm @ V2 ) @ none_trm ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Timeso.cases
% 0.26/0.60 thf(fact_259_case__optionE,axiom,
% 0.26/0.60 ! [P: $o,Q: trm > $o,X2: option_trm] :
% 0.26/0.60 ( ( case_option_o_trm @ P @ Q @ X2 )
% 0.26/0.60 => ( ( ( X2 = none_trm )
% 0.26/0.60 => ~ P )
% 0.26/0.60 => ~ ! [Y4: trm] :
% 0.26/0.60 ( ( X2
% 0.26/0.60 = ( some_trm @ Y4 ) )
% 0.26/0.60 => ~ ( Q @ Y4 ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % case_optionE
% 0.26/0.60 thf(fact_260_case__optionE,axiom,
% 0.26/0.60 ! [P: $o,Q: fml > $o,X2: option_fml] :
% 0.26/0.60 ( ( case_option_o_fml @ P @ Q @ X2 )
% 0.26/0.60 => ( ( ( X2 = none_fml )
% 0.26/0.60 => ~ P )
% 0.26/0.60 => ~ ! [Y4: fml] :
% 0.26/0.60 ( ( X2
% 0.26/0.60 = ( some_fml @ Y4 ) )
% 0.26/0.60 => ~ ( Q @ Y4 ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % case_optionE
% 0.26/0.60 thf(fact_261_case__optionE,axiom,
% 0.26/0.60 ! [P: $o,Q: game > $o,X2: option_game] :
% 0.26/0.60 ( ( case_option_o_game @ P @ Q @ X2 )
% 0.26/0.60 => ( ( ( X2 = none_game )
% 0.26/0.60 => ~ P )
% 0.26/0.60 => ~ ! [Y4: game] :
% 0.26/0.60 ( ( X2
% 0.26/0.60 = ( some_game @ Y4 ) )
% 0.26/0.60 => ~ ( Q @ Y4 ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % case_optionE
% 0.26/0.60 thf(fact_262_Timeso_Opelims,axiom,
% 0.26/0.60 ! [X2: option_trm,Xa: option_trm,Y2: option_trm] :
% 0.26/0.60 ( ( ( uSubst918876924Timeso @ X2 @ Xa )
% 0.26/0.60 = Y2 )
% 0.26/0.60 => ( ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ X2 @ Xa ) )
% 0.26/0.60 => ( ! [Theta2: trm] :
% 0.26/0.60 ( ( X2
% 0.26/0.60 = ( some_trm @ Theta2 ) )
% 0.26/0.60 => ! [Eta2: trm] :
% 0.26/0.60 ( ( Xa
% 0.26/0.60 = ( some_trm @ Eta2 ) )
% 0.26/0.60 => ( ( Y2
% 0.26/0.60 = ( some_trm @ ( times @ Theta2 @ Eta2 ) ) )
% 0.26/0.60 => ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) ) ) ) ) )
% 0.26/0.60 => ( ( ( X2 = none_trm )
% 0.26/0.60 => ( ( Y2 = none_trm )
% 0.26/0.60 => ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ none_trm @ Xa ) ) ) )
% 0.26/0.60 => ~ ! [V2: trm] :
% 0.26/0.60 ( ( X2
% 0.26/0.60 = ( some_trm @ V2 ) )
% 0.26/0.60 => ( ( Xa = none_trm )
% 0.26/0.60 => ( ( Y2 = none_trm )
% 0.26/0.60 => ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ ( some_trm @ V2 ) @ none_trm ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Timeso.pelims
% 0.26/0.60 thf(fact_263_Pluso_Opelims,axiom,
% 0.26/0.60 ! [X2: option_trm,Xa: option_trm,Y2: option_trm] :
% 0.26/0.60 ( ( ( uSubst141955042_Pluso @ X2 @ Xa )
% 0.26/0.60 = Y2 )
% 0.26/0.60 => ( ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ X2 @ Xa ) )
% 0.26/0.60 => ( ! [Theta2: trm] :
% 0.26/0.60 ( ( X2
% 0.26/0.60 = ( some_trm @ Theta2 ) )
% 0.26/0.60 => ! [Eta2: trm] :
% 0.26/0.60 ( ( Xa
% 0.26/0.60 = ( some_trm @ Eta2 ) )
% 0.26/0.60 => ( ( Y2
% 0.26/0.60 = ( some_trm @ ( plus @ Theta2 @ Eta2 ) ) )
% 0.26/0.60 => ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) ) ) ) ) )
% 0.26/0.60 => ( ( ( X2 = none_trm )
% 0.26/0.60 => ( ( Y2 = none_trm )
% 0.26/0.60 => ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ none_trm @ Xa ) ) ) )
% 0.26/0.60 => ~ ! [V2: trm] :
% 0.26/0.60 ( ( X2
% 0.26/0.60 = ( some_trm @ V2 ) )
% 0.26/0.60 => ( ( Xa = none_trm )
% 0.26/0.60 => ( ( Y2 = none_trm )
% 0.26/0.60 => ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ ( some_trm @ V2 ) @ none_trm ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Pluso.pelims
% 0.26/0.60 thf(fact_264_ODEo_Ocases,axiom,
% 0.26/0.60 ! [X2: produc464795408on_trm] :
% 0.26/0.60 ( ! [X: char,Theta2: trm] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc1500300866on_trm @ X @ ( some_trm @ Theta2 ) ) )
% 0.26/0.60 => ~ ! [X: char] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc1500300866on_trm @ X @ none_trm ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % ODEo.cases
% 0.26/0.60 thf(fact_265_Assigno_Ocases,axiom,
% 0.26/0.60 ! [X2: produc1024976764on_trm] :
% 0.26/0.60 ( ! [X: variable,Theta2: trm] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc1743721902on_trm @ X @ ( some_trm @ Theta2 ) ) )
% 0.26/0.60 => ~ ! [X: variable] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc1743721902on_trm @ X @ none_trm ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Assigno.cases
% 0.26/0.60 thf(fact_266_Composeo_Ocases,axiom,
% 0.26/0.60 ! [X2: produc1016592119n_game] :
% 0.26/0.60 ( ! [Alpha: game,Beta: game] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc1111617711n_game @ ( some_game @ Alpha ) @ ( some_game @ Beta ) ) )
% 0.26/0.60 => ( ! [Alpha: option_game] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc1111617711n_game @ Alpha @ none_game ) )
% 0.26/0.60 => ~ ! [V2: game] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc1111617711n_game @ none_game @ ( some_game @ V2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Composeo.cases
% 0.26/0.60 thf(fact_267_Existso_Ocases,axiom,
% 0.26/0.60 ! [X2: produc1408538418on_fml] :
% 0.26/0.60 ( ! [X: variable,Phi2: fml] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc1205977188on_fml @ X @ ( some_fml @ Phi2 ) ) )
% 0.26/0.60 => ~ ! [X: variable] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc1205977188on_fml @ X @ none_fml ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Existso.cases
% 0.26/0.60 thf(fact_268_Ando_Ocases,axiom,
% 0.26/0.60 ! [X2: produc46605351on_fml] :
% 0.26/0.60 ( ! [Phi2: fml,Psi: fml] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc909629463on_fml @ ( some_fml @ Phi2 ) @ ( some_fml @ Psi ) ) )
% 0.26/0.60 => ( ! [Psi: option_fml] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc909629463on_fml @ none_fml @ Psi ) )
% 0.26/0.60 => ~ ! [V2: fml] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc909629463on_fml @ ( some_fml @ V2 ) @ none_fml ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Ando.cases
% 0.26/0.60 thf(fact_269_usubstappt_Opsimps_I7_J,axiom,
% 0.26/0.60 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm] :
% 0.26/0.60 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( differential @ Theta ) ) ) )
% 0.26/0.60 => ( ( uSubst516392818stappt @ Sigma @ U @ ( differential @ Theta ) )
% 0.26/0.60 = ( uSubst716837505ntialo
% 0.26/0.60 @ ( uSubst516392818stappt @ Sigma
% 0.26/0.60 @ ( collect_variable
% 0.26/0.60 @ ^ [X3: variable] : $true )
% 0.26/0.60 @ Theta ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % usubstappt.psimps(7)
% 0.26/0.60 thf(fact_270_usubstappt_Opsimps_I6_J,axiom,
% 0.26/0.60 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.26/0.60 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( times @ Theta @ Eta ) ) ) )
% 0.26/0.60 => ( ( uSubst516392818stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 0.26/0.60 = ( uSubst918876924Timeso @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % usubstappt.psimps(6)
% 0.26/0.60 thf(fact_271_usubstappt_Opsimps_I5_J,axiom,
% 0.26/0.60 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.26/0.60 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( plus @ Theta @ Eta ) ) ) )
% 0.26/0.60 => ( ( uSubst516392818stappt @ Sigma @ U @ ( plus @ Theta @ Eta ) )
% 0.26/0.60 = ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % usubstappt.psimps(5)
% 0.26/0.60 thf(fact_272_usubstappt_Opsimps_I1_J,axiom,
% 0.26/0.60 ! [Sigma: produc1418842292n_game,U: set_variable,X2: variable] :
% 0.26/0.60 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( var @ X2 ) ) ) )
% 0.26/0.60 => ( ( uSubst516392818stappt @ Sigma @ U @ ( var @ X2 ) )
% 0.26/0.60 = ( some_trm @ ( var @ X2 ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % usubstappt.psimps(1)
% 0.26/0.60 thf(fact_273_usubstappt_Opsimps_I2_J,axiom,
% 0.26/0.60 ! [Sigma: produc1418842292n_game,U: set_variable,R3: real] :
% 0.26/0.60 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( number @ R3 ) ) ) )
% 0.26/0.60 => ( ( uSubst516392818stappt @ Sigma @ U @ ( number @ R3 ) )
% 0.26/0.60 = ( some_trm @ ( number @ R3 ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % usubstappt.psimps(2)
% 0.26/0.60 thf(fact_274_in__lex__prod,axiom,
% 0.26/0.60 ! [A3: option_trm,B3: option_fml,A6: option_trm,B6: option_fml,R3: set_Pr1471344007on_trm,S2: set_Pr927595527on_fml] :
% 0.26/0.60 ( ( member1316917136on_fml @ ( produc1235825367on_fml @ ( produc171850061on_fml @ A3 @ B3 ) @ ( produc171850061on_fml @ A6 @ B6 ) ) @ ( lex_pr1724583269on_fml @ R3 @ S2 ) )
% 0.26/0.60 = ( ( member165817296on_trm @ ( produc709594775on_trm @ A3 @ A6 ) @ R3 )
% 0.26/0.60 | ( ( A3 = A6 )
% 0.26/0.60 & ( member1287158352on_fml @ ( produc909629463on_fml @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % in_lex_prod
% 0.26/0.60 thf(fact_275_in__lex__prod,axiom,
% 0.26/0.60 ! [A3: option_fml,B3: option_trm,A6: option_fml,B6: option_trm,R3: set_Pr927595527on_fml,S2: set_Pr1471344007on_trm] :
% 0.26/0.60 ( ( member1883874960on_trm @ ( produc2132972503on_trm @ ( produc1447374177on_trm @ A3 @ B3 ) @ ( produc1447374177on_trm @ A6 @ B6 ) ) @ ( lex_pr852623737on_trm @ R3 @ S2 ) )
% 0.26/0.60 = ( ( member1287158352on_fml @ ( produc909629463on_fml @ A3 @ A6 ) @ R3 )
% 0.26/0.60 | ( ( A3 = A6 )
% 0.26/0.60 & ( member165817296on_trm @ ( produc709594775on_trm @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % in_lex_prod
% 0.26/0.60 thf(fact_276_in__lex__prod,axiom,
% 0.26/0.60 ! [A3: option_game,B3: option_fml,A6: option_game,B6: option_fml,R3: set_Pr1625152599n_game,S2: set_Pr927595527on_fml] :
% 0.26/0.60 ( ( member113767842on_fml @ ( produc556056113on_fml @ ( produc2124676926on_fml @ A3 @ B3 ) @ ( produc2124676926on_fml @ A6 @ B6 ) ) @ ( lex_pr425996582on_fml @ R3 @ S2 ) )
% 0.26/0.60 = ( ( member191809696n_game @ ( produc1111617711n_game @ A3 @ A6 ) @ R3 )
% 0.26/0.60 | ( ( A3 = A6 )
% 0.26/0.60 & ( member1287158352on_fml @ ( produc909629463on_fml @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % in_lex_prod
% 0.26/0.60 thf(fact_277_in__lex__prod,axiom,
% 0.26/0.60 ! [A3: option_trm,B3: option_trm,A6: option_trm,B6: option_trm,R3: set_Pr1471344007on_trm,S2: set_Pr1471344007on_trm] :
% 0.26/0.60 ( ( member602811152on_trm @ ( produc2001752919on_trm @ ( produc709594775on_trm @ A3 @ B3 ) @ ( produc709594775on_trm @ A6 @ B6 ) ) @ ( lex_pr114844335on_trm @ R3 @ S2 ) )
% 0.26/0.60 = ( ( member165817296on_trm @ ( produc709594775on_trm @ A3 @ A6 ) @ R3 )
% 0.26/0.60 | ( ( A3 = A6 )
% 0.26/0.60 & ( member165817296on_trm @ ( produc709594775on_trm @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % in_lex_prod
% 0.26/0.60 thf(fact_278_in__lex__prod,axiom,
% 0.26/0.60 ! [A3: option_fml,B3: option_fml,A6: option_fml,B6: option_fml,R3: set_Pr927595527on_fml,S2: set_Pr927595527on_fml] :
% 0.26/0.60 ( ( member450497296on_fml @ ( produc1367044951on_fml @ ( produc909629463on_fml @ A3 @ B3 ) @ ( produc909629463on_fml @ A6 @ B6 ) ) @ ( lex_pr314879023on_fml @ R3 @ S2 ) )
% 0.26/0.60 = ( ( member1287158352on_fml @ ( produc909629463on_fml @ A3 @ A6 ) @ R3 )
% 0.26/0.60 | ( ( A3 = A6 )
% 0.26/0.60 & ( member1287158352on_fml @ ( produc909629463on_fml @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % in_lex_prod
% 0.26/0.60 thf(fact_279_in__lex__prod,axiom,
% 0.26/0.60 ! [A3: char,B3: option_trm,A6: char,B6: option_trm,R3: set_Pr604539619r_char,S2: set_Pr1471344007on_trm] :
% 0.26/0.60 ( ( member1950256170on_trm @ ( produc444919481on_trm @ ( produc1500300866on_trm @ A3 @ B3 ) @ ( produc1500300866on_trm @ A6 @ B6 ) ) @ ( lex_pr1901327402on_trm @ R3 @ S2 ) )
% 0.26/0.60 = ( ( member1866856748r_char @ ( produc19545147r_char @ A3 @ A6 ) @ R3 )
% 0.26/0.60 | ( ( A3 = A6 )
% 0.26/0.60 & ( member165817296on_trm @ ( produc709594775on_trm @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % in_lex_prod
% 0.26/0.60 thf(fact_280_in__lex__prod,axiom,
% 0.26/0.60 ! [A3: set_variable,B3: trm,A6: set_variable,B6: trm,R3: set_Pr181266295riable,S2: set_Pr491793543rm_trm] :
% 0.26/0.60 ( ( member1150310282le_trm @ ( produc1056455193le_trm @ ( produc1482344242le_trm @ A3 @ B3 ) @ ( produc1482344242le_trm @ A6 @ B6 ) ) @ ( lex_pr1522821402le_trm @ R3 @ S2 ) )
% 0.26/0.60 = ( ( member1978718144riable @ ( produc1766592463riable @ A3 @ A6 ) @ R3 )
% 0.26/0.60 | ( ( A3 = A6 )
% 0.26/0.60 & ( member1735386832rm_trm @ ( product_Pair_trm_trm @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % in_lex_prod
% 0.26/0.60 thf(fact_281_trm_Oinject_I2_J,axiom,
% 0.26/0.60 ! [X23: real,Y23: real] :
% 0.26/0.60 ( ( ( number @ X23 )
% 0.26/0.60 = ( number @ Y23 ) )
% 0.26/0.60 = ( X23 = Y23 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.inject(2)
% 0.26/0.60 thf(fact_282_trm_Oinject_I1_J,axiom,
% 0.26/0.60 ! [X1: variable,Y1: variable] :
% 0.26/0.60 ( ( ( var @ X1 )
% 0.26/0.60 = ( var @ Y1 ) )
% 0.26/0.60 = ( X1 = Y1 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.inject(1)
% 0.26/0.60 thf(fact_283_trm_Odistinct_I17_J,axiom,
% 0.26/0.60 ! [X23: real,X51: trm,X52: trm] :
% 0.26/0.60 ( ( number @ X23 )
% 0.26/0.60 != ( plus @ X51 @ X52 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.distinct(17)
% 0.26/0.60 thf(fact_284_trm_Odistinct_I19_J,axiom,
% 0.26/0.60 ! [X23: real,X61: trm,X62: trm] :
% 0.26/0.60 ( ( number @ X23 )
% 0.26/0.60 != ( times @ X61 @ X62 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.distinct(19)
% 0.26/0.60 thf(fact_285_trm_Odistinct_I21_J,axiom,
% 0.26/0.60 ! [X23: real,X7: trm] :
% 0.26/0.60 ( ( number @ X23 )
% 0.26/0.60 != ( differential @ X7 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.distinct(21)
% 0.26/0.60 thf(fact_286_trm_Odistinct_I7_J,axiom,
% 0.26/0.60 ! [X1: variable,X51: trm,X52: trm] :
% 0.26/0.60 ( ( var @ X1 )
% 0.26/0.60 != ( plus @ X51 @ X52 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.distinct(7)
% 0.26/0.60 thf(fact_287_trm_Odistinct_I9_J,axiom,
% 0.26/0.60 ! [X1: variable,X61: trm,X62: trm] :
% 0.26/0.60 ( ( var @ X1 )
% 0.26/0.60 != ( times @ X61 @ X62 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.distinct(9)
% 0.26/0.60 thf(fact_288_trm_Odistinct_I11_J,axiom,
% 0.26/0.60 ! [X1: variable,X7: trm] :
% 0.26/0.60 ( ( var @ X1 )
% 0.26/0.60 != ( differential @ X7 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.distinct(11)
% 0.26/0.60 thf(fact_289_trm_Odistinct_I1_J,axiom,
% 0.26/0.60 ! [X1: variable,X23: real] :
% 0.26/0.60 ( ( var @ X1 )
% 0.26/0.60 != ( number @ X23 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.distinct(1)
% 0.26/0.60 thf(fact_290_usubstappt_Osimps_I2_J,axiom,
% 0.26/0.60 ! [Sigma: produc1418842292n_game,U: set_variable,R3: real] :
% 0.26/0.60 ( ( uSubst516392818stappt @ Sigma @ U @ ( number @ R3 ) )
% 0.26/0.60 = ( some_trm @ ( number @ R3 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % usubstappt.simps(2)
% 0.26/0.60 thf(fact_291_usubstappt_Osimps_I1_J,axiom,
% 0.26/0.60 ! [Sigma: produc1418842292n_game,U: set_variable,X2: variable] :
% 0.26/0.60 ( ( uSubst516392818stappt @ Sigma @ U @ ( var @ X2 ) )
% 0.26/0.60 = ( some_trm @ ( var @ X2 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % usubstappt.simps(1)
% 0.26/0.60 thf(fact_292_usubstappt_Ocases,axiom,
% 0.26/0.60 ! [X2: produc1699626005le_trm] :
% 0.26/0.60 ( ! [Sigma2: produc1418842292n_game,U3: set_variable,X: variable] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( var @ X ) ) ) )
% 0.26/0.60 => ( ! [Sigma2: produc1418842292n_game,U3: set_variable,R5: real] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( number @ R5 ) ) ) )
% 0.26/0.60 => ( ! [Sigma2: produc1418842292n_game,U3: set_variable,F3: char] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( const @ F3 ) ) ) )
% 0.26/0.60 => ( ! [Sigma2: produc1418842292n_game,U3: set_variable,F3: char,Theta2: trm] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( func @ F3 @ Theta2 ) ) ) )
% 0.26/0.60 => ( ! [Sigma2: produc1418842292n_game,U3: set_variable,Theta2: trm,Eta2: trm] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( plus @ Theta2 @ Eta2 ) ) ) )
% 0.26/0.60 => ( ! [Sigma2: produc1418842292n_game,U3: set_variable,Theta2: trm,Eta2: trm] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( times @ Theta2 @ Eta2 ) ) ) )
% 0.26/0.60 => ~ ! [Sigma2: produc1418842292n_game,U3: set_variable,Theta2: trm] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( differential @ Theta2 ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % usubstappt.cases
% 0.26/0.60 thf(fact_293_Testo_Osimps_I2_J,axiom,
% 0.26/0.60 ( ( uSubst1367128042_Testo @ none_fml )
% 0.26/0.60 = none_game ) ).
% 0.26/0.60
% 0.26/0.60 % Testo.simps(2)
% 0.26/0.60 thf(fact_294_Testo__undef,axiom,
% 0.26/0.60 ! [Phi: option_fml] :
% 0.26/0.60 ( ( ( uSubst1367128042_Testo @ Phi )
% 0.26/0.60 = none_game )
% 0.26/0.60 = ( Phi = none_fml ) ) ).
% 0.26/0.60
% 0.26/0.60 % Testo_undef
% 0.26/0.60 thf(fact_295_trm_Oinject_I4_J,axiom,
% 0.26/0.60 ! [X41: char,X42: trm,Y41: char,Y42: trm] :
% 0.26/0.60 ( ( ( func @ X41 @ X42 )
% 0.26/0.60 = ( func @ Y41 @ Y42 ) )
% 0.26/0.60 = ( ( X41 = Y41 )
% 0.26/0.60 & ( X42 = Y42 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.inject(4)
% 0.26/0.60 thf(fact_296_trm_Oinject_I3_J,axiom,
% 0.26/0.60 ! [X32: char,Y32: char] :
% 0.26/0.60 ( ( ( const @ X32 )
% 0.26/0.60 = ( const @ Y32 ) )
% 0.26/0.60 = ( X32 = Y32 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.inject(3)
% 0.26/0.60 thf(fact_297_trm_Odistinct_I3_J,axiom,
% 0.26/0.60 ! [X1: variable,X32: char] :
% 0.26/0.60 ( ( var @ X1 )
% 0.26/0.60 != ( const @ X32 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.distinct(3)
% 0.26/0.60 thf(fact_298_trm_Odistinct_I5_J,axiom,
% 0.26/0.60 ! [X1: variable,X41: char,X42: trm] :
% 0.26/0.60 ( ( var @ X1 )
% 0.26/0.60 != ( func @ X41 @ X42 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.distinct(5)
% 0.26/0.60 thf(fact_299_trm_Odistinct_I13_J,axiom,
% 0.26/0.60 ! [X23: real,X32: char] :
% 0.26/0.60 ( ( number @ X23 )
% 0.26/0.60 != ( const @ X32 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.distinct(13)
% 0.26/0.60 thf(fact_300_trm_Odistinct_I15_J,axiom,
% 0.26/0.60 ! [X23: real,X41: char,X42: trm] :
% 0.26/0.60 ( ( number @ X23 )
% 0.26/0.60 != ( func @ X41 @ X42 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.distinct(15)
% 0.26/0.60 thf(fact_301_trm_Odistinct_I23_J,axiom,
% 0.26/0.60 ! [X32: char,X41: char,X42: trm] :
% 0.26/0.60 ( ( const @ X32 )
% 0.26/0.60 != ( func @ X41 @ X42 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.distinct(23)
% 0.26/0.60 thf(fact_302_trm_Odistinct_I29_J,axiom,
% 0.26/0.60 ! [X32: char,X7: trm] :
% 0.26/0.60 ( ( const @ X32 )
% 0.26/0.60 != ( differential @ X7 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.distinct(29)
% 0.26/0.60 thf(fact_303_trm_Odistinct_I27_J,axiom,
% 0.26/0.60 ! [X32: char,X61: trm,X62: trm] :
% 0.26/0.60 ( ( const @ X32 )
% 0.26/0.60 != ( times @ X61 @ X62 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.distinct(27)
% 0.26/0.60 thf(fact_304_trm_Odistinct_I25_J,axiom,
% 0.26/0.60 ! [X32: char,X51: trm,X52: trm] :
% 0.26/0.60 ( ( const @ X32 )
% 0.26/0.60 != ( plus @ X51 @ X52 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.distinct(25)
% 0.26/0.60 thf(fact_305_trm_Odistinct_I35_J,axiom,
% 0.26/0.60 ! [X41: char,X42: trm,X7: trm] :
% 0.26/0.60 ( ( func @ X41 @ X42 )
% 0.26/0.60 != ( differential @ X7 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.distinct(35)
% 0.26/0.60 thf(fact_306_trm_Odistinct_I33_J,axiom,
% 0.26/0.60 ! [X41: char,X42: trm,X61: trm,X62: trm] :
% 0.26/0.60 ( ( func @ X41 @ X42 )
% 0.26/0.60 != ( times @ X61 @ X62 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.distinct(33)
% 0.26/0.60 thf(fact_307_trm_Odistinct_I31_J,axiom,
% 0.26/0.60 ! [X41: char,X42: trm,X51: trm,X52: trm] :
% 0.26/0.60 ( ( func @ X41 @ X42 )
% 0.26/0.60 != ( plus @ X51 @ X52 ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.distinct(31)
% 0.26/0.60 thf(fact_308_trm_Oinduct,axiom,
% 0.26/0.60 ! [P: trm > $o,Trm: trm] :
% 0.26/0.60 ( ! [X: variable] : ( P @ ( var @ X ) )
% 0.26/0.60 => ( ! [X: real] : ( P @ ( number @ X ) )
% 0.26/0.60 => ( ! [X: char] : ( P @ ( const @ X ) )
% 0.26/0.60 => ( ! [X1a: char,X2a: trm] :
% 0.26/0.60 ( ( P @ X2a )
% 0.26/0.60 => ( P @ ( func @ X1a @ X2a ) ) )
% 0.26/0.60 => ( ! [X1a: trm,X2a: trm] :
% 0.26/0.60 ( ( P @ X1a )
% 0.26/0.60 => ( ( P @ X2a )
% 0.26/0.60 => ( P @ ( plus @ X1a @ X2a ) ) ) )
% 0.26/0.60 => ( ! [X1a: trm,X2a: trm] :
% 0.26/0.60 ( ( P @ X1a )
% 0.26/0.60 => ( ( P @ X2a )
% 0.26/0.60 => ( P @ ( times @ X1a @ X2a ) ) ) )
% 0.26/0.60 => ( ! [X: trm] :
% 0.26/0.60 ( ( P @ X )
% 0.26/0.60 => ( P @ ( differential @ X ) ) )
% 0.26/0.60 => ( P @ Trm ) ) ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.induct
% 0.26/0.60 thf(fact_309_trm_Oexhaust,axiom,
% 0.26/0.60 ! [Y2: trm] :
% 0.26/0.60 ( ! [X12: variable] :
% 0.26/0.60 ( Y2
% 0.26/0.60 != ( var @ X12 ) )
% 0.26/0.60 => ( ! [X24: real] :
% 0.26/0.60 ( Y2
% 0.26/0.60 != ( number @ X24 ) )
% 0.26/0.60 => ( ! [X33: char] :
% 0.26/0.60 ( Y2
% 0.26/0.60 != ( const @ X33 ) )
% 0.26/0.60 => ( ! [X412: char,X422: trm] :
% 0.26/0.60 ( Y2
% 0.26/0.60 != ( func @ X412 @ X422 ) )
% 0.26/0.60 => ( ! [X512: trm,X522: trm] :
% 0.26/0.60 ( Y2
% 0.26/0.60 != ( plus @ X512 @ X522 ) )
% 0.26/0.60 => ( ! [X612: trm,X622: trm] :
% 0.26/0.60 ( Y2
% 0.26/0.60 != ( times @ X612 @ X622 ) )
% 0.26/0.60 => ~ ! [X72: trm] :
% 0.26/0.60 ( Y2
% 0.26/0.60 != ( differential @ X72 ) ) ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % trm.exhaust
% 0.26/0.60 thf(fact_310_term__sem_Ocases,axiom,
% 0.26/0.60 ! [X2: produc833882726rp_trm] :
% 0.26/0.60 ( ! [I2: denotational_interp,X: variable] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc1132922070rp_trm @ I2 @ ( var @ X ) ) )
% 0.26/0.60 => ( ! [I2: denotational_interp,R5: real] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc1132922070rp_trm @ I2 @ ( number @ R5 ) ) )
% 0.26/0.60 => ( ! [I2: denotational_interp,F3: char] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc1132922070rp_trm @ I2 @ ( const @ F3 ) ) )
% 0.26/0.60 => ( ! [I2: denotational_interp,F3: char,Theta2: trm] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc1132922070rp_trm @ I2 @ ( func @ F3 @ Theta2 ) ) )
% 0.26/0.60 => ( ! [I2: denotational_interp,Theta2: trm,Eta2: trm] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc1132922070rp_trm @ I2 @ ( plus @ Theta2 @ Eta2 ) ) )
% 0.26/0.60 => ( ! [I2: denotational_interp,Theta2: trm,Eta2: trm] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc1132922070rp_trm @ I2 @ ( times @ Theta2 @ Eta2 ) ) )
% 0.26/0.60 => ~ ! [I2: denotational_interp,Theta2: trm] :
% 0.26/0.60 ( X2
% 0.26/0.60 != ( produc1132922070rp_trm @ I2 @ ( differential @ Theta2 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % term_sem.cases
% 0.26/0.60 thf(fact_311_usubstappt_Opsimps_I3_J,axiom,
% 0.26/0.60 ! [Sigma: produc1418842292n_game,U: set_variable,F: char] :
% 0.26/0.60 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( const @ F ) ) ) )
% 0.26/0.60 => ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F ) )
% 0.26/0.60 = ( uSubst1559070963pconst @ Sigma @ U @ F ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % usubstappt.psimps(3)
% 0.26/0.60 thf(fact_312_term__sem_Oinduct,axiom,
% 0.26/0.60 ! [P: denotational_interp > trm > $o,A0: denotational_interp,A1: trm] :
% 0.26/0.60 ( ! [I2: denotational_interp,X: variable] : ( P @ I2 @ ( var @ X ) )
% 0.26/0.60 => ( ! [I2: denotational_interp,R5: real] : ( P @ I2 @ ( number @ R5 ) )
% 0.26/0.60 => ( ! [I2: denotational_interp,F3: char] : ( P @ I2 @ ( const @ F3 ) )
% 0.26/0.60 => ( ! [I2: denotational_interp,F3: char,Theta2: trm] :
% 0.26/0.60 ( ( P @ I2 @ Theta2 )
% 0.26/0.60 => ( P @ I2 @ ( func @ F3 @ Theta2 ) ) )
% 0.26/0.60 => ( ! [I2: denotational_interp,Theta2: trm] :
% 0.26/0.60 ( ( P @ I2 @ Theta2 )
% 0.26/0.60 => ! [Eta2: trm] :
% 0.26/0.60 ( ( P @ I2 @ Eta2 )
% 0.26/0.60 => ( P @ I2 @ ( plus @ Theta2 @ Eta2 ) ) ) )
% 0.26/0.60 => ( ! [I2: denotational_interp,Theta2: trm] :
% 0.26/0.60 ( ( P @ I2 @ Theta2 )
% 0.26/0.60 => ! [Eta2: trm] :
% 0.26/0.60 ( ( P @ I2 @ Eta2 )
% 0.26/0.60 => ( P @ I2 @ ( times @ Theta2 @ Eta2 ) ) ) )
% 0.26/0.60 => ( ! [I2: denotational_interp,Theta2: trm] :
% 0.26/0.60 ( ( ? [Xa2: char] :
% 0.26/0.60 ( member_char @ Xa2
% 0.26/0.60 @ ( collect_char
% 0.26/0.60 @ ^ [Uu: char] : $true ) )
% 0.26/0.60 => ( P @ I2 @ Theta2 ) )
% 0.26/0.60 => ( P @ I2 @ ( differential @ Theta2 ) ) )
% 0.26/0.60 => ( P @ A0 @ A1 ) ) ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % term_sem.induct
% 0.26/0.60 thf(fact_313_usubstappt_Osimps_I3_J,axiom,
% 0.26/0.60 ! [Sigma: produc1418842292n_game,U: set_variable,F: char] :
% 0.26/0.60 ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F ) )
% 0.26/0.60 = ( uSubst1559070963pconst @ Sigma @ U @ F ) ) ).
% 0.26/0.60
% 0.26/0.60 % usubstappt.simps(3)
% 0.26/0.60 thf(fact_314_image2__def,axiom,
% 0.26/0.60 ( bNF_Gr2142503190on_fml
% 0.26/0.60 = ( ^ [A2: set_variable,F2: variable > option_game,G: variable > option_fml] :
% 0.26/0.60 ( collec749447393on_fml
% 0.26/0.60 @ ^ [Uu: produc1739631244on_fml] :
% 0.26/0.60 ? [A4: variable] :
% 0.26/0.60 ( ( Uu
% 0.26/0.60 = ( produc2124676926on_fml @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.26/0.60 & ( member_variable @ A4 @ A2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_def
% 0.26/0.60 thf(fact_315_image2__def,axiom,
% 0.26/0.60 ( bNF_Gr756940202on_fml
% 0.26/0.60 = ( ^ [A2: set_char,F2: char > option_game,G: char > option_fml] :
% 0.26/0.60 ( collec749447393on_fml
% 0.26/0.60 @ ^ [Uu: produc1739631244on_fml] :
% 0.26/0.60 ? [A4: char] :
% 0.26/0.60 ( ( Uu
% 0.26/0.60 = ( produc2124676926on_fml @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.26/0.60 & ( member_char @ A4 @ A2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_def
% 0.26/0.60 thf(fact_316_image2__def,axiom,
% 0.26/0.60 ( bNF_Gr400922303on_trm
% 0.26/0.60 = ( ^ [A2: set_variable,F2: variable > option_trm,G: variable > option_trm] :
% 0.26/0.60 ( collec1697116690on_trm
% 0.26/0.60 @ ^ [Uu: produc1072747943on_trm] :
% 0.26/0.60 ? [A4: variable] :
% 0.26/0.60 ( ( Uu
% 0.26/0.60 = ( produc709594775on_trm @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.26/0.60 & ( member_variable @ A4 @ A2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_def
% 0.26/0.60 thf(fact_317_image2__def,axiom,
% 0.26/0.60 ( bNF_Gr1666135339on_trm
% 0.26/0.60 = ( ^ [A2: set_char,F2: char > option_trm,G: char > option_trm] :
% 0.26/0.60 ( collec1697116690on_trm
% 0.26/0.60 @ ^ [Uu: produc1072747943on_trm] :
% 0.26/0.60 ? [A4: char] :
% 0.26/0.60 ( ( Uu
% 0.26/0.60 = ( produc709594775on_trm @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.26/0.60 & ( member_char @ A4 @ A2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_def
% 0.26/0.60 thf(fact_318_image2__def,axiom,
% 0.26/0.60 ( bNF_Gr600956991on_fml
% 0.26/0.60 = ( ^ [A2: set_variable,F2: variable > option_fml,G: variable > option_fml] :
% 0.26/0.60 ( collec670974098on_fml
% 0.26/0.60 @ ^ [Uu: produc46605351on_fml] :
% 0.26/0.60 ? [A4: variable] :
% 0.26/0.60 ( ( Uu
% 0.26/0.60 = ( produc909629463on_fml @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.26/0.60 & ( member_variable @ A4 @ A2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_def
% 0.26/0.60 thf(fact_319_image2__def,axiom,
% 0.26/0.60 ( bNF_Gr1866170027on_fml
% 0.26/0.60 = ( ^ [A2: set_char,F2: char > option_fml,G: char > option_fml] :
% 0.26/0.60 ( collec670974098on_fml
% 0.26/0.60 @ ^ [Uu: produc46605351on_fml] :
% 0.26/0.60 ? [A4: char] :
% 0.26/0.60 ( ( Uu
% 0.26/0.60 = ( produc909629463on_fml @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.26/0.60 & ( member_char @ A4 @ A2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_def
% 0.26/0.60 thf(fact_320_image2__def,axiom,
% 0.26/0.60 ( bNF_Gr1933470746on_trm
% 0.26/0.60 = ( ^ [A2: set_variable,F2: variable > char,G: variable > option_trm] :
% 0.26/0.60 ( collec1756633317on_trm
% 0.26/0.60 @ ^ [Uu: produc464795408on_trm] :
% 0.26/0.60 ? [A4: variable] :
% 0.26/0.60 ( ( Uu
% 0.26/0.60 = ( produc1500300866on_trm @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.26/0.60 & ( member_variable @ A4 @ A2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_def
% 0.26/0.60 thf(fact_321_image2__def,axiom,
% 0.26/0.60 ( bNF_Gr951178926on_trm
% 0.26/0.60 = ( ^ [A2: set_char,F2: char > char,G: char > option_trm] :
% 0.26/0.60 ( collec1756633317on_trm
% 0.26/0.60 @ ^ [Uu: produc464795408on_trm] :
% 0.26/0.60 ? [A4: char] :
% 0.26/0.60 ( ( Uu
% 0.26/0.60 = ( produc1500300866on_trm @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.26/0.60 & ( member_char @ A4 @ A2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_def
% 0.26/0.60 thf(fact_322_image2__def,axiom,
% 0.26/0.60 ( bNF_Gr1330108682le_trm
% 0.26/0.60 = ( ^ [A2: set_variable,F2: variable > set_variable,G: variable > trm] :
% 0.26/0.60 ( collec575343829le_trm
% 0.26/0.60 @ ^ [Uu: produc1367888000le_trm] :
% 0.26/0.60 ? [A4: variable] :
% 0.26/0.60 ( ( Uu
% 0.26/0.60 = ( produc1482344242le_trm @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.26/0.60 & ( member_variable @ A4 @ A2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_def
% 0.26/0.60 thf(fact_323_image2__def,axiom,
% 0.26/0.60 ( bNF_Gr852774302le_trm
% 0.26/0.60 = ( ^ [A2: set_char,F2: char > set_variable,G: char > trm] :
% 0.26/0.60 ( collec575343829le_trm
% 0.26/0.60 @ ^ [Uu: produc1367888000le_trm] :
% 0.26/0.60 ? [A4: char] :
% 0.26/0.60 ( ( Uu
% 0.26/0.60 = ( produc1482344242le_trm @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.26/0.60 & ( member_char @ A4 @ A2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_def
% 0.26/0.60 thf(fact_324_Testo_Oelims,axiom,
% 0.26/0.60 ! [X2: option_fml,Y2: option_game] :
% 0.26/0.60 ( ( ( uSubst1367128042_Testo @ X2 )
% 0.26/0.60 = Y2 )
% 0.26/0.60 => ( ! [Phi2: fml] :
% 0.26/0.60 ( ( X2
% 0.26/0.60 = ( some_fml @ Phi2 ) )
% 0.26/0.60 => ( Y2
% 0.26/0.60 != ( some_game @ ( test @ Phi2 ) ) ) )
% 0.26/0.60 => ~ ( ( X2 = none_fml )
% 0.26/0.60 => ( Y2 != none_game ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Testo.elims
% 0.26/0.60 thf(fact_325_game_Oinject_I3_J,axiom,
% 0.26/0.60 ! [X32: fml,Y32: fml] :
% 0.26/0.60 ( ( ( test @ X32 )
% 0.26/0.60 = ( test @ Y32 ) )
% 0.26/0.60 = ( X32 = Y32 ) ) ).
% 0.26/0.60
% 0.26/0.60 % game.inject(3)
% 0.26/0.60 thf(fact_326_image2__eqI,axiom,
% 0.26/0.60 ! [B3: option_game,F: variable > option_game,X2: variable,C: option_fml,G2: variable > option_fml,A: set_variable] :
% 0.26/0.60 ( ( B3
% 0.26/0.60 = ( F @ X2 ) )
% 0.26/0.60 => ( ( C
% 0.26/0.60 = ( G2 @ X2 ) )
% 0.26/0.60 => ( ( member_variable @ X2 @ A )
% 0.26/0.60 => ( member1883102883on_fml @ ( produc2124676926on_fml @ B3 @ C ) @ ( bNF_Gr2142503190on_fml @ A @ F @ G2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_eqI
% 0.26/0.60 thf(fact_327_image2__eqI,axiom,
% 0.26/0.60 ! [B3: option_game,F: char > option_game,X2: char,C: option_fml,G2: char > option_fml,A: set_char] :
% 0.26/0.60 ( ( B3
% 0.26/0.60 = ( F @ X2 ) )
% 0.26/0.60 => ( ( C
% 0.26/0.60 = ( G2 @ X2 ) )
% 0.26/0.60 => ( ( member_char @ X2 @ A )
% 0.26/0.60 => ( member1883102883on_fml @ ( produc2124676926on_fml @ B3 @ C ) @ ( bNF_Gr756940202on_fml @ A @ F @ G2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_eqI
% 0.26/0.60 thf(fact_328_image2__eqI,axiom,
% 0.26/0.60 ! [B3: option_trm,F: variable > option_trm,X2: variable,C: option_trm,G2: variable > option_trm,A: set_variable] :
% 0.26/0.60 ( ( B3
% 0.26/0.60 = ( F @ X2 ) )
% 0.26/0.60 => ( ( C
% 0.26/0.60 = ( G2 @ X2 ) )
% 0.26/0.60 => ( ( member_variable @ X2 @ A )
% 0.26/0.60 => ( member165817296on_trm @ ( produc709594775on_trm @ B3 @ C ) @ ( bNF_Gr400922303on_trm @ A @ F @ G2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_eqI
% 0.26/0.60 thf(fact_329_image2__eqI,axiom,
% 0.26/0.60 ! [B3: option_trm,F: char > option_trm,X2: char,C: option_trm,G2: char > option_trm,A: set_char] :
% 0.26/0.60 ( ( B3
% 0.26/0.60 = ( F @ X2 ) )
% 0.26/0.60 => ( ( C
% 0.26/0.60 = ( G2 @ X2 ) )
% 0.26/0.60 => ( ( member_char @ X2 @ A )
% 0.26/0.60 => ( member165817296on_trm @ ( produc709594775on_trm @ B3 @ C ) @ ( bNF_Gr1666135339on_trm @ A @ F @ G2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_eqI
% 0.26/0.60 thf(fact_330_image2__eqI,axiom,
% 0.26/0.60 ! [B3: option_fml,F: variable > option_fml,X2: variable,C: option_fml,G2: variable > option_fml,A: set_variable] :
% 0.26/0.60 ( ( B3
% 0.26/0.60 = ( F @ X2 ) )
% 0.26/0.60 => ( ( C
% 0.26/0.60 = ( G2 @ X2 ) )
% 0.26/0.60 => ( ( member_variable @ X2 @ A )
% 0.26/0.60 => ( member1287158352on_fml @ ( produc909629463on_fml @ B3 @ C ) @ ( bNF_Gr600956991on_fml @ A @ F @ G2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_eqI
% 0.26/0.60 thf(fact_331_image2__eqI,axiom,
% 0.26/0.60 ! [B3: option_fml,F: char > option_fml,X2: char,C: option_fml,G2: char > option_fml,A: set_char] :
% 0.26/0.60 ( ( B3
% 0.26/0.60 = ( F @ X2 ) )
% 0.26/0.60 => ( ( C
% 0.26/0.60 = ( G2 @ X2 ) )
% 0.26/0.60 => ( ( member_char @ X2 @ A )
% 0.26/0.60 => ( member1287158352on_fml @ ( produc909629463on_fml @ B3 @ C ) @ ( bNF_Gr1866170027on_fml @ A @ F @ G2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_eqI
% 0.26/0.60 thf(fact_332_image2__eqI,axiom,
% 0.26/0.60 ! [B3: char,F: variable > char,X2: variable,C: option_trm,G2: variable > option_trm,A: set_variable] :
% 0.26/0.60 ( ( B3
% 0.26/0.60 = ( F @ X2 ) )
% 0.26/0.60 => ( ( C
% 0.26/0.60 = ( G2 @ X2 ) )
% 0.26/0.60 => ( ( member_variable @ X2 @ A )
% 0.26/0.60 => ( member694524327on_trm @ ( produc1500300866on_trm @ B3 @ C ) @ ( bNF_Gr1933470746on_trm @ A @ F @ G2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_eqI
% 0.26/0.60 thf(fact_333_image2__eqI,axiom,
% 0.26/0.60 ! [B3: char,F: char > char,X2: char,C: option_trm,G2: char > option_trm,A: set_char] :
% 0.26/0.60 ( ( B3
% 0.26/0.60 = ( F @ X2 ) )
% 0.26/0.60 => ( ( C
% 0.26/0.60 = ( G2 @ X2 ) )
% 0.26/0.60 => ( ( member_char @ X2 @ A )
% 0.26/0.60 => ( member694524327on_trm @ ( produc1500300866on_trm @ B3 @ C ) @ ( bNF_Gr951178926on_trm @ A @ F @ G2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_eqI
% 0.26/0.60 thf(fact_334_image2__eqI,axiom,
% 0.26/0.60 ! [B3: set_variable,F: variable > set_variable,X2: variable,C: trm,G2: variable > trm,A: set_variable] :
% 0.26/0.60 ( ( B3
% 0.26/0.60 = ( F @ X2 ) )
% 0.26/0.60 => ( ( C
% 0.26/0.60 = ( G2 @ X2 ) )
% 0.26/0.60 => ( ( member_variable @ X2 @ A )
% 0.26/0.60 => ( member2122665623le_trm @ ( produc1482344242le_trm @ B3 @ C ) @ ( bNF_Gr1330108682le_trm @ A @ F @ G2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_eqI
% 0.26/0.60 thf(fact_335_image2__eqI,axiom,
% 0.26/0.60 ! [B3: set_variable,F: char > set_variable,X2: char,C: trm,G2: char > trm,A: set_char] :
% 0.26/0.60 ( ( B3
% 0.26/0.60 = ( F @ X2 ) )
% 0.26/0.60 => ( ( C
% 0.26/0.60 = ( G2 @ X2 ) )
% 0.26/0.60 => ( ( member_char @ X2 @ A )
% 0.26/0.60 => ( member2122665623le_trm @ ( produc1482344242le_trm @ B3 @ C ) @ ( bNF_Gr852774302le_trm @ A @ F @ G2 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % image2_eqI
% 0.26/0.60 thf(fact_336_Testo_Osimps_I1_J,axiom,
% 0.26/0.60 ! [Phi: fml] :
% 0.26/0.60 ( ( uSubst1367128042_Testo @ ( some_fml @ Phi ) )
% 0.26/0.60 = ( some_game @ ( test @ Phi ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Testo.simps(1)
% 0.26/0.60 thf(fact_337_Testo_Opelims,axiom,
% 0.26/0.60 ! [X2: option_fml,Y2: option_game] :
% 0.26/0.60 ( ( ( uSubst1367128042_Testo @ X2 )
% 0.26/0.60 = Y2 )
% 0.26/0.60 => ( ( accp_option_fml @ uSubst954181007to_rel @ X2 )
% 0.26/0.60 => ( ! [Phi2: fml] :
% 0.26/0.60 ( ( X2
% 0.26/0.60 = ( some_fml @ Phi2 ) )
% 0.26/0.60 => ( ( Y2
% 0.26/0.60 = ( some_game @ ( test @ Phi2 ) ) )
% 0.26/0.60 => ~ ( accp_option_fml @ uSubst954181007to_rel @ ( some_fml @ Phi2 ) ) ) )
% 0.26/0.60 => ~ ( ( X2 = none_fml )
% 0.26/0.60 => ( ( Y2 = none_game )
% 0.26/0.60 => ~ ( accp_option_fml @ uSubst954181007to_rel @ none_fml ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Testo.pelims
% 0.26/0.60 thf(fact_338_relImage__def,axiom,
% 0.26/0.60 ( bNF_Gr806120164on_fml
% 0.26/0.60 = ( ^ [R6: set_Pr927595527on_fml,F2: option_fml > option_fml] :
% 0.26/0.60 ( collec670974098on_fml
% 0.26/0.60 @ ^ [Uu: produc46605351on_fml] :
% 0.26/0.60 ? [A12: option_fml,A22: option_fml] :
% 0.26/0.60 ( ( Uu
% 0.26/0.60 = ( produc909629463on_fml @ ( F2 @ A12 ) @ ( F2 @ A22 ) ) )
% 0.26/0.60 & ( member1287158352on_fml @ ( produc909629463on_fml @ A12 @ A22 ) @ R6 ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % relImage_def
% 0.26/0.60 thf(fact_339_Assigno__undef,axiom,
% 0.26/0.60 ! [X2: variable,Theta: option_trm] :
% 0.26/0.60 ( ( ( uSubst834381837ssigno @ X2 @ Theta )
% 0.26/0.60 = none_game )
% 0.26/0.60 = ( Theta = none_trm ) ) ).
% 0.26/0.60
% 0.26/0.60 % Assigno_undef
% 0.26/0.60 thf(fact_340_Assigno_Osimps_I2_J,axiom,
% 0.26/0.60 ! [X2: variable] :
% 0.26/0.60 ( ( uSubst834381837ssigno @ X2 @ none_trm )
% 0.26/0.60 = none_game ) ).
% 0.26/0.60
% 0.26/0.60 % Assigno.simps(2)
% 0.26/0.60 thf(fact_341_Assigno_Oelims,axiom,
% 0.26/0.60 ! [X2: variable,Xa: option_trm,Y2: option_game] :
% 0.26/0.60 ( ( ( uSubst834381837ssigno @ X2 @ Xa )
% 0.26/0.60 = Y2 )
% 0.26/0.60 => ( ! [Theta2: trm] :
% 0.26/0.60 ( ( Xa
% 0.26/0.60 = ( some_trm @ Theta2 ) )
% 0.26/0.60 => ( Y2
% 0.26/0.60 != ( some_game @ ( assign @ X2 @ Theta2 ) ) ) )
% 0.26/0.60 => ~ ( ( Xa = none_trm )
% 0.26/0.60 => ( Y2 != none_game ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Assigno.elims
% 0.26/0.60 thf(fact_342_Assigno_Opelims,axiom,
% 0.26/0.60 ! [X2: variable,Xa: option_trm,Y2: option_game] :
% 0.26/0.60 ( ( ( uSubst834381837ssigno @ X2 @ Xa )
% 0.26/0.60 = Y2 )
% 0.26/0.60 => ( ( accp_P394694195on_trm @ uSubst157155628no_rel @ ( produc1743721902on_trm @ X2 @ Xa ) )
% 0.26/0.60 => ( ! [Theta2: trm] :
% 0.26/0.60 ( ( Xa
% 0.26/0.60 = ( some_trm @ Theta2 ) )
% 0.26/0.60 => ( ( Y2
% 0.26/0.60 = ( some_game @ ( assign @ X2 @ Theta2 ) ) )
% 0.26/0.60 => ~ ( accp_P394694195on_trm @ uSubst157155628no_rel @ ( produc1743721902on_trm @ X2 @ ( some_trm @ Theta2 ) ) ) ) )
% 0.26/0.60 => ~ ( ( Xa = none_trm )
% 0.26/0.60 => ( ( Y2 = none_game )
% 0.26/0.60 => ~ ( accp_P394694195on_trm @ uSubst157155628no_rel @ ( produc1743721902on_trm @ X2 @ none_trm ) ) ) ) ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % Assigno.pelims
% 0.26/0.60 thf(fact_343_game_Oinject_I2_J,axiom,
% 0.26/0.60 ! [X21: variable,X22: trm,Y21: variable,Y22: trm] :
% 0.26/0.60 ( ( ( assign @ X21 @ X22 )
% 0.26/0.60 = ( assign @ Y21 @ Y22 ) )
% 0.26/0.60 = ( ( X21 = Y21 )
% 0.26/0.60 & ( X22 = Y22 ) ) ) ).
% 0.26/0.60
% 0.26/0.60 % game.inject(2)
% 0.26/0.60 thf(fact_344_game_Odistinct_I15_J,axiom,
% 0.26/0.60 ! [X21: variable,X22: trm,X32: fml] :
% 0.26/0.60 ( ( assign @ X21 @ X22 )
% 0.26/0.60 != ( test @ X32 ) ) ).
% 0.26/0.60
% 0.26/0.60 % game.distinct(15)
% 0.26/0.60 thf(fact_345_Assigno_Osimps_I1_J,axiom,
% 0.26/0.60 ! [X2: variable,Theta: trm] :
% 0.26/0.60 ( ( uSubst834381837ssigno @ X2 @ ( some_trm @ Theta ) )
% 0.26/0.60 = ( some_game @ ( assign @ X2 @ Theta ) ) ) ).
% 0.26/0.69
% 0.26/0.69 % Assigno.simps(1)
% 0.26/0.69 thf(fact_346_ODEo__undef,axiom,
% 0.26/0.69 ! [X2: char,Theta: option_trm] :
% 0.26/0.69 ( ( ( uSubst1827052306e_ODEo @ X2 @ Theta )
% 0.26/0.69 = none_game )
% 0.26/0.69 = ( Theta = none_trm ) ) ).
% 0.26/0.69
% 0.26/0.69 % ODEo_undef
% 0.26/0.69 thf(fact_347_ODEo_Osimps_I2_J,axiom,
% 0.26/0.69 ! [X2: char] :
% 0.26/0.69 ( ( uSubst1827052306e_ODEo @ X2 @ none_trm )
% 0.26/0.69 = none_game ) ).
% 0.26/0.69
% 0.26/0.69 % ODEo.simps(2)
% 0.26/0.69 thf(fact_348_ODEo_Oelims,axiom,
% 0.26/0.69 ! [X2: char,Xa: option_trm,Y2: option_game] :
% 0.26/0.69 ( ( ( uSubst1827052306e_ODEo @ X2 @ Xa )
% 0.26/0.69 = Y2 )
% 0.26/0.69 => ( ! [Theta2: trm] :
% 0.26/0.69 ( ( Xa
% 0.26/0.69 = ( some_trm @ Theta2 ) )
% 0.26/0.69 => ( Y2
% 0.26/0.69 != ( some_game @ ( ode @ X2 @ Theta2 ) ) ) )
% 0.26/0.69 => ~ ( ( Xa = none_trm )
% 0.26/0.69 => ( Y2 != none_game ) ) ) ) ).
% 0.26/0.69
% 0.26/0.69 % ODEo.elims
% 0.26/0.69 thf(fact_349_ODEo_Opelims,axiom,
% 0.26/0.69 ! [X2: char,Xa: option_trm,Y2: option_game] :
% 0.26/0.69 ( ( ( uSubst1827052306e_ODEo @ X2 @ Xa )
% 0.26/0.69 = Y2 )
% 0.26/0.69 => ( ( accp_P419951815on_trm @ uSubst299938919Eo_rel @ ( produc1500300866on_trm @ X2 @ Xa ) )
% 0.26/0.69 => ( ! [Theta2: trm] :
% 0.26/0.69 ( ( Xa
% 0.26/0.69 = ( some_trm @ Theta2 ) )
% 0.26/0.69 => ( ( Y2
% 0.26/0.69 = ( some_game @ ( ode @ X2 @ Theta2 ) ) )
% 0.26/0.69 => ~ ( accp_P419951815on_trm @ uSubst299938919Eo_rel @ ( produc1500300866on_trm @ X2 @ ( some_trm @ Theta2 ) ) ) ) )
% 0.26/0.69 => ~ ( ( Xa = none_trm )
% 0.26/0.69 => ( ( Y2 = none_game )
% 0.26/0.69 => ~ ( accp_P419951815on_trm @ uSubst299938919Eo_rel @ ( produc1500300866on_trm @ X2 @ none_trm ) ) ) ) ) ) ) ).
% 0.26/0.69
% 0.26/0.69 % ODEo.pelims
% 0.26/0.69 thf(fact_350_game_Oinject_I8_J,axiom,
% 0.26/0.69 ! [X81: char,X82: trm,Y81: char,Y82: trm] :
% 0.26/0.69 ( ( ( ode @ X81 @ X82 )
% 0.26/0.69 = ( ode @ Y81 @ Y82 ) )
% 0.26/0.69 = ( ( X81 = Y81 )
% 0.26/0.69 & ( X82 = Y82 ) ) ) ).
% 0.26/0.69
% 0.26/0.69 % game.inject(8)
% 0.26/0.69 thf(fact_351_game_Odistinct_I35_J,axiom,
% 0.26/0.69 ! [X32: fml,X81: char,X82: trm] :
% 0.26/0.69 ( ( test @ X32 )
% 0.26/0.69 != ( ode @ X81 @ X82 ) ) ).
% 0.26/0.69
% 0.26/0.69 % game.distinct(35)
% 0.26/0.69
% 0.26/0.69 % Conjectures (1)
% 0.26/0.69 thf(conj_0,conjecture,
% 0.26/0.69 ( ( uSubst516392818stappt @ sigma @ ua @ theta )
% 0.26/0.69 != none_trm ) ).
% 0.26/0.69
% 0.26/0.69 %------------------------------------------------------------------------------
% 0.26/0.69 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.iPX4BoXzbz/cvc5---1.0.5_8267.p...
% 0.26/0.69 (declare-sort $$unsorted 0)
% 0.26/0.69 (declare-sort tptp.produc1699626005le_trm 0)
% 0.26/0.69 (declare-sort tptp.produc1418842292n_game 0)
% 0.26/0.69 (declare-sort tptp.set_Pr1918373977on_fml 0)
% 0.26/0.69 (declare-sort tptp.set_Pr1062384839on_trm 0)
% 0.26/0.69 (declare-sort tptp.set_Pr519625031on_fml 0)
% 0.26/0.69 (declare-sort tptp.set_Pr1588097095on_trm 0)
% 0.26/0.69 (declare-sort tptp.set_Pr1045337287on_fml 0)
% 0.26/0.69 (declare-sort tptp.produc1928189433on_fml 0)
% 0.26/0.69 (declare-sort tptp.produc2024965863on_trm 0)
% 0.26/0.69 (declare-sort tptp.produc591588199on_fml 0)
% 0.26/0.69 (declare-sort tptp.produc1158546023on_trm 0)
% 0.26/0.69 (declare-sort tptp.produc1872652007on_fml 0)
% 0.26/0.69 (declare-sort tptp.set_Pr1481565921on_trm 0)
% 0.26/0.69 (declare-sort tptp.set_Pr1969262145le_trm 0)
% 0.26/0.69 (declare-sort tptp.produc2018724225on_trm 0)
% 0.26/0.69 (declare-sort tptp.produc1279577057le_trm 0)
% 0.26/0.69 (declare-sort tptp.set_Pr1625152599n_game 0)
% 0.26/0.69 (declare-sort tptp.set_Pr622314946on_fml 0)
% 0.26/0.69 (declare-sort tptp.set_Pr1471344007on_trm 0)
% 0.26/0.69 (declare-sort tptp.set_Pr927595527on_fml 0)
% 0.26/0.69 (declare-sort tptp.set_Pr181266295riable 0)
% 0.26/0.69 (declare-sort tptp.produc1016592119n_game 0)
% 0.26/0.69 (declare-sort tptp.produc1739631244on_fml 0)
% 0.26/0.69 (declare-sort tptp.produc1072747943on_trm 0)
% 0.26/0.69 (declare-sort tptp.produc1456309597on_fml 0)
% 0.26/0.69 (declare-sort tptp.produc1810527345on_trm 0)
% 0.26/0.69 (declare-sort tptp.produc46605351on_fml 0)
% 0.26/0.69 (declare-sort tptp.produc432717079riable 0)
% 0.26/0.69 (declare-sort tptp.set_Pr943832262on_trm 0)
% 0.26/0.69 (declare-sort tptp.set_Pr1235432374le_trm 0)
% 0.26/0.69 (declare-sort tptp.produc1024976764on_trm 0)
% 0.26/0.69 (declare-sort tptp.produc1408538418on_fml 0)
% 0.26/0.69 (declare-sort tptp.produc464795408on_trm 0)
% 0.26/0.69 (declare-sort tptp.produc833882726rp_trm 0)
% 0.26/0.69 (declare-sort tptp.produc1367888000le_trm 0)
% 0.26/0.69 (declare-sort tptp.set_Pr604539619r_char 0)
% 0.26/0.69 (declare-sort tptp.set_Pr491793543rm_trm 0)
% 0.26/0.69 (declare-sort tptp.produc1593312387r_char 0)
% 0.26/0.69 (declare-sort tptp.product_prod_trm_trm 0)
% 0.26/0.69 (declare-sort tptp.option_game 0)
% 0.26/0.69 (declare-sort tptp.option_trm 0)
% 0.26/0.69 (declare-sort tptp.option_fml 0)
% 0.26/0.69 (declare-sort tptp.denotational_interp 0)
% 0.26/0.69 (declare-sort tptp.set_variable 0)
% 0.26/0.69 (declare-sort tptp.set_char 0)
% 0.26/0.69 (declare-sort tptp.variable 0)
% 0.26/0.69 (declare-sort tptp.game 0)
% 0.26/0.69 (declare-sort tptp.char 0)
% 0.26/0.69 (declare-sort tptp.trm 0)
% 0.26/0.69 (declare-sort tptp.fml 0)
% 0.26/0.69 (declare-sort tptp.real 0)
% 0.26/0.69 (declare-fun tptp.bNF_Gr1866170027on_fml (tptp.set_char (-> tptp.char tptp.option_fml) (-> tptp.char tptp.option_fml)) tptp.set_Pr927595527on_fml)
% 0.26/0.69 (declare-fun tptp.bNF_Gr756940202on_fml (tptp.set_char (-> tptp.char tptp.option_game) (-> tptp.char tptp.option_fml)) tptp.set_Pr622314946on_fml)
% 0.26/0.69 (declare-fun tptp.bNF_Gr1666135339on_trm (tptp.set_char (-> tptp.char tptp.option_trm) (-> tptp.char tptp.option_trm)) tptp.set_Pr1471344007on_trm)
% 0.26/0.69 (declare-fun tptp.bNF_Gr852774302le_trm (tptp.set_char (-> tptp.char tptp.set_variable) (-> tptp.char tptp.trm)) tptp.set_Pr1235432374le_trm)
% 0.26/0.69 (declare-fun tptp.bNF_Gr951178926on_trm (tptp.set_char (-> tptp.char tptp.char) (-> tptp.char tptp.option_trm)) tptp.set_Pr943832262on_trm)
% 0.26/0.69 (declare-fun tptp.bNF_Gr600956991on_fml (tptp.set_variable (-> tptp.variable tptp.option_fml) (-> tptp.variable tptp.option_fml)) tptp.set_Pr927595527on_fml)
% 0.26/0.69 (declare-fun tptp.bNF_Gr2142503190on_fml (tptp.set_variable (-> tptp.variable tptp.option_game) (-> tptp.variable tptp.option_fml)) tptp.set_Pr622314946on_fml)
% 0.26/0.69 (declare-fun tptp.bNF_Gr400922303on_trm (tptp.set_variable (-> tptp.variable tptp.option_trm) (-> tptp.variable tptp.option_trm)) tptp.set_Pr1471344007on_trm)
% 0.26/0.69 (declare-fun tptp.bNF_Gr1330108682le_trm (tptp.set_variable (-> tptp.variable tptp.set_variable) (-> tptp.variable tptp.trm)) tptp.set_Pr1235432374le_trm)
% 0.26/0.69 (declare-fun tptp.bNF_Gr1933470746on_trm (tptp.set_variable (-> tptp.variable tptp.char) (-> tptp.variable tptp.option_trm)) tptp.set_Pr943832262on_trm)
% 0.26/0.69 (declare-fun tptp.bNF_Gr806120164on_fml (tptp.set_Pr927595527on_fml (-> tptp.option_fml tptp.option_fml)) tptp.set_Pr927595527on_fml)
% 0.26/0.69 (declare-fun tptp.denota1419872369iation ((-> tptp.variable tptp.real) (-> tptp.variable tptp.real) tptp.set_variable) Bool)
% 0.26/0.69 (declare-fun tptp.none_fml () tptp.option_fml)
% 0.26/0.69 (declare-fun tptp.none_game () tptp.option_game)
% 0.26/0.69 (declare-fun tptp.none_trm () tptp.option_trm)
% 0.26/0.69 (declare-fun tptp.some_fml (tptp.fml) tptp.option_fml)
% 0.26/0.69 (declare-fun tptp.some_game (tptp.game) tptp.option_game)
% 0.26/0.69 (declare-fun tptp.some_trm (tptp.trm) tptp.option_trm)
% 0.26/0.69 (declare-fun tptp.case_option_o_fml (Bool (-> tptp.fml Bool) tptp.option_fml) Bool)
% 0.26/0.69 (declare-fun tptp.case_option_o_game (Bool (-> tptp.game Bool) tptp.option_game) Bool)
% 0.26/0.69 (declare-fun tptp.case_option_o_trm (Bool (-> tptp.trm Bool) tptp.option_trm) Bool)
% 0.26/0.69 (declare-fun tptp.the_fml (tptp.option_fml) tptp.fml)
% 0.26/0.69 (declare-fun tptp.the_game (tptp.option_game) tptp.game)
% 0.26/0.69 (declare-fun tptp.the_trm (tptp.option_trm) tptp.trm)
% 0.26/0.69 (declare-fun tptp.ord_le802833166_fml_o ((-> tptp.option_fml tptp.option_fml Bool) (-> tptp.option_fml tptp.option_fml Bool)) Bool)
% 0.26/0.69 (declare-fun tptp.ord_le181580155_fml_o ((-> tptp.option_fml Bool) (-> tptp.option_fml Bool)) Bool)
% 0.26/0.69 (declare-fun tptp.ord_le1588489637_fml_o ((-> tptp.option_game tptp.option_fml Bool) (-> tptp.option_game tptp.option_fml Bool)) Bool)
% 0.26/0.69 (declare-fun tptp.ord_le847028878_trm_o ((-> tptp.option_trm tptp.option_trm Bool) (-> tptp.option_trm tptp.option_trm Bool)) Bool)
% 0.26/0.69 (declare-fun tptp.ord_le1957133745_trm_o ((-> tptp.option_trm Bool) (-> tptp.option_trm Bool)) Bool)
% 0.26/0.69 (declare-fun tptp.ord_le90123726_trm_o ((-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool) (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) Bool)
% 0.26/0.69 (declare-fun tptp.ord_le1721128566_trm_o ((-> tptp.produc1072747943on_trm Bool) (-> tptp.produc1072747943on_trm Bool)) Bool)
% 0.26/0.69 (declare-fun tptp.ord_le157637894_trm_o ((-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool) (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) Bool)
% 0.26/0.69 (declare-fun tptp.ord_le1222882015_trm_o ((-> tptp.produc464795408on_trm Bool) (-> tptp.produc464795408on_trm Bool)) Bool)
% 0.26/0.69 (declare-fun tptp.ord_le370603054_trm_o ((-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool) (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) Bool)
% 0.26/0.69 (declare-fun tptp.ord_le373274227_trm_o ((-> tptp.produc1024976764on_trm Bool) (-> tptp.produc1024976764on_trm Bool)) Bool)
% 0.26/0.69 (declare-fun tptp.ord_le691957041_trm_o ((-> tptp.set_variable tptp.trm Bool) (-> tptp.set_variable tptp.trm Bool)) Bool)
% 0.26/0.69 (declare-fun tptp.ord_le1890124833_trm_o ((-> tptp.char tptp.option_trm Bool) (-> tptp.char tptp.option_trm Bool)) Bool)
% 0.26/0.69 (declare-fun tptp.ord_less_eq_char_o ((-> tptp.char Bool) (-> tptp.char Bool)) Bool)
% 0.26/0.69 (declare-fun tptp.ord_le1407353162able_o ((-> tptp.variable Bool) (-> tptp.variable Bool)) Bool)
% 0.26/0.69 (declare-fun tptp.ord_le778974119on_fml (tptp.set_Pr927595527on_fml tptp.set_Pr927595527on_fml) Bool)
% 0.26/0.69 (declare-fun tptp.ord_le782333474on_fml (tptp.set_Pr622314946on_fml tptp.set_Pr622314946on_fml) Bool)
% 0.26/0.69 (declare-fun tptp.ord_le1322722599on_trm (tptp.set_Pr1471344007on_trm tptp.set_Pr1471344007on_trm) Bool)
% 0.26/0.69 (declare-fun tptp.ord_le2102862870le_trm (tptp.set_Pr1235432374le_trm tptp.set_Pr1235432374le_trm) Bool)
% 0.26/0.69 (declare-fun tptp.ord_le541293862on_trm (tptp.set_Pr943832262on_trm tptp.set_Pr943832262on_trm) Bool)
% 0.26/0.69 (declare-fun tptp.ord_less_eq_set_char (tptp.set_char tptp.set_char) Bool)
% 0.26/0.69 (declare-fun tptp.ord_le282106107riable (tptp.set_variable tptp.set_variable) Bool)
% 0.26/0.69 (declare-fun tptp.order_272405634riable ((-> tptp.set_variable Bool)) tptp.set_variable)
% 0.26/0.69 (declare-fun tptp.produc1132922070rp_trm (tptp.denotational_interp tptp.trm) tptp.produc833882726rp_trm)
% 0.26/0.69 (declare-fun tptp.produc909629463on_fml (tptp.option_fml tptp.option_fml) tptp.produc46605351on_fml)
% 0.26/0.69 (declare-fun tptp.produc1447374177on_trm (tptp.option_fml tptp.option_trm) tptp.produc1810527345on_trm)
% 0.26/0.69 (declare-fun tptp.produc2124676926on_fml (tptp.option_game tptp.option_fml) tptp.produc1739631244on_fml)
% 0.26/0.69 (declare-fun tptp.produc1111617711n_game (tptp.option_game tptp.option_game) tptp.produc1016592119n_game)
% 0.26/0.69 (declare-fun tptp.produc171850061on_fml (tptp.option_trm tptp.option_fml) tptp.produc1456309597on_fml)
% 0.26/0.69 (declare-fun tptp.produc709594775on_trm (tptp.option_trm tptp.option_trm) tptp.produc1072747943on_trm)
% 0.26/0.69 (declare-fun tptp.produc2015636557le_trm (tptp.produc1418842292n_game tptp.produc1367888000le_trm) tptp.produc1699626005le_trm)
% 0.26/0.69 (declare-fun tptp.produc1367044951on_fml (tptp.produc46605351on_fml tptp.produc46605351on_fml) tptp.produc1872652007on_fml)
% 0.26/0.69 (declare-fun tptp.produc2132972503on_trm (tptp.produc1810527345on_trm tptp.produc1810527345on_trm) tptp.produc1158546023on_trm)
% 0.26/0.69 (declare-fun tptp.produc556056113on_fml (tptp.produc1739631244on_fml tptp.produc1739631244on_fml) tptp.produc1928189433on_fml)
% 0.26/0.69 (declare-fun tptp.produc1235825367on_fml (tptp.produc1456309597on_fml tptp.produc1456309597on_fml) tptp.produc591588199on_fml)
% 0.26/0.69 (declare-fun tptp.produc2001752919on_trm (tptp.produc1072747943on_trm tptp.produc1072747943on_trm) tptp.produc2024965863on_trm)
% 0.26/0.69 (declare-fun tptp.produc1056455193le_trm (tptp.produc1367888000le_trm tptp.produc1367888000le_trm) tptp.produc1279577057le_trm)
% 0.26/0.69 (declare-fun tptp.produc444919481on_trm (tptp.produc464795408on_trm tptp.produc464795408on_trm) tptp.produc2018724225on_trm)
% 0.26/0.69 (declare-fun tptp.produc1766592463riable (tptp.set_variable tptp.set_variable) tptp.produc432717079riable)
% 0.26/0.69 (declare-fun tptp.produc1482344242le_trm (tptp.set_variable tptp.trm) tptp.produc1367888000le_trm)
% 0.26/0.69 (declare-fun tptp.produc1500300866on_trm (tptp.char tptp.option_trm) tptp.produc464795408on_trm)
% 0.26/0.69 (declare-fun tptp.produc19545147r_char (tptp.char tptp.char) tptp.produc1593312387r_char)
% 0.26/0.69 (declare-fun tptp.product_Pair_trm_trm (tptp.trm tptp.trm) tptp.product_prod_trm_trm)
% 0.26/0.69 (declare-fun tptp.produc1205977188on_fml (tptp.variable tptp.option_fml) tptp.produc1408538418on_fml)
% 0.26/0.69 (declare-fun tptp.produc1743721902on_trm (tptp.variable tptp.option_trm) tptp.produc1024976764on_trm)
% 0.26/0.69 (declare-fun tptp.collec670974098on_fml ((-> tptp.produc46605351on_fml Bool)) tptp.set_Pr927595527on_fml)
% 0.26/0.69 (declare-fun tptp.collec749447393on_fml ((-> tptp.produc1739631244on_fml Bool)) tptp.set_Pr622314946on_fml)
% 0.26/0.69 (declare-fun tptp.collec1697116690on_trm ((-> tptp.produc1072747943on_trm Bool)) tptp.set_Pr1471344007on_trm)
% 0.26/0.69 (declare-fun tptp.collec575343829le_trm ((-> tptp.produc1367888000le_trm Bool)) tptp.set_Pr1235432374le_trm)
% 0.26/0.69 (declare-fun tptp.collec1756633317on_trm ((-> tptp.produc464795408on_trm Bool)) tptp.set_Pr943832262on_trm)
% 0.26/0.69 (declare-fun tptp.collect_char ((-> tptp.char Bool)) tptp.set_char)
% 0.26/0.69 (declare-fun tptp.collect_variable ((-> tptp.variable Bool)) tptp.set_variable)
% 0.26/0.69 (declare-fun tptp.geq (tptp.trm tptp.trm) tptp.fml)
% 0.26/0.69 (declare-fun tptp.assign (tptp.variable tptp.trm) tptp.game)
% 0.26/0.69 (declare-fun tptp.ode (tptp.char tptp.trm) tptp.game)
% 0.26/0.69 (declare-fun tptp.test (tptp.fml) tptp.game)
% 0.26/0.69 (declare-fun tptp.const (tptp.char) tptp.trm)
% 0.26/0.69 (declare-fun tptp.differential (tptp.trm) tptp.trm)
% 0.26/0.69 (declare-fun tptp.func (tptp.char tptp.trm) tptp.trm)
% 0.26/0.69 (declare-fun tptp.number (tptp.real) tptp.trm)
% 0.26/0.69 (declare-fun tptp.plus (tptp.trm tptp.trm) tptp.trm)
% 0.26/0.69 (declare-fun tptp.times (tptp.trm tptp.trm) tptp.trm)
% 0.26/0.69 (declare-fun tptp.var (tptp.variable) tptp.trm)
% 0.26/0.69 (declare-fun tptp.uSubst834381837ssigno (tptp.variable tptp.option_trm) tptp.option_game)
% 0.26/0.69 (declare-fun tptp.uSubst157155628no_rel (tptp.produc1024976764on_trm tptp.produc1024976764on_trm) Bool)
% 0.26/0.69 (declare-fun tptp.uSubst716837505ntialo (tptp.option_trm) tptp.option_trm)
% 0.26/0.69 (declare-fun tptp.uSubst2051024824lo_rel (tptp.option_trm tptp.option_trm) Bool)
% 0.26/0.69 (declare-fun tptp.uSubst152838031e_Geqo (tptp.option_trm tptp.option_trm) tptp.option_fml)
% 0.26/0.69 (declare-fun tptp.uSubst1304144938qo_rel (tptp.produc1072747943on_trm tptp.produc1072747943on_trm) Bool)
% 0.26/0.69 (declare-fun tptp.uSubst1827052306e_ODEo (tptp.char tptp.option_trm) tptp.option_game)
% 0.26/0.69 (declare-fun tptp.uSubst299938919Eo_rel (tptp.produc464795408on_trm tptp.produc464795408on_trm) Bool)
% 0.26/0.69 (declare-fun tptp.uSubst141955042_Pluso (tptp.option_trm tptp.option_trm) tptp.option_trm)
% 0.26/0.69 (declare-fun tptp.uSubst691094423so_rel (tptp.produc1072747943on_trm tptp.produc1072747943on_trm) Bool)
% 0.26/0.69 (declare-fun tptp.uSubst1367128042_Testo (tptp.option_fml) tptp.option_game)
% 0.26/0.69 (declare-fun tptp.uSubst954181007to_rel (tptp.option_fml tptp.option_fml) Bool)
% 0.26/0.69 (declare-fun tptp.uSubst918876924Timeso (tptp.option_trm tptp.option_trm) tptp.option_trm)
% 0.26/0.69 (declare-fun tptp.uSubst924844285so_rel (tptp.produc1072747943on_trm tptp.produc1072747943on_trm) Bool)
% 0.26/0.69 (declare-fun tptp.uSubst1559070963pconst (tptp.produc1418842292n_game tptp.set_variable tptp.char) tptp.option_trm)
% 0.26/0.69 (declare-fun tptp.uSubst516392804stappf (tptp.produc1418842292n_game tptp.set_variable tptp.fml) tptp.option_fml)
% 0.26/0.69 (declare-fun tptp.uSubst516392818stappt (tptp.produc1418842292n_game tptp.set_variable tptp.trm) tptp.option_trm)
% 0.26/0.69 (declare-fun tptp.uSubst1917534215pt_rel (tptp.produc1699626005le_trm tptp.produc1699626005le_trm) Bool)
% 0.26/0.69 (declare-fun tptp.accp_option_fml ((-> tptp.option_fml tptp.option_fml Bool) tptp.option_fml) Bool)
% 0.26/0.69 (declare-fun tptp.accp_option_trm ((-> tptp.option_trm tptp.option_trm Bool) tptp.option_trm) Bool)
% 0.26/0.69 (declare-fun tptp.accp_P758790320on_trm ((-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool) tptp.produc1072747943on_trm) Bool)
% 0.26/0.69 (declare-fun tptp.accp_P1877119646le_trm ((-> tptp.produc1699626005le_trm tptp.produc1699626005le_trm Bool) tptp.produc1699626005le_trm) Bool)
% 0.26/0.69 (declare-fun tptp.accp_P419951815on_trm ((-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool) tptp.produc464795408on_trm) Bool)
% 0.26/0.69 (declare-fun tptp.accp_P394694195on_trm ((-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool) tptp.produc1024976764on_trm) Bool)
% 0.26/0.69 (declare-fun tptp.lex_pr314879023on_fml (tptp.set_Pr927595527on_fml tptp.set_Pr927595527on_fml) tptp.set_Pr1045337287on_fml)
% 0.26/0.69 (declare-fun tptp.lex_pr852623737on_trm (tptp.set_Pr927595527on_fml tptp.set_Pr1471344007on_trm) tptp.set_Pr1588097095on_trm)
% 0.26/0.69 (declare-fun tptp.lex_pr425996582on_fml (tptp.set_Pr1625152599n_game tptp.set_Pr927595527on_fml) tptp.set_Pr1918373977on_fml)
% 0.26/0.69 (declare-fun tptp.lex_pr1724583269on_fml (tptp.set_Pr1471344007on_trm tptp.set_Pr927595527on_fml) tptp.set_Pr519625031on_fml)
% 0.26/0.69 (declare-fun tptp.lex_pr114844335on_trm (tptp.set_Pr1471344007on_trm tptp.set_Pr1471344007on_trm) tptp.set_Pr1062384839on_trm)
% 0.26/0.69 (declare-fun tptp.lex_pr1522821402le_trm (tptp.set_Pr181266295riable tptp.set_Pr491793543rm_trm) tptp.set_Pr1969262145le_trm)
% 0.26/0.69 (declare-fun tptp.lex_pr1901327402on_trm (tptp.set_Pr604539619r_char tptp.set_Pr1471344007on_trm) tptp.set_Pr1481565921on_trm)
% 0.26/0.69 (declare-fun tptp.member1287158352on_fml (tptp.produc46605351on_fml tptp.set_Pr927595527on_fml) Bool)
% 0.26/0.69 (declare-fun tptp.member1883102883on_fml (tptp.produc1739631244on_fml tptp.set_Pr622314946on_fml) Bool)
% 0.26/0.69 (declare-fun tptp.member191809696n_game (tptp.produc1016592119n_game tptp.set_Pr1625152599n_game) Bool)
% 0.26/0.69 (declare-fun tptp.member165817296on_trm (tptp.produc1072747943on_trm tptp.set_Pr1471344007on_trm) Bool)
% 0.26/0.69 (declare-fun tptp.member450497296on_fml (tptp.produc1872652007on_fml tptp.set_Pr1045337287on_fml) Bool)
% 0.26/0.69 (declare-fun tptp.member1883874960on_trm (tptp.produc1158546023on_trm tptp.set_Pr1588097095on_trm) Bool)
% 0.26/0.69 (declare-fun tptp.member113767842on_fml (tptp.produc1928189433on_fml tptp.set_Pr1918373977on_fml) Bool)
% 0.26/0.69 (declare-fun tptp.member1316917136on_fml (tptp.produc591588199on_fml tptp.set_Pr519625031on_fml) Bool)
% 0.26/0.69 (declare-fun tptp.member602811152on_trm (tptp.produc2024965863on_trm tptp.set_Pr1062384839on_trm) Bool)
% 0.26/0.69 (declare-fun tptp.member1150310282le_trm (tptp.produc1279577057le_trm tptp.set_Pr1969262145le_trm) Bool)
% 0.26/0.69 (declare-fun tptp.member1950256170on_trm (tptp.produc2018724225on_trm tptp.set_Pr1481565921on_trm) Bool)
% 0.26/0.69 (declare-fun tptp.member1978718144riable (tptp.produc432717079riable tptp.set_Pr181266295riable) Bool)
% 0.26/0.69 (declare-fun tptp.member2122665623le_trm (tptp.produc1367888000le_trm tptp.set_Pr1235432374le_trm) Bool)
% 0.26/0.69 (declare-fun tptp.member694524327on_trm (tptp.produc464795408on_trm tptp.set_Pr943832262on_trm) Bool)
% 0.26/0.69 (declare-fun tptp.member1866856748r_char (tptp.produc1593312387r_char tptp.set_Pr604539619r_char) Bool)
% 0.26/0.69 (declare-fun tptp.member1735386832rm_trm (tptp.product_prod_trm_trm tptp.set_Pr491793543rm_trm) Bool)
% 0.26/0.69 (declare-fun tptp.member_char (tptp.char tptp.set_char) Bool)
% 0.26/0.69 (declare-fun tptp.member_variable (tptp.variable tptp.set_variable) Bool)
% 0.26/0.69 (declare-fun tptp.u () tptp.set_variable)
% 0.26/0.69 (declare-fun tptp.ua () tptp.set_variable)
% 0.26/0.69 (declare-fun tptp.eta () tptp.trm)
% 0.26/0.69 (declare-fun tptp.nu (tptp.variable) tptp.real)
% 0.26/0.69 (declare-fun tptp.nu2 (tptp.variable) tptp.real)
% 0.26/0.69 (declare-fun tptp.omega (tptp.variable) tptp.real)
% 0.26/0.69 (declare-fun tptp.omega2 (tptp.variable) tptp.real)
% 0.26/0.69 (declare-fun tptp.sigma () tptp.produc1418842292n_game)
% 0.26/0.69 (declare-fun tptp.theta () tptp.trm)
% 0.26/0.69 (assert (@ (@ (@ tptp.denota1419872369iation tptp.nu) tptp.omega) tptp.u))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (=> (not (= (@ (@ (@ tptp.uSubst516392804stappf Sigma) U) (@ (@ tptp.geq Theta) Eta)) tptp.none_fml)) (and (not (= (@ _let_1 Theta) tptp.none_trm)) (not (= (@ _let_1 Eta) tptp.none_trm)))))))
% 0.26/0.69 (assert (not (= (@ (@ (@ tptp.uSubst516392804stappf tptp.sigma) tptp.ua) (@ (@ tptp.geq tptp.theta) tptp.eta)) tptp.none_fml)))
% 0.26/0.69 (assert (= tptp.none_trm tptp.none_trm))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (V tptp.set_variable)) (let ((_let_1 (@ tptp.uSubst516392818stappt Sigma))) (let ((_let_2 (@ (@ _let_1 V) Theta))) (let ((_let_3 (@ (@ _let_1 U) Theta))) (=> (not (= _let_3 tptp.none_trm)) (=> (not (= _let_2 tptp.none_trm)) (= _let_3 _let_2))))))))
% 0.26/0.69 (assert (@ (@ (@ tptp.denota1419872369iation tptp.nu2) tptp.omega2) tptp.ua))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (=> (not (= (@ _let_1 (@ (@ tptp.plus Theta) Eta)) tptp.none_trm)) (and (not (= (@ _let_1 Theta) tptp.none_trm)) (not (= (@ _let_1 Eta) tptp.none_trm)))))))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (=> (not (= (@ _let_1 (@ (@ tptp.times Theta) Eta)) tptp.none_trm)) (and (not (= (@ _let_1 Theta) tptp.none_trm)) (not (= (@ _let_1 Eta) tptp.none_trm)))))))
% 0.26/0.69 (assert (forall ((V tptp.set_variable) (U tptp.set_variable) (Sigma tptp.produc1418842292n_game) (Theta tptp.trm)) (let ((_let_1 (@ tptp.uSubst516392818stappt Sigma))) (let ((_let_2 (@ (@ _let_1 U) Theta))) (=> (@ (@ tptp.ord_le282106107riable V) U) (=> (not (= _let_2 tptp.none_trm)) (= _let_2 (@ (@ _let_1 V) Theta))))))))
% 0.26/0.69 (assert (= (@ tptp.uSubst716837505ntialo tptp.none_trm) tptp.none_trm))
% 0.26/0.69 (assert (forall ((Theta tptp.option_trm)) (= (= (@ tptp.uSubst716837505ntialo Theta) tptp.none_trm) (= Theta tptp.none_trm))))
% 0.26/0.69 (assert (forall ((Eta tptp.option_trm)) (= (@ (@ tptp.uSubst141955042_Pluso tptp.none_trm) Eta) tptp.none_trm)))
% 0.26/0.69 (assert (forall ((Eta tptp.option_trm)) (= (@ (@ tptp.uSubst918876924Timeso tptp.none_trm) Eta) tptp.none_trm)))
% 0.26/0.69 (assert (forall ((Theta tptp.option_trm) (Eta tptp.option_trm)) (= (= (@ (@ tptp.uSubst141955042_Pluso Theta) Eta) tptp.none_trm) (or (= Theta tptp.none_trm) (= Eta tptp.none_trm)))))
% 0.26/0.69 (assert (forall ((Theta tptp.option_trm) (Eta tptp.option_trm)) (= (= (@ (@ tptp.uSubst918876924Timeso Theta) Eta) tptp.none_trm) (or (= Theta tptp.none_trm) (= Eta tptp.none_trm)))))
% 0.26/0.69 (assert (forall ((Eta tptp.option_trm)) (= (@ (@ tptp.uSubst152838031e_Geqo tptp.none_trm) Eta) tptp.none_fml)))
% 0.26/0.69 (assert (forall ((V tptp.set_variable) (U tptp.set_variable) (Sigma tptp.produc1418842292n_game) (Phi tptp.fml)) (let ((_let_1 (@ tptp.uSubst516392804stappf Sigma))) (let ((_let_2 (@ (@ _let_1 U) Phi))) (=> (@ (@ tptp.ord_le282106107riable V) U) (=> (not (= _let_2 tptp.none_fml)) (= _let_2 (@ (@ _let_1 V) Phi))))))))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Phi tptp.fml) (V tptp.set_variable)) (let ((_let_1 (@ tptp.uSubst516392804stappf Sigma))) (let ((_let_2 (@ (@ _let_1 V) Phi))) (let ((_let_3 (@ (@ _let_1 U) Phi))) (=> (not (= _let_3 tptp.none_fml)) (=> (not (= _let_2 tptp.none_fml)) (= _let_3 _let_2))))))))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (= (@ _let_1 (@ (@ tptp.plus Theta) Eta)) (@ (@ tptp.uSubst141955042_Pluso (@ _let_1 Theta)) (@ _let_1 Eta))))))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (= (@ _let_1 (@ (@ tptp.times Theta) Eta)) (@ (@ tptp.uSubst918876924Timeso (@ _let_1 Theta)) (@ _let_1 Eta))))))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (= (@ (@ (@ tptp.uSubst516392804stappf Sigma) U) (@ (@ tptp.geq Theta) Eta)) (@ (@ tptp.uSubst152838031e_Geqo (@ _let_1 Theta)) (@ _let_1 Eta))))))
% 0.26/0.69 (assert (forall ((Theta tptp.option_trm) (Eta tptp.option_trm)) (= (= (@ (@ tptp.uSubst152838031e_Geqo Theta) Eta) tptp.none_fml) (or (= Theta tptp.none_trm) (= Eta tptp.none_trm)))))
% 0.26/0.69 (assert (forall ((X61 tptp.trm) (X62 tptp.trm) (Y61 tptp.trm) (Y62 tptp.trm)) (= (= (@ (@ tptp.times X61) X62) (@ (@ tptp.times Y61) Y62)) (and (= X61 Y61) (= X62 Y62)))))
% 0.26/0.69 (assert (forall ((X51 tptp.trm) (X52 tptp.trm) (Y51 tptp.trm) (Y52 tptp.trm)) (= (= (@ (@ tptp.plus X51) X52) (@ (@ tptp.plus Y51) Y52)) (and (= X51 Y51) (= X52 Y52)))))
% 0.26/0.69 (assert (forall ((X21 tptp.trm) (X22 tptp.trm) (Y21 tptp.trm) (Y22 tptp.trm)) (= (= (@ (@ tptp.geq X21) X22) (@ (@ tptp.geq Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.26/0.69 (assert (forall ((U tptp.set_variable) (V tptp.set_variable) (Omega (-> tptp.variable tptp.real)) (Nu (-> tptp.variable tptp.real))) (let ((_let_1 (@ (@ tptp.denota1419872369iation Omega) Nu))) (=> (@ (@ tptp.ord_le282106107riable U) V) (=> (@ _let_1 U) (@ _let_1 V))))))
% 0.26/0.69 (assert (forall ((A tptp.set_char) (B tptp.set_char)) (=> (forall ((X tptp.char)) (let ((_let_1 (@ tptp.member_char X))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_char A) B))))
% 0.26/0.69 (assert (forall ((A tptp.set_variable) (B tptp.set_variable)) (=> (forall ((X tptp.variable)) (let ((_let_1 (@ tptp.member_variable X))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le282106107riable A) B))))
% 0.26/0.69 (assert (forall ((A tptp.set_variable) (B tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable A) B) (=> (@ (@ tptp.ord_le282106107riable B) A) (= A B)))))
% 0.26/0.69 (assert (forall ((X51 tptp.trm) (X52 tptp.trm) (X61 tptp.trm) (X62 tptp.trm)) (not (= (@ (@ tptp.plus X51) X52) (@ (@ tptp.times X61) X62)))))
% 0.26/0.69 (assert (forall ((X2 tptp.set_variable)) (@ (@ tptp.ord_le282106107riable X2) X2)))
% 0.26/0.69 (assert (forall ((Nu (-> tptp.variable tptp.real)) (Nu2 (-> tptp.variable tptp.real))) (@ (@ (@ tptp.denota1419872369iation Nu) Nu2) (@ tptp.collect_variable (lambda ((X3 tptp.variable)) true)))))
% 0.26/0.69 (assert (forall ((A tptp.set_char) (P (-> tptp.char Bool))) (@ (@ tptp.ord_less_eq_set_char (@ tptp.collect_char (lambda ((X3 tptp.char)) (and (@ (@ tptp.member_char X3) A) (@ P X3))))) A)))
% 0.26/0.69 (assert (forall ((A tptp.set_variable) (P (-> tptp.variable Bool))) (@ (@ tptp.ord_le282106107riable (@ tptp.collect_variable (lambda ((X3 tptp.variable)) (and (@ (@ tptp.member_variable X3) A) (@ P X3))))) A)))
% 0.26/0.69 (assert (= tptp.ord_less_eq_set_char (lambda ((A2 tptp.set_char) (B2 tptp.set_char)) (@ (@ tptp.ord_less_eq_char_o (lambda ((X3 tptp.char)) (@ (@ tptp.member_char X3) A2))) (lambda ((X3 tptp.char)) (@ (@ tptp.member_char X3) B2))))))
% 0.26/0.69 (assert (= tptp.ord_le282106107riable (lambda ((A2 tptp.set_variable) (B2 tptp.set_variable)) (@ (@ tptp.ord_le1407353162able_o (lambda ((X3 tptp.variable)) (@ (@ tptp.member_variable X3) A2))) (lambda ((X3 tptp.variable)) (@ (@ tptp.member_variable X3) B2))))))
% 0.26/0.69 (assert (forall ((B3 tptp.set_variable) (A3 tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable B3) A3) (=> (@ (@ tptp.ord_le282106107riable A3) B3) (= A3 B3)))))
% 0.26/0.69 (assert (= (lambda ((Y tptp.set_variable) (Z tptp.set_variable)) (= Y Z)) (lambda ((A4 tptp.set_variable) (B4 tptp.set_variable)) (and (@ (@ tptp.ord_le282106107riable B4) A4) (@ (@ tptp.ord_le282106107riable A4) B4)))))
% 0.26/0.69 (assert (forall ((B3 tptp.set_variable) (A3 tptp.set_variable) (C tptp.set_variable)) (let ((_let_1 (@ tptp.ord_le282106107riable C))) (=> (@ (@ tptp.ord_le282106107riable B3) A3) (=> (@ _let_1 B3) (@ _let_1 A3))))))
% 0.26/0.69 (assert (forall ((A3 tptp.set_variable)) (@ (@ tptp.ord_le282106107riable A3) A3)))
% 0.26/0.69 (assert (forall ((X2 tptp.set_variable) (Y2 tptp.set_variable) (Z2 tptp.set_variable)) (let ((_let_1 (@ tptp.ord_le282106107riable X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_le282106107riable Y2) Z2) (@ _let_1 Z2))))))
% 0.26/0.69 (assert (forall ((A3 tptp.set_variable) (B3 tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable A3) B3) (=> (@ (@ tptp.ord_le282106107riable B3) A3) (= A3 B3)))))
% 0.26/0.69 (assert (forall ((A3 tptp.set_variable) (B3 tptp.set_variable) (C tptp.set_variable)) (let ((_let_1 (@ tptp.ord_le282106107riable A3))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))))
% 0.26/0.69 (assert (forall ((A3 tptp.set_variable) (B3 tptp.set_variable) (C tptp.set_variable)) (=> (= A3 B3) (=> (@ (@ tptp.ord_le282106107riable B3) C) (@ (@ tptp.ord_le282106107riable A3) C)))))
% 0.26/0.69 (assert (= (lambda ((Y tptp.set_variable) (Z tptp.set_variable)) (= Y Z)) (lambda ((A4 tptp.set_variable) (B4 tptp.set_variable)) (and (@ (@ tptp.ord_le282106107riable A4) B4) (@ (@ tptp.ord_le282106107riable B4) A4)))))
% 0.26/0.69 (assert (forall ((Y2 tptp.set_variable) (X2 tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable Y2) X2) (= (@ (@ tptp.ord_le282106107riable X2) Y2) (= X2 Y2)))))
% 0.26/0.69 (assert (forall ((A3 tptp.variable) (P (-> tptp.variable Bool))) (= (@ (@ tptp.member_variable A3) (@ tptp.collect_variable P)) (@ P A3))))
% 0.26/0.69 (assert (forall ((A3 tptp.char) (P (-> tptp.char Bool))) (= (@ (@ tptp.member_char A3) (@ tptp.collect_char P)) (@ P A3))))
% 0.26/0.69 (assert (forall ((A tptp.set_variable)) (= (@ tptp.collect_variable (lambda ((X3 tptp.variable)) (@ (@ tptp.member_variable X3) A))) A)))
% 0.26/0.69 (assert (forall ((A tptp.set_char)) (= (@ tptp.collect_char (lambda ((X3 tptp.char)) (@ (@ tptp.member_char X3) A))) A)))
% 0.26/0.69 (assert (forall ((P (-> tptp.variable Bool)) (Q (-> tptp.variable Bool))) (=> (forall ((X tptp.variable)) (= (@ P X) (@ Q X))) (= (@ tptp.collect_variable P) (@ tptp.collect_variable Q)))))
% 0.26/0.69 (assert (forall ((P (-> tptp.char Bool)) (Q (-> tptp.char Bool))) (=> (forall ((X tptp.char)) (= (@ P X) (@ Q X))) (= (@ tptp.collect_char P) (@ tptp.collect_char Q)))))
% 0.26/0.69 (assert (forall ((A3 tptp.set_variable) (B3 tptp.set_variable) (C tptp.set_variable)) (let ((_let_1 (@ tptp.ord_le282106107riable A3))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_le282106107riable B3) C) (@ _let_1 C))))))
% 0.26/0.69 (assert (forall ((X2 tptp.set_variable) (Y2 tptp.set_variable)) (=> (= X2 Y2) (@ (@ tptp.ord_le282106107riable X2) Y2))))
% 0.26/0.69 (assert (forall ((X2 tptp.set_variable) (Y2 tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable X2) Y2) (=> (@ (@ tptp.ord_le282106107riable Y2) X2) (= X2 Y2)))))
% 0.26/0.69 (assert (= (lambda ((Y tptp.set_variable) (Z tptp.set_variable)) (= Y Z)) (lambda ((X3 tptp.set_variable) (Y3 tptp.set_variable)) (and (@ (@ tptp.ord_le282106107riable X3) Y3) (@ (@ tptp.ord_le282106107riable Y3) X3)))))
% 0.26/0.69 (assert (forall ((A3 tptp.set_variable) (B3 tptp.set_variable) (F (-> tptp.set_variable tptp.set_variable)) (C tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable A3) B3) (=> (= (@ F B3) C) (=> (forall ((X tptp.set_variable) (Y4 tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable X) Y4) (@ (@ tptp.ord_le282106107riable (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_le282106107riable (@ F A3)) C))))))
% 0.26/0.69 (assert (forall ((A3 tptp.set_variable) (F (-> tptp.set_variable tptp.set_variable)) (B3 tptp.set_variable) (C tptp.set_variable)) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_le282106107riable B3) C) (=> (forall ((X tptp.set_variable) (Y4 tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable X) Y4) (@ (@ tptp.ord_le282106107riable (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_le282106107riable A3) (@ F C)))))))
% 0.26/0.69 (assert (forall ((A3 tptp.set_variable) (B3 tptp.set_variable) (F (-> tptp.set_variable tptp.set_variable)) (C tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable A3) B3) (=> (@ (@ tptp.ord_le282106107riable (@ F B3)) C) (=> (forall ((X tptp.set_variable) (Y4 tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable X) Y4) (@ (@ tptp.ord_le282106107riable (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_le282106107riable (@ F A3)) C))))))
% 0.26/0.69 (assert (forall ((A3 tptp.set_variable) (F (-> tptp.set_variable tptp.set_variable)) (B3 tptp.set_variable) (C tptp.set_variable)) (let ((_let_1 (@ tptp.ord_le282106107riable A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_le282106107riable B3) C) (=> (forall ((X tptp.set_variable) (Y4 tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable X) Y4) (@ (@ tptp.ord_le282106107riable (@ F X)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 0.26/0.69 (assert (forall ((P (-> tptp.char Bool)) (Q (-> tptp.char Bool))) (= (@ (@ tptp.ord_less_eq_set_char (@ tptp.collect_char P)) (@ tptp.collect_char Q)) (forall ((X3 tptp.char)) (=> (@ P X3) (@ Q X3))))))
% 0.26/0.69 (assert (forall ((P (-> tptp.variable Bool)) (Q (-> tptp.variable Bool))) (= (@ (@ tptp.ord_le282106107riable (@ tptp.collect_variable P)) (@ tptp.collect_variable Q)) (forall ((X3 tptp.variable)) (=> (@ P X3) (@ Q X3))))))
% 0.26/0.69 (assert (= (lambda ((Y tptp.set_variable) (Z tptp.set_variable)) (= Y Z)) (lambda ((A2 tptp.set_variable) (B2 tptp.set_variable)) (and (@ (@ tptp.ord_le282106107riable A2) B2) (@ (@ tptp.ord_le282106107riable B2) A2)))))
% 0.26/0.69 (assert (forall ((A tptp.set_variable) (B tptp.set_variable) (C2 tptp.set_variable)) (let ((_let_1 (@ tptp.ord_le282106107riable A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le282106107riable B) C2) (@ _let_1 C2))))))
% 0.26/0.69 (assert (forall ((P (-> tptp.char Bool)) (Q (-> tptp.char Bool))) (=> (forall ((X tptp.char)) (=> (@ P X) (@ Q X))) (@ (@ tptp.ord_less_eq_set_char (@ tptp.collect_char P)) (@ tptp.collect_char Q)))))
% 0.26/0.69 (assert (forall ((P (-> tptp.variable Bool)) (Q (-> tptp.variable Bool))) (=> (forall ((X tptp.variable)) (=> (@ P X) (@ Q X))) (@ (@ tptp.ord_le282106107riable (@ tptp.collect_variable P)) (@ tptp.collect_variable Q)))))
% 0.26/0.69 (assert (forall ((A tptp.set_variable)) (@ (@ tptp.ord_le282106107riable A) A)))
% 0.26/0.69 (assert (= tptp.ord_less_eq_set_char (lambda ((A2 tptp.set_char) (B2 tptp.set_char)) (forall ((T tptp.char)) (let ((_let_1 (@ tptp.member_char T))) (=> (@ _let_1 A2) (@ _let_1 B2)))))))
% 0.26/0.69 (assert (= tptp.ord_le282106107riable (lambda ((A2 tptp.set_variable) (B2 tptp.set_variable)) (forall ((T tptp.variable)) (let ((_let_1 (@ tptp.member_variable T))) (=> (@ _let_1 A2) (@ _let_1 B2)))))))
% 0.26/0.69 (assert (forall ((A tptp.set_variable) (B tptp.set_variable)) (=> (= A B) (@ (@ tptp.ord_le282106107riable B) A))))
% 0.26/0.69 (assert (forall ((A tptp.set_variable) (B tptp.set_variable)) (=> (= A B) (@ (@ tptp.ord_le282106107riable A) B))))
% 0.26/0.69 (assert (= tptp.ord_less_eq_set_char (lambda ((A2 tptp.set_char) (B2 tptp.set_char)) (forall ((X3 tptp.char)) (let ((_let_1 (@ tptp.member_char X3))) (=> (@ _let_1 A2) (@ _let_1 B2)))))))
% 0.26/0.69 (assert (= tptp.ord_le282106107riable (lambda ((A2 tptp.set_variable) (B2 tptp.set_variable)) (forall ((X3 tptp.variable)) (let ((_let_1 (@ tptp.member_variable X3))) (=> (@ _let_1 A2) (@ _let_1 B2)))))))
% 0.26/0.69 (assert (forall ((A tptp.set_variable) (B tptp.set_variable)) (=> (= A B) (not (=> (@ (@ tptp.ord_le282106107riable A) B) (not (@ (@ tptp.ord_le282106107riable B) A)))))))
% 0.26/0.69 (assert (forall ((A tptp.set_char) (B tptp.set_char) (C tptp.char)) (let ((_let_1 (@ tptp.member_char C))) (=> (@ (@ tptp.ord_less_eq_set_char A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.69 (assert (forall ((A tptp.set_variable) (B tptp.set_variable) (C tptp.variable)) (let ((_let_1 (@ tptp.member_variable C))) (=> (@ (@ tptp.ord_le282106107riable A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.69 (assert (forall ((A tptp.set_char) (B tptp.set_char) (X2 tptp.char)) (let ((_let_1 (@ tptp.member_char X2))) (=> (@ (@ tptp.ord_less_eq_set_char A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.69 (assert (forall ((A tptp.set_variable) (B tptp.set_variable) (X2 tptp.variable)) (let ((_let_1 (@ tptp.member_variable X2))) (=> (@ (@ tptp.ord_le282106107riable A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.69 (assert (forall ((Omega (-> tptp.variable tptp.real)) (Nu (-> tptp.variable tptp.real)) (U tptp.set_variable)) (=> (@ (@ (@ tptp.denota1419872369iation Omega) Nu) U) (@ (@ (@ tptp.denota1419872369iation Nu) Omega) U))))
% 0.26/0.69 (assert (forall ((Nu (-> tptp.variable tptp.real)) (V tptp.set_variable)) (@ (@ (@ tptp.denota1419872369iation Nu) Nu) V)))
% 0.26/0.69 (assert (= tptp.denota1419872369iation (lambda ((Omega2 (-> tptp.variable tptp.real)) (Nu3 (-> tptp.variable tptp.real)) (__flatten_var_0 tptp.set_variable)) (@ (@ (@ tptp.denota1419872369iation Nu3) Omega2) __flatten_var_0))))
% 0.26/0.69 (assert (= tptp.denota1419872369iation (lambda ((Nu3 (-> tptp.variable tptp.real)) (Nu4 (-> tptp.variable tptp.real)) (U2 tptp.set_variable)) (forall ((I tptp.variable)) (=> (not (@ (@ tptp.member_variable I) U2)) (= (@ Nu3 I) (@ Nu4 I)))))))
% 0.26/0.69 (assert (forall ((R tptp.set_char) (S tptp.set_char)) (= (@ (@ tptp.ord_less_eq_char_o (lambda ((X3 tptp.char)) (@ (@ tptp.member_char X3) R))) (lambda ((X3 tptp.char)) (@ (@ tptp.member_char X3) S))) (@ (@ tptp.ord_less_eq_set_char R) S))))
% 0.26/0.69 (assert (forall ((R tptp.set_variable) (S tptp.set_variable)) (= (@ (@ tptp.ord_le1407353162able_o (lambda ((X3 tptp.variable)) (@ (@ tptp.member_variable X3) R))) (lambda ((X3 tptp.variable)) (@ (@ tptp.member_variable X3) S))) (@ (@ tptp.ord_le282106107riable R) S))))
% 0.26/0.69 (assert (forall ((B tptp.set_char) (A tptp.set_char) (P (-> tptp.char Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_char B))) (=> (@ _let_1 A) (= (@ _let_1 (@ tptp.collect_char (lambda ((X3 tptp.char)) (and (@ (@ tptp.member_char X3) A) (@ P X3))))) (forall ((X3 tptp.char)) (=> (@ (@ tptp.member_char X3) B) (@ P X3))))))))
% 0.26/0.69 (assert (forall ((B tptp.set_variable) (A tptp.set_variable) (P (-> tptp.variable Bool))) (let ((_let_1 (@ tptp.ord_le282106107riable B))) (=> (@ _let_1 A) (= (@ _let_1 (@ tptp.collect_variable (lambda ((X3 tptp.variable)) (and (@ (@ tptp.member_variable X3) A) (@ P X3))))) (forall ((X3 tptp.variable)) (=> (@ (@ tptp.member_variable X3) B) (@ P X3))))))))
% 0.26/0.69 (assert (forall ((B tptp.set_char) (A tptp.set_char) (Q (-> tptp.char Bool)) (P (-> tptp.char Bool))) (=> (@ (@ tptp.ord_less_eq_set_char B) A) (=> (forall ((X tptp.char)) (=> (@ (@ tptp.member_char X) B) (=> (@ Q X) (@ P X)))) (@ (@ tptp.ord_less_eq_set_char (@ tptp.collect_char (lambda ((X3 tptp.char)) (and (@ (@ tptp.member_char X3) B) (@ Q X3))))) (@ tptp.collect_char (lambda ((X3 tptp.char)) (and (@ (@ tptp.member_char X3) A) (@ P X3)))))))))
% 0.26/0.69 (assert (forall ((B tptp.set_variable) (A tptp.set_variable) (Q (-> tptp.variable Bool)) (P (-> tptp.variable Bool))) (=> (@ (@ tptp.ord_le282106107riable B) A) (=> (forall ((X tptp.variable)) (=> (@ (@ tptp.member_variable X) B) (=> (@ Q X) (@ P X)))) (@ (@ tptp.ord_le282106107riable (@ tptp.collect_variable (lambda ((X3 tptp.variable)) (and (@ (@ tptp.member_variable X3) B) (@ Q X3))))) (@ tptp.collect_variable (lambda ((X3 tptp.variable)) (and (@ (@ tptp.member_variable X3) A) (@ P X3)))))))))
% 0.26/0.69 (assert (forall ((X4 tptp.set_char) (P (-> tptp.char Bool))) (@ (@ tptp.ord_less_eq_set_char (@ tptp.collect_char (lambda ((X3 tptp.char)) (and (@ (@ tptp.member_char X3) X4) (@ P X3))))) X4)))
% 0.26/0.69 (assert (forall ((X4 tptp.set_variable) (P (-> tptp.variable Bool))) (@ (@ tptp.ord_le282106107riable (@ tptp.collect_variable (lambda ((X3 tptp.variable)) (and (@ (@ tptp.member_variable X3) X4) (@ P X3))))) X4)))
% 0.26/0.69 (assert (forall ((X2 tptp.char) (Z3 tptp.set_char) (X4 tptp.set_char) (P (-> tptp.char Bool))) (=> (@ (@ tptp.member_char X2) Z3) (=> (@ (@ tptp.ord_less_eq_set_char Z3) (@ tptp.collect_char (lambda ((X3 tptp.char)) (and (@ (@ tptp.member_char X3) X4) (@ P X3))))) (@ P X2)))))
% 0.26/0.69 (assert (forall ((X2 tptp.variable) (Z3 tptp.set_variable) (X4 tptp.set_variable) (P (-> tptp.variable Bool))) (=> (@ (@ tptp.member_variable X2) Z3) (=> (@ (@ tptp.ord_le282106107riable Z3) (@ tptp.collect_variable (lambda ((X3 tptp.variable)) (and (@ (@ tptp.member_variable X3) X4) (@ P X3))))) (@ P X2)))))
% 0.26/0.69 (assert (forall ((A tptp.set_char) (P (-> tptp.char Bool)) (Q (-> tptp.char Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_char A))) (= (@ _let_1 (@ tptp.collect_char (lambda ((X3 tptp.char)) (and (@ P X3) (@ Q X3))))) (and (@ _let_1 (@ tptp.collect_char P)) (@ _let_1 (@ tptp.collect_char Q)))))))
% 0.26/0.69 (assert (forall ((A tptp.set_variable) (P (-> tptp.variable Bool)) (Q (-> tptp.variable Bool))) (let ((_let_1 (@ tptp.ord_le282106107riable A))) (= (@ _let_1 (@ tptp.collect_variable (lambda ((X3 tptp.variable)) (and (@ P X3) (@ Q X3))))) (and (@ _let_1 (@ tptp.collect_variable P)) (@ _let_1 (@ tptp.collect_variable Q)))))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_trm) (Xa tptp.option_trm) (Y2 tptp.option_trm)) (let ((_let_1 (not (= Y2 tptp.none_trm)))) (=> (= (@ (@ tptp.uSubst141955042_Pluso X2) Xa) Y2) (=> (forall ((Theta2 tptp.trm)) (=> (= X2 (@ tptp.some_trm Theta2)) (forall ((Eta2 tptp.trm)) (=> (= Xa (@ tptp.some_trm Eta2)) (not (= Y2 (@ tptp.some_trm (@ (@ tptp.plus Theta2) Eta2)))))))) (=> (=> (= X2 tptp.none_trm) _let_1) (not (=> (exists ((V2 tptp.trm)) (= X2 (@ tptp.some_trm V2))) (=> (= Xa tptp.none_trm) _let_1)))))))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_trm) (Xa tptp.option_trm) (Y2 tptp.option_trm)) (let ((_let_1 (not (= Y2 tptp.none_trm)))) (=> (= (@ (@ tptp.uSubst918876924Timeso X2) Xa) Y2) (=> (forall ((Theta2 tptp.trm)) (=> (= X2 (@ tptp.some_trm Theta2)) (forall ((Eta2 tptp.trm)) (=> (= Xa (@ tptp.some_trm Eta2)) (not (= Y2 (@ tptp.some_trm (@ (@ tptp.times Theta2) Eta2)))))))) (=> (=> (= X2 tptp.none_trm) _let_1) (not (=> (exists ((V2 tptp.trm)) (= X2 (@ tptp.some_trm V2))) (=> (= Xa tptp.none_trm) _let_1)))))))))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm)) (let ((_let_1 (@ tptp.uSubst516392818stappt Sigma))) (= (@ (@ _let_1 U) (@ tptp.differential Theta)) (@ tptp.uSubst716837505ntialo (@ (@ _let_1 (@ tptp.collect_variable (lambda ((X3 tptp.variable)) true))) Theta))))))
% 0.26/0.69 (assert (forall ((X23 tptp.trm) (Y23 tptp.trm)) (= (= (@ tptp.some_trm X23) (@ tptp.some_trm Y23)) (= X23 Y23))))
% 0.26/0.69 (assert (forall ((X23 tptp.fml) (Y23 tptp.fml)) (= (= (@ tptp.some_fml X23) (@ tptp.some_fml Y23)) (= X23 Y23))))
% 0.26/0.69 (assert (forall ((X23 tptp.game) (Y23 tptp.game)) (= (= (@ tptp.some_game X23) (@ tptp.some_game Y23)) (= X23 Y23))))
% 0.26/0.69 (assert (forall ((X7 tptp.trm) (Y7 tptp.trm)) (= (= (@ tptp.differential X7) (@ tptp.differential Y7)) (= X7 Y7))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_trm)) (= (forall ((Y3 tptp.trm)) (not (= X2 (@ tptp.some_trm Y3)))) (= X2 tptp.none_trm))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_fml)) (= (forall ((Y3 tptp.fml)) (not (= X2 (@ tptp.some_fml Y3)))) (= X2 tptp.none_fml))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_game)) (= (forall ((Y3 tptp.game)) (not (= X2 (@ tptp.some_game Y3)))) (= X2 tptp.none_game))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_trm)) (= (not (= X2 tptp.none_trm)) (exists ((Y3 tptp.trm)) (= X2 (@ tptp.some_trm Y3))))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_fml)) (= (not (= X2 tptp.none_fml)) (exists ((Y3 tptp.fml)) (= X2 (@ tptp.some_fml Y3))))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_game)) (= (not (= X2 tptp.none_game)) (exists ((Y3 tptp.game)) (= X2 (@ tptp.some_game Y3))))))
% 0.26/0.69 (assert (= tptp.some_trm tptp.some_trm))
% 0.26/0.69 (assert (forall ((Theta tptp.trm)) (= (@ tptp.uSubst716837505ntialo (@ tptp.some_trm Theta)) (@ tptp.some_trm (@ tptp.differential Theta)))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_trm) (P (-> tptp.option_trm tptp.option_trm Bool)) (Y2 tptp.option_trm)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_trm) _let_1) (=> (=> (= Y2 tptp.none_trm) _let_1) (=> (forall ((A5 tptp.trm) (B5 tptp.trm)) (=> (= X2 (@ tptp.some_trm A5)) (=> (= Y2 (@ tptp.some_trm B5)) (@ (@ P X2) Y2)))) _let_1))))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_trm) (P (-> tptp.option_trm tptp.option_fml Bool)) (Y2 tptp.option_fml)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_trm) _let_1) (=> (=> (= Y2 tptp.none_fml) _let_1) (=> (forall ((A5 tptp.trm) (B5 tptp.fml)) (=> (= X2 (@ tptp.some_trm A5)) (=> (= Y2 (@ tptp.some_fml B5)) (@ (@ P X2) Y2)))) _let_1))))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_trm) (P (-> tptp.option_trm tptp.option_game Bool)) (Y2 tptp.option_game)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_trm) _let_1) (=> (=> (= Y2 tptp.none_game) _let_1) (=> (forall ((A5 tptp.trm) (B5 tptp.game)) (=> (= X2 (@ tptp.some_trm A5)) (=> (= Y2 (@ tptp.some_game B5)) (@ (@ P X2) Y2)))) _let_1))))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_fml) (P (-> tptp.option_fml tptp.option_trm Bool)) (Y2 tptp.option_trm)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_fml) _let_1) (=> (=> (= Y2 tptp.none_trm) _let_1) (=> (forall ((A5 tptp.fml) (B5 tptp.trm)) (=> (= X2 (@ tptp.some_fml A5)) (=> (= Y2 (@ tptp.some_trm B5)) (@ (@ P X2) Y2)))) _let_1))))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_fml) (P (-> tptp.option_fml tptp.option_fml Bool)) (Y2 tptp.option_fml)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_fml) _let_1) (=> (=> (= Y2 tptp.none_fml) _let_1) (=> (forall ((A5 tptp.fml) (B5 tptp.fml)) (=> (= X2 (@ tptp.some_fml A5)) (=> (= Y2 (@ tptp.some_fml B5)) (@ (@ P X2) Y2)))) _let_1))))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_fml) (P (-> tptp.option_fml tptp.option_game Bool)) (Y2 tptp.option_game)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_fml) _let_1) (=> (=> (= Y2 tptp.none_game) _let_1) (=> (forall ((A5 tptp.fml) (B5 tptp.game)) (=> (= X2 (@ tptp.some_fml A5)) (=> (= Y2 (@ tptp.some_game B5)) (@ (@ P X2) Y2)))) _let_1))))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_game) (P (-> tptp.option_game tptp.option_trm Bool)) (Y2 tptp.option_trm)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_game) _let_1) (=> (=> (= Y2 tptp.none_trm) _let_1) (=> (forall ((A5 tptp.game) (B5 tptp.trm)) (=> (= X2 (@ tptp.some_game A5)) (=> (= Y2 (@ tptp.some_trm B5)) (@ (@ P X2) Y2)))) _let_1))))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_game) (P (-> tptp.option_game tptp.option_fml Bool)) (Y2 tptp.option_fml)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_game) _let_1) (=> (=> (= Y2 tptp.none_fml) _let_1) (=> (forall ((A5 tptp.game) (B5 tptp.fml)) (=> (= X2 (@ tptp.some_game A5)) (=> (= Y2 (@ tptp.some_fml B5)) (@ (@ P X2) Y2)))) _let_1))))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_game) (P (-> tptp.option_game tptp.option_game Bool)) (Y2 tptp.option_game)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_game) _let_1) (=> (=> (= Y2 tptp.none_game) _let_1) (=> (forall ((A5 tptp.game) (B5 tptp.game)) (=> (= X2 (@ tptp.some_game A5)) (=> (= Y2 (@ tptp.some_game B5)) (@ (@ P X2) Y2)))) _let_1))))))
% 0.26/0.69 (assert (= (lambda ((P2 (-> tptp.option_trm Bool))) (forall ((X5 tptp.option_trm)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_trm Bool))) (and (@ P3 tptp.none_trm) (forall ((X3 tptp.trm)) (@ P3 (@ tptp.some_trm X3)))))))
% 0.26/0.69 (assert (= (lambda ((P2 (-> tptp.option_fml Bool))) (forall ((X5 tptp.option_fml)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_fml Bool))) (and (@ P3 tptp.none_fml) (forall ((X3 tptp.fml)) (@ P3 (@ tptp.some_fml X3)))))))
% 0.26/0.69 (assert (= (lambda ((P2 (-> tptp.option_game Bool))) (forall ((X5 tptp.option_game)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_game Bool))) (and (@ P3 tptp.none_game) (forall ((X3 tptp.game)) (@ P3 (@ tptp.some_game X3)))))))
% 0.26/0.69 (assert (= (lambda ((P2 (-> tptp.option_trm Bool))) (exists ((X5 tptp.option_trm)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_trm Bool))) (or (@ P3 tptp.none_trm) (exists ((X3 tptp.trm)) (@ P3 (@ tptp.some_trm X3)))))))
% 0.26/0.69 (assert (= (lambda ((P2 (-> tptp.option_fml Bool))) (exists ((X5 tptp.option_fml)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_fml Bool))) (or (@ P3 tptp.none_fml) (exists ((X3 tptp.fml)) (@ P3 (@ tptp.some_fml X3)))))))
% 0.26/0.69 (assert (= (lambda ((P2 (-> tptp.option_game Bool))) (exists ((X5 tptp.option_game)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_game Bool))) (or (@ P3 tptp.none_game) (exists ((X3 tptp.game)) (@ P3 (@ tptp.some_game X3)))))))
% 0.26/0.69 (assert (forall ((P (-> tptp.option_trm Bool)) (Option tptp.option_trm)) (=> (@ P tptp.none_trm) (=> (forall ((X tptp.trm)) (@ P (@ tptp.some_trm X))) (@ P Option)))))
% 0.26/0.69 (assert (forall ((P (-> tptp.option_fml Bool)) (Option tptp.option_fml)) (=> (@ P tptp.none_fml) (=> (forall ((X tptp.fml)) (@ P (@ tptp.some_fml X))) (@ P Option)))))
% 0.26/0.69 (assert (forall ((P (-> tptp.option_game Bool)) (Option tptp.option_game)) (=> (@ P tptp.none_game) (=> (forall ((X tptp.game)) (@ P (@ tptp.some_game X))) (@ P Option)))))
% 0.26/0.69 (assert (forall ((Y2 tptp.option_trm)) (=> (not (= Y2 tptp.none_trm)) (not (forall ((X24 tptp.trm)) (not (= Y2 (@ tptp.some_trm X24))))))))
% 0.26/0.69 (assert (forall ((Y2 tptp.option_fml)) (=> (not (= Y2 tptp.none_fml)) (not (forall ((X24 tptp.fml)) (not (= Y2 (@ tptp.some_fml X24))))))))
% 0.26/0.69 (assert (forall ((Y2 tptp.option_game)) (=> (not (= Y2 tptp.none_game)) (not (forall ((X24 tptp.game)) (not (= Y2 (@ tptp.some_game X24))))))))
% 0.26/0.69 (assert (forall ((Option tptp.option_trm) (X23 tptp.trm)) (=> (= Option (@ tptp.some_trm X23)) (not (= Option tptp.none_trm)))))
% 0.26/0.69 (assert (forall ((Option tptp.option_fml) (X23 tptp.fml)) (=> (= Option (@ tptp.some_fml X23)) (not (= Option tptp.none_fml)))))
% 0.26/0.69 (assert (forall ((Option tptp.option_game) (X23 tptp.game)) (=> (= Option (@ tptp.some_game X23)) (not (= Option tptp.none_game)))))
% 0.26/0.69 (assert (forall ((X23 tptp.trm)) (not (= tptp.none_trm (@ tptp.some_trm X23)))))
% 0.26/0.69 (assert (forall ((X23 tptp.fml)) (not (= tptp.none_fml (@ tptp.some_fml X23)))))
% 0.26/0.69 (assert (forall ((X23 tptp.game)) (not (= tptp.none_game (@ tptp.some_game X23)))))
% 0.26/0.69 (assert (forall ((P (-> tptp.option_trm Bool)) (A0 tptp.option_trm)) (=> (forall ((Theta2 tptp.trm)) (@ P (@ tptp.some_trm Theta2))) (=> (@ P tptp.none_trm) (@ P A0)))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_trm)) (=> (forall ((Theta2 tptp.trm)) (not (= X2 (@ tptp.some_trm Theta2)))) (= X2 tptp.none_trm))))
% 0.26/0.69 (assert (forall ((P (-> tptp.variable tptp.option_trm Bool)) (A0 tptp.variable) (A1 tptp.option_trm)) (=> (forall ((X tptp.variable) (Theta2 tptp.trm)) (@ (@ P X) (@ tptp.some_trm Theta2))) (=> (forall ((X tptp.variable)) (@ (@ P X) tptp.none_trm)) (@ (@ P A0) A1)))))
% 0.26/0.69 (assert (forall ((P (-> tptp.option_trm tptp.option_trm Bool)) (A0 tptp.option_trm) (A1 tptp.option_trm)) (=> (forall ((Theta2 tptp.trm) (Eta2 tptp.trm)) (@ (@ P (@ tptp.some_trm Theta2)) (@ tptp.some_trm Eta2))) (=> (forall ((X_1 tptp.option_trm)) (@ (@ P tptp.none_trm) X_1)) (=> (forall ((V2 tptp.trm)) (@ (@ P (@ tptp.some_trm V2)) tptp.none_trm)) (@ (@ P A0) A1))))))
% 0.26/0.69 (assert (forall ((Theta tptp.option_trm)) (= (not (= Theta tptp.none_trm)) (exists ((T tptp.trm)) (= Theta (@ tptp.some_trm T))))))
% 0.26/0.69 (assert (forall ((P (-> tptp.char tptp.option_trm Bool)) (A0 tptp.char) (A1 tptp.option_trm)) (=> (forall ((X tptp.char) (Theta2 tptp.trm)) (@ (@ P X) (@ tptp.some_trm Theta2))) (=> (forall ((X tptp.char)) (@ (@ P X) tptp.none_trm)) (@ (@ P A0) A1)))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_trm) (Y2 tptp.option_trm)) (=> (= (@ tptp.uSubst716837505ntialo X2) Y2) (=> (forall ((Theta2 tptp.trm)) (=> (= X2 (@ tptp.some_trm Theta2)) (not (= Y2 (@ tptp.some_trm (@ tptp.differential Theta2)))))) (not (=> (= X2 tptp.none_trm) (not (= Y2 tptp.none_trm))))))))
% 0.26/0.69 (assert (forall ((X61 tptp.trm) (X62 tptp.trm) (X7 tptp.trm)) (not (= (@ (@ tptp.times X61) X62) (@ tptp.differential X7)))))
% 0.26/0.69 (assert (forall ((X51 tptp.trm) (X52 tptp.trm) (X7 tptp.trm)) (not (= (@ (@ tptp.plus X51) X52) (@ tptp.differential X7)))))
% 0.26/0.69 (assert (forall ((V3 tptp.trm)) (= (@ (@ tptp.uSubst918876924Timeso (@ tptp.some_trm V3)) tptp.none_trm) tptp.none_trm)))
% 0.26/0.69 (assert (forall ((V3 tptp.trm)) (= (@ (@ tptp.uSubst141955042_Pluso (@ tptp.some_trm V3)) tptp.none_trm) tptp.none_trm)))
% 0.26/0.69 (assert (forall ((Theta tptp.trm) (Eta tptp.trm)) (= (@ (@ tptp.uSubst141955042_Pluso (@ tptp.some_trm Theta)) (@ tptp.some_trm Eta)) (@ tptp.some_trm (@ (@ tptp.plus Theta) Eta)))))
% 0.26/0.69 (assert (forall ((Theta tptp.trm) (Eta tptp.trm)) (= (@ (@ tptp.uSubst918876924Timeso (@ tptp.some_trm Theta)) (@ tptp.some_trm Eta)) (@ tptp.some_trm (@ (@ tptp.times Theta) Eta)))))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm)) (let ((_let_1 (@ tptp.uSubst516392818stappt Sigma))) (=> (not (= (@ (@ _let_1 U) (@ tptp.differential Theta)) tptp.none_trm)) (not (= (@ (@ _let_1 (@ tptp.collect_variable (lambda ((X3 tptp.variable)) true))) Theta) tptp.none_trm))))))
% 0.26/0.69 (assert (forall ((V3 tptp.trm)) (= (@ (@ tptp.uSubst152838031e_Geqo (@ tptp.some_trm V3)) tptp.none_trm) tptp.none_fml)))
% 0.26/0.69 (assert (forall ((X2 tptp.option_trm) (Xa tptp.option_trm) (Y2 tptp.option_fml)) (let ((_let_1 (not (= Y2 tptp.none_fml)))) (=> (= (@ (@ tptp.uSubst152838031e_Geqo X2) Xa) Y2) (=> (forall ((Theta2 tptp.trm)) (=> (= X2 (@ tptp.some_trm Theta2)) (forall ((Eta2 tptp.trm)) (=> (= Xa (@ tptp.some_trm Eta2)) (not (= Y2 (@ tptp.some_fml (@ (@ tptp.geq Theta2) Eta2)))))))) (=> (=> (= X2 tptp.none_trm) _let_1) (not (=> (exists ((V2 tptp.trm)) (= X2 (@ tptp.some_trm V2))) (=> (= Xa tptp.none_trm) _let_1)))))))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_trm) (Y2 tptp.option_trm)) (let ((_let_1 (@ tptp.accp_option_trm tptp.uSubst2051024824lo_rel))) (=> (= (@ tptp.uSubst716837505ntialo X2) Y2) (=> (@ _let_1 X2) (=> (forall ((Theta2 tptp.trm)) (let ((_let_1 (@ tptp.some_trm Theta2))) (=> (= X2 _let_1) (=> (= Y2 (@ tptp.some_trm (@ tptp.differential Theta2))) (not (@ (@ tptp.accp_option_trm tptp.uSubst2051024824lo_rel) _let_1)))))) (not (=> (= X2 tptp.none_trm) (=> (= Y2 tptp.none_trm) (not (@ _let_1 tptp.none_trm)))))))))))
% 0.26/0.69 (assert (forall ((Theta tptp.trm) (Eta tptp.trm)) (= (@ (@ tptp.uSubst152838031e_Geqo (@ tptp.some_trm Theta)) (@ tptp.some_trm Eta)) (@ tptp.some_fml (@ (@ tptp.geq Theta) Eta)))))
% 0.26/0.69 (assert (forall ((P (-> tptp.set_variable Bool)) (X2 tptp.set_variable) (Q (-> tptp.set_variable Bool))) (=> (@ P X2) (=> (forall ((Y4 tptp.set_variable)) (=> (@ P Y4) (@ (@ tptp.ord_le282106107riable Y4) X2))) (=> (forall ((X tptp.set_variable)) (=> (@ P X) (=> (forall ((Y5 tptp.set_variable)) (=> (@ P Y5) (@ (@ tptp.ord_le282106107riable Y5) X))) (@ Q X)))) (@ Q (@ tptp.order_272405634riable P)))))))
% 0.26/0.69 (assert (forall ((P (-> tptp.set_variable Bool)) (X2 tptp.set_variable)) (=> (@ P X2) (=> (forall ((Y4 tptp.set_variable)) (=> (@ P Y4) (@ (@ tptp.ord_le282106107riable Y4) X2))) (= (@ tptp.order_272405634riable P) X2)))))
% 0.26/0.69 (assert (forall ((P (-> tptp.option_game tptp.option_fml Bool)) (A0 tptp.option_game) (A1 tptp.option_fml)) (=> (forall ((Alpha tptp.game) (Phi2 tptp.fml)) (@ (@ P (@ tptp.some_game Alpha)) (@ tptp.some_fml Phi2))) (=> (forall ((X_1 tptp.option_fml)) (@ (@ P tptp.none_game) X_1)) (=> (forall ((V2 tptp.game)) (@ (@ P (@ tptp.some_game V2)) tptp.none_fml)) (@ (@ P A0) A1))))))
% 0.26/0.69 (assert (forall ((P (-> tptp.variable tptp.option_fml Bool)) (A0 tptp.variable) (A1 tptp.option_fml)) (=> (forall ((X tptp.variable) (Phi2 tptp.fml)) (@ (@ P X) (@ tptp.some_fml Phi2))) (=> (forall ((X tptp.variable)) (@ (@ P X) tptp.none_fml)) (@ (@ P A0) A1)))))
% 0.26/0.69 (assert (forall ((Phi tptp.option_fml)) (= (not (= Phi tptp.none_fml)) (exists ((F2 tptp.fml)) (= Phi (@ tptp.some_fml F2))))))
% 0.26/0.69 (assert (forall ((P (-> tptp.option_fml Bool)) (A0 tptp.option_fml)) (=> (forall ((Phi2 tptp.fml)) (@ P (@ tptp.some_fml Phi2))) (=> (@ P tptp.none_fml) (@ P A0)))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_fml)) (=> (forall ((Phi2 tptp.fml)) (not (= X2 (@ tptp.some_fml Phi2)))) (= X2 tptp.none_fml))))
% 0.26/0.69 (assert (forall ((P (-> tptp.option_fml tptp.option_fml Bool)) (A0 tptp.option_fml) (A1 tptp.option_fml)) (=> (forall ((Phi2 tptp.fml) (Psi tptp.fml)) (@ (@ P (@ tptp.some_fml Phi2)) (@ tptp.some_fml Psi))) (=> (forall ((X_1 tptp.option_fml)) (@ (@ P tptp.none_fml) X_1)) (=> (forall ((V2 tptp.fml)) (@ (@ P (@ tptp.some_fml V2)) tptp.none_fml)) (@ (@ P A0) A1))))))
% 0.26/0.69 (assert (forall ((R1 (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (R2 (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool))) (=> (@ (@ tptp.ord_le370603054_trm_o R1) R2) (@ (@ tptp.ord_le373274227_trm_o (@ tptp.accp_P394694195on_trm R2)) (@ tptp.accp_P394694195on_trm R1)))))
% 0.26/0.69 (assert (forall ((R1 (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (R2 (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool))) (=> (@ (@ tptp.ord_le90123726_trm_o R1) R2) (@ (@ tptp.ord_le1721128566_trm_o (@ tptp.accp_P758790320on_trm R2)) (@ tptp.accp_P758790320on_trm R1)))))
% 0.26/0.69 (assert (forall ((R1 (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (R2 (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool))) (=> (@ (@ tptp.ord_le157637894_trm_o R1) R2) (@ (@ tptp.ord_le1222882015_trm_o (@ tptp.accp_P419951815on_trm R2)) (@ tptp.accp_P419951815on_trm R1)))))
% 0.26/0.69 (assert (forall ((R1 (-> tptp.option_trm tptp.option_trm Bool)) (R2 (-> tptp.option_trm tptp.option_trm Bool))) (=> (@ (@ tptp.ord_le847028878_trm_o R1) R2) (@ (@ tptp.ord_le1957133745_trm_o (@ tptp.accp_option_trm R2)) (@ tptp.accp_option_trm R1)))))
% 0.26/0.69 (assert (forall ((R1 (-> tptp.option_fml tptp.option_fml Bool)) (R2 (-> tptp.option_fml tptp.option_fml Bool))) (=> (@ (@ tptp.ord_le802833166_fml_o R1) R2) (@ (@ tptp.ord_le181580155_fml_o (@ tptp.accp_option_fml R2)) (@ tptp.accp_option_fml R1)))))
% 0.26/0.69 (assert (forall ((D (-> tptp.produc1024976764on_trm Bool)) (R (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (X2 tptp.produc1024976764on_trm) (P (-> tptp.produc1024976764on_trm Bool))) (=> (@ (@ tptp.ord_le373274227_trm_o D) (@ tptp.accp_P394694195on_trm R)) (=> (forall ((X tptp.produc1024976764on_trm) (Z4 tptp.produc1024976764on_trm)) (=> (@ D X) (=> (@ (@ R Z4) X) (@ D Z4)))) (=> (@ D X2) (=> (forall ((X tptp.produc1024976764on_trm)) (=> (@ D X) (=> (forall ((Z5 tptp.produc1024976764on_trm)) (=> (@ (@ R Z5) X) (@ P Z5))) (@ P X)))) (@ P X2)))))))
% 0.26/0.69 (assert (forall ((D (-> tptp.produc1072747943on_trm Bool)) (R (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (X2 tptp.produc1072747943on_trm) (P (-> tptp.produc1072747943on_trm Bool))) (=> (@ (@ tptp.ord_le1721128566_trm_o D) (@ tptp.accp_P758790320on_trm R)) (=> (forall ((X tptp.produc1072747943on_trm) (Z4 tptp.produc1072747943on_trm)) (=> (@ D X) (=> (@ (@ R Z4) X) (@ D Z4)))) (=> (@ D X2) (=> (forall ((X tptp.produc1072747943on_trm)) (=> (@ D X) (=> (forall ((Z5 tptp.produc1072747943on_trm)) (=> (@ (@ R Z5) X) (@ P Z5))) (@ P X)))) (@ P X2)))))))
% 0.26/0.69 (assert (forall ((D (-> tptp.produc464795408on_trm Bool)) (R (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (X2 tptp.produc464795408on_trm) (P (-> tptp.produc464795408on_trm Bool))) (=> (@ (@ tptp.ord_le1222882015_trm_o D) (@ tptp.accp_P419951815on_trm R)) (=> (forall ((X tptp.produc464795408on_trm) (Z4 tptp.produc464795408on_trm)) (=> (@ D X) (=> (@ (@ R Z4) X) (@ D Z4)))) (=> (@ D X2) (=> (forall ((X tptp.produc464795408on_trm)) (=> (@ D X) (=> (forall ((Z5 tptp.produc464795408on_trm)) (=> (@ (@ R Z5) X) (@ P Z5))) (@ P X)))) (@ P X2)))))))
% 0.26/0.69 (assert (forall ((D (-> tptp.option_trm Bool)) (R (-> tptp.option_trm tptp.option_trm Bool)) (X2 tptp.option_trm) (P (-> tptp.option_trm Bool))) (=> (@ (@ tptp.ord_le1957133745_trm_o D) (@ tptp.accp_option_trm R)) (=> (forall ((X tptp.option_trm) (Z4 tptp.option_trm)) (=> (@ D X) (=> (@ (@ R Z4) X) (@ D Z4)))) (=> (@ D X2) (=> (forall ((X tptp.option_trm)) (=> (@ D X) (=> (forall ((Z5 tptp.option_trm)) (=> (@ (@ R Z5) X) (@ P Z5))) (@ P X)))) (@ P X2)))))))
% 0.26/0.69 (assert (forall ((D (-> tptp.option_fml Bool)) (R (-> tptp.option_fml tptp.option_fml Bool)) (X2 tptp.option_fml) (P (-> tptp.option_fml Bool))) (=> (@ (@ tptp.ord_le181580155_fml_o D) (@ tptp.accp_option_fml R)) (=> (forall ((X tptp.option_fml) (Z4 tptp.option_fml)) (=> (@ D X) (=> (@ (@ R Z4) X) (@ D Z4)))) (=> (@ D X2) (=> (forall ((X tptp.option_fml)) (=> (@ D X) (=> (forall ((Z5 tptp.option_fml)) (=> (@ (@ R Z5) X) (@ P Z5))) (@ P X)))) (@ P X2)))))))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (let ((_let_2 (@ (@ (@ tptp.uSubst516392804stappf Sigma) U) (@ (@ tptp.geq Theta) Eta)))) (=> (not (= _let_2 tptp.none_fml)) (= _let_2 (@ tptp.some_fml (@ (@ tptp.geq (@ tptp.the_trm (@ _let_1 Theta))) (@ tptp.the_trm (@ _let_1 Eta))))))))))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (let ((_let_2 (@ _let_1 Eta))) (let ((_let_3 (@ _let_1 Theta))) (=> (not (= _let_3 tptp.none_trm)) (=> (not (= _let_2 tptp.none_trm)) (= (@ (@ (@ tptp.uSubst516392804stappf Sigma) U) (@ (@ tptp.geq Theta) Eta)) (@ tptp.some_fml (@ (@ tptp.geq (@ tptp.the_trm _let_3)) (@ tptp.the_trm _let_2)))))))))))
% 0.26/0.69 (assert (forall ((Option tptp.option_trm)) (=> (not (= Option tptp.none_trm)) (= (@ tptp.some_trm (@ tptp.the_trm Option)) Option))))
% 0.26/0.69 (assert (forall ((Option tptp.option_fml)) (=> (not (= Option tptp.none_fml)) (= (@ tptp.some_fml (@ tptp.the_fml Option)) Option))))
% 0.26/0.69 (assert (forall ((Option tptp.option_game)) (=> (not (= Option tptp.none_game)) (= (@ tptp.some_game (@ tptp.the_game Option)) Option))))
% 0.26/0.69 (assert (forall ((P (-> tptp.option_game tptp.option_game Bool)) (A0 tptp.option_game) (A1 tptp.option_game)) (=> (forall ((Alpha tptp.game) (Beta tptp.game)) (@ (@ P (@ tptp.some_game Alpha)) (@ tptp.some_game Beta))) (=> (forall ((Alpha tptp.option_game)) (@ (@ P Alpha) tptp.none_game)) (=> (forall ((V2 tptp.game)) (@ (@ P tptp.none_game) (@ tptp.some_game V2))) (@ (@ P A0) A1))))))
% 0.26/0.69 (assert (forall ((Alpha2 tptp.option_game)) (= (not (= Alpha2 tptp.none_game)) (exists ((G tptp.game)) (= Alpha2 (@ tptp.some_game G))))))
% 0.26/0.69 (assert (forall ((P (-> tptp.option_game Bool)) (A0 tptp.option_game)) (=> (forall ((Alpha tptp.game)) (@ P (@ tptp.some_game Alpha))) (=> (@ P tptp.none_game) (@ P A0)))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_game)) (=> (forall ((Alpha tptp.game)) (not (= X2 (@ tptp.some_game Alpha)))) (= X2 tptp.none_game))))
% 0.26/0.69 (assert (forall ((Option tptp.option_trm) (Option2 tptp.option_trm)) (let ((_let_1 (= Option2 tptp.none_trm))) (let ((_let_2 (= Option tptp.none_trm))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_trm Option) (@ tptp.the_trm Option2)))) (= Option Option2)))))))
% 0.26/0.69 (assert (forall ((Option tptp.option_fml) (Option2 tptp.option_fml)) (let ((_let_1 (= Option2 tptp.none_fml))) (let ((_let_2 (= Option tptp.none_fml))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_fml Option) (@ tptp.the_fml Option2)))) (= Option Option2)))))))
% 0.26/0.69 (assert (forall ((Option tptp.option_game) (Option2 tptp.option_game)) (let ((_let_1 (= Option2 tptp.none_game))) (let ((_let_2 (= Option tptp.none_game))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_game Option) (@ tptp.the_game Option2)))) (= Option Option2)))))))
% 0.26/0.69 (assert (forall ((X23 tptp.trm)) (= (@ tptp.the_trm (@ tptp.some_trm X23)) X23)))
% 0.26/0.69 (assert (forall ((X23 tptp.fml)) (= (@ tptp.the_fml (@ tptp.some_fml X23)) X23)))
% 0.26/0.69 (assert (forall ((X23 tptp.game)) (= (@ tptp.the_game (@ tptp.some_game X23)) X23)))
% 0.26/0.69 (assert (forall ((Option tptp.option_trm)) (=> (not (= Option tptp.none_trm)) (= Option (@ tptp.some_trm (@ tptp.the_trm Option))))))
% 0.26/0.69 (assert (forall ((Option tptp.option_fml)) (=> (not (= Option tptp.none_fml)) (= Option (@ tptp.some_fml (@ tptp.the_fml Option))))))
% 0.26/0.69 (assert (forall ((Option tptp.option_game)) (=> (not (= Option tptp.none_game)) (= Option (@ tptp.some_game (@ tptp.the_game Option))))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (A3 tptp.produc1024976764on_trm)) (=> (@ (@ tptp.accp_P394694195on_trm R3) A3) (forall ((Y5 tptp.produc1024976764on_trm)) (=> (@ (@ R3 Y5) A3) (@ (@ tptp.accp_P394694195on_trm R3) Y5))))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (A3 tptp.produc1072747943on_trm)) (=> (@ (@ tptp.accp_P758790320on_trm R3) A3) (forall ((Y5 tptp.produc1072747943on_trm)) (=> (@ (@ R3 Y5) A3) (@ (@ tptp.accp_P758790320on_trm R3) Y5))))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (A3 tptp.produc464795408on_trm)) (=> (@ (@ tptp.accp_P419951815on_trm R3) A3) (forall ((Y5 tptp.produc464795408on_trm)) (=> (@ (@ R3 Y5) A3) (@ (@ tptp.accp_P419951815on_trm R3) Y5))))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.option_trm tptp.option_trm Bool)) (A3 tptp.option_trm)) (=> (@ (@ tptp.accp_option_trm R3) A3) (forall ((Y5 tptp.option_trm)) (=> (@ (@ R3 Y5) A3) (@ (@ tptp.accp_option_trm R3) Y5))))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.option_fml tptp.option_fml Bool)) (A3 tptp.option_fml)) (=> (@ (@ tptp.accp_option_fml R3) A3) (forall ((Y5 tptp.option_fml)) (=> (@ (@ R3 Y5) A3) (@ (@ tptp.accp_option_fml R3) Y5))))))
% 0.26/0.69 (assert (= tptp.accp_P394694195on_trm (lambda ((R4 (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (A4 tptp.produc1024976764on_trm)) (exists ((X3 tptp.produc1024976764on_trm)) (and (= A4 X3) (forall ((Y3 tptp.produc1024976764on_trm)) (=> (@ (@ R4 Y3) X3) (@ (@ tptp.accp_P394694195on_trm R4) Y3))))))))
% 0.26/0.69 (assert (= tptp.accp_P758790320on_trm (lambda ((R4 (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (A4 tptp.produc1072747943on_trm)) (exists ((X3 tptp.produc1072747943on_trm)) (and (= A4 X3) (forall ((Y3 tptp.produc1072747943on_trm)) (=> (@ (@ R4 Y3) X3) (@ (@ tptp.accp_P758790320on_trm R4) Y3))))))))
% 0.26/0.69 (assert (= tptp.accp_P419951815on_trm (lambda ((R4 (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (A4 tptp.produc464795408on_trm)) (exists ((X3 tptp.produc464795408on_trm)) (and (= A4 X3) (forall ((Y3 tptp.produc464795408on_trm)) (=> (@ (@ R4 Y3) X3) (@ (@ tptp.accp_P419951815on_trm R4) Y3))))))))
% 0.26/0.69 (assert (= tptp.accp_option_trm (lambda ((R4 (-> tptp.option_trm tptp.option_trm Bool)) (A4 tptp.option_trm)) (exists ((X3 tptp.option_trm)) (and (= A4 X3) (forall ((Y3 tptp.option_trm)) (=> (@ (@ R4 Y3) X3) (@ (@ tptp.accp_option_trm R4) Y3))))))))
% 0.26/0.69 (assert (= tptp.accp_option_fml (lambda ((R4 (-> tptp.option_fml tptp.option_fml Bool)) (A4 tptp.option_fml)) (exists ((X3 tptp.option_fml)) (and (= A4 X3) (forall ((Y3 tptp.option_fml)) (=> (@ (@ R4 Y3) X3) (@ (@ tptp.accp_option_fml R4) Y3))))))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (X2 tptp.produc1024976764on_trm)) (=> (forall ((Y4 tptp.produc1024976764on_trm)) (=> (@ (@ R3 Y4) X2) (@ (@ tptp.accp_P394694195on_trm R3) Y4))) (@ (@ tptp.accp_P394694195on_trm R3) X2))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (X2 tptp.produc1072747943on_trm)) (=> (forall ((Y4 tptp.produc1072747943on_trm)) (=> (@ (@ R3 Y4) X2) (@ (@ tptp.accp_P758790320on_trm R3) Y4))) (@ (@ tptp.accp_P758790320on_trm R3) X2))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (X2 tptp.produc464795408on_trm)) (=> (forall ((Y4 tptp.produc464795408on_trm)) (=> (@ (@ R3 Y4) X2) (@ (@ tptp.accp_P419951815on_trm R3) Y4))) (@ (@ tptp.accp_P419951815on_trm R3) X2))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.option_trm tptp.option_trm Bool)) (X2 tptp.option_trm)) (=> (forall ((Y4 tptp.option_trm)) (=> (@ (@ R3 Y4) X2) (@ (@ tptp.accp_option_trm R3) Y4))) (@ (@ tptp.accp_option_trm R3) X2))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.option_fml tptp.option_fml Bool)) (X2 tptp.option_fml)) (=> (forall ((Y4 tptp.option_fml)) (=> (@ (@ R3 Y4) X2) (@ (@ tptp.accp_option_fml R3) Y4))) (@ (@ tptp.accp_option_fml R3) X2))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (A3 tptp.produc1024976764on_trm) (P (-> tptp.produc1024976764on_trm Bool))) (=> (@ (@ tptp.accp_P394694195on_trm R3) A3) (=> (forall ((X tptp.produc1024976764on_trm)) (=> (@ (@ tptp.accp_P394694195on_trm R3) X) (=> (forall ((Y5 tptp.produc1024976764on_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (A3 tptp.produc1072747943on_trm) (P (-> tptp.produc1072747943on_trm Bool))) (=> (@ (@ tptp.accp_P758790320on_trm R3) A3) (=> (forall ((X tptp.produc1072747943on_trm)) (=> (@ (@ tptp.accp_P758790320on_trm R3) X) (=> (forall ((Y5 tptp.produc1072747943on_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (A3 tptp.produc464795408on_trm) (P (-> tptp.produc464795408on_trm Bool))) (=> (@ (@ tptp.accp_P419951815on_trm R3) A3) (=> (forall ((X tptp.produc464795408on_trm)) (=> (@ (@ tptp.accp_P419951815on_trm R3) X) (=> (forall ((Y5 tptp.produc464795408on_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.option_trm tptp.option_trm Bool)) (A3 tptp.option_trm) (P (-> tptp.option_trm Bool))) (=> (@ (@ tptp.accp_option_trm R3) A3) (=> (forall ((X tptp.option_trm)) (=> (@ (@ tptp.accp_option_trm R3) X) (=> (forall ((Y5 tptp.option_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.option_fml tptp.option_fml Bool)) (A3 tptp.option_fml) (P (-> tptp.option_fml Bool))) (=> (@ (@ tptp.accp_option_fml R3) A3) (=> (forall ((X tptp.option_fml)) (=> (@ (@ tptp.accp_option_fml R3) X) (=> (forall ((Y5 tptp.option_fml)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (X2 tptp.produc1024976764on_trm) (P (-> tptp.produc1024976764on_trm Bool))) (=> (@ (@ tptp.accp_P394694195on_trm R3) X2) (=> (forall ((X tptp.produc1024976764on_trm)) (=> (forall ((Y5 tptp.produc1024976764on_trm)) (=> (@ (@ R3 Y5) X) (@ (@ tptp.accp_P394694195on_trm R3) Y5))) (=> (forall ((Y5 tptp.produc1024976764on_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P X2)))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (X2 tptp.produc1072747943on_trm) (P (-> tptp.produc1072747943on_trm Bool))) (=> (@ (@ tptp.accp_P758790320on_trm R3) X2) (=> (forall ((X tptp.produc1072747943on_trm)) (=> (forall ((Y5 tptp.produc1072747943on_trm)) (=> (@ (@ R3 Y5) X) (@ (@ tptp.accp_P758790320on_trm R3) Y5))) (=> (forall ((Y5 tptp.produc1072747943on_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P X2)))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (X2 tptp.produc464795408on_trm) (P (-> tptp.produc464795408on_trm Bool))) (=> (@ (@ tptp.accp_P419951815on_trm R3) X2) (=> (forall ((X tptp.produc464795408on_trm)) (=> (forall ((Y5 tptp.produc464795408on_trm)) (=> (@ (@ R3 Y5) X) (@ (@ tptp.accp_P419951815on_trm R3) Y5))) (=> (forall ((Y5 tptp.produc464795408on_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P X2)))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.option_trm tptp.option_trm Bool)) (X2 tptp.option_trm) (P (-> tptp.option_trm Bool))) (=> (@ (@ tptp.accp_option_trm R3) X2) (=> (forall ((X tptp.option_trm)) (=> (forall ((Y5 tptp.option_trm)) (=> (@ (@ R3 Y5) X) (@ (@ tptp.accp_option_trm R3) Y5))) (=> (forall ((Y5 tptp.option_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P X2)))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.option_fml tptp.option_fml Bool)) (X2 tptp.option_fml) (P (-> tptp.option_fml Bool))) (=> (@ (@ tptp.accp_option_fml R3) X2) (=> (forall ((X tptp.option_fml)) (=> (forall ((Y5 tptp.option_fml)) (=> (@ (@ R3 Y5) X) (@ (@ tptp.accp_option_fml R3) Y5))) (=> (forall ((Y5 tptp.option_fml)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P X2)))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (B3 tptp.produc1024976764on_trm) (A3 tptp.produc1024976764on_trm)) (let ((_let_1 (@ tptp.accp_P394694195on_trm R3))) (=> (@ _let_1 B3) (=> (@ (@ R3 A3) B3) (@ _let_1 A3))))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (B3 tptp.produc1072747943on_trm) (A3 tptp.produc1072747943on_trm)) (let ((_let_1 (@ tptp.accp_P758790320on_trm R3))) (=> (@ _let_1 B3) (=> (@ (@ R3 A3) B3) (@ _let_1 A3))))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (B3 tptp.produc464795408on_trm) (A3 tptp.produc464795408on_trm)) (let ((_let_1 (@ tptp.accp_P419951815on_trm R3))) (=> (@ _let_1 B3) (=> (@ (@ R3 A3) B3) (@ _let_1 A3))))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.option_trm tptp.option_trm Bool)) (B3 tptp.option_trm) (A3 tptp.option_trm)) (let ((_let_1 (@ tptp.accp_option_trm R3))) (=> (@ _let_1 B3) (=> (@ (@ R3 A3) B3) (@ _let_1 A3))))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.option_fml tptp.option_fml Bool)) (B3 tptp.option_fml) (A3 tptp.option_fml)) (let ((_let_1 (@ tptp.accp_option_fml R3))) (=> (@ _let_1 B3) (=> (@ (@ R3 A3) B3) (@ _let_1 A3))))))
% 0.26/0.69 (assert (forall ((R (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (X2 tptp.produc1024976764on_trm)) (=> (not (@ (@ tptp.accp_P394694195on_trm R) X2)) (not (forall ((Z4 tptp.produc1024976764on_trm)) (=> (@ (@ R Z4) X2) (@ (@ tptp.accp_P394694195on_trm R) Z4)))))))
% 0.26/0.69 (assert (forall ((R (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (X2 tptp.produc1072747943on_trm)) (=> (not (@ (@ tptp.accp_P758790320on_trm R) X2)) (not (forall ((Z4 tptp.produc1072747943on_trm)) (=> (@ (@ R Z4) X2) (@ (@ tptp.accp_P758790320on_trm R) Z4)))))))
% 0.26/0.69 (assert (forall ((R (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (X2 tptp.produc464795408on_trm)) (=> (not (@ (@ tptp.accp_P419951815on_trm R) X2)) (not (forall ((Z4 tptp.produc464795408on_trm)) (=> (@ (@ R Z4) X2) (@ (@ tptp.accp_P419951815on_trm R) Z4)))))))
% 0.26/0.69 (assert (forall ((R (-> tptp.option_trm tptp.option_trm Bool)) (X2 tptp.option_trm)) (=> (not (@ (@ tptp.accp_option_trm R) X2)) (not (forall ((Z4 tptp.option_trm)) (=> (@ (@ R Z4) X2) (@ (@ tptp.accp_option_trm R) Z4)))))))
% 0.26/0.69 (assert (forall ((R (-> tptp.option_fml tptp.option_fml Bool)) (X2 tptp.option_fml)) (=> (not (@ (@ tptp.accp_option_fml R) X2)) (not (forall ((Z4 tptp.option_fml)) (=> (@ (@ R Z4) X2) (@ (@ tptp.accp_option_fml R) Z4)))))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (A3 tptp.produc1024976764on_trm) (P (-> tptp.produc1024976764on_trm Bool))) (=> (@ (@ tptp.accp_P394694195on_trm R3) A3) (=> (forall ((X tptp.produc1024976764on_trm)) (=> (@ (@ tptp.accp_P394694195on_trm R3) X) (=> (forall ((Y5 tptp.produc1024976764on_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (A3 tptp.produc1072747943on_trm) (P (-> tptp.produc1072747943on_trm Bool))) (=> (@ (@ tptp.accp_P758790320on_trm R3) A3) (=> (forall ((X tptp.produc1072747943on_trm)) (=> (@ (@ tptp.accp_P758790320on_trm R3) X) (=> (forall ((Y5 tptp.produc1072747943on_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (A3 tptp.produc464795408on_trm) (P (-> tptp.produc464795408on_trm Bool))) (=> (@ (@ tptp.accp_P419951815on_trm R3) A3) (=> (forall ((X tptp.produc464795408on_trm)) (=> (@ (@ tptp.accp_P419951815on_trm R3) X) (=> (forall ((Y5 tptp.produc464795408on_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.option_trm tptp.option_trm Bool)) (A3 tptp.option_trm) (P (-> tptp.option_trm Bool))) (=> (@ (@ tptp.accp_option_trm R3) A3) (=> (forall ((X tptp.option_trm)) (=> (@ (@ tptp.accp_option_trm R3) X) (=> (forall ((Y5 tptp.option_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))))
% 0.26/0.69 (assert (forall ((R3 (-> tptp.option_fml tptp.option_fml Bool)) (A3 tptp.option_fml) (P (-> tptp.option_fml Bool))) (=> (@ (@ tptp.accp_option_fml R3) A3) (=> (forall ((X tptp.option_fml)) (=> (@ (@ tptp.accp_option_fml R3) X) (=> (forall ((Y5 tptp.option_fml)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_trm) (Xa tptp.option_trm) (Y2 tptp.option_fml)) (let ((_let_1 (@ tptp.accp_P758790320on_trm tptp.uSubst1304144938qo_rel))) (=> (= (@ (@ tptp.uSubst152838031e_Geqo X2) Xa) Y2) (=> (@ _let_1 (@ (@ tptp.produc709594775on_trm X2) Xa)) (=> (forall ((Theta2 tptp.trm)) (=> (= X2 (@ tptp.some_trm Theta2)) (forall ((Eta2 tptp.trm)) (let ((_let_1 (@ tptp.some_trm Eta2))) (=> (= Xa _let_1) (=> (= Y2 (@ tptp.some_fml (@ (@ tptp.geq Theta2) Eta2))) (not (@ (@ tptp.accp_P758790320on_trm tptp.uSubst1304144938qo_rel) (@ (@ tptp.produc709594775on_trm (@ tptp.some_trm Theta2)) _let_1))))))))) (=> (=> (= X2 tptp.none_trm) (=> (= Y2 tptp.none_fml) (not (@ _let_1 (@ (@ tptp.produc709594775on_trm tptp.none_trm) Xa))))) (not (forall ((V2 tptp.trm)) (let ((_let_1 (@ tptp.some_trm V2))) (=> (= X2 _let_1) (=> (= Xa tptp.none_trm) (=> (= Y2 tptp.none_fml) (not (@ (@ tptp.accp_P758790320on_trm tptp.uSubst1304144938qo_rel) (@ (@ tptp.produc709594775on_trm _let_1) tptp.none_trm))))))))))))))))
% 0.26/0.69 (assert (forall ((X2 tptp.produc1739631244on_fml)) (=> (forall ((Alpha tptp.game) (Phi2 tptp.fml)) (not (= X2 (@ (@ tptp.produc2124676926on_fml (@ tptp.some_game Alpha)) (@ tptp.some_fml Phi2))))) (=> (forall ((Phi2 tptp.option_fml)) (not (= X2 (@ (@ tptp.produc2124676926on_fml tptp.none_game) Phi2)))) (not (forall ((V2 tptp.game)) (not (= X2 (@ (@ tptp.produc2124676926on_fml (@ tptp.some_game V2)) tptp.none_fml)))))))))
% 0.26/0.69 (assert (forall ((R3 tptp.set_Pr622314946on_fml) (S2 tptp.set_Pr622314946on_fml)) (=> (forall ((X tptp.option_game) (Y4 tptp.option_fml)) (let ((_let_1 (@ tptp.member1883102883on_fml (@ (@ tptp.produc2124676926on_fml X) Y4)))) (=> (@ _let_1 R3) (@ _let_1 S2)))) (@ (@ tptp.ord_le782333474on_fml R3) S2))))
% 0.26/0.69 (assert (forall ((R3 tptp.set_Pr1471344007on_trm) (S2 tptp.set_Pr1471344007on_trm)) (=> (forall ((X tptp.option_trm) (Y4 tptp.option_trm)) (let ((_let_1 (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm X) Y4)))) (=> (@ _let_1 R3) (@ _let_1 S2)))) (@ (@ tptp.ord_le1322722599on_trm R3) S2))))
% 0.26/0.69 (assert (forall ((R3 tptp.set_Pr927595527on_fml) (S2 tptp.set_Pr927595527on_fml)) (=> (forall ((X tptp.option_fml) (Y4 tptp.option_fml)) (let ((_let_1 (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml X) Y4)))) (=> (@ _let_1 R3) (@ _let_1 S2)))) (@ (@ tptp.ord_le778974119on_fml R3) S2))))
% 0.26/0.69 (assert (forall ((R3 tptp.set_Pr943832262on_trm) (S2 tptp.set_Pr943832262on_trm)) (=> (forall ((X tptp.char) (Y4 tptp.option_trm)) (let ((_let_1 (@ tptp.member694524327on_trm (@ (@ tptp.produc1500300866on_trm X) Y4)))) (=> (@ _let_1 R3) (@ _let_1 S2)))) (@ (@ tptp.ord_le541293862on_trm R3) S2))))
% 0.26/0.69 (assert (forall ((R3 tptp.set_Pr1235432374le_trm) (S2 tptp.set_Pr1235432374le_trm)) (=> (forall ((X tptp.set_variable) (Y4 tptp.trm)) (let ((_let_1 (@ tptp.member2122665623le_trm (@ (@ tptp.produc1482344242le_trm X) Y4)))) (=> (@ _let_1 R3) (@ _let_1 S2)))) (@ (@ tptp.ord_le2102862870le_trm R3) S2))))
% 0.26/0.69 (assert (forall ((R3 tptp.option_game) (S2 tptp.option_fml) (R tptp.set_Pr622314946on_fml) (S3 tptp.option_fml)) (let ((_let_1 (@ tptp.produc2124676926on_fml R3))) (=> (@ (@ tptp.member1883102883on_fml (@ _let_1 S2)) R) (=> (= S3 S2) (@ (@ tptp.member1883102883on_fml (@ _let_1 S3)) R))))))
% 0.26/0.69 (assert (forall ((R3 tptp.option_trm) (S2 tptp.option_trm) (R tptp.set_Pr1471344007on_trm) (S3 tptp.option_trm)) (let ((_let_1 (@ tptp.produc709594775on_trm R3))) (=> (@ (@ tptp.member165817296on_trm (@ _let_1 S2)) R) (=> (= S3 S2) (@ (@ tptp.member165817296on_trm (@ _let_1 S3)) R))))))
% 0.26/0.69 (assert (forall ((R3 tptp.option_fml) (S2 tptp.option_fml) (R tptp.set_Pr927595527on_fml) (S3 tptp.option_fml)) (let ((_let_1 (@ tptp.produc909629463on_fml R3))) (=> (@ (@ tptp.member1287158352on_fml (@ _let_1 S2)) R) (=> (= S3 S2) (@ (@ tptp.member1287158352on_fml (@ _let_1 S3)) R))))))
% 0.26/0.69 (assert (forall ((R3 tptp.char) (S2 tptp.option_trm) (R tptp.set_Pr943832262on_trm) (S3 tptp.option_trm)) (let ((_let_1 (@ tptp.produc1500300866on_trm R3))) (=> (@ (@ tptp.member694524327on_trm (@ _let_1 S2)) R) (=> (= S3 S2) (@ (@ tptp.member694524327on_trm (@ _let_1 S3)) R))))))
% 0.26/0.69 (assert (forall ((R3 tptp.set_variable) (S2 tptp.trm) (R tptp.set_Pr1235432374le_trm) (S3 tptp.trm)) (let ((_let_1 (@ tptp.produc1482344242le_trm R3))) (=> (@ (@ tptp.member2122665623le_trm (@ _let_1 S2)) R) (=> (= S3 S2) (@ (@ tptp.member2122665623le_trm (@ _let_1 S3)) R))))))
% 0.26/0.69 (assert (forall ((R tptp.set_Pr622314946on_fml) (S tptp.set_Pr622314946on_fml)) (= (= (lambda ((X3 tptp.option_game) (Y3 tptp.option_fml)) (@ (@ tptp.member1883102883on_fml (@ (@ tptp.produc2124676926on_fml X3) Y3)) R)) (lambda ((X3 tptp.option_game) (Y3 tptp.option_fml)) (@ (@ tptp.member1883102883on_fml (@ (@ tptp.produc2124676926on_fml X3) Y3)) S))) (= R S))))
% 0.26/0.69 (assert (forall ((R tptp.set_Pr1471344007on_trm) (S tptp.set_Pr1471344007on_trm)) (= (= (lambda ((X3 tptp.option_trm) (Y3 tptp.option_trm)) (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm X3) Y3)) R)) (lambda ((X3 tptp.option_trm) (Y3 tptp.option_trm)) (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm X3) Y3)) S))) (= R S))))
% 0.26/0.69 (assert (forall ((R tptp.set_Pr927595527on_fml) (S tptp.set_Pr927595527on_fml)) (= (= (lambda ((X3 tptp.option_fml) (Y3 tptp.option_fml)) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml X3) Y3)) R)) (lambda ((X3 tptp.option_fml) (Y3 tptp.option_fml)) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml X3) Y3)) S))) (= R S))))
% 0.26/0.69 (assert (forall ((R tptp.set_Pr943832262on_trm) (S tptp.set_Pr943832262on_trm)) (= (= (lambda ((X3 tptp.char) (Y3 tptp.option_trm)) (@ (@ tptp.member694524327on_trm (@ (@ tptp.produc1500300866on_trm X3) Y3)) R)) (lambda ((X3 tptp.char) (Y3 tptp.option_trm)) (@ (@ tptp.member694524327on_trm (@ (@ tptp.produc1500300866on_trm X3) Y3)) S))) (= R S))))
% 0.26/0.69 (assert (forall ((R tptp.set_Pr1235432374le_trm) (S tptp.set_Pr1235432374le_trm)) (= (= (lambda ((X3 tptp.set_variable) (Y3 tptp.trm)) (@ (@ tptp.member2122665623le_trm (@ (@ tptp.produc1482344242le_trm X3) Y3)) R)) (lambda ((X3 tptp.set_variable) (Y3 tptp.trm)) (@ (@ tptp.member2122665623le_trm (@ (@ tptp.produc1482344242le_trm X3) Y3)) S))) (= R S))))
% 0.26/0.69 (assert (forall ((R tptp.set_Pr622314946on_fml) (S tptp.set_Pr622314946on_fml)) (= (@ (@ tptp.ord_le1588489637_fml_o (lambda ((X3 tptp.option_game) (Y3 tptp.option_fml)) (@ (@ tptp.member1883102883on_fml (@ (@ tptp.produc2124676926on_fml X3) Y3)) R))) (lambda ((X3 tptp.option_game) (Y3 tptp.option_fml)) (@ (@ tptp.member1883102883on_fml (@ (@ tptp.produc2124676926on_fml X3) Y3)) S))) (@ (@ tptp.ord_le782333474on_fml R) S))))
% 0.26/0.69 (assert (forall ((R tptp.set_Pr1471344007on_trm) (S tptp.set_Pr1471344007on_trm)) (= (@ (@ tptp.ord_le847028878_trm_o (lambda ((X3 tptp.option_trm) (Y3 tptp.option_trm)) (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm X3) Y3)) R))) (lambda ((X3 tptp.option_trm) (Y3 tptp.option_trm)) (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm X3) Y3)) S))) (@ (@ tptp.ord_le1322722599on_trm R) S))))
% 0.26/0.69 (assert (forall ((R tptp.set_Pr927595527on_fml) (S tptp.set_Pr927595527on_fml)) (= (@ (@ tptp.ord_le802833166_fml_o (lambda ((X3 tptp.option_fml) (Y3 tptp.option_fml)) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml X3) Y3)) R))) (lambda ((X3 tptp.option_fml) (Y3 tptp.option_fml)) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml X3) Y3)) S))) (@ (@ tptp.ord_le778974119on_fml R) S))))
% 0.26/0.69 (assert (forall ((R tptp.set_Pr943832262on_trm) (S tptp.set_Pr943832262on_trm)) (= (@ (@ tptp.ord_le1890124833_trm_o (lambda ((X3 tptp.char) (Y3 tptp.option_trm)) (@ (@ tptp.member694524327on_trm (@ (@ tptp.produc1500300866on_trm X3) Y3)) R))) (lambda ((X3 tptp.char) (Y3 tptp.option_trm)) (@ (@ tptp.member694524327on_trm (@ (@ tptp.produc1500300866on_trm X3) Y3)) S))) (@ (@ tptp.ord_le541293862on_trm R) S))))
% 0.26/0.69 (assert (forall ((R tptp.set_Pr1235432374le_trm) (S tptp.set_Pr1235432374le_trm)) (= (@ (@ tptp.ord_le691957041_trm_o (lambda ((X3 tptp.set_variable) (Y3 tptp.trm)) (@ (@ tptp.member2122665623le_trm (@ (@ tptp.produc1482344242le_trm X3) Y3)) R))) (lambda ((X3 tptp.set_variable) (Y3 tptp.trm)) (@ (@ tptp.member2122665623le_trm (@ (@ tptp.produc1482344242le_trm X3) Y3)) S))) (@ (@ tptp.ord_le2102862870le_trm R) S))))
% 0.26/0.69 (assert (forall ((Option tptp.option_trm)) (= (= Option tptp.none_trm) (@ (@ (@ tptp.case_option_o_trm true) (lambda ((Uu tptp.trm)) false)) Option))))
% 0.26/0.69 (assert (forall ((Option tptp.option_fml)) (= (= Option tptp.none_fml) (@ (@ (@ tptp.case_option_o_fml true) (lambda ((Uu tptp.fml)) false)) Option))))
% 0.26/0.69 (assert (forall ((Option tptp.option_game)) (= (= Option tptp.none_game) (@ (@ (@ tptp.case_option_o_game true) (lambda ((Uu tptp.game)) false)) Option))))
% 0.26/0.69 (assert (forall ((Option tptp.option_trm)) (= (not (= Option tptp.none_trm)) (@ (@ (@ tptp.case_option_o_trm false) (lambda ((Uu tptp.trm)) true)) Option))))
% 0.26/0.69 (assert (forall ((Option tptp.option_fml)) (= (not (= Option tptp.none_fml)) (@ (@ (@ tptp.case_option_o_fml false) (lambda ((Uu tptp.fml)) true)) Option))))
% 0.26/0.69 (assert (forall ((Option tptp.option_game)) (= (not (= Option tptp.none_game)) (@ (@ (@ tptp.case_option_o_game false) (lambda ((Uu tptp.game)) true)) Option))))
% 0.26/0.69 (assert (forall ((X2 tptp.produc1072747943on_trm)) (=> (forall ((Theta2 tptp.trm) (Eta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc709594775on_trm (@ tptp.some_trm Theta2)) (@ tptp.some_trm Eta2))))) (=> (forall ((Eta2 tptp.option_trm)) (not (= X2 (@ (@ tptp.produc709594775on_trm tptp.none_trm) Eta2)))) (not (forall ((V2 tptp.trm)) (not (= X2 (@ (@ tptp.produc709594775on_trm (@ tptp.some_trm V2)) tptp.none_trm)))))))))
% 0.26/0.69 (assert (forall ((P Bool) (Q (-> tptp.trm Bool)) (X2 tptp.option_trm)) (=> (@ (@ (@ tptp.case_option_o_trm P) Q) X2) (=> (=> (= X2 tptp.none_trm) (not P)) (not (forall ((Y4 tptp.trm)) (=> (= X2 (@ tptp.some_trm Y4)) (not (@ Q Y4)))))))))
% 0.26/0.69 (assert (forall ((P Bool) (Q (-> tptp.fml Bool)) (X2 tptp.option_fml)) (=> (@ (@ (@ tptp.case_option_o_fml P) Q) X2) (=> (=> (= X2 tptp.none_fml) (not P)) (not (forall ((Y4 tptp.fml)) (=> (= X2 (@ tptp.some_fml Y4)) (not (@ Q Y4)))))))))
% 0.26/0.69 (assert (forall ((P Bool) (Q (-> tptp.game Bool)) (X2 tptp.option_game)) (=> (@ (@ (@ tptp.case_option_o_game P) Q) X2) (=> (=> (= X2 tptp.none_game) (not P)) (not (forall ((Y4 tptp.game)) (=> (= X2 (@ tptp.some_game Y4)) (not (@ Q Y4)))))))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_trm) (Xa tptp.option_trm) (Y2 tptp.option_trm)) (let ((_let_1 (@ tptp.accp_P758790320on_trm tptp.uSubst924844285so_rel))) (=> (= (@ (@ tptp.uSubst918876924Timeso X2) Xa) Y2) (=> (@ _let_1 (@ (@ tptp.produc709594775on_trm X2) Xa)) (=> (forall ((Theta2 tptp.trm)) (=> (= X2 (@ tptp.some_trm Theta2)) (forall ((Eta2 tptp.trm)) (let ((_let_1 (@ tptp.some_trm Eta2))) (=> (= Xa _let_1) (=> (= Y2 (@ tptp.some_trm (@ (@ tptp.times Theta2) Eta2))) (not (@ (@ tptp.accp_P758790320on_trm tptp.uSubst924844285so_rel) (@ (@ tptp.produc709594775on_trm (@ tptp.some_trm Theta2)) _let_1))))))))) (=> (=> (= X2 tptp.none_trm) (=> (= Y2 tptp.none_trm) (not (@ _let_1 (@ (@ tptp.produc709594775on_trm tptp.none_trm) Xa))))) (not (forall ((V2 tptp.trm)) (let ((_let_1 (@ tptp.some_trm V2))) (=> (= X2 _let_1) (=> (= Xa tptp.none_trm) (=> (= Y2 tptp.none_trm) (not (@ (@ tptp.accp_P758790320on_trm tptp.uSubst924844285so_rel) (@ (@ tptp.produc709594775on_trm _let_1) tptp.none_trm))))))))))))))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_trm) (Xa tptp.option_trm) (Y2 tptp.option_trm)) (let ((_let_1 (@ tptp.accp_P758790320on_trm tptp.uSubst691094423so_rel))) (=> (= (@ (@ tptp.uSubst141955042_Pluso X2) Xa) Y2) (=> (@ _let_1 (@ (@ tptp.produc709594775on_trm X2) Xa)) (=> (forall ((Theta2 tptp.trm)) (=> (= X2 (@ tptp.some_trm Theta2)) (forall ((Eta2 tptp.trm)) (let ((_let_1 (@ tptp.some_trm Eta2))) (=> (= Xa _let_1) (=> (= Y2 (@ tptp.some_trm (@ (@ tptp.plus Theta2) Eta2))) (not (@ (@ tptp.accp_P758790320on_trm tptp.uSubst691094423so_rel) (@ (@ tptp.produc709594775on_trm (@ tptp.some_trm Theta2)) _let_1))))))))) (=> (=> (= X2 tptp.none_trm) (=> (= Y2 tptp.none_trm) (not (@ _let_1 (@ (@ tptp.produc709594775on_trm tptp.none_trm) Xa))))) (not (forall ((V2 tptp.trm)) (let ((_let_1 (@ tptp.some_trm V2))) (=> (= X2 _let_1) (=> (= Xa tptp.none_trm) (=> (= Y2 tptp.none_trm) (not (@ (@ tptp.accp_P758790320on_trm tptp.uSubst691094423so_rel) (@ (@ tptp.produc709594775on_trm _let_1) tptp.none_trm))))))))))))))))
% 0.26/0.69 (assert (forall ((X2 tptp.produc464795408on_trm)) (=> (forall ((X tptp.char) (Theta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc1500300866on_trm X) (@ tptp.some_trm Theta2))))) (not (forall ((X tptp.char)) (not (= X2 (@ (@ tptp.produc1500300866on_trm X) tptp.none_trm))))))))
% 0.26/0.69 (assert (forall ((X2 tptp.produc1024976764on_trm)) (=> (forall ((X tptp.variable) (Theta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc1743721902on_trm X) (@ tptp.some_trm Theta2))))) (not (forall ((X tptp.variable)) (not (= X2 (@ (@ tptp.produc1743721902on_trm X) tptp.none_trm))))))))
% 0.26/0.69 (assert (forall ((X2 tptp.produc1016592119n_game)) (=> (forall ((Alpha tptp.game) (Beta tptp.game)) (not (= X2 (@ (@ tptp.produc1111617711n_game (@ tptp.some_game Alpha)) (@ tptp.some_game Beta))))) (=> (forall ((Alpha tptp.option_game)) (not (= X2 (@ (@ tptp.produc1111617711n_game Alpha) tptp.none_game)))) (not (forall ((V2 tptp.game)) (not (= X2 (@ (@ tptp.produc1111617711n_game tptp.none_game) (@ tptp.some_game V2))))))))))
% 0.26/0.69 (assert (forall ((X2 tptp.produc1408538418on_fml)) (=> (forall ((X tptp.variable) (Phi2 tptp.fml)) (not (= X2 (@ (@ tptp.produc1205977188on_fml X) (@ tptp.some_fml Phi2))))) (not (forall ((X tptp.variable)) (not (= X2 (@ (@ tptp.produc1205977188on_fml X) tptp.none_fml))))))))
% 0.26/0.69 (assert (forall ((X2 tptp.produc46605351on_fml)) (=> (forall ((Phi2 tptp.fml) (Psi tptp.fml)) (not (= X2 (@ (@ tptp.produc909629463on_fml (@ tptp.some_fml Phi2)) (@ tptp.some_fml Psi))))) (=> (forall ((Psi tptp.option_fml)) (not (= X2 (@ (@ tptp.produc909629463on_fml tptp.none_fml) Psi)))) (not (forall ((V2 tptp.fml)) (not (= X2 (@ (@ tptp.produc909629463on_fml (@ tptp.some_fml V2)) tptp.none_fml)))))))))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm)) (let ((_let_1 (@ tptp.uSubst516392818stappt Sigma))) (let ((_let_2 (@ tptp.differential Theta))) (=> (@ (@ tptp.accp_P1877119646le_trm tptp.uSubst1917534215pt_rel) (@ (@ tptp.produc2015636557le_trm Sigma) (@ (@ tptp.produc1482344242le_trm U) _let_2))) (= (@ (@ _let_1 U) _let_2) (@ tptp.uSubst716837505ntialo (@ (@ _let_1 (@ tptp.collect_variable (lambda ((X3 tptp.variable)) true))) Theta))))))))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (let ((_let_2 (@ (@ tptp.times Theta) Eta))) (=> (@ (@ tptp.accp_P1877119646le_trm tptp.uSubst1917534215pt_rel) (@ (@ tptp.produc2015636557le_trm Sigma) (@ (@ tptp.produc1482344242le_trm U) _let_2))) (= (@ _let_1 _let_2) (@ (@ tptp.uSubst918876924Timeso (@ _let_1 Theta)) (@ _let_1 Eta))))))))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (let ((_let_2 (@ (@ tptp.plus Theta) Eta))) (=> (@ (@ tptp.accp_P1877119646le_trm tptp.uSubst1917534215pt_rel) (@ (@ tptp.produc2015636557le_trm Sigma) (@ (@ tptp.produc1482344242le_trm U) _let_2))) (= (@ _let_1 _let_2) (@ (@ tptp.uSubst141955042_Pluso (@ _let_1 Theta)) (@ _let_1 Eta))))))))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (X2 tptp.variable)) (let ((_let_1 (@ tptp.var X2))) (=> (@ (@ tptp.accp_P1877119646le_trm tptp.uSubst1917534215pt_rel) (@ (@ tptp.produc2015636557le_trm Sigma) (@ (@ tptp.produc1482344242le_trm U) _let_1))) (= (@ (@ (@ tptp.uSubst516392818stappt Sigma) U) _let_1) (@ tptp.some_trm _let_1))))))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (R3 tptp.real)) (let ((_let_1 (@ tptp.number R3))) (=> (@ (@ tptp.accp_P1877119646le_trm tptp.uSubst1917534215pt_rel) (@ (@ tptp.produc2015636557le_trm Sigma) (@ (@ tptp.produc1482344242le_trm U) _let_1))) (= (@ (@ (@ tptp.uSubst516392818stappt Sigma) U) _let_1) (@ tptp.some_trm _let_1))))))
% 0.26/0.69 (assert (forall ((A3 tptp.option_trm) (B3 tptp.option_fml) (A6 tptp.option_trm) (B6 tptp.option_fml) (R3 tptp.set_Pr1471344007on_trm) (S2 tptp.set_Pr927595527on_fml)) (= (@ (@ tptp.member1316917136on_fml (@ (@ tptp.produc1235825367on_fml (@ (@ tptp.produc171850061on_fml A3) B3)) (@ (@ tptp.produc171850061on_fml A6) B6))) (@ (@ tptp.lex_pr1724583269on_fml R3) S2)) (or (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm A3) A6)) R3) (and (= A3 A6) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml B3) B6)) S2))))))
% 0.26/0.69 (assert (forall ((A3 tptp.option_fml) (B3 tptp.option_trm) (A6 tptp.option_fml) (B6 tptp.option_trm) (R3 tptp.set_Pr927595527on_fml) (S2 tptp.set_Pr1471344007on_trm)) (= (@ (@ tptp.member1883874960on_trm (@ (@ tptp.produc2132972503on_trm (@ (@ tptp.produc1447374177on_trm A3) B3)) (@ (@ tptp.produc1447374177on_trm A6) B6))) (@ (@ tptp.lex_pr852623737on_trm R3) S2)) (or (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml A3) A6)) R3) (and (= A3 A6) (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm B3) B6)) S2))))))
% 0.26/0.69 (assert (forall ((A3 tptp.option_game) (B3 tptp.option_fml) (A6 tptp.option_game) (B6 tptp.option_fml) (R3 tptp.set_Pr1625152599n_game) (S2 tptp.set_Pr927595527on_fml)) (= (@ (@ tptp.member113767842on_fml (@ (@ tptp.produc556056113on_fml (@ (@ tptp.produc2124676926on_fml A3) B3)) (@ (@ tptp.produc2124676926on_fml A6) B6))) (@ (@ tptp.lex_pr425996582on_fml R3) S2)) (or (@ (@ tptp.member191809696n_game (@ (@ tptp.produc1111617711n_game A3) A6)) R3) (and (= A3 A6) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml B3) B6)) S2))))))
% 0.26/0.69 (assert (forall ((A3 tptp.option_trm) (B3 tptp.option_trm) (A6 tptp.option_trm) (B6 tptp.option_trm) (R3 tptp.set_Pr1471344007on_trm) (S2 tptp.set_Pr1471344007on_trm)) (let ((_let_1 (@ tptp.produc709594775on_trm A3))) (= (@ (@ tptp.member602811152on_trm (@ (@ tptp.produc2001752919on_trm (@ _let_1 B3)) (@ (@ tptp.produc709594775on_trm A6) B6))) (@ (@ tptp.lex_pr114844335on_trm R3) S2)) (or (@ (@ tptp.member165817296on_trm (@ _let_1 A6)) R3) (and (= A3 A6) (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm B3) B6)) S2)))))))
% 0.26/0.69 (assert (forall ((A3 tptp.option_fml) (B3 tptp.option_fml) (A6 tptp.option_fml) (B6 tptp.option_fml) (R3 tptp.set_Pr927595527on_fml) (S2 tptp.set_Pr927595527on_fml)) (let ((_let_1 (@ tptp.produc909629463on_fml A3))) (= (@ (@ tptp.member450497296on_fml (@ (@ tptp.produc1367044951on_fml (@ _let_1 B3)) (@ (@ tptp.produc909629463on_fml A6) B6))) (@ (@ tptp.lex_pr314879023on_fml R3) S2)) (or (@ (@ tptp.member1287158352on_fml (@ _let_1 A6)) R3) (and (= A3 A6) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml B3) B6)) S2)))))))
% 0.26/0.69 (assert (forall ((A3 tptp.char) (B3 tptp.option_trm) (A6 tptp.char) (B6 tptp.option_trm) (R3 tptp.set_Pr604539619r_char) (S2 tptp.set_Pr1471344007on_trm)) (= (@ (@ tptp.member1950256170on_trm (@ (@ tptp.produc444919481on_trm (@ (@ tptp.produc1500300866on_trm A3) B3)) (@ (@ tptp.produc1500300866on_trm A6) B6))) (@ (@ tptp.lex_pr1901327402on_trm R3) S2)) (or (@ (@ tptp.member1866856748r_char (@ (@ tptp.produc19545147r_char A3) A6)) R3) (and (= A3 A6) (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm B3) B6)) S2))))))
% 0.26/0.69 (assert (forall ((A3 tptp.set_variable) (B3 tptp.trm) (A6 tptp.set_variable) (B6 tptp.trm) (R3 tptp.set_Pr181266295riable) (S2 tptp.set_Pr491793543rm_trm)) (= (@ (@ tptp.member1150310282le_trm (@ (@ tptp.produc1056455193le_trm (@ (@ tptp.produc1482344242le_trm A3) B3)) (@ (@ tptp.produc1482344242le_trm A6) B6))) (@ (@ tptp.lex_pr1522821402le_trm R3) S2)) (or (@ (@ tptp.member1978718144riable (@ (@ tptp.produc1766592463riable A3) A6)) R3) (and (= A3 A6) (@ (@ tptp.member1735386832rm_trm (@ (@ tptp.product_Pair_trm_trm B3) B6)) S2))))))
% 0.26/0.69 (assert (forall ((X23 tptp.real) (Y23 tptp.real)) (= (= (@ tptp.number X23) (@ tptp.number Y23)) (= X23 Y23))))
% 0.26/0.69 (assert (forall ((X1 tptp.variable) (Y1 tptp.variable)) (= (= (@ tptp.var X1) (@ tptp.var Y1)) (= X1 Y1))))
% 0.26/0.69 (assert (forall ((X23 tptp.real) (X51 tptp.trm) (X52 tptp.trm)) (not (= (@ tptp.number X23) (@ (@ tptp.plus X51) X52)))))
% 0.26/0.69 (assert (forall ((X23 tptp.real) (X61 tptp.trm) (X62 tptp.trm)) (not (= (@ tptp.number X23) (@ (@ tptp.times X61) X62)))))
% 0.26/0.69 (assert (forall ((X23 tptp.real) (X7 tptp.trm)) (not (= (@ tptp.number X23) (@ tptp.differential X7)))))
% 0.26/0.69 (assert (forall ((X1 tptp.variable) (X51 tptp.trm) (X52 tptp.trm)) (not (= (@ tptp.var X1) (@ (@ tptp.plus X51) X52)))))
% 0.26/0.69 (assert (forall ((X1 tptp.variable) (X61 tptp.trm) (X62 tptp.trm)) (not (= (@ tptp.var X1) (@ (@ tptp.times X61) X62)))))
% 0.26/0.69 (assert (forall ((X1 tptp.variable) (X7 tptp.trm)) (not (= (@ tptp.var X1) (@ tptp.differential X7)))))
% 0.26/0.69 (assert (forall ((X1 tptp.variable) (X23 tptp.real)) (not (= (@ tptp.var X1) (@ tptp.number X23)))))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (R3 tptp.real)) (let ((_let_1 (@ tptp.number R3))) (= (@ (@ (@ tptp.uSubst516392818stappt Sigma) U) _let_1) (@ tptp.some_trm _let_1)))))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (X2 tptp.variable)) (let ((_let_1 (@ tptp.var X2))) (= (@ (@ (@ tptp.uSubst516392818stappt Sigma) U) _let_1) (@ tptp.some_trm _let_1)))))
% 0.26/0.69 (assert (forall ((X2 tptp.produc1699626005le_trm)) (=> (forall ((Sigma2 tptp.produc1418842292n_game) (U3 tptp.set_variable) (X tptp.variable)) (not (= X2 (@ (@ tptp.produc2015636557le_trm Sigma2) (@ (@ tptp.produc1482344242le_trm U3) (@ tptp.var X)))))) (=> (forall ((Sigma2 tptp.produc1418842292n_game) (U3 tptp.set_variable) (R5 tptp.real)) (not (= X2 (@ (@ tptp.produc2015636557le_trm Sigma2) (@ (@ tptp.produc1482344242le_trm U3) (@ tptp.number R5)))))) (=> (forall ((Sigma2 tptp.produc1418842292n_game) (U3 tptp.set_variable) (F3 tptp.char)) (not (= X2 (@ (@ tptp.produc2015636557le_trm Sigma2) (@ (@ tptp.produc1482344242le_trm U3) (@ tptp.const F3)))))) (=> (forall ((Sigma2 tptp.produc1418842292n_game) (U3 tptp.set_variable) (F3 tptp.char) (Theta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc2015636557le_trm Sigma2) (@ (@ tptp.produc1482344242le_trm U3) (@ (@ tptp.func F3) Theta2)))))) (=> (forall ((Sigma2 tptp.produc1418842292n_game) (U3 tptp.set_variable) (Theta2 tptp.trm) (Eta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc2015636557le_trm Sigma2) (@ (@ tptp.produc1482344242le_trm U3) (@ (@ tptp.plus Theta2) Eta2)))))) (=> (forall ((Sigma2 tptp.produc1418842292n_game) (U3 tptp.set_variable) (Theta2 tptp.trm) (Eta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc2015636557le_trm Sigma2) (@ (@ tptp.produc1482344242le_trm U3) (@ (@ tptp.times Theta2) Eta2)))))) (not (forall ((Sigma2 tptp.produc1418842292n_game) (U3 tptp.set_variable) (Theta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc2015636557le_trm Sigma2) (@ (@ tptp.produc1482344242le_trm U3) (@ tptp.differential Theta2)))))))))))))))
% 0.26/0.69 (assert (= (@ tptp.uSubst1367128042_Testo tptp.none_fml) tptp.none_game))
% 0.26/0.69 (assert (forall ((Phi tptp.option_fml)) (= (= (@ tptp.uSubst1367128042_Testo Phi) tptp.none_game) (= Phi tptp.none_fml))))
% 0.26/0.69 (assert (forall ((X41 tptp.char) (X42 tptp.trm) (Y41 tptp.char) (Y42 tptp.trm)) (= (= (@ (@ tptp.func X41) X42) (@ (@ tptp.func Y41) Y42)) (and (= X41 Y41) (= X42 Y42)))))
% 0.26/0.69 (assert (forall ((X32 tptp.char) (Y32 tptp.char)) (= (= (@ tptp.const X32) (@ tptp.const Y32)) (= X32 Y32))))
% 0.26/0.69 (assert (forall ((X1 tptp.variable) (X32 tptp.char)) (not (= (@ tptp.var X1) (@ tptp.const X32)))))
% 0.26/0.69 (assert (forall ((X1 tptp.variable) (X41 tptp.char) (X42 tptp.trm)) (not (= (@ tptp.var X1) (@ (@ tptp.func X41) X42)))))
% 0.26/0.69 (assert (forall ((X23 tptp.real) (X32 tptp.char)) (not (= (@ tptp.number X23) (@ tptp.const X32)))))
% 0.26/0.69 (assert (forall ((X23 tptp.real) (X41 tptp.char) (X42 tptp.trm)) (not (= (@ tptp.number X23) (@ (@ tptp.func X41) X42)))))
% 0.26/0.69 (assert (forall ((X32 tptp.char) (X41 tptp.char) (X42 tptp.trm)) (not (= (@ tptp.const X32) (@ (@ tptp.func X41) X42)))))
% 0.26/0.69 (assert (forall ((X32 tptp.char) (X7 tptp.trm)) (not (= (@ tptp.const X32) (@ tptp.differential X7)))))
% 0.26/0.69 (assert (forall ((X32 tptp.char) (X61 tptp.trm) (X62 tptp.trm)) (not (= (@ tptp.const X32) (@ (@ tptp.times X61) X62)))))
% 0.26/0.69 (assert (forall ((X32 tptp.char) (X51 tptp.trm) (X52 tptp.trm)) (not (= (@ tptp.const X32) (@ (@ tptp.plus X51) X52)))))
% 0.26/0.69 (assert (forall ((X41 tptp.char) (X42 tptp.trm) (X7 tptp.trm)) (not (= (@ (@ tptp.func X41) X42) (@ tptp.differential X7)))))
% 0.26/0.69 (assert (forall ((X41 tptp.char) (X42 tptp.trm) (X61 tptp.trm) (X62 tptp.trm)) (not (= (@ (@ tptp.func X41) X42) (@ (@ tptp.times X61) X62)))))
% 0.26/0.69 (assert (forall ((X41 tptp.char) (X42 tptp.trm) (X51 tptp.trm) (X52 tptp.trm)) (not (= (@ (@ tptp.func X41) X42) (@ (@ tptp.plus X51) X52)))))
% 0.26/0.69 (assert (forall ((P (-> tptp.trm Bool)) (Trm tptp.trm)) (=> (forall ((X tptp.variable)) (@ P (@ tptp.var X))) (=> (forall ((X tptp.real)) (@ P (@ tptp.number X))) (=> (forall ((X tptp.char)) (@ P (@ tptp.const X))) (=> (forall ((X1a tptp.char) (X2a tptp.trm)) (=> (@ P X2a) (@ P (@ (@ tptp.func X1a) X2a)))) (=> (forall ((X1a tptp.trm) (X2a tptp.trm)) (=> (@ P X1a) (=> (@ P X2a) (@ P (@ (@ tptp.plus X1a) X2a))))) (=> (forall ((X1a tptp.trm) (X2a tptp.trm)) (=> (@ P X1a) (=> (@ P X2a) (@ P (@ (@ tptp.times X1a) X2a))))) (=> (forall ((X tptp.trm)) (=> (@ P X) (@ P (@ tptp.differential X)))) (@ P Trm))))))))))
% 0.26/0.69 (assert (forall ((Y2 tptp.trm)) (=> (forall ((X12 tptp.variable)) (not (= Y2 (@ tptp.var X12)))) (=> (forall ((X24 tptp.real)) (not (= Y2 (@ tptp.number X24)))) (=> (forall ((X33 tptp.char)) (not (= Y2 (@ tptp.const X33)))) (=> (forall ((X412 tptp.char) (X422 tptp.trm)) (not (= Y2 (@ (@ tptp.func X412) X422)))) (=> (forall ((X512 tptp.trm) (X522 tptp.trm)) (not (= Y2 (@ (@ tptp.plus X512) X522)))) (=> (forall ((X612 tptp.trm) (X622 tptp.trm)) (not (= Y2 (@ (@ tptp.times X612) X622)))) (not (forall ((X72 tptp.trm)) (not (= Y2 (@ tptp.differential X72)))))))))))))
% 0.26/0.69 (assert (forall ((X2 tptp.produc833882726rp_trm)) (=> (forall ((I2 tptp.denotational_interp) (X tptp.variable)) (not (= X2 (@ (@ tptp.produc1132922070rp_trm I2) (@ tptp.var X))))) (=> (forall ((I2 tptp.denotational_interp) (R5 tptp.real)) (not (= X2 (@ (@ tptp.produc1132922070rp_trm I2) (@ tptp.number R5))))) (=> (forall ((I2 tptp.denotational_interp) (F3 tptp.char)) (not (= X2 (@ (@ tptp.produc1132922070rp_trm I2) (@ tptp.const F3))))) (=> (forall ((I2 tptp.denotational_interp) (F3 tptp.char) (Theta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc1132922070rp_trm I2) (@ (@ tptp.func F3) Theta2))))) (=> (forall ((I2 tptp.denotational_interp) (Theta2 tptp.trm) (Eta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc1132922070rp_trm I2) (@ (@ tptp.plus Theta2) Eta2))))) (=> (forall ((I2 tptp.denotational_interp) (Theta2 tptp.trm) (Eta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc1132922070rp_trm I2) (@ (@ tptp.times Theta2) Eta2))))) (not (forall ((I2 tptp.denotational_interp) (Theta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc1132922070rp_trm I2) (@ tptp.differential Theta2))))))))))))))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (F tptp.char)) (let ((_let_1 (@ tptp.const F))) (=> (@ (@ tptp.accp_P1877119646le_trm tptp.uSubst1917534215pt_rel) (@ (@ tptp.produc2015636557le_trm Sigma) (@ (@ tptp.produc1482344242le_trm U) _let_1))) (= (@ (@ (@ tptp.uSubst516392818stappt Sigma) U) _let_1) (@ (@ (@ tptp.uSubst1559070963pconst Sigma) U) F))))))
% 0.26/0.69 (assert (forall ((P (-> tptp.denotational_interp tptp.trm Bool)) (A0 tptp.denotational_interp) (A1 tptp.trm)) (=> (forall ((I2 tptp.denotational_interp) (X tptp.variable)) (@ (@ P I2) (@ tptp.var X))) (=> (forall ((I2 tptp.denotational_interp) (R5 tptp.real)) (@ (@ P I2) (@ tptp.number R5))) (=> (forall ((I2 tptp.denotational_interp) (F3 tptp.char)) (@ (@ P I2) (@ tptp.const F3))) (=> (forall ((I2 tptp.denotational_interp) (F3 tptp.char) (Theta2 tptp.trm)) (let ((_let_1 (@ P I2))) (=> (@ _let_1 Theta2) (@ _let_1 (@ (@ tptp.func F3) Theta2))))) (=> (forall ((I2 tptp.denotational_interp) (Theta2 tptp.trm)) (=> (@ (@ P I2) Theta2) (forall ((Eta2 tptp.trm)) (let ((_let_1 (@ P I2))) (=> (@ _let_1 Eta2) (@ _let_1 (@ (@ tptp.plus Theta2) Eta2))))))) (=> (forall ((I2 tptp.denotational_interp) (Theta2 tptp.trm)) (=> (@ (@ P I2) Theta2) (forall ((Eta2 tptp.trm)) (let ((_let_1 (@ P I2))) (=> (@ _let_1 Eta2) (@ _let_1 (@ (@ tptp.times Theta2) Eta2))))))) (=> (forall ((I2 tptp.denotational_interp) (Theta2 tptp.trm)) (let ((_let_1 (@ P I2))) (=> (=> (exists ((Xa2 tptp.char)) (@ (@ tptp.member_char Xa2) (@ tptp.collect_char (lambda ((Uu tptp.char)) true)))) (@ _let_1 Theta2)) (@ _let_1 (@ tptp.differential Theta2))))) (@ (@ P A0) A1))))))))))
% 0.26/0.69 (assert (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (F tptp.char)) (= (@ (@ (@ tptp.uSubst516392818stappt Sigma) U) (@ tptp.const F)) (@ (@ (@ tptp.uSubst1559070963pconst Sigma) U) F))))
% 0.26/0.69 (assert (= tptp.bNF_Gr2142503190on_fml (lambda ((A2 tptp.set_variable) (F2 (-> tptp.variable tptp.option_game)) (G (-> tptp.variable tptp.option_fml))) (@ tptp.collec749447393on_fml (lambda ((Uu tptp.produc1739631244on_fml)) (exists ((A4 tptp.variable)) (and (= Uu (@ (@ tptp.produc2124676926on_fml (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_variable A4) A2))))))))
% 0.26/0.69 (assert (= tptp.bNF_Gr756940202on_fml (lambda ((A2 tptp.set_char) (F2 (-> tptp.char tptp.option_game)) (G (-> tptp.char tptp.option_fml))) (@ tptp.collec749447393on_fml (lambda ((Uu tptp.produc1739631244on_fml)) (exists ((A4 tptp.char)) (and (= Uu (@ (@ tptp.produc2124676926on_fml (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_char A4) A2))))))))
% 0.26/0.69 (assert (= tptp.bNF_Gr400922303on_trm (lambda ((A2 tptp.set_variable) (F2 (-> tptp.variable tptp.option_trm)) (G (-> tptp.variable tptp.option_trm))) (@ tptp.collec1697116690on_trm (lambda ((Uu tptp.produc1072747943on_trm)) (exists ((A4 tptp.variable)) (and (= Uu (@ (@ tptp.produc709594775on_trm (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_variable A4) A2))))))))
% 0.26/0.69 (assert (= tptp.bNF_Gr1666135339on_trm (lambda ((A2 tptp.set_char) (F2 (-> tptp.char tptp.option_trm)) (G (-> tptp.char tptp.option_trm))) (@ tptp.collec1697116690on_trm (lambda ((Uu tptp.produc1072747943on_trm)) (exists ((A4 tptp.char)) (and (= Uu (@ (@ tptp.produc709594775on_trm (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_char A4) A2))))))))
% 0.26/0.69 (assert (= tptp.bNF_Gr600956991on_fml (lambda ((A2 tptp.set_variable) (F2 (-> tptp.variable tptp.option_fml)) (G (-> tptp.variable tptp.option_fml))) (@ tptp.collec670974098on_fml (lambda ((Uu tptp.produc46605351on_fml)) (exists ((A4 tptp.variable)) (and (= Uu (@ (@ tptp.produc909629463on_fml (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_variable A4) A2))))))))
% 0.26/0.69 (assert (= tptp.bNF_Gr1866170027on_fml (lambda ((A2 tptp.set_char) (F2 (-> tptp.char tptp.option_fml)) (G (-> tptp.char tptp.option_fml))) (@ tptp.collec670974098on_fml (lambda ((Uu tptp.produc46605351on_fml)) (exists ((A4 tptp.char)) (and (= Uu (@ (@ tptp.produc909629463on_fml (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_char A4) A2))))))))
% 0.26/0.69 (assert (= tptp.bNF_Gr1933470746on_trm (lambda ((A2 tptp.set_variable) (F2 (-> tptp.variable tptp.char)) (G (-> tptp.variable tptp.option_trm))) (@ tptp.collec1756633317on_trm (lambda ((Uu tptp.produc464795408on_trm)) (exists ((A4 tptp.variable)) (and (= Uu (@ (@ tptp.produc1500300866on_trm (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_variable A4) A2))))))))
% 0.26/0.69 (assert (= tptp.bNF_Gr951178926on_trm (lambda ((A2 tptp.set_char) (F2 (-> tptp.char tptp.char)) (G (-> tptp.char tptp.option_trm))) (@ tptp.collec1756633317on_trm (lambda ((Uu tptp.produc464795408on_trm)) (exists ((A4 tptp.char)) (and (= Uu (@ (@ tptp.produc1500300866on_trm (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_char A4) A2))))))))
% 0.26/0.69 (assert (= tptp.bNF_Gr1330108682le_trm (lambda ((A2 tptp.set_variable) (F2 (-> tptp.variable tptp.set_variable)) (G (-> tptp.variable tptp.trm))) (@ tptp.collec575343829le_trm (lambda ((Uu tptp.produc1367888000le_trm)) (exists ((A4 tptp.variable)) (and (= Uu (@ (@ tptp.produc1482344242le_trm (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_variable A4) A2))))))))
% 0.26/0.69 (assert (= tptp.bNF_Gr852774302le_trm (lambda ((A2 tptp.set_char) (F2 (-> tptp.char tptp.set_variable)) (G (-> tptp.char tptp.trm))) (@ tptp.collec575343829le_trm (lambda ((Uu tptp.produc1367888000le_trm)) (exists ((A4 tptp.char)) (and (= Uu (@ (@ tptp.produc1482344242le_trm (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_char A4) A2))))))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_fml) (Y2 tptp.option_game)) (=> (= (@ tptp.uSubst1367128042_Testo X2) Y2) (=> (forall ((Phi2 tptp.fml)) (=> (= X2 (@ tptp.some_fml Phi2)) (not (= Y2 (@ tptp.some_game (@ tptp.test Phi2)))))) (not (=> (= X2 tptp.none_fml) (not (= Y2 tptp.none_game))))))))
% 0.26/0.69 (assert (forall ((X32 tptp.fml) (Y32 tptp.fml)) (= (= (@ tptp.test X32) (@ tptp.test Y32)) (= X32 Y32))))
% 0.26/0.69 (assert (forall ((B3 tptp.option_game) (F (-> tptp.variable tptp.option_game)) (X2 tptp.variable) (C tptp.option_fml) (G2 (-> tptp.variable tptp.option_fml)) (A tptp.set_variable)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_variable X2) A) (@ (@ tptp.member1883102883on_fml (@ (@ tptp.produc2124676926on_fml B3) C)) (@ (@ (@ tptp.bNF_Gr2142503190on_fml A) F) G2)))))))
% 0.26/0.69 (assert (forall ((B3 tptp.option_game) (F (-> tptp.char tptp.option_game)) (X2 tptp.char) (C tptp.option_fml) (G2 (-> tptp.char tptp.option_fml)) (A tptp.set_char)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_char X2) A) (@ (@ tptp.member1883102883on_fml (@ (@ tptp.produc2124676926on_fml B3) C)) (@ (@ (@ tptp.bNF_Gr756940202on_fml A) F) G2)))))))
% 0.26/0.69 (assert (forall ((B3 tptp.option_trm) (F (-> tptp.variable tptp.option_trm)) (X2 tptp.variable) (C tptp.option_trm) (G2 (-> tptp.variable tptp.option_trm)) (A tptp.set_variable)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_variable X2) A) (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm B3) C)) (@ (@ (@ tptp.bNF_Gr400922303on_trm A) F) G2)))))))
% 0.26/0.69 (assert (forall ((B3 tptp.option_trm) (F (-> tptp.char tptp.option_trm)) (X2 tptp.char) (C tptp.option_trm) (G2 (-> tptp.char tptp.option_trm)) (A tptp.set_char)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_char X2) A) (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm B3) C)) (@ (@ (@ tptp.bNF_Gr1666135339on_trm A) F) G2)))))))
% 0.26/0.69 (assert (forall ((B3 tptp.option_fml) (F (-> tptp.variable tptp.option_fml)) (X2 tptp.variable) (C tptp.option_fml) (G2 (-> tptp.variable tptp.option_fml)) (A tptp.set_variable)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_variable X2) A) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml B3) C)) (@ (@ (@ tptp.bNF_Gr600956991on_fml A) F) G2)))))))
% 0.26/0.69 (assert (forall ((B3 tptp.option_fml) (F (-> tptp.char tptp.option_fml)) (X2 tptp.char) (C tptp.option_fml) (G2 (-> tptp.char tptp.option_fml)) (A tptp.set_char)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_char X2) A) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml B3) C)) (@ (@ (@ tptp.bNF_Gr1866170027on_fml A) F) G2)))))))
% 0.26/0.69 (assert (forall ((B3 tptp.char) (F (-> tptp.variable tptp.char)) (X2 tptp.variable) (C tptp.option_trm) (G2 (-> tptp.variable tptp.option_trm)) (A tptp.set_variable)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_variable X2) A) (@ (@ tptp.member694524327on_trm (@ (@ tptp.produc1500300866on_trm B3) C)) (@ (@ (@ tptp.bNF_Gr1933470746on_trm A) F) G2)))))))
% 0.26/0.69 (assert (forall ((B3 tptp.char) (F (-> tptp.char tptp.char)) (X2 tptp.char) (C tptp.option_trm) (G2 (-> tptp.char tptp.option_trm)) (A tptp.set_char)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_char X2) A) (@ (@ tptp.member694524327on_trm (@ (@ tptp.produc1500300866on_trm B3) C)) (@ (@ (@ tptp.bNF_Gr951178926on_trm A) F) G2)))))))
% 0.26/0.69 (assert (forall ((B3 tptp.set_variable) (F (-> tptp.variable tptp.set_variable)) (X2 tptp.variable) (C tptp.trm) (G2 (-> tptp.variable tptp.trm)) (A tptp.set_variable)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_variable X2) A) (@ (@ tptp.member2122665623le_trm (@ (@ tptp.produc1482344242le_trm B3) C)) (@ (@ (@ tptp.bNF_Gr1330108682le_trm A) F) G2)))))))
% 0.26/0.69 (assert (forall ((B3 tptp.set_variable) (F (-> tptp.char tptp.set_variable)) (X2 tptp.char) (C tptp.trm) (G2 (-> tptp.char tptp.trm)) (A tptp.set_char)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_char X2) A) (@ (@ tptp.member2122665623le_trm (@ (@ tptp.produc1482344242le_trm B3) C)) (@ (@ (@ tptp.bNF_Gr852774302le_trm A) F) G2)))))))
% 0.26/0.69 (assert (forall ((Phi tptp.fml)) (= (@ tptp.uSubst1367128042_Testo (@ tptp.some_fml Phi)) (@ tptp.some_game (@ tptp.test Phi)))))
% 0.26/0.69 (assert (forall ((X2 tptp.option_fml) (Y2 tptp.option_game)) (let ((_let_1 (@ tptp.accp_option_fml tptp.uSubst954181007to_rel))) (=> (= (@ tptp.uSubst1367128042_Testo X2) Y2) (=> (@ _let_1 X2) (=> (forall ((Phi2 tptp.fml)) (let ((_let_1 (@ tptp.some_fml Phi2))) (=> (= X2 _let_1) (=> (= Y2 (@ tptp.some_game (@ tptp.test Phi2))) (not (@ (@ tptp.accp_option_fml tptp.uSubst954181007to_rel) _let_1)))))) (not (=> (= X2 tptp.none_fml) (=> (= Y2 tptp.none_game) (not (@ _let_1 tptp.none_fml)))))))))))
% 0.26/0.69 (assert (= tptp.bNF_Gr806120164on_fml (lambda ((R6 tptp.set_Pr927595527on_fml) (F2 (-> tptp.option_fml tptp.option_fml))) (@ tptp.collec670974098on_fml (lambda ((Uu tptp.produc46605351on_fml)) (exists ((A12 tptp.option_fml) (A22 tptp.option_fml)) (and (= Uu (@ (@ tptp.produc909629463on_fml (@ F2 A12)) (@ F2 A22))) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml A12) A22)) R6))))))))
% 0.26/0.69 (assert (forall ((X2 tptp.variable) (Theta tptp.option_trm)) (= (= (@ (@ tptp.uSubst834381837ssigno X2) Theta) tptp.none_game) (= Theta tptp.none_trm))))
% 0.26/0.69 (assert (forall ((X2 tptp.variable)) (= (@ (@ tptp.uSubst834381837ssigno X2) tptp.none_trm) tptp.none_game)))
% 0.26/0.69 (assert (forall ((X2 tptp.variable) (Xa tptp.option_trm) (Y2 tptp.option_game)) (=> (= (@ (@ tptp.uSubst834381837ssigno X2) Xa) Y2) (=> (forall ((Theta2 tptp.trm)) (=> (= Xa (@ tptp.some_trm Theta2)) (not (= Y2 (@ tptp.some_game (@ (@ tptp.assign X2) Theta2)))))) (not (=> (= Xa tptp.none_trm) (not (= Y2 tptp.none_game))))))))
% 0.26/0.69 (assert (forall ((X2 tptp.variable) (Xa tptp.option_trm) (Y2 tptp.option_game)) (let ((_let_1 (@ tptp.produc1743721902on_trm X2))) (let ((_let_2 (@ tptp.accp_P394694195on_trm tptp.uSubst157155628no_rel))) (=> (= (@ (@ tptp.uSubst834381837ssigno X2) Xa) Y2) (=> (@ _let_2 (@ _let_1 Xa)) (=> (forall ((Theta2 tptp.trm)) (let ((_let_1 (@ tptp.some_trm Theta2))) (=> (= Xa _let_1) (=> (= Y2 (@ tptp.some_game (@ (@ tptp.assign X2) Theta2))) (not (@ (@ tptp.accp_P394694195on_trm tptp.uSubst157155628no_rel) (@ (@ tptp.produc1743721902on_trm X2) _let_1))))))) (not (=> (= Xa tptp.none_trm) (=> (= Y2 tptp.none_game) (not (@ _let_2 (@ _let_1 tptp.none_trm)))))))))))))
% 0.26/0.69 (assert (forall ((X21 tptp.variable) (X22 tptp.trm) (Y21 tptp.variable) (Y22 tptp.trm)) (= (= (@ (@ tptp.assign X21) X22) (@ (@ tptp.assign Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.26/0.69 (assert (forall ((X21 tptp.variable) (X22 tptp.trm) (X32 tptp.fml)) (not (= (@ (@ tptp.assign X21) X22) (@ tptp.test X32)))))
% 0.26/0.69 (assert (forall ((X2 tptp.variable) (Theta tptp.trm)) (= (@ (@ tptp.uSubst834381837ssigno X2) (@ tptp.some_trm Theta)) (@ tptp.some_game (@ (@ tptp.assign X2) Theta)))))
% 0.26/0.69 (assert (forall ((X2 tptp.char) (Theta tptp.option_trm)) (= (= (@ (@ tptp.uSubst1827052306e_ODEo X2) Theta) tptp.none_game) (= Theta tptp.none_trm))))
% 0.26/0.69 (assert (forall ((X2 tptp.char)) (= (@ (@ tptp.uSubst1827052306e_ODEo X2) tptp.none_trm) tptp.none_game)))
% 0.26/0.69 (assert (forall ((X2 tptp.char) (Xa tptp.option_trm) (Y2 tptp.option_game)) (=> (= (@ (@ tptp.uSubst1827052306e_ODEo X2) Xa) Y2) (=> (forall ((Theta2 tptp.trm)) (=> (= Xa (@ tptp.some_trm Theta2)) (not (= Y2 (@ tptp.some_game (@ (@ tptp.ode X2) Theta2)))))) (not (=> (= Xa tptp.none_trm) (not (= Y2 tptp.none_game))))))))
% 0.26/0.69 (assert (forall ((X2 tptp.char) (Xa tptp.option_trm) (Y2 tptp.option_game)) (let ((_let_1 (@ tptp.produc1500300866on_trm X2))) (let ((_let_2 (@ tptp.accp_P419951815on_trm tptp.uSubst299938919Eo_rel))) (=> (= (@ (@ tptp.uSubst1827052306e_ODEo X2) Xa) Y2) (=> (@ _let_2 (@ _let_1 Xa)) (=> (forall ((Theta2 tptp.trm)) (let ((_let_1 (@ tptp.some_trm Theta2))) (=> (= Xa _let_1) (=> (= Y2 (@ tptp.some_game (@ (@ tptp.ode X2) Theta2))) (not (@ (@ tptp.accp_P419951815on_trm tptp.uSubst299938919Eo_rel) (@ (@ tptp.produc1500300866on_trm X2) _let_1))))))) (not (=> (= Xa tptp.none_trm) (=> (= Y2 tptp.none_game) (not (@ _let_2 (@ _let_1 tptp.none_trm)))))))))))))
% 0.53/1.14 (assert (forall ((X81 tptp.char) (X82 tptp.trm) (Y81 tptp.char) (Y82 tptp.trm)) (= (= (@ (@ tptp.ode X81) X82) (@ (@ tptp.ode Y81) Y82)) (and (= X81 Y81) (= X82 Y82)))))
% 0.53/1.14 (assert (forall ((X32 tptp.fml) (X81 tptp.char) (X82 tptp.trm)) (not (= (@ tptp.test X32) (@ (@ tptp.ode X81) X82)))))
% 0.53/1.14 (assert (not (not (= (@ (@ (@ tptp.uSubst516392818stappt tptp.sigma) tptp.ua) tptp.theta) tptp.none_trm))))
% 0.53/1.14 (set-info :filename cvc5---1.0.5_8267)
% 0.53/1.14 (check-sat-assuming ( true ))
% 0.53/1.14 ------- get file name : TPTP file name is ITP200^1
% 0.53/1.14 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_8267.smt2...
% 0.53/1.14 --- Run --ho-elim --full-saturate-quant at 10...
% 0.53/1.14 % SZS status Theorem for ITP200^1
% 0.53/1.14 % SZS output start Proof for ITP200^1
% 0.53/1.14 (
% 0.53/1.14 (let ((_let_1 (not (not (= (@ (@ (@ tptp.uSubst516392818stappt tptp.sigma) tptp.ua) tptp.theta) tptp.none_trm))))) (let ((_let_2 (= tptp.bNF_Gr806120164on_fml (lambda ((R6 tptp.set_Pr927595527on_fml) (F2 (-> tptp.option_fml tptp.option_fml))) (@ tptp.collec670974098on_fml (lambda ((Uu tptp.produc46605351on_fml)) (exists ((A12 tptp.option_fml) (A22 tptp.option_fml)) (and (= Uu (@ (@ tptp.produc909629463on_fml (@ F2 A12)) (@ F2 A22))) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml A12) A22)) R6))))))))) (let ((_let_3 (= tptp.bNF_Gr852774302le_trm (lambda ((A2 tptp.set_char) (F2 (-> tptp.char tptp.set_variable)) (G (-> tptp.char tptp.trm))) (@ tptp.collec575343829le_trm (lambda ((Uu tptp.produc1367888000le_trm)) (exists ((A4 tptp.char)) (and (= Uu (@ (@ tptp.produc1482344242le_trm (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_char A4) A2))))))))) (let ((_let_4 (= tptp.bNF_Gr1330108682le_trm (lambda ((A2 tptp.set_variable) (F2 (-> tptp.variable tptp.set_variable)) (G (-> tptp.variable tptp.trm))) (@ tptp.collec575343829le_trm (lambda ((Uu tptp.produc1367888000le_trm)) (exists ((A4 tptp.variable)) (and (= Uu (@ (@ tptp.produc1482344242le_trm (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_variable A4) A2))))))))) (let ((_let_5 (= tptp.bNF_Gr951178926on_trm (lambda ((A2 tptp.set_char) (F2 (-> tptp.char tptp.char)) (G (-> tptp.char tptp.option_trm))) (@ tptp.collec1756633317on_trm (lambda ((Uu tptp.produc464795408on_trm)) (exists ((A4 tptp.char)) (and (= Uu (@ (@ tptp.produc1500300866on_trm (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_char A4) A2))))))))) (let ((_let_6 (= tptp.bNF_Gr1933470746on_trm (lambda ((A2 tptp.set_variable) (F2 (-> tptp.variable tptp.char)) (G (-> tptp.variable tptp.option_trm))) (@ tptp.collec1756633317on_trm (lambda ((Uu tptp.produc464795408on_trm)) (exists ((A4 tptp.variable)) (and (= Uu (@ (@ tptp.produc1500300866on_trm (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_variable A4) A2))))))))) (let ((_let_7 (= tptp.bNF_Gr1866170027on_fml (lambda ((A2 tptp.set_char) (F2 (-> tptp.char tptp.option_fml)) (G (-> tptp.char tptp.option_fml))) (@ tptp.collec670974098on_fml (lambda ((Uu tptp.produc46605351on_fml)) (exists ((A4 tptp.char)) (and (= Uu (@ (@ tptp.produc909629463on_fml (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_char A4) A2))))))))) (let ((_let_8 (= tptp.bNF_Gr600956991on_fml (lambda ((A2 tptp.set_variable) (F2 (-> tptp.variable tptp.option_fml)) (G (-> tptp.variable tptp.option_fml))) (@ tptp.collec670974098on_fml (lambda ((Uu tptp.produc46605351on_fml)) (exists ((A4 tptp.variable)) (and (= Uu (@ (@ tptp.produc909629463on_fml (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_variable A4) A2))))))))) (let ((_let_9 (= tptp.bNF_Gr1666135339on_trm (lambda ((A2 tptp.set_char) (F2 (-> tptp.char tptp.option_trm)) (G (-> tptp.char tptp.option_trm))) (@ tptp.collec1697116690on_trm (lambda ((Uu tptp.produc1072747943on_trm)) (exists ((A4 tptp.char)) (and (= Uu (@ (@ tptp.produc709594775on_trm (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_char A4) A2))))))))) (let ((_let_10 (= tptp.bNF_Gr400922303on_trm (lambda ((A2 tptp.set_variable) (F2 (-> tptp.variable tptp.option_trm)) (G (-> tptp.variable tptp.option_trm))) (@ tptp.collec1697116690on_trm (lambda ((Uu tptp.produc1072747943on_trm)) (exists ((A4 tptp.variable)) (and (= Uu (@ (@ tptp.produc709594775on_trm (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_variable A4) A2))))))))) (let ((_let_11 (= tptp.bNF_Gr756940202on_fml (lambda ((A2 tptp.set_char) (F2 (-> tptp.char tptp.option_game)) (G (-> tptp.char tptp.option_fml))) (@ tptp.collec749447393on_fml (lambda ((Uu tptp.produc1739631244on_fml)) (exists ((A4 tptp.char)) (and (= Uu (@ (@ tptp.produc2124676926on_fml (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_char A4) A2))))))))) (let ((_let_12 (= tptp.bNF_Gr2142503190on_fml (lambda ((A2 tptp.set_variable) (F2 (-> tptp.variable tptp.option_game)) (G (-> tptp.variable tptp.option_fml))) (@ tptp.collec749447393on_fml (lambda ((Uu tptp.produc1739631244on_fml)) (exists ((A4 tptp.variable)) (and (= Uu (@ (@ tptp.produc2124676926on_fml (@ F2 A4)) (@ G A4))) (@ (@ tptp.member_variable A4) A2))))))))) (let ((_let_13 (= (@ tptp.uSubst1367128042_Testo tptp.none_fml) tptp.none_game))) (let ((_let_14 (= tptp.denota1419872369iation (lambda ((Nu3 (-> tptp.variable tptp.real)) (Nu4 (-> tptp.variable tptp.real)) (U2 tptp.set_variable)) (forall ((I tptp.variable)) (=> (not (@ (@ tptp.member_variable I) U2)) (= (@ Nu3 I) (@ Nu4 I)))))))) (let ((_let_15 (= tptp.ord_le282106107riable (lambda ((A2 tptp.set_variable) (B2 tptp.set_variable)) (@ (@ tptp.ord_le1407353162able_o (lambda ((X3 tptp.variable)) (@ (@ tptp.member_variable X3) A2))) (lambda ((X3 tptp.variable)) (@ (@ tptp.member_variable X3) B2))))))) (let ((_let_16 (= tptp.ord_less_eq_set_char (lambda ((A2 tptp.set_char) (B2 tptp.set_char)) (@ (@ tptp.ord_less_eq_char_o (lambda ((X3 tptp.char)) (@ (@ tptp.member_char X3) A2))) (lambda ((X3 tptp.char)) (@ (@ tptp.member_char X3) B2))))))) (let ((_let_17 (@ (@ (@ tptp.uSubst516392804stappf tptp.sigma) tptp.ua) (@ (@ tptp.geq tptp.theta) tptp.eta)))) (let ((_let_18 (not (= _let_17 tptp.none_fml)))) (let ((_let_19 (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (=> (not (= (@ (@ (@ tptp.uSubst516392804stappf Sigma) U) (@ (@ tptp.geq Theta) Eta)) tptp.none_fml)) (and (not (= (@ _let_1 Theta) tptp.none_trm)) (not (= (@ _let_1 Eta) tptp.none_trm)))))))) (let ((_let_20 (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (ho_491 (ho_490 k_489 Sigma) U))) (let ((_let_2 (ho_488 (ho_491 (ho_490 k_489 tptp.sigma) tptp.ua) tptp.theta))) (or (= tptp.none_fml (ho_483 (ho_693 (ho_692 k_691 Sigma) U) (ho_690 (ho_689 k_688 Theta) Eta))) (and (not (= _let_2 (ho_488 _let_1 Theta))) (not (= _let_2 (ho_488 _let_1 Eta)))))))))) (let ((_let_21 (= tptp.none_fml (ho_483 (ho_693 (ho_692 k_691 tptp.sigma) tptp.ua) (ho_690 (ho_689 k_688 tptp.theta) tptp.eta))))) (let ((_let_22 (EQ_RESOLVE (ASSUME :args (_let_19)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))) (SYMM (ASSUME :args (_let_13))) (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_15)) (ASSUME :args (_let_16))) :args ((forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (or (= tptp.none_fml (@ (@ (@ tptp.uSubst516392804stappf Sigma) U) (@ (@ tptp.geq Theta) Eta))) (and (not (= tptp.none_trm (@ _let_1 Theta))) (not (= tptp.none_trm (@ _let_1 Eta))))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ (@ tptp.uSubst516392818stappt tptp.sigma) tptp.ua) tptp.theta))) (let ((_let_2 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (or (= tptp.none_fml (@ (@ (@ tptp.uSubst516392804stappf Sigma) U) (@ (@ tptp.geq Theta) Eta))) (and (not (= (@ _let_2 Theta) _let_1)) (not (= (@ _let_2 Eta) _let_1))))))) _let_20))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_22 :args (tptp.sigma tptp.ua tptp.theta tptp.eta QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_20)))) :args ((or _let_21 (not _let_20)))) (EQ_RESOLVE (ASSUME :args (_let_18)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (= tptp.none_fml _let_17)) (not _let_21)))))) _let_22 :args (false true _let_21 false _let_20)) :args ((@ (@ (@ tptp.denota1419872369iation tptp.nu) tptp.omega) tptp.u) _let_19 _let_18 (= tptp.none_trm tptp.none_trm) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (V tptp.set_variable)) (let ((_let_1 (@ tptp.uSubst516392818stappt Sigma))) (let ((_let_2 (@ (@ _let_1 V) Theta))) (let ((_let_3 (@ (@ _let_1 U) Theta))) (=> (not (= _let_3 tptp.none_trm)) (=> (not (= _let_2 tptp.none_trm)) (= _let_3 _let_2))))))) (@ (@ (@ tptp.denota1419872369iation tptp.nu2) tptp.omega2) tptp.ua) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (=> (not (= (@ _let_1 (@ (@ tptp.plus Theta) Eta)) tptp.none_trm)) (and (not (= (@ _let_1 Theta) tptp.none_trm)) (not (= (@ _let_1 Eta) tptp.none_trm)))))) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (=> (not (= (@ _let_1 (@ (@ tptp.times Theta) Eta)) tptp.none_trm)) (and (not (= (@ _let_1 Theta) tptp.none_trm)) (not (= (@ _let_1 Eta) tptp.none_trm)))))) (forall ((V tptp.set_variable) (U tptp.set_variable) (Sigma tptp.produc1418842292n_game) (Theta tptp.trm)) (let ((_let_1 (@ tptp.uSubst516392818stappt Sigma))) (let ((_let_2 (@ (@ _let_1 U) Theta))) (=> (@ (@ tptp.ord_le282106107riable V) U) (=> (not (= _let_2 tptp.none_trm)) (= _let_2 (@ (@ _let_1 V) Theta))))))) (= (@ tptp.uSubst716837505ntialo tptp.none_trm) tptp.none_trm) (forall ((Theta tptp.option_trm)) (= (= (@ tptp.uSubst716837505ntialo Theta) tptp.none_trm) (= Theta tptp.none_trm))) (forall ((Eta tptp.option_trm)) (= (@ (@ tptp.uSubst141955042_Pluso tptp.none_trm) Eta) tptp.none_trm)) (forall ((Eta tptp.option_trm)) (= (@ (@ tptp.uSubst918876924Timeso tptp.none_trm) Eta) tptp.none_trm)) (forall ((Theta tptp.option_trm) (Eta tptp.option_trm)) (= (= (@ (@ tptp.uSubst141955042_Pluso Theta) Eta) tptp.none_trm) (or (= Theta tptp.none_trm) (= Eta tptp.none_trm)))) (forall ((Theta tptp.option_trm) (Eta tptp.option_trm)) (= (= (@ (@ tptp.uSubst918876924Timeso Theta) Eta) tptp.none_trm) (or (= Theta tptp.none_trm) (= Eta tptp.none_trm)))) (forall ((Eta tptp.option_trm)) (= (@ (@ tptp.uSubst152838031e_Geqo tptp.none_trm) Eta) tptp.none_fml)) (forall ((V tptp.set_variable) (U tptp.set_variable) (Sigma tptp.produc1418842292n_game) (Phi tptp.fml)) (let ((_let_1 (@ tptp.uSubst516392804stappf Sigma))) (let ((_let_2 (@ (@ _let_1 U) Phi))) (=> (@ (@ tptp.ord_le282106107riable V) U) (=> (not (= _let_2 tptp.none_fml)) (= _let_2 (@ (@ _let_1 V) Phi))))))) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Phi tptp.fml) (V tptp.set_variable)) (let ((_let_1 (@ tptp.uSubst516392804stappf Sigma))) (let ((_let_2 (@ (@ _let_1 V) Phi))) (let ((_let_3 (@ (@ _let_1 U) Phi))) (=> (not (= _let_3 tptp.none_fml)) (=> (not (= _let_2 tptp.none_fml)) (= _let_3 _let_2))))))) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (= (@ _let_1 (@ (@ tptp.plus Theta) Eta)) (@ (@ tptp.uSubst141955042_Pluso (@ _let_1 Theta)) (@ _let_1 Eta))))) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (= (@ _let_1 (@ (@ tptp.times Theta) Eta)) (@ (@ tptp.uSubst918876924Timeso (@ _let_1 Theta)) (@ _let_1 Eta))))) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (= (@ (@ (@ tptp.uSubst516392804stappf Sigma) U) (@ (@ tptp.geq Theta) Eta)) (@ (@ tptp.uSubst152838031e_Geqo (@ _let_1 Theta)) (@ _let_1 Eta))))) (forall ((Theta tptp.option_trm) (Eta tptp.option_trm)) (= (= (@ (@ tptp.uSubst152838031e_Geqo Theta) Eta) tptp.none_fml) (or (= Theta tptp.none_trm) (= Eta tptp.none_trm)))) (forall ((X61 tptp.trm) (X62 tptp.trm) (Y61 tptp.trm) (Y62 tptp.trm)) (= (= (@ (@ tptp.times X61) X62) (@ (@ tptp.times Y61) Y62)) (and (= X61 Y61) (= X62 Y62)))) (forall ((X51 tptp.trm) (X52 tptp.trm) (Y51 tptp.trm) (Y52 tptp.trm)) (= (= (@ (@ tptp.plus X51) X52) (@ (@ tptp.plus Y51) Y52)) (and (= X51 Y51) (= X52 Y52)))) (forall ((X21 tptp.trm) (X22 tptp.trm) (Y21 tptp.trm) (Y22 tptp.trm)) (= (= (@ (@ tptp.geq X21) X22) (@ (@ tptp.geq Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))) (forall ((U tptp.set_variable) (V tptp.set_variable) (Omega (-> tptp.variable tptp.real)) (Nu (-> tptp.variable tptp.real))) (let ((_let_1 (@ (@ tptp.denota1419872369iation Omega) Nu))) (=> (@ (@ tptp.ord_le282106107riable U) V) (=> (@ _let_1 U) (@ _let_1 V))))) (forall ((A tptp.set_char) (B tptp.set_char)) (=> (forall ((X tptp.char)) (let ((_let_1 (@ tptp.member_char X))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_char A) B))) (forall ((A tptp.set_variable) (B tptp.set_variable)) (=> (forall ((X tptp.variable)) (let ((_let_1 (@ tptp.member_variable X))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le282106107riable A) B))) (forall ((A tptp.set_variable) (B tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable A) B) (=> (@ (@ tptp.ord_le282106107riable B) A) (= A B)))) (forall ((X51 tptp.trm) (X52 tptp.trm) (X61 tptp.trm) (X62 tptp.trm)) (not (= (@ (@ tptp.plus X51) X52) (@ (@ tptp.times X61) X62)))) (forall ((X2 tptp.set_variable)) (@ (@ tptp.ord_le282106107riable X2) X2)) (forall ((Nu (-> tptp.variable tptp.real)) (Nu2 (-> tptp.variable tptp.real))) (@ (@ (@ tptp.denota1419872369iation Nu) Nu2) (@ tptp.collect_variable (lambda ((X3 tptp.variable)) true)))) (forall ((A tptp.set_char) (P (-> tptp.char Bool))) (@ (@ tptp.ord_less_eq_set_char (@ tptp.collect_char (lambda ((X3 tptp.char)) (and (@ (@ tptp.member_char X3) A) (@ P X3))))) A)) (forall ((A tptp.set_variable) (P (-> tptp.variable Bool))) (@ (@ tptp.ord_le282106107riable (@ tptp.collect_variable (lambda ((X3 tptp.variable)) (and (@ (@ tptp.member_variable X3) A) (@ P X3))))) A)) _let_16 _let_15 (forall ((B3 tptp.set_variable) (A3 tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable B3) A3) (=> (@ (@ tptp.ord_le282106107riable A3) B3) (= A3 B3)))) (= (lambda ((Y tptp.set_variable) (Z tptp.set_variable)) (= Y Z)) (lambda ((A4 tptp.set_variable) (B4 tptp.set_variable)) (and (@ (@ tptp.ord_le282106107riable B4) A4) (@ (@ tptp.ord_le282106107riable A4) B4)))) (forall ((B3 tptp.set_variable) (A3 tptp.set_variable) (C tptp.set_variable)) (let ((_let_1 (@ tptp.ord_le282106107riable C))) (=> (@ (@ tptp.ord_le282106107riable B3) A3) (=> (@ _let_1 B3) (@ _let_1 A3))))) (forall ((A3 tptp.set_variable)) (@ (@ tptp.ord_le282106107riable A3) A3)) (forall ((X2 tptp.set_variable) (Y2 tptp.set_variable) (Z2 tptp.set_variable)) (let ((_let_1 (@ tptp.ord_le282106107riable X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_le282106107riable Y2) Z2) (@ _let_1 Z2))))) (forall ((A3 tptp.set_variable) (B3 tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable A3) B3) (=> (@ (@ tptp.ord_le282106107riable B3) A3) (= A3 B3)))) (forall ((A3 tptp.set_variable) (B3 tptp.set_variable) (C tptp.set_variable)) (let ((_let_1 (@ tptp.ord_le282106107riable A3))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))) (forall ((A3 tptp.set_variable) (B3 tptp.set_variable) (C tptp.set_variable)) (=> (= A3 B3) (=> (@ (@ tptp.ord_le282106107riable B3) C) (@ (@ tptp.ord_le282106107riable A3) C)))) (= (lambda ((Y tptp.set_variable) (Z tptp.set_variable)) (= Y Z)) (lambda ((A4 tptp.set_variable) (B4 tptp.set_variable)) (and (@ (@ tptp.ord_le282106107riable A4) B4) (@ (@ tptp.ord_le282106107riable B4) A4)))) (forall ((Y2 tptp.set_variable) (X2 tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable Y2) X2) (= (@ (@ tptp.ord_le282106107riable X2) Y2) (= X2 Y2)))) (forall ((A3 tptp.variable) (P (-> tptp.variable Bool))) (= (@ (@ tptp.member_variable A3) (@ tptp.collect_variable P)) (@ P A3))) (forall ((A3 tptp.char) (P (-> tptp.char Bool))) (= (@ (@ tptp.member_char A3) (@ tptp.collect_char P)) (@ P A3))) (forall ((A tptp.set_variable)) (= (@ tptp.collect_variable (lambda ((X3 tptp.variable)) (@ (@ tptp.member_variable X3) A))) A)) (forall ((A tptp.set_char)) (= (@ tptp.collect_char (lambda ((X3 tptp.char)) (@ (@ tptp.member_char X3) A))) A)) (forall ((P (-> tptp.variable Bool)) (Q (-> tptp.variable Bool))) (=> (forall ((X tptp.variable)) (= (@ P X) (@ Q X))) (= (@ tptp.collect_variable P) (@ tptp.collect_variable Q)))) (forall ((P (-> tptp.char Bool)) (Q (-> tptp.char Bool))) (=> (forall ((X tptp.char)) (= (@ P X) (@ Q X))) (= (@ tptp.collect_char P) (@ tptp.collect_char Q)))) (forall ((A3 tptp.set_variable) (B3 tptp.set_variable) (C tptp.set_variable)) (let ((_let_1 (@ tptp.ord_le282106107riable A3))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_le282106107riable B3) C) (@ _let_1 C))))) (forall ((X2 tptp.set_variable) (Y2 tptp.set_variable)) (=> (= X2 Y2) (@ (@ tptp.ord_le282106107riable X2) Y2))) (forall ((X2 tptp.set_variable) (Y2 tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable X2) Y2) (=> (@ (@ tptp.ord_le282106107riable Y2) X2) (= X2 Y2)))) (= (lambda ((Y tptp.set_variable) (Z tptp.set_variable)) (= Y Z)) (lambda ((X3 tptp.set_variable) (Y3 tptp.set_variable)) (and (@ (@ tptp.ord_le282106107riable X3) Y3) (@ (@ tptp.ord_le282106107riable Y3) X3)))) (forall ((A3 tptp.set_variable) (B3 tptp.set_variable) (F (-> tptp.set_variable tptp.set_variable)) (C tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable A3) B3) (=> (= (@ F B3) C) (=> (forall ((X tptp.set_variable) (Y4 tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable X) Y4) (@ (@ tptp.ord_le282106107riable (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_le282106107riable (@ F A3)) C))))) (forall ((A3 tptp.set_variable) (F (-> tptp.set_variable tptp.set_variable)) (B3 tptp.set_variable) (C tptp.set_variable)) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_le282106107riable B3) C) (=> (forall ((X tptp.set_variable) (Y4 tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable X) Y4) (@ (@ tptp.ord_le282106107riable (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_le282106107riable A3) (@ F C)))))) (forall ((A3 tptp.set_variable) (B3 tptp.set_variable) (F (-> tptp.set_variable tptp.set_variable)) (C tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable A3) B3) (=> (@ (@ tptp.ord_le282106107riable (@ F B3)) C) (=> (forall ((X tptp.set_variable) (Y4 tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable X) Y4) (@ (@ tptp.ord_le282106107riable (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_le282106107riable (@ F A3)) C))))) (forall ((A3 tptp.set_variable) (F (-> tptp.set_variable tptp.set_variable)) (B3 tptp.set_variable) (C tptp.set_variable)) (let ((_let_1 (@ tptp.ord_le282106107riable A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_le282106107riable B3) C) (=> (forall ((X tptp.set_variable) (Y4 tptp.set_variable)) (=> (@ (@ tptp.ord_le282106107riable X) Y4) (@ (@ tptp.ord_le282106107riable (@ F X)) (@ F Y4)))) (@ _let_1 (@ F C))))))) (forall ((P (-> tptp.char Bool)) (Q (-> tptp.char Bool))) (= (@ (@ tptp.ord_less_eq_set_char (@ tptp.collect_char P)) (@ tptp.collect_char Q)) (forall ((X3 tptp.char)) (=> (@ P X3) (@ Q X3))))) (forall ((P (-> tptp.variable Bool)) (Q (-> tptp.variable Bool))) (= (@ (@ tptp.ord_le282106107riable (@ tptp.collect_variable P)) (@ tptp.collect_variable Q)) (forall ((X3 tptp.variable)) (=> (@ P X3) (@ Q X3))))) (= (lambda ((Y tptp.set_variable) (Z tptp.set_variable)) (= Y Z)) (lambda ((A2 tptp.set_variable) (B2 tptp.set_variable)) (and (@ (@ tptp.ord_le282106107riable A2) B2) (@ (@ tptp.ord_le282106107riable B2) A2)))) (forall ((A tptp.set_variable) (B tptp.set_variable) (C2 tptp.set_variable)) (let ((_let_1 (@ tptp.ord_le282106107riable A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le282106107riable B) C2) (@ _let_1 C2))))) (forall ((P (-> tptp.char Bool)) (Q (-> tptp.char Bool))) (=> (forall ((X tptp.char)) (=> (@ P X) (@ Q X))) (@ (@ tptp.ord_less_eq_set_char (@ tptp.collect_char P)) (@ tptp.collect_char Q)))) (forall ((P (-> tptp.variable Bool)) (Q (-> tptp.variable Bool))) (=> (forall ((X tptp.variable)) (=> (@ P X) (@ Q X))) (@ (@ tptp.ord_le282106107riable (@ tptp.collect_variable P)) (@ tptp.collect_variable Q)))) (forall ((A tptp.set_variable)) (@ (@ tptp.ord_le282106107riable A) A)) (= tptp.ord_less_eq_set_char (lambda ((A2 tptp.set_char) (B2 tptp.set_char)) (forall ((T tptp.char)) (let ((_let_1 (@ tptp.member_char T))) (=> (@ _let_1 A2) (@ _let_1 B2)))))) (= tptp.ord_le282106107riable (lambda ((A2 tptp.set_variable) (B2 tptp.set_variable)) (forall ((T tptp.variable)) (let ((_let_1 (@ tptp.member_variable T))) (=> (@ _let_1 A2) (@ _let_1 B2)))))) (forall ((A tptp.set_variable) (B tptp.set_variable)) (=> (= A B) (@ (@ tptp.ord_le282106107riable B) A))) (forall ((A tptp.set_variable) (B tptp.set_variable)) (=> (= A B) (@ (@ tptp.ord_le282106107riable A) B))) (= tptp.ord_less_eq_set_char (lambda ((A2 tptp.set_char) (B2 tptp.set_char)) (forall ((X3 tptp.char)) (let ((_let_1 (@ tptp.member_char X3))) (=> (@ _let_1 A2) (@ _let_1 B2)))))) (= tptp.ord_le282106107riable (lambda ((A2 tptp.set_variable) (B2 tptp.set_variable)) (forall ((X3 tptp.variable)) (let ((_let_1 (@ tptp.member_variable X3))) (=> (@ _let_1 A2) (@ _let_1 B2)))))) (forall ((A tptp.set_variable) (B tptp.set_variable)) (=> (= A B) (not (=> (@ (@ tptp.ord_le282106107riable A) B) (not (@ (@ tptp.ord_le282106107riable B) A)))))) (forall ((A tptp.set_char) (B tptp.set_char) (C tptp.char)) (let ((_let_1 (@ tptp.member_char C))) (=> (@ (@ tptp.ord_less_eq_set_char A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_variable) (B tptp.set_variable) (C tptp.variable)) (let ((_let_1 (@ tptp.member_variable C))) (=> (@ (@ tptp.ord_le282106107riable A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_char) (B tptp.set_char) (X2 tptp.char)) (let ((_let_1 (@ tptp.member_char X2))) (=> (@ (@ tptp.ord_less_eq_set_char A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_variable) (B tptp.set_variable) (X2 tptp.variable)) (let ((_let_1 (@ tptp.member_variable X2))) (=> (@ (@ tptp.ord_le282106107riable A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((Omega (-> tptp.variable tptp.real)) (Nu (-> tptp.variable tptp.real)) (U tptp.set_variable)) (=> (@ (@ (@ tptp.denota1419872369iation Omega) Nu) U) (@ (@ (@ tptp.denota1419872369iation Nu) Omega) U))) (forall ((Nu (-> tptp.variable tptp.real)) (V tptp.set_variable)) (@ (@ (@ tptp.denota1419872369iation Nu) Nu) V)) (= tptp.denota1419872369iation (lambda ((Omega2 (-> tptp.variable tptp.real)) (Nu3 (-> tptp.variable tptp.real)) (__flatten_var_0 tptp.set_variable)) (@ (@ (@ tptp.denota1419872369iation Nu3) Omega2) __flatten_var_0))) _let_14 (forall ((R tptp.set_char) (S tptp.set_char)) (= (@ (@ tptp.ord_less_eq_char_o (lambda ((X3 tptp.char)) (@ (@ tptp.member_char X3) R))) (lambda ((X3 tptp.char)) (@ (@ tptp.member_char X3) S))) (@ (@ tptp.ord_less_eq_set_char R) S))) (forall ((R tptp.set_variable) (S tptp.set_variable)) (= (@ (@ tptp.ord_le1407353162able_o (lambda ((X3 tptp.variable)) (@ (@ tptp.member_variable X3) R))) (lambda ((X3 tptp.variable)) (@ (@ tptp.member_variable X3) S))) (@ (@ tptp.ord_le282106107riable R) S))) (forall ((B tptp.set_char) (A tptp.set_char) (P (-> tptp.char Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_char B))) (=> (@ _let_1 A) (= (@ _let_1 (@ tptp.collect_char (lambda ((X3 tptp.char)) (and (@ (@ tptp.member_char X3) A) (@ P X3))))) (forall ((X3 tptp.char)) (=> (@ (@ tptp.member_char X3) B) (@ P X3))))))) (forall ((B tptp.set_variable) (A tptp.set_variable) (P (-> tptp.variable Bool))) (let ((_let_1 (@ tptp.ord_le282106107riable B))) (=> (@ _let_1 A) (= (@ _let_1 (@ tptp.collect_variable (lambda ((X3 tptp.variable)) (and (@ (@ tptp.member_variable X3) A) (@ P X3))))) (forall ((X3 tptp.variable)) (=> (@ (@ tptp.member_variable X3) B) (@ P X3))))))) (forall ((B tptp.set_char) (A tptp.set_char) (Q (-> tptp.char Bool)) (P (-> tptp.char Bool))) (=> (@ (@ tptp.ord_less_eq_set_char B) A) (=> (forall ((X tptp.char)) (=> (@ (@ tptp.member_char X) B) (=> (@ Q X) (@ P X)))) (@ (@ tptp.ord_less_eq_set_char (@ tptp.collect_char (lambda ((X3 tptp.char)) (and (@ (@ tptp.member_char X3) B) (@ Q X3))))) (@ tptp.collect_char (lambda ((X3 tptp.char)) (and (@ (@ tptp.member_char X3) A) (@ P X3)))))))) (forall ((B tptp.set_variable) (A tptp.set_variable) (Q (-> tptp.variable Bool)) (P (-> tptp.variable Bool))) (=> (@ (@ tptp.ord_le282106107riable B) A) (=> (forall ((X tptp.variable)) (=> (@ (@ tptp.member_variable X) B) (=> (@ Q X) (@ P X)))) (@ (@ tptp.ord_le282106107riable (@ tptp.collect_variable (lambda ((X3 tptp.variable)) (and (@ (@ tptp.member_variable X3) B) (@ Q X3))))) (@ tptp.collect_variable (lambda ((X3 tptp.variable)) (and (@ (@ tptp.member_variable X3) A) (@ P X3)))))))) (forall ((X4 tptp.set_char) (P (-> tptp.char Bool))) (@ (@ tptp.ord_less_eq_set_char (@ tptp.collect_char (lambda ((X3 tptp.char)) (and (@ (@ tptp.member_char X3) X4) (@ P X3))))) X4)) (forall ((X4 tptp.set_variable) (P (-> tptp.variable Bool))) (@ (@ tptp.ord_le282106107riable (@ tptp.collect_variable (lambda ((X3 tptp.variable)) (and (@ (@ tptp.member_variable X3) X4) (@ P X3))))) X4)) (forall ((X2 tptp.char) (Z3 tptp.set_char) (X4 tptp.set_char) (P (-> tptp.char Bool))) (=> (@ (@ tptp.member_char X2) Z3) (=> (@ (@ tptp.ord_less_eq_set_char Z3) (@ tptp.collect_char (lambda ((X3 tptp.char)) (and (@ (@ tptp.member_char X3) X4) (@ P X3))))) (@ P X2)))) (forall ((X2 tptp.variable) (Z3 tptp.set_variable) (X4 tptp.set_variable) (P (-> tptp.variable Bool))) (=> (@ (@ tptp.member_variable X2) Z3) (=> (@ (@ tptp.ord_le282106107riable Z3) (@ tptp.collect_variable (lambda ((X3 tptp.variable)) (and (@ (@ tptp.member_variable X3) X4) (@ P X3))))) (@ P X2)))) (forall ((A tptp.set_char) (P (-> tptp.char Bool)) (Q (-> tptp.char Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_char A))) (= (@ _let_1 (@ tptp.collect_char (lambda ((X3 tptp.char)) (and (@ P X3) (@ Q X3))))) (and (@ _let_1 (@ tptp.collect_char P)) (@ _let_1 (@ tptp.collect_char Q)))))) (forall ((A tptp.set_variable) (P (-> tptp.variable Bool)) (Q (-> tptp.variable Bool))) (let ((_let_1 (@ tptp.ord_le282106107riable A))) (= (@ _let_1 (@ tptp.collect_variable (lambda ((X3 tptp.variable)) (and (@ P X3) (@ Q X3))))) (and (@ _let_1 (@ tptp.collect_variable P)) (@ _let_1 (@ tptp.collect_variable Q)))))) (forall ((X2 tptp.option_trm) (Xa tptp.option_trm) (Y2 tptp.option_trm)) (let ((_let_1 (not (= Y2 tptp.none_trm)))) (=> (= (@ (@ tptp.uSubst141955042_Pluso X2) Xa) Y2) (=> (forall ((Theta2 tptp.trm)) (=> (= X2 (@ tptp.some_trm Theta2)) (forall ((Eta2 tptp.trm)) (=> (= Xa (@ tptp.some_trm Eta2)) (not (= Y2 (@ tptp.some_trm (@ (@ tptp.plus Theta2) Eta2)))))))) (=> (=> (= X2 tptp.none_trm) _let_1) (not (=> (exists ((V2 tptp.trm)) (= X2 (@ tptp.some_trm V2))) (=> (= Xa tptp.none_trm) _let_1)))))))) (forall ((X2 tptp.option_trm) (Xa tptp.option_trm) (Y2 tptp.option_trm)) (let ((_let_1 (not (= Y2 tptp.none_trm)))) (=> (= (@ (@ tptp.uSubst918876924Timeso X2) Xa) Y2) (=> (forall ((Theta2 tptp.trm)) (=> (= X2 (@ tptp.some_trm Theta2)) (forall ((Eta2 tptp.trm)) (=> (= Xa (@ tptp.some_trm Eta2)) (not (= Y2 (@ tptp.some_trm (@ (@ tptp.times Theta2) Eta2)))))))) (=> (=> (= X2 tptp.none_trm) _let_1) (not (=> (exists ((V2 tptp.trm)) (= X2 (@ tptp.some_trm V2))) (=> (= Xa tptp.none_trm) _let_1)))))))) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm)) (let ((_let_1 (@ tptp.uSubst516392818stappt Sigma))) (= (@ (@ _let_1 U) (@ tptp.differential Theta)) (@ tptp.uSubst716837505ntialo (@ (@ _let_1 (@ tptp.collect_variable (lambda ((X3 tptp.variable)) true))) Theta))))) (forall ((X23 tptp.trm) (Y23 tptp.trm)) (= (= (@ tptp.some_trm X23) (@ tptp.some_trm Y23)) (= X23 Y23))) (forall ((X23 tptp.fml) (Y23 tptp.fml)) (= (= (@ tptp.some_fml X23) (@ tptp.some_fml Y23)) (= X23 Y23))) (forall ((X23 tptp.game) (Y23 tptp.game)) (= (= (@ tptp.some_game X23) (@ tptp.some_game Y23)) (= X23 Y23))) (forall ((X7 tptp.trm) (Y7 tptp.trm)) (= (= (@ tptp.differential X7) (@ tptp.differential Y7)) (= X7 Y7))) (forall ((X2 tptp.option_trm)) (= (forall ((Y3 tptp.trm)) (not (= X2 (@ tptp.some_trm Y3)))) (= X2 tptp.none_trm))) (forall ((X2 tptp.option_fml)) (= (forall ((Y3 tptp.fml)) (not (= X2 (@ tptp.some_fml Y3)))) (= X2 tptp.none_fml))) (forall ((X2 tptp.option_game)) (= (forall ((Y3 tptp.game)) (not (= X2 (@ tptp.some_game Y3)))) (= X2 tptp.none_game))) (forall ((X2 tptp.option_trm)) (= (not (= X2 tptp.none_trm)) (exists ((Y3 tptp.trm)) (= X2 (@ tptp.some_trm Y3))))) (forall ((X2 tptp.option_fml)) (= (not (= X2 tptp.none_fml)) (exists ((Y3 tptp.fml)) (= X2 (@ tptp.some_fml Y3))))) (forall ((X2 tptp.option_game)) (= (not (= X2 tptp.none_game)) (exists ((Y3 tptp.game)) (= X2 (@ tptp.some_game Y3))))) (= tptp.some_trm tptp.some_trm) (forall ((Theta tptp.trm)) (= (@ tptp.uSubst716837505ntialo (@ tptp.some_trm Theta)) (@ tptp.some_trm (@ tptp.differential Theta)))) (forall ((X2 tptp.option_trm) (P (-> tptp.option_trm tptp.option_trm Bool)) (Y2 tptp.option_trm)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_trm) _let_1) (=> (=> (= Y2 tptp.none_trm) _let_1) (=> (forall ((A5 tptp.trm) (B5 tptp.trm)) (=> (= X2 (@ tptp.some_trm A5)) (=> (= Y2 (@ tptp.some_trm B5)) (@ (@ P X2) Y2)))) _let_1))))) (forall ((X2 tptp.option_trm) (P (-> tptp.option_trm tptp.option_fml Bool)) (Y2 tptp.option_fml)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_trm) _let_1) (=> (=> (= Y2 tptp.none_fml) _let_1) (=> (forall ((A5 tptp.trm) (B5 tptp.fml)) (=> (= X2 (@ tptp.some_trm A5)) (=> (= Y2 (@ tptp.some_fml B5)) (@ (@ P X2) Y2)))) _let_1))))) (forall ((X2 tptp.option_trm) (P (-> tptp.option_trm tptp.option_game Bool)) (Y2 tptp.option_game)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_trm) _let_1) (=> (=> (= Y2 tptp.none_game) _let_1) (=> (forall ((A5 tptp.trm) (B5 tptp.game)) (=> (= X2 (@ tptp.some_trm A5)) (=> (= Y2 (@ tptp.some_game B5)) (@ (@ P X2) Y2)))) _let_1))))) (forall ((X2 tptp.option_fml) (P (-> tptp.option_fml tptp.option_trm Bool)) (Y2 tptp.option_trm)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_fml) _let_1) (=> (=> (= Y2 tptp.none_trm) _let_1) (=> (forall ((A5 tptp.fml) (B5 tptp.trm)) (=> (= X2 (@ tptp.some_fml A5)) (=> (= Y2 (@ tptp.some_trm B5)) (@ (@ P X2) Y2)))) _let_1))))) (forall ((X2 tptp.option_fml) (P (-> tptp.option_fml tptp.option_fml Bool)) (Y2 tptp.option_fml)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_fml) _let_1) (=> (=> (= Y2 tptp.none_fml) _let_1) (=> (forall ((A5 tptp.fml) (B5 tptp.fml)) (=> (= X2 (@ tptp.some_fml A5)) (=> (= Y2 (@ tptp.some_fml B5)) (@ (@ P X2) Y2)))) _let_1))))) (forall ((X2 tptp.option_fml) (P (-> tptp.option_fml tptp.option_game Bool)) (Y2 tptp.option_game)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_fml) _let_1) (=> (=> (= Y2 tptp.none_game) _let_1) (=> (forall ((A5 tptp.fml) (B5 tptp.game)) (=> (= X2 (@ tptp.some_fml A5)) (=> (= Y2 (@ tptp.some_game B5)) (@ (@ P X2) Y2)))) _let_1))))) (forall ((X2 tptp.option_game) (P (-> tptp.option_game tptp.option_trm Bool)) (Y2 tptp.option_trm)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_game) _let_1) (=> (=> (= Y2 tptp.none_trm) _let_1) (=> (forall ((A5 tptp.game) (B5 tptp.trm)) (=> (= X2 (@ tptp.some_game A5)) (=> (= Y2 (@ tptp.some_trm B5)) (@ (@ P X2) Y2)))) _let_1))))) (forall ((X2 tptp.option_game) (P (-> tptp.option_game tptp.option_fml Bool)) (Y2 tptp.option_fml)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_game) _let_1) (=> (=> (= Y2 tptp.none_fml) _let_1) (=> (forall ((A5 tptp.game) (B5 tptp.fml)) (=> (= X2 (@ tptp.some_game A5)) (=> (= Y2 (@ tptp.some_fml B5)) (@ (@ P X2) Y2)))) _let_1))))) (forall ((X2 tptp.option_game) (P (-> tptp.option_game tptp.option_game Bool)) (Y2 tptp.option_game)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_game) _let_1) (=> (=> (= Y2 tptp.none_game) _let_1) (=> (forall ((A5 tptp.game) (B5 tptp.game)) (=> (= X2 (@ tptp.some_game A5)) (=> (= Y2 (@ tptp.some_game B5)) (@ (@ P X2) Y2)))) _let_1))))) (= (lambda ((P2 (-> tptp.option_trm Bool))) (forall ((X5 tptp.option_trm)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_trm Bool))) (and (@ P3 tptp.none_trm) (forall ((X3 tptp.trm)) (@ P3 (@ tptp.some_trm X3)))))) (= (lambda ((P2 (-> tptp.option_fml Bool))) (forall ((X5 tptp.option_fml)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_fml Bool))) (and (@ P3 tptp.none_fml) (forall ((X3 tptp.fml)) (@ P3 (@ tptp.some_fml X3)))))) (= (lambda ((P2 (-> tptp.option_game Bool))) (forall ((X5 tptp.option_game)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_game Bool))) (and (@ P3 tptp.none_game) (forall ((X3 tptp.game)) (@ P3 (@ tptp.some_game X3)))))) (= (lambda ((P2 (-> tptp.option_trm Bool))) (exists ((X5 tptp.option_trm)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_trm Bool))) (or (@ P3 tptp.none_trm) (exists ((X3 tptp.trm)) (@ P3 (@ tptp.some_trm X3)))))) (= (lambda ((P2 (-> tptp.option_fml Bool))) (exists ((X5 tptp.option_fml)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_fml Bool))) (or (@ P3 tptp.none_fml) (exists ((X3 tptp.fml)) (@ P3 (@ tptp.some_fml X3)))))) (= (lambda ((P2 (-> tptp.option_game Bool))) (exists ((X5 tptp.option_game)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_game Bool))) (or (@ P3 tptp.none_game) (exists ((X3 tptp.game)) (@ P3 (@ tptp.some_game X3)))))) (forall ((P (-> tptp.option_trm Bool)) (Option tptp.option_trm)) (=> (@ P tptp.none_trm) (=> (forall ((X tptp.trm)) (@ P (@ tptp.some_trm X))) (@ P Option)))) (forall ((P (-> tptp.option_fml Bool)) (Option tptp.option_fml)) (=> (@ P tptp.none_fml) (=> (forall ((X tptp.fml)) (@ P (@ tptp.some_fml X))) (@ P Option)))) (forall ((P (-> tptp.option_game Bool)) (Option tptp.option_game)) (=> (@ P tptp.none_game) (=> (forall ((X tptp.game)) (@ P (@ tptp.some_game X))) (@ P Option)))) (forall ((Y2 tptp.option_trm)) (=> (not (= Y2 tptp.none_trm)) (not (forall ((X24 tptp.trm)) (not (= Y2 (@ tptp.some_trm X24))))))) (forall ((Y2 tptp.option_fml)) (=> (not (= Y2 tptp.none_fml)) (not (forall ((X24 tptp.fml)) (not (= Y2 (@ tptp.some_fml X24))))))) (forall ((Y2 tptp.option_game)) (=> (not (= Y2 tptp.none_game)) (not (forall ((X24 tptp.game)) (not (= Y2 (@ tptp.some_game X24))))))) (forall ((Option tptp.option_trm) (X23 tptp.trm)) (=> (= Option (@ tptp.some_trm X23)) (not (= Option tptp.none_trm)))) (forall ((Option tptp.option_fml) (X23 tptp.fml)) (=> (= Option (@ tptp.some_fml X23)) (not (= Option tptp.none_fml)))) (forall ((Option tptp.option_game) (X23 tptp.game)) (=> (= Option (@ tptp.some_game X23)) (not (= Option tptp.none_game)))) (forall ((X23 tptp.trm)) (not (= tptp.none_trm (@ tptp.some_trm X23)))) (forall ((X23 tptp.fml)) (not (= tptp.none_fml (@ tptp.some_fml X23)))) (forall ((X23 tptp.game)) (not (= tptp.none_game (@ tptp.some_game X23)))) (forall ((P (-> tptp.option_trm Bool)) (A0 tptp.option_trm)) (=> (forall ((Theta2 tptp.trm)) (@ P (@ tptp.some_trm Theta2))) (=> (@ P tptp.none_trm) (@ P A0)))) (forall ((X2 tptp.option_trm)) (=> (forall ((Theta2 tptp.trm)) (not (= X2 (@ tptp.some_trm Theta2)))) (= X2 tptp.none_trm))) (forall ((P (-> tptp.variable tptp.option_trm Bool)) (A0 tptp.variable) (A1 tptp.option_trm)) (=> (forall ((X tptp.variable) (Theta2 tptp.trm)) (@ (@ P X) (@ tptp.some_trm Theta2))) (=> (forall ((X tptp.variable)) (@ (@ P X) tptp.none_trm)) (@ (@ P A0) A1)))) (forall ((P (-> tptp.option_trm tptp.option_trm Bool)) (A0 tptp.option_trm) (A1 tptp.option_trm)) (=> (forall ((Theta2 tptp.trm) (Eta2 tptp.trm)) (@ (@ P (@ tptp.some_trm Theta2)) (@ tptp.some_trm Eta2))) (=> (forall ((X_1 tptp.option_trm)) (@ (@ P tptp.none_trm) X_1)) (=> (forall ((V2 tptp.trm)) (@ (@ P (@ tptp.some_trm V2)) tptp.none_trm)) (@ (@ P A0) A1))))) (forall ((Theta tptp.option_trm)) (= (not (= Theta tptp.none_trm)) (exists ((T tptp.trm)) (= Theta (@ tptp.some_trm T))))) (forall ((P (-> tptp.char tptp.option_trm Bool)) (A0 tptp.char) (A1 tptp.option_trm)) (=> (forall ((X tptp.char) (Theta2 tptp.trm)) (@ (@ P X) (@ tptp.some_trm Theta2))) (=> (forall ((X tptp.char)) (@ (@ P X) tptp.none_trm)) (@ (@ P A0) A1)))) (forall ((X2 tptp.option_trm) (Y2 tptp.option_trm)) (=> (= (@ tptp.uSubst716837505ntialo X2) Y2) (=> (forall ((Theta2 tptp.trm)) (=> (= X2 (@ tptp.some_trm Theta2)) (not (= Y2 (@ tptp.some_trm (@ tptp.differential Theta2)))))) (not (=> (= X2 tptp.none_trm) (not (= Y2 tptp.none_trm))))))) (forall ((X61 tptp.trm) (X62 tptp.trm) (X7 tptp.trm)) (not (= (@ (@ tptp.times X61) X62) (@ tptp.differential X7)))) (forall ((X51 tptp.trm) (X52 tptp.trm) (X7 tptp.trm)) (not (= (@ (@ tptp.plus X51) X52) (@ tptp.differential X7)))) (forall ((V3 tptp.trm)) (= (@ (@ tptp.uSubst918876924Timeso (@ tptp.some_trm V3)) tptp.none_trm) tptp.none_trm)) (forall ((V3 tptp.trm)) (= (@ (@ tptp.uSubst141955042_Pluso (@ tptp.some_trm V3)) tptp.none_trm) tptp.none_trm)) (forall ((Theta tptp.trm) (Eta tptp.trm)) (= (@ (@ tptp.uSubst141955042_Pluso (@ tptp.some_trm Theta)) (@ tptp.some_trm Eta)) (@ tptp.some_trm (@ (@ tptp.plus Theta) Eta)))) (forall ((Theta tptp.trm) (Eta tptp.trm)) (= (@ (@ tptp.uSubst918876924Timeso (@ tptp.some_trm Theta)) (@ tptp.some_trm Eta)) (@ tptp.some_trm (@ (@ tptp.times Theta) Eta)))) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm)) (let ((_let_1 (@ tptp.uSubst516392818stappt Sigma))) (=> (not (= (@ (@ _let_1 U) (@ tptp.differential Theta)) tptp.none_trm)) (not (= (@ (@ _let_1 (@ tptp.collect_variable (lambda ((X3 tptp.variable)) true))) Theta) tptp.none_trm))))) (forall ((V3 tptp.trm)) (= (@ (@ tptp.uSubst152838031e_Geqo (@ tptp.some_trm V3)) tptp.none_trm) tptp.none_fml)) (forall ((X2 tptp.option_trm) (Xa tptp.option_trm) (Y2 tptp.option_fml)) (let ((_let_1 (not (= Y2 tptp.none_fml)))) (=> (= (@ (@ tptp.uSubst152838031e_Geqo X2) Xa) Y2) (=> (forall ((Theta2 tptp.trm)) (=> (= X2 (@ tptp.some_trm Theta2)) (forall ((Eta2 tptp.trm)) (=> (= Xa (@ tptp.some_trm Eta2)) (not (= Y2 (@ tptp.some_fml (@ (@ tptp.geq Theta2) Eta2)))))))) (=> (=> (= X2 tptp.none_trm) _let_1) (not (=> (exists ((V2 tptp.trm)) (= X2 (@ tptp.some_trm V2))) (=> (= Xa tptp.none_trm) _let_1)))))))) (forall ((X2 tptp.option_trm) (Y2 tptp.option_trm)) (let ((_let_1 (@ tptp.accp_option_trm tptp.uSubst2051024824lo_rel))) (=> (= (@ tptp.uSubst716837505ntialo X2) Y2) (=> (@ _let_1 X2) (=> (forall ((Theta2 tptp.trm)) (let ((_let_1 (@ tptp.some_trm Theta2))) (=> (= X2 _let_1) (=> (= Y2 (@ tptp.some_trm (@ tptp.differential Theta2))) (not (@ (@ tptp.accp_option_trm tptp.uSubst2051024824lo_rel) _let_1)))))) (not (=> (= X2 tptp.none_trm) (=> (= Y2 tptp.none_trm) (not (@ _let_1 tptp.none_trm)))))))))) (forall ((Theta tptp.trm) (Eta tptp.trm)) (= (@ (@ tptp.uSubst152838031e_Geqo (@ tptp.some_trm Theta)) (@ tptp.some_trm Eta)) (@ tptp.some_fml (@ (@ tptp.geq Theta) Eta)))) (forall ((P (-> tptp.set_variable Bool)) (X2 tptp.set_variable) (Q (-> tptp.set_variable Bool))) (=> (@ P X2) (=> (forall ((Y4 tptp.set_variable)) (=> (@ P Y4) (@ (@ tptp.ord_le282106107riable Y4) X2))) (=> (forall ((X tptp.set_variable)) (=> (@ P X) (=> (forall ((Y5 tptp.set_variable)) (=> (@ P Y5) (@ (@ tptp.ord_le282106107riable Y5) X))) (@ Q X)))) (@ Q (@ tptp.order_272405634riable P)))))) (forall ((P (-> tptp.set_variable Bool)) (X2 tptp.set_variable)) (=> (@ P X2) (=> (forall ((Y4 tptp.set_variable)) (=> (@ P Y4) (@ (@ tptp.ord_le282106107riable Y4) X2))) (= (@ tptp.order_272405634riable P) X2)))) (forall ((P (-> tptp.option_game tptp.option_fml Bool)) (A0 tptp.option_game) (A1 tptp.option_fml)) (=> (forall ((Alpha tptp.game) (Phi2 tptp.fml)) (@ (@ P (@ tptp.some_game Alpha)) (@ tptp.some_fml Phi2))) (=> (forall ((X_1 tptp.option_fml)) (@ (@ P tptp.none_game) X_1)) (=> (forall ((V2 tptp.game)) (@ (@ P (@ tptp.some_game V2)) tptp.none_fml)) (@ (@ P A0) A1))))) (forall ((P (-> tptp.variable tptp.option_fml Bool)) (A0 tptp.variable) (A1 tptp.option_fml)) (=> (forall ((X tptp.variable) (Phi2 tptp.fml)) (@ (@ P X) (@ tptp.some_fml Phi2))) (=> (forall ((X tptp.variable)) (@ (@ P X) tptp.none_fml)) (@ (@ P A0) A1)))) (forall ((Phi tptp.option_fml)) (= (not (= Phi tptp.none_fml)) (exists ((F2 tptp.fml)) (= Phi (@ tptp.some_fml F2))))) (forall ((P (-> tptp.option_fml Bool)) (A0 tptp.option_fml)) (=> (forall ((Phi2 tptp.fml)) (@ P (@ tptp.some_fml Phi2))) (=> (@ P tptp.none_fml) (@ P A0)))) (forall ((X2 tptp.option_fml)) (=> (forall ((Phi2 tptp.fml)) (not (= X2 (@ tptp.some_fml Phi2)))) (= X2 tptp.none_fml))) (forall ((P (-> tptp.option_fml tptp.option_fml Bool)) (A0 tptp.option_fml) (A1 tptp.option_fml)) (=> (forall ((Phi2 tptp.fml) (Psi tptp.fml)) (@ (@ P (@ tptp.some_fml Phi2)) (@ tptp.some_fml Psi))) (=> (forall ((X_1 tptp.option_fml)) (@ (@ P tptp.none_fml) X_1)) (=> (forall ((V2 tptp.fml)) (@ (@ P (@ tptp.some_fml V2)) tptp.none_fml)) (@ (@ P A0) A1))))) (forall ((R1 (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (R2 (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool))) (=> (@ (@ tptp.ord_le370603054_trm_o R1) R2) (@ (@ tptp.ord_le373274227_trm_o (@ tptp.accp_P394694195on_trm R2)) (@ tptp.accp_P394694195on_trm R1)))) (forall ((R1 (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (R2 (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool))) (=> (@ (@ tptp.ord_le90123726_trm_o R1) R2) (@ (@ tptp.ord_le1721128566_trm_o (@ tptp.accp_P758790320on_trm R2)) (@ tptp.accp_P758790320on_trm R1)))) (forall ((R1 (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (R2 (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool))) (=> (@ (@ tptp.ord_le157637894_trm_o R1) R2) (@ (@ tptp.ord_le1222882015_trm_o (@ tptp.accp_P419951815on_trm R2)) (@ tptp.accp_P419951815on_trm R1)))) (forall ((R1 (-> tptp.option_trm tptp.option_trm Bool)) (R2 (-> tptp.option_trm tptp.option_trm Bool))) (=> (@ (@ tptp.ord_le847028878_trm_o R1) R2) (@ (@ tptp.ord_le1957133745_trm_o (@ tptp.accp_option_trm R2)) (@ tptp.accp_option_trm R1)))) (forall ((R1 (-> tptp.option_fml tptp.option_fml Bool)) (R2 (-> tptp.option_fml tptp.option_fml Bool))) (=> (@ (@ tptp.ord_le802833166_fml_o R1) R2) (@ (@ tptp.ord_le181580155_fml_o (@ tptp.accp_option_fml R2)) (@ tptp.accp_option_fml R1)))) (forall ((D (-> tptp.produc1024976764on_trm Bool)) (R (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (X2 tptp.produc1024976764on_trm) (P (-> tptp.produc1024976764on_trm Bool))) (=> (@ (@ tptp.ord_le373274227_trm_o D) (@ tptp.accp_P394694195on_trm R)) (=> (forall ((X tptp.produc1024976764on_trm) (Z4 tptp.produc1024976764on_trm)) (=> (@ D X) (=> (@ (@ R Z4) X) (@ D Z4)))) (=> (@ D X2) (=> (forall ((X tptp.produc1024976764on_trm)) (=> (@ D X) (=> (forall ((Z5 tptp.produc1024976764on_trm)) (=> (@ (@ R Z5) X) (@ P Z5))) (@ P X)))) (@ P X2)))))) (forall ((D (-> tptp.produc1072747943on_trm Bool)) (R (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (X2 tptp.produc1072747943on_trm) (P (-> tptp.produc1072747943on_trm Bool))) (=> (@ (@ tptp.ord_le1721128566_trm_o D) (@ tptp.accp_P758790320on_trm R)) (=> (forall ((X tptp.produc1072747943on_trm) (Z4 tptp.produc1072747943on_trm)) (=> (@ D X) (=> (@ (@ R Z4) X) (@ D Z4)))) (=> (@ D X2) (=> (forall ((X tptp.produc1072747943on_trm)) (=> (@ D X) (=> (forall ((Z5 tptp.produc1072747943on_trm)) (=> (@ (@ R Z5) X) (@ P Z5))) (@ P X)))) (@ P X2)))))) (forall ((D (-> tptp.produc464795408on_trm Bool)) (R (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (X2 tptp.produc464795408on_trm) (P (-> tptp.produc464795408on_trm Bool))) (=> (@ (@ tptp.ord_le1222882015_trm_o D) (@ tptp.accp_P419951815on_trm R)) (=> (forall ((X tptp.produc464795408on_trm) (Z4 tptp.produc464795408on_trm)) (=> (@ D X) (=> (@ (@ R Z4) X) (@ D Z4)))) (=> (@ D X2) (=> (forall ((X tptp.produc464795408on_trm)) (=> (@ D X) (=> (forall ((Z5 tptp.produc464795408on_trm)) (=> (@ (@ R Z5) X) (@ P Z5))) (@ P X)))) (@ P X2)))))) (forall ((D (-> tptp.option_trm Bool)) (R (-> tptp.option_trm tptp.option_trm Bool)) (X2 tptp.option_trm) (P (-> tptp.option_trm Bool))) (=> (@ (@ tptp.ord_le1957133745_trm_o D) (@ tptp.accp_option_trm R)) (=> (forall ((X tptp.option_trm) (Z4 tptp.option_trm)) (=> (@ D X) (=> (@ (@ R Z4) X) (@ D Z4)))) (=> (@ D X2) (=> (forall ((X tptp.option_trm)) (=> (@ D X) (=> (forall ((Z5 tptp.option_trm)) (=> (@ (@ R Z5) X) (@ P Z5))) (@ P X)))) (@ P X2)))))) (forall ((D (-> tptp.option_fml Bool)) (R (-> tptp.option_fml tptp.option_fml Bool)) (X2 tptp.option_fml) (P (-> tptp.option_fml Bool))) (=> (@ (@ tptp.ord_le181580155_fml_o D) (@ tptp.accp_option_fml R)) (=> (forall ((X tptp.option_fml) (Z4 tptp.option_fml)) (=> (@ D X) (=> (@ (@ R Z4) X) (@ D Z4)))) (=> (@ D X2) (=> (forall ((X tptp.option_fml)) (=> (@ D X) (=> (forall ((Z5 tptp.option_fml)) (=> (@ (@ R Z5) X) (@ P Z5))) (@ P X)))) (@ P X2)))))) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (let ((_let_2 (@ (@ (@ tptp.uSubst516392804stappf Sigma) U) (@ (@ tptp.geq Theta) Eta)))) (=> (not (= _let_2 tptp.none_fml)) (= _let_2 (@ tptp.some_fml (@ (@ tptp.geq (@ tptp.the_trm (@ _let_1 Theta))) (@ tptp.the_trm (@ _let_1 Eta))))))))) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (let ((_let_2 (@ _let_1 Eta))) (let ((_let_3 (@ _let_1 Theta))) (=> (not (= _let_3 tptp.none_trm)) (=> (not (= _let_2 tptp.none_trm)) (= (@ (@ (@ tptp.uSubst516392804stappf Sigma) U) (@ (@ tptp.geq Theta) Eta)) (@ tptp.some_fml (@ (@ tptp.geq (@ tptp.the_trm _let_3)) (@ tptp.the_trm _let_2)))))))))) (forall ((Option tptp.option_trm)) (=> (not (= Option tptp.none_trm)) (= (@ tptp.some_trm (@ tptp.the_trm Option)) Option))) (forall ((Option tptp.option_fml)) (=> (not (= Option tptp.none_fml)) (= (@ tptp.some_fml (@ tptp.the_fml Option)) Option))) (forall ((Option tptp.option_game)) (=> (not (= Option tptp.none_game)) (= (@ tptp.some_game (@ tptp.the_game Option)) Option))) (forall ((P (-> tptp.option_game tptp.option_game Bool)) (A0 tptp.option_game) (A1 tptp.option_game)) (=> (forall ((Alpha tptp.game) (Beta tptp.game)) (@ (@ P (@ tptp.some_game Alpha)) (@ tptp.some_game Beta))) (=> (forall ((Alpha tptp.option_game)) (@ (@ P Alpha) tptp.none_game)) (=> (forall ((V2 tptp.game)) (@ (@ P tptp.none_game) (@ tptp.some_game V2))) (@ (@ P A0) A1))))) (forall ((Alpha2 tptp.option_game)) (= (not (= Alpha2 tptp.none_game)) (exists ((G tptp.game)) (= Alpha2 (@ tptp.some_game G))))) (forall ((P (-> tptp.option_game Bool)) (A0 tptp.option_game)) (=> (forall ((Alpha tptp.game)) (@ P (@ tptp.some_game Alpha))) (=> (@ P tptp.none_game) (@ P A0)))) (forall ((X2 tptp.option_game)) (=> (forall ((Alpha tptp.game)) (not (= X2 (@ tptp.some_game Alpha)))) (= X2 tptp.none_game))) (forall ((Option tptp.option_trm) (Option2 tptp.option_trm)) (let ((_let_1 (= Option2 tptp.none_trm))) (let ((_let_2 (= Option tptp.none_trm))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_trm Option) (@ tptp.the_trm Option2)))) (= Option Option2)))))) (forall ((Option tptp.option_fml) (Option2 tptp.option_fml)) (let ((_let_1 (= Option2 tptp.none_fml))) (let ((_let_2 (= Option tptp.none_fml))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_fml Option) (@ tptp.the_fml Option2)))) (= Option Option2)))))) (forall ((Option tptp.option_game) (Option2 tptp.option_game)) (let ((_let_1 (= Option2 tptp.none_game))) (let ((_let_2 (= Option tptp.none_game))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_game Option) (@ tptp.the_game Option2)))) (= Option Option2)))))) (forall ((X23 tptp.trm)) (= (@ tptp.the_trm (@ tptp.some_trm X23)) X23)) (forall ((X23 tptp.fml)) (= (@ tptp.the_fml (@ tptp.some_fml X23)) X23)) (forall ((X23 tptp.game)) (= (@ tptp.the_game (@ tptp.some_game X23)) X23)) (forall ((Option tptp.option_trm)) (=> (not (= Option tptp.none_trm)) (= Option (@ tptp.some_trm (@ tptp.the_trm Option))))) (forall ((Option tptp.option_fml)) (=> (not (= Option tptp.none_fml)) (= Option (@ tptp.some_fml (@ tptp.the_fml Option))))) (forall ((Option tptp.option_game)) (=> (not (= Option tptp.none_game)) (= Option (@ tptp.some_game (@ tptp.the_game Option))))) (forall ((R3 (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (A3 tptp.produc1024976764on_trm)) (=> (@ (@ tptp.accp_P394694195on_trm R3) A3) (forall ((Y5 tptp.produc1024976764on_trm)) (=> (@ (@ R3 Y5) A3) (@ (@ tptp.accp_P394694195on_trm R3) Y5))))) (forall ((R3 (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (A3 tptp.produc1072747943on_trm)) (=> (@ (@ tptp.accp_P758790320on_trm R3) A3) (forall ((Y5 tptp.produc1072747943on_trm)) (=> (@ (@ R3 Y5) A3) (@ (@ tptp.accp_P758790320on_trm R3) Y5))))) (forall ((R3 (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (A3 tptp.produc464795408on_trm)) (=> (@ (@ tptp.accp_P419951815on_trm R3) A3) (forall ((Y5 tptp.produc464795408on_trm)) (=> (@ (@ R3 Y5) A3) (@ (@ tptp.accp_P419951815on_trm R3) Y5))))) (forall ((R3 (-> tptp.option_trm tptp.option_trm Bool)) (A3 tptp.option_trm)) (=> (@ (@ tptp.accp_option_trm R3) A3) (forall ((Y5 tptp.option_trm)) (=> (@ (@ R3 Y5) A3) (@ (@ tptp.accp_option_trm R3) Y5))))) (forall ((R3 (-> tptp.option_fml tptp.option_fml Bool)) (A3 tptp.option_fml)) (=> (@ (@ tptp.accp_option_fml R3) A3) (forall ((Y5 tptp.option_fml)) (=> (@ (@ R3 Y5) A3) (@ (@ tptp.accp_option_fml R3) Y5))))) (= tptp.accp_P394694195on_trm (lambda ((R4 (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (A4 tptp.produc1024976764on_trm)) (exists ((X3 tptp.produc1024976764on_trm)) (and (= A4 X3) (forall ((Y3 tptp.produc1024976764on_trm)) (=> (@ (@ R4 Y3) X3) (@ (@ tptp.accp_P394694195on_trm R4) Y3))))))) (= tptp.accp_P758790320on_trm (lambda ((R4 (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (A4 tptp.produc1072747943on_trm)) (exists ((X3 tptp.produc1072747943on_trm)) (and (= A4 X3) (forall ((Y3 tptp.produc1072747943on_trm)) (=> (@ (@ R4 Y3) X3) (@ (@ tptp.accp_P758790320on_trm R4) Y3))))))) (= tptp.accp_P419951815on_trm (lambda ((R4 (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (A4 tptp.produc464795408on_trm)) (exists ((X3 tptp.produc464795408on_trm)) (and (= A4 X3) (forall ((Y3 tptp.produc464795408on_trm)) (=> (@ (@ R4 Y3) X3) (@ (@ tptp.accp_P419951815on_trm R4) Y3))))))) (= tptp.accp_option_trm (lambda ((R4 (-> tptp.option_trm tptp.option_trm Bool)) (A4 tptp.option_trm)) (exists ((X3 tptp.option_trm)) (and (= A4 X3) (forall ((Y3 tptp.option_trm)) (=> (@ (@ R4 Y3) X3) (@ (@ tptp.accp_option_trm R4) Y3))))))) (= tptp.accp_option_fml (lambda ((R4 (-> tptp.option_fml tptp.option_fml Bool)) (A4 tptp.option_fml)) (exists ((X3 tptp.option_fml)) (and (= A4 X3) (forall ((Y3 tptp.option_fml)) (=> (@ (@ R4 Y3) X3) (@ (@ tptp.accp_option_fml R4) Y3))))))) (forall ((R3 (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (X2 tptp.produc1024976764on_trm)) (=> (forall ((Y4 tptp.produc1024976764on_trm)) (=> (@ (@ R3 Y4) X2) (@ (@ tptp.accp_P394694195on_trm R3) Y4))) (@ (@ tptp.accp_P394694195on_trm R3) X2))) (forall ((R3 (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (X2 tptp.produc1072747943on_trm)) (=> (forall ((Y4 tptp.produc1072747943on_trm)) (=> (@ (@ R3 Y4) X2) (@ (@ tptp.accp_P758790320on_trm R3) Y4))) (@ (@ tptp.accp_P758790320on_trm R3) X2))) (forall ((R3 (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (X2 tptp.produc464795408on_trm)) (=> (forall ((Y4 tptp.produc464795408on_trm)) (=> (@ (@ R3 Y4) X2) (@ (@ tptp.accp_P419951815on_trm R3) Y4))) (@ (@ tptp.accp_P419951815on_trm R3) X2))) (forall ((R3 (-> tptp.option_trm tptp.option_trm Bool)) (X2 tptp.option_trm)) (=> (forall ((Y4 tptp.option_trm)) (=> (@ (@ R3 Y4) X2) (@ (@ tptp.accp_option_trm R3) Y4))) (@ (@ tptp.accp_option_trm R3) X2))) (forall ((R3 (-> tptp.option_fml tptp.option_fml Bool)) (X2 tptp.option_fml)) (=> (forall ((Y4 tptp.option_fml)) (=> (@ (@ R3 Y4) X2) (@ (@ tptp.accp_option_fml R3) Y4))) (@ (@ tptp.accp_option_fml R3) X2))) (forall ((R3 (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (A3 tptp.produc1024976764on_trm) (P (-> tptp.produc1024976764on_trm Bool))) (=> (@ (@ tptp.accp_P394694195on_trm R3) A3) (=> (forall ((X tptp.produc1024976764on_trm)) (=> (@ (@ tptp.accp_P394694195on_trm R3) X) (=> (forall ((Y5 tptp.produc1024976764on_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))) (forall ((R3 (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (A3 tptp.produc1072747943on_trm) (P (-> tptp.produc1072747943on_trm Bool))) (=> (@ (@ tptp.accp_P758790320on_trm R3) A3) (=> (forall ((X tptp.produc1072747943on_trm)) (=> (@ (@ tptp.accp_P758790320on_trm R3) X) (=> (forall ((Y5 tptp.produc1072747943on_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))) (forall ((R3 (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (A3 tptp.produc464795408on_trm) (P (-> tptp.produc464795408on_trm Bool))) (=> (@ (@ tptp.accp_P419951815on_trm R3) A3) (=> (forall ((X tptp.produc464795408on_trm)) (=> (@ (@ tptp.accp_P419951815on_trm R3) X) (=> (forall ((Y5 tptp.produc464795408on_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))) (forall ((R3 (-> tptp.option_trm tptp.option_trm Bool)) (A3 tptp.option_trm) (P (-> tptp.option_trm Bool))) (=> (@ (@ tptp.accp_option_trm R3) A3) (=> (forall ((X tptp.option_trm)) (=> (@ (@ tptp.accp_option_trm R3) X) (=> (forall ((Y5 tptp.option_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))) (forall ((R3 (-> tptp.option_fml tptp.option_fml Bool)) (A3 tptp.option_fml) (P (-> tptp.option_fml Bool))) (=> (@ (@ tptp.accp_option_fml R3) A3) (=> (forall ((X tptp.option_fml)) (=> (@ (@ tptp.accp_option_fml R3) X) (=> (forall ((Y5 tptp.option_fml)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))) (forall ((R3 (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (X2 tptp.produc1024976764on_trm) (P (-> tptp.produc1024976764on_trm Bool))) (=> (@ (@ tptp.accp_P394694195on_trm R3) X2) (=> (forall ((X tptp.produc1024976764on_trm)) (=> (forall ((Y5 tptp.produc1024976764on_trm)) (=> (@ (@ R3 Y5) X) (@ (@ tptp.accp_P394694195on_trm R3) Y5))) (=> (forall ((Y5 tptp.produc1024976764on_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P X2)))) (forall ((R3 (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (X2 tptp.produc1072747943on_trm) (P (-> tptp.produc1072747943on_trm Bool))) (=> (@ (@ tptp.accp_P758790320on_trm R3) X2) (=> (forall ((X tptp.produc1072747943on_trm)) (=> (forall ((Y5 tptp.produc1072747943on_trm)) (=> (@ (@ R3 Y5) X) (@ (@ tptp.accp_P758790320on_trm R3) Y5))) (=> (forall ((Y5 tptp.produc1072747943on_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P X2)))) (forall ((R3 (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (X2 tptp.produc464795408on_trm) (P (-> tptp.produc464795408on_trm Bool))) (=> (@ (@ tptp.accp_P419951815on_trm R3) X2) (=> (forall ((X tptp.produc464795408on_trm)) (=> (forall ((Y5 tptp.produc464795408on_trm)) (=> (@ (@ R3 Y5) X) (@ (@ tptp.accp_P419951815on_trm R3) Y5))) (=> (forall ((Y5 tptp.produc464795408on_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P X2)))) (forall ((R3 (-> tptp.option_trm tptp.option_trm Bool)) (X2 tptp.option_trm) (P (-> tptp.option_trm Bool))) (=> (@ (@ tptp.accp_option_trm R3) X2) (=> (forall ((X tptp.option_trm)) (=> (forall ((Y5 tptp.option_trm)) (=> (@ (@ R3 Y5) X) (@ (@ tptp.accp_option_trm R3) Y5))) (=> (forall ((Y5 tptp.option_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P X2)))) (forall ((R3 (-> tptp.option_fml tptp.option_fml Bool)) (X2 tptp.option_fml) (P (-> tptp.option_fml Bool))) (=> (@ (@ tptp.accp_option_fml R3) X2) (=> (forall ((X tptp.option_fml)) (=> (forall ((Y5 tptp.option_fml)) (=> (@ (@ R3 Y5) X) (@ (@ tptp.accp_option_fml R3) Y5))) (=> (forall ((Y5 tptp.option_fml)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P X2)))) (forall ((R3 (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (B3 tptp.produc1024976764on_trm) (A3 tptp.produc1024976764on_trm)) (let ((_let_1 (@ tptp.accp_P394694195on_trm R3))) (=> (@ _let_1 B3) (=> (@ (@ R3 A3) B3) (@ _let_1 A3))))) (forall ((R3 (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (B3 tptp.produc1072747943on_trm) (A3 tptp.produc1072747943on_trm)) (let ((_let_1 (@ tptp.accp_P758790320on_trm R3))) (=> (@ _let_1 B3) (=> (@ (@ R3 A3) B3) (@ _let_1 A3))))) (forall ((R3 (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (B3 tptp.produc464795408on_trm) (A3 tptp.produc464795408on_trm)) (let ((_let_1 (@ tptp.accp_P419951815on_trm R3))) (=> (@ _let_1 B3) (=> (@ (@ R3 A3) B3) (@ _let_1 A3))))) (forall ((R3 (-> tptp.option_trm tptp.option_trm Bool)) (B3 tptp.option_trm) (A3 tptp.option_trm)) (let ((_let_1 (@ tptp.accp_option_trm R3))) (=> (@ _let_1 B3) (=> (@ (@ R3 A3) B3) (@ _let_1 A3))))) (forall ((R3 (-> tptp.option_fml tptp.option_fml Bool)) (B3 tptp.option_fml) (A3 tptp.option_fml)) (let ((_let_1 (@ tptp.accp_option_fml R3))) (=> (@ _let_1 B3) (=> (@ (@ R3 A3) B3) (@ _let_1 A3))))) (forall ((R (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (X2 tptp.produc1024976764on_trm)) (=> (not (@ (@ tptp.accp_P394694195on_trm R) X2)) (not (forall ((Z4 tptp.produc1024976764on_trm)) (=> (@ (@ R Z4) X2) (@ (@ tptp.accp_P394694195on_trm R) Z4)))))) (forall ((R (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (X2 tptp.produc1072747943on_trm)) (=> (not (@ (@ tptp.accp_P758790320on_trm R) X2)) (not (forall ((Z4 tptp.produc1072747943on_trm)) (=> (@ (@ R Z4) X2) (@ (@ tptp.accp_P758790320on_trm R) Z4)))))) (forall ((R (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (X2 tptp.produc464795408on_trm)) (=> (not (@ (@ tptp.accp_P419951815on_trm R) X2)) (not (forall ((Z4 tptp.produc464795408on_trm)) (=> (@ (@ R Z4) X2) (@ (@ tptp.accp_P419951815on_trm R) Z4)))))) (forall ((R (-> tptp.option_trm tptp.option_trm Bool)) (X2 tptp.option_trm)) (=> (not (@ (@ tptp.accp_option_trm R) X2)) (not (forall ((Z4 tptp.option_trm)) (=> (@ (@ R Z4) X2) (@ (@ tptp.accp_option_trm R) Z4)))))) (forall ((R (-> tptp.option_fml tptp.option_fml Bool)) (X2 tptp.option_fml)) (=> (not (@ (@ tptp.accp_option_fml R) X2)) (not (forall ((Z4 tptp.option_fml)) (=> (@ (@ R Z4) X2) (@ (@ tptp.accp_option_fml R) Z4)))))) (forall ((R3 (-> tptp.produc1024976764on_trm tptp.produc1024976764on_trm Bool)) (A3 tptp.produc1024976764on_trm) (P (-> tptp.produc1024976764on_trm Bool))) (=> (@ (@ tptp.accp_P394694195on_trm R3) A3) (=> (forall ((X tptp.produc1024976764on_trm)) (=> (@ (@ tptp.accp_P394694195on_trm R3) X) (=> (forall ((Y5 tptp.produc1024976764on_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))) (forall ((R3 (-> tptp.produc1072747943on_trm tptp.produc1072747943on_trm Bool)) (A3 tptp.produc1072747943on_trm) (P (-> tptp.produc1072747943on_trm Bool))) (=> (@ (@ tptp.accp_P758790320on_trm R3) A3) (=> (forall ((X tptp.produc1072747943on_trm)) (=> (@ (@ tptp.accp_P758790320on_trm R3) X) (=> (forall ((Y5 tptp.produc1072747943on_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))) (forall ((R3 (-> tptp.produc464795408on_trm tptp.produc464795408on_trm Bool)) (A3 tptp.produc464795408on_trm) (P (-> tptp.produc464795408on_trm Bool))) (=> (@ (@ tptp.accp_P419951815on_trm R3) A3) (=> (forall ((X tptp.produc464795408on_trm)) (=> (@ (@ tptp.accp_P419951815on_trm R3) X) (=> (forall ((Y5 tptp.produc464795408on_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))) (forall ((R3 (-> tptp.option_trm tptp.option_trm Bool)) (A3 tptp.option_trm) (P (-> tptp.option_trm Bool))) (=> (@ (@ tptp.accp_option_trm R3) A3) (=> (forall ((X tptp.option_trm)) (=> (@ (@ tptp.accp_option_trm R3) X) (=> (forall ((Y5 tptp.option_trm)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))) (forall ((R3 (-> tptp.option_fml tptp.option_fml Bool)) (A3 tptp.option_fml) (P (-> tptp.option_fml Bool))) (=> (@ (@ tptp.accp_option_fml R3) A3) (=> (forall ((X tptp.option_fml)) (=> (@ (@ tptp.accp_option_fml R3) X) (=> (forall ((Y5 tptp.option_fml)) (=> (@ (@ R3 Y5) X) (@ P Y5))) (@ P X)))) (@ P A3)))) (forall ((X2 tptp.option_trm) (Xa tptp.option_trm) (Y2 tptp.option_fml)) (let ((_let_1 (@ tptp.accp_P758790320on_trm tptp.uSubst1304144938qo_rel))) (=> (= (@ (@ tptp.uSubst152838031e_Geqo X2) Xa) Y2) (=> (@ _let_1 (@ (@ tptp.produc709594775on_trm X2) Xa)) (=> (forall ((Theta2 tptp.trm)) (=> (= X2 (@ tptp.some_trm Theta2)) (forall ((Eta2 tptp.trm)) (let ((_let_1 (@ tptp.some_trm Eta2))) (=> (= Xa _let_1) (=> (= Y2 (@ tptp.some_fml (@ (@ tptp.geq Theta2) Eta2))) (not (@ (@ tptp.accp_P758790320on_trm tptp.uSubst1304144938qo_rel) (@ (@ tptp.produc709594775on_trm (@ tptp.some_trm Theta2)) _let_1))))))))) (=> (=> (= X2 tptp.none_trm) (=> (= Y2 tptp.none_fml) (not (@ _let_1 (@ (@ tptp.produc709594775on_trm tptp.none_trm) Xa))))) (not (forall ((V2 tptp.trm)) (let ((_let_1 (@ tptp.some_trm V2))) (=> (= X2 _let_1) (=> (= Xa tptp.none_trm) (=> (= Y2 tptp.none_fml) (not (@ (@ tptp.accp_P758790320on_trm tptp.uSubst1304144938qo_rel) (@ (@ tptp.produc709594775on_trm _let_1) tptp.none_trm))))))))))))))) (forall ((X2 tptp.produc1739631244on_fml)) (=> (forall ((Alpha tptp.game) (Phi2 tptp.fml)) (not (= X2 (@ (@ tptp.produc2124676926on_fml (@ tptp.some_game Alpha)) (@ tptp.some_fml Phi2))))) (=> (forall ((Phi2 tptp.option_fml)) (not (= X2 (@ (@ tptp.produc2124676926on_fml tptp.none_game) Phi2)))) (not (forall ((V2 tptp.game)) (not (= X2 (@ (@ tptp.produc2124676926on_fml (@ tptp.some_game V2)) tptp.none_fml)))))))) (forall ((R3 tptp.set_Pr622314946on_fml) (S2 tptp.set_Pr622314946on_fml)) (=> (forall ((X tptp.option_game) (Y4 tptp.option_fml)) (let ((_let_1 (@ tptp.member1883102883on_fml (@ (@ tptp.produc2124676926on_fml X) Y4)))) (=> (@ _let_1 R3) (@ _let_1 S2)))) (@ (@ tptp.ord_le782333474on_fml R3) S2))) (forall ((R3 tptp.set_Pr1471344007on_trm) (S2 tptp.set_Pr1471344007on_trm)) (=> (forall ((X tptp.option_trm) (Y4 tptp.option_trm)) (let ((_let_1 (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm X) Y4)))) (=> (@ _let_1 R3) (@ _let_1 S2)))) (@ (@ tptp.ord_le1322722599on_trm R3) S2))) (forall ((R3 tptp.set_Pr927595527on_fml) (S2 tptp.set_Pr927595527on_fml)) (=> (forall ((X tptp.option_fml) (Y4 tptp.option_fml)) (let ((_let_1 (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml X) Y4)))) (=> (@ _let_1 R3) (@ _let_1 S2)))) (@ (@ tptp.ord_le778974119on_fml R3) S2))) (forall ((R3 tptp.set_Pr943832262on_trm) (S2 tptp.set_Pr943832262on_trm)) (=> (forall ((X tptp.char) (Y4 tptp.option_trm)) (let ((_let_1 (@ tptp.member694524327on_trm (@ (@ tptp.produc1500300866on_trm X) Y4)))) (=> (@ _let_1 R3) (@ _let_1 S2)))) (@ (@ tptp.ord_le541293862on_trm R3) S2))) (forall ((R3 tptp.set_Pr1235432374le_trm) (S2 tptp.set_Pr1235432374le_trm)) (=> (forall ((X tptp.set_variable) (Y4 tptp.trm)) (let ((_let_1 (@ tptp.member2122665623le_trm (@ (@ tptp.produc1482344242le_trm X) Y4)))) (=> (@ _let_1 R3) (@ _let_1 S2)))) (@ (@ tptp.ord_le2102862870le_trm R3) S2))) (forall ((R3 tptp.option_game) (S2 tptp.option_fml) (R tptp.set_Pr622314946on_fml) (S3 tptp.option_fml)) (let ((_let_1 (@ tptp.produc2124676926on_fml R3))) (=> (@ (@ tptp.member1883102883on_fml (@ _let_1 S2)) R) (=> (= S3 S2) (@ (@ tptp.member1883102883on_fml (@ _let_1 S3)) R))))) (forall ((R3 tptp.option_trm) (S2 tptp.option_trm) (R tptp.set_Pr1471344007on_trm) (S3 tptp.option_trm)) (let ((_let_1 (@ tptp.produc709594775on_trm R3))) (=> (@ (@ tptp.member165817296on_trm (@ _let_1 S2)) R) (=> (= S3 S2) (@ (@ tptp.member165817296on_trm (@ _let_1 S3)) R))))) (forall ((R3 tptp.option_fml) (S2 tptp.option_fml) (R tptp.set_Pr927595527on_fml) (S3 tptp.option_fml)) (let ((_let_1 (@ tptp.produc909629463on_fml R3))) (=> (@ (@ tptp.member1287158352on_fml (@ _let_1 S2)) R) (=> (= S3 S2) (@ (@ tptp.member1287158352on_fml (@ _let_1 S3)) R))))) (forall ((R3 tptp.char) (S2 tptp.option_trm) (R tptp.set_Pr943832262on_trm) (S3 tptp.option_trm)) (let ((_let_1 (@ tptp.produc1500300866on_trm R3))) (=> (@ (@ tptp.member694524327on_trm (@ _let_1 S2)) R) (=> (= S3 S2) (@ (@ tptp.member694524327on_trm (@ _let_1 S3)) R))))) (forall ((R3 tptp.set_variable) (S2 tptp.trm) (R tptp.set_Pr1235432374le_trm) (S3 tptp.trm)) (let ((_let_1 (@ tptp.produc1482344242le_trm R3))) (=> (@ (@ tptp.member2122665623le_trm (@ _let_1 S2)) R) (=> (= S3 S2) (@ (@ tptp.member2122665623le_trm (@ _let_1 S3)) R))))) (forall ((R tptp.set_Pr622314946on_fml) (S tptp.set_Pr622314946on_fml)) (= (= (lambda ((X3 tptp.option_game) (Y3 tptp.option_fml)) (@ (@ tptp.member1883102883on_fml (@ (@ tptp.produc2124676926on_fml X3) Y3)) R)) (lambda ((X3 tptp.option_game) (Y3 tptp.option_fml)) (@ (@ tptp.member1883102883on_fml (@ (@ tptp.produc2124676926on_fml X3) Y3)) S))) (= R S))) (forall ((R tptp.set_Pr1471344007on_trm) (S tptp.set_Pr1471344007on_trm)) (= (= (lambda ((X3 tptp.option_trm) (Y3 tptp.option_trm)) (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm X3) Y3)) R)) (lambda ((X3 tptp.option_trm) (Y3 tptp.option_trm)) (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm X3) Y3)) S))) (= R S))) (forall ((R tptp.set_Pr927595527on_fml) (S tptp.set_Pr927595527on_fml)) (= (= (lambda ((X3 tptp.option_fml) (Y3 tptp.option_fml)) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml X3) Y3)) R)) (lambda ((X3 tptp.option_fml) (Y3 tptp.option_fml)) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml X3) Y3)) S))) (= R S))) (forall ((R tptp.set_Pr943832262on_trm) (S tptp.set_Pr943832262on_trm)) (= (= (lambda ((X3 tptp.char) (Y3 tptp.option_trm)) (@ (@ tptp.member694524327on_trm (@ (@ tptp.produc1500300866on_trm X3) Y3)) R)) (lambda ((X3 tptp.char) (Y3 tptp.option_trm)) (@ (@ tptp.member694524327on_trm (@ (@ tptp.produc1500300866on_trm X3) Y3)) S))) (= R S))) (forall ((R tptp.set_Pr1235432374le_trm) (S tptp.set_Pr1235432374le_trm)) (= (= (lambda ((X3 tptp.set_variable) (Y3 tptp.trm)) (@ (@ tptp.member2122665623le_trm (@ (@ tptp.produc1482344242le_trm X3) Y3)) R)) (lambda ((X3 tptp.set_variable) (Y3 tptp.trm)) (@ (@ tptp.member2122665623le_trm (@ (@ tptp.produc1482344242le_trm X3) Y3)) S))) (= R S))) (forall ((R tptp.set_Pr622314946on_fml) (S tptp.set_Pr622314946on_fml)) (= (@ (@ tptp.ord_le1588489637_fml_o (lambda ((X3 tptp.option_game) (Y3 tptp.option_fml)) (@ (@ tptp.member1883102883on_fml (@ (@ tptp.produc2124676926on_fml X3) Y3)) R))) (lambda ((X3 tptp.option_game) (Y3 tptp.option_fml)) (@ (@ tptp.member1883102883on_fml (@ (@ tptp.produc2124676926on_fml X3) Y3)) S))) (@ (@ tptp.ord_le782333474on_fml R) S))) (forall ((R tptp.set_Pr1471344007on_trm) (S tptp.set_Pr1471344007on_trm)) (= (@ (@ tptp.ord_le847028878_trm_o (lambda ((X3 tptp.option_trm) (Y3 tptp.option_trm)) (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm X3) Y3)) R))) (lambda ((X3 tptp.option_trm) (Y3 tptp.option_trm)) (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm X3) Y3)) S))) (@ (@ tptp.ord_le1322722599on_trm R) S))) (forall ((R tptp.set_Pr927595527on_fml) (S tptp.set_Pr927595527on_fml)) (= (@ (@ tptp.ord_le802833166_fml_o (lambda ((X3 tptp.option_fml) (Y3 tptp.option_fml)) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml X3) Y3)) R))) (lambda ((X3 tptp.option_fml) (Y3 tptp.option_fml)) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml X3) Y3)) S))) (@ (@ tptp.ord_le778974119on_fml R) S))) (forall ((R tptp.set_Pr943832262on_trm) (S tptp.set_Pr943832262on_trm)) (= (@ (@ tptp.ord_le1890124833_trm_o (lambda ((X3 tptp.char) (Y3 tptp.option_trm)) (@ (@ tptp.member694524327on_trm (@ (@ tptp.produc1500300866on_trm X3) Y3)) R))) (lambda ((X3 tptp.char) (Y3 tptp.option_trm)) (@ (@ tptp.member694524327on_trm (@ (@ tptp.produc1500300866on_trm X3) Y3)) S))) (@ (@ tptp.ord_le541293862on_trm R) S))) (forall ((R tptp.set_Pr1235432374le_trm) (S tptp.set_Pr1235432374le_trm)) (= (@ (@ tptp.ord_le691957041_trm_o (lambda ((X3 tptp.set_variable) (Y3 tptp.trm)) (@ (@ tptp.member2122665623le_trm (@ (@ tptp.produc1482344242le_trm X3) Y3)) R))) (lambda ((X3 tptp.set_variable) (Y3 tptp.trm)) (@ (@ tptp.member2122665623le_trm (@ (@ tptp.produc1482344242le_trm X3) Y3)) S))) (@ (@ tptp.ord_le2102862870le_trm R) S))) (forall ((Option tptp.option_trm)) (= (= Option tptp.none_trm) (@ (@ (@ tptp.case_option_o_trm true) (lambda ((Uu tptp.trm)) false)) Option))) (forall ((Option tptp.option_fml)) (= (= Option tptp.none_fml) (@ (@ (@ tptp.case_option_o_fml true) (lambda ((Uu tptp.fml)) false)) Option))) (forall ((Option tptp.option_game)) (= (= Option tptp.none_game) (@ (@ (@ tptp.case_option_o_game true) (lambda ((Uu tptp.game)) false)) Option))) (forall ((Option tptp.option_trm)) (= (not (= Option tptp.none_trm)) (@ (@ (@ tptp.case_option_o_trm false) (lambda ((Uu tptp.trm)) true)) Option))) (forall ((Option tptp.option_fml)) (= (not (= Option tptp.none_fml)) (@ (@ (@ tptp.case_option_o_fml false) (lambda ((Uu tptp.fml)) true)) Option))) (forall ((Option tptp.option_game)) (= (not (= Option tptp.none_game)) (@ (@ (@ tptp.case_option_o_game false) (lambda ((Uu tptp.game)) true)) Option))) (forall ((X2 tptp.produc1072747943on_trm)) (=> (forall ((Theta2 tptp.trm) (Eta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc709594775on_trm (@ tptp.some_trm Theta2)) (@ tptp.some_trm Eta2))))) (=> (forall ((Eta2 tptp.option_trm)) (not (= X2 (@ (@ tptp.produc709594775on_trm tptp.none_trm) Eta2)))) (not (forall ((V2 tptp.trm)) (not (= X2 (@ (@ tptp.produc709594775on_trm (@ tptp.some_trm V2)) tptp.none_trm)))))))) (forall ((P Bool) (Q (-> tptp.trm Bool)) (X2 tptp.option_trm)) (=> (@ (@ (@ tptp.case_option_o_trm P) Q) X2) (=> (=> (= X2 tptp.none_trm) (not P)) (not (forall ((Y4 tptp.trm)) (=> (= X2 (@ tptp.some_trm Y4)) (not (@ Q Y4)))))))) (forall ((P Bool) (Q (-> tptp.fml Bool)) (X2 tptp.option_fml)) (=> (@ (@ (@ tptp.case_option_o_fml P) Q) X2) (=> (=> (= X2 tptp.none_fml) (not P)) (not (forall ((Y4 tptp.fml)) (=> (= X2 (@ tptp.some_fml Y4)) (not (@ Q Y4)))))))) (forall ((P Bool) (Q (-> tptp.game Bool)) (X2 tptp.option_game)) (=> (@ (@ (@ tptp.case_option_o_game P) Q) X2) (=> (=> (= X2 tptp.none_game) (not P)) (not (forall ((Y4 tptp.game)) (=> (= X2 (@ tptp.some_game Y4)) (not (@ Q Y4)))))))) (forall ((X2 tptp.option_trm) (Xa tptp.option_trm) (Y2 tptp.option_trm)) (let ((_let_1 (@ tptp.accp_P758790320on_trm tptp.uSubst924844285so_rel))) (=> (= (@ (@ tptp.uSubst918876924Timeso X2) Xa) Y2) (=> (@ _let_1 (@ (@ tptp.produc709594775on_trm X2) Xa)) (=> (forall ((Theta2 tptp.trm)) (=> (= X2 (@ tptp.some_trm Theta2)) (forall ((Eta2 tptp.trm)) (let ((_let_1 (@ tptp.some_trm Eta2))) (=> (= Xa _let_1) (=> (= Y2 (@ tptp.some_trm (@ (@ tptp.times Theta2) Eta2))) (not (@ (@ tptp.accp_P758790320on_trm tptp.uSubst924844285so_rel) (@ (@ tptp.produc709594775on_trm (@ tptp.some_trm Theta2)) _let_1))))))))) (=> (=> (= X2 tptp.none_trm) (=> (= Y2 tptp.none_trm) (not (@ _let_1 (@ (@ tptp.produc709594775on_trm tptp.none_trm) Xa))))) (not (forall ((V2 tptp.trm)) (let ((_let_1 (@ tptp.some_trm V2))) (=> (= X2 _let_1) (=> (= Xa tptp.none_trm) (=> (= Y2 tptp.none_trm) (not (@ (@ tptp.accp_P758790320on_trm tptp.uSubst924844285so_rel) (@ (@ tptp.produc709594775on_trm _let_1) tptp.none_trm))))))))))))))) (forall ((X2 tptp.option_trm) (Xa tptp.option_trm) (Y2 tptp.option_trm)) (let ((_let_1 (@ tptp.accp_P758790320on_trm tptp.uSubst691094423so_rel))) (=> (= (@ (@ tptp.uSubst141955042_Pluso X2) Xa) Y2) (=> (@ _let_1 (@ (@ tptp.produc709594775on_trm X2) Xa)) (=> (forall ((Theta2 tptp.trm)) (=> (= X2 (@ tptp.some_trm Theta2)) (forall ((Eta2 tptp.trm)) (let ((_let_1 (@ tptp.some_trm Eta2))) (=> (= Xa _let_1) (=> (= Y2 (@ tptp.some_trm (@ (@ tptp.plus Theta2) Eta2))) (not (@ (@ tptp.accp_P758790320on_trm tptp.uSubst691094423so_rel) (@ (@ tptp.produc709594775on_trm (@ tptp.some_trm Theta2)) _let_1))))))))) (=> (=> (= X2 tptp.none_trm) (=> (= Y2 tptp.none_trm) (not (@ _let_1 (@ (@ tptp.produc709594775on_trm tptp.none_trm) Xa))))) (not (forall ((V2 tptp.trm)) (let ((_let_1 (@ tptp.some_trm V2))) (=> (= X2 _let_1) (=> (= Xa tptp.none_trm) (=> (= Y2 tptp.none_trm) (not (@ (@ tptp.accp_P758790320on_trm tptp.uSubst691094423so_rel) (@ (@ tptp.produc709594775on_trm _let_1) tptp.none_trm))))))))))))))) (forall ((X2 tptp.produc464795408on_trm)) (=> (forall ((X tptp.char) (Theta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc1500300866on_trm X) (@ tptp.some_trm Theta2))))) (not (forall ((X tptp.char)) (not (= X2 (@ (@ tptp.produc1500300866on_trm X) tptp.none_trm))))))) (forall ((X2 tptp.produc1024976764on_trm)) (=> (forall ((X tptp.variable) (Theta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc1743721902on_trm X) (@ tptp.some_trm Theta2))))) (not (forall ((X tptp.variable)) (not (= X2 (@ (@ tptp.produc1743721902on_trm X) tptp.none_trm))))))) (forall ((X2 tptp.produc1016592119n_game)) (=> (forall ((Alpha tptp.game) (Beta tptp.game)) (not (= X2 (@ (@ tptp.produc1111617711n_game (@ tptp.some_game Alpha)) (@ tptp.some_game Beta))))) (=> (forall ((Alpha tptp.option_game)) (not (= X2 (@ (@ tptp.produc1111617711n_game Alpha) tptp.none_game)))) (not (forall ((V2 tptp.game)) (not (= X2 (@ (@ tptp.produc1111617711n_game tptp.none_game) (@ tptp.some_game V2))))))))) (forall ((X2 tptp.produc1408538418on_fml)) (=> (forall ((X tptp.variable) (Phi2 tptp.fml)) (not (= X2 (@ (@ tptp.produc1205977188on_fml X) (@ tptp.some_fml Phi2))))) (not (forall ((X tptp.variable)) (not (= X2 (@ (@ tptp.produc1205977188on_fml X) tptp.none_fml))))))) (forall ((X2 tptp.produc46605351on_fml)) (=> (forall ((Phi2 tptp.fml) (Psi tptp.fml)) (not (= X2 (@ (@ tptp.produc909629463on_fml (@ tptp.some_fml Phi2)) (@ tptp.some_fml Psi))))) (=> (forall ((Psi tptp.option_fml)) (not (= X2 (@ (@ tptp.produc909629463on_fml tptp.none_fml) Psi)))) (not (forall ((V2 tptp.fml)) (not (= X2 (@ (@ tptp.produc909629463on_fml (@ tptp.some_fml V2)) tptp.none_fml)))))))) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm)) (let ((_let_1 (@ tptp.uSubst516392818stappt Sigma))) (let ((_let_2 (@ tptp.differential Theta))) (=> (@ (@ tptp.accp_P1877119646le_trm tptp.uSubst1917534215pt_rel) (@ (@ tptp.produc2015636557le_trm Sigma) (@ (@ tptp.produc1482344242le_trm U) _let_2))) (= (@ (@ _let_1 U) _let_2) (@ tptp.uSubst716837505ntialo (@ (@ _let_1 (@ tptp.collect_variable (lambda ((X3 tptp.variable)) true))) Theta))))))) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (let ((_let_2 (@ (@ tptp.times Theta) Eta))) (=> (@ (@ tptp.accp_P1877119646le_trm tptp.uSubst1917534215pt_rel) (@ (@ tptp.produc2015636557le_trm Sigma) (@ (@ tptp.produc1482344242le_trm U) _let_2))) (= (@ _let_1 _let_2) (@ (@ tptp.uSubst918876924Timeso (@ _let_1 Theta)) (@ _let_1 Eta))))))) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (Theta tptp.trm) (Eta tptp.trm)) (let ((_let_1 (@ (@ tptp.uSubst516392818stappt Sigma) U))) (let ((_let_2 (@ (@ tptp.plus Theta) Eta))) (=> (@ (@ tptp.accp_P1877119646le_trm tptp.uSubst1917534215pt_rel) (@ (@ tptp.produc2015636557le_trm Sigma) (@ (@ tptp.produc1482344242le_trm U) _let_2))) (= (@ _let_1 _let_2) (@ (@ tptp.uSubst141955042_Pluso (@ _let_1 Theta)) (@ _let_1 Eta))))))) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (X2 tptp.variable)) (let ((_let_1 (@ tptp.var X2))) (=> (@ (@ tptp.accp_P1877119646le_trm tptp.uSubst1917534215pt_rel) (@ (@ tptp.produc2015636557le_trm Sigma) (@ (@ tptp.produc1482344242le_trm U) _let_1))) (= (@ (@ (@ tptp.uSubst516392818stappt Sigma) U) _let_1) (@ tptp.some_trm _let_1))))) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (R3 tptp.real)) (let ((_let_1 (@ tptp.number R3))) (=> (@ (@ tptp.accp_P1877119646le_trm tptp.uSubst1917534215pt_rel) (@ (@ tptp.produc2015636557le_trm Sigma) (@ (@ tptp.produc1482344242le_trm U) _let_1))) (= (@ (@ (@ tptp.uSubst516392818stappt Sigma) U) _let_1) (@ tptp.some_trm _let_1))))) (forall ((A3 tptp.option_trm) (B3 tptp.option_fml) (A6 tptp.option_trm) (B6 tptp.option_fml) (R3 tptp.set_Pr1471344007on_trm) (S2 tptp.set_Pr927595527on_fml)) (= (@ (@ tptp.member1316917136on_fml (@ (@ tptp.produc1235825367on_fml (@ (@ tptp.produc171850061on_fml A3) B3)) (@ (@ tptp.produc171850061on_fml A6) B6))) (@ (@ tptp.lex_pr1724583269on_fml R3) S2)) (or (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm A3) A6)) R3) (and (= A3 A6) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml B3) B6)) S2))))) (forall ((A3 tptp.option_fml) (B3 tptp.option_trm) (A6 tptp.option_fml) (B6 tptp.option_trm) (R3 tptp.set_Pr927595527on_fml) (S2 tptp.set_Pr1471344007on_trm)) (= (@ (@ tptp.member1883874960on_trm (@ (@ tptp.produc2132972503on_trm (@ (@ tptp.produc1447374177on_trm A3) B3)) (@ (@ tptp.produc1447374177on_trm A6) B6))) (@ (@ tptp.lex_pr852623737on_trm R3) S2)) (or (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml A3) A6)) R3) (and (= A3 A6) (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm B3) B6)) S2))))) (forall ((A3 tptp.option_game) (B3 tptp.option_fml) (A6 tptp.option_game) (B6 tptp.option_fml) (R3 tptp.set_Pr1625152599n_game) (S2 tptp.set_Pr927595527on_fml)) (= (@ (@ tptp.member113767842on_fml (@ (@ tptp.produc556056113on_fml (@ (@ tptp.produc2124676926on_fml A3) B3)) (@ (@ tptp.produc2124676926on_fml A6) B6))) (@ (@ tptp.lex_pr425996582on_fml R3) S2)) (or (@ (@ tptp.member191809696n_game (@ (@ tptp.produc1111617711n_game A3) A6)) R3) (and (= A3 A6) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml B3) B6)) S2))))) (forall ((A3 tptp.option_trm) (B3 tptp.option_trm) (A6 tptp.option_trm) (B6 tptp.option_trm) (R3 tptp.set_Pr1471344007on_trm) (S2 tptp.set_Pr1471344007on_trm)) (let ((_let_1 (@ tptp.produc709594775on_trm A3))) (= (@ (@ tptp.member602811152on_trm (@ (@ tptp.produc2001752919on_trm (@ _let_1 B3)) (@ (@ tptp.produc709594775on_trm A6) B6))) (@ (@ tptp.lex_pr114844335on_trm R3) S2)) (or (@ (@ tptp.member165817296on_trm (@ _let_1 A6)) R3) (and (= A3 A6) (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm B3) B6)) S2)))))) (forall ((A3 tptp.option_fml) (B3 tptp.option_fml) (A6 tptp.option_fml) (B6 tptp.option_fml) (R3 tptp.set_Pr927595527on_fml) (S2 tptp.set_Pr927595527on_fml)) (let ((_let_1 (@ tptp.produc909629463on_fml A3))) (= (@ (@ tptp.member450497296on_fml (@ (@ tptp.produc1367044951on_fml (@ _let_1 B3)) (@ (@ tptp.produc909629463on_fml A6) B6))) (@ (@ tptp.lex_pr314879023on_fml R3) S2)) (or (@ (@ tptp.member1287158352on_fml (@ _let_1 A6)) R3) (and (= A3 A6) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml B3) B6)) S2)))))) (forall ((A3 tptp.char) (B3 tptp.option_trm) (A6 tptp.char) (B6 tptp.option_trm) (R3 tptp.set_Pr604539619r_char) (S2 tptp.set_Pr1471344007on_trm)) (= (@ (@ tptp.member1950256170on_trm (@ (@ tptp.produc444919481on_trm (@ (@ tptp.produc1500300866on_trm A3) B3)) (@ (@ tptp.produc1500300866on_trm A6) B6))) (@ (@ tptp.lex_pr1901327402on_trm R3) S2)) (or (@ (@ tptp.member1866856748r_char (@ (@ tptp.produc19545147r_char A3) A6)) R3) (and (= A3 A6) (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm B3) B6)) S2))))) (forall ((A3 tptp.set_variable) (B3 tptp.trm) (A6 tptp.set_variable) (B6 tptp.trm) (R3 tptp.set_Pr181266295riable) (S2 tptp.set_Pr491793543rm_trm)) (= (@ (@ tptp.member1150310282le_trm (@ (@ tptp.produc1056455193le_trm (@ (@ tptp.produc1482344242le_trm A3) B3)) (@ (@ tptp.produc1482344242le_trm A6) B6))) (@ (@ tptp.lex_pr1522821402le_trm R3) S2)) (or (@ (@ tptp.member1978718144riable (@ (@ tptp.produc1766592463riable A3) A6)) R3) (and (= A3 A6) (@ (@ tptp.member1735386832rm_trm (@ (@ tptp.product_Pair_trm_trm B3) B6)) S2))))) (forall ((X23 tptp.real) (Y23 tptp.real)) (= (= (@ tptp.number X23) (@ tptp.number Y23)) (= X23 Y23))) (forall ((X1 tptp.variable) (Y1 tptp.variable)) (= (= (@ tptp.var X1) (@ tptp.var Y1)) (= X1 Y1))) (forall ((X23 tptp.real) (X51 tptp.trm) (X52 tptp.trm)) (not (= (@ tptp.number X23) (@ (@ tptp.plus X51) X52)))) (forall ((X23 tptp.real) (X61 tptp.trm) (X62 tptp.trm)) (not (= (@ tptp.number X23) (@ (@ tptp.times X61) X62)))) (forall ((X23 tptp.real) (X7 tptp.trm)) (not (= (@ tptp.number X23) (@ tptp.differential X7)))) (forall ((X1 tptp.variable) (X51 tptp.trm) (X52 tptp.trm)) (not (= (@ tptp.var X1) (@ (@ tptp.plus X51) X52)))) (forall ((X1 tptp.variable) (X61 tptp.trm) (X62 tptp.trm)) (not (= (@ tptp.var X1) (@ (@ tptp.times X61) X62)))) (forall ((X1 tptp.variable) (X7 tptp.trm)) (not (= (@ tptp.var X1) (@ tptp.differential X7)))) (forall ((X1 tptp.variable) (X23 tptp.real)) (not (= (@ tptp.var X1) (@ tptp.number X23)))) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (R3 tptp.real)) (let ((_let_1 (@ tptp.number R3))) (= (@ (@ (@ tptp.uSubst516392818stappt Sigma) U) _let_1) (@ tptp.some_trm _let_1)))) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (X2 tptp.variable)) (let ((_let_1 (@ tptp.var X2))) (= (@ (@ (@ tptp.uSubst516392818stappt Sigma) U) _let_1) (@ tptp.some_trm _let_1)))) (forall ((X2 tptp.produc1699626005le_trm)) (=> (forall ((Sigma2 tptp.produc1418842292n_game) (U3 tptp.set_variable) (X tptp.variable)) (not (= X2 (@ (@ tptp.produc2015636557le_trm Sigma2) (@ (@ tptp.produc1482344242le_trm U3) (@ tptp.var X)))))) (=> (forall ((Sigma2 tptp.produc1418842292n_game) (U3 tptp.set_variable) (R5 tptp.real)) (not (= X2 (@ (@ tptp.produc2015636557le_trm Sigma2) (@ (@ tptp.produc1482344242le_trm U3) (@ tptp.number R5)))))) (=> (forall ((Sigma2 tptp.produc1418842292n_game) (U3 tptp.set_variable) (F3 tptp.char)) (not (= X2 (@ (@ tptp.produc2015636557le_trm Sigma2) (@ (@ tptp.produc1482344242le_trm U3) (@ tptp.const F3)))))) (=> (forall ((Sigma2 tptp.produc1418842292n_game) (U3 tptp.set_variable) (F3 tptp.char) (Theta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc2015636557le_trm Sigma2) (@ (@ tptp.produc1482344242le_trm U3) (@ (@ tptp.func F3) Theta2)))))) (=> (forall ((Sigma2 tptp.produc1418842292n_game) (U3 tptp.set_variable) (Theta2 tptp.trm) (Eta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc2015636557le_trm Sigma2) (@ (@ tptp.produc1482344242le_trm U3) (@ (@ tptp.plus Theta2) Eta2)))))) (=> (forall ((Sigma2 tptp.produc1418842292n_game) (U3 tptp.set_variable) (Theta2 tptp.trm) (Eta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc2015636557le_trm Sigma2) (@ (@ tptp.produc1482344242le_trm U3) (@ (@ tptp.times Theta2) Eta2)))))) (not (forall ((Sigma2 tptp.produc1418842292n_game) (U3 tptp.set_variable) (Theta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc2015636557le_trm Sigma2) (@ (@ tptp.produc1482344242le_trm U3) (@ tptp.differential Theta2)))))))))))))) _let_13 (forall ((Phi tptp.option_fml)) (= (= (@ tptp.uSubst1367128042_Testo Phi) tptp.none_game) (= Phi tptp.none_fml))) (forall ((X41 tptp.char) (X42 tptp.trm) (Y41 tptp.char) (Y42 tptp.trm)) (= (= (@ (@ tptp.func X41) X42) (@ (@ tptp.func Y41) Y42)) (and (= X41 Y41) (= X42 Y42)))) (forall ((X32 tptp.char) (Y32 tptp.char)) (= (= (@ tptp.const X32) (@ tptp.const Y32)) (= X32 Y32))) (forall ((X1 tptp.variable) (X32 tptp.char)) (not (= (@ tptp.var X1) (@ tptp.const X32)))) (forall ((X1 tptp.variable) (X41 tptp.char) (X42 tptp.trm)) (not (= (@ tptp.var X1) (@ (@ tptp.func X41) X42)))) (forall ((X23 tptp.real) (X32 tptp.char)) (not (= (@ tptp.number X23) (@ tptp.const X32)))) (forall ((X23 tptp.real) (X41 tptp.char) (X42 tptp.trm)) (not (= (@ tptp.number X23) (@ (@ tptp.func X41) X42)))) (forall ((X32 tptp.char) (X41 tptp.char) (X42 tptp.trm)) (not (= (@ tptp.const X32) (@ (@ tptp.func X41) X42)))) (forall ((X32 tptp.char) (X7 tptp.trm)) (not (= (@ tptp.const X32) (@ tptp.differential X7)))) (forall ((X32 tptp.char) (X61 tptp.trm) (X62 tptp.trm)) (not (= (@ tptp.const X32) (@ (@ tptp.times X61) X62)))) (forall ((X32 tptp.char) (X51 tptp.trm) (X52 tptp.trm)) (not (= (@ tptp.const X32) (@ (@ tptp.plus X51) X52)))) (forall ((X41 tptp.char) (X42 tptp.trm) (X7 tptp.trm)) (not (= (@ (@ tptp.func X41) X42) (@ tptp.differential X7)))) (forall ((X41 tptp.char) (X42 tptp.trm) (X61 tptp.trm) (X62 tptp.trm)) (not (= (@ (@ tptp.func X41) X42) (@ (@ tptp.times X61) X62)))) (forall ((X41 tptp.char) (X42 tptp.trm) (X51 tptp.trm) (X52 tptp.trm)) (not (= (@ (@ tptp.func X41) X42) (@ (@ tptp.plus X51) X52)))) (forall ((P (-> tptp.trm Bool)) (Trm tptp.trm)) (=> (forall ((X tptp.variable)) (@ P (@ tptp.var X))) (=> (forall ((X tptp.real)) (@ P (@ tptp.number X))) (=> (forall ((X tptp.char)) (@ P (@ tptp.const X))) (=> (forall ((X1a tptp.char) (X2a tptp.trm)) (=> (@ P X2a) (@ P (@ (@ tptp.func X1a) X2a)))) (=> (forall ((X1a tptp.trm) (X2a tptp.trm)) (=> (@ P X1a) (=> (@ P X2a) (@ P (@ (@ tptp.plus X1a) X2a))))) (=> (forall ((X1a tptp.trm) (X2a tptp.trm)) (=> (@ P X1a) (=> (@ P X2a) (@ P (@ (@ tptp.times X1a) X2a))))) (=> (forall ((X tptp.trm)) (=> (@ P X) (@ P (@ tptp.differential X)))) (@ P Trm))))))))) (forall ((Y2 tptp.trm)) (=> (forall ((X12 tptp.variable)) (not (= Y2 (@ tptp.var X12)))) (=> (forall ((X24 tptp.real)) (not (= Y2 (@ tptp.number X24)))) (=> (forall ((X33 tptp.char)) (not (= Y2 (@ tptp.const X33)))) (=> (forall ((X412 tptp.char) (X422 tptp.trm)) (not (= Y2 (@ (@ tptp.func X412) X422)))) (=> (forall ((X512 tptp.trm) (X522 tptp.trm)) (not (= Y2 (@ (@ tptp.plus X512) X522)))) (=> (forall ((X612 tptp.trm) (X622 tptp.trm)) (not (= Y2 (@ (@ tptp.times X612) X622)))) (not (forall ((X72 tptp.trm)) (not (= Y2 (@ tptp.differential X72)))))))))))) (forall ((X2 tptp.produc833882726rp_trm)) (=> (forall ((I2 tptp.denotational_interp) (X tptp.variable)) (not (= X2 (@ (@ tptp.produc1132922070rp_trm I2) (@ tptp.var X))))) (=> (forall ((I2 tptp.denotational_interp) (R5 tptp.real)) (not (= X2 (@ (@ tptp.produc1132922070rp_trm I2) (@ tptp.number R5))))) (=> (forall ((I2 tptp.denotational_interp) (F3 tptp.char)) (not (= X2 (@ (@ tptp.produc1132922070rp_trm I2) (@ tptp.const F3))))) (=> (forall ((I2 tptp.denotational_interp) (F3 tptp.char) (Theta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc1132922070rp_trm I2) (@ (@ tptp.func F3) Theta2))))) (=> (forall ((I2 tptp.denotational_interp) (Theta2 tptp.trm) (Eta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc1132922070rp_trm I2) (@ (@ tptp.plus Theta2) Eta2))))) (=> (forall ((I2 tptp.denotational_interp) (Theta2 tptp.trm) (Eta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc1132922070rp_trm I2) (@ (@ tptp.times Theta2) Eta2))))) (not (forall ((I2 tptp.denotational_interp) (Theta2 tptp.trm)) (not (= X2 (@ (@ tptp.produc1132922070rp_trm I2) (@ tptp.differential Theta2))))))))))))) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (F tptp.char)) (let ((_let_1 (@ tptp.const F))) (=> (@ (@ tptp.accp_P1877119646le_trm tptp.uSubst1917534215pt_rel) (@ (@ tptp.produc2015636557le_trm Sigma) (@ (@ tptp.produc1482344242le_trm U) _let_1))) (= (@ (@ (@ tptp.uSubst516392818stappt Sigma) U) _let_1) (@ (@ (@ tptp.uSubst1559070963pconst Sigma) U) F))))) (forall ((P (-> tptp.denotational_interp tptp.trm Bool)) (A0 tptp.denotational_interp) (A1 tptp.trm)) (=> (forall ((I2 tptp.denotational_interp) (X tptp.variable)) (@ (@ P I2) (@ tptp.var X))) (=> (forall ((I2 tptp.denotational_interp) (R5 tptp.real)) (@ (@ P I2) (@ tptp.number R5))) (=> (forall ((I2 tptp.denotational_interp) (F3 tptp.char)) (@ (@ P I2) (@ tptp.const F3))) (=> (forall ((I2 tptp.denotational_interp) (F3 tptp.char) (Theta2 tptp.trm)) (let ((_let_1 (@ P I2))) (=> (@ _let_1 Theta2) (@ _let_1 (@ (@ tptp.func F3) Theta2))))) (=> (forall ((I2 tptp.denotational_interp) (Theta2 tptp.trm)) (=> (@ (@ P I2) Theta2) (forall ((Eta2 tptp.trm)) (let ((_let_1 (@ P I2))) (=> (@ _let_1 Eta2) (@ _let_1 (@ (@ tptp.plus Theta2) Eta2))))))) (=> (forall ((I2 tptp.denotational_interp) (Theta2 tptp.trm)) (=> (@ (@ P I2) Theta2) (forall ((Eta2 tptp.trm)) (let ((_let_1 (@ P I2))) (=> (@ _let_1 Eta2) (@ _let_1 (@ (@ tptp.times Theta2) Eta2))))))) (=> (forall ((I2 tptp.denotational_interp) (Theta2 tptp.trm)) (let ((_let_1 (@ P I2))) (=> (=> (exists ((Xa2 tptp.char)) (@ (@ tptp.member_char Xa2) (@ tptp.collect_char (lambda ((Uu tptp.char)) true)))) (@ _let_1 Theta2)) (@ _let_1 (@ tptp.differential Theta2))))) (@ (@ P A0) A1))))))))) (forall ((Sigma tptp.produc1418842292n_game) (U tptp.set_variable) (F tptp.char)) (= (@ (@ (@ tptp.uSubst516392818stappt Sigma) U) (@ tptp.const F)) (@ (@ (@ tptp.uSubst1559070963pconst Sigma) U) F))) _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 (forall ((X2 tptp.option_fml) (Y2 tptp.option_game)) (=> (= (@ tptp.uSubst1367128042_Testo X2) Y2) (=> (forall ((Phi2 tptp.fml)) (=> (= X2 (@ tptp.some_fml Phi2)) (not (= Y2 (@ tptp.some_game (@ tptp.test Phi2)))))) (not (=> (= X2 tptp.none_fml) (not (= Y2 tptp.none_game))))))) (forall ((X32 tptp.fml) (Y32 tptp.fml)) (= (= (@ tptp.test X32) (@ tptp.test Y32)) (= X32 Y32))) (forall ((B3 tptp.option_game) (F (-> tptp.variable tptp.option_game)) (X2 tptp.variable) (C tptp.option_fml) (G2 (-> tptp.variable tptp.option_fml)) (A tptp.set_variable)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_variable X2) A) (@ (@ tptp.member1883102883on_fml (@ (@ tptp.produc2124676926on_fml B3) C)) (@ (@ (@ tptp.bNF_Gr2142503190on_fml A) F) G2)))))) (forall ((B3 tptp.option_game) (F (-> tptp.char tptp.option_game)) (X2 tptp.char) (C tptp.option_fml) (G2 (-> tptp.char tptp.option_fml)) (A tptp.set_char)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_char X2) A) (@ (@ tptp.member1883102883on_fml (@ (@ tptp.produc2124676926on_fml B3) C)) (@ (@ (@ tptp.bNF_Gr756940202on_fml A) F) G2)))))) (forall ((B3 tptp.option_trm) (F (-> tptp.variable tptp.option_trm)) (X2 tptp.variable) (C tptp.option_trm) (G2 (-> tptp.variable tptp.option_trm)) (A tptp.set_variable)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_variable X2) A) (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm B3) C)) (@ (@ (@ tptp.bNF_Gr400922303on_trm A) F) G2)))))) (forall ((B3 tptp.option_trm) (F (-> tptp.char tptp.option_trm)) (X2 tptp.char) (C tptp.option_trm) (G2 (-> tptp.char tptp.option_trm)) (A tptp.set_char)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_char X2) A) (@ (@ tptp.member165817296on_trm (@ (@ tptp.produc709594775on_trm B3) C)) (@ (@ (@ tptp.bNF_Gr1666135339on_trm A) F) G2)))))) (forall ((B3 tptp.option_fml) (F (-> tptp.variable tptp.option_fml)) (X2 tptp.variable) (C tptp.option_fml) (G2 (-> tptp.variable tptp.option_fml)) (A tptp.set_variable)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_variable X2) A) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml B3) C)) (@ (@ (@ tptp.bNF_Gr600956991on_fml A) F) G2)))))) (forall ((B3 tptp.option_fml) (F (-> tptp.char tptp.option_fml)) (X2 tptp.char) (C tptp.option_fml) (G2 (-> tptp.char tptp.option_fml)) (A tptp.set_char)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_char X2) A) (@ (@ tptp.member1287158352on_fml (@ (@ tptp.produc909629463on_fml B3) C)) (@ (@ (@ tptp.bNF_Gr1866170027on_fml A) F) G2)))))) (forall ((B3 tptp.char) (F (-> tptp.variable tptp.char)) (X2 tptp.variable) (C tptp.option_trm) (G2 (-> tptp.variable tptp.option_trm)) (A tptp.set_variable)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_variable X2) A) (@ (@ tptp.member694524327on_trm (@ (@ tptp.produc1500300866on_trm B3) C)) (@ (@ (@ tptp.bNF_Gr1933470746on_trm A) F) G2)))))) (forall ((B3 tptp.char) (F (-> tptp.char tptp.char)) (X2 tptp.char) (C tptp.option_trm) (G2 (-> tptp.char tptp.option_trm)) (A tptp.set_char)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_char X2) A) (@ (@ tptp.member694524327on_trm (@ (@ tptp.produc1500300866on_trm B3) C)) (@ (@ (@ tptp.bNF_Gr951178926on_trm A) F) G2)))))) (forall ((B3 tptp.set_variable) (F (-> tptp.variable tptp.set_variable)) (X2 tptp.variable) (C tptp.trm) (G2 (-> tptp.variable tptp.trm)) (A tptp.set_variable)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_variable X2) A) (@ (@ tptp.member2122665623le_trm (@ (@ tptp.produc1482344242le_trm B3) C)) (@ (@ (@ tptp.bNF_Gr1330108682le_trm A) F) G2)))))) (forall ((B3 tptp.set_variable) (F (-> tptp.char tptp.set_variable)) (X2 tptp.char) (C tptp.trm) (G2 (-> tptp.char tptp.trm)) (A tptp.set_char)) (=> (= B3 (@ F X2)) (=> (= C (@ G2 X2)) (=> (@ (@ tptp.member_char X2) A) (@ (@ tptp.member2122665623le_trm (@ (@ tptp.produc1482344242le_trm B3) C)) (@ (@ (@ tptp.bNF_Gr852774302le_trm A) F) G2)))))) (forall ((Phi tptp.fml)) (= (@ tptp.uSubst1367128042_Testo (@ tptp.some_fml Phi)) (@ tptp.some_game (@ tptp.test Phi)))) (forall ((X2 tptp.option_fml) (Y2 tptp.option_game)) (let ((_let_1 (@ tptp.accp_option_fml tptp.uSubst954181007to_rel))) (=> (= (@ tptp.uSubst1367128042_Testo X2) Y2) (=> (@ _let_1 X2) (=> (forall ((Phi2 tptp.fml)) (let ((_let_1 (@ tptp.some_fml Phi2))) (=> (= X2 _let_1) (=> (= Y2 (@ tptp.some_game (@ tptp.test Phi2))) (not (@ (@ tptp.accp_option_fml tptp.uSubst954181007to_rel) _let_1)))))) (not (=> (= X2 tptp.none_fml) (=> (= Y2 tptp.none_game) (not (@ _let_1 tptp.none_fml)))))))))) _let_2 (forall ((X2 tptp.variable) (Theta tptp.option_trm)) (= (= (@ (@ tptp.uSubst834381837ssigno X2) Theta) tptp.none_game) (= Theta tptp.none_trm))) (forall ((X2 tptp.variable)) (= (@ (@ tptp.uSubst834381837ssigno X2) tptp.none_trm) tptp.none_game)) (forall ((X2 tptp.variable) (Xa tptp.option_trm) (Y2 tptp.option_game)) (=> (= (@ (@ tptp.uSubst834381837ssigno X2) Xa) Y2) (=> (forall ((Theta2 tptp.trm)) (=> (= Xa (@ tptp.some_trm Theta2)) (not (= Y2 (@ tptp.some_game (@ (@ tptp.assign X2) Theta2)))))) (not (=> (= Xa tptp.none_trm) (not (= Y2 tptp.none_game))))))) (forall ((X2 tptp.variable) (Xa tptp.option_trm) (Y2 tptp.option_game)) (let ((_let_1 (@ tptp.produc1743721902on_trm X2))) (let ((_let_2 (@ tptp.accp_P394694195on_trm tptp.uSubst157155628no_rel))) (=> (= (@ (@ tptp.uSubst834381837ssigno X2) Xa) Y2) (=> (@ _let_2 (@ _let_1 Xa)) (=> (forall ((Theta2 tptp.trm)) (let ((_let_1 (@ tptp.some_trm Theta2))) (=> (= Xa _let_1) (=> (= Y2 (@ tptp.some_game (@ (@ tptp.assign X2) Theta2))) (not (@ (@ tptp.accp_P394694195on_trm tptp.uSubst157155628no_rel) (@ (@ tptp.produc1743721902on_trm X2) _let_1))))))) (not (=> (= Xa tptp.none_trm) (=> (= Y2 tptp.none_game) (not (@ _let_2 (@ _let_1 tptp.none_trm)))))))))))) (forall ((X21 tptp.variable) (X22 tptp.trm) (Y21 tptp.variable) (Y22 tptp.trm)) (= (= (@ (@ tptp.assign X21) X22) (@ (@ tptp.assign Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))) (forall ((X21 tptp.variable) (X22 tptp.trm) (X32 tptp.fml)) (not (= (@ (@ tptp.assign X21) X22) (@ tptp.test X32)))) (forall ((X2 tptp.variable) (Theta tptp.trm)) (= (@ (@ tptp.uSubst834381837ssigno X2) (@ tptp.some_trm Theta)) (@ tptp.some_game (@ (@ tptp.assign X2) Theta)))) (forall ((X2 tptp.char) (Theta tptp.option_trm)) (= (= (@ (@ tptp.uSubst1827052306e_ODEo X2) Theta) tptp.none_game) (= Theta tptp.none_trm))) (forall ((X2 tptp.char)) (= (@ (@ tptp.uSubst1827052306e_ODEo X2) tptp.none_trm) tptp.none_game)) (forall ((X2 tptp.char) (Xa tptp.option_trm) (Y2 tptp.option_game)) (=> (= (@ (@ tptp.uSubst1827052306e_ODEo X2) Xa) Y2) (=> (forall ((Theta2 tptp.trm)) (=> (= Xa (@ tptp.some_trm Theta2)) (not (= Y2 (@ tptp.some_game (@ (@ tptp.ode X2) Theta2)))))) (not (=> (= Xa tptp.none_trm) (not (= Y2 tptp.none_game))))))) (forall ((X2 tptp.char) (Xa tptp.option_trm) (Y2 tptp.option_game)) (let ((_let_1 (@ tptp.produc1500300866on_trm X2))) (let ((_let_2 (@ tptp.accp_P419951815on_trm tptp.uSubst299938919Eo_rel))) (=> (= (@ (@ tptp.uSubst1827052306e_ODEo X2) Xa) Y2) (=> (@ _let_2 (@ _let_1 Xa)) (=> (forall ((Theta2 tptp.trm)) (let ((_let_1 (@ tptp.some_trm Theta2))) (=> (= Xa _let_1) (=> (= Y2 (@ tptp.some_game (@ (@ tptp.ode X2) Theta2))) (not (@ (@ tptp.accp_P419951815on_trm tptp.uSubst299938919Eo_rel) (@ (@ tptp.produc1500300866on_trm X2) _let_1))))))) (not (=> (= Xa tptp.none_trm) (=> (= Y2 tptp.none_game) (not (@ _let_2 (@ _let_1 tptp.none_trm)))))))))))) (forall ((X81 tptp.char) (X82 tptp.trm) (Y81 tptp.char) (Y82 tptp.trm)) (= (= (@ (@ tptp.ode X81) X82) (@ (@ tptp.ode Y81) Y82)) (and (= X81 Y81) (= X82 Y82)))) (forall ((X32 tptp.fml) (X81 tptp.char) (X82 tptp.trm)) (not (= (@ tptp.test X32) (@ (@ tptp.ode X81) X82)))) _let_1 true)))))))))))))))))))))))))
% 0.53/1.15 )
% 0.53/1.15 % SZS output end Proof for ITP200^1
% 0.53/1.15 % cvc5---1.0.5 exiting
% 0.53/1.15 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------