%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP201^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n002.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 Oct 9 01:45:25 PM UTC 2025
% Result : Theorem 20.51s 20.73s
% Output : Proof 20.51s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_set_variable_real,type,
set_variable_real: $tType ).
thf(ty_variable,type,
variable: $tType ).
thf(ty_real,type,
real: $tType ).
thf(ty_sigma,type,
sigma: produc1418842292n_game ).
thf(ty_member_variable_real,type,
member_variable_real: ( variable > real ) > set_variable_real > $o ).
thf(ty_i,type,
i: denotational_interp ).
thf(ty_denota1245701238me_sem,type,
denota1245701238me_sem: denotational_interp > game > set_variable_real > set_variable_real ).
thf(ty_the_game,type,
the_game: option_game > game ).
thf(ty_uminus430703407e_real,type,
uminus430703407e_real: set_variable_real > set_variable_real ).
thf(ty_ua,type,
ua: set_variable ).
thf(ty_uSubst516392814stappp,type,
uSubst516392814stappp: produc1418842292n_game > set_variable > game > produc1078154247n_game ).
thf(ty_xa,type,
xa: set_variable_real ).
thf(ty_alpha,type,
alpha: game ).
thf(ty_produc293487213n_game,type,
produc293487213n_game: produc1078154247n_game > option_game ).
thf(ty_uSubst1599435252djoint,type,
uSubst1599435252djoint: produc1418842292n_game > denotational_interp > ( variable > real ) > denotational_interp ).
thf(ty_omega2,type,
omega2: variable > real ).
thf(ty_nu2,type,
nu2: variable > real ).
thf(sP1,plain,
( sP1
<=> ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
= sP1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
= ( ~ ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) )
= sP4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: variable > real,X2: set_variable_real] :
( ~ ( member_variable_real @ X1 @ X2 )
=> ( member_variable_real @ X1 @ ( uminus430703407e_real @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP1 = ( ~ sP4 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: set_variable_real] :
( ~ ( member_variable_real @ nu2 @ X1 )
=> ( member_variable_real @ nu2 @ ( uminus430703407e_real @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: set_variable_real] :
( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ X1 ) )
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: set_variable_real] :
( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ X1 ) )
= ( ~ ( member_variable_real @ nu2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: variable > real,X2: set_variable_real] :
( ( member_variable_real @ X1 @ ( uminus430703407e_real @ X2 ) )
= ( ~ ( member_variable_real @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ sP4
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(conj_0,conjecture,
sP2 ).
thf(h0,negated_conjecture,
~ sP2,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP7
| ~ sP1
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP3
| ~ sP8
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP15
| sP4
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP9
| sP10
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP5
| ~ sP10
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP5
| sP10
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP13
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP13
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP11
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP11
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP12
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( sP2
| ~ sP8
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( sP2
| sP8
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP14
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP6
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_13_Compl__iff,axiom,
sP14 ).
thf(fact_10_ComplI,axiom,
sP6 ).
thf(fact_0__092_060open_062_092_060And_062X_O_A_I_092_060nu_062_A_092_060in_062_Agame__sem_AI_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_J_AX_J_A_061_A_I_092_060nu_062_A_092_060in_062_Agame__sem_A_IUSubst__Mirabelle__vidvnmlwwz_Oadjoint_A_092_060sigma_062_AI_A_092_060omega_062_J_A_092_060alpha_062_AX_J_092_060close_062,axiom,
sP12 ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h0,fact_13_Compl__iff,fact_10_ComplI,fact_0__092_060open_062_092_060And_062X_O_A_I_092_060nu_062_A_092_060in_062_Agame__sem_AI_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_J_AX_J_A_061_A_I_092_060nu_062_A_092_060in_062_Agame__sem_A_IUSubst__Mirabelle__vidvnmlwwz_Oadjoint_A_092_060sigma_062_AI_A_092_060omega_062_J_A_092_060alpha_062_AX_J_092_060close_062]) ).
thf(0,theorem,
sP2,
inference(contra,[status(thm),contra(discharge,[h0])],[16,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP201^1 : TPTP v9.2.0. Released v7.5.0.
% 0.11/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 17:56:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 20.51/20.73 % SZS status Theorem
% 20.51/20.73 % Mode: cade22sinegrackle2xfaf3
% 20.51/20.73 % Steps: 2913
% 20.51/20.73 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------