%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP201^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:07:09 AM UTC 2026
% Result : Theorem 23.91s 7.39s
% Output : Refutation 25.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 309
% Syntax : Number of formulae : 620 ( 322 unt; 0 typ; 0 def)
% Number of atoms : 1478 ( 597 equ; 18 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 4572 ( 106 ~; 0 |; 64 &;3834 @)
% ( 0 <=>; 568 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 16 ( 15 usr)
% Number of type conns : 276 ( 276 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 55 usr; 11 con; 0-3 aty)
% Number of variables : 1636 ( 164 ^;1456 !; 16 ?;1636 :)
% Comments :
%------------------------------------------------------------------------------
thf(produc1418842292n_game_type,type,
produc1418842292n_game: $tType ).
thf(produc2038871085e_real_type,type,
produc2038871085e_real: $tType ).
thf(produc1794985442e_real_type,type,
produc1794985442e_real: $tType ).
thf(produc1755325794riable_type,type,
produc1755325794riable: $tType ).
thf(set_Pr166476775n_game_type,type,
set_Pr166476775n_game: $tType ).
thf(produc1078154247n_game_type,type,
produc1078154247n_game: $tType ).
thf(produc735959047riable_type,type,
produc735959047riable: $tType ).
thf(produc432717079riable_type,type,
produc432717079riable: $tType ).
thf(set_variable_real_type,type,
set_variable_real: $tType ).
thf(option_game_type,type,
option_game: $tType ).
thf(denotational_interp_type,type,
denotational_interp: $tType ).
thf(set_variable_type,type,
set_variable: $tType ).
thf(variable_type,type,
variable: $tType ).
thf(game_type,type,
game: $tType ).
thf(real_type,type,
real: $tType ).
thf(denota1419872369iation_decl,type,
denota1419872369iation: ( variable > real ) > ( variable > real ) > set_variable > $o ).
thf(denota1245701238me_sem_decl,type,
denota1245701238me_sem: denotational_interp > game > set_variable_real > set_variable_real ).
thf(uminus970116630real_o_decl,type,
uminus970116630real_o: ( ( variable > real ) > $o ) > ( variable > real ) > $o ).
thf(uminus_uminus_o_decl,type,
uminus_uminus_o: $o > $o ).
thf(uminus501400228e_real_decl,type,
uminus501400228e_real: produc2038871085e_real > produc2038871085e_real ).
thf(uminus2115124697riable_decl,type,
uminus2115124697riable: produc1755325794riable > produc1755325794riable ).
thf(uminus7300697e_real_decl,type,
uminus7300697e_real: produc1794985442e_real > produc1794985442e_real ).
thf(uminus430703407e_real_decl,type,
uminus430703407e_real: set_variable_real > set_variable_real ).
thf(uminus1851247844riable_decl,type,
uminus1851247844riable: set_variable > set_variable ).
thf(sup_su1685293586e_real_decl,type,
sup_su1685293586e_real: set_variable_real > set_variable_real > set_variable_real ).
thf(sup_sup_set_variable_decl,type,
sup_sup_set_variable: set_variable > set_variable > set_variable ).
thf(none_game_decl,type,
none_game: option_game ).
thf(the_game_decl,type,
the_game: option_game > game ).
thf(ord_le1354144447real_o_decl,type,
ord_le1354144447real_o: ( ( variable > real ) > $o ) > ( ( variable > real ) > $o ) > $o ).
thf(ord_le1113654598e_real_decl,type,
ord_le1113654598e_real: set_variable_real > set_variable_real > $o ).
thf(ord_le282106107riable_decl,type,
ord_le282106107riable: set_variable > set_variable > $o ).
thf(produc1140431679riable_decl,type,
produc1140431679riable: option_game > set_variable > produc735959047riable ).
thf(produc86945893e_real_decl,type,
produc86945893e_real: set_variable_real > set_variable_real > produc2038871085e_real ).
thf(produc544095770riable_decl,type,
produc544095770riable: set_variable_real > set_variable > produc1755325794riable ).
thf(produc1149443391n_game_decl,type,
produc1149443391n_game: set_variable > option_game > produc1078154247n_game ).
thf(produc1400669210e_real_decl,type,
produc1400669210e_real: set_variable > set_variable_real > produc1794985442e_real ).
thf(produc884810027riable_decl,type,
produc884810027riable: produc735959047riable > option_game ).
thf(produc702045265e_real_decl,type,
produc702045265e_real: produc2038871085e_real > set_variable_real ).
thf(produc944271878riable_decl,type,
produc944271878riable: produc1755325794riable > set_variable_real ).
thf(produc893821739n_game_decl,type,
produc893821739n_game: produc1078154247n_game > set_variable ).
thf(produc1800845318e_real_decl,type,
produc1800845318e_real: produc1794985442e_real > set_variable ).
thf(produc284475501riable_decl,type,
produc284475501riable: produc735959047riable > set_variable ).
thf(produc220849299e_real_decl,type,
produc220849299e_real: produc2038871085e_real > set_variable_real ).
thf(produc1192298056riable_decl,type,
produc1192298056riable: produc1755325794riable > set_variable ).
thf(produc293487213n_game_decl,type,
produc293487213n_game: produc1078154247n_game > option_game ).
thf(produc2048871496e_real_decl,type,
produc2048871496e_real: produc1794985442e_real > set_variable_real ).
thf(produc345397471riable_decl,type,
produc345397471riable: produc735959047riable > produc1078154247n_game ).
thf(produc354409183n_game_decl,type,
produc354409183n_game: produc1078154247n_game > produc735959047riable ).
thf(collec633296133e_real_decl,type,
collec633296133e_real: ( ( variable > real ) > $o ) > set_variable_real ).
thf(collect_variable_decl,type,
collect_variable: ( variable > $o ) > set_variable ).
thf(skip_decl,type,
skip: game ).
thf(choice_decl,type,
choice: game > game > game ).
thf(dual_decl,type,
dual: game > game ).
thf(loop_decl,type,
loop: game > game ).
thf(uSubst1484167963hoiceo_decl,type,
uSubst1484167963hoiceo: option_game > option_game > option_game ).
thf(uSubst1916713664_Dualo_decl,type,
uSubst1916713664_Dualo: option_game > option_game ).
thf(uSubst23177304_Loopo_decl,type,
uSubst23177304_Loopo: option_game > option_game ).
thf(uSubst1599435252djoint_decl,type,
uSubst1599435252djoint: produc1418842292n_game > denotational_interp > ( variable > real ) > denotational_interp ).
thf(uSubst516392814stappp_decl,type,
uSubst516392814stappp: produc1418842292n_game > set_variable > game > produc1078154247n_game ).
thf(member_variable_real_decl,type,
member_variable_real: ( variable > real ) > set_variable_real > $o ).
thf(i_decl,type,
i: denotational_interp ).
thf(u_decl,type,
u: set_variable ).
thf(ua_decl,type,
ua: set_variable ).
thf(xa_decl,type,
xa: set_variable_real ).
thf(alpha_decl,type,
alpha: game ).
thf(nu_decl,type,
nu: variable > real ).
thf(nu2_decl,type,
nu2: variable > real ).
thf(omega_decl,type,
omega: variable > real ).
thf(omega2_decl,type,
omega2: variable > real ).
thf(sigma_decl,type,
sigma: produc1418842292n_game ).
thf(109,axiom,
! [A: game,B: game] :
( ( ( dual @ A )
= ( dual @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_game_Oinject_I7_J) ).
thf(645,plain,
! [A: game,B: game] :
( ( ( dual @ A )
= ( dual @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(219,axiom,
! [A: set_variable,B: set_variable,C: set_variable,D: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ C @ D )
=> ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ C ) @ ( sup_sup_set_variable @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_Un__mono) ).
thf(1036,plain,
! [A: set_variable,B: set_variable,C: set_variable,D: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ C @ D )
=> ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ C ) @ ( sup_sup_set_variable @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(154,axiom,
! [A: set_variable_real,B: set_variable > set_variable_real,C: set_variable,D: set_variable] :
( ( ord_le1113654598e_real @ A @ ( B @ C ) )
=> ( ( ord_le282106107riable @ C @ D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le1113654598e_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1113654598e_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_order__subst1) ).
thf(809,plain,
! [A: set_variable_real,B: set_variable > set_variable_real,C: set_variable,D: set_variable] :
( ( ord_le1113654598e_real @ A @ ( B @ C ) )
=> ( ( ord_le282106107riable @ C @ D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le1113654598e_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1113654598e_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(215,axiom,
! [A: option_game] :
( ( ( uSubst23177304_Loopo @ A )
= none_game )
= ( A = none_game ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_Loopo__undef) ).
thf(1024,plain,
! [A: option_game] :
( ( ( uSubst23177304_Loopo @ A )
= none_game )
= ( A = none_game ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(12,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ C @ B )
=> ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_le__supI) ).
thf(347,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ C @ B )
=> ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(279,axiom,
! [A: set_variable_real] :
( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ A ) )
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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(1237,plain,
! [A: set_variable_real] :
( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ A ) )
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(177,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_order__class_Oorder_Oantisym) ).
thf(893,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(67,axiom,
! [A: set_variable] :
( ( sup_sup_set_variable @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_sup__idem) ).
thf(518,plain,
! [A: set_variable] :
( ( sup_sup_set_variable @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(234,axiom,
! [A: variable > real,B: set_variable_real,C: set_variable_real] :
( ( member_variable_real @ A @ B )
=> ( member_variable_real @ A @ ( sup_su1685293586e_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_UnI2) ).
thf(1083,plain,
! [A: variable > real,B: set_variable_real,C: set_variable_real] :
( ( member_variable_real @ A @ B )
=> ( member_variable_real @ A @ ( sup_su1685293586e_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(114,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real > set_variable_real,D: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_variable_real,F: set_variable_real] :
( ( ord_le1113654598e_real @ E @ F )
=> ( ord_le1113654598e_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1113654598e_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_ord__le__eq__subst) ).
thf(666,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real > set_variable_real,D: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_variable_real,F: set_variable_real] :
( ( ord_le1113654598e_real @ E @ F )
=> ( ord_le1113654598e_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1113654598e_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(57,axiom,
! [A: set_variable > set_variable > set_variable,B: set_variable,C: set_variable] :
( ! [D: set_variable,E: set_variable] : ( ord_le282106107riable @ D @ ( A @ D @ E ) )
=> ( ! [D: set_variable,E: set_variable] : ( ord_le282106107riable @ E @ ( A @ D @ E ) )
=> ( ! [D: set_variable,E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ D )
=> ( ( ord_le282106107riable @ F @ D )
=> ( ord_le282106107riable @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup_sup_set_variable @ B @ C )
= ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_sup__unique) ).
thf(481,plain,
! [A: set_variable > set_variable > set_variable,B: set_variable,C: set_variable] :
( ! [D: set_variable,E: set_variable] : ( ord_le282106107riable @ D @ ( A @ D @ E ) )
=> ( ! [D: set_variable,E: set_variable] : ( ord_le282106107riable @ E @ ( A @ D @ E ) )
=> ( ! [D: set_variable,E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ D )
=> ( ( ord_le282106107riable @ F @ D )
=> ( ord_le282106107riable @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup_sup_set_variable @ B @ C )
= ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(19,axiom,
! [A: produc1755325794riable,B: produc1755325794riable] :
( ( ( produc944271878riable @ A )
= ( produc944271878riable @ B ) )
=> ( ( ( produc1192298056riable @ A )
= ( produc1192298056riable @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_prod__eqI) ).
thf(365,plain,
! [A: produc1755325794riable,B: produc1755325794riable] :
( ( ( produc944271878riable @ A )
= ( produc944271878riable @ B ) )
=> ( ( ( produc1192298056riable @ A )
= ( produc1192298056riable @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(263,axiom,
! [A: set_variable_real,B: set_variable_real,C: variable > real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( member_variable_real @ C @ A )
=> ( member_variable_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_in__mono) ).
thf(1190,plain,
! [A: set_variable_real,B: set_variable_real,C: variable > real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( member_variable_real @ C @ A )
=> ( member_variable_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(258,axiom,
! [A: variable > real,B: variable > real,C: set_variable,D: produc1418842292n_game,E: game,F: denotational_interp,G: set_variable_real] :
( ( denota1419872369iation @ A @ B @ C )
=> ( ! [H: variable > real,I: variable > real,J: set_variable_real] :
( ( denota1419872369iation @ H @ I @ ( produc893821739n_game @ ( uSubst516392814stappp @ D @ C @ E ) ) )
=> ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ D @ ( produc893821739n_game @ ( uSubst516392814stappp @ D @ C @ E ) ) @ E ) )
!= none_game )
=> ( ( member_variable_real @ H @ ( denota1245701238me_sem @ F @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ D @ ( produc893821739n_game @ ( uSubst516392814stappp @ D @ C @ E ) ) @ E ) ) ) @ J ) )
= ( member_variable_real @ H @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ D @ F @ I ) @ E @ J ) ) ) ) )
=> ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ D @ C @ ( loop @ E ) ) )
!= none_game )
=> ( ( member_variable_real @ A @ ( denota1245701238me_sem @ F @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ D @ C @ ( loop @ E ) ) ) ) @ G ) )
= ( member_variable_real @ A @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ D @ F @ B ) @ ( loop @ E ) @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_usubst__game__loop) ).
thf(1168,plain,
! [A: variable > real,B: variable > real,C: set_variable,D: produc1418842292n_game,E: game,F: denotational_interp,G: set_variable_real] :
( ( denota1419872369iation @ A @ B @ C )
=> ( ! [H: variable > real,I: variable > real,J: set_variable_real] :
( ( denota1419872369iation @ H @ I @ ( produc893821739n_game @ ( uSubst516392814stappp @ D @ C @ E ) ) )
=> ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ D @ ( produc893821739n_game @ ( uSubst516392814stappp @ D @ C @ E ) ) @ E ) )
!= none_game )
=> ( ( member_variable_real @ H @ ( denota1245701238me_sem @ F @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ D @ ( produc893821739n_game @ ( uSubst516392814stappp @ D @ C @ E ) ) @ E ) ) ) @ J ) )
= ( member_variable_real @ H @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ D @ F @ I ) @ E @ J ) ) ) ) )
=> ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ D @ C @ ( loop @ E ) ) )
!= none_game )
=> ( ( member_variable_real @ A @ ( denota1245701238me_sem @ F @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ D @ C @ ( loop @ E ) ) ) ) @ G ) )
= ( member_variable_real @ A @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ D @ F @ B ) @ ( loop @ E ) @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(143,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_sup_OcoboundedI2) ).
thf(760,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(267,axiom,
! [A: set_variable,B: option_game] :
( ( produc293487213n_game @ ( produc1149443391n_game @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_snd__pair) ).
thf(1200,plain,
! [A: set_variable,B: option_game] :
( ( produc293487213n_game @ ( produc1149443391n_game @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(271,axiom,
! [A: set_variable_real,B: set_variable_real,C: ( variable > real ) > $o,D: ( variable > real ) > $o] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ! [E: variable > real] :
( ( member_variable_real @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le1113654598e_real
@ ( collec633296133e_real
@ ^ [E: variable > real] :
( ( member_variable_real @ E @ A )
& ( C @ E ) ) )
@ ( collec633296133e_real
@ ^ [E: variable > real] :
( ( member_variable_real @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_subset__CollectI) ).
thf(1211,plain,
! [A: set_variable_real,B: set_variable_real,C: ( variable > real ) > $o,D: ( variable > real ) > $o] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ! [E: variable > real] :
( ( member_variable_real @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le1113654598e_real
@ ( collec633296133e_real
@ ^ [E: variable > real] :
( ( member_variable_real @ E @ A )
& ( C @ E ) ) )
@ ( collec633296133e_real
@ ^ [E: variable > real] :
( ( member_variable_real @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(231,axiom,
! [A: produc1078154247n_game,B: set_variable,C: option_game] :
( ( A
= ( produc1149443391n_game @ B @ C ) )
=> ( ( produc293487213n_game @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_sndI) ).
thf(1073,plain,
! [A: produc1078154247n_game,B: set_variable,C: option_game] :
( ( A
= ( produc1149443391n_game @ B @ C ) )
=> ( ( produc293487213n_game @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(48,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( A = B )
=> ( ( ord_le282106107riable @ B @ C )
=> ( ord_le282106107riable @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_ord__eq__le__trans) ).
thf(449,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( A = B )
=> ( ( ord_le282106107riable @ B @ C )
=> ( ord_le282106107riable @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(24,axiom,
! [A: set_variable] : ( ord_le282106107riable @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_order__refl) ).
thf(379,plain,
! [A: set_variable] : ( ord_le282106107riable @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(116,axiom,
! [A: set_variable,B: set_variable > set_variable,C: set_variable,D: set_variable] :
( ( A
= ( B @ C ) )
=> ( ( ord_le282106107riable @ C @ D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le282106107riable @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le282106107riable @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_ord__eq__le__subst) ).
thf(677,plain,
! [A: set_variable,B: set_variable > set_variable,C: set_variable,D: set_variable] :
( ( A
= ( B @ C ) )
=> ( ( ord_le282106107riable @ C @ D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le282106107riable @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le282106107riable @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(90,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_sup_OcoboundedI1) ).
thf(597,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(221,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ B ) @ C )
= ( ( ord_le1113654598e_real @ A @ C )
& ( ord_le1113654598e_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_sup_Obounded__iff) ).
thf(1041,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ B ) @ C )
= ( ( ord_le1113654598e_real @ A @ C )
& ( ord_le1113654598e_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(27,axiom,
! [A: set_variable,B: set_variable,C: set_variable,D: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ C @ D )
=> ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ C ) @ ( sup_sup_set_variable @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_sup__mono) ).
thf(385,plain,
! [A: set_variable,B: set_variable,C: set_variable,D: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ C @ D )
=> ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ C ) @ ( sup_sup_set_variable @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(247,axiom,
! [A: produc1418842292n_game,B: set_variable,C: game] :
( ( uSubst516392814stappp @ A @ B @ ( dual @ C ) )
= ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) @ ( uSubst1916713664_Dualo @ ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_usubstappp_Osimps_I7_J) ).
thf(1137,plain,
! [A: produc1418842292n_game,B: set_variable,C: game] :
( ( uSubst516392814stappp @ A @ B @ ( dual @ C ) )
= ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) @ ( uSubst1916713664_Dualo @ ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(257,axiom,
! [A: set_variable,B: set_variable,C: produc1418842292n_game,D: game] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ C @ B @ D ) )
!= none_game )
=> ( ( produc293487213n_game @ ( uSubst516392814stappp @ C @ B @ D ) )
= ( produc293487213n_game @ ( uSubst516392814stappp @ C @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_usubstappp__antimon) ).
thf(1164,plain,
! [A: set_variable,B: set_variable,C: produc1418842292n_game,D: game] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ C @ B @ D ) )
!= none_game )
=> ( ( produc293487213n_game @ ( uSubst516392814stappp @ C @ B @ D ) )
= ( produc293487213n_game @ ( uSubst516392814stappp @ C @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(128,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( A = B )
=> ( ord_le1113654598e_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_equalityD2) ).
thf(715,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( A = B )
=> ( ord_le1113654598e_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(155,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ C @ A )
=> ( ord_le1113654598e_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_dual__order_Otrans) ).
thf(814,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ C @ A )
=> ( ord_le1113654598e_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(228,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ( uminus430703407e_real @ A )
= ( uminus430703407e_real @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_compl__eq__compl__iff) ).
thf(1063,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ( uminus430703407e_real @ A )
= ( uminus430703407e_real @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(265,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ( uminus430703407e_real @ A )
= ( uminus430703407e_real @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Compl__eq__Compl__iff) ).
thf(1196,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ( uminus430703407e_real @ A )
= ( uminus430703407e_real @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(208,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( B = C )
=> ( ord_le282106107riable @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_ord__le__eq__trans) ).
thf(1001,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( B = C )
=> ( ord_le282106107riable @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(5,axiom,
! [A: variable > $o] :
( ( collect_variable
@ ^ [B: variable] :
~ ( A @ B ) )
= ( uminus1851247844riable @ ( collect_variable @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_Collect__neg__eq) ).
thf(320,plain,
! [A: variable > $o] :
( ( collect_variable
@ ^ [B: variable] :
~ ( A @ B ) )
= ( uminus1851247844riable @ ( collect_variable @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(111,axiom,
! [A: set_variable_real,B: set_variable > set_variable_real,C: set_variable,D: set_variable] :
( ( A
= ( B @ C ) )
=> ( ( ord_le282106107riable @ C @ D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le1113654598e_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1113654598e_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_ord__eq__le__subst) ).
thf(651,plain,
! [A: set_variable_real,B: set_variable > set_variable_real,C: set_variable,D: set_variable] :
( ( A
= ( B @ C ) )
=> ( ( ord_le282106107riable @ C @ D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le1113654598e_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1113654598e_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(82,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_order__class_Oorder_Oantisym) ).
thf(570,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(129,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ C @ B )
=> ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_le__supI) ).
thf(719,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ C @ B )
=> ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(62,axiom,
! [A: game,B: game,C: game,D: game] :
( ( ( choice @ A @ B )
= ( choice @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_game_Oinject_I4_J) ).
thf(504,plain,
! [A: game,B: game,C: game,D: game] :
( ( ( choice @ A @ B )
= ( choice @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(287,axiom,
! [A: variable > real,B: set_variable_real,C: set_variable_real] :
( ( member_variable_real @ A @ B )
=> ( member_variable_real @ A @ ( sup_su1685293586e_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_UnI1) ).
thf(1264,plain,
! [A: variable > real,B: set_variable_real,C: set_variable_real] :
( ( member_variable_real @ A @ B )
=> ( member_variable_real @ A @ ( sup_su1685293586e_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(292,axiom,
! [A: denotational_interp,B: game] :
( ( denota1245701238me_sem @ A @ ( dual @ B ) )
= ( ^ [C: set_variable_real] : ( uminus430703407e_real @ ( denota1245701238me_sem @ A @ B @ ( uminus430703407e_real @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_game__sem_Osimps_I7_J) ).
thf(1279,plain,
! [A: denotational_interp,B: game] :
( ( denota1245701238me_sem @ A @ ( dual @ B ) )
= ( ^ [C: set_variable_real] : ( uminus430703407e_real @ ( denota1245701238me_sem @ A @ B @ ( uminus430703407e_real @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(192,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real,D: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ C @ D )
=> ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ C ) @ ( sup_su1685293586e_real @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_sup_Omono) ).
thf(949,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real,D: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ C @ D )
=> ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ C ) @ ( sup_su1685293586e_real @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(74,axiom,
( ( (=) @ set_variable_real )
= ( ^ [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
& ( ord_le1113654598e_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_order__class_Oorder_Oeq__iff) ).
thf(542,plain,
( ( (=) @ set_variable_real )
= ( ^ [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
& ( ord_le1113654598e_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(87,axiom,
( ( (=) @ set_variable )
= ( ^ [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ B @ A )
& ( ord_le282106107riable @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_dual__order_Oeq__iff) ).
thf(587,plain,
( ( (=) @ set_variable )
= ( ^ [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ B @ A )
& ( ord_le282106107riable @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(309,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ ( uminus430703407e_real @ B ) )
=> ( ord_le1113654598e_real @ B @ ( uminus430703407e_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_compl__le__swap1) ).
thf(1323,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ ( uminus430703407e_real @ B ) )
=> ( ord_le1113654598e_real @ B @ ( uminus430703407e_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(99,axiom,
! [A: set_variable_real,B: set_variable_real] : ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_sup__ge2) ).
thf(619,plain,
! [A: set_variable_real,B: set_variable_real] : ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(123,axiom,
! [A: set_variable_real,B: set_variable_real] : ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_inf__sup__ord_I4_J) ).
thf(702,plain,
! [A: set_variable_real,B: set_variable_real] : ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(140,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ C )
=> ( ord_le282106107riable @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_order__trans) ).
thf(751,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ C )
=> ( ord_le282106107riable @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(151,axiom,
! [A: set_variable,B: set_variable] :
( ( ( uminus1851247844riable @ A )
= ( uminus1851247844riable @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_compl__eq__compl__iff) ).
thf(802,plain,
! [A: set_variable,B: set_variable] :
( ( ( uminus1851247844riable @ A )
= ( uminus1851247844riable @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(11,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ C @ B )
=> ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_Un__least) ).
thf(344,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ C @ B )
=> ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(156,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ C @ B )
=> ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_sup_OboundedI) ).
thf(817,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ C @ B )
=> ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(250,axiom,
! [A: option_game > set_variable > $o,B: option_game,C: set_variable] :
( ( A @ B @ C )
=> ( A @ ( produc293487213n_game @ ( produc1149443391n_game @ C @ B ) ) @ ( produc893821739n_game @ ( produc1149443391n_game @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_exI__realizer) ).
thf(1147,plain,
! [A: option_game > set_variable > $o,B: option_game,C: set_variable] :
( ( A @ B @ C )
=> ( A @ ( produc293487213n_game @ ( produc1149443391n_game @ C @ B ) ) @ ( produc893821739n_game @ ( produc1149443391n_game @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(198,axiom,
! [A: set_variable_real,B: set_variable_real > set_variable_real,C: set_variable_real,D: set_variable_real] :
( ( A
= ( B @ C ) )
=> ( ( ord_le1113654598e_real @ C @ D )
=> ( ! [E: set_variable_real,F: set_variable_real] :
( ( ord_le1113654598e_real @ E @ F )
=> ( ord_le1113654598e_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1113654598e_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_ord__eq__le__subst) ).
thf(969,plain,
! [A: set_variable_real,B: set_variable_real > set_variable_real,C: set_variable_real,D: set_variable_real] :
( ( A
= ( B @ C ) )
=> ( ( ord_le1113654598e_real @ C @ D )
=> ( ! [E: set_variable_real,F: set_variable_real] :
( ( ord_le1113654598e_real @ E @ F )
=> ( ord_le1113654598e_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1113654598e_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(37,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ B ) @ C )
=> ~ ( ( ord_le1113654598e_real @ A @ C )
=> ~ ( ord_le1113654598e_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_le__supE) ).
thf(416,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ B ) @ C )
=> ~ ( ( ord_le1113654598e_real @ A @ C )
=> ~ ( ord_le1113654598e_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(4,axiom,
! [A: variable > $o,B: variable > $o] :
( ! [C: variable] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le282106107riable @ ( collect_variable @ A ) @ ( collect_variable @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_Collect__mono) ).
thf(316,plain,
! [A: variable > $o,B: variable > $o] :
( ! [C: variable] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le282106107riable @ ( collect_variable @ A ) @ ( collect_variable @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(300,axiom,
denota1419872369iation @ nu2 @ omega2 @ ua,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_uv) ).
thf(1302,plain,
denota1419872369iation @ nu2 @ omega2 @ ua,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(162,axiom,
( uminus970116630real_o
= ( ^ [A: ( variable > real ) > $o,B: variable > real] : ( uminus_uminus_o @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_uminus__apply) ).
thf(834,plain,
( uminus970116630real_o
= ( ^ [A: ( variable > real ) > $o,B: variable > real] : ( uminus_uminus_o @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(252,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ ( uminus430703407e_real @ A ) @ B )
=> ( ord_le1113654598e_real @ ( uminus430703407e_real @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_compl__le__swap2) ).
thf(1151,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ ( uminus430703407e_real @ A ) @ B )
=> ( ord_le1113654598e_real @ ( uminus430703407e_real @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(14,axiom,
! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_Un__upper2) ).
thf(353,plain,
! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(172,axiom,
! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_inf__sup__ord_I4_J) ).
thf(877,plain,
! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(169,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_le__supI1) ).
thf(866,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(243,axiom,
! [A: set_variable_real,B: set_variable_real,C: denotational_interp,D: game] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ord_le1113654598e_real @ ( denota1245701238me_sem @ C @ D @ A ) @ ( denota1245701238me_sem @ C @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_monotone) ).
thf(1119,plain,
! [A: set_variable_real,B: set_variable_real,C: denotational_interp,D: game] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ord_le1113654598e_real @ ( denota1245701238me_sem @ C @ D @ A ) @ ( denota1245701238me_sem @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(31,axiom,
( ord_le1113654598e_real
= ( ^ [A: set_variable_real,B: set_variable_real] :
( B
= ( sup_su1685293586e_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_sup_Oorder__iff) ).
thf(396,plain,
( ord_le1113654598e_real
= ( ^ [A: set_variable_real,B: set_variable_real] :
( B
= ( sup_su1685293586e_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(112,axiom,
! [A: set_variable,B: set_variable] :
( ( A = B )
=> ( ord_le282106107riable @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_equalityD2) ).
thf(660,plain,
! [A: set_variable,B: set_variable] :
( ( A = B )
=> ( ord_le282106107riable @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(36,axiom,
! [A: set_variable,B: set_variable > set_variable,C: set_variable,D: set_variable] :
( ( ord_le282106107riable @ A @ ( B @ C ) )
=> ( ( ord_le282106107riable @ C @ D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le282106107riable @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le282106107riable @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_order__subst1) ).
thf(411,plain,
! [A: set_variable,B: set_variable > set_variable,C: set_variable,D: set_variable] :
( ( ord_le282106107riable @ A @ ( B @ C ) )
=> ( ( ord_le282106107riable @ C @ D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le282106107riable @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le282106107riable @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(41,axiom,
( ( uSubst1916713664_Dualo @ none_game )
= none_game ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_Dualo_Osimps_I2_J) ).
thf(428,plain,
( ( uSubst1916713664_Dualo @ none_game )
= none_game ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(281,axiom,
! [A: set_variable_real > $o] :
( ( ? [B: set_variable_real] : ( A @ ( uminus430703407e_real @ B ) ) )
= ( ? [B: set_variable_real] : ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_exists__diff) ).
thf(1242,plain,
! [A: set_variable_real > $o] :
( ( ? [B: set_variable_real] : ( A @ ( uminus430703407e_real @ B ) ) )
= ( ? [B: set_variable_real] : ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(63,axiom,
! [A: set_variable,B: set_variable] :
( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ A @ B ) )
= ( sup_sup_set_variable @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_Un__left__absorb) ).
thf(507,plain,
! [A: set_variable,B: set_variable] :
( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ A @ B ) )
= ( sup_sup_set_variable @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(200,axiom,
! [A: set_variable_real,B: ( variable > real ) > $o,C: ( variable > real ) > $o] :
( ( ord_le1113654598e_real @ A
@ ( collec633296133e_real
@ ^ [D: variable > real] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_le1113654598e_real @ A @ ( collec633296133e_real @ B ) )
& ( ord_le1113654598e_real @ A @ ( collec633296133e_real @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_conj__subset__def) ).
thf(981,plain,
! [A: set_variable_real,B: ( variable > real ) > $o,C: ( variable > real ) > $o] :
( ( ord_le1113654598e_real @ A
@ ( collec633296133e_real
@ ^ [D: variable > real] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_le1113654598e_real @ A @ ( collec633296133e_real @ B ) )
& ( ord_le1113654598e_real @ A @ ( collec633296133e_real @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(145,axiom,
! [A: set_variable,B: option_game,C: set_variable,D: option_game] :
( ( ( produc1149443391n_game @ A @ B )
= ( produc1149443391n_game @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_Pair__inject) ).
thf(766,plain,
! [A: set_variable,B: option_game,C: set_variable,D: option_game] :
( ( ( produc1149443391n_game @ A @ B )
= ( produc1149443391n_game @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(269,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ord_le1113654598e_real @ ( uminus430703407e_real @ B ) @ ( uminus430703407e_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_compl__mono) ).
thf(1206,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ord_le1113654598e_real @ ( uminus430703407e_real @ B ) @ ( uminus430703407e_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(65,axiom,
! [A: ( variable > real ) > $o,B: ( variable > real ) > $o] :
( ( ord_le1113654598e_real @ ( collec633296133e_real @ A ) @ ( collec633296133e_real @ B ) )
= ( ! [C: variable > real] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_Collect__mono__iff) ).
thf(512,plain,
! [A: ( variable > real ) > $o,B: ( variable > real ) > $o] :
( ( ord_le1113654598e_real @ ( collec633296133e_real @ A ) @ ( collec633296133e_real @ B ) )
= ( ! [C: variable > real] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(186,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_antisym__conv) ).
thf(925,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(302,axiom,
! [A: variable > real,B: set_variable_real,C: set_variable_real] :
( ( member_variable_real @ A @ ( sup_su1685293586e_real @ B @ C ) )
=> ( ~ ( member_variable_real @ A @ B )
=> ( member_variable_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_UnE) ).
thf(1306,plain,
! [A: variable > real,B: set_variable_real,C: set_variable_real] :
( ( member_variable_real @ A @ ( sup_su1685293586e_real @ B @ C ) )
=> ( ~ ( member_variable_real @ A @ B )
=> ( member_variable_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(266,axiom,
denota1419872369iation @ nu2 @ omega2 @ ua,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_Dual_Oprems_I2_J) ).
thf(1199,plain,
denota1419872369iation @ nu2 @ omega2 @ ua,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(253,axiom,
! [A: produc1418842292n_game,B: set_variable,C: game,D: game] :
( ( uSubst516392814stappp @ A @ B @ ( choice @ C @ D ) )
= ( produc1149443391n_game @ ( sup_sup_set_variable @ ( produc893821739n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ A @ B @ D ) ) ) @ ( uSubst1484167963hoiceo @ ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) @ ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_usubstappp__choice) ).
thf(1153,plain,
! [A: produc1418842292n_game,B: set_variable,C: game,D: game] :
( ( uSubst516392814stappp @ A @ B @ ( choice @ C @ D ) )
= ( produc1149443391n_game @ ( sup_sup_set_variable @ ( produc893821739n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ A @ B @ D ) ) ) @ ( uSubst1484167963hoiceo @ ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) @ ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(25,axiom,
! [A: set_variable_real,B: set_variable_real] : ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_sup_Ocobounded1) ).
thf(381,plain,
! [A: set_variable_real,B: set_variable_real] : ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(304,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( uminus501400228e_real @ ( produc86945893e_real @ A @ B ) )
= ( produc86945893e_real @ ( uminus430703407e_real @ A ) @ ( uminus430703407e_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_uminus__Pair) ).
thf(1311,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( uminus501400228e_real @ ( produc86945893e_real @ A @ B ) )
= ( produc86945893e_real @ ( uminus430703407e_real @ A ) @ ( uminus430703407e_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(72,axiom,
! [A: set_variable,B: set_variable_real > set_variable,C: set_variable_real,D: set_variable_real] :
( ( ord_le282106107riable @ A @ ( B @ C ) )
=> ( ( ord_le1113654598e_real @ C @ D )
=> ( ! [E: set_variable_real,F: set_variable_real] :
( ( ord_le1113654598e_real @ E @ F )
=> ( ord_le282106107riable @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le282106107riable @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_order__subst1) ).
thf(534,plain,
! [A: set_variable,B: set_variable_real > set_variable,C: set_variable_real,D: set_variable_real] :
( ( ord_le282106107riable @ A @ ( B @ C ) )
=> ( ( ord_le1113654598e_real @ C @ D )
=> ( ! [E: set_variable_real,F: set_variable_real] :
( ( ord_le1113654598e_real @ E @ F )
=> ( ord_le282106107riable @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le282106107riable @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(195,axiom,
( ( uSubst23177304_Loopo @ none_game )
= none_game ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_Loopo_Osimps_I2_J) ).
thf(957,plain,
( ( uSubst23177304_Loopo @ none_game )
= none_game ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(158,axiom,
! [A: set_variable,B: set_variable] :
( ( A
= ( sup_sup_set_variable @ A @ B ) )
=> ( ord_le282106107riable @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_sup_OorderI) ).
thf(825,plain,
! [A: set_variable,B: set_variable] :
( ( A
= ( sup_sup_set_variable @ A @ B ) )
=> ( ord_le282106107riable @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(214,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( sup_su1685293586e_real @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_Un__absorb1) ).
thf(1021,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( sup_su1685293586e_real @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(193,axiom,
! [A: variable > real,B: variable > real,C: set_variable] :
( ( denota1419872369iation @ A @ B @ C )
=> ( denota1419872369iation @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_Uvariation__sym__rel) ).
thf(952,plain,
! [A: variable > real,B: variable > real,C: set_variable] :
( ( denota1419872369iation @ A @ B @ C )
=> ( denota1419872369iation @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(272,axiom,
! [A: set_variable_real,B: ( variable > real ) > $o] :
( ord_le1113654598e_real
@ ( collec633296133e_real
@ ^ [C: variable > real] :
( ( member_variable_real @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_Collect__restrict) ).
thf(1217,plain,
! [A: set_variable_real,B: ( variable > real ) > $o] :
( ord_le1113654598e_real
@ ( collec633296133e_real
@ ^ [C: variable > real] :
( ( member_variable_real @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(157,axiom,
! [A: produc1078154247n_game > $o,B: produc1078154247n_game] :
( ! [C: set_variable,D: option_game] : ( A @ ( produc1149443391n_game @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_prod__cases) ).
thf(820,plain,
! [A: produc1078154247n_game > $o,B: produc1078154247n_game] :
( ! [C: set_variable,D: option_game] : ( A @ ( produc1149443391n_game @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(103,axiom,
! [A: set_variable_real] : ( ord_le1113654598e_real @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_subset__refl) ).
thf(630,plain,
! [A: set_variable_real] : ( ord_le1113654598e_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(217,axiom,
( ord_le282106107riable
= ( ^ [A: set_variable,B: set_variable] :
( ( sup_sup_set_variable @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_le__iff__sup) ).
thf(1032,plain,
( ord_le282106107riable
= ( ^ [A: set_variable,B: set_variable] :
( ( sup_sup_set_variable @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(17,axiom,
( ord_le1113654598e_real
= ( ^ [A: set_variable_real,B: set_variable_real] :
( ( sup_su1685293586e_real @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_le__iff__sup) ).
thf(361,plain,
( ord_le1113654598e_real
= ( ^ [A: set_variable_real,B: set_variable_real] :
( ( sup_su1685293586e_real @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(173,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( sup_sup_set_variable @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_sup_Oabsorb2) ).
thf(879,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( sup_sup_set_variable @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(44,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_le__supI2) ).
thf(435,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(8,axiom,
! [A: set_variable_real > set_variable_real > set_variable_real,B: set_variable_real,C: set_variable_real] :
( ! [D: set_variable_real,E: set_variable_real] : ( ord_le1113654598e_real @ D @ ( A @ D @ E ) )
=> ( ! [D: set_variable_real,E: set_variable_real] : ( ord_le1113654598e_real @ E @ ( A @ D @ E ) )
=> ( ! [D: set_variable_real,E: set_variable_real,F: set_variable_real] :
( ( ord_le1113654598e_real @ E @ D )
=> ( ( ord_le1113654598e_real @ F @ D )
=> ( ord_le1113654598e_real @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup_su1685293586e_real @ B @ C )
= ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_sup__unique) ).
thf(329,plain,
! [A: set_variable_real > set_variable_real > set_variable_real,B: set_variable_real,C: set_variable_real] :
( ! [D: set_variable_real,E: set_variable_real] : ( ord_le1113654598e_real @ D @ ( A @ D @ E ) )
=> ( ! [D: set_variable_real,E: set_variable_real] : ( ord_le1113654598e_real @ E @ ( A @ D @ E ) )
=> ( ! [D: set_variable_real,E: set_variable_real,F: set_variable_real] :
( ( ord_le1113654598e_real @ E @ D )
=> ( ( ord_le1113654598e_real @ F @ D )
=> ( ord_le1113654598e_real @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup_su1685293586e_real @ B @ C )
= ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(160,axiom,
! [A: set_variable_real,B: set_variable_real] : ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_Un__upper2) ).
thf(830,plain,
! [A: set_variable_real,B: set_variable_real] : ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(255,axiom,
( produc354409183n_game
= ( ^ [A: produc1078154247n_game] : ( produc1140431679riable @ ( produc293487213n_game @ A ) @ ( produc893821739n_game @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_prod_Oswap__def) ).
thf(1159,plain,
( produc354409183n_game
= ( ^ [A: produc1078154247n_game] : ( produc1140431679riable @ ( produc293487213n_game @ A ) @ ( produc893821739n_game @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(59,axiom,
! [A: set_variable] : ( ord_le282106107riable @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_dual__order_Orefl) ).
thf(493,plain,
! [A: set_variable] : ( ord_le282106107riable @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(216,axiom,
! [A: produc1078154247n_game > $o,B: produc1078154247n_game] :
( ! [C: set_variable,D: option_game] : ( A @ ( produc1149443391n_game @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_old_Oprod_Oinducts) ).
thf(1027,plain,
! [A: produc1078154247n_game > $o,B: produc1078154247n_game] :
( ! [C: set_variable,D: option_game] : ( A @ ( produc1149443391n_game @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(142,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( sup_sup_set_variable @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_sup_Oabsorb1) ).
thf(757,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( sup_sup_set_variable @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(126,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real,D: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ C @ D )
=> ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ C ) @ ( sup_su1685293586e_real @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_Un__mono) ).
thf(710,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real,D: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ C @ D )
=> ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ C ) @ ( sup_su1685293586e_real @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(211,axiom,
! [A: set_variable,B: option_game] :
( ( produc893821739n_game @ ( produc1149443391n_game @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_fst__conv) ).
thf(1012,plain,
! [A: set_variable,B: option_game] :
( ( produc893821739n_game @ ( produc1149443391n_game @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(249,axiom,
! [A: variable > real,B: set_variable_real,C: set_variable_real] :
( ( ~ ( member_variable_real @ A @ B )
=> ( member_variable_real @ A @ C ) )
=> ( member_variable_real @ A @ ( sup_su1685293586e_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_UnCI) ).
thf(1143,plain,
! [A: variable > real,B: set_variable_real,C: set_variable_real] :
( ( ~ ( member_variable_real @ A @ B )
=> ( member_variable_real @ A @ C ) )
=> ( member_variable_real @ A @ ( sup_su1685293586e_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(289,axiom,
! [A: variable > real,B: set_variable_real,C: set_variable_real,D: ( variable > real ) > $o] :
( ( member_variable_real @ A @ B )
=> ( ( ord_le1113654598e_real @ B
@ ( collec633296133e_real
@ ^ [E: variable > real] :
( ( member_variable_real @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_prop__restrict) ).
thf(1270,plain,
! [A: variable > real,B: set_variable_real,C: set_variable_real,D: ( variable > real ) > $o] :
( ( member_variable_real @ A @ B )
=> ( ( ord_le1113654598e_real @ B
@ ( collec633296133e_real
@ ^ [E: variable > real] :
( ( member_variable_real @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(97,axiom,
( ( (=) @ set_variable )
= ( ^ [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
& ( ord_le282106107riable @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_eq__iff) ).
thf(615,plain,
( ( (=) @ set_variable )
= ( ^ [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
& ( ord_le282106107riable @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(131,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real,D: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ C @ D )
=> ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ C ) @ ( sup_su1685293586e_real @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_sup__mono) ).
thf(725,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real,D: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ C @ D )
=> ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ C ) @ ( sup_su1685293586e_real @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(209,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ C )
= ( ( ord_le282106107riable @ A @ C )
& ( ord_le282106107riable @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_Un__subset__iff) ).
thf(1006,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ C )
= ( ( ord_le282106107riable @ A @ C )
& ( ord_le282106107riable @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(28,axiom,
! [A: set_variable_real,B: set_variable_real] : ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_Un__upper1) ).
thf(388,plain,
! [A: set_variable_real,B: set_variable_real] : ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(170,axiom,
! [A: set_variable] :
( ( sup_sup_set_variable @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_Un__absorb) ).
thf(869,plain,
! [A: set_variable] :
( ( sup_sup_set_variable @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(95,axiom,
! [A: set_variable_real] : ( ord_le1113654598e_real @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_order__refl) ).
thf(610,plain,
! [A: set_variable_real] : ( ord_le1113654598e_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(38,axiom,
! [A: produc1078154247n_game] :
? [B: set_variable,C: option_game] :
( A
= ( produc1149443391n_game @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_surj__pair) ).
thf(420,plain,
! [A: produc1078154247n_game] :
? [B: set_variable,C: option_game] :
( A
= ( produc1149443391n_game @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(61,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( B = C )
=> ( ord_le1113654598e_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_ord__le__eq__trans) ).
thf(499,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( B = C )
=> ( ord_le1113654598e_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(203,axiom,
! [A: produc2038871085e_real,B: produc2038871085e_real] :
( ( ( produc702045265e_real @ A )
= ( produc702045265e_real @ B ) )
=> ( ( ( produc220849299e_real @ A )
= ( produc220849299e_real @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_prod__eqI) ).
thf(989,plain,
! [A: produc2038871085e_real,B: produc2038871085e_real] :
( ( ( produc702045265e_real @ A )
= ( produc702045265e_real @ B ) )
=> ( ( ( produc220849299e_real @ A )
= ( produc220849299e_real @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(166,axiom,
! [A: set_variable,B: option_game,C: set_variable,D: option_game] :
( ( ( produc1149443391n_game @ A @ B )
= ( produc1149443391n_game @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_prod_Oinject) ).
thf(857,plain,
! [A: set_variable,B: option_game,C: set_variable,D: option_game] :
( ( ( produc1149443391n_game @ A @ B )
= ( produc1149443391n_game @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(121,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ ( uminus1851247844riable @ A ) @ ( uminus1851247844riable @ B ) )
= ( ord_le282106107riable @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_Compl__subset__Compl__iff) ).
thf(697,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ ( uminus1851247844riable @ A ) @ ( uminus1851247844riable @ B ) )
= ( ord_le282106107riable @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(236,axiom,
! [A: produc735959047riable] :
( ( produc293487213n_game @ ( produc345397471riable @ A ) )
= ( produc884810027riable @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_snd__swap) ).
thf(1089,plain,
! [A: produc735959047riable] :
( ( produc293487213n_game @ ( produc345397471riable @ A ) )
= ( produc884810027riable @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(296,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ord_le1113654598e_real @ ( uminus430703407e_real @ B ) @ ( uminus430703407e_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_Compl__anti__mono) ).
thf(1292,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ord_le1113654598e_real @ ( uminus430703407e_real @ B ) @ ( uminus430703407e_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(108,axiom,
! [A: set_variable,B: set_variable] :
( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ A @ B ) )
= ( sup_sup_set_variable @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_sup_Oleft__idem) ).
thf(642,plain,
! [A: set_variable,B: set_variable] :
( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ A @ B ) )
= ( sup_sup_set_variable @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(106,axiom,
! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_sup_Ocobounded2) ).
thf(637,plain,
! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(220,axiom,
( ord_le1113654598e_real
= ( ^ [A: set_variable_real,B: set_variable_real] :
( ( sup_su1685293586e_real @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_sup_Oabsorb__iff2) ).
thf(1039,plain,
( ord_le1113654598e_real
= ( ^ [A: set_variable_real,B: set_variable_real] :
( ( sup_su1685293586e_real @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(76,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ B @ C ) )
=> ~ ! [D: set_variable] :
( ( ord_le282106107riable @ D @ B )
=> ! [E: set_variable] :
( ( ord_le282106107riable @ E @ C )
=> ( A
!= ( sup_sup_set_variable @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_subset__UnE) ).
thf(547,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ B @ C ) )
=> ~ ! [D: set_variable] :
( ( ord_le282106107riable @ D @ B )
=> ! [E: set_variable] :
( ( ord_le282106107riable @ E @ C )
=> ( A
!= ( sup_sup_set_variable @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(117,axiom,
! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_sup__ge1) ).
thf(686,plain,
! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(55,axiom,
( ord_le282106107riable
= ( ^ [A: set_variable,B: set_variable] :
( ( sup_sup_set_variable @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_subset__Un__eq) ).
thf(476,plain,
( ord_le282106107riable
= ( ^ [A: set_variable,B: set_variable] :
( ( sup_sup_set_variable @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(30,axiom,
! [A: set_variable > $o] :
( ( ? [B: set_variable] : ( A @ ( uminus1851247844riable @ B ) ) )
= ( ? [B: set_variable] : ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_exists__diff) ).
thf(393,plain,
! [A: set_variable > $o] :
( ( ? [B: set_variable] : ( A @ ( uminus1851247844riable @ B ) ) )
= ( ? [B: set_variable] : ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(206,axiom,
( uminus970116630real_o
= ( ^ [A: ( variable > real ) > $o,B: variable > real] : ( uminus_uminus_o @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_fun__Compl__def) ).
thf(997,plain,
( uminus970116630real_o
= ( ^ [A: ( variable > real ) > $o,B: variable > real] : ( uminus_uminus_o @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(66,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( A
= ( sup_su1685293586e_real @ A @ B ) )
=> ( ord_le1113654598e_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_sup_OorderI) ).
thf(515,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( A
= ( sup_su1685293586e_real @ A @ B ) )
=> ( ord_le1113654598e_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(298,axiom,
( uminus7300697e_real
= ( ^ [A: produc1794985442e_real] : ( produc1400669210e_real @ ( uminus1851247844riable @ ( produc1800845318e_real @ A ) ) @ ( uminus430703407e_real @ ( produc2048871496e_real @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_uminus__prod__def) ).
thf(1297,plain,
( uminus7300697e_real
= ( ^ [A: produc1794985442e_real] : ( produc1400669210e_real @ ( uminus1851247844riable @ ( produc1800845318e_real @ A ) ) @ ( uminus430703407e_real @ ( produc2048871496e_real @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(277,axiom,
! [A: set_variable_real] :
( ( denota1419872369iation @ nu2 @ omega2 @ ua )
=> ( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ A ) )
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_IH_092_060alpha_062) ).
thf(1231,plain,
! [A: set_variable_real] :
( ( denota1419872369iation @ nu2 @ omega2 @ ua )
=> ( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ A ) )
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(147,axiom,
! [A: set_variable,B: set_variable] :
( ( A = B )
=> ~ ( ( ord_le282106107riable @ A @ B )
=> ~ ( ord_le282106107riable @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_equalityE) ).
thf(779,plain,
! [A: set_variable,B: set_variable] :
( ( A = B )
=> ~ ( ( ord_le282106107riable @ A @ B )
=> ~ ( ord_le282106107riable @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(93,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( sup_sup_set_variable @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_sup__absorb2) ).
thf(605,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( sup_sup_set_variable @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(201,axiom,
! [A: set_variable_real] : ( ord_le1113654598e_real @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_dual__order_Orefl) ).
thf(984,plain,
! [A: set_variable_real] : ( ord_le1113654598e_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(182,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_sup_OcoboundedI1) ).
thf(911,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(307,axiom,
! [A: produc1755325794riable] :
( ( produc944271878riable @ ( uminus2115124697riable @ A ) )
= ( uminus430703407e_real @ ( produc944271878riable @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_fst__uminus) ).
thf(1318,plain,
! [A: produc1755325794riable] :
( ( produc944271878riable @ ( uminus2115124697riable @ A ) )
= ( uminus430703407e_real @ ( produc944271878riable @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(235,axiom,
! [A: set_variable_real] :
( ( uminus430703407e_real @ ( uminus430703407e_real @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_double__compl) ).
thf(1086,plain,
! [A: set_variable_real] :
( ( uminus430703407e_real @ ( uminus430703407e_real @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(152,axiom,
( sup_sup_set_variable
= ( ^ [A: set_variable,B: set_variable] : ( sup_sup_set_variable @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_inf__sup__aci_I5_J) ).
thf(805,plain,
( sup_sup_set_variable
= ( ^ [A: set_variable,B: set_variable] : ( sup_sup_set_variable @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(1,conjecture,
( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
= ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
!= ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(311,plain,
( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
!= ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(225,axiom,
! [A: set_variable,B: option_game,C: set_variable] :
( ( ( produc893821739n_game @ ( produc1149443391n_game @ A @ B ) )
= C )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_fst__eqD) ).
thf(1054,plain,
! [A: set_variable,B: option_game,C: set_variable] :
( ( ( produc893821739n_game @ ( produc1149443391n_game @ A @ B ) )
= C )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(32,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( A = B )
=> ( ord_le1113654598e_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_eq__refl) ).
thf(398,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( A = B )
=> ( ord_le1113654598e_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(262,axiom,
! [A: set_variable_real] :
( ( uminus430703407e_real @ ( uminus430703407e_real @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_double__complement) ).
thf(1187,plain,
! [A: set_variable_real] :
( ( uminus430703407e_real @ ( uminus430703407e_real @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(175,axiom,
! [A: set_variable,B: option_game,C: set_variable,D: option_game] :
( ( ( produc1149443391n_game @ A @ B )
= ( produc1149443391n_game @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_old_Oprod_Oinject) ).
thf(888,plain,
! [A: set_variable,B: option_game,C: set_variable,D: option_game] :
( ( ( produc1149443391n_game @ A @ B )
= ( produc1149443391n_game @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(246,axiom,
! [A: variable > real,B: set_variable_real] :
( ~ ( member_variable_real @ A @ B )
=> ( member_variable_real @ A @ ( uminus430703407e_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_ComplI) ).
thf(1135,plain,
! [A: variable > real,B: set_variable_real] :
( ~ ( member_variable_real @ A @ B )
=> ( member_variable_real @ A @ ( uminus430703407e_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(42,axiom,
( ord_le282106107riable
= ( ^ [A: set_variable,B: set_variable] :
( B
= ( sup_sup_set_variable @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_sup_Oorder__iff) ).
thf(430,plain,
( ord_le282106107riable
= ( ^ [A: set_variable,B: set_variable] :
( B
= ( sup_sup_set_variable @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(240,axiom,
! [A: option_game,B: option_game] :
( ( ( A = none_game )
= ( B = none_game ) )
=> ( ( ( A != none_game )
=> ( ( B != none_game )
=> ( ( the_game @ A )
= ( the_game @ B ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_option_Oexpand) ).
thf(1103,plain,
! [A: option_game,B: option_game] :
( ( ( A = none_game )
= ( B = none_game ) )
=> ( ( ( A != none_game )
=> ( ( B != none_game )
=> ( ( the_game @ A )
= ( the_game @ B ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(273,axiom,
( ord_le1113654598e_real
= ( ^ [A: set_variable_real,B: set_variable_real] :
! [C: variable > real] :
( ( member_variable_real @ C @ A )
=> ( member_variable_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_subset__iff) ).
thf(1219,plain,
( ord_le1113654598e_real
= ( ^ [A: set_variable_real,B: set_variable_real] :
! [C: variable > real] :
( ( member_variable_real @ C @ A )
=> ( member_variable_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(290,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ ( uminus430703407e_real @ A ) @ ( uminus430703407e_real @ B ) )
= ( ord_le1113654598e_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_Compl__subset__Compl__iff) ).
thf(1273,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ ( uminus430703407e_real @ A ) @ ( uminus430703407e_real @ B ) )
= ( ord_le1113654598e_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(138,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ C @ B )
=> ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_sup__least) ).
thf(745,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ C @ B )
=> ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(83,axiom,
! [A: ( variable > real ) > $o,B: ( variable > real ) > $o] :
( ! [C: variable > real] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec633296133e_real @ A )
= ( collec633296133e_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Collect__cong) ).
thf(573,plain,
! [A: ( variable > real ) > $o,B: ( variable > real ) > $o] :
( ! [C: variable > real] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec633296133e_real @ A )
= ( collec633296133e_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(47,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( A = B )
=> ( ( ord_le1113654598e_real @ B @ C )
=> ( ord_le1113654598e_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_ord__eq__le__trans) ).
thf(444,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( A = B )
=> ( ( ord_le1113654598e_real @ B @ C )
=> ( ord_le1113654598e_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(180,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ C )
=> ~ ( ( ord_le282106107riable @ A @ C )
=> ~ ( ord_le282106107riable @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_le__supE) ).
thf(904,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ C )
=> ~ ( ( ord_le282106107riable @ A @ C )
=> ~ ( ord_le282106107riable @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(39,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_dual__order_Oantisym) ).
thf(423,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(120,axiom,
! [A: set_variable,B: set_variable,C: set_variable,D: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ C @ D )
=> ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ C ) @ ( sup_sup_set_variable @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_sup_Omono) ).
thf(694,plain,
! [A: set_variable,B: set_variable,C: set_variable,D: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ C @ D )
=> ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ C ) @ ( sup_sup_set_variable @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(33,axiom,
! [A: ( variable > real ) > $o,B: ( variable > real ) > $o] :
( ! [C: variable > real] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le1113654598e_real @ ( collec633296133e_real @ A ) @ ( collec633296133e_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_Collect__mono) ).
thf(402,plain,
! [A: ( variable > real ) > $o,B: ( variable > real ) > $o] :
( ! [C: variable > real] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le1113654598e_real @ ( collec633296133e_real @ A ) @ ( collec633296133e_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(137,axiom,
! [A: set_variable_real,B: set_variable_real] : ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_inf__sup__ord_I3_J) ).
thf(743,plain,
! [A: set_variable_real,B: set_variable_real] : ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(275,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ ( uminus430703407e_real @ A ) @ ( uminus430703407e_real @ B ) )
= ( ord_le1113654598e_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_compl__le__compl__iff) ).
thf(1226,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ ( uminus430703407e_real @ A ) @ ( uminus430703407e_real @ B ) )
= ( ord_le1113654598e_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(3,axiom,
! [A: variable > $o,B: variable > $o] :
( ( ord_le282106107riable @ ( collect_variable @ A ) @ ( collect_variable @ B ) )
= ( ! [C: variable] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_Collect__mono__iff) ).
thf(313,plain,
! [A: variable > $o,B: variable > $o] :
( ( ord_le282106107riable @ ( collect_variable @ A ) @ ( collect_variable @ B ) )
= ( ! [C: variable] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(148,axiom,
! [A: set_variable,B: set_variable_real > set_variable,C: set_variable_real,D: set_variable_real] :
( ( A
= ( B @ C ) )
=> ( ( ord_le1113654598e_real @ C @ D )
=> ( ! [E: set_variable_real,F: set_variable_real] :
( ( ord_le1113654598e_real @ E @ F )
=> ( ord_le282106107riable @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le282106107riable @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_ord__eq__le__subst) ).
thf(787,plain,
! [A: set_variable,B: set_variable_real > set_variable,C: set_variable_real,D: set_variable_real] :
( ( A
= ( B @ C ) )
=> ( ( ord_le1113654598e_real @ C @ D )
=> ( ! [E: set_variable_real,F: set_variable_real] :
( ( ord_le1113654598e_real @ E @ F )
=> ( ord_le282106107riable @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le282106107riable @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(127,axiom,
! [A: set_variable_real,B: set_variable_real] : ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_sup_Ocobounded2) ).
thf(713,plain,
! [A: set_variable_real,B: set_variable_real] : ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(226,axiom,
( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( dual @ alpha ) ) )
!= none_game ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_def) ).
thf(1058,plain,
( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( dual @ alpha ) ) )
!= none_game ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(184,axiom,
! [A: game,B: game] :
( ( ( loop @ A )
= ( loop @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_game_Oinject_I6_J) ).
thf(919,plain,
! [A: game,B: game] :
( ( ( loop @ A )
= ( loop @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(13,axiom,
! [A: set_variable,B: option_game] :
( ( produc354409183n_game @ ( produc1149443391n_game @ A @ B ) )
= ( produc1140431679riable @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_swap__simp) ).
thf(350,plain,
! [A: set_variable,B: option_game] :
( ( produc354409183n_game @ ( produc1149443391n_game @ A @ B ) )
= ( produc1140431679riable @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(52,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A @ B ) @ C )
= ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_sup_Oassoc) ).
thf(466,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A @ B ) @ C )
= ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(237,axiom,
! [A: produc1418842292n_game,B: set_variable,C: game,D: game] :
( ( ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ ( choice @ C @ D ) ) )
!= none_game )
=> ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ C ) )
!= none_game )
& ( ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ D ) )
!= none_game ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_usubstappp__choice__conv) ).
thf(1092,plain,
! [A: produc1418842292n_game,B: set_variable,C: game,D: game] :
( ( ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ ( choice @ C @ D ) ) )
!= none_game )
=> ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ C ) )
!= none_game )
& ( ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ D ) )
!= none_game ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(285,axiom,
! [A: ( variable > real ) > $o] :
( ( collec633296133e_real
@ ^ [B: variable > real] :
~ ( A @ B ) )
= ( uminus430703407e_real @ ( collec633296133e_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_Collect__neg__eq) ).
thf(1258,plain,
! [A: ( variable > real ) > $o] :
( ( collec633296133e_real
@ ^ [B: variable > real] :
~ ( A @ B ) )
= ( uminus430703407e_real @ ( collec633296133e_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(124,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( B
= ( sup_sup_set_variable @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_sup_OorderE) ).
thf(704,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( B
= ( sup_sup_set_variable @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(92,axiom,
denota1419872369iation @ nu @ omega @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_vaouter) ).
thf(604,plain,
denota1419872369iation @ nu @ omega @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(34,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C ) )
= ( sup_sup_set_variable @ B @ ( sup_sup_set_variable @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_Un__left__commute) ).
thf(406,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C ) )
= ( sup_sup_set_variable @ B @ ( sup_sup_set_variable @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(293,axiom,
! [A: produc1078154247n_game,B: produc1078154247n_game] :
( ( ( produc893821739n_game @ A )
= ( produc893821739n_game @ B ) )
=> ( ( ( produc293487213n_game @ A )
= ( produc293487213n_game @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_prod__eqI) ).
thf(1282,plain,
! [A: produc1078154247n_game,B: produc1078154247n_game] :
( ( ( produc893821739n_game @ A )
= ( produc893821739n_game @ B ) )
=> ( ( ( produc293487213n_game @ A )
= ( produc293487213n_game @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(23,axiom,
! [A: set_variable_real,B: set_variable_real] : ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_sup__ge1) ).
thf(377,plain,
! [A: set_variable_real,B: set_variable_real] : ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(81,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ C )
= ( ( ord_le282106107riable @ A @ C )
& ( ord_le282106107riable @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_sup_Obounded__iff) ).
thf(567,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ C )
= ( ( ord_le282106107riable @ A @ C )
& ( ord_le282106107riable @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(135,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_dual__order_Oantisym) ).
thf(737,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(244,axiom,
! [A: set_variable > $o,B: set_variable,C: option_game > $o,D: option_game] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( produc893821739n_game @ ( produc1149443391n_game @ B @ D ) ) )
& ( C @ ( produc293487213n_game @ ( produc1149443391n_game @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_conjI__realizer) ).
thf(1122,plain,
! [A: set_variable > $o,B: set_variable,C: option_game > $o,D: option_game] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( produc893821739n_game @ ( produc1149443391n_game @ B @ D ) ) )
& ( C @ ( produc293487213n_game @ ( produc1149443391n_game @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(168,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_antisym__conv) ).
thf(863,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(233,axiom,
! [A: produc1078154247n_game] :
( ( produc1149443391n_game @ ( produc893821739n_game @ A ) @ ( produc293487213n_game @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_prod_Ocollapse) ).
thf(1080,plain,
! [A: produc1078154247n_game] :
( ( produc1149443391n_game @ ( produc893821739n_game @ A ) @ ( produc293487213n_game @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(6,axiom,
! [A: variable > $o,B: variable > $o] :
( ! [C: variable] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_variable @ A )
= ( collect_variable @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Collect__cong) ).
thf(323,plain,
! [A: variable > $o,B: variable > $o] :
( ! [C: variable] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_variable @ A )
= ( collect_variable @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(89,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_le__supI1) ).
thf(594,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(150,axiom,
! [A: ( variable > real ) > $o] :
( ( uminus970116630real_o @ ( uminus970116630real_o @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_double__compl) ).
thf(799,plain,
! [A: ( variable > real ) > $o] :
( ( uminus970116630real_o @ ( uminus970116630real_o @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(100,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ C @ B )
=> ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_sup_OboundedI) ).
thf(621,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ C @ B )
=> ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(122,axiom,
( ord_le282106107riable
= ( ^ [A: set_variable,B: set_variable] :
( ( sup_sup_set_variable @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_sup_Oabsorb__iff1) ).
thf(700,plain,
( ord_le282106107riable
= ( ^ [A: set_variable,B: set_variable] :
( ( sup_sup_set_variable @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(310,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ! [C: variable > real] :
( ( member_variable_real @ C @ A )
=> ( member_variable_real @ C @ B ) )
=> ( ord_le1113654598e_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_subsetI) ).
thf(1325,plain,
! [A: set_variable_real,B: set_variable_real] :
( ! [C: variable > real] :
( ( member_variable_real @ C @ A )
=> ( member_variable_real @ C @ B ) )
=> ( ord_le1113654598e_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(190,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_antisym) ).
thf(943,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(259,axiom,
! [A: set_variable_real,B: set_variable_real,C: variable > real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( member_variable_real @ C @ A )
=> ( member_variable_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_subsetD) ).
thf(1177,plain,
! [A: set_variable_real,B: set_variable_real,C: variable > real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( member_variable_real @ C @ A )
=> ( member_variable_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(251,axiom,
( ord_le1113654598e_real
= ( ^ [A: set_variable_real,B: set_variable_real] :
! [C: variable > real] :
( ( member_variable_real @ C @ A )
=> ( member_variable_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_subset__eq) ).
thf(1149,plain,
( ord_le1113654598e_real
= ( ^ [A: set_variable_real,B: set_variable_real] :
! [C: variable > real] :
( ( member_variable_real @ C @ A )
=> ( member_variable_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(197,axiom,
! [A: set_variable_real,B: set_variable_real > set_variable_real,C: set_variable_real,D: set_variable_real] :
( ( ord_le1113654598e_real @ A @ ( B @ C ) )
=> ( ( ord_le1113654598e_real @ C @ D )
=> ( ! [E: set_variable_real,F: set_variable_real] :
( ( ord_le1113654598e_real @ E @ F )
=> ( ord_le1113654598e_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1113654598e_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_order__subst1) ).
thf(964,plain,
! [A: set_variable_real,B: set_variable_real > set_variable_real,C: set_variable_real,D: set_variable_real] :
( ( ord_le1113654598e_real @ A @ ( B @ C ) )
=> ( ( ord_le1113654598e_real @ C @ D )
=> ( ! [E: set_variable_real,F: set_variable_real] :
( ( ord_le1113654598e_real @ E @ F )
=> ( ord_le1113654598e_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1113654598e_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(50,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ord_le282106107riable @ ( uminus1851247844riable @ B ) @ ( uminus1851247844riable @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_Compl__anti__mono) ).
thf(462,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ord_le282106107riable @ ( uminus1851247844riable @ B ) @ ( uminus1851247844riable @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(227,axiom,
( uminus430703407e_real
= ( ^ [A: set_variable_real] :
( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [B: variable > real] : ( member_variable_real @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_uminus__set__def) ).
thf(1061,plain,
( uminus430703407e_real
= ( ^ [A: set_variable_real] :
( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [B: variable > real] : ( member_variable_real @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(68,axiom,
! [A: set_variable > option_game > $o,B: produc735959047riable] :
( ( A @ ( produc284475501riable @ B ) @ ( produc884810027riable @ B ) )
=> ~ ! [C: option_game,D: set_variable] :
~ ( A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_exE__realizer_H) ).
thf(521,plain,
! [A: set_variable > option_game > $o,B: produc735959047riable] :
( ( A @ ( produc284475501riable @ B ) @ ( produc884810027riable @ B ) )
=> ~ ! [C: option_game,D: set_variable] :
~ ( A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(196,axiom,
! [A: set_variable,B: set_variable,C: set_variable > set_variable,D: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ ( C @ B ) @ D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le282106107riable @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le282106107riable @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_order__subst2) ).
thf(959,plain,
! [A: set_variable,B: set_variable,C: set_variable > set_variable,D: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ ( C @ B ) @ D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le282106107riable @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le282106107riable @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(229,axiom,
! [A: denotational_interp,B: set_variable_real] :
( ( denota1245701238me_sem @ A @ skip @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_skip__id) ).
thf(1066,plain,
! [A: denotational_interp,B: set_variable_real] :
( ( denota1245701238me_sem @ A @ skip @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(212,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ B ) @ C )
= ( ( ord_le1113654598e_real @ A @ C )
& ( ord_le1113654598e_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_le__sup__iff) ).
thf(1015,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ B ) @ C )
= ( ( ord_le1113654598e_real @ A @ C )
& ( ord_le1113654598e_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(94,axiom,
! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_Un__upper1) ).
thf(608,plain,
! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(202,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ ( uminus1851247844riable @ A ) @ ( uminus1851247844riable @ B ) )
= ( ord_le282106107riable @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_compl__le__compl__iff) ).
thf(986,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ ( uminus1851247844riable @ A ) @ ( uminus1851247844riable @ B ) )
= ( ord_le282106107riable @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(241,axiom,
! [A: set_variable,B: set_variable_real] :
( ( uminus7300697e_real @ ( produc1400669210e_real @ A @ B ) )
= ( produc1400669210e_real @ ( uminus1851247844riable @ A ) @ ( uminus430703407e_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_uminus__Pair) ).
thf(1113,plain,
! [A: set_variable,B: set_variable_real] :
( ( uminus7300697e_real @ ( produc1400669210e_real @ A @ B ) )
= ( produc1400669210e_real @ ( uminus1851247844riable @ A ) @ ( uminus430703407e_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(45,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( sup_su1685293586e_real @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_Un__absorb2) ).
thf(438,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( sup_su1685293586e_real @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(185,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C ) )
= ( sup_sup_set_variable @ B @ ( sup_sup_set_variable @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_sup_Oleft__commute) ).
thf(922,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C ) )
= ( sup_sup_set_variable @ B @ ( sup_sup_set_variable @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(222,axiom,
! [A: set_variable,B: set_variable,C: set_variable > set_variable_real,D: set_variable_real] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le1113654598e_real @ ( C @ B ) @ D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le1113654598e_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1113654598e_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_order__subst2) ).
thf(1044,plain,
! [A: set_variable,B: set_variable,C: set_variable > set_variable_real,D: set_variable_real] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le1113654598e_real @ ( C @ B ) @ D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le1113654598e_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1113654598e_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(282,axiom,
! [A: produc1078154247n_game,B: produc1078154247n_game] :
( ( ( ( produc893821739n_game @ A )
= ( produc893821739n_game @ B ) )
& ( ( produc293487213n_game @ A )
= ( produc293487213n_game @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_prod_Oexpand) ).
thf(1245,plain,
! [A: produc1078154247n_game,B: produc1078154247n_game] :
( ( ( ( produc893821739n_game @ A )
= ( produc893821739n_game @ B ) )
& ( ( produc293487213n_game @ A )
= ( produc293487213n_game @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(54,axiom,
! [A: set_variable] :
( ( uminus1851247844riable @ ( uminus1851247844riable @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_double__complement) ).
thf(473,plain,
! [A: set_variable] :
( ( uminus1851247844riable @ ( uminus1851247844riable @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(130,axiom,
! [A: set_variable,B: set_variable] :
( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A @ B ) @ B )
= ( sup_sup_set_variable @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_sup_Oright__idem) ).
thf(722,plain,
! [A: set_variable,B: set_variable] :
( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A @ B ) @ B )
= ( sup_sup_set_variable @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(218,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ord_le282106107riable @ ( uminus1851247844riable @ B ) @ ( uminus1851247844riable @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_compl__mono) ).
thf(1034,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ord_le282106107riable @ ( uminus1851247844riable @ B ) @ ( uminus1851247844riable @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(40,axiom,
( ( (=) @ set_variable )
= ( ^ [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
& ( ord_le282106107riable @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_set__eq__subset) ).
thf(426,plain,
( ( (=) @ set_variable )
= ( ^ [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
& ( ord_le282106107riable @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(71,axiom,
! [A: set_variable_real > set_variable_real > $o,B: produc2038871085e_real] :
( ( A @ ( produc220849299e_real @ B ) @ ( produc702045265e_real @ B ) )
=> ~ ! [C: set_variable_real,D: set_variable_real] :
~ ( A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_exE__realizer_H) ).
thf(531,plain,
! [A: set_variable_real > set_variable_real > $o,B: produc2038871085e_real] :
( ( A @ ( produc220849299e_real @ B ) @ ( produc702045265e_real @ B ) )
=> ~ ! [C: set_variable_real,D: set_variable_real] :
~ ( A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(22,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( sup_sup_set_variable @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_Un__absorb1) ).
thf(374,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( sup_sup_set_variable @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(110,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( sup_sup_set_variable @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_Un__absorb2) ).
thf(648,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( sup_sup_set_variable @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(98,axiom,
! [A: variable > real,B: set_variable] : ( denota1419872369iation @ A @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Uvariation__refl) ).
thf(617,plain,
! [A: variable > real,B: set_variable] : ( denota1419872369iation @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(213,axiom,
! [A: set_variable,B: produc1078154247n_game] :
( ( A
= ( produc893821739n_game @ B ) )
= ( ? [C: option_game] :
( B
= ( produc1149443391n_game @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_eq__fst__iff) ).
thf(1018,plain,
! [A: set_variable,B: produc1078154247n_game] :
( ( A
= ( produc893821739n_game @ B ) )
= ( ? [C: option_game] :
( B
= ( produc1149443391n_game @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(15,axiom,
! [A: produc1078154247n_game] :
( ( produc284475501riable @ ( produc354409183n_game @ A ) )
= ( produc893821739n_game @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_snd__swap) ).
thf(355,plain,
! [A: produc1078154247n_game] :
( ( produc284475501riable @ ( produc354409183n_game @ A ) )
= ( produc893821739n_game @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(141,axiom,
! [A: produc1794985442e_real,B: produc1794985442e_real] :
( ( ( produc1800845318e_real @ A )
= ( produc1800845318e_real @ B ) )
=> ( ( ( produc2048871496e_real @ A )
= ( produc2048871496e_real @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_prod__eqI) ).
thf(754,plain,
! [A: produc1794985442e_real,B: produc1794985442e_real] :
( ( ( produc1800845318e_real @ A )
= ( produc1800845318e_real @ B ) )
=> ( ( ( produc2048871496e_real @ A )
= ( produc2048871496e_real @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(77,axiom,
! [A: set_variable,B: set_variable] :
( ( ( uminus1851247844riable @ A )
= ( uminus1851247844riable @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Compl__eq__Compl__iff) ).
thf(553,plain,
! [A: set_variable,B: set_variable] :
( ( ( uminus1851247844riable @ A )
= ( uminus1851247844riable @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(163,axiom,
! [A: set_variable,B: set_variable,C: set_variable > set_variable,D: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le282106107riable @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le282106107riable @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_ord__le__eq__subst) ).
thf(836,plain,
! [A: set_variable,B: set_variable,C: set_variable > set_variable,D: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le282106107riable @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le282106107riable @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(223,axiom,
! [A: set_variable,B: option_game] :
( ( produc893821739n_game @ ( produc1149443391n_game @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_fst__pair) ).
thf(1049,plain,
! [A: set_variable,B: option_game] :
( ( produc893821739n_game @ ( produc1149443391n_game @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(58,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ B ) @ C )
= ( ( ord_le1113654598e_real @ A @ C )
& ( ord_le1113654598e_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_Un__subset__iff) ).
thf(490,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ B ) @ C )
= ( ( ord_le1113654598e_real @ A @ C )
& ( ord_le1113654598e_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(115,axiom,
( ord_le1113654598e_real
= ( ^ [A: set_variable_real,B: set_variable_real] :
( ( sup_su1685293586e_real @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_subset__Un__eq) ).
thf(675,plain,
( ord_le1113654598e_real
= ( ^ [A: set_variable_real,B: set_variable_real] :
( ( sup_su1685293586e_real @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(268,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1354144447real_o
@ ^ [C: variable > real] : ( member_variable_real @ C @ A )
@ ^ [C: variable > real] : ( member_variable_real @ C @ B ) )
= ( ord_le1113654598e_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_pred__subset__eq) ).
thf(1203,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1354144447real_o
@ ^ [C: variable > real] : ( member_variable_real @ C @ A )
@ ^ [C: variable > real] : ( member_variable_real @ C @ B ) )
= ( ord_le1113654598e_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(270,axiom,
! [A: produc1418842292n_game,B: set_variable,C: game] :
( ( uSubst516392814stappp @ A @ B @ ( loop @ C ) )
= ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) @ ( uSubst23177304_Loopo @ ( produc293487213n_game @ ( uSubst516392814stappp @ A @ ( produc893821739n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_usubstappp__loop) ).
thf(1208,plain,
! [A: produc1418842292n_game,B: set_variable,C: game] :
( ( uSubst516392814stappp @ A @ B @ ( loop @ C ) )
= ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) @ ( uSubst23177304_Loopo @ ( produc293487213n_game @ ( uSubst516392814stappp @ A @ ( produc893821739n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(88,axiom,
! [A: produc1078154247n_game,B: set_variable,C: option_game] :
( ( A
= ( produc1149443391n_game @ B @ C ) )
=> ( ( produc893821739n_game @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_fstI) ).
thf(589,plain,
! [A: produc1078154247n_game,B: set_variable,C: option_game] :
( ( A
= ( produc1149443391n_game @ B @ C ) )
=> ( ( produc893821739n_game @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(146,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_le__supI2) ).
thf(776,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(171,axiom,
! [A: set_variable,B: set_variable,C: set_variable,D: set_variable] :
( ( A
= ( sup_sup_set_variable @ B @ C ) )
=> ( ( sup_sup_set_variable @ D @ A )
= ( sup_sup_set_variable @ B @ ( sup_sup_set_variable @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_boolean__algebra__cancel_Osup2) ).
thf(872,plain,
! [A: set_variable,B: set_variable,C: set_variable,D: set_variable] :
( ( A
= ( sup_sup_set_variable @ B @ C ) )
=> ( ( sup_sup_set_variable @ D @ A )
= ( sup_sup_set_variable @ B @ ( sup_sup_set_variable @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(254,axiom,
! [A: variable > real,B: ( variable > real ) > $o] :
( ( member_variable_real @ A @ ( collec633296133e_real @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_mem__Collect__eq) ).
thf(1156,plain,
! [A: variable > real,B: ( variable > real ) > $o] :
( ( member_variable_real @ A @ ( collec633296133e_real @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(125,axiom,
! [A: option_game] :
( ( ( uSubst1916713664_Dualo @ A )
= none_game )
= ( A = none_game ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_Dualo__undef) ).
thf(707,plain,
! [A: option_game] :
( ( ( uSubst1916713664_Dualo @ A )
= none_game )
= ( A = none_game ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(288,axiom,
! [A: produc2038871085e_real] :
( ( produc702045265e_real @ ( uminus501400228e_real @ A ) )
= ( uminus430703407e_real @ ( produc702045265e_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_fst__uminus) ).
thf(1267,plain,
! [A: produc2038871085e_real] :
( ( produc702045265e_real @ ( uminus501400228e_real @ A ) )
= ( uminus430703407e_real @ ( produc702045265e_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(35,axiom,
( sup_sup_set_variable
= ( ^ [A: set_variable,B: set_variable] : ( sup_sup_set_variable @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_sup__commute) ).
thf(409,plain,
( sup_sup_set_variable
= ( ^ [A: set_variable,B: set_variable] : ( sup_sup_set_variable @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(238,axiom,
! [A: option_game,B: produc1078154247n_game] :
( ( A
= ( produc293487213n_game @ B ) )
= ( ? [C: set_variable] :
( B
= ( produc1149443391n_game @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_eq__snd__iff) ).
thf(1098,plain,
! [A: option_game,B: produc1078154247n_game] :
( ( A
= ( produc293487213n_game @ B ) )
= ( ? [C: set_variable] :
( B
= ( produc1149443391n_game @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(194,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( B
= ( sup_su1685293586e_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_sup_OorderE) ).
thf(954,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( B
= ( sup_su1685293586e_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(284,axiom,
! [A: produc1418842292n_game,B: set_variable,C: game] :
( ( ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ ( loop @ C ) ) )
!= none_game )
=> ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ C ) )
!= none_game )
& ( ( produc293487213n_game @ ( uSubst516392814stappp @ A @ ( produc893821739n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) @ C ) )
!= none_game ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_usubstappp__loop__conv) ).
thf(1252,plain,
! [A: produc1418842292n_game,B: set_variable,C: game] :
( ( ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ ( loop @ C ) ) )
!= none_game )
=> ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ C ) )
!= none_game )
& ( ( produc293487213n_game @ ( uSubst516392814stappp @ A @ ( produc893821739n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) @ C ) )
!= none_game ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(46,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ C @ B )
=> ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_Un__least) ).
thf(441,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ C @ B )
=> ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(278,axiom,
( uminus2115124697riable
= ( ^ [A: produc1755325794riable] : ( produc544095770riable @ ( uminus430703407e_real @ ( produc944271878riable @ A ) ) @ ( uminus1851247844riable @ ( produc1192298056riable @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_uminus__prod__def) ).
thf(1235,plain,
( uminus2115124697riable
= ( ^ [A: produc1755325794riable] : ( produc544095770riable @ ( uminus430703407e_real @ ( produc944271878riable @ A ) ) @ ( uminus1851247844riable @ ( produc1192298056riable @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(9,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( sup_sup_set_variable @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_sup__absorb1) ).
thf(338,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( sup_sup_set_variable @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(84,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real > set_variable,D: set_variable] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le282106107riable @ ( C @ B ) @ D )
=> ( ! [E: set_variable_real,F: set_variable_real] :
( ( ord_le1113654598e_real @ E @ F )
=> ( ord_le282106107riable @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le282106107riable @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_order__subst2) ).
thf(576,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real > set_variable,D: set_variable] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le282106107riable @ ( C @ B ) @ D )
=> ( ! [E: set_variable_real,F: set_variable_real] :
( ( ord_le1113654598e_real @ E @ F )
=> ( ord_le282106107riable @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le282106107riable @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(294,axiom,
! [A: set_variable,B: option_game] :
( ( produc293487213n_game @ ( produc1149443391n_game @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_snd__conv) ).
thf(1285,plain,
! [A: set_variable,B: option_game] :
( ( produc293487213n_game @ ( produc1149443391n_game @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(75,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_subset__antisym) ).
thf(544,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(86,axiom,
( denota1419872369iation
= ( ^ [A: variable > real,B: variable > real] : ( denota1419872369iation @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_Uvariation__sym) ).
thf(585,plain,
( denota1419872369iation
= ( ^ [A: variable > real,B: variable > real] : ( denota1419872369iation @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(21,axiom,
! [A: produc1078154247n_game] :
~ ! [B: set_variable,C: option_game] :
( A
!= ( produc1149443391n_game @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_old_Oprod_Oexhaust) ).
thf(370,plain,
! [A: produc1078154247n_game] :
~ ! [B: set_variable,C: option_game] :
( A
!= ( produc1149443391n_game @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(274,axiom,
! [A: set_variable > option_game > $o,B: set_variable,C: option_game,D: produc1078154247n_game] :
( ( A @ B @ C )
=> ( ( D
= ( produc1149443391n_game @ B @ C ) )
=> ( A @ ( produc893821739n_game @ D ) @ ( produc293487213n_game @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_BNF__Greatest__Fixpoint_Osubst__Pair) ).
thf(1221,plain,
! [A: set_variable > option_game > $o,B: set_variable,C: option_game,D: produc1078154247n_game] :
( ( A @ B @ C )
=> ( ( D
= ( produc1149443391n_game @ B @ C ) )
=> ( A @ ( produc893821739n_game @ D ) @ ( produc293487213n_game @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(91,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ C )
=> ~ ( ( ord_le282106107riable @ A @ C )
=> ~ ( ord_le282106107riable @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_sup_OboundedE) ).
thf(600,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ C )
=> ~ ( ( ord_le282106107riable @ A @ C )
=> ~ ( ord_le282106107riable @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(224,axiom,
! [A: set_variable] : ( ord_le282106107riable @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_subset__refl) ).
thf(1052,plain,
! [A: set_variable] : ( ord_le282106107riable @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(96,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ C )
= ( ( ord_le282106107riable @ A @ C )
& ( ord_le282106107riable @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_le__sup__iff) ).
thf(612,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ C )
= ( ( ord_le282106107riable @ A @ C )
& ( ord_le282106107riable @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(280,axiom,
! [A: set_variable_real,B: ( variable > real ) > $o] :
( ord_le1113654598e_real
@ ( collec633296133e_real
@ ^ [C: variable > real] :
( ( member_variable_real @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_Collect__subset) ).
thf(1240,plain,
! [A: set_variable_real,B: ( variable > real ) > $o] :
( ord_le1113654598e_real
@ ( collec633296133e_real
@ ^ [C: variable > real] :
( ( member_variable_real @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(199,axiom,
! [A: produc1794985442e_real] :
( ( produc1800845318e_real @ ( uminus7300697e_real @ A ) )
= ( uminus1851247844riable @ ( produc1800845318e_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_fst__uminus) ).
thf(978,plain,
! [A: produc1794985442e_real] :
( ( produc1800845318e_real @ ( uminus7300697e_real @ A ) )
= ( uminus1851247844riable @ ( produc1800845318e_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(248,axiom,
! [A: produc1418842292n_game,B: set_variable,C: game] :
( ( uSubst516392814stappp @ A @ B @ ( loop @ C ) )
= ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) @ ( uSubst23177304_Loopo @ ( produc293487213n_game @ ( uSubst516392814stappp @ A @ ( produc893821739n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_usubstappp_Osimps_I6_J) ).
thf(1140,plain,
! [A: produc1418842292n_game,B: set_variable,C: game] :
( ( uSubst516392814stappp @ A @ B @ ( loop @ C ) )
= ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) @ ( uSubst23177304_Loopo @ ( produc293487213n_game @ ( uSubst516392814stappp @ A @ ( produc893821739n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(164,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real > set_variable,D: set_variable] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_variable_real,F: set_variable_real] :
( ( ord_le1113654598e_real @ E @ F )
=> ( ord_le282106107riable @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le282106107riable @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_ord__le__eq__subst) ).
thf(845,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real > set_variable,D: set_variable] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_variable_real,F: set_variable_real] :
( ( ord_le1113654598e_real @ E @ F )
=> ( ord_le282106107riable @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le282106107riable @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(102,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ C @ B )
=> ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_sup__least) ).
thf(627,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ C @ B )
=> ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(306,axiom,
( ord_le1113654598e_real
= ( ^ [A: set_variable_real,B: set_variable_real] :
( ord_le1354144447real_o
@ ^ [C: variable > real] : ( member_variable_real @ C @ A )
@ ^ [C: variable > real] : ( member_variable_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_less__eq__set__def) ).
thf(1316,plain,
( ord_le1113654598e_real
= ( ^ [A: set_variable_real,B: set_variable_real] :
( ord_le1354144447real_o
@ ^ [C: variable > real] : ( member_variable_real @ C @ A )
@ ^ [C: variable > real] : ( member_variable_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(260,axiom,
! [A: variable > real,B: variable > real,C: set_variable_real] :
( ( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) )
!= none_game )
=> ( ( denota1419872369iation @ A @ B @ ua )
=> ( ( member_variable_real @ A @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ C ) )
= ( member_variable_real @ A @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ B ) @ alpha @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Dual_OIH) ).
thf(1180,plain,
! [A: variable > real,B: variable > real,C: set_variable_real] :
( ( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) )
!= none_game )
=> ( ( denota1419872369iation @ A @ B @ ua )
=> ( ( member_variable_real @ A @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ C ) )
= ( member_variable_real @ A @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ B ) @ alpha @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(308,axiom,
( uminus430703407e_real
= ( ^ [A: set_variable_real] :
( collec633296133e_real
@ ^ [B: variable > real] :
~ ( member_variable_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_Compl__eq) ).
thf(1321,plain,
( uminus430703407e_real
= ( ^ [A: set_variable_real] :
( collec633296133e_real
@ ^ [B: variable > real] :
~ ( member_variable_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(118,axiom,
! [A: produc735959047riable,B: produc735959047riable] :
( ( ( produc884810027riable @ A )
= ( produc884810027riable @ B ) )
=> ( ( ( produc284475501riable @ A )
= ( produc284475501riable @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_prod__eqI) ).
thf(688,plain,
! [A: produc735959047riable,B: produc735959047riable] :
( ( ( produc884810027riable @ A )
= ( produc884810027riable @ B ) )
=> ( ( ( produc284475501riable @ A )
= ( produc284475501riable @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(60,axiom,
! [A: game,B: game] :
( ( loop @ A )
!= ( dual @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_game_Odistinct_I51_J) ).
thf(495,plain,
! [A: game,B: game] :
( ( loop @ A )
!= ( dual @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(176,axiom,
! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_inf__sup__ord_I3_J) ).
thf(891,plain,
! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(20,axiom,
( ( (=) @ set_variable_real )
= ( ^ [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ B @ A )
& ( ord_le1113654598e_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_dual__order_Oeq__iff) ).
thf(368,plain,
( ( (=) @ set_variable_real )
= ( ^ [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ B @ A )
& ( ord_le1113654598e_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(18,axiom,
! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_sup_Ocobounded1) ).
thf(363,plain,
! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(78,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ B ) @ C )
=> ~ ( ( ord_le1113654598e_real @ A @ C )
=> ~ ( ord_le1113654598e_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_sup_OboundedE) ).
thf(556,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ B ) @ C )
=> ~ ( ( ord_le1113654598e_real @ A @ C )
=> ~ ( ord_le1113654598e_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(188,axiom,
! [A: set_variable,B: set_variable,C: set_variable > set_variable_real,D: set_variable_real] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le1113654598e_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1113654598e_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_ord__le__eq__subst) ).
thf(931,plain,
! [A: set_variable,B: set_variable,C: set_variable > set_variable_real,D: set_variable_real] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le1113654598e_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1113654598e_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(73,axiom,
! [A: option_game,B: set_variable] :
( ( produc345397471riable @ ( produc1140431679riable @ A @ B ) )
= ( produc1149443391n_game @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_swap__simp) ).
thf(539,plain,
! [A: option_game,B: set_variable] :
( ( produc345397471riable @ ( produc1140431679riable @ A @ B ) )
= ( produc1149443391n_game @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(69,axiom,
! [A: game,B: game,C: game] :
( ( choice @ A @ B )
!= ( dual @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_game_Odistinct_I41_J) ).
thf(524,plain,
! [A: game,B: game,C: game] :
( ( choice @ A @ B )
!= ( dual @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(85,axiom,
! [A: set_variable,B: set_variable] :
( ( A = B )
=> ( ord_le282106107riable @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_equalityD1) ).
thf(581,plain,
! [A: set_variable,B: set_variable] :
( ( A = B )
=> ( ord_le282106107riable @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(291,axiom,
! [A: produc1078154247n_game] :
( A
= ( produc1149443391n_game @ ( produc893821739n_game @ A ) @ ( produc293487213n_game @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_surjective__pairing) ).
thf(1276,plain,
! [A: produc1078154247n_game] :
( A
= ( produc1149443391n_game @ ( produc893821739n_game @ A ) @ ( produc293487213n_game @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(29,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ C @ A )
=> ( ord_le282106107riable @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_dual__order_Otrans) ).
thf(390,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ C @ A )
=> ( ord_le282106107riable @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(104,axiom,
! [A: produc735959047riable] :
( ( produc893821739n_game @ ( produc345397471riable @ A ) )
= ( produc284475501riable @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_fst__swap) ).
thf(632,plain,
! [A: produc735959047riable] :
( ( produc893821739n_game @ ( produc345397471riable @ A ) )
= ( produc284475501riable @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(133,axiom,
! [A: game,B: game,C: game] :
( ( choice @ A @ B )
!= ( loop @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_game_Odistinct_I39_J) ).
thf(731,plain,
! [A: game,B: game,C: game] :
( ( choice @ A @ B )
!= ( loop @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(205,axiom,
( ( (=) @ set_variable_real )
= ( ^ [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
& ( ord_le1113654598e_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_eq__iff) ).
thf(995,plain,
( ( (=) @ set_variable_real )
= ( ^ [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
& ( ord_le1113654598e_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(178,axiom,
! [A: produc1755325794riable] :
( ( produc1192298056riable @ ( uminus2115124697riable @ A ) )
= ( uminus1851247844riable @ ( produc1192298056riable @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_snd__uminus) ).
thf(896,plain,
! [A: produc1755325794riable] :
( ( produc1192298056riable @ ( uminus2115124697riable @ A ) )
= ( uminus1851247844riable @ ( produc1192298056riable @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(139,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( sup_su1685293586e_real @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_sup_Oabsorb1) ).
thf(748,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( sup_su1685293586e_real @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(191,axiom,
! [A: set_variable,B: set_variable,C: variable > real,D: variable > real] :
( ( ord_le282106107riable @ A @ B )
=> ( ( denota1419872369iation @ C @ D @ A )
=> ( denota1419872369iation @ C @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_Uvariation__mon) ).
thf(946,plain,
! [A: set_variable,B: set_variable,C: variable > real,D: variable > real] :
( ( ord_le282106107riable @ A @ B )
=> ( ( denota1419872369iation @ C @ D @ A )
=> ( denota1419872369iation @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(239,axiom,
! [A: set_variable,B: produc1418842292n_game,C: game] : ( ord_le282106107riable @ A @ ( produc893821739n_game @ ( uSubst516392814stappp @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_usubst__taboos__mon) ).
thf(1101,plain,
! [A: set_variable,B: produc1418842292n_game,C: game] : ( ord_le282106107riable @ A @ ( produc893821739n_game @ ( uSubst516392814stappp @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(183,axiom,
! [A: set_variable,B: set_variable,C: set_variable,D: set_variable] :
( ( A
= ( sup_sup_set_variable @ B @ C ) )
=> ( ( sup_sup_set_variable @ A @ D )
= ( sup_sup_set_variable @ B @ ( sup_sup_set_variable @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_boolean__algebra__cancel_Osup1) ).
thf(914,plain,
! [A: set_variable,B: set_variable,C: set_variable,D: set_variable] :
( ( A
= ( sup_sup_set_variable @ B @ C ) )
=> ( ( sup_sup_set_variable @ A @ D )
= ( sup_sup_set_variable @ B @ ( sup_sup_set_variable @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(64,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ ( uminus1851247844riable @ B ) )
=> ( ord_le282106107riable @ B @ ( uminus1851247844riable @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_compl__le__swap1) ).
thf(510,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ ( uminus1851247844riable @ B ) )
=> ( ord_le282106107riable @ B @ ( uminus1851247844riable @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(297,axiom,
! [A: produc1078154247n_game] :
( A
= ( produc1149443391n_game @ ( produc893821739n_game @ A ) @ ( produc293487213n_game @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_prod_Oexhaust__sel) ).
thf(1294,plain,
! [A: produc1078154247n_game] :
( A
= ( produc1149443391n_game @ ( produc893821739n_game @ A ) @ ( produc293487213n_game @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(303,axiom,
! [A: set_variable_real,B: set_variable] :
( ( uminus2115124697riable @ ( produc544095770riable @ A @ B ) )
= ( produc544095770riable @ ( uminus430703407e_real @ A ) @ ( uminus1851247844riable @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_uminus__Pair) ).
thf(1308,plain,
! [A: set_variable_real,B: set_variable] :
( ( uminus2115124697riable @ ( produc544095770riable @ A @ B ) )
= ( produc544095770riable @ ( uminus430703407e_real @ A ) @ ( uminus1851247844riable @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(264,axiom,
! [A: produc1078154247n_game] :
( ( produc884810027riable @ ( produc354409183n_game @ A ) )
= ( produc293487213n_game @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_fst__swap) ).
thf(1193,plain,
! [A: produc1078154247n_game] :
( ( produc884810027riable @ ( produc354409183n_game @ A ) )
= ( produc293487213n_game @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(144,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ B @ C )
=> ( ord_le1113654598e_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_order_Otrans) ).
thf(763,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ B @ C )
=> ( ord_le1113654598e_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(26,axiom,
( ord_le282106107riable
= ( ^ [A: set_variable,B: set_variable] :
( ( sup_sup_set_variable @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_sup_Oabsorb__iff2) ).
thf(383,plain,
( ord_le282106107riable
= ( ^ [A: set_variable,B: set_variable] :
( ( sup_sup_set_variable @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(179,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real > set_variable_real,D: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ ( C @ B ) @ D )
=> ( ! [E: set_variable_real,F: set_variable_real] :
( ( ord_le1113654598e_real @ E @ F )
=> ( ord_le1113654598e_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1113654598e_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_order__subst2) ).
thf(899,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real > set_variable_real,D: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ ( C @ B ) @ D )
=> ( ! [E: set_variable_real,F: set_variable_real] :
( ( ord_le1113654598e_real @ E @ F )
=> ( ord_le1113654598e_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1113654598e_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(161,axiom,
( ord_le1113654598e_real
= ( ^ [A: set_variable_real,B: set_variable_real] :
( ( sup_su1685293586e_real @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_sup_Oabsorb__iff1) ).
thf(832,plain,
( ord_le1113654598e_real
= ( ^ [A: set_variable_real,B: set_variable_real] :
( ( sup_su1685293586e_real @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(256,axiom,
! [A: set_variable,B: set_variable,C: produc1418842292n_game,D: game] :
( ( ord_le282106107riable @ A @ B )
=> ( ord_le282106107riable @ ( produc893821739n_game @ ( uSubst516392814stappp @ C @ A @ D ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ C @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_usubstappp__fst__mon) ).
thf(1161,plain,
! [A: set_variable,B: set_variable,C: produc1418842292n_game,D: game] :
( ( ord_le282106107riable @ A @ B )
=> ( ord_le282106107riable @ ( produc893821739n_game @ ( uSubst516392814stappp @ C @ A @ D ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ C @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(232,axiom,
! [A: variable > real,B: set_variable_real] :
( ( member_variable_real @ A @ ( uminus430703407e_real @ B ) )
= ( ~ ( member_variable_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Compl__iff) ).
thf(1077,plain,
! [A: variable > real,B: set_variable_real] :
( ( member_variable_real @ A @ ( uminus430703407e_real @ B ) )
= ( ~ ( member_variable_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(56,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C ) )
= ( sup_sup_set_variable @ B @ ( sup_sup_set_variable @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_inf__sup__aci_I7_J) ).
thf(478,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C ) )
= ( sup_sup_set_variable @ B @ ( sup_sup_set_variable @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(242,axiom,
! [A: produc2038871085e_real] :
( ( produc220849299e_real @ ( uminus501400228e_real @ A ) )
= ( uminus430703407e_real @ ( produc220849299e_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_snd__uminus) ).
thf(1116,plain,
! [A: produc2038871085e_real] :
( ( produc220849299e_real @ ( uminus501400228e_real @ A ) )
= ( uminus430703407e_real @ ( produc220849299e_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(245,axiom,
( uminus501400228e_real
= ( ^ [A: produc2038871085e_real] : ( produc86945893e_real @ ( uminus430703407e_real @ ( produc702045265e_real @ A ) ) @ ( uminus430703407e_real @ ( produc220849299e_real @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_uminus__prod__def) ).
thf(1133,plain,
( uminus501400228e_real
= ( ^ [A: produc2038871085e_real] : ( produc86945893e_real @ ( uminus430703407e_real @ ( produc702045265e_real @ A ) ) @ ( uminus430703407e_real @ ( produc220849299e_real @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(207,axiom,
( ( (=) @ set_variable )
= ( ^ [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
& ( ord_le282106107riable @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_order__class_Oorder_Oeq__iff) ).
thf(999,plain,
( ( (=) @ set_variable )
= ( ^ [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
& ( ord_le282106107riable @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(43,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( sup_su1685293586e_real @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_sup_Oabsorb2) ).
thf(432,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( sup_su1685293586e_real @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(276,axiom,
( ( (=) @ produc1078154247n_game )
= ( ^ [A: produc1078154247n_game,B: produc1078154247n_game] :
( ( ( produc893821739n_game @ A )
= ( produc893821739n_game @ B ) )
& ( ( produc293487213n_game @ A )
= ( produc293487213n_game @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_prod__eq__iff) ).
thf(1229,plain,
( ( (=) @ produc1078154247n_game )
= ( ^ [A: produc1078154247n_game,B: produc1078154247n_game] :
( ( ( produc893821739n_game @ A )
= ( produc893821739n_game @ B ) )
& ( ( produc293487213n_game @ A )
= ( produc293487213n_game @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(283,axiom,
! [A: produc1418842292n_game,B: set_variable,C: game,D: set_variable] :
( ( ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ C ) )
!= none_game )
=> ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ A @ D @ C ) )
!= none_game )
=> ( ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ C ) )
= ( produc293487213n_game @ ( uSubst516392814stappp @ A @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_usubstappp__det) ).
thf(1248,plain,
! [A: produc1418842292n_game,B: set_variable,C: game,D: set_variable] :
( ( ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ C ) )
!= none_game )
=> ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ A @ D @ C ) )
!= none_game )
=> ( ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ C ) )
= ( produc293487213n_game @ ( uSubst516392814stappp @ A @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(134,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ ( uminus1851247844riable @ A ) @ B )
=> ( ord_le282106107riable @ ( uminus1851247844riable @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_compl__le__swap2) ).
thf(735,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ ( uminus1851247844riable @ A ) @ B )
=> ( ord_le282106107riable @ ( uminus1851247844riable @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(165,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ B @ C )
=> ( ord_le1113654598e_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_subset__trans) ).
thf(854,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ B @ C )
=> ( ord_le1113654598e_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(301,axiom,
! [A: produc1418842292n_game,B: set_variable,C: game] :
( ( uSubst516392814stappp @ A @ B @ ( dual @ C ) )
= ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) @ ( uSubst1916713664_Dualo @ ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_usubstappp__dual) ).
thf(1303,plain,
! [A: produc1418842292n_game,B: set_variable,C: game] :
( ( uSubst516392814stappp @ A @ B @ ( dual @ C ) )
= ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) @ ( uSubst1916713664_Dualo @ ( produc293487213n_game @ ( uSubst516392814stappp @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(80,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_subset__antisym) ).
thf(564,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(7,axiom,
! [A: set_variable,B: variable > $o,C: variable > $o] :
( ( ord_le282106107riable @ A
@ ( collect_variable
@ ^ [D: variable] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_le282106107riable @ A @ ( collect_variable @ B ) )
& ( ord_le282106107riable @ A @ ( collect_variable @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_conj__subset__def) ).
thf(326,plain,
! [A: set_variable,B: variable > $o,C: variable > $o] :
( ( ord_le282106107riable @ A
@ ( collect_variable
@ ^ [D: variable] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_le282106107riable @ A @ ( collect_variable @ B ) )
& ( ord_le282106107riable @ A @ ( collect_variable @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(305,axiom,
! [A: variable > real,B: set_variable_real] :
( ( member_variable_real @ A @ ( uminus430703407e_real @ B ) )
=> ~ ( member_variable_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_ComplD) ).
thf(1314,plain,
! [A: variable > real,B: set_variable_real] :
( ( member_variable_real @ A @ ( uminus430703407e_real @ B ) )
=> ~ ( member_variable_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(10,axiom,
! [A: set_variable] :
( ( sup_sup_set_variable @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_sup_Oidem) ).
thf(341,plain,
! [A: set_variable] :
( ( sup_sup_set_variable @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(113,axiom,
( sup_sup_set_variable
= ( ^ [A: set_variable,B: set_variable] : ( sup_sup_set_variable @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_sup_Ocommute) ).
thf(664,plain,
( sup_sup_set_variable
= ( ^ [A: set_variable,B: set_variable] : ( sup_sup_set_variable @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(295,axiom,
! [A: set_variable,B: option_game,C: option_game] :
( ( ( produc293487213n_game @ ( produc1149443391n_game @ A @ B ) )
= C )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_snd__eqD) ).
thf(1288,plain,
! [A: set_variable,B: option_game,C: option_game] :
( ( ( produc293487213n_game @ ( produc1149443391n_game @ A @ B ) )
= C )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(159,axiom,
( ( (=) @ set_variable_real )
= ( ^ [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
& ( ord_le1113654598e_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_set__eq__subset) ).
thf(828,plain,
( ( (=) @ set_variable_real )
= ( ^ [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
& ( ord_le1113654598e_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(105,axiom,
! [A: variable > real,B: variable > real] :
( denota1419872369iation @ A @ B
@ ( collect_variable
@ ^ [C: variable] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_Uvariation__univ) ).
thf(635,plain,
! [A: variable > real,B: variable > real] :
( denota1419872369iation @ A @ B
@ ( collect_variable
@ ^ [C: variable] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(149,axiom,
! [A: set_variable,B: set_variable] :
( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ A @ B ) )
= ( sup_sup_set_variable @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_sup__left__idem) ).
thf(796,plain,
! [A: set_variable,B: set_variable] :
( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ A @ B ) )
= ( sup_sup_set_variable @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(187,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A @ B ) @ C )
= ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_Un__assoc) ).
thf(928,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A @ B ) @ C )
= ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(16,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_antisym) ).
thf(358,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(153,axiom,
! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_sup__ge2) ).
thf(807,plain,
! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(101,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( sup_su1685293586e_real @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_sup__absorb2) ).
thf(624,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( sup_su1685293586e_real @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(51,axiom,
( produc345397471riable
= ( ^ [A: produc735959047riable] : ( produc1149443391n_game @ ( produc284475501riable @ A ) @ ( produc884810027riable @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_prod_Oswap__def) ).
thf(464,plain,
( produc345397471riable
= ( ^ [A: produc735959047riable] : ( produc1149443391n_game @ ( produc284475501riable @ A ) @ ( produc884810027riable @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(286,axiom,
! [A: produc1794985442e_real] :
( ( produc2048871496e_real @ ( uminus7300697e_real @ A ) )
= ( uminus430703407e_real @ ( produc2048871496e_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_snd__uminus) ).
thf(1261,plain,
! [A: produc1794985442e_real] :
( ( produc2048871496e_real @ ( uminus7300697e_real @ A ) )
= ( uminus430703407e_real @ ( produc2048871496e_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(167,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( sup_su1685293586e_real @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_sup__absorb1) ).
thf(860,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( sup_su1685293586e_real @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(70,axiom,
! [A: ( variable > real ) > $o,B: ( variable > real ) > $o] :
( ( ( uminus970116630real_o @ A )
= ( uminus970116630real_o @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_compl__eq__compl__iff) ).
thf(528,plain,
! [A: ( variable > real ) > $o,B: ( variable > real ) > $o] :
( ( ( uminus970116630real_o @ A )
= ( uminus970116630real_o @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(299,axiom,
! [A: set_variable_real] :
( ( collec633296133e_real
@ ^ [B: variable > real] : ( member_variable_real @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_Collect__mem__eq) ).
thf(1299,plain,
! [A: set_variable_real] :
( ( collec633296133e_real
@ ^ [B: variable > real] : ( member_variable_real @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(119,axiom,
! [A: set_variable,B: set_variable] :
( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ A @ B ) )
= ( sup_sup_set_variable @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_inf__sup__aci_I8_J) ).
thf(691,plain,
! [A: set_variable,B: set_variable] :
( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ A @ B ) )
= ( sup_sup_set_variable @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(132,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ C )
=> ( ord_le282106107riable @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_subset__trans) ).
thf(728,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ C )
=> ( ord_le282106107riable @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(136,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ B @ C )
=> ( ord_le1113654598e_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_order__trans) ).
thf(740,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ B @ C )
=> ( ord_le1113654598e_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(181,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ C )
=> ( ord_le282106107riable @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_order_Otrans) ).
thf(908,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ C )
=> ( ord_le282106107riable @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(204,axiom,
! [A: set_variable] :
( ( uminus1851247844riable @ ( uminus1851247844riable @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_double__compl) ).
thf(992,plain,
! [A: set_variable] :
( ( uminus1851247844riable @ ( uminus1851247844riable @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(210,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A @ B ) @ C )
= ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_sup__assoc) ).
thf(1009,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A @ B ) @ C )
= ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(261,axiom,
! [A: option_game > set_variable > $o,B: produc1078154247n_game] :
( ( A @ ( produc293487213n_game @ B ) @ ( produc893821739n_game @ B ) )
=> ~ ! [C: set_variable,D: option_game] :
~ ( A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_exE__realizer_H) ).
thf(1184,plain,
! [A: option_game > set_variable > $o,B: produc1078154247n_game] :
( ( A @ ( produc293487213n_game @ B ) @ ( produc893821739n_game @ B ) )
=> ~ ! [C: set_variable,D: option_game] :
~ ( A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(79,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( A = B )
=> ( ord_le1113654598e_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_equalityD1) ).
thf(560,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( A = B )
=> ( ord_le1113654598e_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(107,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_sup_OcoboundedI2) ).
thf(639,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(174,axiom,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ B @ C ) )
=> ~ ! [D: set_variable_real] :
( ( ord_le1113654598e_real @ D @ B )
=> ! [E: set_variable_real] :
( ( ord_le1113654598e_real @ E @ C )
=> ( A
!= ( sup_su1685293586e_real @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_subset__UnE) ).
thf(882,plain,
! [A: set_variable_real,B: set_variable_real,C: set_variable_real] :
( ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ B @ C ) )
=> ~ ! [D: set_variable_real] :
( ( ord_le1113654598e_real @ D @ B )
=> ! [E: set_variable_real] :
( ( ord_le1113654598e_real @ E @ C )
=> ( A
!= ( sup_su1685293586e_real @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(53,axiom,
! [A: set_variable,B: set_variable] :
( ( A = B )
=> ( ord_le282106107riable @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_eq__refl) ).
thf(469,plain,
! [A: set_variable,B: set_variable] :
( ( A = B )
=> ( ord_le282106107riable @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(189,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A @ B ) @ C )
= ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_inf__sup__aci_I6_J) ).
thf(940,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A @ B ) @ C )
= ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(49,axiom,
! [A: set_variable_real,B: set_variable_real] :
( ( A = B )
=> ~ ( ( ord_le1113654598e_real @ A @ B )
=> ~ ( ord_le1113654598e_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_equalityE) ).
thf(454,plain,
! [A: set_variable_real,B: set_variable_real] :
( ( A = B )
=> ~ ( ( ord_le1113654598e_real @ A @ B )
=> ~ ( ord_le1113654598e_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(230,axiom,
! [A: set_variable_real,B: set_variable_real,C: ( variable > real ) > $o] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ A
@ ( collec633296133e_real
@ ^ [D: variable > real] :
( ( member_variable_real @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: variable > real] :
( ( member_variable_real @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_subset__Collect__iff) ).
thf(1069,plain,
! [A: set_variable_real,B: set_variable_real,C: ( variable > real ) > $o] :
( ( ord_le1113654598e_real @ A @ B )
=> ( ( ord_le1113654598e_real @ A
@ ( collec633296133e_real
@ ^ [D: variable > real] :
( ( member_variable_real @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: variable > real] :
( ( member_variable_real @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(1354,plain,
$false,
inference(e,[status(thm)],[645,1036,809,1024,347,1237,893,518,1083,666,481,365,1190,1168,760,1200,1211,1073,449,379,677,597,1041,385,1137,1164,715,814,1063,1196,1001,320,651,570,719,504,1264,1279,949,542,587,1323,619,702,751,802,344,817,1147,969,416,316,1302,834,1151,353,877,866,1119,396,660,411,428,1242,507,981,766,1206,512,925,1306,1199,1153,381,1311,534,957,825,1021,952,1217,820,630,1032,361,879,435,329,830,1159,493,1027,757,710,1012,1143,1270,615,725,1006,388,869,610,420,499,989,857,697,1089,1292,642,637,1039,547,686,476,393,997,515,1297,1231,779,605,984,911,1318,1086,805,311,1054,398,1187,888,1135,430,1103,1219,1273,745,573,444,904,423,694,402,743,1226,313,787,713,1058,919,350,466,1092,1258,704,604,406,1282,377,567,737,1122,863,1080,323,594,799,621,700,1325,943,1177,1149,964,462,1061,521,959,1066,1015,608,986,1113,438,922,1044,1245,473,722,1034,426,531,374,648,617,1018,355,754,553,836,1049,490,675,1203,1208,589,776,872,1156,707,1267,409,1098,954,1252,441,1235,338,576,1285,544,585,370,1221,600,1052,612,1240,978,1140,845,627,1316,1180,1321,688,495,891,368,363,556,931,539,524,581,1276,390,632,731,995,896,748,946,1101,914,510,1294,1308,1193,763,383,899,832,1161,1077,478,1116,1133,999,432,1229,1248,735,854,1303,564,326,1314,341,664,1288,828,635,796,928,358,807,624,464,1261,860,528,1299,691,728,740,908,992,1009,1184,560,639,882,469,940,454,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP201^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.22 % Computer : n013.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 20:10:21 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.20/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.21/1.54 % [INFO] Parsing done (637ms).
% 3.21/1.56 % [INFO] Running in sequential loop mode.
% 5.03/2.13 % [INFO] eprover registered as external prover.
% 5.03/2.14 % [INFO] Scanning for conjecture ...
% 5.62/2.32 % [INFO] Found a conjecture (or negated_conjecture) and 354 axioms. Running axiom selection ...
% 6.25/2.51 % [INFO] Axiom selection finished. Selected 308 axioms (removed 46 axioms).
% 7.48/2.90 % [INFO] Problem is higher-order (TPTP THF).
% 7.48/2.95 % [INFO] Type checking passed.
% 7.48/2.95 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 23.91/7.39 % External prover 'e' found a proof!
% 23.91/7.39 % [INFO] Killing All external provers ...
% 23.91/7.39 % Time passed: 7023ms (effective reasoning time: 5814ms)
% 23.91/7.39 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 23.91/7.39 % Axioms used in derivation (308): fact_58_Collect__neg__eq, fact_347_boolean__algebra__cancel_Osup1, fact_278_sup_OcoboundedI1, fact_270_Un__upper1, fact_49_fst__uminus, fact_214_order__subst1, fact_182_order__trans, fact_110_prod__cases, fact_295_sup__absorb1, fact_144_compl__le__swap2, fact_83_prod_Oexpand, fact_264_Un__absorb2, fact_116_set__eq__subset, fact_153_prod_Oexhaust__sel, fact_284_sup_Ocobounded2, fact_44_Uvariation__sym__rel, fact_348_boolean__algebra__cancel_Osup2, fact_139_Collect__subset, fact_224_fstI, fact_260_subset__Un__eq, fact_303_sup_OorderI, fact_52_Uvariation__univ, fact_162_usubstappp_Osimps_I6_J, fact_78_prod__eqI, fact_164_order__refl, fact_324_le__supI, fact_241_snd__swap, fact_105_Compl__subset__Compl__iff, fact_180_dual__order_Orefl, fact_175_dual__order_Oeq__iff, fact_220_subset__Collect__iff, fact_6_snd__uminus, fact_174_dual__order_Oantisym, fact_183_order__class_Oorder_Oantisym, fact_320_sup__ge2, fact_228_Collect__restrict, fact_62_game_Odistinct_I51_J, fact_80_exE__realizer_H, fact_77_prod__eqI, fact_31_double__complement, fact_333_inf__sup__aci_I6_J, fact_298_sup_Oabsorb2, fact_195_eq__refl, fact_119_subset__trans, fact_208_ord__eq__le__subst, fact_155_exI__realizer, fact_39_option_Oexpand, fact_265_Un__absorb1, fact_281_sup_Oabsorb__iff1, fact_254_sup_Obounded__iff, fact_46_game_Oinject_I6_J, fact_258_Un__subset__iff, fact_350_sup__assoc, fact_50_fst__uminus, fact_129_equalityD1, fact_244_fst__swap, fact_289_sup_OboundedI, fact_206_ord__eq__le__subst, fact_135_subsetD, fact_280_sup_Oabsorb__iff2, fact_98_subset__antisym, fact_277_sup_OcoboundedI1, fact_283_sup_Ocobounded2, fact_7_def, fact_151_snd__pair, fact_275_sup_OcoboundedI2, fact_112_old_Oprod_Oexhaust, fact_313_sup_Omono, fact_282_sup_Oabsorb__iff1, fact_297_sup_Oabsorb2, fact_107_Compl__anti__mono, fact_14_Compl__eq__Compl__iff, fact_179_dual__order_Orefl, fact_316_le__supI2, fact_140_fst__eqD, fact_38_Dual_Oprems_I2_J, fact_344_Un__absorb, fact_111_Pair__inject, fact_274_Un__mono, fact_296_sup__absorb1, fact_327_inf__sup__ord_I3_J, fact_332_inf__sup__aci_I7_J, fact_240_swap__simp, fact_308_le__iff__sup, fact_326_le__supE, fact_90_exists__diff, fact_172_Dualo_Osimps_I2_J, fact_304_sup_OorderI, fact_288_sup_Oorder__iff, fact_17_uminus__apply, fact_36_Dual_OIH, 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, fact_2_uv, fact_201_ord__le__eq__subst, fact_69_Collect__mem__eq, fact_185_ord__le__eq__trans, fact_176_dual__order_Oeq__iff, fact_255_le__sup__iff, fact_128_equalityD1, fact_314_sup_Omono, fact_205_ord__eq__le__subst, fact_204_ord__le__eq__subst, fact_66_mem__Collect__eq, fact_157_usubstappp__fst__mon, fact_108_prod_Ocollapse, fact_10_ComplI, fact_21_double__compl, fact_330_inf__sup__ord_I4_J, fact_29_fun__Compl__def, fact_143_snd__eqD, fact_160_BNF__Greatest__Fixpoint_Osubst__Pair, fact_323_le__supI, fact_268_Un__upper2, fact_25_compl__eq__compl__iff, fact_1_IH_092_060alpha_062, fact_20_double__compl, fact_86_uminus__prod__def, fact_79_prod__eqI, fact_102_compl__le__compl__iff, fact_319_sup__ge2, fact_223_eq__fst__iff, fact_257_Un__subset__iff, fact_334_inf__sup__aci_I5_J, fact_243_fst__swap, fact_163_usubstappp__loop, fact_51_fst__uminus, fact_248_sup_Oleft__idem, fact_19_double__compl, fact_57_Collect__neg__eq, fact_262_subset__UnE, fact_312_sup__mono, fact_309_sup__least, fact_200_eq__iff, fact_171_Loopo_Osimps_I2_J, fact_197_antisym, fact_43_Uvariation__refl, fact_173_dual__order_Oantisym, fact_125_subset__iff, fact_94_uminus__Pair, fact_210_order__subst2, fact_263_Un__absorb2, fact_121_Collect__mono, fact_301_sup__unique, fact_104_Compl__subset__Compl__iff, fact_190_order__class_Oorder_Oeq__iff, fact_203_ord__le__eq__subst, fact_294_sup__absorb2, fact_81_exE__realizer_H, fact_237_prod_Oswap__def, fact_253_sup_Obounded__iff, fact_89_usubstappp__antimon, fact_215_order__subst1, fact_186_ord__le__eq__trans, fact_273_Un__mono, fact_97_old_Oprod_Oinject, fact_87_uminus__prod__def, fact_213_order__subst1, fact_92_uminus__Pair, fact_30_double__complement, fact_196_eq__refl, fact_239_swap__simp, fact_106_Compl__anti__mono, fact_45_usubstappp__choice__conv, fact_321_sup__ge1, fact_145_compl__le__swap2, fact_96_prod_Oinject, fact_115_Collect__mono__iff, fact_147_compl__le__swap1, fact_159_usubstappp__dual, fact_279_sup_Oabsorb__iff2, fact_84_prod__eq__iff, fact_103_compl__le__compl__iff, fact_152_surjective__pairing, fact_117_set__eq__subset, fact_85_uminus__prod__def, fact_247_sup__idem, fact_13_Compl__iff, fact_82_exE__realizer_H, fact_267_Un__upper2, fact_156_Uvariation__mon, fact_76_prod__eqI, fact_118_subset__trans, fact_181_order__trans, fact_202_ord__le__eq__subst, fact_149_compl__mono, fact_251_UnCI, fact_291_sup_OboundedE, fact_285_sup_Ocobounded1, fact_266_Un__absorb1, fact_169_Loopo__undef, fact_209_order__subst2, fact_73_skip__id, fact_328_inf__sup__ord_I3_J, fact_222_eq__snd__iff, fact_91_exists__diff, fact_177_dual__order_Otrans, fact_339_UnI2, fact_292_sup_OboundedE, fact_184_order__class_Oorder_Oantisym, fact_198_antisym, fact_37_game_Oinject_I7_J, fact_55_uminus__set__def, fact_286_sup_Ocobounded1, fact_188_ord__eq__le__trans, fact_269_Un__upper1, fact_271_Un__least, fact_236_conj__subset__def, fact_154_conjI__realizer, fact_207_ord__eq__le__subst, fact_311_sup__mono, fact_122_subset__refl, fact_93_uminus__Pair, fact_272_Un__least, fact_318_le__supI1, fact_218_subset__CollectI, fact_178_dual__order_Otrans, fact_290_sup_OboundedI, fact_351_sup_Ocommute, fact_343_Un__assoc, fact_276_sup_OcoboundedI2, fact_187_ord__eq__le__trans, fact_64_usubstappp__loop__conv, fact_261_subset__UnE, fact_75_prod__eqI, fact_317_le__supI1, fact_192_antisym__conv, fact_335_UnE, fact_199_eq__iff, fact_216_order__subst1, fact_234_prop__restrict, fact_235_conj__subset__def, fact_120_Collect__mono, fact_142_snd__conv, fact_99_subset__antisym, fact_300_sup_Oabsorb1, fact_27_usubstappp__det, fact_137_in__mono, fact_211_order__subst2, fact_133_equalityE, fact_132_equalityE, fact_238_prod_Oswap__def, fact_170_Dualo__undef, fact_287_sup_Oorder__iff, fact_306_sup_OorderE, fact_307_le__iff__sup, fact_42_Uvariation__sym, fact_226_pred__subset__eq, fact_249_sup__left__idem, fact_256_le__sup__iff, fact_193_order_Otrans, fact_325_le__supE, fact_353_sup_Oleft__commute, fact_166_monotone, fact_194_order_Otrans, fact_168_less__eq__set__def, fact_221_sndI, fact_60_Compl__eq, fact_127_equalityD2, fact_101_subsetI, fact_123_subset__refl, fact_161_usubstappp_Osimps_I7_J, fact_246_sup_Oidem, fact_5_snd__uminus, fact_35_game__sem_Osimps_I7_J, fact_293_sup__absorb2, fact_191_antisym__conv, fact_26_compl__eq__compl__iff, fact_146_compl__le__swap1, fact_53_game_Odistinct_I39_J, fact_126_equalityD2, fact_109_surj__pair, fact_345_Un__left__absorb, fact_165_order__refl, fact_131_subset__eq, fact_349_sup_Oassoc, fact_299_sup_Oabsorb1, fact_141_fst__conv, fact_315_le__supI2, fact_114_Collect__mono__iff, fact_33_ComplD, fact_242_snd__swap, fact_47_game_Oinject_I4_J, fact_150_fst__pair, fact_302_sup__unique, fact_40_usubst__game__loop, fact_63_game_Odistinct_I41_J, fact_212_order__subst2, fact_72_Collect__cong, fact_24_compl__eq__compl__iff, fact_71_Collect__cong, fact_346_Un__left__commute, fact_22_vaouter, fact_337_UnI1, fact_310_sup__least, fact_113_old_Oprod_Oinducts, fact_189_order__class_Oorder_Oeq__iff, fact_322_sup__ge1, fact_329_inf__sup__ord_I4_J, fact_305_sup_OorderE, fact_158_usubst__taboos__mon, fact_15_Compl__eq__Compl__iff, fact_148_compl__mono, fact_352_sup__commute, fact_250_sup_Oright__idem, fact_245_usubstappp__choice, fact_331_inf__sup__aci_I8_J, fact_259_subset__Un__eq, fact_4_snd__uminus
% 23.91/7.39 % No. of inferences in proof: 620
% 23.91/7.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7023 ms resp. 5814 ms w/o parsing
% 25.62/7.67 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.62/7.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------