%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP201^2 : 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 : n018.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 08:07:10 AM UTC 2026
% Result : Theorem 33.84s 13.87s
% Output : Refutation 35.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 288
% Syntax : Number of formulae : 578 ( 218 unt; 0 typ; 0 def)
% Number of atoms : 2050 ( 503 equ; 16 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 8019 ( 122 ~; 10 |; 74 &;7191 @)
% ( 0 <=>; 622 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 456 ( 456 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 49 usr; 13 con; 0-7 aty)
% Number of variables : 2152 ( 172 ^;1962 !; 18 ?;2152 :)
% Comments :
%------------------------------------------------------------------------------
thf(denotational_interp_type,type,
denotational_interp: $tType ).
thf(variable_type,type,
variable: $tType ).
thf(game_type,type,
game: $tType ).
thf(char_type,type,
char: $tType ).
thf(trm_type,type,
trm: $tType ).
thf(fml_type,type,
fml: $tType ).
thf(real_type,type,
real: $tType ).
thf(uminus_decl,type,
uminus:
!>[TA: $tType] : $o ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : $o ).
thf(lattice_decl,type,
lattice:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(boolean_algebra_decl,type,
boolean_algebra:
!>[TA: $tType] : $o ).
thf(semilattice_sup_decl,type,
semilattice_sup:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_decl,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(bNF_Ca1785829860lChain_decl,type,
bNF_Ca1785829860lChain:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TB ) ) > ( TB > TA ) > $o ) ).
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(uminus_uminus_decl,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(sup_sup_decl,type,
sup_sup:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(none_decl,type,
none:
!>[TA: $tType] : ( option @ TA ) ).
thf(the_decl,type,
the:
!>[TA: $tType] : ( ( option @ TA ) > TA ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(produc2004651681e_prod_decl,type,
produc2004651681e_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_rec_prod_decl,type,
product_rec_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_fst_decl,type,
product_fst:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ TB @ TA ) > TB ) ).
thf(product_snd_decl,type,
product_snd:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ TB @ TA ) > TA ) ).
thf(product_swap_decl,type,
product_swap:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ TB @ TA ) > ( product_prod @ TA @ TB ) ) ).
thf(product_scomp_decl,type,
product_scomp:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > ( product_prod @ TC @ TB ) ) > ( TC > TB > TA ) > TD > TA ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
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(uSubst1976112797hoiceo_decl,type,
uSubst1976112797hoiceo: ( option @ game ) > ( option @ game ) > ( option @ game ) ).
thf(uSubst739989314_Dualo_decl,type,
uSubst739989314_Dualo: ( option @ game ) > ( option @ game ) ).
thf(uSubst993936602_Loopo_decl,type,
uSubst993936602_Loopo: ( option @ game ) > ( option @ game ) ).
thf(uSubst2091380086djoint_decl,type,
uSubst2091380086djoint: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > denotational_interp > ( variable > real ) > denotational_interp ).
thf(uSubst95898988stappp_decl,type,
uSubst95898988stappp: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > game > ( product_prod @ ( set @ variable ) @ ( option @ game ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $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: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ).
thf(121,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_fst__conv) ).
thf(645,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(251,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_surjective__pairing) ).
thf(1024,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(161,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_subset__iff) ).
thf(760,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(23,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_antisym) ).
thf(347,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(254,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > $o,D: TA] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) )
& ( C @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_conjI__realizer) ).
thf(1031,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > $o,D: TA] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) )
& ( C @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(206,axiom,
! [TA: $tType] : ( lattice @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Olattice_4) ).
thf(893,plain,
! [TA: $tType] : ( lattice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_sup__fun__def) ).
thf(518,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(231,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Collect__mono__iff) ).
thf(962,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(223,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_Un__absorb) ).
thf(941,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(71,axiom,
ord @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_13) ).
thf(479,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(275,axiom,
! [A: variable > real,B: variable > real,C: set @ ( variable > real )] :
( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) )
!= ( none @ game ) )
=> ( ( denota1419872369iation @ A @ B @ ua )
=> ( ( member @ ( variable > real ) @ A @ ( denota1245701238me_sem @ i @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) ) @ C ) )
= ( member @ ( variable > real ) @ A @ ( denota1245701238me_sem @ ( uSubst2091380086djoint @ sigma @ i @ B ) @ alpha @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_Dual_OIH) ).
thf(1105,plain,
! [A: variable > real,B: variable > real,C: set @ ( variable > real )] :
( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) )
!= ( none @ game ) )
=> ( ( denota1419872369iation @ A @ B @ ua )
=> ( ( member @ ( variable > real ) @ A @ ( denota1245701238me_sem @ i @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) ) @ C ) )
= ( member @ ( variable > real ) @ A @ ( denota1245701238me_sem @ ( uSubst2091380086djoint @ sigma @ i @ B ) @ alpha @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(44,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_eq__iff) ).
thf(408,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(134,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TA )
=> ( semilattice_sup @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__sup) ).
thf(683,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TA )
=> ( semilattice_sup @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(243,axiom,
! [A: set @ ( variable > real ),B: set @ ( variable > real ),C: denotational_interp,D: game] :
( ( ord_less_eq @ ( set @ ( variable > real ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( variable > real ) ) @ ( denota1245701238me_sem @ C @ D @ A ) @ ( denota1245701238me_sem @ C @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_monotone) ).
thf(994,plain,
! [A: set @ ( variable > real ),B: set @ ( variable > real ),C: denotational_interp,D: game] :
( ( ord_less_eq @ ( set @ ( variable > real ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( variable > real ) ) @ ( denota1245701238me_sem @ C @ D @ A ) @ ( denota1245701238me_sem @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(8,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_sup_Oleft__idem) ).
thf(308,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_prod__induct4) ).
thf(379,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_prod__cases3) ).
thf(440,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(132,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_sup__ge2) ).
thf(677,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(155,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_compl__le__compl__iff) ).
thf(741,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(267,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_ComplI) ).
thf(1073,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(255,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_compl__mono) ).
thf(1041,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(195,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_subrelI) ).
thf(861,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(145,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_prod_Oexhaust__sel) ).
thf(715,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(68,axiom,
! [TA: $tType,A: TA > TA > $o] :
( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA )
@ ^ [B: TA,C: TA] :
( ( A @ B @ C )
| ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_eq__subset) ).
thf(472,plain,
! [TA: $tType,A: TA > TA > $o] :
( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA )
@ ^ [B: TA,C: TA] :
( ( A @ B @ C )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(139,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( ( ord_less_eq @ TA @ A @ C )
& ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_sup_Obounded__iff) ).
thf(698,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( ( ord_less_eq @ TA @ A @ C )
& ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(19,axiom,
lattice @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Olattice_11) ).
thf(340,plain,
lattice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_ord__le__eq__subst) ).
thf(538,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_order__subst1) ).
thf(670,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(157,axiom,
! [TA: $tType,A: TA > $o] :
( ( collect @ TA
@ ^ [B: TA] :
~ ( A @ B ) )
= ( uminus_uminus @ ( set @ TA ) @ ( collect @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_Collect__neg__eq) ).
thf(747,plain,
! [TA: $tType,A: TA > $o] :
( ( collect @ TA
@ ^ [B: TA] :
~ ( A @ B ) )
= ( uminus_uminus @ ( set @ TA ) @ ( collect @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(215,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: game] :
( ( uSubst95898988stappp @ A @ B @ ( dual @ C ) )
= ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) @ ( uSubst739989314_Dualo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_usubstappp_Osimps_I7_J) ).
thf(913,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: game] :
( ( uSubst95898988stappp @ A @ B @ ( dual @ C ) )
= ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) @ ( uSubst739989314_Dualo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(43,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_predicate1I) ).
thf(404,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(189,axiom,
! [TA: $tType,TB: $tType] :
( ( ( uminus @ TA )
& ( uminus @ TB ) )
=> ( ( uminus_uminus @ ( product_prod @ TA @ TB ) )
= ( ^ [A: product_prod @ TA @ TB] : ( product_Pair @ TA @ TB @ ( uminus_uminus @ TA @ ( product_fst @ TA @ TB @ A ) ) @ ( uminus_uminus @ TB @ ( product_snd @ TA @ TB @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_uminus__prod__def) ).
thf(841,plain,
! [TA: $tType,TB: $tType] :
( ( ( uminus @ TA )
& ( uminus @ TB ) )
=> ( ( uminus_uminus @ ( product_prod @ TA @ TB ) )
= ( ^ [A: product_prod @ TA @ TB] : ( product_Pair @ TA @ TB @ ( uminus_uminus @ TA @ ( product_fst @ TA @ TB @ A ) ) @ ( uminus_uminus @ TB @ ( product_snd @ TA @ TB @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(235,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_Un__absorb1) ).
thf(973,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(6,axiom,
! [A: game,B: game,C: game] :
( ( choice @ A @ B )
!= ( dual @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_game_Odistinct_I41_J) ).
thf(301,plain,
! [A: game,B: game,C: game] :
( ( choice @ A @ B )
!= ( dual @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(98,axiom,
semilattice_sup @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__sup_8) ).
thf(565,plain,
semilattice_sup @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(260,axiom,
preorder @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Opreorder_16) ).
thf(1055,plain,
preorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(31,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_sup_Oabsorb1) ).
thf(372,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(188,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_equation__minus__iff) ).
thf(838,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(226,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( TA > TB > $o )
@ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
@ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
= ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_pred__subset__eq2) ).
thf(949,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( TA > TB > $o )
@ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
@ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
= ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(221,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( D = B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_ssubst__Pair__rhs) ).
thf(934,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( D = B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(26,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_sup_Oidem) ).
thf(357,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(165,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_Un__upper2) ).
thf(770,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(47,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_linear) ).
thf(416,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(59,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_inf__sup__aci_I5_J) ).
thf(448,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(57,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_sup__least) ).
thf(443,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(287,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_Collect__restrict) ).
thf(1136,plain,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(175,axiom,
lattice @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Lattices_Olattice_18) ).
thf(806,plain,
lattice @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(258,axiom,
! [TA: $tType] : ( semilattice_sup @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__sup_1) ).
thf(1051,plain,
! [TA: $tType] : ( semilattice_sup @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(276,axiom,
! [TA: $tType,TB: $tType] :
( ( ( uminus @ TA )
& ( uminus @ TB ) )
=> ! [A: TB,B: TA] :
( ( uminus_uminus @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) )
= ( product_Pair @ TB @ TA @ ( uminus_uminus @ TB @ A ) @ ( uminus_uminus @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_uminus__Pair) ).
thf(1109,plain,
! [TA: $tType,TB: $tType] :
( ( ( uminus @ TA )
& ( uminus @ TB ) )
=> ! [A: TB,B: TA] :
( ( uminus_uminus @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) )
= ( product_Pair @ TB @ TA @ ( uminus_uminus @ TB @ A ) @ ( uminus_uminus @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType] :
( ( ( uminus @ TB )
& ( uminus @ TA ) )
=> ( uminus @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Groups_Ouminus_23) ).
thf(321,plain,
! [TA: $tType,TB: $tType] :
( ( ( uminus @ TB )
& ( uminus @ TA ) )
=> ( uminus @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(250,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_equalityD2) ).
thf(1020,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(102,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_sup_Oabsorb__iff2) ).
thf(574,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(212,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
=> ( ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_prod__eqI) ).
thf(905,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
=> ( ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_swap @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_swap__swap) ).
thf(480,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_swap @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(163,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_Un__upper1) ).
thf(766,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(200,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_mem__Collect__eq) ).
thf(877,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(152,axiom,
ord @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oord_20) ).
thf(734,plain,
ord @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(61,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
| ~ ( ord_less_eq @ TA @ A @ B )
| ~ ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_verit__la__disequality) ).
thf(453,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
| ~ ( ord_less_eq @ TA @ A @ B )
| ~ ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(52,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_34_game_Oinject_I4_J) ).
thf(428,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)],[52]) ).
thf(45,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_inf__sup__aci_I7_J) ).
thf(411,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(240,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_set__eq__subset) ).
thf(988,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_prod__cases) ).
thf(292,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(217,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: game,D: game] :
( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ ( choice @ C @ D ) ) )
!= ( none @ game ) )
=> ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) )
!= ( none @ game ) )
& ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ D ) )
!= ( none @ game ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_usubstappp__choice__conv) ).
thf(920,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: game,D: game] :
( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ ( choice @ C @ D ) ) )
!= ( none @ game ) )
=> ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) )
!= ( none @ game ) )
& ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ D ) )
!= ( none @ game ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(82,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
=> ~ ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_le__supE) ).
thf(512,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
=> ~ ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(88,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_inf__sup__aci_I6_J) ).
thf(529,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_sup__apply) ).
thf(546,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(177,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_snd @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= ( product_fst @ TA @ TB @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_snd__swap) ).
thf(810,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_snd @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= ( product_fst @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(29,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_sup__left__idem) ).
thf(366,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(265,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_subsetD) ).
thf(1067,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(172,axiom,
! [TA: $tType,TB: $tType] :
( ( ( uminus @ TA )
& ( uminus @ TB ) )
=> ! [A: product_prod @ TA @ TB] :
( ( product_snd @ TA @ TB @ ( uminus_uminus @ ( product_prod @ TA @ TB ) @ A ) )
= ( uminus_uminus @ TB @ ( product_snd @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_snd__uminus) ).
thf(798,plain,
! [TA: $tType,TB: $tType] :
( ( ( uminus @ TA )
& ( uminus @ TB ) )
=> ! [A: product_prod @ TA @ TB] :
( ( product_snd @ TA @ TB @ ( uminus_uminus @ ( product_prod @ TA @ TB ) @ A ) )
= ( uminus_uminus @ TB @ ( product_snd @ TA @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(229,axiom,
( ( uSubst739989314_Dualo @ ( none @ game ) )
= ( none @ game ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_Dualo_Osimps_I2_J) ).
thf(957,plain,
( ( uSubst739989314_Dualo @ ( none @ game ) )
= ( none @ game ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(272,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_equalityE) ).
thf(1091,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(168,axiom,
! [A: variable > real,B: variable > real,C: set @ variable,D: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ 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 @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ D @ C @ E ) ) )
=> ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ D @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ D @ C @ E ) ) @ E ) )
!= ( none @ game ) )
=> ( ( member @ ( variable > real ) @ H @ ( denota1245701238me_sem @ F @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ D @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ D @ C @ E ) ) @ E ) ) ) @ J ) )
= ( member @ ( variable > real ) @ H @ ( denota1245701238me_sem @ ( uSubst2091380086djoint @ D @ F @ I ) @ E @ J ) ) ) ) )
=> ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ D @ C @ ( loop @ E ) ) )
!= ( none @ game ) )
=> ( ( member @ ( variable > real ) @ A @ ( denota1245701238me_sem @ F @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ D @ C @ ( loop @ E ) ) ) ) @ G ) )
= ( member @ ( variable > real ) @ A @ ( denota1245701238me_sem @ ( uSubst2091380086djoint @ D @ F @ B ) @ ( loop @ E ) @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_usubst__game__loop) ).
thf(778,plain,
! [A: variable > real,B: variable > real,C: set @ variable,D: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ 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 @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ D @ C @ E ) ) )
=> ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ D @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ D @ C @ E ) ) @ E ) )
!= ( none @ game ) )
=> ( ( member @ ( variable > real ) @ H @ ( denota1245701238me_sem @ F @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ D @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ D @ C @ E ) ) @ E ) ) ) @ J ) )
= ( member @ ( variable > real ) @ H @ ( denota1245701238me_sem @ ( uSubst2091380086djoint @ D @ F @ I ) @ E @ J ) ) ) ) )
=> ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ D @ C @ ( loop @ E ) ) )
!= ( none @ game ) )
=> ( ( member @ ( variable > real ) @ A @ ( denota1245701238me_sem @ F @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ D @ C @ ( loop @ E ) ) ) ) @ G ) )
= ( member @ ( variable > real ) @ A @ ( denota1245701238me_sem @ ( uSubst2091380086djoint @ D @ F @ B ) @ ( loop @ E ) @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(227,axiom,
( ( uSubst993936602_Loopo @ ( none @ game ) )
= ( none @ game ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_Loopo_Osimps_I2_J) ).
thf(952,plain,
( ( uSubst993936602_Loopo @ ( none @ game ) )
= ( none @ game ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(282,axiom,
! [A: denotational_interp,B: game] :
( ( denota1245701238me_sem @ A @ ( dual @ B ) )
= ( ^ [C: set @ ( variable > real )] : ( uminus_uminus @ ( set @ ( variable > real ) ) @ ( denota1245701238me_sem @ A @ B @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_game__sem_Osimps_I7_J) ).
thf(1123,plain,
! [A: denotational_interp,B: game] :
( ( denota1245701238me_sem @ A @ ( dual @ B ) )
= ( ^ [C: set @ ( variable > real )] : ( uminus_uminus @ ( set @ ( variable > real ) ) @ ( denota1245701238me_sem @ A @ B @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: TB,B: product_prod @ TB @ TA] :
( ( A
= ( product_fst @ TB @ TA @ B ) )
= ( ? [C: TA] :
( B
= ( product_Pair @ TB @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_eq__fst__iff) ).
thf(392,plain,
! [TA: $tType,TB: $tType,A: TB,B: product_prod @ TB @ TA] :
( ( A
= ( product_fst @ TB @ TA @ B ) )
= ( ? [C: TA] :
( B
= ( product_Pair @ TB @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: TA,C: TB] :
( ( A
= ( product_Pair @ TA @ TB @ B @ C ) )
=> ( ( product_fst @ TA @ TB @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_fstI) ).
thf(424,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: TA,C: TB] :
( ( A
= ( product_Pair @ TA @ TB @ B @ C ) )
=> ( ( product_fst @ TA @ TB @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(179,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_Compl__subset__Compl__iff) ).
thf(815,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(150,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_bex__Un) ).
thf(729,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(99,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_dual__order_Oeq__iff) ).
thf(566,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType] :
( ( ( group_add @ TB )
& ( group_add @ TA ) )
=> ( group_add @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Groups_Ogroup__add_22) ).
thf(435,plain,
! [TA: $tType,TB: $tType] :
( ( ( group_add @ TB )
& ( group_add @ TA ) )
=> ( group_add @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(77,axiom,
( denota1419872369iation
= ( ^ [A: variable > real,B: variable > real] : ( denota1419872369iation @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_Uvariation__sym) ).
thf(493,plain,
( denota1419872369iation
= ( ^ [A: variable > real,B: variable > real] : ( denota1419872369iation @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(160,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_minus__le__iff) ).
thf(757,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(94,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_sup__absorb1) ).
thf(551,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(143,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_sup_Ocobounded1) ).
thf(710,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_old_Oprod_Oexhaust) ).
thf(456,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(216,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: game,D: set @ variable] :
( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) )
!= ( none @ game ) )
=> ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ D @ C ) )
!= ( none @ game ) )
=> ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) )
= ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_usubstappp__det) ).
thf(916,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: game,D: set @ variable] :
( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) )
!= ( none @ game ) )
=> ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ D @ C ) )
!= ( none @ game ) )
=> ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) )
= ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_swap @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= ( product_Pair @ TB @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_swap__simp) ).
thf(467,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_swap @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= ( product_Pair @ TB @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(105,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( sup_sup @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_sup_OorderI) ).
thf(583,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( sup_sup @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(185,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA,D: TA > $o] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_prop__restrict) ).
thf(830,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA,D: TA > $o] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(269,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_Un__absorb2) ).
thf(1079,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(252,axiom,
group_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ogroup__add) ).
thf(1027,plain,
group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(199,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_prod_Ocollapse) ).
thf(874,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(11,axiom,
preorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_10) ).
thf(317,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(123,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_fst__pair) ).
thf(650,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(281,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_subset__trans) ).
thf(1121,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(237,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_subset__eq) ).
thf(980,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(36,axiom,
! [A: variable > real,B: set @ variable] : ( denota1419872369iation @ A @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_Uvariation__refl) ).
thf(388,plain,
! [A: variable > real,B: set @ variable] : ( denota1419872369iation @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(288,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_subset__Collect__iff) ).
thf(1138,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(610,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(49,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_sup_OcoboundedI2) ).
thf(420,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(280,axiom,
! [TA: $tType] :
( ( uminus_uminus @ ( set @ TA ) )
= ( ^ [A: set @ TA] :
( collect @ TA
@ ^ [B: TA] :
~ ( member @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_Compl__eq) ).
thf(1118,plain,
! [TA: $tType] :
( ( uminus_uminus @ ( set @ TA ) )
= ( ^ [A: set @ TA] :
( collect @ TA
@ ^ [B: TA] :
~ ( member @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(18,axiom,
boolean_algebra @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Oboolean__algebra_9) ).
thf(339,plain,
boolean_algebra @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_prod__induct7) ).
thf(554,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_prod__cases7) ).
thf(526,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(75,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_sup__ge1) ).
thf(489,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_le__funI) ).
thf(590,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(133,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_prod__induct3) ).
thf(679,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(253,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_prod_Oexpand) ).
thf(1028,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(270,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: game] :
( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ ( loop @ C ) ) )
!= ( none @ game ) )
=> ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) )
!= ( none @ game ) )
& ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) @ C ) )
!= ( none @ game ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_usubstappp__loop__conv) ).
thf(1082,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: game] :
( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ ( loop @ C ) ) )
!= ( none @ game ) )
=> ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) )
!= ( none @ game ) )
& ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) @ C ) )
!= ( none @ game ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(210,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_Un__least) ).
thf(901,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(268,axiom,
! [A: set @ ( variable > real )] :
( ( denota1419872369iation @ nu2 @ omega2 @ ua )
=> ( ( member @ ( variable > real ) @ nu2 @ ( denota1245701238me_sem @ i @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) ) @ A ) )
= ( member @ ( variable > real ) @ nu2 @ ( denota1245701238me_sem @ ( uSubst2091380086djoint @ sigma @ i @ omega2 ) @ alpha @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_IH_092_060alpha_062) ).
thf(1075,plain,
! [A: set @ ( variable > real )] :
( ( denota1419872369iation @ nu2 @ omega2 @ ua )
=> ( ( member @ ( variable > real ) @ nu2 @ ( denota1245701238me_sem @ i @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) ) @ A ) )
= ( member @ ( variable > real ) @ nu2 @ ( denota1245701238me_sem @ ( uSubst2091380086djoint @ sigma @ i @ omega2 ) @ alpha @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(70,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__cong) ).
thf(476,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(244,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_6) ).
thf(997,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(273,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_Un__left__absorb) ).
thf(1099,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(140,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( sup_sup @ TA @ B @ C ) )
=> ( ( sup_sup @ TA @ D @ A )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_boolean__algebra__cancel_Osup2) ).
thf(701,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( sup_sup @ TA @ B @ C ) )
=> ( ( sup_sup @ TA @ D @ A )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(154,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_add_Oinverse__inverse) ).
thf(738,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(262,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_UnI1) ).
thf(1060,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(214,axiom,
! [TA: $tType] : ( uminus @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ouminus_7) ).
thf(911,plain,
! [TA: $tType] : ( uminus @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(147,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: product_prod @ TA @ TB] :
( ( A @ ( product_snd @ TA @ TB @ B ) @ ( product_fst @ TA @ TB @ B ) )
=> ~ ! [C: TA,D: TB] :
~ ( A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_exE__realizer_H) ).
thf(721,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: product_prod @ TA @ TB] :
( ( A @ ( product_snd @ TA @ TB @ B ) @ ( product_fst @ TA @ TB @ B ) )
=> ~ ! [C: TA,D: TB] :
~ ( A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(246,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_subset__refl) ).
thf(1002,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(100,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_sup__assoc) ).
thf(569,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(21,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_inf__sup__aci_I8_J) ).
thf(343,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(222,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_Un__subset__iff) ).
thf(938,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(81,axiom,
! [A: game,B: game,C: game] :
( ( choice @ A @ B )
!= ( loop @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_game_Odistinct_I39_J) ).
thf(508,plain,
! [A: game,B: game,C: game] :
( ( choice @ A @ B )
!= ( loop @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA] :
( ( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= C )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_fst__eqD) ).
thf(311,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA] :
( ( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= C )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(40,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_rev__predicate1D) ).
thf(398,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(96,axiom,
! [A: game,B: game] :
( ( loop @ A )
!= ( dual @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_game_Odistinct_I51_J) ).
thf(558,plain,
! [A: game,B: game] :
( ( loop @ A )
!= ( dual @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(131,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( ( ord_less_eq @ TA @ A @ C )
& ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_le__sup__iff) ).
thf(674,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( ( ord_less_eq @ TA @ A @ C )
& ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(218,axiom,
( denota1419872369iation
= ( ^ [A: variable > real,B: variable > real,C: set @ variable] :
! [D: variable] :
( ~ ( member @ variable @ D @ C )
=> ( ( A @ D )
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_Uvariation__def) ).
thf(926,plain,
( denota1419872369iation
= ( ^ [A: variable > real,B: variable > real,C: set @ variable] :
! [D: variable] :
( ~ ( member @ variable @ D @ C )
=> ( ( A @ D )
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(118,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_le__supI) ).
thf(633,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_old_Oprod_Oinducts) ).
thf(360,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(171,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_subsetI) ).
thf(794,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(106,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( B
= ( sup_sup @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_sup_Oorder__iff) ).
thf(586,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( B
= ( sup_sup @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(127,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_dual__order_Orefl) ).
thf(662,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(146,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_le__minus__iff) ).
thf(718,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(183,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_neg__equal__iff__equal) ).
thf(824,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(4,axiom,
! [A: game,B: game] :
( ( ( loop @ A )
= ( loop @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_game_Oinject_I6_J) ).
thf(296,plain,
! [A: game,B: game] :
( ( ( loop @ A )
= ( loop @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_prod__induct6) ).
thf(375,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(232,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_neg__le__iff__le) ).
thf(965,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(158,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ TA ) @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_Un__mono) ).
thf(750,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ TA ) @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(181,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_UnCI) ).
thf(819,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_prod_Oinject) ).
thf(562,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(248,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_Un__assoc) ).
thf(1007,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: TB,D: TA] :
( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
=> ( ( A @ C @ D )
=> ( B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_predicate2D) ).
thf(402,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: TB,D: TA] :
( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
=> ( ( A @ C @ D )
=> ( B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(151,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
=> ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_compl__le__swap1) ).
thf(732,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
=> ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(166,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( product_scomp @ TA @ TB @ TC @ TD )
= ( ^ [A: TA > ( product_prod @ TB @ TC ),B: TB > TC > TD,C: TA] : ( B @ ( product_fst @ TB @ TC @ ( A @ C ) ) @ ( product_snd @ TB @ TC @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_scomp__unfold) ).
thf(772,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( product_scomp @ TA @ TB @ TC @ TD )
= ( ^ [A: TA > ( product_prod @ TB @ TC ),B: TB > TC > TD,C: TA] : ( B @ ( product_fst @ TB @ TC @ ( A @ C ) ) @ ( product_snd @ TB @ TC @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_prod__induct5) ).
thf(577,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_prod__cases4) ).
thf(445,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: TB > TA > $o] :
( ( A @ B @ C )
=> ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ D )
=> ( D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_rev__predicate2D) ).
thf(572,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: TB > TA > $o] :
( ( A @ B @ C )
=> ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ D )
=> ( D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(169,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB,D: product_prod @ TA @ TB] :
( ( A @ B @ C )
=> ( ( D
= ( product_Pair @ TA @ TB @ B @ C ) )
=> ( A @ ( product_fst @ TA @ TB @ D ) @ ( product_snd @ TA @ TB @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_BNF__Greatest__Fixpoint_Osubst__Pair) ).
thf(787,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB,D: product_prod @ TA @ TB] :
( ( A @ B @ C )
=> ( ( D
= ( product_Pair @ TA @ TB @ B @ C ) )
=> ( A @ ( product_fst @ TA @ TB @ D ) @ ( product_snd @ TA @ TB @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(79,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_ord__eq__le__subst) ).
thf(498,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(65,axiom,
order @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_12) ).
thf(466,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(174,axiom,
! [A: variable > real,B: variable > real] :
( denota1419872369iation @ A @ B
@ ( collect @ variable
@ ^ [C: variable] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Uvariation__univ) ).
thf(804,plain,
! [A: variable > real,B: variable > real] :
( denota1419872369iation @ A @ B
@ ( collect @ variable
@ ^ [C: variable] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(24,axiom,
denota1419872369iation @ nu @ omega @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_vaouter) ).
thf(350,plain,
denota1419872369iation @ nu @ omega @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(60,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_le__supI1) ).
thf(451,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_prod__cases6) ).
thf(318,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(116,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_le__cases3) ).
thf(616,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(201,axiom,
! [A: set @ variable,B: set @ variable,C: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),D: game] :
( ( ord_less_eq @ ( set @ variable ) @ A @ B )
=> ( ord_less_eq @ ( set @ variable ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ C @ A @ D ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ C @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_usubstappp__fst__mon) ).
thf(880,plain,
! [A: set @ variable,B: set @ variable,C: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),D: game] :
( ( ord_less_eq @ ( set @ variable ) @ A @ B )
=> ( ord_less_eq @ ( set @ variable ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ C @ A @ D ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ C @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(256,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ~ ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ! [E: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ E @ C )
=> ( A
!= ( sup_sup @ ( set @ TA ) @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_subset__UnE) ).
thf(1043,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ~ ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ! [E: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ E @ C )
=> ( A
!= ( sup_sup @ ( set @ TA ) @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(204,axiom,
semilattice_sup @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Lattices_Osemilattice__sup_15) ).
thf(890,plain,
semilattice_sup @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(117,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_inf__sup__ord_I3_J) ).
thf(631,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(194,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: game] :
( ( uSubst95898988stappp @ A @ B @ ( dual @ C ) )
= ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) @ ( uSubst739989314_Dualo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_usubstappp__dual) ).
thf(858,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: game] :
( ( uSubst95898988stappp @ A @ B @ ( dual @ C ) )
= ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) @ ( uSubst739989314_Dualo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(90,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_sup_Oleft__commute) ).
thf(535,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_old_Oprod_Oinject) ).
thf(323,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(149,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_less__eq__set__def) ).
thf(726,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(73,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_sup_Oabsorb2) ).
thf(483,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(191,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: game,D: game] :
( ( uSubst95898988stappp @ A @ B @ ( choice @ C @ D ) )
= ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( sup_sup @ ( set @ variable ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ D ) ) ) @ ( uSubst1976112797hoiceo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_usubstappp__choice) ).
thf(848,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: game,D: game] :
( ( uSubst95898988stappp @ A @ B @ ( choice @ C @ D ) )
= ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( sup_sup @ ( set @ variable ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ D ) ) ) @ ( uSubst1976112797hoiceo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(207,axiom,
ordered_ab_group_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__group__add) ).
thf(895,plain,
ordered_ab_group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_order__subst2) ).
thf(462,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(277,axiom,
linorder @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Olinorder_17) ).
thf(1112,plain,
linorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(238,axiom,
( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ ( dual @ alpha ) ) )
!= ( none @ game ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_def) ).
thf(983,plain,
( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ ( dual @ alpha ) ) )
!= ( none @ game ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(230,axiom,
! [TA: $tType,TB: $tType,A: TB,B: product_prod @ TA @ TB] :
( ( A
= ( product_snd @ TA @ TB @ B ) )
= ( ? [C: TA] :
( B
= ( product_Pair @ TA @ TB @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_eq__snd__iff) ).
thf(959,plain,
! [TA: $tType,TB: $tType,A: TB,B: product_prod @ TA @ TB] :
( ( A
= ( product_snd @ TA @ TB @ B ) )
= ( ? [C: TA] :
( B
= ( product_Pair @ TA @ TB @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(197,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_snd__conv) ).
thf(868,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(202,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_Collect__mono) ).
thf(883,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(239,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_in__mono) ).
thf(986,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(278,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( uminus_uminus @ ( set @ TA ) @ A )
= ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Compl__eq__Compl__iff) ).
thf(1113,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( uminus_uminus @ ( set @ TA ) @ A )
= ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(5,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_le__supI2) ).
thf(299,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o] :
( ! [C: TA,D: TB] :
( ( A @ C @ D )
=> ( B @ C @ D ) )
=> ( ord_less_eq @ ( TA > TB > $o ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_predicate2I) ).
thf(431,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o] :
( ! [C: TA,D: TB] :
( ( A @ C @ D )
=> ( B @ C @ D ) )
=> ( ord_less_eq @ ( TA > TB > $o ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(124,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_sup__commute) ).
thf(653,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(135,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ B )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_sup_Oright__idem) ).
thf(685,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ B )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(85,axiom,
! [A: game,B: game] :
( ( ( dual @ A )
= ( dual @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_game_Oinject_I7_J) ).
thf(521,plain,
! [A: game,B: game] :
( ( ( dual @ A )
= ( dual @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(164,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_UnE) ).
thf(768,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(184,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ~ ( member @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_Compl__iff) ).
thf(827,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ~ ( member @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(192,axiom,
! [A: set @ variable,B: set @ variable,C: variable > real,D: variable > real] :
( ( ord_less_eq @ ( set @ variable ) @ A @ B )
=> ( ( denota1419872369iation @ C @ D @ A )
=> ( denota1419872369iation @ C @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_Uvariation__mon) ).
thf(851,plain,
! [A: set @ variable,B: set @ variable,C: variable > real,D: variable > real] :
( ( ord_less_eq @ ( set @ variable ) @ A @ B )
=> ( ( denota1419872369iation @ C @ D @ A )
=> ( denota1419872369iation @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(274,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_verit__minus__simplify_I4_J) ).
thf(1102,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(107,axiom,
linorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(589,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(224,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_le__imp__neg__le) ).
thf(944,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(122,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_inf__sup__ord_I4_J) ).
thf(648,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA )
=> ( uminus @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Groups_Ouminus) ).
thf(516,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA )
=> ( uminus @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(257,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ B ) @ ( uminus_uminus @ ( set @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_Compl__anti__mono) ).
thf(1049,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ B ) @ ( uminus_uminus @ ( set @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(233,axiom,
! [TA: $tType,TB: $tType] :
( ( product_swap @ TA @ TB )
= ( ^ [A: product_prod @ TA @ TB] : ( product_Pair @ TB @ TA @ ( product_snd @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_prod_Oswap__def) ).
thf(968,plain,
! [TA: $tType,TB: $tType] :
( ( product_swap @ TA @ TB )
= ( ^ [A: product_prod @ TA @ TB] : ( product_Pair @ TB @ TA @ ( product_snd @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(182,axiom,
uminus @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ouminus_21) ).
thf(823,plain,
uminus @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(144,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_antisym__conv) ).
thf(712,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(141,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_order__trans) ).
thf(705,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(142,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_old_Oprod_Orec) ).
thf(707,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(203,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
= ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_pred__equals__eq2) ).
thf(887,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
= ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(228,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: game] :
( ( uSubst95898988stappp @ A @ B @ ( loop @ C ) )
= ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) @ ( uSubst993936602_Loopo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_usubstappp__loop) ).
thf(954,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: game] :
( ( uSubst95898988stappp @ A @ B @ ( loop @ C ) )
= ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) @ ( uSubst993936602_Loopo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(414,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(234,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_5) ).
thf(971,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(259,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_UnI2) ).
thf(1053,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(170,axiom,
! [TA: $tType,A: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_double__complement) ).
thf(791,plain,
! [TA: $tType,A: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(67,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_31_Uvariation__sym__rel) ).
thf(470,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)],[67]) ).
thf(285,axiom,
! [TA: $tType] :
( ( uminus_uminus @ ( set @ TA ) )
= ( ^ [A: set @ TA] :
( collect @ TA
@ ( uminus_uminus @ ( TA > $o )
@ ^ [B: TA] : ( member @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_uminus__set__def) ).
thf(1130,plain,
! [TA: $tType] :
( ( uminus_uminus @ ( set @ TA ) )
= ( ^ [A: set @ TA] :
( collect @ TA
@ ( uminus_uminus @ ( TA > $o )
@ ^ [B: TA] : ( member @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(120,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_sup_Ocobounded2) ).
thf(643,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(156,axiom,
! [TA: $tType,TB: $tType] :
( ( ( uminus @ TA )
& ( uminus @ TB ) )
=> ! [A: product_prod @ TA @ TB] :
( ( product_fst @ TA @ TB @ ( uminus_uminus @ ( product_prod @ TA @ TB ) @ A ) )
= ( uminus_uminus @ TA @ ( product_fst @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_fst__uminus) ).
thf(744,plain,
! [TA: $tType,TB: $tType] :
( ( ( uminus @ TA )
& ( uminus @ TB ) )
=> ! [A: product_prod @ TA @ TB] :
( ( product_fst @ TA @ TB @ ( uminus_uminus @ ( product_prod @ TA @ TB ) @ A ) )
= ( uminus_uminus @ TA @ ( product_fst @ TA @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(17,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_sup_Oassoc) ).
thf(336,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(289,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_ball__Un) ).
thf(1141,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(125,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( sup_sup @ TA @ B @ A )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_sup_Oabsorb__iff1) ).
thf(656,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( sup_sup @ TA @ B @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(111,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_order__class_Oorder_Oantisym) ).
thf(600,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(35,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_sup_OboundedI) ).
thf(386,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(115,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_ord__eq__le__trans) ).
thf(612,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(241,axiom,
order @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oorder_19) ).
thf(991,plain,
order @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(220,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_minus__equation__iff) ).
thf(931,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_surj__pair) ).
thf(495,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(205,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_compl__le__swap2) ).
thf(891,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(283,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_fst @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= ( product_snd @ TA @ TB @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_fst__swap) ).
thf(1126,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_fst @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= ( product_snd @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(249,axiom,
! [TA: $tType,A: option @ TA,B: option @ TA] :
( ( ( A
= ( none @ TA ) )
= ( B
= ( none @ TA ) ) )
=> ( ( ( A
!= ( none @ TA ) )
=> ( ( B
!= ( none @ TA ) )
=> ( ( the @ TA @ A )
= ( the @ TA @ B ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_option_Oexpand) ).
thf(1010,plain,
! [TA: $tType,A: option @ TA,B: option @ TA] :
( ( ( A
= ( none @ TA ) )
= ( B
= ( none @ TA ) ) )
=> ( ( ( A
!= ( none @ TA ) )
=> ( ( B
!= ( none @ TA ) )
=> ( ( the @ TA @ A )
= ( the @ TA @ B ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(190,axiom,
! [A: set @ variable,B: set @ variable,C: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),D: game] :
( ( ord_less_eq @ ( set @ variable ) @ A @ B )
=> ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ C @ B @ D ) )
!= ( none @ game ) )
=> ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ C @ B @ D ) )
= ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ C @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_usubstappp__antimon) ).
thf(844,plain,
! [A: set @ variable,B: set @ variable,C: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),D: game] :
( ( ord_less_eq @ ( set @ variable ) @ A @ B )
=> ( ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ C @ B @ D ) )
!= ( none @ game ) )
=> ( ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ C @ B @ D ) )
= ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ C @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(236,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_equalityD1) ).
thf(976,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(136,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_internal__case__prod__conv) ).
thf(688,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(211,axiom,
! [TA: $tType] : ( boolean_algebra @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Oboolean__algebra_2) ).
thf(903,plain,
! [TA: $tType] : ( boolean_algebra @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(86,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_dual__order_Otrans) ).
thf(524,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(581,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(178,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_3) ).
thf(813,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(208,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_fun__Compl__def) ).
thf(896,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(263,axiom,
! [A: set @ ( variable > real )] :
( ( member @ ( variable > real ) @ nu2 @ ( denota1245701238me_sem @ i @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) ) @ A ) )
= ( member @ ( variable > real ) @ nu2 @ ( denota1245701238me_sem @ ( uSubst2091380086djoint @ 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__nnnzepxswx_Oadjoint_A_092_060sigma_062_AI_A_092_060omega_062_J_A_092_060alpha_062_AX_J_092_060close_062) ).
thf(1062,plain,
! [A: set @ ( variable > real )] :
( ( member @ ( variable > real ) @ nu2 @ ( denota1245701238me_sem @ i @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) ) @ A ) )
= ( member @ ( variable > real ) @ nu2 @ ( denota1245701238me_sem @ ( uSubst2091380086djoint @ sigma @ i @ omega2 ) @ alpha @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(225,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_compl__eq__compl__iff) ).
thf(946,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_Pair__inject) ).
thf(351,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(37,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_order__refl) ).
thf(390,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_le__funE) ).
thf(418,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1,conjecture,
( ( member @ ( variable > real ) @ nu2 @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ ( denota1245701238me_sem @ i @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ xa ) ) ) )
= ( member @ ( variable > real ) @ nu2 @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ ( denota1245701238me_sem @ ( uSubst2091380086djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ xa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( member @ ( variable > real ) @ nu2 @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ ( denota1245701238me_sem @ i @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ xa ) ) ) )
!= ( member @ ( variable > real ) @ nu2 @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ ( denota1245701238me_sem @ ( uSubst2091380086djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ xa ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(290,plain,
( ( member @ ( variable > real ) @ nu2 @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ ( denota1245701238me_sem @ i @ ( the @ game @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ xa ) ) ) )
!= ( member @ ( variable > real ) @ nu2 @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ ( denota1245701238me_sem @ ( uSubst2091380086djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ xa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(129,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_order__class_Oorder_Oeq__iff) ).
thf(667,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(162,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Collect__mem__eq) ).
thf(763,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_prod__cases5) ).
thf(383,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(209,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Collect__subset) ).
thf(899,plain,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(186,axiom,
! [TA: $tType,A: ( set @ TA ) > $o] :
( ( ? [B: set @ TA] : ( A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) )
= ( ? [B: set @ TA] : ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_exists__diff) ).
thf(832,plain,
! [TA: $tType,A: ( set @ TA ) > $o] :
( ( ? [B: set @ TA] : ( A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) )
= ( ? [B: set @ TA] : ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(22,axiom,
uminus @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ouminus_14) ).
thf(346,plain,
uminus @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(93,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA] :
( ( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA ) @ A )
=> ( A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_ge__eq__refl) ).
thf(549,plain,
! [TA: $tType,A: TA > TA > $o,B: TA] :
( ( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA ) @ A )
=> ( A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(279,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB] :
( ( A @ B @ C )
=> ( A @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_exI__realizer) ).
thf(1116,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB] :
( ( A @ B @ C )
=> ( A @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(286,axiom,
! [A: option @ game] :
( ( ( uSubst739989314_Dualo @ A )
= ( none @ game ) )
= ( A
= ( none @ game ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_Dualo__undef) ).
thf(1133,plain,
! [A: option @ game] :
( ( ( uSubst739989314_Dualo @ A )
= ( none @ game ) )
= ( A
= ( none @ game ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(245,axiom,
! [A: option @ game] :
( ( ( uSubst993936602_Loopo @ A )
= ( none @ game ) )
= ( A
= ( none @ game ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_Loopo__undef) ).
thf(999,plain,
! [A: option @ game] :
( ( ( uSubst993936602_Loopo @ A )
= ( none @ game ) )
= ( A
= ( none @ game ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(159,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E ) ) )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_subset__CollectI) ).
thf(752,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E ) ) )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(10,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_order_Otrans) ).
thf(315,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(187,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
& ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_conj__subset__def) ).
thf(835,plain,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
& ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(180,axiom,
denota1419872369iation @ nu2 @ omega2 @ ua,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Dual_Oprems_I2_J) ).
thf(818,plain,
denota1419872369iation @ nu2 @ omega2 @ ua,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(193,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: TB,C: TA] :
( ( A
= ( product_Pair @ TB @ TA @ B @ C ) )
=> ( ( product_snd @ TB @ TA @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_sndI) ).
thf(854,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: TB,C: TA] :
( ( A
= ( product_Pair @ TB @ TA @ B @ C ) )
=> ( ( product_snd @ TB @ TA @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(50,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_le__cases) ).
thf(422,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(196,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_subset__antisym) ).
thf(865,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(112,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
=> ~ ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_sup_OboundedE) ).
thf(603,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
=> ~ ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(153,axiom,
! [TA: $tType,TB: $tType] :
( ( (=) @ ( product_prod @ TA @ TB ) )
= ( ^ [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_prod__eq__iff) ).
thf(735,plain,
! [TA: $tType,TB: $tType] :
( ( (=) @ ( product_prod @ TA @ TB ) )
= ( ^ [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(7,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_sup__absorb2) ).
thf(305,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_linorder__wlog) ).
thf(326,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(173,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( bNF_Ca1785829860lChain @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TA ),B: TA > TB] :
! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( ord_less_eq @ TB @ ( B @ C ) @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_relChain__def) ).
thf(801,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( bNF_Ca1785829860lChain @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TA ),B: TA > TB] :
! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( ord_less_eq @ TB @ ( B @ C ) @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_le__funD) ).
thf(341,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(80,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_sup_OcoboundedI1) ).
thf(506,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(176,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_pred__subset__eq) ).
thf(807,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_le__fun__def) ).
thf(437,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA )
=> ( boolean_algebra @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Oboolean__algebra) ).
thf(474,plain,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA )
=> ( boolean_algebra @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(41,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_predicate1D) ).
thf(400,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(119,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA > TA > TA,B: TA,C: TA] :
( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ D @ ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ E @ ( A @ D @ E ) )
=> ( ! [D: TA,E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ D )
=> ( ( ord_less_eq @ TA @ F @ D )
=> ( ord_less_eq @ TA @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup_sup @ TA @ B @ C )
= ( A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_sup__unique) ).
thf(635,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA > TA > TA,B: TA,C: TA] :
( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ D @ ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ E @ ( A @ D @ E ) )
=> ( ! [D: TA,E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ D )
=> ( ( ord_less_eq @ TA @ F @ D )
=> ( ord_less_eq @ TA @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup_sup @ TA @ B @ C )
= ( A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(138,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ ( sup_sup @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_sup_Omono) ).
thf(696,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ ( sup_sup @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(219,axiom,
! [A: denotational_interp,B: set @ ( variable > real )] :
( ( denota1245701238me_sem @ A @ skip @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_skip__id) ).
thf(928,plain,
! [A: denotational_interp,B: set @ ( variable > real )] :
( ( denota1245701238me_sem @ A @ skip @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(261,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_verit__negate__coefficient_I3_J) ).
thf(1056,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(128,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_dual__order_Oantisym) ).
thf(664,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TA > TC > TB] :
( ( product_scomp @ TC @ TA @ TC @ TB @ ( product_Pair @ TA @ TC @ A ) @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_Pair__scomp) ).
thf(532,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TA > TC > TB] :
( ( product_scomp @ TC @ TA @ TC @ TB @ ( product_Pair @ TA @ TC @ A ) @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(264,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
=> ~ ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_ComplD) ).
thf(1065,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
=> ~ ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(39,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_le__iff__sup) ).
thf(395,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(110,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( sup_sup @ TA @ B @ C ) )
=> ( ( sup_sup @ TA @ A @ D )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_boolean__algebra__cancel_Osup1) ).
thf(596,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( sup_sup @ TA @ B @ C ) )
=> ( ( sup_sup @ TA @ A @ D )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(63,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( B
= ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_sup_OorderE) ).
thf(459,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( B
= ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(148,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_Un__left__commute) ).
thf(723,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(247,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_double__compl) ).
thf(1004,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(137,axiom,
! [TA: $tType,A: TA > TA > $o] :
( ! [B: TA] : ( A @ B @ B )
=> ( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_refl__ge__eq) ).
thf(691,plain,
! [TA: $tType,A: TA > TA > $o] :
( ! [B: TA] : ( A @ B @ B )
=> ( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(198,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_uminus__apply) ).
thf(871,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(16,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_eq__refl) ).
thf(332,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(284,axiom,
denota1419872369iation @ nu2 @ omega2 @ ua,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_uv) ).
thf(1129,plain,
denota1419872369iation @ nu2 @ omega2 @ ua,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(213,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: game] :
( ( uSubst95898988stappp @ A @ B @ ( loop @ C ) )
= ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) @ ( uSubst993936602_Loopo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_usubstappp_Osimps_I6_J) ).
thf(908,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: game] :
( ( uSubst95898988stappp @ A @ B @ ( loop @ C ) )
= ( product_Pair @ ( set @ variable ) @ ( option @ game ) @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) @ ( uSubst993936602_Loopo @ ( product_snd @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ A @ B @ C ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(242,axiom,
! [A: set @ variable,B: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),C: game] : ( ord_less_eq @ ( set @ variable ) @ A @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_usubst__taboos__mon) ).
thf(992,plain,
! [A: set @ variable,B: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),C: game] : ( ord_less_eq @ ( set @ variable ) @ A @ ( product_fst @ ( set @ variable ) @ ( option @ game ) @ ( uSubst95898988stappp @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(30,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_sup_Ocommute) ).
thf(369,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF > ( product_prod @ TA @ TB ),B: TA > TB > ( product_prod @ TE @ TD ),C: TE > TD > TC] :
( ( product_scomp @ TF @ TE @ TD @ TC @ ( product_scomp @ TF @ TA @ TB @ ( product_prod @ TE @ TD ) @ A @ B ) @ C )
= ( product_scomp @ TF @ TA @ TB @ TC @ A
@ ^ [D: TA] : ( product_scomp @ TB @ TE @ TD @ TC @ ( B @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_scomp__scomp) ).
thf(607,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF > ( product_prod @ TA @ TB ),B: TA > TB > ( product_prod @ TE @ TD ),C: TE > TD > TC] :
( ( product_scomp @ TF @ TE @ TD @ TC @ ( product_scomp @ TF @ TA @ TB @ ( product_prod @ TE @ TD ) @ A @ B ) @ C )
= ( product_scomp @ TF @ TA @ TB @ TC @ A
@ ^ [D: TA] : ( product_scomp @ TB @ TE @ TD @ TC @ ( B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(74,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_sup__idem) ).
thf(486,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(126,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > ( product_prod @ TB @ TC )] :
( ( product_scomp @ TA @ TB @ TC @ ( product_prod @ TB @ TC ) @ A @ ( product_Pair @ TB @ TC ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_scomp__Pair) ).
thf(659,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > ( product_prod @ TB @ TC )] :
( ( product_scomp @ TA @ TB @ TC @ ( product_prod @ TB @ TC ) @ A @ ( product_Pair @ TB @ TC ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(167,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_snd__pair) ).
thf(775,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(109,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_ord__le__eq__trans) ).
thf(592,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(266,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TA] :
( ( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= C )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_snd__eqD) ).
thf(1069,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TA] :
( ( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= C )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( lattice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Olattice) ).
thf(364,plain,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( lattice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(76,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ ( sup_sup @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_sup__mono) ).
thf(491,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ ( sup_sup @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(271,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_subset__Un__eq) ).
thf(1088,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(1316,plain,
$false,
inference(e,[status(thm)],[645,1024,760,347,1031,893,518,962,941,479,1105,408,683,994,308,379,440,677,741,1073,1041,861,715,472,698,340,538,670,747,913,404,841,973,301,565,1055,372,838,949,934,357,770,416,448,443,1136,806,1051,1109,321,1020,574,905,480,766,877,734,453,428,411,988,292,920,512,529,546,810,366,1067,798,957,1091,778,952,1123,392,424,815,729,566,435,493,757,551,710,456,916,467,583,830,1079,1027,874,317,650,1121,980,388,1138,610,420,1118,339,554,526,489,590,679,1028,1082,901,1075,476,997,1099,701,738,1060,911,721,1002,569,343,938,508,311,398,558,674,926,633,360,794,586,662,718,824,296,375,965,750,819,562,1007,402,732,772,577,445,572,787,498,466,804,350,451,318,616,880,1043,890,631,858,535,323,726,483,848,895,462,1112,983,959,868,883,986,1113,299,431,653,685,521,768,827,851,1102,589,944,648,516,1049,968,823,712,705,707,887,954,414,971,1053,791,470,1130,643,744,336,1141,656,600,386,612,991,931,495,891,1126,1010,844,976,688,903,524,581,813,896,1062,946,351,390,418,290,667,763,383,899,832,346,549,1116,1133,999,752,315,835,818,854,422,865,603,735,305,326,801,341,506,807,437,474,400,635,696,928,1056,664,532,1065,395,596,459,723,1004,691,871,332,1129,908,992,369,607,486,659,775,592,1069,364,491,1088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP201^2 : 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
% 0.11/0.22 % Computer : n018.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 20:13:26 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 1.04/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.31/1.24 % [INFO] Parsing done (413ms).
% 2.31/1.26 % [INFO] Running in sequential loop mode.
% 3.60/1.64 % [INFO] eprover registered as external prover.
% 3.60/1.64 % [INFO] Scanning for conjecture ...
% 4.04/1.81 % [INFO] Found a conjecture (or negated_conjecture) and 288 axioms. Running axiom selection ...
% 4.35/1.97 % [INFO] Axiom selection finished. Selected 287 axioms (removed 1 axioms).
% 5.33/2.29 % [INFO] Problem is higher-order (TPTP THF).
% 5.57/2.32 % [INFO] Type checking passed.
% 5.57/2.33 % [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 ...
% 33.84/13.86 % External prover 'e' found a proof!
% 33.84/13.86 % [INFO] Killing All external provers ...
% 33.84/13.86 % Time passed: 13503ms (effective reasoning time: 12601ms)
% 33.84/13.87 % 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)>
% 33.84/13.87 % Axioms used in derivation (287): fact_214_sup_OboundedE, fact_54_usubstappp__antimon, fact_203_Un__upper1, fact_243_Un__assoc, tcon_HOL_Obool___Lattices_Olattice_11, fact_215_sup__absorb2, fact_235_inf__sup__aci_I7_J, fact_10_add_Oinverse__inverse, fact_170_pred__subset__eq2, tcon_Set_Oset___Lattices_Osemilattice__sup_1, fact_150_le__funI, fact_81_verit__la__disequality, fact_138_le__cases3, fact_28_Uvariation__def, fact_168_subrelI, fact_27_usubst__game__loop, fact_191_sup_Oleft__idem, fact_224_sup__mono, fact_118_usubstappp_Osimps_I6_J, fact_182_predicate2D, fact_71_prod__cases5, fact_100_minus__le__iff, fact_111_Uvariation__mon, fact_34_game_Oinject_I4_J, fact_31_Uvariation__sym__rel, fact_220_sup_OorderI, fact_218_sup_Oabsorb1, fact_192_sup__left__idem, tcon_Real_Oreal___Groups_Ouminus_21, fact_82_Collect__mono__iff, tcon_Product__Type_Oprod___Groups_Ouminus_23, fact_207_sup_OcoboundedI1, fact_142_linear, fact_33_game_Oinject_I6_J, fact_184_ge__eq__refl, fact_6_Compl__iff, fact_86_subset__refl, fact_165_scomp__Pair, fact_64_Compl__anti__mono, fact_97_snd__conv, fact_127_dual__order_Oantisym, fact_245_Un__left__absorb, fact_202_Un__upper2, tcon_fun___Orderings_Oord, tcon_Real_Oreal___Orderings_Opreorder_16, fact_169_ssubst__Pair__rhs, fact_76_prod__induct5, fact_61_compl__le__compl__iff, fact_181_rev__predicate2D, fact_98_snd__eqD, fact_5_ComplI, fact_55_exists__diff, fact_120_order__refl, fact_210_sup_Ocobounded2, fact_209_sup_Oabsorb__iff1, fact_39_Collect__neg__eq, fact_222_le__iff__sup, tcon_HOL_Obool___Orderings_Olinorder, fact_7_Compl__eq__Compl__iff, fact_52_prod__eq__iff, fact_244_Un__absorb, fact_42_game_Odistinct_I41_J, fact_35_fst__uminus, fact_226_le__supI2, fact_22_game__sem_Osimps_I7_J, fact_69_prod__cases3, fact_233_inf__sup__ord_I4_J, fact_135_ord__eq__le__trans, fact_141_eq__refl, fact_57_prod_Oinject, fact_132_order__trans, fact_160_predicate1D, fact_48_skip__id, fact_239_UnI1, tcon_HOL_Obool___Lattices_Oboolean__algebra_9, fact_104_compl__mono, fact_146_ord__eq__le__subst, fact_58_old_Oprod_Oinject, fact_206_sup_OcoboundedI2, tcon_Real_Oreal___Orderings_Olinorder_17, fact_148_order__subst1, fact_25_Dual_Oprems_I2_J, fact_2_uv, fact_89_equalityD1, fact_15_usubstappp__det, fact_129_dual__order_Otrans, fact_24_game_Oinject_I7_J, fact_242_ball__Un, fact_227_le__supI1, fact_70_prod__cases4, fact_176_predicate2I, fact_37_game_Odistinct_I39_J, fact_51_prod_Oexpand, fact_1_IH_092_060alpha_062, fact_250_sup_Oassoc, fact_94_Collect__subset, fact_199_subset__UnE, fact_143_antisym, fact_254_sup_Oleft__commute, fact_90_subset__eq, fact_241_bex__Un, fact_3_snd__uminus, fact_95_fst__eqD, tcon_Real_Oreal___Orderings_Oord_20, fact_225_sup_Omono, fact_92_subsetD, fact_65_prod_Ocollapse, fact_228_sup__ge2, fact_63_Compl__subset__Compl__iff, fact_188_sup__apply, tcon_Real_Oreal___Groups_Oordered__ab__group__add, tcon_fun___Lattices_Osemilattice__sup, fact_107_surjective__pairing, fact_43_usubstappp__loop__conv, fact_49_prod__eqI, fact_13_vaouter, fact_20_double__complement, fact_196_le__sup__iff, fact_4_def, tcon_Set_Oset___Orderings_Oord_6, fact_154_subset__Collect__iff, fact_163_scomp__unfold, fact_110_exI__realizer, fact_17_equation__minus__iff, fact_124_Dualo__undef, fact_84_subset__trans, fact_103_compl__le__swap1, fact_252_sup_Ocommute, fact_50_exE__realizer_H, fact_99_le__imp__neg__le, fact_137_antisym__conv, fact_179_snd__swap, fact_217_sup_Oabsorb2, fact_11_neg__equal__iff__equal, fact_145_ord__le__eq__subst, tcon_HOL_Obool___Orderings_Oorder_12, fact_158_fstI, fact_153_subset__CollectI, fact_205_Un__mono, fact_113_usubst__taboos__mon, fact_253_sup__commute, fact_122_less__eq__set__def, fact_117_usubstappp_Osimps_I7_J, fact_116_BNF__Greatest__Fixpoint_Osubst__Pair, fact_67_prod__cases, fact_123_Loopo__undef, fact_221_sup_OorderE, fact_213_sup_OboundedI, fact_161_rev__predicate1D, tcon_HOL_Obool___Orderings_Opreorder_10, fact_83_set__eq__subset, fact_130_linorder__wlog, fact_201_Un__absorb1, fact_126_Dualo_Osimps_I2_J, fact_105_fst__pair, fact_198_subset__Un__eq, fact_251_sup__assoc, fact_114_old_Oprod_Orec, fact_204_Un__least, fact_183_refl__ge__eq, tcon_Set_Oset___Lattices_Olattice_4, fact_151_le__funE, fact_78_prod__induct7, tcon_Real_Oreal___Lattices_Osemilattice__sup_15, tcon_Set_Oset___Orderings_Opreorder_3, fact_174_internal__case__prod__conv, fact_139_order_Otrans, fact_68_Pair__inject, fact_155_sndI, fact_162_pred__subset__eq, fact_108_prod_Oexhaust__sel, fact_177_swap__swap, tcon_Set_Oset___Groups_Ouminus_7, fact_96_fst__conv, fact_85_Collect__mono, fact_237_inf__sup__aci_I5_J, fact_109_conjI__realizer, fact_156_eq__snd__iff, fact_247_sup__fun__def, fact_9_uminus__apply, tcon_Real_Oreal___Lattices_Olattice_18, fact_131_dual__order_Orefl, fact_236_inf__sup__aci_I6_J, tcon_fun___Lattices_Oboolean__algebra, fact_29_Uvariation__sym, fact_171_pred__equals__eq2, fact_167_Pair__scomp, fact_72_prod__cases6, fact_166_scomp__scomp, tcon_Real_Oreal___Groups_Ogroup__add, fact_74_prod__induct3, fact_14_compl__eq__compl__iff, fact_102_compl__le__swap2, fact_223_sup__least, fact_234_inf__sup__aci_I8_J, tcon_HOL_Obool___Orderings_Oord_13, fact_21_ComplD, fact_238_UnE, fact_231_le__supE, fact_180_fst__swap, fact_164_Collect__restrict, fact_249_boolean__algebra__cancel_Osup2, fact_157_eq__fst__iff, fact_246_Un__left__commute, tcon_Product__Type_Oprod___Groups_Ogroup__add_22, fact_59_subset__antisym, tcon_fun___Orderings_Opreorder, tcon_Set_Oset___Orderings_Oorder_5, fact_128_dual__order_Oeq__iff, fact_45_Collect__mem__eq, fact_208_sup_Oabsorb__iff2, fact_77_prod__induct6, fact_200_Un__absorb2, fact_159_predicate1I, fact_75_prod__induct4, fact_88_equalityD2, fact_30_Uvariation__refl, fact_56_uminus__Pair, fact_19_verit__negate__coefficient_I3_J, fact_101_le__minus__iff, fact_186_usubstappp__choice, fact_248_boolean__algebra__cancel_Osup1, fact_112_usubstappp__fst__mon, fact_119_usubstappp__loop, fact_66_surj__pair, fact_41_game_Odistinct_I51_J, tcon_HOL_Obool___Lattices_Osemilattice__sup_8, fact_230_le__supI, fact_115_usubstappp__dual, fact_193_sup_Oright__idem, fact_187_relChain__def, fact_87_subset__iff, fact_26_option_Oexpand, fact_79_old_Oprod_Oexhaust, tcon_fun___Orderings_Oorder, fact_93_in__mono, fact_178_swap__simp, fact_8_verit__minus__simplify_I4_J, fact_197_Un__subset__iff, fact_60_subsetI, fact_12_double__compl, tcon_Real_Oreal___Orderings_Oorder_19, fact_16_minus__equation__iff, fact_152_le__funD, tcon_fun___Groups_Ouminus, fact_194_UnCI, fact_229_sup__ge1, fact_40_Compl__eq, fact_53_uminus__prod__def, fact_91_equalityE, fact_23_Dual_OIH, fact_140_le__cases, fact_18_fun__Compl__def, tcon_HOL_Obool___Groups_Ouminus_14, fact_144_eq__iff, fact_211_sup_Ocobounded1, fact_172_prop__restrict, fact_147_order__subst2, fact_32_usubstappp__choice__conv, fact_232_inf__sup__ord_I3_J, fact_80_old_Oprod_Oinducts, fact_136_order__class_Oorder_Oeq__iff, fact_212_sup_Oorder__iff, 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__nnnzepxswx_Oadjoint_A_092_060sigma_062_AI_A_092_060omega_062_J_A_092_060alpha_062_AX_J_092_060close_062, fact_175_prod_Oswap__def, fact_133_order__class_Oorder_Oantisym, fact_125_Loopo_Osimps_I2_J, fact_195_sup_Obounded__iff, fact_173_conj__subset__def, fact_38_uminus__set__def, fact_189_sup_Oidem, fact_185_eq__subset, fact_149_le__fun__def, fact_73_prod__cases7, fact_36_Uvariation__univ, fact_134_ord__le__eq__trans, fact_44_mem__Collect__eq, fact_219_sup__unique, tcon_fun___Lattices_Olattice, tcon_Set_Oset___Lattices_Oboolean__algebra_2, fact_121_monotone, fact_216_sup__absorb1, fact_106_snd__pair, fact_190_sup__idem, fact_46_Collect__cong, fact_240_UnI2, fact_62_neg__le__iff__le
% 33.84/13.87 % No. of inferences in proof: 578
% 33.84/13.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 13503 ms resp. 12601 ms w/o parsing
% 35.46/14.13 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 35.46/14.13 % [INFO] Killing All external provers ...
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