%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW526_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/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 : Sun Sep 27 09:10:44 AM UTC 2026
% Result : Theorem 18.72s 7.11s
% Output : Refutation 19.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 132
% Syntax : Number of formulae : 266 ( 74 unt; 0 typ; 0 def)
% Number of atoms : 1319 ( 199 equ; 0 cnn)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 6097 ( 68 ~; 16 |; 62 &;5668 @)
% ( 18 <=>; 265 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 9 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 40 usr; 8 con; 0-6 aty)
% Number of variables : 846 ( 0 ^; 834 !; 12 ?; 846 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(skt1_type,type,
skt1: $tType ).
thf(bounded_lattice_decl,type,
bounded_lattice:
!>[TA: $tType] : $o ).
thf(bot_decl,type,
bot:
!>[TA: $tType] : $o ).
thf(lattice_decl,type,
lattice:
!>[TA: $tType] : $o ).
thf(finite_finite1_decl,type,
finite_finite1:
!>[TA: $tType] : $o ).
thf(semilattice_inf_decl,type,
semilattice_inf:
!>[TA: $tType] : $o ).
thf(semilattice_sup_decl,type,
semilattice_sup:
!>[TA: $tType] : $o ).
thf(bounded_lattice_bot_decl,type,
bounded_lattice_bot:
!>[TA: $tType] : $o ).
thf(big_comm_monoid_big_decl,type,
big_comm_monoid_big:
!>[TA: $tType,TB: $tType] : ( ( TB @ ( TB @ fun ) @ ( TB @ fun ) ) > TB > ( TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) ) > $o ) ).
thf(big_lattice_Sup_fin_decl,type,
big_lattice_Sup_fin:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > TA ) ).
thf(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB @ ( TC @ fun ) ) > ( TC @ ( TA @ fun ) ) > ( TB @ ( TA @ fun ) ) ) ).
thf(combc_decl,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > TB > ( TA @ ( TC @ fun ) ) ) ).
thf(combk_decl,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ fun ) ) ) ).
thf(combs_decl,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ fun ) ) > ( TA @ ( TC @ fun ) ) ) ).
thf(finite_finite_decl,type,
finite_finite:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > $o ) ).
thf(finite_fold_image_decl,type,
finite_fold_image:
!>[TA: $tType,TB: $tType] : ( ( TB @ ( TB @ fun ) @ ( TB @ fun ) ) > ( TB @ ( TA @ fun ) ) > TB > ( bool @ ( TA @ fun ) ) > TB ) ).
thf(finite908156982e_idem_decl,type,
finite908156982e_idem:
!>[TA: $tType,TB: $tType] : ( ( TB @ ( TB @ fun ) @ ( TB @ fun ) ) > TB > ( TB @ ( TA @ fun ) ) > ( TB @ ( bool @ ( TA @ fun ) @ fun ) ) > $o ) ).
thf(finite2073411215e_idem_decl,type,
finite2073411215e_idem:
!>[TA: $tType] : ( ( TA @ ( TA @ fun ) @ ( TA @ fun ) ) > ( TA @ ( bool @ ( TA @ fun ) @ fun ) ) > $o ) ).
thf(huffma675207370phabet_decl,type,
huffma675207370phabet:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > ( bool @ ( TA @ fun ) ) ) ).
thf(huffma1146269203erNode_decl,type,
huffma1146269203erNode:
!>[TA: $tType] : ( nat > ( TA @ huffma1450048681e_tree ) > ( TA @ huffma1450048681e_tree ) > ( TA @ huffma1450048681e_tree ) ) ).
thf(huffma107959123e_case_decl,type,
huffma107959123e_case:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) @ ( nat @ fun ) ) > ( TA @ ( TB @ huffma1450048681e_tree @ fun ) @ ( TB @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ) ) > ( TB @ huffma1450048681e_tree ) > TA ) ).
thf(huffma1280178957ee_rec_decl,type,
huffma1280178957ee_rec:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) @ ( nat @ fun ) ) > ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( TB @ huffma1450048681e_tree @ fun ) @ ( TB @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ) ) > ( TB @ huffma1450048681e_tree ) > TA ) ).
thf(inf_inf_decl,type,
inf_inf:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(sup_sup_decl,type,
sup_sup:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(inv_imagep_decl,type,
inv_imagep:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TB @ fun ) @ ( TB @ fun ) ) > ( TB @ ( TA @ fun ) ) > TA > TA > $o ) ).
thf(field_decl,type,
field:
!>[TA: $tType] : ( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
thf(refl_on_decl,type,
refl_on:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
thf(pow_decl,type,
pow:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( bool @ ( TA @ fun ) @ fun ) ) ) ).
thf(sum_Plus_decl,type,
sum_Plus:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TB @ fun ) ) > ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ ( TB @ sum_sum ) @ fun ) ) ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fdisj_decl,type,
fdisj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ fun ) ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(81,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_Un__left__absorb) ).
thf(391,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ lattice )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ sup_sup ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ sup_sup ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_sup__apply) ).
thf(365,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ lattice )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ sup_sup ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ sup_sup ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(68,axiom,
nat @ lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Olattice) ).
thf(347,plain,
nat @ lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TB @ ( bool @ ( TA @ fun ) @ fun ),D: TB @ ( TA @ fun ),E: TB,F: TB @ ( TB @ fun ) @ ( TB @ fun )] :
( ( C @ ( D @ ( E @ ( F @ ( TA @ ( TB @ finite908156982e_idem ) ) ) ) ) )
=> ( ( B @ ( TA @ finite_finite ) )
=> ( ( A @ ( TA @ finite_finite ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( C @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( F @ ( TB @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_folding__image__simple__idem_Ounion__idem) ).
thf(518,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TB @ ( bool @ ( TA @ fun ) @ fun ),D: TB @ ( TA @ fun ),E: TB,F: TB @ ( TB @ fun ) @ ( TB @ fun )] :
( ( C @ ( D @ ( E @ ( F @ ( TA @ ( TB @ finite908156982e_idem ) ) ) ) ) )
=> ( ( B @ ( TA @ finite_finite ) )
=> ( ( A @ ( TA @ finite_finite ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( C @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( F @ ( TB @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(105,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ ( TA @ product_prod ) @ fun ),D: bool @ ( TA @ fun )] :
( ( C @ ( D @ ( TA @ refl_on ) ) )
=> ( ( A @ ( B @ ( TA @ refl_on ) ) )
=> ( A @ ( C @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ sup_sup ) ) @ ( B @ ( D @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( TA @ refl_on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_refl__on__Un) ).
thf(468,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ ( TA @ product_prod ) @ fun ),D: bool @ ( TA @ fun )] :
( ( C @ ( D @ ( TA @ refl_on ) ) )
=> ( ( A @ ( B @ ( TA @ refl_on ) ) )
=> ( A @ ( C @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ sup_sup ) ) @ ( B @ ( D @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( TA @ refl_on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(42,axiom,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ sup_sup ) ) )
= ( B @ ( A @ ( TA @ sup_sup ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_inf__sup__aci_I5_J) ).
thf(234,plain,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ sup_sup ) ) )
= ( B @ ( A @ ( TA @ sup_sup ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(133,axiom,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite ) )
=> ( ( B
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( A @ ( TA @ finite_finite ) )
=> ( ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( TA @ big_lattice_Sup_fin ) )
= ( A @ ( TA @ big_lattice_Sup_fin ) @ ( B @ ( TA @ big_lattice_Sup_fin ) @ ( TA @ sup_sup ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_Sup__fin_Ounion__disjoint) ).
thf(555,plain,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite ) )
=> ( ( B
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( A @ ( TA @ finite_finite ) )
=> ( ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( TA @ big_lattice_Sup_fin ) )
= ( A @ ( TA @ big_lattice_Sup_fin ) @ ( B @ ( TA @ big_lattice_Sup_fin ) @ ( TA @ sup_sup ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(108,axiom,
! [TA: $tType,A: TA,B: TA @ ( bool @ ( TA @ fun ) @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( B @ ( C @ ( TA @ finite2073411215e_idem ) ) )
=> ( ( A @ ( A @ ( C @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_folding__one__idem_Oidem) ).
thf(481,plain,
! [TA: $tType,A: TA,B: TA @ ( bool @ ( TA @ fun ) @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( B @ ( C @ ( TA @ finite2073411215e_idem ) ) )
=> ( ( A @ ( A @ ( C @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(71,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( ~ ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_UnCI) ).
thf(352,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( ~ ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(35,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Un__assoc) ).
thf(217,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(408,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(16,axiom,
nat @ semilattice_inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Osemilattice__inf) ).
thf(170,plain,
nat @ semilattice_inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(131,axiom,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA,B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite ) )
=> ( ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( B @ ( TA @ big_lattice_Sup_fin ) @ ( A @ ( TA @ sup_sup ) ) )
= ( B @ ( TA @ big_lattice_Sup_fin ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_Sup__fin_Oin__idem) ).
thf(550,plain,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA,B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite ) )
=> ( ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( B @ ( TA @ big_lattice_Sup_fin ) @ ( A @ ( TA @ sup_sup ) ) )
= ( B @ ( TA @ big_lattice_Sup_fin ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(5,axiom,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ sup_sup ) ) @ ( TA @ sup_sup ) ) )
= ( A @ ( B @ ( TA @ sup_sup ) ) @ ( C @ ( TA @ sup_sup ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_sup_Oassoc) ).
thf(142,plain,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ sup_sup ) ) @ ( TA @ sup_sup ) ) )
= ( A @ ( B @ ( TA @ sup_sup ) ) @ ( C @ ( TA @ sup_sup ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,axiom,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ sup_sup ) ) @ ( B @ ( TA @ sup_sup ) ) )
= ( A @ ( B @ ( TA @ sup_sup ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_sup_Oleft__idem) ).
thf(174,plain,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ sup_sup ) ) @ ( B @ ( TA @ sup_sup ) ) )
= ( A @ ( B @ ( TA @ sup_sup ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(23,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( B @ ( C @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_sup1CI) ).
thf(185,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( B @ ( C @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(57,axiom,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ sup_sup ) ) @ ( TA @ sup_sup ) ) )
= ( A @ ( B @ ( TA @ sup_sup ) ) @ ( C @ ( TA @ sup_sup ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_inf__sup__aci_I6_J) ).
thf(288,plain,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ sup_sup ) ) @ ( TA @ sup_sup ) ) )
= ( A @ ( B @ ( TA @ sup_sup ) ) @ ( C @ ( TA @ sup_sup ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(320,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(80,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ pow ) @ ( A @ ( bool @ ( TA @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_Pow__top) ).
thf(389,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ pow ) @ ( A @ ( bool @ ( TA @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(27,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_UnI2) ).
thf(196,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(127,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ ( TA @ product_prod ) @ finite_finite ) )
=> ( A @ ( TA @ field ) @ ( TA @ finite_finite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_finite__Field) ).
thf(542,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ ( TA @ product_prod ) @ finite_finite ) )
=> ( A @ ( TA @ field ) @ ( TA @ finite_finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(24,axiom,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ sup_sup ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Sup__fin_Oidem) ).
thf(189,plain,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ sup_sup ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(9,axiom,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ sup_sup ) ) @ ( C @ ( TA @ sup_sup ) ) )
= ( A @ ( C @ ( TA @ sup_sup ) ) @ ( B @ ( TA @ sup_sup ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_sup_Oleft__commute) ).
thf(152,plain,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ sup_sup ) ) @ ( C @ ( TA @ sup_sup ) ) )
= ( A @ ( C @ ( TA @ sup_sup ) ) @ ( B @ ( TA @ sup_sup ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(39,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_sup1I1) ).
thf(228,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(101,axiom,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_emptyE) ).
thf(448,plain,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(99,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ sup_sup ) ) @ ( TA @ field ) )
= ( A @ ( TA @ field ) @ ( B @ ( TA @ field ) @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Field__Un) ).
thf(443,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ sup_sup ) ) @ ( TA @ field ) )
= ( A @ ( TA @ field ) @ ( B @ ( TA @ field ) @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(348,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(112,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( TA @ finite_finite ) )
<=> ( ( A @ ( TA @ finite_finite ) )
& ( B @ ( TA @ finite_finite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_finite__Un) ).
thf(492,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( A @ ( TA @ finite_finite ) )
& ( B @ ( TA @ finite_finite ) ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( TA @ finite_finite ) ) )
& ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( TA @ finite_finite ) )
=> ( ( A @ ( TA @ finite_finite ) )
& ( B @ ( TA @ finite_finite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(14,axiom,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ sup_sup ) ) )
= ( B @ ( A @ ( TA @ sup_sup ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_sup__commute) ).
thf(164,plain,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ sup_sup ) ) )
= ( B @ ( A @ ( TA @ sup_sup ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ( TA @ ( TB @ fun ) @ bot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
thf(411,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ( TA @ ( TB @ fun ) @ bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ finite_finite1 )
& ( TA @ finite_finite1 ) )
=> ( TA @ ( TB @ sum_sum ) @ finite_finite1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum___Finite__Set_Ofinite) ).
thf(243,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ finite_finite1 )
& ( TA @ finite_finite1 ) )
=> ( TA @ ( TB @ sum_sum ) @ finite_finite1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(47,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_Un__def) ).
thf(248,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ lattice )
=> ( TA @ ( TB @ fun ) @ semilattice_sup ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Osemilattice__sup) ).
thf(439,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ lattice )
=> ( TA @ ( TB @ fun ) @ semilattice_sup ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(270,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(129,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite ) )
=> ( ( A @ ( TA @ finite_finite ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( TA @ finite_finite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_finite__UnI) ).
thf(546,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite ) )
=> ( ( A @ ( TA @ finite_finite ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( TA @ finite_finite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(29,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_equals0I) ).
thf(201,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(77,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(381,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_bot__fun__def) ).
thf(220,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(12,axiom,
nat @ bot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Obot) ).
thf(160,plain,
nat @ bot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(91,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(424,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(25,axiom,
bool @ lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Olattice) ).
thf(192,plain,
bool @ lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(94,axiom,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) @ ( B @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_inf_Oleft__idem) ).
thf(429,plain,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) @ ( B @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(52,axiom,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot )
= ( fFalse @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_empty__def) ).
thf(275,plain,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot )
= ( fFalse @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(109,axiom,
! [TA: $tType] : ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ refl_on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_refl__on__empty) ).
thf(484,plain,
! [TA: $tType] : ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ refl_on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(103,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
<=> ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
& ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_Un__empty) ).
thf(456,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
& ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
& ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(64,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_inf1I) ).
thf(324,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(56,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( B @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_Un__commute) ).
thf(285,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( B @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(61,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ pow ) )
!= ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_Pow__not__empty) ).
thf(317,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ pow ) )
!= ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(72,axiom,
! [TA: $tType] :
( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( TA @ field ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Field__empty) ).
thf(356,plain,
! [TA: $tType] :
( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( TA @ field ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(114,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA @ ( bool @ ( TA @ fun ) @ fun ),D: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( C @ ( D @ ( TA @ finite2073411215e_idem ) ) )
=> ( ( B @ ( TA @ finite_finite ) )
=> ( ( B
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( A @ ( TA @ finite_finite ) )
=> ( ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_folding__one__idem_Ounion__idem) ).
thf(499,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA @ ( bool @ ( TA @ fun ) @ fun ),D: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( C @ ( D @ ( TA @ finite2073411215e_idem ) ) )
=> ( ( B @ ( TA @ finite_finite ) )
=> ( ( B
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( A @ ( TA @ finite_finite ) )
=> ( ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ lattice )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TA] :
( ( C @ ( A @ ( B @ ( TB @ ( TA @ fun ) @ sup_sup ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ sup_sup ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_sup__fun__def) ).
thf(225,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ lattice )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TA] :
( ( C @ ( A @ ( B @ ( TB @ ( TA @ fun ) @ sup_sup ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ sup_sup ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(26,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Un__empty__right) ).
thf(193,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(111,axiom,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ sup_sup ) ) @ ( C @ ( TA @ sup_sup ) ) )
= ( A @ ( C @ ( TA @ sup_sup ) ) @ ( B @ ( TA @ sup_sup ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_inf__sup__aci_I7_J) ).
thf(489,plain,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ sup_sup ) ) @ ( C @ ( TA @ sup_sup ) ) )
= ( A @ ( C @ ( TA @ sup_sup ) ) @ ( B @ ( TA @ sup_sup ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(33,axiom,
bool @ semilattice_inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Osemilattice__inf) ).
thf(212,plain,
bool @ semilattice_inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1,conjecture,
! [TA: $tType,A: TA @ huffma1450048681e_tree] : ( A @ ( TA @ huffma675207370phabet ) @ ( TA @ finite_finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA @ huffma1450048681e_tree] : ( A @ ( TA @ huffma675207370phabet ) @ ( TA @ finite_finite ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(134,plain,
~ ! [TA: $tType,A: TA @ huffma1450048681e_tree] : ( A @ ( TA @ huffma675207370phabet ) @ ( TA @ finite_finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_bot__apply) ).
thf(237,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ ( TB @ sum_Plus ) ) ) @ ( TA @ ( TB @ sum_sum ) @ finite_finite ) )
<=> ( ( A @ ( TA @ finite_finite ) )
& ( B @ ( TB @ finite_finite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_finite__Plus__iff) ).
thf(508,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TB @ fun )] :
( ( ( ( A @ ( TA @ finite_finite ) )
& ( B @ ( TB @ finite_finite ) ) )
=> ( A @ ( B @ ( TA @ ( TB @ sum_Plus ) ) ) @ ( TA @ ( TB @ sum_sum ) @ finite_finite ) ) )
& ( ( A @ ( B @ ( TA @ ( TB @ sum_Plus ) ) ) @ ( TA @ ( TB @ sum_sum ) @ finite_finite ) )
=> ( ( A @ ( TA @ finite_finite ) )
& ( B @ ( TB @ finite_finite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(83,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_UnI1) ).
thf(398,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(123,axiom,
! [TA: $tType] :
( ( TA @ finite_finite1 )
=> ! [A: bool @ ( TA @ fun )] : ( A @ ( TA @ finite_finite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_finite__code) ).
thf(530,plain,
! [TA: $tType] :
( ( TA @ finite_finite1 )
=> ! [A: bool @ ( TA @ fun )] : ( A @ ( TA @ finite_finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(92,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( C @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_sup1I2) ).
thf(425,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( C @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(118,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma675207370phabet ) )
= ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ huffma675207370phabet ) @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_alphabet_Osimps_I2_J) ).
thf(513,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma675207370phabet ) )
= ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ huffma675207370phabet ) @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(7,axiom,
nat @ semilattice_sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Osemilattice__sup) ).
thf(148,plain,
nat @ semilattice_sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ sup_sup ) ) )
= ( B @ ( A @ ( TA @ sup_sup ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_sup_Ocommute) ).
thf(161,plain,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ sup_sup ) ) )
= ( B @ ( A @ ( TA @ sup_sup ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TB @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( bool @ ( TB @ fun ) @ bot_bot @ ( A @ ( B @ ( C @ ( TB @ ( TA @ finite_fold_image ) ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_fold__image__empty) ).
thf(180,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TB @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( bool @ ( TB @ fun ) @ bot_bot @ ( A @ ( B @ ( C @ ( TB @ ( TA @ finite_fold_image ) ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(8,axiom,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ sup_sup ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_sup__idem) ).
thf(149,plain,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ sup_sup ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(58,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_Un__absorb) ).
thf(291,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(49,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TA @ huffma1450048681e_tree,E: TA @ huffma1450048681e_tree,F: nat] :
( ( ( D @ ( E @ ( F @ ( TA @ huffma1146269203erNode ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_tree_Osimps_I2_J) ).
thf(259,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TA @ huffma1450048681e_tree,E: TA @ huffma1450048681e_tree,F: nat] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ ( TA @ huffma1146269203erNode ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ ( TA @ huffma1146269203erNode ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(88,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_IntI) ).
thf(413,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(54,axiom,
bool @ bounded_lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice) ).
thf(281,plain,
bool @ bounded_lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(30,axiom,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) @ ( B @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_inf__left__idem) ).
thf(204,plain,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) @ ( B @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(76,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ~ ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_equals0D) ).
thf(377,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ~ ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(40,axiom,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(230,plain,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(245,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(96,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Int__iff) ).
thf(434,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(60,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ? [D: TA] :
( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
<=> ( ? [D: TA] :
( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( B @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
| ? [D: TA] :
( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( C @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_bex__Un) ).
thf(303,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( ( ? [D: TA] :
( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( B @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
| ? [D: TA] :
( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( C @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) )
=> ? [D: TA] :
( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) )
& ( ? [D: TA] :
( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( ? [D: TA] :
( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( B @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
| ? [D: TA] :
( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( C @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(107,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_IntE) ).
thf(477,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(79,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ finite_finite1 )
& ( TA @ finite_finite1 ) )
=> ( TA @ ( TB @ fun ) @ finite_finite1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
thf(387,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ finite_finite1 )
& ( TA @ finite_finite1 ) )
=> ( TA @ ( TB @ fun ) @ finite_finite1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(125,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ pow ) @ ( bool @ ( TA @ fun ) @ finite_finite ) )
<=> ( A @ ( TA @ finite_finite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_finite__Pow__iff) ).
thf(535,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A @ ( TA @ finite_finite ) )
=> ( A @ ( TA @ pow ) @ ( bool @ ( TA @ fun ) @ finite_finite ) ) )
& ( ( A @ ( TA @ pow ) @ ( bool @ ( TA @ fun ) @ finite_finite ) )
=> ( A @ ( TA @ finite_finite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(63,axiom,
bool @ bounded_lattice_bot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice__bot) ).
thf(323,plain,
bool @ bounded_lattice_bot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(34,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_bot__empty__eq) ).
thf(213,plain,
! [TA: $tType,A: TA] :
( ( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(10,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(155,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(28,axiom,
! [TA: $tType] :
( ( TA @ bounded_lattice_bot )
=> ! [A: TA] :
( ( A @ ( TA @ bot_bot @ ( TA @ sup_sup ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_sup__bot__left) ).
thf(198,plain,
! [TA: $tType] :
( ( TA @ bounded_lattice_bot )
=> ! [A: TA] :
( ( A @ ( TA @ bot_bot @ ( TA @ sup_sup ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(44,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Un__empty__left) ).
thf(240,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: bool @ ( TA @ fun ),E: TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ fun ),F: TB,G: TB @ ( TB @ fun ) @ ( TB @ fun )] :
( ( E @ ( F @ ( G @ ( TA @ ( TB @ big_comm_monoid_big ) ) ) ) )
=> ( ( D = C )
=> ( ! [H: TA] :
( ( C @ ( H @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( H @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( H @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ( ( D @ ( B @ ( E @ ( TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( C @ ( A @ ( E @ ( TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_comm__monoid__big_OF__cong) ).
thf(251,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: bool @ ( TA @ fun ),E: TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ fun ),F: TB,G: TB @ ( TB @ fun ) @ ( TB @ fun )] :
( ( E @ ( F @ ( G @ ( TA @ ( TB @ big_comm_monoid_big ) ) ) ) )
=> ( ( D = C )
=> ( ! [H: TA] :
( ( C @ ( H @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( H @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( H @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ( ( D @ ( B @ ( E @ ( TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( C @ ( A @ ( E @ ( TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(121,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA @ ( bool @ ( TA @ fun ) @ fun ),D: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( C @ ( D @ ( TA @ finite2073411215e_idem ) ) )
=> ( ( B @ ( TA @ finite_finite ) )
=> ( ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_folding__one__idem_Oin__idem) ).
thf(521,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA @ ( bool @ ( TA @ fun ) @ fun ),D: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( C @ ( D @ ( TA @ finite2073411215e_idem ) ) )
=> ( ( B @ ( TA @ finite_finite ) )
=> ( ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ sup_sup ) ) @ ( B @ ( TA @ sup_sup ) ) )
= ( A @ ( B @ ( TA @ sup_sup ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_inf__sup__aci_I8_J) ).
thf(278,plain,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ sup_sup ) ) @ ( B @ ( TA @ sup_sup ) ) )
= ( A @ ( B @ ( TA @ sup_sup ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(37,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ~ ( A @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_sup1E) ).
thf(223,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ~ ( A @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(82,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(394,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun ),B: bool @ ( TB @ fun ),C: TA @ ( bool @ ( TB @ fun ) @ fun ) @ ( TA @ ( TB @ fun ) @ fun ),D: TA,E: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( C @ ( D @ ( E @ ( TB @ ( TA @ big_comm_monoid_big ) ) ) ) )
=> ( ~ ( B @ ( TB @ finite_finite ) )
=> ( ( B @ ( A @ ( C @ ( TA @ ( bool @ ( TB @ fun ) @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ ( bool @ ( TB @ fun ) @ aa ) ) ) )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_comm__monoid__big_Oinfinite) ).
thf(505,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun ),B: bool @ ( TB @ fun ),C: TA @ ( bool @ ( TB @ fun ) @ fun ) @ ( TA @ ( TB @ fun ) @ fun ),D: TA,E: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( C @ ( D @ ( E @ ( TB @ ( TA @ big_comm_monoid_big ) ) ) ) )
=> ( ~ ( B @ ( TB @ finite_finite ) )
=> ( ( B @ ( A @ ( C @ ( TA @ ( bool @ ( TB @ fun ) @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ ( bool @ ( TB @ fun ) @ aa ) ) ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(15,axiom,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ sup_sup ) ) @ ( C @ ( TA @ sup_sup ) ) )
= ( A @ ( C @ ( TA @ sup_sup ) ) @ ( B @ ( TA @ sup_sup ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_sup__left__commute) ).
thf(167,plain,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ sup_sup ) ) @ ( C @ ( TA @ sup_sup ) ) )
= ( A @ ( C @ ( TA @ sup_sup ) ) @ ( B @ ( TA @ sup_sup ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(130,axiom,
! [TA: $tType] :
( ( TA @ finite_finite1 )
=> ! [A: bool @ ( TA @ fun )] : ( A @ ( TA @ finite_finite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_finite) ).
thf(548,plain,
! [TA: $tType] :
( ( TA @ finite_finite1 )
=> ! [A: bool @ ( TA @ fun )] : ( A @ ( TA @ finite_finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),E: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( D @ ( E @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) )
= ( A @ ( D @ ( E @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) @ ( B @ ( D @ ( E @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( D @ ( TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_tree_Orecs_I2_J) ).
thf(209,plain,
! [TA: $tType,TB: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),E: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( D @ ( E @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) )
= ( A @ ( D @ ( E @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) @ ( B @ ( D @ ( E @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( D @ ( TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(119,axiom,
! [TA: $tType] : ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ finite_finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_finite_OemptyI) ).
thf(516,plain,
! [TA: $tType] : ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ finite_finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(132,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ ( TB @ sum_Plus ) ) ) @ ( TA @ ( TB @ sum_sum ) @ finite_finite ) )
=> ( A @ ( TA @ finite_finite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_finite__PlusD_I2_J) ).
thf(553,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ ( TB @ sum_Plus ) ) ) @ ( TA @ ( TB @ sum_sum ) @ finite_finite ) )
=> ( A @ ( TA @ finite_finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(6,axiom,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ sup_sup ) ) @ ( B @ ( TA @ sup_sup ) ) )
= ( A @ ( B @ ( TA @ sup_sup ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_sup__left__idem) ).
thf(145,plain,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ sup_sup ) ) @ ( B @ ( TA @ sup_sup ) ) )
= ( A @ ( B @ ( TA @ sup_sup ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(55,axiom,
! [TA: $tType] :
( ( TA @ bounded_lattice_bot )
=> ! [A: TA] :
( ( TA @ bot_bot @ ( A @ ( TA @ sup_sup ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_sup__bot__right) ).
thf(282,plain,
! [TA: $tType] :
( ( TA @ bounded_lattice_bot )
=> ! [A: TA] :
( ( TA @ bot_bot @ ( A @ ( TA @ sup_sup ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB @ ( TA @ fun ),D: bool @ ( TB @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) )
<=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_in__inv__imagep) ).
thf(327,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB @ ( TA @ fun ),D: bool @ ( TB @ fun ) @ ( TB @ fun )] :
( ( ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(19,axiom,
bool @ semilattice_sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Osemilattice__sup) ).
thf(177,plain,
bool @ semilattice_sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(67,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ! [D: TA] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
<=> ( ! [D: TA] :
( ( B @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ! [D: TA] :
( ( C @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_ball__Un) ).
thf(331,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( ( ! [D: TA] :
( ( B @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ! [D: TA] :
( ( C @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) )
=> ! [D: TA] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) )
& ( ! [D: TA] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ! [D: TA] :
( ( B @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ! [D: TA] :
( ( C @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(98,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(441,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(115,axiom,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite ) )
=> ( ( B
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( A @ ( TA @ finite_finite ) )
=> ( ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( TA @ big_lattice_Sup_fin ) )
= ( A @ ( TA @ big_lattice_Sup_fin ) @ ( B @ ( TA @ big_lattice_Sup_fin ) @ ( TA @ sup_sup ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_Sup__fin_Ounion__idem) ).
thf(502,plain,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite ) )
=> ( ( B
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( A @ ( TA @ finite_finite ) )
=> ( ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( TA @ big_lattice_Sup_fin ) )
= ( A @ ( TA @ big_lattice_Sup_fin ) @ ( B @ ( TA @ big_lattice_Sup_fin ) @ ( TA @ sup_sup ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(106,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_all__not__in__conv) ).
thf(470,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(73,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) )
<=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_empty__Collect__eq) ).
thf(359,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) ) )
& ( ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) )
=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(128,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TB @ fun )] :
( ( B @ ( TB @ finite_finite ) )
=> ( ( A @ ( TA @ finite_finite ) )
=> ( A @ ( B @ ( TA @ ( TB @ sum_Plus ) ) ) @ ( TA @ ( TB @ sum_sum ) @ finite_finite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_finite__Plus) ).
thf(544,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TB @ fun )] :
( ( B @ ( TB @ finite_finite ) )
=> ( ( A @ ( TA @ finite_finite ) )
=> ( A @ ( B @ ( TA @ ( TB @ sum_Plus ) ) ) @ ( TA @ ( TB @ sum_sum ) @ finite_finite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(100,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ~ ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_UnE) ).
thf(446,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ~ ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ sum_Plus ) ) ) @ ( TB @ ( TA @ sum_sum ) @ finite_finite ) )
=> ( B @ ( TA @ finite_finite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_finite__PlusD_I1_J) ).
thf(497,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ sum_Plus ) ) ) @ ( TB @ ( TA @ sum_sum ) @ finite_finite ) )
=> ( B @ ( TA @ finite_finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( bool @ ( TB @ fun ) @ fun ),C: TA @ ( TB @ fun ),D: TA,E: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( B @ ( C @ ( D @ ( E @ ( TB @ ( TA @ finite908156982e_idem ) ) ) ) ) )
=> ( ( A @ ( A @ ( E @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_folding__image__simple__idem_Oidem) ).
thf(465,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( bool @ ( TB @ fun ) @ fun ),C: TA @ ( TB @ fun ),D: TA,E: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( B @ ( C @ ( D @ ( E @ ( TB @ ( TA @ finite908156982e_idem ) ) ) ) ) )
=> ( ( A @ ( A @ ( E @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(102,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
<=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Collect__empty__eq) ).
thf(450,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(126,axiom,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite ) )
=> ( ( A @ ( TA @ finite_finite ) )
=> ( ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( TA @ big_lattice_Sup_fin ) @ ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( TA @ big_lattice_Sup_fin ) @ ( TA @ sup_sup ) ) )
= ( A @ ( TA @ big_lattice_Sup_fin ) @ ( B @ ( TA @ big_lattice_Sup_fin ) @ ( TA @ sup_sup ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Sup__fin_Ounion__inter) ).
thf(539,plain,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite ) )
=> ( ( A @ ( TA @ finite_finite ) )
=> ( ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( TA @ big_lattice_Sup_fin ) @ ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( TA @ big_lattice_Sup_fin ) @ ( TA @ sup_sup ) ) )
= ( A @ ( TA @ big_lattice_Sup_fin ) @ ( B @ ( TA @ big_lattice_Sup_fin ) @ ( TA @ sup_sup ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(122,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun ),B: bool @ ( TB @ fun ),C: TA @ ( bool @ ( TB @ fun ) @ fun ) @ ( TA @ ( TB @ fun ) @ fun ),D: TA,E: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( C @ ( D @ ( E @ ( TB @ ( TA @ big_comm_monoid_big ) ) ) ) )
=> ( ( ~ ( B @ ( TB @ finite_finite ) )
=> ( ( B @ ( A @ ( C @ ( TA @ ( bool @ ( TB @ fun ) @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ ( bool @ ( TB @ fun ) @ aa ) ) ) )
= D ) )
& ( ( B @ ( TB @ finite_finite ) )
=> ( ( B @ ( A @ ( C @ ( TA @ ( bool @ ( TB @ fun ) @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ ( bool @ ( TB @ fun ) @ aa ) ) ) )
= ( B @ ( D @ ( A @ ( E @ ( TB @ ( TA @ finite_fold_image ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_comm__monoid__big_OF__eq) ).
thf(524,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun ),B: bool @ ( TB @ fun ),C: TA @ ( bool @ ( TB @ fun ) @ fun ) @ ( TA @ ( TB @ fun ) @ fun ),D: TA,E: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( C @ ( D @ ( E @ ( TB @ ( TA @ big_comm_monoid_big ) ) ) ) )
=> ( ( ~ ( B @ ( TB @ finite_finite ) )
=> ( ( B @ ( A @ ( C @ ( TA @ ( bool @ ( TB @ fun ) @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ ( bool @ ( TB @ fun ) @ aa ) ) ) )
= D ) )
& ( ( B @ ( TB @ finite_finite ) )
=> ( ( B @ ( A @ ( C @ ( TA @ ( bool @ ( TB @ fun ) @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ ( bool @ ( TB @ fun ) @ aa ) ) ) )
= ( B @ ( D @ ( A @ ( E @ ( TB @ ( TA @ finite_fold_image ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ bounded_lattice_bot )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ sup_sup ) ) )
= ( TA @ bot_bot ) )
<=> ( ( A
= ( TA @ bot_bot ) )
& ( B
= ( TA @ bot_bot ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_sup__eq__bot__iff) ).
thf(368,plain,
! [TA: $tType] :
( ( TA @ bounded_lattice_bot )
=> ! [A: TA,B: TA] :
( ( ( ( A
= ( TA @ bot_bot ) )
& ( B
= ( TA @ bot_bot ) ) )
=> ( ( A @ ( B @ ( TA @ sup_sup ) ) )
= ( TA @ bot_bot ) ) )
& ( ( ( A @ ( B @ ( TA @ sup_sup ) ) )
= ( TA @ bot_bot ) )
=> ( ( A
= ( TA @ bot_bot ) )
& ( B
= ( TA @ bot_bot ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(17,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(171,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,axiom,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ sup_sup ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_sup_Oidem) ).
thf(139,plain,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ sup_sup ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bounded_lattice )
=> ( TA @ ( TB @ fun ) @ bounded_lattice_bot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Obounded__lattice__bot) ).
thf(158,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bounded_lattice )
=> ( TA @ ( TB @ fun ) @ bounded_lattice_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(70,axiom,
bool @ bot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
thf(351,plain,
bool @ bot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bounded_lattice )
=> ( TA @ ( TB @ fun ) @ bounded_lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Obounded__lattice) ).
thf(207,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bounded_lattice )
=> ( TA @ ( TB @ fun ) @ bounded_lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(78,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ~ ( ( A @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ~ ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_inf1E) ).
thf(383,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ~ ( ( A @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ~ ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ lattice )
=> ( TA @ ( TB @ fun ) @ semilattice_inf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Osemilattice__inf) ).
thf(432,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ lattice )
=> ( TA @ ( TB @ fun ) @ semilattice_inf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),E: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( D @ ( E @ ( TB @ ( TA @ huffma107959123e_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ aa ) ) ) @ ( TB @ ( TA @ huffma1450048681e_tree @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_tree_Osimps_I6_J) ).
thf(405,plain,
! [TA: $tType,TB: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),E: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( D @ ( E @ ( TB @ ( TA @ huffma107959123e_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ aa ) ) ) @ ( TB @ ( TA @ huffma1450048681e_tree @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ finite_finite1 )
& ( TA @ finite_finite1 ) )
=> ( TA @ ( TB @ product_prod ) @ finite_finite1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod___Finite__Set_Ofinite) ).
thf(183,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ finite_finite1 )
& ( TA @ finite_finite1 ) )
=> ( TA @ ( TB @ product_prod ) @ finite_finite1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(90,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(422,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(51,axiom,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_empty__iff) ).
thf(273,plain,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(65,axiom,
bool @ finite_finite1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
thf(326,plain,
bool @ finite_finite1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(84,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
| ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_Un__iff) ).
thf(400,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
| ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
| ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TA @ fun ),C: TB @ ( bool @ ( TA @ fun ) @ fun ),D: TB @ ( TA @ fun ),E: TB,F: TB @ ( TB @ fun ) @ ( TB @ fun )] :
( ( C @ ( D @ ( E @ ( F @ ( TA @ ( TB @ finite908156982e_idem ) ) ) ) ) )
=> ( ( B @ ( TA @ finite_finite ) )
=> ( ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( D @ ( TB @ ( TA @ aa ) ) ) @ ( F @ ( TB @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) )
= ( B @ ( C @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_folding__image__simple__idem_Oin__idem) ).
thf(532,plain,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TA @ fun ),C: TB @ ( bool @ ( TA @ fun ) @ fun ),D: TB @ ( TA @ fun ),E: TB,F: TB @ ( TB @ fun ) @ ( TB @ fun )] :
( ( C @ ( D @ ( E @ ( F @ ( TA @ ( TB @ finite908156982e_idem ) ) ) ) ) )
=> ( ( B @ ( TA @ finite_finite ) )
=> ( ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( D @ ( TB @ ( TA @ aa ) ) ) @ ( F @ ( TB @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) )
= ( B @ ( C @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(89,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ? [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_ex__in__conv) ).
thf(415,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ? [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ? [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TB @ fun )] :
( ( ( A @ ( B @ ( TA @ ( TB @ sum_Plus ) ) ) )
= ( bool @ ( TA @ ( TB @ sum_sum ) @ fun ) @ bot_bot ) )
<=> ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
& ( B
= ( bool @ ( TB @ fun ) @ bot_bot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Plus__eq__empty__conv) ).
thf(294,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TB @ fun )] :
( ( ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
& ( B
= ( bool @ ( TB @ fun ) @ bot_bot ) ) )
=> ( ( A @ ( B @ ( TA @ ( TB @ sum_Plus ) ) ) )
= ( bool @ ( TA @ ( TB @ sum_sum ) @ fun ) @ bot_bot ) ) )
& ( ( ( A @ ( B @ ( TA @ ( TB @ sum_Plus ) ) ) )
= ( bool @ ( TA @ ( TB @ sum_sum ) @ fun ) @ bot_bot ) )
=> ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
& ( B
= ( bool @ ( TB @ fun ) @ bot_bot ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(3,axiom,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ sup_sup ) ) @ ( TA @ sup_sup ) ) )
= ( A @ ( B @ ( TA @ sup_sup ) ) @ ( C @ ( TA @ sup_sup ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_sup__assoc) ).
thf(136,plain,
! [TA: $tType] :
( ( TA @ semilattice_sup )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ sup_sup ) ) @ ( TA @ sup_sup ) ) )
= ( A @ ( B @ ( TA @ sup_sup ) ) @ ( C @ ( TA @ sup_sup ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(93,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ( B @ pp )
| ~ ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(427,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ( B @ pp )
| ~ ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ lattice )
=> ( TA @ ( TB @ fun ) @ lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Olattice) ).
thf(178,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ lattice )
=> ( TA @ ( TB @ fun ) @ lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(110,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( A @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_Un__left__commute) ).
thf(486,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( A @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(41,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ pow ) @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Pow__bottom) ).
thf(232,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ pow ) @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(569,plain,
$false,
inference(e,[status(thm)],[391,365,347,518,468,234,555,481,352,217,408,170,550,142,174,185,288,320,389,196,542,189,152,228,448,443,348,492,164,411,243,248,439,270,546,201,381,220,160,424,192,429,275,484,456,324,285,317,356,499,225,193,489,212,134,237,508,398,530,425,513,148,161,180,149,291,259,413,281,204,377,230,245,434,303,477,387,535,323,213,155,198,240,251,521,278,223,394,505,167,548,209,516,553,145,282,327,177,331,441,502,470,359,544,446,497,465,450,539,524,368,171,139,158,351,207,383,432,405,183,422,273,326,400,532,415,294,136,427,178,486,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW526_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n018.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sat Sep 26 16:12:51 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.83/0.96 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.47/1.29 % [INFO] Parsing done (325ms).
% 1.93/1.30 % [INFO] Running in sequential loop mode.
% 2.64/1.52 % [INFO] eprover registered as external prover.
% 2.64/1.52 % [INFO] Scanning for conjecture ...
% 3.07/1.63 % [INFO] Found a conjecture (or negated_conjecture) and 131 axioms. Running axiom selection ...
% 3.48/1.71 % [INFO] Axiom selection finished. Selected 131 axioms (removed 0 axioms).
% 3.93/1.87 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.34/1.90 % [INFO] Type checking passed.
% 4.34/1.90 % [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 ...
% 4.91/2.10 % [INFO] [Domain constraints] Detected constraint on bool
% 4.91/2.10 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 18.72/7.11 % External prover 'e' found a proof!
% 18.72/7.11 % [INFO] Killing All external provers ...
% 18.72/7.11 % Time passed: 6577ms (effective reasoning time: 5801ms)
% 18.72/7.11 % 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)>
% 18.72/7.11 % Axioms used in derivation (131): fact_8_finite__PlusD_I1_J, fact_23_sup1CI, fact_62_Collect__empty__eq, fact_69_Field__empty, fact_74_fold__image__empty, arity_Nat_Onat___Orderings_Obot, fact_89_Sup__fin_Ounion__idem, fact_86_bot__fun__def, fact_96_inf1I, arity_HOL_Obool___Finite__Set_Ofinite, fact_24_UnCI, fact_71_ex__in__conv, fact_10_finite__Field, fact_9_finite__PlusD_I2_J, help_COMBS_1_1_U, fact_44_sup1I1, fact_72_empty__def, fact_94_inf__left__idem, fact_11_finite__Pow__iff, arity_fun___Orderings_Obot, fact_51_Un__def, fact_15_Sup__fin_Oidem, fact_81_sup__bot__left, fact_2_comm__monoid__big_Oinfinite, fact_12_tree_Osimps_I2_J, fact_3_alphabet_Osimps_I2_J, fact_30_inf__sup__aci_I6_J, fact_99_inf1E, arity_sum___Finite__Set_Ofinite, fact_1_finite, fact_53_Pow__top, fact_64_empty__Collect__eq, fact_16_folding__one__idem_Oidem, fact_17_folding__image__simple__idem_Oidem, arity_fun___Lattices_Olattice, fact_37_inf__sup__aci_I5_J, fact_25_sup_Oleft__idem, arity_HOL_Obool___Lattices_Obounded__lattice__bot, fact_45_ball__Un, fact_60_refl__on__Un, fact_84_Pow__not__empty, fact_87_bot__apply, fact_56_tree_Orecs_I2_J, fact_80_Un__empty__right, fact_34_sup_Oleft__commute, help_fFalse_1_1_T, fact_6_folding__one__idem_Oin__idem, help_COMBB_1_1_U, fact_35_inf__sup__aci_I8_J, fact_40_sup_Oidem, fact_93_inf_Oleft__idem, fact_49_Un__left__absorb, fact_47_Un__assoc, arity_HOL_Obool___Lattices_Osemilattice__inf, fact_48_Un__left__commute, fact_4_folding__image__simple__idem_Oin__idem, fact_95_Int__iff, help_fdisj_1_1_U, fact_39_sup__idem, fact_78_refl__on__empty, fact_36_sup__commute, fact_82_sup__bot__right, fact_19_finite__UnI, fact_92_Sup__fin_Ounion__inter, fact_43_sup1I2, fact_73_bot__empty__eq, fact_52_Un__absorb, arity_Nat_Onat___Lattices_Olattice, arity_fun___Lattices_Osemilattice__inf, fact_42_UnI1, fact_14_Field__Un, fact_20_Un__iff, fact_5_finite__Plus__iff, arity_Nat_Onat___Lattices_Osemilattice__sup, fact_22_sup1E, arity_HOL_Obool___Lattices_Osemilattice__sup, arity_fun___Finite__Set_Ofinite, fact_65_all__not__in__conv, fact_66_finite_OemptyI, fact_31_sup_Oassoc, fact_68_Un__empty, fact_54_sup__apply, fact_38_sup_Ocommute, fact_76_mem__def, arity_Nat_Onat___Lattices_Osemilattice__inf, fact_7_finite__Plus, fact_57_folding__one__idem_Ounion__idem, fact_55_tree_Osimps_I6_J, fact_79_Un__empty__left, help_fdisj_2_1_U, help_COMBK_1_1_U, arity_HOL_Obool___Lattices_Obounded__lattice, fact_27_comm__monoid__big_OF__cong, help_COMBC_1_1_U, arity_HOL_Obool___Orderings_Obot, fact_70_equals0D, fact_41_UnI2, arity_prod___Finite__Set_Ofinite, fact_59_comm__monoid__big_OF__eq, fact_0_finite__code, fact_58_in__inv__imagep, help_fdisj_3_1_U, fact_88_equals0I, fact_83_Pow__bottom, fact_50_Un__commute, help_fFalse_1_1_U, fact_97_IntI, fact_98_IntE, fact_33_inf__sup__aci_I7_J, fact_77_Collect__def, arity_HOL_Obool___Lattices_Olattice, fact_90_Sup__fin_Oin__idem, fact_46_bex__Un, help_pp_1_1_U, fact_13_finite__Un, fact_32_sup__left__commute, fact_63_empty__iff, arity_fun___Lattices_Osemilattice__sup, arity_fun___Lattices_Obounded__lattice__bot, fact_29_sup__assoc, fact_91_Sup__fin_Ounion__disjoint, fact_75_ext, fact_61_emptyE, fact_85_Plus__eq__empty__conv, help_pp_2_1_U, arity_fun___Lattices_Obounded__lattice, fact_67_sup__eq__bot__iff, fact_28_sup__fun__def, fact_18_folding__image__simple__idem_Ounion__idem, fact_21_UnE, fact_26_sup__left__idem
% 18.72/7.11 % No. of inferences in proof: 266
% 18.72/7.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6577 ms resp. 5801 ms w/o parsing
% 19.54/7.25 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.54/7.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------