TSTP Solution File: SWW526_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW526_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:24:59 EDT 2023
% Result : Theorem 15.16s 6.60s
% Output : Refutation 15.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 171
% Syntax : Number of formulae : 305 ( 74 unt; 39 typ; 0 def)
% Number of atoms : 1319 ( 199 equ; 0 cnn)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 6245 ( 68 ~; 16 |; 62 &;5816 @)
% ( 18 <=>; 265 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 9 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 40 usr; 8 con; 0-6 aty)
% Number of variables : 893 ( 0 ^; 834 !; 12 ?; 893 :)
% ( 47 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(bounded_lattice_type,type,
bounded_lattice:
!>[TA: $tType] : $o ).
thf(bot_type,type,
bot:
!>[TA: $tType] : $o ).
thf(lattice_type,type,
lattice:
!>[TA: $tType] : $o ).
thf(finite_finite1_type,type,
finite_finite1:
!>[TA: $tType] : $o ).
thf(semilattice_inf_type,type,
semilattice_inf:
!>[TA: $tType] : $o ).
thf(semilattice_sup_type,type,
semilattice_sup:
!>[TA: $tType] : $o ).
thf(bounded_lattice_bot_type,type,
bounded_lattice_bot:
!>[TA: $tType] : $o ).
thf(big_comm_monoid_big_type,type,
big_comm_monoid_big:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TB @ TB ) ) > TB > ( fun @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ) ) > $o ) ).
thf(big_lattice_Sup_fin_type,type,
big_lattice_Sup_fin:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > TA ) ).
thf(combb_type,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ TB ) > ( fun @ TA @ TC ) > ( fun @ TA @ TB ) ) ).
thf(combc_type,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > TB > ( fun @ TC @ TA ) ) ).
thf(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).
thf(combs_type,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ TC @ TB ) > ( fun @ TC @ TA ) ) ).
thf(finite_finite_type,type,
finite_finite:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > $o ) ).
thf(finite_fold_image_type,type,
finite_fold_image:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TB @ TB ) ) > ( fun @ TA @ TB ) > TB > ( fun @ TA @ bool ) > TB ) ).
thf(finite908156982e_idem_type,type,
finite908156982e_idem:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TB @ TB ) ) > TB > ( fun @ TA @ TB ) > ( fun @ ( fun @ TA @ bool ) @ TB ) > $o ) ).
thf(finite2073411215e_idem_type,type,
finite2073411215e_idem:
!>[TA: $tType] : ( ( fun @ TA @ ( fun @ TA @ TA ) ) > ( fun @ ( fun @ TA @ bool ) @ TA ) > $o ) ).
thf(huffma675207370phabet_type,type,
huffma675207370phabet:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > ( fun @ TA @ bool ) ) ).
thf(huffma1146269203erNode_type,type,
huffma1146269203erNode:
!>[TA: $tType] : ( nat > ( huffma1450048681e_tree @ TA ) > ( huffma1450048681e_tree @ TA ) > ( huffma1450048681e_tree @ TA ) ) ).
thf(huffma107959123e_case_type,type,
huffma107959123e_case:
!>[TA: $tType,TB: $tType] : ( ( fun @ nat @ ( fun @ TB @ TA ) ) > ( fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TB ) @ ( fun @ ( huffma1450048681e_tree @ TB ) @ TA ) ) ) > ( huffma1450048681e_tree @ TB ) > TA ) ).
thf(huffma1280178957ee_rec_type,type,
huffma1280178957ee_rec:
!>[TA: $tType,TB: $tType] : ( ( fun @ nat @ ( fun @ TB @ TA ) ) > ( fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TB ) @ ( fun @ ( huffma1450048681e_tree @ TB ) @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ) ) > ( huffma1450048681e_tree @ TB ) > TA ) ).
thf(inf_inf_type,type,
inf_inf:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(sup_sup_type,type,
sup_sup:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(bot_bot_type,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(inv_imagep_type,type,
inv_imagep:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TB @ bool ) ) > ( fun @ TA @ TB ) > TA > TA > $o ) ).
thf(field_type,type,
field:
!>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > ( fun @ TA @ bool ) ) ).
thf(refl_on_type,type,
refl_on:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
thf(pow_type,type,
pow:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( fun @ TA @ bool ) @ bool ) ) ).
thf(sum_Plus_type,type,
sum_Plus:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ bool ) > ( fun @ TA @ bool ) > ( fun @ ( sum_sum @ TB @ TA ) @ bool ) ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fdisj_type,type,
fdisj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(skt1_type,type,
skt1: $tType ).
thf(126,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ B )
=> ( ( finite_finite @ TA @ A )
=> ( ( ( inf_inf @ ( fun @ TA @ bool ) @ B @ A )
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( sup_sup @ TA @ ( big_lattice_Sup_fin @ TA @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) @ ( big_lattice_Sup_fin @ TA @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
= ( sup_sup @ TA @ ( big_lattice_Sup_fin @ TA @ B ) @ ( big_lattice_Sup_fin @ TA @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Sup__fin_Ounion__inter) ).
thf(515,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ B )
=> ( ( finite_finite @ TA @ A )
=> ( ( ( inf_inf @ ( fun @ TA @ bool ) @ B @ A )
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( sup_sup @ TA @ ( big_lattice_Sup_fin @ TA @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) @ ( big_lattice_Sup_fin @ TA @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
= ( sup_sup @ TA @ ( big_lattice_Sup_fin @ TA @ B ) @ ( big_lattice_Sup_fin @ TA @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(314,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(72,axiom,
! [TA: $tType] :
( ( field @ TA @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Field__empty) ).
thf(347,plain,
! [TA: $tType] :
( ( field @ TA @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB,C: fun @ TA @ bool,D: fun @ TA @ bool,E: fun @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ),F: TB,G: fun @ TB @ ( fun @ TB @ TB )] :
( ( big_comm_monoid_big @ TB @ TA @ G @ F @ E )
=> ( ( D = C )
=> ( ! [H: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ H ) @ C ) )
=> ( ( aa @ TA @ TB @ B @ H )
= ( aa @ TA @ TB @ A @ H ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ) @ E @ B ) @ D )
= ( aa @ ( fun @ TA @ bool ) @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ) @ E @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_comm__monoid__big_OF__cong) ).
thf(249,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB,C: fun @ TA @ bool,D: fun @ TA @ bool,E: fun @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ),F: TB,G: fun @ TB @ ( fun @ TB @ TB )] :
( ( big_comm_monoid_big @ TB @ TA @ G @ F @ E )
=> ( ( D = C )
=> ( ! [H: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ H ) @ C ) )
=> ( ( aa @ TA @ TB @ B @ H )
= ( aa @ TA @ TB @ A @ H ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ) @ E @ B ) @ D )
= ( aa @ ( fun @ TA @ bool ) @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ bool ) @ TB ) @ E @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(127,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( finite_finite @ ( product_prod @ TA @ TA ) @ A )
=> ( finite_finite @ TA @ ( field @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_finite__Field) ).
thf(518,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( finite_finite @ ( product_prod @ TA @ TA ) @ A )
=> ( finite_finite @ TA @ ( field @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(115,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( finite_finite @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( big_lattice_Sup_fin @ TA @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
= ( sup_sup @ TA @ ( big_lattice_Sup_fin @ TA @ B ) @ ( big_lattice_Sup_fin @ TA @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_Sup__fin_Ounion__idem) ).
thf(481,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( finite_finite @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( big_lattice_Sup_fin @ TA @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
= ( sup_sup @ TA @ ( big_lattice_Sup_fin @ TA @ B ) @ ( big_lattice_Sup_fin @ TA @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(16,axiom,
semilattice_inf @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Osemilattice__inf) ).
thf(170,plain,
semilattice_inf @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(81,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ B @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
= ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_Un__left__absorb) ).
thf(379,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ B @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
= ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(51,axiom,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_empty__iff) ).
thf(269,plain,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(83,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_UnI1) ).
thf(385,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(5,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ C @ B ) @ A )
= ( sup_sup @ TA @ C @ ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_sup_Oassoc) ).
thf(142,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ C @ B ) @ A )
= ( sup_sup @ TA @ C @ ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(112,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
<=> ( ( finite_finite @ TA @ B )
& ( finite_finite @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_finite__Un) ).
thf(472,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( finite_finite @ TA @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
=> ( ( finite_finite @ TA @ B )
& ( finite_finite @ TA @ A ) ) )
& ( ( ( finite_finite @ TA @ B )
& ( finite_finite @ TA @ A ) )
=> ( finite_finite @ TA @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(340,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(18,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ B @ ( sup_sup @ TA @ B @ A ) )
= ( sup_sup @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_sup_Oleft__idem) ).
thf(174,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ B @ ( sup_sup @ TA @ B @ A ) )
= ( sup_sup @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(23,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( ~ ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( sup_sup @ ( fun @ TA @ bool ) @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_sup1CI) ).
thf(185,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( ~ ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( sup_sup @ ( fun @ TA @ bool ) @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( semilattice_inf @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Osemilattice__inf) ).
thf(417,plain,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( semilattice_inf @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(65,axiom,
finite_finite1 @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
thf(320,plain,
finite_finite1 @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(78,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
=> ~ ( ( pp @ ( aa @ TA @ bool @ C @ A ) )
=> ~ ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_inf1E) ).
thf(372,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
=> ~ ( ( pp @ ( aa @ TA @ bool @ C @ A ) )
=> ~ ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(71,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_UnCI) ).
thf(344,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(57,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ C @ B ) @ A )
= ( sup_sup @ TA @ C @ ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_inf__sup__aci_I6_J) ).
thf(284,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ C @ B ) @ A )
= ( sup_sup @ TA @ C @ ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(9,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ C @ ( sup_sup @ TA @ B @ A ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_sup_Oleft__commute) ).
thf(152,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ C @ ( sup_sup @ TA @ B @ A ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(40,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(228,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(14,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ B @ A )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_sup__commute) ).
thf(164,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ B @ A )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TA @ TB,D: fun @ TB @ ( fun @ TB @ bool )] :
( ( inv_imagep @ TB @ TA @ D @ C @ B @ A )
<=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_in__inv__imagep) ).
thf(321,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TA @ TB,D: fun @ TB @ ( fun @ TB @ bool )] :
( ( ( inv_imagep @ TB @ TA @ D @ C @ B @ A )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) ) )
& ( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) )
=> ( inv_imagep @ TB @ TA @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(33,axiom,
semilattice_inf @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Osemilattice__inf) ).
thf(211,plain,
semilattice_inf @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(44,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Un__empty__left) ).
thf(238,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
thf(397,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(37,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
=> ( ~ ( pp @ ( aa @ TA @ bool @ C @ A ) )
=> ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_sup1E) ).
thf(221,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
=> ( ~ ( pp @ ( aa @ TA @ bool @ C @ A ) )
=> ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(243,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(123,axiom,
! [TA: $tType] :
( ( finite_finite1 @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_finite__code) ).
thf(507,plain,
! [TA: $tType] :
( ( finite_finite1 @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Obounded__lattice) ).
thf(206,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(106,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_all__not__in__conv) ).
thf(452,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(132,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ bool] :
( ( finite_finite @ ( sum_sum @ TB @ TA ) @ ( sum_Plus @ TB @ TA @ B @ A ) )
=> ( finite_finite @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_finite__PlusD_I2_J) ).
thf(529,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ bool] :
( ( finite_finite @ ( sum_sum @ TB @ TA ) @ ( sum_Plus @ TB @ TA @ B @ A ) )
=> ( finite_finite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(76,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_equals0D) ).
thf(366,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(125,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( finite_finite @ ( fun @ TA @ bool ) @ ( pow @ TA @ A ) )
<=> ( finite_finite @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_finite__Pow__iff) ).
thf(512,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( finite_finite @ ( fun @ TA @ bool ) @ ( pow @ TA @ A ) )
=> ( finite_finite @ TA @ A ) )
& ( ( finite_finite @ TA @ A )
=> ( finite_finite @ ( fun @ TA @ bool ) @ ( pow @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(103,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( sup_sup @ ( fun @ TA @ bool ) @ B @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
<=> ( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
& ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_Un__empty) ).
thf(439,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( ( sup_sup @ ( fun @ TA @ bool ) @ B @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
& ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
& ( ( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
& ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( ( sup_sup @ ( fun @ TA @ bool ) @ B @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(12,axiom,
bot @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Obot) ).
thf(160,plain,
bot @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(26,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Un__empty__right) ).
thf(192,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(90,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(407,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA,B: fun @ TB @ bool,C: fun @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ TB @ bool ) @ TA ),D: TA,E: fun @ TA @ ( fun @ TA @ TA )] :
( ( big_comm_monoid_big @ TA @ TB @ E @ D @ C )
=> ( ~ ( finite_finite @ TB @ B )
=> ( ( aa @ ( fun @ TB @ bool ) @ TA @ ( aa @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ TB @ bool ) @ TA ) @ C @ A ) @ B )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_comm__monoid__big_Oinfinite) ).
thf(484,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA,B: fun @ TB @ bool,C: fun @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ TB @ bool ) @ TA ),D: TA,E: fun @ TA @ ( fun @ TA @ TA )] :
( ( big_comm_monoid_big @ TA @ TB @ E @ D @ C )
=> ( ~ ( finite_finite @ TB @ B )
=> ( ( aa @ ( fun @ TB @ bool ) @ TA @ ( aa @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ TB @ bool ) @ TA ) @ C @ A ) @ B )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(28,axiom,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_sup__bot__left) ).
thf(197,plain,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(129,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ B )
=> ( ( finite_finite @ TA @ A )
=> ( finite_finite @ TA @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_finite__UnI) ).
thf(522,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ B )
=> ( ( finite_finite @ TA @ A )
=> ( finite_finite @ TA @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(108,axiom,
! [TA: $tType,A: TA,B: fun @ ( fun @ TA @ bool ) @ TA,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite2073411215e_idem @ TA @ C @ B )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ C @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_folding__one__idem_Oidem) ).
thf(461,plain,
! [TA: $tType,A: TA,B: fun @ ( fun @ TA @ bool ) @ TA,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite2073411215e_idem @ TA @ C @ B )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ C @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(67,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
<=> ( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
& ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ B ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_ball__Un) ).
thf(324,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
=> ( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
& ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ B ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) ) )
& ( ( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
& ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ B ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) )
=> ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(63,axiom,
bounded_lattice_bot @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice__bot) ).
thf(317,plain,
bounded_lattice_bot @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(24,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Sup__fin_Oidem) ).
thf(188,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(121,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ ( fun @ TA @ bool ) @ TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite2073411215e_idem @ TA @ D @ C )
=> ( ( finite_finite @ TA @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ A ) @ ( aa @ ( fun @ TA @ bool ) @ TA @ C @ B ) )
= ( aa @ ( fun @ TA @ bool ) @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_folding__one__idem_Oin__idem) ).
thf(499,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ ( fun @ TA @ bool ) @ TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite2073411215e_idem @ TA @ D @ C )
=> ( ( finite_finite @ TA @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ A ) @ ( aa @ ( fun @ TA @ bool ) @ TA @ C @ B ) )
= ( aa @ ( fun @ TA @ bool ) @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(49,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: huffma1450048681e_tree @ TA,E: huffma1450048681e_tree @ TA,F: nat] :
( ( ( huffma1146269203erNode @ TA @ F @ E @ D )
= ( huffma1146269203erNode @ TA @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_tree_Osimps_I2_J) ).
thf(256,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: huffma1450048681e_tree @ TA,E: huffma1450048681e_tree @ TA,F: nat] :
( ( ( ( huffma1146269203erNode @ TA @ F @ E @ D )
= ( huffma1146269203erNode @ TA @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( huffma1146269203erNode @ TA @ F @ E @ D )
= ( huffma1146269203erNode @ TA @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(68,axiom,
lattice @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Olattice) ).
thf(339,plain,
lattice @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ bool,B: fun @ TA @ bool] :
( ( finite_finite @ ( sum_sum @ TA @ TB ) @ ( sum_Plus @ TA @ TB @ B @ A ) )
=> ( finite_finite @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_finite__PlusD_I1_J) ).
thf(476,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ bool,B: fun @ TA @ bool] :
( ( finite_finite @ ( sum_sum @ TA @ TB ) @ ( sum_Plus @ TA @ TB @ B @ A ) )
=> ( finite_finite @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(131,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) )
=> ( ( sup_sup @ TA @ A @ ( big_lattice_Sup_fin @ TA @ B ) )
= ( big_lattice_Sup_fin @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_Sup__fin_Oin__idem) ).
thf(526,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) )
=> ( ( sup_sup @ TA @ A @ ( big_lattice_Sup_fin @ TA @ B ) )
= ( big_lattice_Sup_fin @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(34,axiom,
! [TA: $tType,A: TA] :
( ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) )
<=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_bot__empty__eq) ).
thf(212,plain,
! [TA: $tType,A: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
& ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1,conjecture,
! [TA: $tType,A: huffma1450048681e_tree @ TA] : ( finite_finite @ TA @ ( huffma675207370phabet @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: huffma1450048681e_tree @ TA] : ( finite_finite @ TA @ ( huffma675207370phabet @ TA @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(134,plain,
~ ! [TA: $tType,A: huffma1450048681e_tree @ TA] : ( finite_finite @ TA @ ( huffma675207370phabet @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(70,axiom,
bot @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
thf(343,plain,
bot @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(266,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(61,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( pow @ TA @ A )
!= ( bot_bot @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_Pow__not__empty) ).
thf(311,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( pow @ TA @ A )
!= ( bot_bot @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(60,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) ) )
& ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
<=> ( ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
& ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
| ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ B ) )
& ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_bex__Un) ).
thf(298,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) ) )
& ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
=> ( ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
& ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
| ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ B ) )
& ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) ) )
& ( ( ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
& ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
| ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ B ) )
& ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) )
=> ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) ) )
& ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(93,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) )
| ( pp @ B )
| ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(412,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) )
| ( pp @ B )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(98,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(425,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(100,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_UnE) ).
thf(430,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(7,axiom,
semilattice_sup @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Osemilattice__sup) ).
thf(148,plain,
semilattice_sup @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ B @ A )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_sup_Ocommute) ).
thf(161,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ B @ A )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ TA,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_fold_image @ TA @ TB @ C @ B @ A @ ( bot_bot @ ( fun @ TB @ bool ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_fold__image__empty) ).
thf(180,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ TA,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_fold_image @ TA @ TB @ C @ B @ A @ ( bot_bot @ ( fun @ TB @ bool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(8,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_sup__idem) ).
thf(149,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(79,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite1 @ TA )
& ( finite_finite1 @ TB ) )
=> ( finite_finite1 @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
thf(375,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite1 @ TA )
& ( finite_finite1 @ TB ) )
=> ( finite_finite1 @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( semilattice_sup @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Osemilattice__sup) ).
thf(423,plain,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( semilattice_sup @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(25,axiom,
lattice @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Olattice) ).
thf(191,plain,
lattice @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(56,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ B @ A )
= ( sup_sup @ ( fun @ TA @ bool ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_Un__commute) ).
thf(281,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ B @ A )
= ( sup_sup @ ( fun @ TA @ bool ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ),E: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma107959123e_case @ TA @ TB @ E @ D @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( aa @ ( huffma1450048681e_tree @ TA ) @ TB @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) @ ( aa @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_tree_Osimps_I6_J) ).
thf(391,plain,
! [TA: $tType,TB: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ),E: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma107959123e_case @ TA @ TB @ E @ D @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( aa @ ( huffma1450048681e_tree @ TA ) @ TB @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) @ ( aa @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(82,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(382,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(110,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ C @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
= ( sup_sup @ ( fun @ TA @ bool ) @ B @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_Un__left__commute) ).
thf(466,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ C @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
= ( sup_sup @ ( fun @ TA @ bool ) @ B @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(73,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) )
<=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_empty__Collect__eq) ).
thf(350,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(53,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ B @ ( sup_sup @ TA @ B @ A ) )
= ( sup_sup @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_inf__sup__aci_I8_J) ).
thf(274,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ B @ ( sup_sup @ TA @ B @ A ) )
= ( sup_sup @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(96,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
<=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
& ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Int__iff) ).
thf(419,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
& ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) )
& ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
& ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(80,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ bool ) ) @ A ) @ ( pow @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_Pow__top) ).
thf(377,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ bool ) ) @ A ) @ ( pow @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(41,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) @ ( pow @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Pow__bottom) ).
thf(230,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) @ ( pow @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(64,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( pp @ ( aa @ TA @ bool @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_inf1I) ).
thf(318,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( pp @ ( aa @ TA @ bool @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ bool,C: fun @ ( fun @ TA @ bool ) @ TB,D: fun @ TA @ TB,E: TB,F: fun @ TB @ ( fun @ TB @ TB )] :
( ( finite908156982e_idem @ TB @ TA @ F @ E @ D @ C )
=> ( ( finite_finite @ TA @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) )
=> ( ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ F @ ( aa @ TA @ TB @ D @ A ) ) @ ( aa @ ( fun @ TA @ bool ) @ TB @ C @ B ) )
= ( aa @ ( fun @ TA @ bool ) @ TB @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_folding__image__simple__idem_Oin__idem) ).
thf(509,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ bool,C: fun @ ( fun @ TA @ bool ) @ TB,D: fun @ TA @ TB,E: TB,F: fun @ TB @ ( fun @ TB @ TB )] :
( ( finite908156982e_idem @ TB @ TA @ F @ E @ D @ C )
=> ( ( finite_finite @ TA @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) )
=> ( ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ F @ ( aa @ TA @ TB @ D @ A ) ) @ ( aa @ ( fun @ TA @ bool ) @ TB @ C @ B ) )
= ( aa @ ( fun @ TA @ bool ) @ TB @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(102,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
<=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Collect__empty__eq) ).
thf(434,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(52,axiom,
! [TA: $tType] :
( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fFalse ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_empty__def) ).
thf(271,plain,
! [TA: $tType] :
( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fFalse ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ),E: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) @ ( aa @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ) @ D @ C ) @ B ) @ A ) @ ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ B ) ) @ ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_tree_Orecs_I2_J) ).
thf(208,plain,
! [TA: $tType,TB: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ),E: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) @ ( aa @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ) @ D @ C ) @ B ) @ A ) @ ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ B ) ) @ ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(84,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) )
<=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_Un__iff) ).
thf(387,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) )
& ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(119,axiom,
! [TA: $tType] : ( finite_finite @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_finite_OemptyI) ).
thf(494,plain,
! [TA: $tType] : ( finite_finite @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(128,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ bool] :
( ( finite_finite @ TB @ B )
=> ( ( finite_finite @ TA @ A )
=> ( finite_finite @ ( sum_sum @ TB @ TA ) @ ( sum_Plus @ TB @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_finite__Plus) ).
thf(520,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ bool] :
( ( finite_finite @ TB @ B )
=> ( ( finite_finite @ TA @ A )
=> ( finite_finite @ ( sum_sum @ TB @ TA ) @ ( sum_Plus @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(10,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(155,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(88,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_IntI) ).
thf(399,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(55,axiom,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_sup__bot__right) ).
thf(278,plain,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType] :
( ( lattice @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB,C: TA] :
( ( aa @ TA @ TB @ ( sup_sup @ ( fun @ TA @ TB ) @ B @ A ) @ C )
= ( sup_sup @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_sup__fun__def) ).
thf(223,plain,
! [TA: $tType,TB: $tType] :
( ( lattice @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB,C: TA] :
( ( aa @ TA @ TB @ ( sup_sup @ ( fun @ TA @ TB ) @ B @ A ) @ C )
= ( sup_sup @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(394,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(39,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( pp @ ( aa @ TA @ bool @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_sup1I1) ).
thf(226,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( pp @ ( aa @ TA @ bool @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite1 @ TA )
& ( finite_finite1 @ TB ) )
=> ( finite_finite1 @ ( sum_sum @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum___Finite__Set_Ofinite) ).
thf(241,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite1 @ TA )
& ( finite_finite1 @ TB ) )
=> ( finite_finite1 @ ( sum_sum @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(15,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ C @ ( sup_sup @ TA @ B @ A ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_sup__left__commute) ).
thf(167,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ C @ ( sup_sup @ TA @ B @ A ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(133,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( finite_finite @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( ( inf_inf @ ( fun @ TA @ bool ) @ B @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( big_lattice_Sup_fin @ TA @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
= ( sup_sup @ TA @ ( big_lattice_Sup_fin @ TA @ B ) @ ( big_lattice_Sup_fin @ TA @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_Sup__fin_Ounion__disjoint) ).
thf(531,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( finite_finite @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( ( inf_inf @ ( fun @ TA @ bool ) @ B @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( big_lattice_Sup_fin @ TA @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
= ( sup_sup @ TA @ ( big_lattice_Sup_fin @ TA @ B ) @ ( big_lattice_Sup_fin @ TA @ A ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ bool] :
( ( finite_finite @ ( sum_sum @ TB @ TA ) @ ( sum_Plus @ TB @ TA @ B @ A ) )
<=> ( ( finite_finite @ TB @ B )
& ( finite_finite @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_finite__Plus__iff) ).
thf(487,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ bool] :
( ( ( finite_finite @ ( sum_sum @ TB @ TA ) @ ( sum_Plus @ TB @ TA @ B @ A ) )
=> ( ( finite_finite @ TB @ B )
& ( finite_finite @ TA @ A ) ) )
& ( ( ( finite_finite @ TB @ B )
& ( finite_finite @ TA @ A ) )
=> ( finite_finite @ ( sum_sum @ TB @ TA ) @ ( sum_Plus @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType] :
( ( lattice @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( aa @ TA @ TB @ ( sup_sup @ ( fun @ TA @ TB ) @ C @ B ) @ A )
= ( sup_sup @ TB @ ( aa @ TA @ TB @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_sup__apply) ).
thf(355,plain,
! [TA: $tType,TB: $tType] :
( ( lattice @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( aa @ TA @ TB @ ( sup_sup @ ( fun @ TA @ TB ) @ C @ B ) @ A )
= ( sup_sup @ TB @ ( aa @ TA @ TB @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(107,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ~ ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_IntE) ).
thf(458,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ~ ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(6,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ B @ ( sup_sup @ TA @ B @ A ) )
= ( sup_sup @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_sup__left__idem) ).
thf(145,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ B @ ( sup_sup @ TA @ B @ A ) )
= ( sup_sup @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(94,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ B @ ( inf_inf @ TA @ B @ A ) )
= ( inf_inf @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_inf_Oleft__idem) ).
thf(414,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ B @ ( inf_inf @ TA @ B @ A ) )
= ( inf_inf @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(91,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(409,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(19,axiom,
semilattice_sup @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Osemilattice__sup) ).
thf(177,plain,
semilattice_sup @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(77,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(370,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(122,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA,B: fun @ TB @ bool,C: fun @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ TB @ bool ) @ TA ),D: TA,E: fun @ TA @ ( fun @ TA @ TA )] :
( ( big_comm_monoid_big @ TA @ TB @ E @ D @ C )
=> ( ( ( finite_finite @ TB @ B )
=> ( ( aa @ ( fun @ TB @ bool ) @ TA @ ( aa @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ TB @ bool ) @ TA ) @ C @ A ) @ B )
= ( finite_fold_image @ TA @ TB @ E @ A @ D @ B ) ) )
& ( ~ ( finite_finite @ TB @ B )
=> ( ( aa @ ( fun @ TB @ bool ) @ TA @ ( aa @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ TB @ bool ) @ TA ) @ C @ A ) @ B )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_comm__monoid__big_OF__eq) ).
thf(502,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA,B: fun @ TB @ bool,C: fun @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ TB @ bool ) @ TA ),D: TA,E: fun @ TA @ ( fun @ TA @ TA )] :
( ( big_comm_monoid_big @ TA @ TB @ E @ D @ C )
=> ( ( ( finite_finite @ TB @ B )
=> ( ( aa @ ( fun @ TB @ bool ) @ TA @ ( aa @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ TB @ bool ) @ TA ) @ C @ A ) @ B )
= ( finite_fold_image @ TA @ TB @ E @ A @ D @ B ) ) )
& ( ~ ( finite_finite @ TB @ B )
=> ( ( aa @ ( fun @ TB @ bool ) @ TA @ ( aa @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ TB @ bool ) @ TA ) @ C @ A ) @ B )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(105,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool,C: fun @ ( product_prod @ TA @ TA ) @ bool,D: fun @ TA @ bool] :
( ( refl_on @ TA @ D @ C )
=> ( ( refl_on @ TA @ B @ A )
=> ( refl_on @ TA @ ( sup_sup @ ( fun @ TA @ bool ) @ D @ B ) @ ( sup_sup @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_refl__on__Un) ).
thf(450,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool,C: fun @ ( product_prod @ TA @ TA ) @ bool,D: fun @ TA @ bool] :
( ( refl_on @ TA @ D @ C )
=> ( ( refl_on @ TA @ B @ A )
=> ( refl_on @ TA @ ( sup_sup @ ( fun @ TA @ bool ) @ D @ B ) @ ( sup_sup @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(30,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ B @ ( inf_inf @ TA @ B @ A ) )
= ( inf_inf @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_inf__left__idem) ).
thf(203,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ B @ ( inf_inf @ TA @ B @ A ) )
= ( inf_inf @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(130,axiom,
! [TA: $tType] :
( ( finite_finite1 @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_finite) ).
thf(524,plain,
! [TA: $tType] :
( ( finite_finite1 @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_bot__fun__def) ).
thf(218,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice_bot @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Obounded__lattice__bot) ).
thf(158,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice_bot @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(89,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_ex__in__conv) ).
thf(401,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(17,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(171,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_sup_Oidem) ).
thf(139,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ bool] :
( ( ( sum_Plus @ TB @ TA @ B @ A )
= ( bot_bot @ ( fun @ ( sum_sum @ TB @ TA ) @ bool ) ) )
<=> ( ( B
= ( bot_bot @ ( fun @ TB @ bool ) ) )
& ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Plus__eq__empty__conv) ).
thf(290,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ bool] :
( ( ( ( sum_Plus @ TB @ TA @ B @ A )
= ( bot_bot @ ( fun @ ( sum_sum @ TB @ TA ) @ bool ) ) )
=> ( ( B
= ( bot_bot @ ( fun @ TB @ bool ) ) )
& ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
& ( ( ( B
= ( bot_bot @ ( fun @ TB @ bool ) ) )
& ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( ( sum_Plus @ TB @ TA @ B @ A )
= ( bot_bot @ ( fun @ ( sum_sum @ TB @ TA ) @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(114,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ ( fun @ TA @ bool ) @ TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite2073411215e_idem @ TA @ D @ C )
=> ( ( finite_finite @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( finite_finite @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ C @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ ( aa @ ( fun @ TA @ bool ) @ TA @ C @ B ) ) @ ( aa @ ( fun @ TA @ bool ) @ TA @ C @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_folding__one__idem_Ounion__idem) ).
thf(478,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ ( fun @ TA @ bool ) @ TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite2073411215e_idem @ TA @ D @ C )
=> ( ( finite_finite @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( finite_finite @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ C @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ ( aa @ ( fun @ TA @ bool ) @ TA @ C @ B ) ) @ ( aa @ ( fun @ TA @ bool ) @ TA @ C @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(58,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_Un__absorb) ).
thf(287,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_bot__apply) ).
thf(235,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(47,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ B @ A )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_Un__def) ).
thf(246,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ B @ A )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ ( fun @ TB @ bool ) @ TA,C: fun @ TB @ TA,D: TA,E: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite908156982e_idem @ TA @ TB @ E @ D @ C @ B )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ E @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_folding__image__simple__idem_Oidem) ).
thf(447,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ ( fun @ TB @ bool ) @ TA,C: fun @ TB @ TA,D: TA,E: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite908156982e_idem @ TA @ TB @ E @ D @ C @ B )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ E @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(101,axiom,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_emptyE) ).
thf(432,plain,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(92,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( pp @ ( aa @ TA @ bool @ ( sup_sup @ ( fun @ TA @ bool ) @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_sup1I2) ).
thf(410,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( pp @ ( aa @ TA @ bool @ ( sup_sup @ ( fun @ TA @ bool ) @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite1 @ TA )
& ( finite_finite1 @ TB ) )
=> ( finite_finite1 @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod___Finite__Set_Ofinite) ).
thf(183,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite1 @ TA )
& ( finite_finite1 @ TB ) )
=> ( finite_finite1 @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ C @ B ) @ A )
= ( sup_sup @ TA @ C @ ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_sup__assoc) ).
thf(136,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ C @ B ) @ A )
= ( sup_sup @ TA @ C @ ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(75,axiom,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( sup_sup @ TA @ B @ A )
= ( bot_bot @ TA ) )
<=> ( ( B
= ( bot_bot @ TA ) )
& ( A
= ( bot_bot @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_sup__eq__bot__iff) ).
thf(358,plain,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( ( sup_sup @ TA @ B @ A )
= ( bot_bot @ TA ) )
=> ( ( B
= ( bot_bot @ TA ) )
& ( A
= ( bot_bot @ TA ) ) ) )
& ( ( ( B
= ( bot_bot @ TA ) )
& ( A
= ( bot_bot @ TA ) ) )
=> ( ( sup_sup @ TA @ B @ A )
= ( bot_bot @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(27,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_UnI2) ).
thf(195,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(109,axiom,
! [TA: $tType] : ( refl_on @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_refl__on__empty) ).
thf(464,plain,
! [TA: $tType] : ( refl_on @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(99,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( field @ TA @ ( sup_sup @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ B @ A ) )
= ( sup_sup @ ( fun @ TA @ bool ) @ ( field @ TA @ B ) @ ( field @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Field__Un) ).
thf(427,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( field @ TA @ ( sup_sup @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ B @ A ) )
= ( sup_sup @ ( fun @ TA @ bool ) @ ( field @ TA @ B ) @ ( field @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(29,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_equals0I) ).
thf(200,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( lattice @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Olattice) ).
thf(178,plain,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( lattice @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(54,axiom,
bounded_lattice @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice) ).
thf(277,plain,
bounded_lattice @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(111,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ C @ ( sup_sup @ TA @ B @ A ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_inf__sup__aci_I7_J) ).
thf(469,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ C @ ( sup_sup @ TA @ B @ A ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(35,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) @ A )
= ( sup_sup @ ( fun @ TA @ bool ) @ C @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Un__assoc) ).
thf(215,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) @ A )
= ( sup_sup @ ( fun @ TA @ bool ) @ C @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(118,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
( ( huffma675207370phabet @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( sup_sup @ ( fun @ TA @ bool ) @ ( huffma675207370phabet @ TA @ B ) @ ( huffma675207370phabet @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_alphabet_Osimps_I2_J) ).
thf(491,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
( ( huffma675207370phabet @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( sup_sup @ ( fun @ TA @ bool ) @ ( huffma675207370phabet @ TA @ B ) @ ( huffma675207370phabet @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ ( fun @ TA @ bool ) @ TB,D: fun @ TA @ TB,E: TB,F: fun @ TB @ ( fun @ TB @ TB )] :
( ( finite908156982e_idem @ TB @ TA @ F @ E @ D @ C )
=> ( ( finite_finite @ TA @ B )
=> ( ( finite_finite @ TA @ A )
=> ( ( aa @ ( fun @ TA @ bool ) @ TB @ C @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
= ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ F @ ( aa @ ( fun @ TA @ bool ) @ TB @ C @ B ) ) @ ( aa @ ( fun @ TA @ bool ) @ TB @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_folding__image__simple__idem_Ounion__idem) ).
thf(496,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ ( fun @ TA @ bool ) @ TB,D: fun @ TA @ TB,E: TB,F: fun @ TB @ ( fun @ TB @ TB )] :
( ( finite908156982e_idem @ TB @ TA @ F @ E @ D @ C )
=> ( ( finite_finite @ TA @ B )
=> ( ( finite_finite @ TA @ A )
=> ( ( aa @ ( fun @ TA @ bool ) @ TB @ C @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
= ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ F @ ( aa @ ( fun @ TA @ bool ) @ TB @ C @ B ) ) @ ( aa @ ( fun @ TA @ bool ) @ TB @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(42,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ B @ A )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_inf__sup__aci_I5_J) ).
thf(232,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ B @ A )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(534,plain,
$false,
inference(e,[status(thm)],[515,314,347,249,518,481,170,379,269,385,142,472,340,174,185,417,320,372,344,284,152,228,164,321,211,238,397,221,243,507,206,452,529,366,512,439,160,192,407,484,197,522,461,324,317,188,499,256,339,476,526,212,134,343,266,311,298,412,425,430,148,161,180,149,375,423,191,281,391,382,466,350,274,419,377,230,318,509,434,271,208,387,494,520,155,399,278,223,394,226,241,167,531,487,355,458,145,414,409,177,370,502,450,203,524,218,158,401,171,139,290,478,287,235,246,447,432,410,183,136,358,195,464,427,200,178,277,469,215,491,496,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWW526_5 : TPTP v8.1.2. Released v6.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 22:41:06 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.99/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.73/1.09 % [INFO] Parsing done (214ms).
% 1.73/1.10 % [INFO] Running in sequential loop mode.
% 2.12/1.30 % [INFO] eprover registered as external prover.
% 2.12/1.30 % [INFO] cvc4 registered as external prover.
% 2.12/1.31 % [INFO] Scanning for conjecture ...
% 2.56/1.41 % [INFO] Found a conjecture and 131 axioms. Running axiom selection ...
% 2.95/1.49 % [INFO] Axiom selection finished. Selected 131 axioms (removed 0 axioms).
% 3.37/1.64 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.37/1.66 % [INFO] Type checking passed.
% 3.37/1.66 % [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 ...
% 3.88/1.84 % [INFO] [Domain constraints] Detected constraint on bool
% 3.88/1.84 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 15.16/6.59 % External prover 'e' found a proof!
% 15.16/6.59 % [INFO] Killing All external provers ...
% 15.16/6.59 % Time passed: 6078ms (effective reasoning time: 5491ms)
% 15.16/6.59 % 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)>
% 15.16/6.60 % 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
% 15.16/6.60 % No. of inferences in proof: 266
% 15.16/6.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6078 ms resp. 5491 ms w/o parsing
% 15.83/6.68 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.83/6.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------